Fundamentals of Corporate Finance, 3rd Edition Solution Manual by Ace Test Banks

Fundamentals of Corporate Finance, 3rd Edition

By Parrino, Kidwell, Bates

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Chapter 1 The Financial Manager and the Firm Before You Go On Questions and Answers

Section 1.1 1. What are the three most basic types of financial decisions managers must make? The three most basic decisions each business must make are the capital budgeting decision, the financing decision, and the working capital management decision. These decisions determine which productive assets to buy, how to pay for or finance these purchases, and how to manage the day-to-day financial matters so the company can pay its bills.

2. Explain why you would make an investment if the value of the expected cash flows exceeds the cost of the project. You would accept an investment project whose cash flows exceed the cost of the project because such projects will increase the value of the firm, making the owners wealthier. Most people start a business to increase their wealth.

Why are capital budgeting decisions among the most important decisions in the life of a firm? The capital budgeting decisions are considered the most important in the life of the firm because these decisions determine which productive assets the firm purchases and these assets generate most of the firm’s cash flows. Furthermore, capital decisions are long-term decisions and if you make a mistake in selecting a productive asset, you are stuck with the decision for a long time.

Section 1.2 1. Why are many businesses operated as sole proprietorships or partnerships?

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Many businesses elect to operate as sole proprietorships or partnerships because of the small operating scale and capital base of their firms. Both of these forms of business organization are fairly easy to start and impose few regulations on the owners.

2. What are some advantages and disadvantages of operating as a public corporation? The main advantages of operating as a public corporation are the access to the public securities markets, which makes it easier to raise large amounts of capital, and the ease of ownership transfer. All the shareholders have to do is to call their broker to buy or sell shares of stock. And because a public corporation usually has many shares outstanding, large blocks of securities can be purchased or sold without an appreciable impact on the price of the stock. The major disadvantage of corporations is the tax situation. Not only must the corporation pay taxes on its income, but the owners of the corporation get taxed again when dividends are paid to them. This is referred to as double taxation. 3. Explain why professional partnerships such as physicians’ groups organize as limited liability partnerships. Professional partnerships such as physicians’ groups desire to organize as limited liability partnerships (LLPs) to take advantage of the tax arrangements of partnerships combined with the advantages of the limited liability of a corporation. By operating as an LLP, the partnership is able to avoid a potential financial disaster resulting from the misconduct of one partner.

Section 1.3 1. What are the major responsibilities of the CFO? The major responsibilities of a CFO are recommendation and financial analysis of financial decisions. Although all top managers in a firm participate in these decisions, the final report and analysis is ultimately the responsibility of the CFO.

2. Identify three financial officers who typically report to the CFO and describe their duties.

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The financial officers discussed in the chapter who report to the CFO are the controller, the treasurer, and the internal auditor. The controller is the firm’s chief accounting officer, and thus prepares the financial statements and taxes. This position also requires close cooperation with the external auditors. The treasurer’s responsibility is the collection and disbursement of cash, investing excess cash, raising new capital, handling foreign exchange, and overseeing the company’s pension fund management. He also assists the CFO in handling important Wall Street relationships. Finally, the internal auditor is responsible for conducting risk assessment and for performing audits of high-risk areas.

3. Why does the internal auditor report to both the CFO and the board of directors? The internal auditor reports to the CFO on a day-to-day basis but is ultimately accountable for reporting any accounting irregularities to the board of directors. The dual reporting system serves as a check to ensure that there are no discrepancies in the company’s financial statements.

Section 1.4 1. Why is profit maximization an unsatisfactory goal for managing a firm? Profit maximization is not a satisfactory goal when managing a firm because it is rather difficult to define profits since accountants can apply and interpret the same accounting principles differently. Also, profit maximization does not define the size, the uncertainty, and the timing of cash flows; it ignores the time value of money concept. 2. Explain why maximizing the current market price of a firm’s stock is an appropriate goal for the firm’s management. Maximizing the current market price of a firm’s stock is an appropriate goal for the firm’s management because it is an unambiguous objective and it is easy to measure. One can simply look at the value of the company’s stock on any given day to determine whether it went up or down. 3. What is the fundamental determinant of an asset’s value?

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The fundamental determinant of an asset’s value is the future cash flow the asset is expected to generate. Other factors that may help determine the price of an asset are internal decisions, such as the company’s expansion strategy, as well as external stimulants, such as the state of the economy.

Section 1.5 1. What are agency conflicts? An agency conflict occurs when the goals of the principals are not aligned with the goals of the agents. Management is often more concerned with pursuing its own self-interest, and so the maximization of shareholder value is pushed to the side.

2. What are corporate raiders? Corporate raiders can make the economy more efficient by keeping the top managers on their toes. Top managers know that if the company’s performance declines and its stock slips, it makes itself vulnerable to takeovers by corporate raiders who are just waiting to temporarily acquire a company, turn it around, and sell it for profit. Therefore, the role of the corporate raiders in the economy is twofold: first, the fear of takeovers pushes managers to do a better job, and second, if the managers are not performing up to expectations, the company can be rescued and restructured into a contributor again.

3. List the three main objectives of the Sarbanes-Oxley Act. The three main goals of the Sarbanes-Oxley Act are to reduce agency costs in corporations, to restore ethical conduct in the business sector, and to improve the integrity of accounting reporting systems within firms.

Section 1.6 1. What is a conflict of interest in a business setting? Conflict of interest in the business setting refers to a conflict between a person’s personal or institutional gain and the obligation to serve the interest of another party. For example, the chapter discussed the problem that arises when the real estate agent helping you buy a house is also the listing agent. Copyright © 2015 John Wiley & Sons, Inc.

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2. How would you define an ethical business culture? An ethical business culture means that people have a set of principles, or moral values, that helps them identify moral issues and then make ethical judgments without being told what to do.

Self-Study Problems and Solutions

1.1

Give an example of a capital budgeting decision and a financing decision.

Solution:

Capital budgeting involves deciding which productive assets the firm invests in, such as buying a new plant or investing in the renovation of an existing facility. Financing decisions determine how a firm will raise capital. Examples of financing decisions include the decision to borrow from a bank or issue debt in the public capital markets.

LO: 1 Level: Basic

1.2

What is the appropriate decision criterion for financial managers to use when selecting a capital project?

Solution:

Financial managers should select a capital project only if the value of the project’s expected future cash flows exceeds the cost of the project. In other words, managers should only make investments that will increase firm value, and thus increase the stockholders’ wealth.

LO: 1 Level: Basic

1.3

What are some of the things that managers do to manage a firm’s working capital?

Solution:

Working capital management is the day-to-day management of a firm’s shortterm assets and liabilities. Working capital can be managed by maintaining the optimal level of inventory, managing receivables and payables, deciding to whom

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the firm should extend credit, and making appropriate investments with excess cash. LO: 1 Level: Basic

1.4

Which one of the following characteristics does not pertain to corporations? a.

Can enter into contracts

Can borrow money

Are the easiest type of business to form

Can be sued

Can own stock in other companies

Solution:

The answer that does not pertain to corporations is: c. Are the easiest type of business to form.

LO: 2 Level: Basic

1.5

What are typically the main components of an executive compensation package?

Solution:

The three main components of a typical executive compensation package are: base salary, bonus based on accounting performance, and compensation tied to the firm’s stock price.

LO: 5 Level: Basic

Discussion Questions and Answers 1.1

Describe the cash flows between a firm and its stakeholders. Cash flows are generated by a firm’s productive assets that were purchased through either issuing debt or raising equity. These assets generate revenues through the sale of goods

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and services. A portion of this revenue is then used to pay wages and salaries to employees, pay suppliers, pay taxes, and pay interest on the borrowed money. The leftover money, residual cash, is then either reinvested back in the business or is paid out to stockholders in the form of dividends. LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

1.2

What are the three fundamental decisions the financial manager is concerned with, and how do they affect the firm’s balance sheet? The primary financial management decisions every company faces are capital budgeting decisions, financing decisions, and working capital management decisions. Capital budgeting addresses the question of which productive assets to buy; thus, it affects the asset side of the balance sheet. Financing decisions focus on raising the money the firm needs to buy productive assets. This is typically accomplished by selling long-term debt and equity. Finally, working capital decisions involve how firms manage their current assets and liabilities. The focus here is seeing that a firm has enough money to pay its bills and that any spare money is invested to earn a return.

LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Decision Analysis AICPA: Decision Modeling

1.3

What is the difference between stockholders and stakeholders? Stockholders, also referred to as shareholders, are the owners of the company. A stakeholder, on the other hand, is anyone with a claim on the assets of the firm, including,

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but not limited to, shareholders. Stakeholders include the firm’s employees, suppliers, creditors, and the government. LO: 1 Level: Basic Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

1.4

Suppose that a group of accountants wants to start an accounting business. What organizational form would they most likely choose, and why? Most lawyers, accountants, and doctors form what are known as limited liability partnerships. This formation combines the tax advantages of partnerships with the limited liability of corporations.

LO: 2 Level: Basic Bloomcode: Application AACSB: Analysis IMA: Business Economics AICPA: Industry/Sector Perspective

1.5

Why would the owners of a business choose to form a corporation even though they will face double taxation? Because the benefits, such as limited liability and access to large amounts of capital at relatively low cost in the public markets, outweigh the cost of double taxation (as well as the higher costs associated with forming a corporation).

LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Analytic

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IMA: Business Economics AICPA: Industry/Sector Perspective

1.6

Explain why profit maximization is not the best goal for a company. What is a better goal? Although profit maximization appears to be the logical goal for any company, it has many drawbacks. First, profit can be defined in a number of different ways, and variations in net income for similar firms can vary widely. Second, accounting profits do not exactly equal cash flows. Third, profit maximization does not account for timing and ignores risk associated with cash flows. An appropriate goal for financial managers who do not have these objections is to maximize the value of the firm’s current stock price. In order to achieve this goal, management must make financial decisions so that the total value of cash inflows exceeds the total value of cash outflows.

LO: 4 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Performance Measurement AICPA: Strategic/Critical Thinking

1.7

What are some of the major external and internal factors that affect a firm’s stock price? What is the difference between the two general types of factors? External factors that affect the firm’s stock price are: (1) economic shocks, such as natural disasters or wars, (2) the state of the economy, such as the level of interest rates, and (3) the business environment, such as taxes or regulations. On one hand, external factors are variables over which the management has no control. On the other hand, internal factors that affect the stock price can be controlled by management to some degree, because they are firm specific, such as financial management decisions, product quality and cost, and the line of business, the management has selected to enter. Finally, perhaps the most important internal variable that determines the stock price is the expected cash flow stream: its magnitude, timing, and riskiness.

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LO: 4 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Strategic Marketing AICPA: Measurement

1.8

Identify the sources of agency costs. What are some ways these costs can be controlled in a company? Agency costs are the costs that result from conflicts of interest between the agent and the principal. They can either be direct, such as lavish dinners or trips, or indirect, which are usually missed investment opportunities. A company can control these costs by tying management compensation to company’s performance and by establishing an independent board of directors. Outside factors that contribute to the minimization of agency costs are the threat of corporate raiders that can take over a company not performing up to expectations and the competitive nature of the managerial labor market.

LO: 5 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.9

What is the Sarbanes-Oxley Act, and what does it focus on? Why does it focus in these areas? The Sarbanes-Oxley Act is an act of Congress that was passed in 2002. This act was passed in the aftermath of several corporate scandals that occurred at the turn of the century. The act focuses on (1) reducing agency costs in corporations, (2) restoring ethical conduct within the business sector, and (3) improving the integrity of accounting reporting system within firms. Failures in these areas led to the corporate scandals that preceded passage of Sarbanes-Oxley.

LO: 5

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Level: Basic Bloomcode: Knowledge AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective

1.10

Give an example of a conflict of interest in a business setting, other than the one involving the real estate agent discussed in the chapter text. For example, imagine a situation in which you are a financial officer at a growing software company and your firm has decided to hire outside consultants to formulate a global expansion strategy. Coincidentally, your wife works for one of the major consulting firms that your company is considering hiring. In this scenario, you have a conflict of interest, because instinctively, you might be inclined to give the business to your wife’s firm, because it will benefit your family’s financial situation if she lands the contract, regardless of whether or not it makes the best sense for your firm.

LO: 6 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

Questions and Problems and their Solutions BASIC 1.1

Capital: What are the two basic sources of funds for all businesses?

Solution: The two basic sources of funds for all businesses are debt and equity. LO:

1.1

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Bloomcode: Knowledge AACSB: Analytic IMA: Investment Decisions; Corporate Finance AICPA: Resource Management

1.2

Management role: What is net working capital?

Solution: Net working capital is the difference between a firm’s total current assets and its total current liabilities. LO:

1.1

Bloomcode: Knowledge AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

1.3

Cash flows: Explain the difference between profitable and unprofitable firms.

Solution: A profitable firm is able to generate enough cash flows from productive assets to cover its operating expenses, taxes, and payments to creditors. Unprofitable firms fail to do this, and therefore they may be forced to declare bankruptcy. LO:

1.1

Bloomcode: Analysis AACSB: Analytic IMA: Cost Management AICPA: Measurement

1.4

Management role: What three major decisions are of most concern to financial managers?

Solution: Financial managers are most concerned with the capital budgeting decisions, the financing decisions, and the working capital management decisions. LO:

1.1

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Bloomcode: Comprehension AACSB: Analytic IMA: FSA AICPA: Resource Management

1.5

Cash flows: What is the appropriate decision rule for a firm considering undertaking a capital project? Give a real-life example.

Solution: A firm should undertake a capital project only if the value of its future cash flows exceeds the cost of the project. For example, a financial manager would not invest $10,000,000 in a new production line if the future cash flows from that line are expected to produce only $9,000,000 in future cash flows. That would be like throwing $1,000,000 away. LO:

1.1

Bloomcode: Application AACSB: Analytic IMA: Decision Analysis AICPA: Problem Solving and Decision Making

1.6

Management role: What is a firm’s capital structure, and why is it important?

Solution: Capital structure shows how a company is financed; it is the mix of debt and equity on the liability side of the balance sheet. It is important as it affects the risk and the value of the company. In general, companies with higher debt-to-equity proportions are riskier because debt comes with legal obligations to pay periodic payments to creditors and to repay the principal at the end. LO:

1.1

Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 1.7

Management role: What are some of the working capital decisions that a financial manager faces?

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Solution: The financial manager must make working capital decisions regarding the level of inventory to hold, the terms of granting credit (account receivables), and the firm’s policy on paying accounts payable. LO:

1.1

Bloomcode: Comprehension AACSB: Analytic IMA: Decision Analysis AICPA: Strategic/Critical Thinking

1.8

Organizational form: What are the common forms of business organization discussed in this chapter?

Solution: The common forms of business organization discussed are sole proprietorship, partnership, corporation, and limited liability company and partnerships. LO:

1.2

Bloomcode: Knowledge AACSB: Reflective Thinking IMA: Business Economics AICPA: Industry/Sector Perspective

1.9

Organizational form: What are the advantages and disadvantages of a sole proprietorship?

Solution: Advantages: •

It is the easiest business organization to start.

•

It is the least regulated.

•

Owners keep all the profits and do not have to share the decision-making authority with anyone.

•

All income is taxed as personal income, which is usually in a lower tax bracket than corporate income.

Disadvantages: •

The proprietor has an unlimited liability for all business debt and financial obligations of the firm.

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•

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The amount of capital that can be invested in the firm is limited by the proprietor’s wealth.

• LO:

It is difficult to transfer ownership (requires sale of the business).

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.10

Organizational form: What is a partnership, and what is the biggest disadvantage of this form of business organization? How can this disadvantage be avoided?

Solution: A partnership consists of two or more owners legally joined together to manage a business. The major disadvantage to partnerships is that all partners have unlimited liability for the organization’s debts and legal obligations no matter what stake they have in the business. One way to avoid this is to form a limited partnership in which only general partners have unlimited liability and limited partners are only responsible for business obligations up to the amount of capital they have invested to the partnership. LO:

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.11

Organizational form: Who are the owners in a corporation, and how is their ownership represented?

Solution: The owners of a corporation are its stockholders or shareholders, and the evidence of their ownership is represented by shares of common stock. Other types of ownership do exist and include preferred stock. LO:

1.2

Bloomcode: Comprehension AACSB: Analytic

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IMA: Business Economics AICPA: Industry/Sector Perspective 1.12

Organizational form: Explain what is meant by stockholders’ limited liability.

Solution: Limited Liability for a stockholder means that the stockholder’s legal liability extends only to the capital contributed or the amount invested. LO:

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Strategic/Critical Thinking

1.13

Organizational form: What is double taxation?

Solution: Double taxation occurs when earnings are taxed twice. The owners of a C-corporation are subject to double taxation—first at the corporate level when the firm’s earnings are taxed and then again at a personal level when they receive the dividends. LO:

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.14

Organizational form: What is the form of business organization taken by most large companies and why?

Solution: Most large companies prefer to operate as public corporations because large amounts of capital can be raised in public markets at a relatively low cost. LO:

1.2

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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1.15

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Finance function: What is the primary responsibility of the board of directors in a corporation?

Solution: The board of directors of a corporation is responsible for serving the interests of stockholders in managing the corporation. It is possible that the interest of managers may deviate from those of the stockholders. The board’s objective is to monitor and correct any management decisions that might not be in the best interest of the stockholders. For example, board duties include hiring and firing the CEO, setting CEO pay, and monitoring the investment decisions of managers. LO:

1.3

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Resource Management

1.16

Finance function: All public companies must hire a certified public accounting firm to perform an independent audit of their financial statements. What exactly does the term audit mean?

Solution: An independent CPA firm that performs an audit of a firm ensures that the financial numbers are reasonably accurate, that accounting principles have been adhered to year after year and not in a manner that distorts the firm’s performance, and that the accounting principles used are in accordance with generally accepted accounting principles (GAAP). LO:

1.3

Bloomcode: Comprehension AACSB: Analytic IMA: FSA; Reporting AICPA: Risk Analysis; Reporting

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1.17

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Firm’s goal: What are some of the drawbacks to setting profit maximization as the main goal of a company?

Solution: •

It is difficult to determine what is meant by profits.

•

It does not address the size and timing of cash flows—it does not account for the time value of money.

• LO:

It ignores the uncertainty or risk of cash flows.

1.4

Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Corporate Finance

1.18

Firm’s goal: What is the appropriate goal of financial managers? How do managers’ decisions affect how successful the firm is in achieving this goal?

Solution: The appropriate goal of financial managers should be to maximize the current value of the firm’s stock price. Managers’ decisions affect the stock price in many ways as the value of the stock is determined by the future cash flows the firm can generate. Managers can affect the cash flows by, for example, selecting what products or services to produce, what type of assets to purchase, or what advertising campaign to undertake. LO:

1.4

Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Decision Analysis

1.19

Firm’s goal: What are the major factors that affect a firm’s stock price?

Solution: The factors affecting the stock price include: the characteristics of the firm, the economy, economic shocks, the business environment, expected cash flows, and current market conditions.

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LO:

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1.4

Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Corporate Finance

1.20

Agency conflicts: What is an agency relationship, and what is an agency conflict? How can agency conflicts be reduced in a corporation?

Solution: Agency relationships develop when a principal hires an agent to perform some service or represent the firm. An agency conflict arises when the agent’s interests and behaviors are at odds with those of the principal. Agency conflicts can be reduced through the following three mechanisms: management compensation, control of the firm, and the board of directors. LO:

1.5

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.21

Firm’s goal: What can happen if a firm is poorly managed and its stock price falls substantially below its maximum potential price?

Solution: If the stock price falls below its maximum potential price, it attracts corporate raiders, who look for fundamentally sound but poorly managed companies they can buy, turn around, and sell for a handsome profit. LO:

1.4

Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Strategic/Critical Thinking

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1.22

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Agency conflicts: What are some of the regulations that pertain to boards of directors that were put in place to reduce agency conflicts?

Solution: Some of the regulations include:

LO:

•

The majority of board members must be outsiders.

•

A separation of the CEO and chairman of the board positions is recommended.

•

Firm is required to have a code of ethics approved by the board.

1.5

Bloomcode: Comprehension AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective 1.23

Business ethics: How can a lack of business ethics negatively affect the performance of an economy? Give an example.

Solution: A lack of business ethics can lead to corruption, which, in turn, creates inefficiencies in an economy, inhibits the growth of capital markets, and slows the rate of overall economic growth. For example, the Russian economy has had a relatively difficult time attracting foreign investment since the fall of the Soviet Union due, in part, weak ethics in the business community and corruption in the business community and local and national governments. Lower foreign investment has led to slower overall economic growth than the country might otherwise have enjoyed. LO:

1.6

Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Global Perspective

1.24

Agency conflicts: What are some ways to resolve a conflict of interest?

Solution: One way to resolve a conflict of interest is by complete disclosure. As long as both parties are aware of the fact that, for example, both parties in a lawsuit are represented by the same firm, disclosure is sufficient. Another way to avoid a conflict of interest is for the company to remove itself from serving the interest of one of the

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parties. This is, for example, the case with accounting firms not being allowed to serve as consultants to companies for whom they perform audits. LO:

1.5

Bloomcode: Application AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective

1.25

Information asymmetry: Describe what an information asymmetry is in a business transaction. Explain how the inequity associated with an information asymmetry might be, at least partially, solved through the market for goods or services.

Solution: An information asymmetry exists when one party to a business transaction possesses information that is not available to the other parties in the transaction. If the parties with less information understand their relative disadvantage, they are likely to pay lower prices for the goods and services they purchase, or charge higher prices for the goods and services they sell. LO:

1.6

Bloomcode: Comprehension AACSB: Analytic IMA: Strategic Marketing AICPA: Marketing/Client Focus

1.26

Business ethics: What ethical conflict does insider trading present?

Solution: Insider trading is an example of information asymmetry. The main idea is that investment decisions should be made on an even playing field. Insider trading is morally wrong and has also been made illegal. LO: 1.6 Bloomcode: Comprehension AACSB: Ethics IMA: Business Applications AICPA: Professional Demeanor

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Sample Test Problems 1.1

Identify three fundamental types of decisions that financial managers make and identify which part of the balance sheet each of these decisions affects.

Solution: 1. Capital Budgeting Decisions – identifying the productive assets the firm should buy. These decisions affect long-term assets on the balance sheet. 2. Financing Decisions – determining how the firm should finance or pay for assets. These decisions affect long-term debt and stockholders’ equity on the balance sheet. 3. Working Capital Management Decisions – determining how day-to-day financial matters should be managed. These decisions affect current assets and current liabilities on the balance sheet. LO:

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Decision Analysis AICPA: Decision Modeling

1.2 Which of the following is/are advantages of the corporate form of organization? a. Reduced start-up costs b. Greater access to capital markets c. Unlimited liability d. Single taxation

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Solution: b. (Shares in a corporation can be sold to raise capital from investors who are not involved in the business. This greatly increases the amount of capital that can be raised to fund the business.) LO:

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

1.3

Why is stock value maximization superior to profit maximization as a goal for management?

Solution: While profit maximization appears to be a logical goal at first glance, it has some serious drawbacks. First, since accounting profit is the difference between revenues and expenses, it can be distorted by accounting decisions. Second, accounting profits are quite different from cash flows. Since cash flows are the focus of investors, they should also be the focus of managers. Third, profit maximization does not account for when cash flows actually occur. Finally, profit maximization as a goal ignores the risk involved in generating the cash flows. Stock value maximization is superior to profit maximization because it overcomes all of the listed shortcomings of profit maximization. This is because the value of a firm’s stock is determined by the cash flows that the firm is expected to produce. It accounts for (1) the size of the expected cash flows, (2) the timing of the expected cash flows, and (3) the riskiness of the expected cash flows. LO:

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Strategic/Critical thinking AICPA: Corporate Finance

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1.4

Solutions Manual

What are agency costs? Explain.

Solution: Agency costs are costs that result from an agency relationship in which there is a conflict of interest between a principal and an agent. An agency relationship exists in a business when a firm’s managers (agents) are not also its owners (principals). Agency costs are incurred when managers act in ways that harm owners’ interests. The cost of mechanisms, such as audits, that help control agency conflicts are also agency costs. LO:

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic AICPA: Industry/Sector Perpsective IMA: Business Economics

1.5

Identify seven mechanisms that can help better align the goals of managers with those of stockholders.

Solution: Mechanisms that can help align the goals of managers with those of stockholders are as follows: (1) the board of directors, (2) management compensation, (3) the managerial labor market, (4) competition among managers, (5) large stockholders, (6) the takeover market, and (7) the legal and regulatory environment. Boards of directors that are independent from managers can help limit the extent to which managers are able to act solely in their own interest. Firms design compensation plans that are tied to firm performance in order to provide managers with incentives to make decisions consistent with the goal of stockholder value maximization. A third mechanism that helps align the goals of managers is the managerial labor market. It is difficult for poorly performing managers to find a good job elsewhere, and it is difficult for a poorly performing firm to hire good managers, which a firm’s current managers typically want to do. Competition among managers within a firm is a fourth mechanism that helps align the goals of managers with those

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of stockholders. This is because managers who act in the interest of stockholders are more likely to advance within the firm. Because large stockholders have a lot to gain from aligning the goals of managers with their own, they are likely to expend resources to encourage managers to maximize stock value. Sixth, the threat of a takeover, which leads to firing of poor managers, can provide current managers with incentives to perform well. Finally, laws and regulations limit the ability of managers to make decisions that harm stockholders. LO:

Level: Intermediate Bloomcode: Comprehension AACSB: Analytic AICPA: Strategic/Critical Thinking IMA: Performance Measurement

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Chapter 2 The Financial System and the Level of Interest Rates

Before You Go On Questions and Answers Section 2.1 1.

What critical economic role does the financial system play in the economy? The financial system is in place to gather money from people and businesses and then channel these funds to those who need it. An efficient financial system is essential for a healthy economy. The major players in the U.S. financial system are big institutions such as the New York Stock Exchange, Citigroup, or State Farm Insurance.

What are the two basic ways in which funds flow through the financial system from lender–savers to borrower–spenders? There are two basic mechanisms by which funds flow through the financial system: 1) Funds can flow directly through financial markets, and (2) funds can flow indirectly through financial institutions.

Section 2.2 1.

Why is it difficult for individuals to participate in the direct financial markets? The financial markets where direct transactions take place are wholesale markets with a typical minimum transaction size of $1 million. Major buyers and sellers of securities in direct financial markets include commercial banks, large corporations, the federal government, hedge funds, and some wealthy individuals.

Why might a firm prefer to have a security issue underwritten by an investment banking firm?

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In the most common type of underwriting arrangement, called firm-commitment underwriting, the investment banker assumes the risk of buying the new securities from the issuing company and reselling them to investors. The investment banker guarantees to buy the entire security issue from the company at a fixed price.

Section 2.3 1.

What is the difference between primary and secondary markets? Primary markets are markets where new securities are sold for the first time. Secondary markets are where the owners of outstanding securities can sell them to other investors. They provide the means for investors to sell their securities and get cash.

How and why do large business firms use money markets? Large businesses use money markets to adjust their liquidity positions. If a firm has idle cash sitting around, it can invest it in negotiable CDs, Treasury bills, or other money market instruments. On the other hand, if a company has a temporary cash shortage, it can borrow in the money markets by selling commercial paper at lower interest rates than it could borrow through a commercial bank.

What are capital markets, and why are they important to corporations? Capital markets refer to the segment of the marketplace where capital goods are financed with long-term debt or equities. The most important capital market instruments are common stocks and corporate bonds. Capital markets are important to corporations because they allow them to obtain necessary financing.

Section 2.4 1.

How does information about a firm’s prospects get reflected in its share price? Investors act upon the expectations of a firm’s prospects through trading of the securities. The buying and selling then causes the price of the security to reflect their assessment of its value.

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What is strong-form market efficiency? semistrong-form market efficiency? weak-form market efficiency? Strong-form market efficiency is a market in which all information, private and public, is reflected in the price of the security. The semistrong-form of market efficiency suggests that only public information is reflected in a security’s price, while the weak-form market efficiency holds that both public and private information is reflected in the current price of a security, but also both public and private information has not been taken into account.

Section 2.5 1.

What is financial intermediation, and why is it important? Financial intermediation is the process of converting financial securities with one set of characteristics into securities with another set of characteristics. For example, commercial banks use consumer CD deposits to make loans to small businesses.

What are some services that commercial banks provide to businesses? Commercial banks are the largest financial intermediaries in the economy and offer the widest range of financial services to businesses. Nearly every business has a significant relationship with a commercial bank – usually a checking or transaction account and some type of credit or loan arrangement. In addition, banks do a significant amount of equipment lease financing.

What is an IPO, and what role does an investment banker play in the process? Investment bankers specialize in helping firms to sell their new debt or equity issues in financial markets. In an initial public offering (IPO), the investment banker prepares the new issue for sale and then underwrites the deal. Other functions of the investment banker

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in an IPO process include preparing the prospectus, registering the documentation with the SEC, and providing general financial advice to the issuer.

Section 2.6 1. Explain how the real rate of interest is determined. The real rate of interest depends on interaction between the rate of return that businesses can expect to earn on investments in capital goods and savers’ time preference for consumption today versus willingness to save. Therefore, the real rate of interest is determined when the desired saving level equals the desired level of investment.

2. How are inflationary expectations accounted for in the nominal rate of interest? The nominal interest rate is the rate that is actually observed in the financial markets, and it is equal to the real interest rate plus the expected annualized changes in commodity prices, or inflation premium. This is commonly referred to as the Fisher effect.

3. Explain why interest rates follow the business cycle. Interest rates tend to follow the business cycle to rise during economic expansion and decline during recession. On the one hand, during an expansion, there is upward pressure on interest rates as businesses begin to grow and borrow more money. On the other hand, during a recession, the demand for goods and services is lower, businesses borrow less, and as a result the economy slows down and the interest rates decline. Typically, the Fed also loosens credit to stimulate the economy, which puts further downward pressure on the interest rates.

Self-Study Problems and Solutions

2.1

Economic units that need to borrow money are said to be: a.

Lender–savers

Borrower–spenders

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Balanced budget keepers.

None of the above.

Solution: LO:

Solutions Manual

Such units are said to be (b) Borrower-spenders.

Level: Basic

2.2

Explain what the marketability of a security is and how it is determined.

Solution:

Marketability refers to the ease with which a security can be sold and converted into cash. The level of marketability depends on the cost of trading the security and the cost of searching for information. The lower these costs are, the greater the security’s marketability.

LO:

Level: Basic

2.3

What are over-the-counter markets (OTCs), and how do they differ from organized exchanges?

Solution:

Securities that are not listed on an organized exchange are sold OTC. An OTC market differs from an organized exchange in that there is no central trading location. OTC security transactions are made via phone or computer as opposed to on the floor of an exchange.

LO:

Level: Basic

2.4

What effect does an increase in the demand for business goods and services have on the real interest rate? What other factors can affect the real interest rate?

Solution:

An increase in the demand for business goods and services will cause the borrowing schedule in Exhibit 2.4 to shift to the right, thus increasing the real rate of interest. Other factors that can affect the real interest rate include increases in

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productivity, changes in technology, or changes in the corporate tax rate. Demographic factors, such as growth or age of the population, and cultural differences can also affect the real rate of interest. LO:

Level: Intermediate

2.5

How does the business cycle affect the nominal interest rate and inflation rate?

Solution:

Both the nominal interest and inflation rates tend to follow the business cycle; that is, they rise with economic expansion and fall during a recession.

LO:

Level: Basic

Discussion Questions 2.1

Explain why total financial assets in the economy must equal total financial liabilities. Every financial asset must be financed with some type of a claim or liability. Since all of an economy’s financial assets are just a collection of the individual financial assets, then they should also sum to the collective claims on those assets in the economy.

LO:

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance; Business Economics AICPA: Resource Management

2.2

Why don’t small businesses make greater use of the direct credit markets since these markets enable firms to finance their activities at a very low cost? Direct credit markets are geared toward big, established companies since they are wholesale in nature and the minimum transaction size is far beyond the needs of a small

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business. Small businesses are better off borrowing money from financial intermediaries, such as commercial banks. LO:

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.3

Explain the economic role of brokers and dealers. How does each make a profit? Brokers and dealers play a similar economic role in that they both bring buyers and sellers of a commodity together in a market. However, brokers only facilitate a transaction by helping the two parties make a transaction and brokers are therefore only compensated for taking on that role. They bear no risk of ownership of securities during the transaction. Dealers on the other hand, take risk in that they will purchase (sell) a commodity from a seller (buyer) without another buyer (seller) necessarily being available. In other words, a dealer will take the risk of purchasing (selling) a commodity and will therefore be compensated for taking that risk.

LO:

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Resource Management

2.4

Why were commercial banks prohibited from engaging in investment banking activities until 1999? Banks had been barred from investment banking following the Great Depression because it was believed that these activities were too risky for banks. At the time, it was believed that excessive risk taking by banks had resulted in a large number of bank failures, which precipitated the Great Depression. Recent research has exonerated the banking system of this charge.

LO:

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Level: Basic Bloomcode: Knowledge AACSB: Analytic IMA: FSA AICPA: Legal/Regulatory Perspective

2.5

What are two basic services that investment banks provide in the economy? Investment banks specialize in helping companies sell new debt or equity as well as provide other services such as broker and dealer services.

LO:

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.6

How do large corporations adjust their liquidity in the money markets? Large corporations can take advantage of money markets to adjust for their liquidity by selling or buying short-term financial instruments such as commercial paper, CDs, or Treasury bills. Large corporations with cash surplus can invest in short-term securities, while corporations with cash shortfall can sell securities or borrow funds on a short-term basis. Money market instruments have a maturity anywhere between one day and one year and therefore are very liquid and less risky than long-term debt.

LO:

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.7

The CFO of a certain company always wears his green suit on a day that the firm is about to release positive information about his company. You believe that you can profit from this information by buying the firm’s shares at the beginning of every day that the

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CFO shows up wearing this green suit. Describe which form of market efficiency is consistent with your belief. You believe that the CFO’s decision to wear a green suit indicates that positive information will be announced and that the company’s stock price will increase following that announcement. If you are correct, knowing what the CFO is wearing before any announcement is valuable private information which should enable you to earn abnormally high returns. Therefore, your belief is consistent with the semistrong form of market efficiency – according to which it is possible to earn abnormally high returns by trading on private information. LO:

Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Strategic/Critical Thinking

2.8

Shouldn’t the nominal rate of interest (Equation 2.1) be determined by the actual rate of inflation (∆Pa), which can be easily measured, rather than by the expected rate of inflation (∆Pe)? The nominal rate of interest is a forward-looking measure, and therefore it makes sense that it is using the expected rate of inflation as opposed to the actual rate of inflation. The expected rate of inflation is the market’s best estimate of what the inflation rate will be in the future.

LO:

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.9

How does Exhibit 2.5 help explain why interest rates were so high during the early 1980s as compared to the relatively low interest rates in the early 1960s?

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The nominal rate of interest is determined by the real rate of interest plus the expected rate of inflation, and during the 1980s, the U.S. economy experienced a very high rate of inflation and, thus, high interest rates. Looking at Exhibit 2.5 we can see that the inflation increased from less than 2 percent in the 1960s to almost 13 percent in the 1980s. This was a result of the monetary policy instituted by the U.S. government during this period of time. LO:

Level: Basic Bloomcode: Analysis AACSB: Analytic IMA: Business Economics AICPA: Resource Management

2.10

When determining the real interest rate, what happens to businesses that find themselves with unfunded capital projects whose rate of return exceeds the cost of capital? The real rate of interest reflects a complex set of forces that control the desired level of lending and borrowing in the economy. In this example, businesses are not investing in projects where the rate of return exceeds the cost of capital. This means that there is lessened a demand for investment funds at the current real interest rate. This will remain so until either the real interest rate changes or until something changes for the firm such as introducing a new technology that will increase the rate of return on projects for the firm.

LO:

Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

Questions and Problems

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BASIC

2.1

Financial System: What is the role of the financial system, and what are the two major components of the financial system?

Solution: The role of the financial system is to gather money from businesses and individuals who have surplus funds and channel funds to those who need them. The financial system consists of financial markets and financial institutions. LO: 2.1 Bloomcode: Knowledge AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.2

Financial System: What does a competitive financial system imply about interest rates?

Solution: If the financial system is competitive, one will receive the highest possible rate for money invested with a bank and the lowest possible interest rate when borrowing money. Also, only firms with good credit ratings and projects with high rates of return will be financed. LO: 2.1 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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2.3

Solutions Manual

Financial System: What is the difference between saver–lenders and borrower–spenders, and who are the major representatives of each group?

Solution: Saver–lenders are those who have more money than they need right now. The principal saver–lenders in the economy are households. Borrower–spenders are those who need the money saver–lenders are offering. The main borrower–spenders in the economy are businesses followed by the federal government, although households are important mortgage borrowers. LO: 2.1 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Business Economics AICPA: Industry/Sector Perspective

2.4

Financial Markets: List the two ways in which a transfer of funds takes place in an economy. What is the main difference between these two?

Solution: Funds can flow directly through financial markets or indirectly through intermediation markets where funds flow through financial institutions first. LO: 2.2 Bloomcode: Knowledge AACSB: Analytic IMA: Business Economics AICPA: Resource Management

2.5

Financial Markets: Suppose you own a security that you know can be easily sold in the secondary market, but the security will sell at a lower price than you paid for it. What does this imply for the security’s marketability and liquidity?

Solution: As the price of the security is lower than that you paid for it, it has a lower degree of liquidity to you, the owner. That is because the security cannot now be sold without a loss in

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value to the owner. Marketability refers to the ease with which a security can be sold or converted to cash. The information in the problem mentions that the security could be easily sold in secondary market, which implies it has high degree of marketability to you. LO: 2.3 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.6

Financial Markets: Why are direct financial markets also called wholesale markets?

Solution: The financial markets are also called wholesale markets because the minimum transaction or security denomination is $1 million or more. LO: 2.2 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.7

Financial Markets: Trader Inc.is a $300 million company, as measured by asset value, and Horst Corp. is a $35 million company. Both are privately held corporations. Explain which firm more likely to go public and register with the SEC, and why.

Solution: Trader Inc. is more likely to go public because of its larger size. Though the cost of SEC registration and compliance is very high, larger firms can offset these costs by the lower funding cost in public markets. Smaller companies find the cost prohibitive for the dollar amount of securities they sell. LO: 2.3 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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2.8

Solutions Manual

Primary Markets: What is a primary market? What does IPO stand for?

Solution: A primary market is where new securities are sold for the first time. IPO stands for Initial Public Offering. LO: 2.3 Bloomcode: Knowledge AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.9

Primary Markets: Identify whether the following transactions are primary market or secondary market transactions. a. Jim Hendry bought 300 shares of IBM through his brokerage account. b. Peggy Jones bought $5,000 of General Motors bonds from another investor. c. Hathaway Insurance Company bought 500,000 shares of Trigen Corp. when the company issued stock.

Solution: a. Secondary market transactions. b. Secondary market transactions. c. Primary market transactions. LO: 2.3 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.10

Investment Banking: What does it mean to “underwrite” a new security issue? What compensation does an investment banker get from underwriting a security issue?

Solution: To underwrite a new security issue means that the investment banker buys the entire issue from the firm at a guaranteed price and then resells the security to individual investors or other institutions at a higher price. The difference between the banker’s purchase price and the total resale price is called the underwriting spread, and it is the banker’s compensation. In

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addition to underwriting new securities, investment banks also provide other services, such as preparing the prospectus, preparing legal documents to be filed with the SEC, and providing general financial advice to the issuer. LO: 2.2 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.11

Investment Banking: Cranjet Inc. is issuing 10,000 bonds, and its investment banker has guaranteed a price of $985 per bond. If the investment banker sells the entire issue to investors for $10,150,000. a. What is the underwriting spread for this issue? b. What is the percentage underwriting cost? c. How much did Cranjet raise?

Solution: a. $300,000 ($10,150,000 – $985 x 10,000) b. 3.05 percent ($30/$985) c. $9,850,000 ($985 x 10,000) LO: 2.2 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.12

Financial Institutions: What are some of the ways in which a financial institution or intermediary can raise money?

Solution: A financial intermediary can raise money through the sale of financial products that individuals or businesses will purchase, such as checking and savings accounts, life insurance policies, pension or retirement funds. LO: 2.1

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Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.13

Financial Institutions: How do financial institutions act as intermediaries to provide services to small businesses?

Solution: Financial intermediaries allow smaller companies to access the financial markets. They do this by converting securities with one set of characteristics into securities with another set of characteristics that meets the needs of smaller companies. By repackaging securities, they are able to meet the needs of different clients. LO: 2.5 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.14

Financial Institutions: Which financial institution is usually the most important to businesses?

Solution: The primary financial intermediaries are commercial banks, life insurance companies, casualty insurance companies, pension funds, investment funds, and business finance companies. Commercial banks are the largest and most prominent financial intermediaries in the economy and offer the widest range of financial services to businesses. LO: 2.5 Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.15

Financial Markets: What is the main difference between money markets and capital markets?

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Solution: Money markets are markets in which short-term debt instruments with maturities of less than one year are bought and sold. Capital markets are markets in which equity securities and debt instruments with maturities of more than one year are bought and sold. LO: 2.3 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.16

Money Markets: What is the primary role of money markets? Explain how the money markets work.

Solution: Money markets provide an option for large corporations to adjust their liquidity positions. Since only seldom are cash receipts and cash expenditures perfectly synchronized, money markets allow companies to temporarily invest idle cash in Treasury bills or negotiable CDs. If a company is short on cash, it can borrow the money from money markets by selling commercial paper at lower interest rates than through commercial banks. LO: 2.3 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.17

Money Markets: What are the main types of securities in the money markets?

Solution: Treasury bills, bank negotiable CDs, and commercial paper. LO: 2.3 Bloomcode: Knowledge AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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2.18

Solutions Manual

Capital Markets: How do capital market instruments differ from money market instruments?

Solution: Capital market instruments are less liquid or marketable, they have longer maturities, usually between 1 and 30 years, and they carry more financial risk. LO: 2.3 Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.19

Market Efficiency: Describe the informational differences that distinguish the three forms of market efficiency.

Solution: The strong form of market efficiency states that all information is reflected in the security prices. In other words, there is no private or inside information, that if released would potentially change the price. The semistrong-form holds that all public information available to investors is reflected in the security’s price. Therefore, insiders with access to private information could potentially profit from trading on this knowledge before it becomes public. Finally, the weak form of market efficiency holds that there is both public and private information that is not reflected in the security’s price and having access to it can lead to abnormal profits. LO: 2.4 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.20

Market Efficiency: Zippy Computers announced strong fourth quarter results. Sales and earnings were both above analysts’ expectations. You notice in the newspaper that Zippy’s stock price went up sharply on the day of the announcement. If no other information about Zippy became public on the day of the announcement and the overall market was down, is this evidence of market efficiency?

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Solution: Yes, if no other information became public and the market was down, the increase in Zippy’s price most likely reflects the effects of investors trading on the good news. Investors, believing that Zippy is now more valuable than they had thought, are willing to pay a higher price for the shares. LO: 2.4 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.21

Market Efficiency: In problem 2.20, if the market is efficient, would it have been possible for Zippy’s stock price to go down in the day that the firm announced the strong fourth quarter results?

Solution: Yes. The last sentence in the statement of problem 2.20 suggests why this might happen. If, on the same day of the announcement, some very bad news about the future prospects for Zippy became public or if the market went down substantially, Zippy’s stock price might also have gone down despite the positive sales and earnings announcement. LO: 2.4 Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

2.22

Market Efficiency: If the market is strong-form efficient, then trading on tips you hear from Jim Cramer (the host of Mad Money on CNBC) will generate no excess returns (i.e., returns in excess of fair compensation for the risk you are bearing). True or false?

Solution: True. If the market is strong-form efficient then all new information gets reflected in stock prices very quickly. In such a market there is nothing you will hear from Jim Cramer on his TV show that will enable you to consistently earn excess returns. The information in his tips will already be reflected in stock prices by the time you can trade on them. LO: 2.4

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Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.23

Financial Markets: What are the major differences between public and private markets?

Solution: Public markets are organized financial markets (also referred as Exchange) where the public buys and sells securities through their stock brokers. The SEC regulates public securities markets in the United States. In contrast, private markets involve direct transactions between two parties. These transactions lack SEC regulation. LO: 2.3 Bloomcode: Analysis AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.24

Financial Instruments: What are the two risk-hedging instruments discussed in the chapter?

Solution: The two risk-hedging instruments discussed are futures and options contracts. LO: 2.3 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Risk Analysis

2.25

Interest Rates: What is the real rate of interest, and how is it determined?

Solution: The real rate of interest measures the return earned on savings, and it represents the cost of borrowing to finance capital goods. It is the interest rate determined in the absence of inflation. The real rate of interest is determined by the interaction between firms that invest in capital projects and the rate of return businesses can expect to earn on investments in capital

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goods, and individuals’ time preference for consumption. Graphically, it is that point when the desired saving level equals the desired level of investment in the economy. LO: 2.6 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.26

Interest Rates: How does the nominal rate of interest vary over time?

Solution: The nominal rate is the rate that we observe in the marketplace. It is determined by both the real rate as well expected inflation. Therefore, the nominal rate will fluctuate according the changes in the real rate as well as changes in expected inflation. LO: 2.6 Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.27

Interest Rates: What is the Fisher equation, and how is it used?

Solution: The Fisher equation is the expected, not the reported or actual, annualized change in commodity prices (∆Pe). It is used to protect the buying power from changes in inflation, and it is incorporated into a loan contract by adding it to the real interest rate that would exist in the absence of inflation. LO: 2.6 Bloomcode: Knowledge AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.28

Interest Rates: Imagine you borrow $500 from your roommate, agreeing to pay her back $500 plus 7 percent nominal interest in one year. Assume inflation over the life of the

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contract is expected to be 4.25 percent. What is the total dollar amount you will have to pay her back in a year? What percentage of the interest payment is the result of the real rate of interest? Solution: You will pay her back $535 ($500 × 1.07) in one year. Given an inflation of 4.25 percent, the real rate of interest is 2.75 percent. This means that $13.75 will be a result of the real interest rate ($500 × 1.0275). LO: 2.6 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Corporate Finance AICPA: Resource Management

2.29

Interest Rates: Your parents have given you $1,000 a year before your graduation so that you can take a trip when you graduate. You wisely decide to invest the money in a bank CD that pays 6.75 percent interest. You know that the trip costs $1,025 right now and that the inflation for the year is predicted to be 4 percent. Will you have enough money in a year to purchase the trip?

Solution: Yes. The CD will be worth $1,067.50 at the end of the year ($1,000 x 6.75% + $1,000), and the price of the trip will be $1,066 ($1,025 x 4% + $1,025). The CD will be able to cover the trip. LO: 2.6 Bloomcode: Analysis AACSB: Reflective Thinking IMA: Corporate Finance AICPA: Resource Management

2.30

Interest Rates: When are the nominal and real interest rates equal?

Solution: The only time the nominal and real interest rates are equal is when the expected rate of inflation over the contract period is zero. LO: 2.6 Bloomcode: Comprehension

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AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

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Sample Test Problems 2.1

What are the two basic mechanisms through which funds flow through the financial

system, and how do they differ? Solution: The two basic mechanisms are the direct financing mechanism and the indirect financing mechanism. In the direct financing mechanism, issuers of securities (borrowerspenders) sell the securities directly to investors (lender-savers). In the indirect financing mechanism, financial institutions aggregate money from lender-savers and make this capital available through loans to borrower-spenders. LO: 1 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.2

You just purchased a share of IBM stock on the New York Stock Exchange. What kind of

transaction was this? a.

Primary market transaction.

Secondary market transaction.

Futures market transaction.

Private placement.

Solution: b (The primary market is the one in which owners of outstanding securities sell their securities to other investors.) LO: 3 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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How are brokers different from dealers?

Solution: Brokers bring buyers and sellers together. They execute a transaction for their client and are compensated with a commission fee. Brokers never own the securities being sold and therefore do not bear any risk of ownership. In contrast, dealers purchase securities and sell them from an inventory that they own. Dealers profit if they are able to sell securities for than they paid for them. Because they own the securities, dealers face the risk that the prices of the securities in their inventory will fall below what they paid for those securities. LO: 3 Level: Intermediate Bloomcode: Analysis AACSB: Reflective Thinking IMA: Business Economics AICPA: Industry/Sector Perspective

2.4

List the three forms of the efficient market hypothesis, and describe what information is

assumed to be reflected in security prices under each of these hypotheses. Solution: 1) Strong-Form Efficiency – all information is reflected in the security prices 2) Semistrong-Form Efficiency – all public information is reflected in the security prices. 3) Weak-Form Efficiency – all information contained in past prices is reflected in security prices. LO: 4 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

2.5 If the nominal rate of interest is 4.25 percent and the expected rate of inflation is 1.75 percent, what is the real rate of interest?

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Solution: Using the Fisher equation: i = r + ∆Pe + r ∆Pe where i = 0.0425 and ∆Pe = 0.0175 Solving for r, we get r = 0.02457, or 2.457% LO: 6 Level: Intermediate Bloomcode: Application AACSB: Analytic IMA: Corporate Finance AICPA: Resource Management

2.6

What is the relation between business cycles and the general level of interest rates?

Solution: As Exhibit 2.5 shows, interest rates tend to follow the business cycle. The level of interest rates tends to rise during periods of economic expansion and decline during periods of economic contraction. LO: 6 Level: Intermediate Bloomcode: Comprehension AACSB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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Chapter 3 Financial Statements, Cash Flows, and Taxes

Before You Go On Questions and Answers Section 3.1 1.

What types of information does a firm’s annual report contain? A firm’s annual report is typically divided into three sections: financial tables with an accompanying verbal explanation of the firm’s performance over the past year; a corporate public relations section discussing the firm’s operations, and the audited financial statements (balance sheet, income statement, statement of cash flows, and statement of retained earnings).

What is the realization principle, and why may it lead to a difference in the timing of when revenues are recognized on the books and cash is collected? According to the realization principle, revenue should only be recognized when the earning process is completed and the exchange of goods or services can be determined by an arm’s length transaction. Although this principle works in theory, it still does not specify whether this is the point when the goods are ordered, when they are shipped, or when the payment is actually received from the customer. Also, not many purchases are paid for in cash any more. Therefore, even if the transaction is recognized at the point at which the customer receives the goods, the actual cash flow might not occur until days later (depending what the terms are).

Section 3.2 1.

What is net working capital? Why might a low value for this number be considered undesirable?

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Net working capital is the difference between total current assets and total current liabilities. A low value for this number is undesirable, for it indicates that the company may not have enough cash on hand to cover its immediate expenses.

Explain the accounting concept behind depreciation. Depreciation in accounting is a noncash expense that helps to allocate the cost of an item over its expected life. It reflects the estimated decrease in the value of an asset due to wear and tear and obsolescence.

What is treasury stock? Treasury stock is the stock that the company purchased back from its investors. These shares do not pay dividends, have no voting rights, and should not be included in sharesoutstanding calculations.

Section 3.3 1.

What is the difference between book value and market value? Book value is the price you paid for a particular asset. This price does not change as long as you own the asset. On the other hand, market value is the price at which you can sell an asset today, as it takes into account how much it can earn in the future.

What are some objections to the preparation of marked-to-market balance sheets? Marked-to-market balance sheets list the firm’s assets and liabilities at their current market prices. Even though a balance sheet constructed with actual market values might paint a more accurate picture of the company’s financial situation, current values are difficult to estimate, and a lot of the complicated models are potentially open to abuse. Therefore, as of the present, the norm is to use book values.

Section 3.4 1.

How is net income computed?

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Net income is calculated as revenues minus expenses. It is the most comprehensive accounting measure of a company’s performance because it reflects the firm’s accomplishments (revenues) relative to its efforts (expenses) during a time period.

What is EBITDA, and what does it measure? EBITDA stands for earnings before interest, taxes, depreciation, and amortization. EBIT is defined as earnings before taxes and interest. The main difference between these two figures is that EBITDA shows the income earned purely from operations and reflects how efficiently a firm can manufacture and sell its products without taking into account the cost of the productive asset base.

What accounting events trigger changes to the retained earnings account? Two events will trigger changes to the retained earnings account: (1) a firm’s report of a net income or loss and (2) the board of directors’ declaration of a cash dividend.

Section 3.5 1.

How do increases in fixed assets from one period to the next affect cash holdings for the firm? An increase in fixed assets from one period to the next is a use of cash. If a company purchases fixed assets during the year, it decreases cash because it must use cash to pay for the purchase.

Name two working capital accounts that represent sources of cash for the firm. An increase in current liabilities is a source of cash. Two common current liabilities are accounts and notes payable. An increase in either of these accounts from one period to the next will represent a source of cash for the firm.

Explain the difference between cash flows from financing and investing activities.

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Cash flows from financing activities occur when cash is obtained from or repaid to creditors or owners (stockholders). Cash flows from investing activities relate to the buying and selling of long-term assets.

Section 3.6 1.

Explain how the four financial statements are related. The four financial statements are linked together as follows: the ending cash balance from the statement of cash flows is used as the cash balance on the balance sheet, and the net income reported in the income statement is transferred to retained earnings on the balance sheet. So as you can see, the balance sheet is the one financial statement that ties all four statements together.

Section 3.7 1.

How does the calculation of net income differ from the calculation of cash flow to investors from operating activity? Net income is calculated as the difference between revenues and expenses from the income statement. Cash flow from operating activity is equal to the firm’s earnings before interest and taxes (EBIT) minus taxes paid in cash plus the firm’s noncash expenses including depreciation and amortization.

All else being equal, if a firm increases its accounts payable, what effect will this have on cash flow to investors? An increase in a current liability such as accounts payable from one period to the next will reduce the cash flow from net working capital and will, therefore, increase cash flow to investors.

What does it mean when a firm’s cash flow to investors is negative? When a firm’s investment of cash flow from net working capital and long-term assets exceed the firm’s cash flow from operating activity, the cash flow to investors will be

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negative. A negative cash flow to investors means that the firm must raise money from new issues of debt or equity.

Section 3.8 1.

Why is it important to consider the consequences of taxes when financing a new project? When financing a new project, it is important to consider the consequences of taxes because ultimately they have a significant impact on the company’s income.

Which type of tax rate, marginal or average, should be used in analyzing the expansion of a product line, and why? When analyzing the expansion of a product line, the marginal tax rate should be the type to consider because it is the amount paid on an additional dollar of income earned. Since expansion of a product line is expected to generate new cash flows, the company will be taxed based on the additional earnings. Average tax rate is not as relevant when making financing decisions because it is simply the total taxes paid divided by taxable income.

What are the tax implications of a decision to finance a project using debt rather than new equity? The difference between debt financing and financing through new equity is in the tax treatment of interest and dividends. While interest payments on debt are tax-deductible business expenses, dividends paid to common or preferred stockholders are not deductible.

Self-Study Problems and Solutions 3.1

The going concern assumption of GAAP implies that the firm: a.

Is going under and needs to be liquidated at historical cost.

Will continue to operate and its assets should be recorded at historical cost.

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Will continue to operate and that all assets should be recorded at their cost rather than at their liquidation value.

d. Solution:

Is going under and needs to be liquidated at liquidation value. One of the key assumptions under GAAP is the going concern assumption, which states that the firm: (c) will continue to operate and that all assets should be recorded at their cost rather than at their liquidation value.

LO: 1 Level: Basic

3.2

The Ellicott City Ice Cream Company management has just completed an assessment of the company’s assets and liabilities and has obtained the following information. The firm has total current assets worth $625,000 at book value and $519,000 at market value. In addition, its long-term assets include plant and equipment valued at market for $695,000, while their book value is $940,000. The company’s total current liabilities are valued at market for $543,000, while their book value is $495,000. Both the book value and the market value of long-term debt is $350,000. If the company’s total assets are equal to a market value of $1,214,000 (book value of $1,565,000), what are the book value and market value of its stockholders’ equity?

Solution:

The book value and market value of stockholders’ equity are shown below (in thousands of dollars):

Assets

Liabilities and Equity Book

Total current assets Fixed assets

Market

$ 625

$ 519

940

695

Book Total current liabilities

Market

$ 495

$ 543

Long-term debt

350

Stockholders’ equity

720

321

$1,565

$1,214

Total liabilities and Total assets

$1,565

$1,214

stockholders’ equity

LO: 3 Level: Basic

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Depreciation and amortization expenses are: a.

Part of current assets on the balance sheet.

After-tax expenses that reduce a firm’s cash flows.

Long-term liabilities that reduce a firm’s net worth.

Noncash expenses that cause a firm’s after-tax cash flows to exceed its net income.

Solution:

Depreciation and amortization expenses are: (d) noncash expenses that cause a firm’s after-tax cash flows to exceed its net income.

LO: 4 Level: Basic

3.4

You are given the following information about Clarkesville Plumbing Company. Revenues in 2014 totaled $896, depreciation expenses $75, costs of goods sold $365, and interest expenses $54. At the end of the year, current assets were $121 and current liabilities were $107. The company has an average tax rate of 34 percent. Calculate its net income by setting up an income statement.

Solution:

Clarkesville’s income statement and net income are as follows: Clarkesville Plumbing Company Income Statement for the Fiscal Year Ending December 31, 2014 Amount Revenues

$896.00

COGS

365.00

EBITDA

$531.00

Depreciation

75.00

EBIT

$456.00

Interest

54.00

EBT

$402.00

Taxes (34%)

136.68

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Net income

$265.32

LO: 4 Level: Basic

3.5

The Huntington Rain Gear Company had $633,125 in taxable income in the year ending September 30, 2013. Calculate the company’s tax using the tax schedule in Exhibit 3.6.

Solution:

Huntington’s tax bill is calculated as follows: Tax rate

Income

Tax

15%

$50,000

$ 7,500

(75,000–50,000)

6,250

(100,000–75,000)

8,500

(335,000–100,000)

91,650

(633,125–335,000)

101,363

Total taxes payable

$215,263

LO: 8 Level: Basic

Discussion Questions 3.1

What is a major reason for the accounting scandals in the early 2000s? How do firms sometimes attempt to meet Wall Street analysts’ earnings projections? Most people believe that managers’ short-term focus is driven by Wall Street’s demand that companies meet or beat the earnings forecasted by stock analysts. Rather than report the actual earnings of the firm, managers try to meet the market’s expectations by starting with the bottom-line number and backing into a sales figure. Thus, the sales may be consistent with the reported earnings figure, but do not represent the true revenue generated by the firm.

LO: 1

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Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.2

Why are taxes and the tax code important for managerial decision making? Understanding the tax code is critical to finance managers, since most decisions are made on an after-tax basis. Furthermore, taxes affect any valuation analysis and also determine the bottom-line figure that is of concern to shareholders and managers.

LO: 8 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Budget Preparation AICPA: Decision Modeling

3.3

Identify the five fundamental principles of GAAP, and explain briefly their importance. The assumption of arm’slength transaction assumes that all business transactions between two parties are made rationally from an economic perspective and both parties will make the deal that provides them the best value. The cost principle calls for the recognition of all accounting transactions at historic cost, or the amount paid or received when the transaction was concluded at arm’s length. The realization principle implies that revenue should be recognized only at the time of the sale. The matching principle dictates that revenue is first recognized and then is matched with the costs incurred in producing the revenue. Finally, the going concern assumption implies that the firm will continue to operate and that all assets should be recorded at their cost rather than at their liquidation value.

LO: 1 Level: Basic Bloomcode: Comprehension AACSB: Communication

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IMA: Reporting AICPA: Reporting

3.4

Explain why firms prefer to use accelerated depreciation methods over the straight-line method for tax purposes. When a firm uses accelerated depreciation, the depreciation expense is higher than with the straight-line method. This reduces the taxable income and the amount of tax paid by the firm. As a result of this higher noncash expense, the firm’s cash flow is higher.

LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Budget Preparation AICPA: Reporting

3.5

What is treasury stock? Why do firms have treasury stock? Any shares repurchased by the company in the open market are recorded as treasury stock in the shareholders’ equity account in the balance sheet. The most common reason for firms doing this is to reduce the number of shares outstanding in the market when the management believes that its firm’s stock is undervalued. This reduction in the number of shares outstanding is expected to boost the share price.

LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Analytic IMA: Coorporate Finance AICPA: Resource Management

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Define book-value accounting and market-value accounting. Book-value accounting implies that all assets and liabilities are recorded and reported at the historical cost when they were acquired. Market-value accounting requires that all assets and liabilities are reported at their current market value.

LO: 3 Level: Basic Bloomcode: Knowledge AACSB: Analytic IMA: Reporting AICPA: Reporting

3.7

Compare and contrast depreciation expense and amortization expense. Depreciation expense is the amount by which a firm’s fixed assets are written down in a period during which the assets are utilized for generating cash flows. Amortization is the amount by which intangible assets like goodwill, patents, license, copyrights, and trademarks are written down in any period that they are utilized by the firm to generate benefits. Both depreciation and amortization are noncash expenses that will serve to boost the firm’s after-tax cash flows, and generate actual value of the asset at the end of a period.

LO: 4 Level: Basic Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Measurement

3.8

Why are retained earnings not considered an asset of the firm? Retained earnings are part of shareholders’ equity that has already been utilized by the company. It is a liability of the company and corresponds to a claim by the firm’s

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shareholders. The retained earnings reported on the balance sheet have already been allocated by the company among various assets and hence are not available for current or future uses. New retained earnings have to be generated to provide for new uses. LO: 2 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.9

How does a firm’s cash flow to investors from operating activity differ from net income, and why? Net income is an accounting figure that includes both cash and noncash expenses. In addition, revenues are recognized before they are collected and expenses are recognized before they are paid. Cash flow from operating activity recognizes that certain revenues and expenses, while recognized for accounting purposes, do not actually involve a cash flow and ignores the effects of these non-cash items on the income statement.

LO: 5 Level: Basic Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.10

What is the statement of cash flows, and what is its role? This financial statement records both the cash inflows and cash outflows for a period of time. Thus, it reports the changes in the cash position of a firm between successive accounting periods.

LO: 5

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Level: Basic Bloomcode: Knowledge AACSB: Communication IMA: Reporting AICPA: Reporting

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Questions and Problems BASIC 3.1

Balance sheet: Given the following information about Elkridge Sporting Goods, Inc., construct a balance sheet for June 30, 2014. On that date the firm had cash and marketable securities of $25,135, accounts receivables of $43,758, inventory of $167,112, net fixed assets of $325,422, and other assets of $13,125. It had accounts payables of $67,855, notes payables of $36,454, long-term debt of $223,125, and common stock of $150,000. How much retained earnings did the firm have?

Solution: Assets

Book Value

Liabilities and Stockholders’

Book Value

Equity

Cash and marketable

$ 25,135

Accounts payables

$ 67,855

securities Accounts receivable

43,758

Notes payables

36,454

Inventories

167,112

Total current assets

$236,005

Total current liabilities

$104,309

Net fixed assets

325,422

Long-term debt

223,125

Other assets

13,125

Common stock

150,000

Retained earnings

97,118

Total liabilities and Total assets

$574,552

stockholders’ equity

$574,552

LO: 3.2 Bloomcode: Analysis AACSB: Communication IMA: Reporting AICPA: Reporting

3.2

Inventory accounting: Differentiate between FIFO and LIFO accounting.

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Solution: FIFO (first in, first out) refers to the practice of firms, when making sales, assuming that the inventory that came in first (at a lower price) is being sold first. During the period of rising prices, LIFO (last in, last out) implies that a firm is selling the higher cost, newer inventory first, leaving the lower cost, older inventory on the balance sheet. LO: 3.2 Bloomcode: Comprehension AACSB: Communication IMA: Budget Preparation AICPA: Reporting

3.3

Inventory accounting: Explain how the choice of FIFO versus LIFO can affect a firm’s balance sheet and income statement.

Solution: FIFO makes sense during times of rising prices because it allows the firm to eliminate the lower priced inventory first, resulting in higher profit margin. This allows the firm to leave higher valued inventory on the balance sheet. During inflationary times, a firm using LIFO would see a lower profit margin and lower values of inventory on the balance sheet. It is important that anyone who is analyzing firms using different accounting methods on inventory recognize the impact on the bottom line (profit margin and net income) and on current assets. LO: 3.2 Bloomcode: Comprehension AACSB: Communication IMA: Budget Preparation AICPA: Reporting

3.4

Market-value accounting: How does the use of market-value accounting help managers?

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Solution: Market-value accounting of both assets and liabilities allows managers to have a truer picture of their company’s financial condition and to do a better job of estimating cash flows that the assets would generate. However, marking-to-market is not as easy as it sounds because of the difficulties involved in coming up with the correct market value of current assets and liabilities. LO: 3.3 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.5

Working capital: Laurel Electronics reported the following information at its annual meetings: The company had cash and marketable securities worth $1,235,455, accounts payables worth $4,159,357, inventory of $7,121,599, accounts receivables of $3,488,121, short-term notes payable worth $1,151,663, and other current assets of $121,455. What is the company’s net working capital?

Solution: Total current assets

= $1,235,455 + $3,488,121 + $7,121, 599 + 121,455 = $11,966,630

Total current liabilities = $4,159,357 + $1,151,663 = $5,311,020 Net working capital

= $11,966,630 - $5,311,020 = $6,655,610

LO: 3.2 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Reporting

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Working capital: The financial information for Laurel Electronics referred to in Problem 3.5 is all at book value. Suppose marking to market reveals that the market value of the firm’s inventory is 20 percent below its book value, its receivables are 25 percent below their book value, and the market value of its current liabilities is identical to the book value. What is the firm’s net working capital using market values? What is the percentage change in net working capital?

Solution: Market value of inventory = $7,121,599 × 0.80 = $5,697,279 Market value of receivables = $3,488,121 × 0.75 = $2,616,091 Total current assets

$1,235,455 + $2,616,091 + $5,697,279 + 121,455

= $9,670,280 Total current liabilities = $4,159,357 + $1,151,663 = $5,311,020 Net working capital = $9,670,280 - $5,311,020 = $4,359,260 Percent Change =

$4,359,260 − $6,655,610 $6,655,610

= −𝟑𝟒. 𝟓% LO: 3.2 Bloomcode: Analysis AACSB: Communication IMA: Reporting AICPA: Reporting

3.7

Income statement: The Oakland Mills Company has disclosed the following financial information in its annual reports for the period ending March 31, 2014: sales of $1.45 million, cost of goods sold of $812,500, depreciation expenses of $175,000, and interest expenses of $89,575. Assume that the firm has an average tax rate of 35 percent. What is the company’s net income? Set up an income statement to answer the question.

Solution: Oakland Mills Company Income Statement

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For the period ended on March 31, 2014 Amount Revenues

$1,450,000.00

COGS

812,500.00

EBITDA

$ 637,500.00

Depreciation EBIT Interest EBT

175,000.00 $ 462,500.00 89,575.00 $ 372,925.00

Taxes (35%)

130,523.75

Net income

$ 242,401.25

LO: 3.4 Bloomcode: Analysis AACSB: Communication IMA: Reporting AICPA: Reporting

3.8

Cash flow: Describe the organization of the statement of cash flows.

Solution: The statement of cash flows identifies the cash inflows and cash outflows of the firms for a specified period. This allows one to estimate the net cash flows from operations. This financial statement is organized to report the cash flows resulting from the three basic activities in any firm—operating, investing, and financing. The cash flows from operations are the results of netting all revenues and expenses that result from the operating activities of the firm. Buying and selling a firm’s assets lead to cash flows from investing activities. Cash flows from financing activities arise from the firm borrowing from its investors and/or making payments to its lenders and shareholders. LO: 3.5 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

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Cash flows: During 2014, Towson Recording Company increased its investment in marketable securities by $36,845, funded fixed-assets acquisitions of $109,455, and had marketable securities of $14,215 mature. What is the net cash used in investing activities?

Solution: Long-Term Investing Activities Net property, equipment, and other assets

$(109,455.00)

Net acquisitions and dispositions

0.00

Investments in marketable securities

(22,630.00)

Net cash used in investing activities

$(132,085.00)

LO: 3.5 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.10

Cash flows: Caustic Chemicals management identified the following cash flows as significant in its year-end meeting with analysts. During the year Caustic had repaid existing debt of $312,080 and raised additional debt capital of $650,000. It also repurchased stock in the open market for a total of $45,250. What is the net cash provided by financing activities?

Solution: Financing Activities Loan repayment

$(312,080)

Increase in long-term debt

650,000

Purchase of treasury stock

(45,250)

Net cash provided by financing activities

$ 292,670

LO: 3.5

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Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

3.11

Cash flows: Identify and describe the noncash expenses that a firm may incur.

Solution: A firm may have several items on its income statement that did not result in any cash outflow to the firm. The two largest are depreciation expenses and amortization expenses. Other non-cash expenses include deferred taxes, deferred wages, and depletion charges, which is similar to depreciation and used for natural resource assets. Prepaid expenses also fit into this category as they represent expenses to the firm that were paid in previous period, but yet to incur. LO: 3.5 Bloomcode: Comprehension AACSB: Communication IMA: Reporting AICPA: Reporting

3.12 Cash flows: Given the data for Oakland Mills Company in problem 3.7 above, compute the cash flows to investors from operating activity. Solution: CFOA = EBIT – current taxes + Non-cash expenses = $462,500.00 - $130,523.75 + $175,000.00 = $506,976.25 LO: 3.7 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

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3.13 Cash flows: Hillman Corporation reported current assets of $3,495,055 for the year ending December 31, 2014 and current assets of $3,103,839 on December 31, 2013. Current liabilities for the firm were $2,867,225 and $2,760,124 at the end of 2014 and 2013 respectively. Compute the cash flow invested in net working capital at Hillman Corporation during 2014. Solution: CFNWC = ($3,495,055 - $2,867,225) – ($3,103,839 - $2,760,124) = $284,115 LO: 3.7 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

3.14

Cash flows: Del Bridge Construction had long- term assets before depreciation of $990,560 on December 31, 2013 and $1,211,105 on December 31, 2014. How much cash flow was invested in long-term assets for Del Bridge during 2014?

Solution: CFLTA = $1,211,105 - $990,560 = $220,545. LO: 3.7 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Reporting

3.15

Tax: Define average tax rate and marginal tax rate.

Solution: The average tax rate is defined as the total taxes paid divided by taxable income. The marginal tax rate, meanwhile, represents the tax rate that is paid on the last dollar of income earned, or the rate that will be paid on the next dollar earned. LO: 3.8 Bloomcode: Knowledge AACSB: Communication IMA: Reporting

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AICPA: Reporting

3.16

Tax: What is the relevant tax rate to use when making financial decisions? Explain why.

Solution: Managers need to use the marginal tax rate for making financial decisions. This is because any additional cash flows that result from a firm’s new projects will be taxed at the marginal tax rate. Thus, this is the appropriate rate to use. LO: 3.8 Bloomcode: Comprehension AACSB: Communication IMA: Investment Decisions AICPA: Decision Modeling

3.17

Tax: Manz Property Management Company announced that in the year ended June 30, 2014, its earnings before taxes amounted to $1,478,936. Calculate its taxes using Exhibit 3.6.

Solution: Earnings before tax = $1,478,936 Tax rate

Income

Tax

15%

$0 to $50,000

$ 7,500.00

50,001 − 75,000

6,250.00

75,001 − 100,000

8,500.00

100,001 − 335,000

91,650.00

335,001 − 10,000,000

388,938.24

10,000,001 − 15,000,000

15,000,001 − 18,333,333

More than $18,333,333 Total taxes payable

$502,838.24

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LO: 3.8 Bloomcode: Application AACSB: Communication IMA: Reporting AICPA: Measurement

INTERMEDIATE 3.18

Balance sheet: Tim Dye, the CFO of Blackwell Automotive, Inc., is putting together this year’s financial statements. He has gathered the following balance sheet information. The firm had a cash balance of $23,015, accounts payable of $163,257, common stock of $313,299, retained earnings of $512,159, inventory of $212,444, goodwill and other assets equal to $78,656, net plant and equipment of $711,256, and short-term notes payable of $21,115. It also has accounts receivables of $141,258 and other current assets of $11,223. How much long-term debt does Blackwell Automotive have?

Solution: Blackwell Automotive, Inc. Balance Sheet as of December 31 Liabilities and Stockholders’ Assets Cash

Equity $

23,015

Accounts payable and accruals

Accounts receivable

141,258

Notes payable

Inventories

212,444

Other current assets

11,223

Total current assets

$ 387,940

Net plant and equipment

711,256

Long-term debt

168,022

Goodwill and other assets

78,656

Total liabilities

$ 352,394

Total current liabilities

21,115

$ 184,372

Common stock

313,299

Retained earnings

512,159

Stockholders’ Equity

$ 163,257

$ 825,458

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Total liabilities and Total assets

$1,177,852

stockholders’ equity

$1,177,852

LO: 3.2 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.19

Working capital: Mukhopadhya Network Associates has a current ratio of 1.60, where the current ratio is defined as follows: current ratio = current assets/current liabilities. The firm’s current assets are equal to $1,233,265, its accounts payables are $419,357, and its notes payables are $351,663. Its inventory is currently at $721,599. The company plans to raise funds in the short-term debt market and invest the entire amount in additional inventory. How much can notes payable increase without the current ratio falling below 1.50?

Solution: Let x be the amount raised through notes payables. New current liabilities = $419,357+ $351,663 + x New current assets = $1,233,265 + x Current assets $1, 233, 265 + x = 1.5 = Current liabilities $771,020 + x 1.5  ($771,020 + x ) = $1, 233, 265 + x 1.5 x − x = $1, 233, 265 − $1,156,530 0.5 x = $76,735 x = $76,735 0.5 = $153, 470

Thus the firm can add up to $153,470 in inventory by raising money through notes payable without changing the ratio of current assets to current liabilities to more than

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1.50. (This ratio of current assets to current liabilities is known as the current ratio and will be discussed in the next chapter.) LO: 3.2 Bloomcode: Analysis AACSB: Analytic IMA: Corporate Finance AICPA: Measurement

3.20

Market value: Reservoir Bottling Co. reported the following information at the end of the year. Total current assets are worth $237,513 at book value and $219,344 at market value. In addition, plant and equipment have a market value of $343,222, and a book value of $362,145. The company’s total current liabilities are valued at market for $134,889 and have a book value of $129,175. Both the book value and the market value of long-term debt is $144,000. If the company’s total assets have a market value of $562,566 and a book value of $599,658, what is the difference between the book value and market value of its stockholders’ equity?

Solution: Assets

Book

Market

Value

Book Value Liabilities and

Market Value

stockholders’ equity Total current assets

$237,513

$219,344

Total current liabilities

$129,175

$134,889

Net fixed assets

362,145

343,222

Long-term debt

144,000

Other assets

Common stock

326,483

283,677

Total assets

$599,658

$562,566

Total liabilities and

$599,658

$562,566

stockholders’ equity

Change in value of stockholders’ equity = $283,677 – $326,483 = $(42,806) LO: 3.3 Bloomcode: Analysis AACSB: Analytic IMA: Corporate finance AICPA: Measurement

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Income statement: Nimitz Rental Company provided the following information to its auditors. For the year ended March 31, 2014, the company had revenues of $878,412, general and administrative expenses of $352,666, depreciation expenses of $131,455, leasing expenses of $108,195, and interest expenses equal to $78,122. If the company’s average tax rate is 34 percent, what is its net income after taxes?

Solution: Nimitz Rental Company Income Statement as of March 31, 2014 Amount Revenues

$878,412

General and administrative expenses

352,666

Leasing expenses

108,195

EBITDA

$417,551

Depreciation expenses

131,455

EBIT

$286,096

Interest expenses EBT

78,122 $207,974

Taxes (34%)

70,711

Net income

$137,263

LO: 3.4 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.22

Income statement: Sosa Corporation recently reported an EBITDA of $31.3 million and net income of $9.7 million. The company had $6.8 million in interest expense, and its

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average corporate tax rate was 35 percent. What was its depreciation and amortization expense? Solution: Amount EBITDA Less: Depreciation and amortization

$31,300,000.00 9,576,923.08

EBIT

$21,723,076.92

Interest

6,800,000.00

EBT

$14,923,076.92

Taxes (35%)

5,223,076.92

Net income

$ 9,700,000.00

LO: 3.4 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.23

Income statement: Fraser Corporation has announced that its net income for the year ended June 30, 2014, was $1,353,412. The company had EBITDA of $ 4,967,855, and its depreciation and amortization expense was equal to $1,112,685. The company’s average tax rate is 34 percent. What was its interest expense?

Solution: Amount EBITDA

$4,967,855.00

Depreciation and Amortization

1,112,685.00

EBIT

$3,855,170.00

Interest

1,804,545.76

EBT

$2,050,624.24

Taxes (34%)

697,212.24

Net income

$1,353,412.00

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LO: 3.4 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.24

Income Statement: For its most recent fiscal year, Carmichael Hobby Shop recorded EBITDA of $512,725.20, EBIT of $362,450.20, zero interest expense, and cash flow to investors from operating activity of $348,461.25. Assuming there are no non-cash revenues recorded on the income statement, what is the firm’s net income after taxes?

Solution: We know that: Cash flow from operating activity = CFOA = EBIT − Current taxes + Noncash expenses

Since interest expense = $0, we know that: EBIT = EBT Therefore, Net income = EBIT - Current taxes and so: Current taxes = EBIT – Net income Substituting into the equation for CFOA above (Equation 3.4) yields: CFOA = EBIT – (EBIT – Net Income) + Noncash expenses CFOA = Net income + Noncash expenses Since:

Depreciation and amortization = Noncash expenses = EBITDA − EBIT = $512, 275.20 − $362, 450.20 = $150, 275 We can calculate net income as:

Net income = CFOA − Depreciation & amortization = $348, 461.25 - $150, 275 = $198,186.25

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LO: 3.4, 3.7 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.25

Retained earnings: Columbia Construction Company earned $451,888 during the year ended June 30, 2014. After paying out $225,794 in dividends, the balance went into retained earnings. If the firm’s total retained earnings were $846,972 at the end of fiscal year 2014, what were the retained earnings on its balance sheet on July 1, 2013?

Solution: Columbia Construction Company Retained Earnings for 2014 Balance of retained earnings, July 1, 2013

$ 620,878.00

Add: Net income for the year

451,888.00

Less: Dividends to common stockholders

(225,794.00)

Balance of retained earnings, June 30, 2014

$ 846,972.00

LO: 3.4 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.26

Cash flow: Refer to the information given in Problem 3.21. What is the cash flow from operations for Nimitz Rental?

Solution: Cash flow from operations

Net income + Depreciation

$137,263 + $131,455

$268,718

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LO: 3.5 Bloomcode: Application AACSB: Analytic IMA: Reporting AICPA: Measurement

3.27

Tax: Mount Hebron Electrical Company’s financial statements indicated that the company had earnings before interest and taxes of $718,323. The interest rate on its $850,000 debt was 8.95 percent. Calculate the taxes the company is likely to owe. What are the marginal and the average tax rates for this company?

Solution: EBIT

$718,323.00

Interest

76,075.00

EBT

$642,248.00

Tax rate

Tax

Income

15%

$0 to $50,000

$ 7,500.00

50,001 − 75,000

6,250.00

75,001 − 100,000

8,500.00

100,001 − 335,000

91,650.00

335,001 − 10,000,000

104,464.32

10,000,001 − 15,000,000

15,000,001 − 18,333,333

More than $18,333,333 Total taxes payable

$218,364.32

Marginal tax rate

34%

Average tax rate

Total taxes payable / Taxable income

$218,364.22 / $642,248

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34%

LO: 3.8 Bloomcode: Analysis AACSB: Analytic IMA: Budget Preparation AICPA: Measurement

ADVANCED 3.28

The Centennial Chemical Corporation announced that, for the period ending March 31, 2014, it had earned income after taxes of $2,768,028.25 on revenues of $13,144,680. The company’s costs (excluding depreciation and amortization) amounted to 61 percent of sales and it had interest expenses of $392,168. What is the firm’s depreciation and amortization expense if its average tax rate is 34 percent?

Solution: Centennial Chemical Corporation Income statement For the period ending March 31, 2014 Amount Revenues

$13,144,680.00

Costs

$8,018,254.80

EBITDA

$5,126,425.20

Depreciation and amortization

$540,275.00

EBIT

$4,586,150.20

Interest

$392,168.00

EBT

$4,193,982.20

Taxes (34%)

$1,425,953.95

Net income

$2,768,028.25

LO: 3.4

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Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.29

Eau Claire Paper Mill, Inc., had, at the beginning of the current fiscal year, April 1, 2013, retained earnings of $323,325. During the year ended March 31, 2014, the company produced net income after taxes of $713,445 and paid out 45 percent of its net income as dividends. Construct a statement of retained earnings and compute the year-end balance of retained earnings.

Solution: Eau Claire Paper Mill, Inc. Retained Earnings for 2014 Balance of retained earnings, April 1, 2013

$ 323,325.00

Add: Net income, 2014

713,445.00

Less: Dividends to common stockholders

(321,050.25)

Balance of retained earnings, March 31, 2014

$ 715,719.75

LO: 3.4 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.30

Menomonie Casino Company earned $23,458,933 before interest and taxes for the fiscal year ending March 31, 2014. If the casino had interest expenses of $1,645,123, calculate its tax obligation using Exhibit 3.6. What are the marginal and the average tax rates for this company?

Solution: EBIT

$23,458,933.00

Interest

1,645,123.00

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EBT

$21,813,810.00

Tax rate

Tax

Income

15%

$0 to $50,000

50,001 − 75,000

6,250.00

75,001 − 100,000

8,500.00

100,001 − 335,000

91,650.00

335,001 − 10,000,000

3,286,100.00

10,000,001 − 15,000,000

1,750,000.00

15,000,001 − 18,333,333

1,266,666.54

More than $18,333,333

1,218,166.95

Total taxes payable

$7,634,833.49

Marginal tax rate

35%

Average tax rate

Total taxes payable / Taxable income

$7,634,833.49 / $21,813,810

35%

7,500.00

LO: 3.8 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.31

Vanderheiden Hog Products Corp. provided the following financial information for the quarter ending June 30, 2014: Net income: $189,425 Depreciation and amortization: $63,114 Increase in receivables: $ 62,154 Increase in inventory: $57,338 Increase in accounts payables: $37,655

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Decrease in other current assets: $27,450 What is this firm’s cash flow from operating activities during this quarter? Solution: Vanderheiden Hog Products Corp. Statement of Cash Flows (Partial) For the quarter ended on June 30, 2014 Operating Activities Net income

$189,425

Additions (sources of cash) Depreciation and amortization

63,114

Increase in accounts payable

37,655

Decrease in other current assets

27,450

Increase in accrued income taxes

Subtractions (uses of cash) Increase in receivable

(62,154)

Increase in inventories

(57,338)

Net cash provided by operating activities

$198,152

LO: 3.5 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.32

Cash flows: Analysts following the Tomkovick Golf Company were given the following balance sheet information for the years ended June 30, 2014 and June 30 2013: 2014

2013

Assets Cash and marketable securities

33,411

16,566

Accounts receivable

260,205

318,768

Inventory

423,819

352,740

Other current assets

41,251

29,912

Total current assets

$ 758,686

$ 717,986

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Plant and equipment

1,931,719

1,609,898

Less: Accumulated depreciation

(419,044)

(206,678)

Net plant and equipment

$1,512,675

$1,403,220

Goodwill and other assets

382,145

412,565

Total assets

$2,653,506

$2,533,771

Liabilities and Equity

2014

2013

Accounts payable and accruals

$ 378,236

$ 332,004

Notes payable

14,487

7,862

Accrued income taxes

21,125

16,815

$ 413,848

$ 356,681

Long-term debt

679,981

793,515

Total liabilities

$1,093,829

$1,150,196

Common stock (10,000 shares)

10,000

Additional paid-in capital

975,465

Retained earnings

587,546

398,110

Less: Treasury stock

(13,334)

Total common equity

$1,559,677

$1,383,575

Total liabilities and equity

$2,653,506

$2,533,771

Total current liabilities

Preferred stock

In addition, it was reported that the company had a net income of $ 3,155,848 and that depreciation expenses were equal to $212,366 during 2014. Assume amortization expense was $0 in 2014. a. Construct a 2014 cash flow statement for this firm. b. Calculate the net cash provided by operating activities for the statement of cash flows. c. What is the net cash used in investing activities? d. Compute the net cash provided by financing activities. Solution: a. Tomkovick Golf Company Statement of Cash FlowsYear Ended June 30, 2014 Operating Activities Net income

$ 3,155,848.00

Additions (sources of cash) Depreciation

212,366.00

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Increase in accounts payable

46,232.00

Decrease in accounts receivable

58,563.00

Increase in accrued income taxes

4,310.00

Subtractions (uses of cash) Increase in other current assets

(11,339.00)

Increase in inventories

(71,079.00)

Net cash provided by operating activities

$ 3,394,901.00

Long-Term Investing Activities Increase in property equipment

$ (321,821.00)

Decrease in goodwill and other assets Net cash used in investing activities

30,420.00 $ (291,401.00)

Financing Activities Increase in notes payable

6,625.00

Decrease in long-term debt

(113,534.00)

Payment of cash dividends

(2,966,412.00)

Purchase of treasury stock

(13,334.00)

Net cash provided by financing activities

$(3,086.655.00)

Effect of exchange rates on cash

0.00

Net increase in cash and marketable securities

16,845.00

Cash and marketable securities at beginning of

16,566.00

year Cash and marketable securities at end of year

33,411.00

b. $ 3,394,901.00 c. $ (291,401.00) d. $(3,086.655.00) LO: 3.5 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.33

Cash flows: Based on the financial statements for Tomkovick Golf Company in Problem 3.32, compute the cash flow invested in net working capital and the cash flow invested in

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long-term assets that you would use in a calculation of the cash flows to investors for 2014. Solution: CFNWC = ($758,686 – $413,848) – ($717,986 – $356,681) = -$16,467 CFLTA = ($1,931,719 – $1,609,898) + ($382,145 - $412,565) = $291,401 LO: 3.7 Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

Sample Test Problems 3.1

What is the matching principle, and how can it cause accounting expenses to differ from actual cash outflows?

Solution: The matching principle is an accounting principle under which accountants match revenues with the costs incurred to generate those revenues when they prepare an income statement. Because the actual cash flows associated with expenses might not be incurred in the same period that those expenses are recognized in the income statement, the accounting expenses can differ from actual cash outflows. LO: 1 Level: Intermediate Bloomcode: Knowledge AACSB: Analytic IMA: Budget Preparation AICPA: Measurement

3.2

Wolf Pack Enterprises has total current assets of $346,002 and fixed assets of $476,306. The company also has long-term debt of $276,400, $100,000 in its common stock

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account, and retained earnings of $187,567. What is the value of its total current liabilities? Solution: Assets

Liabilities and Equity

Total current assets

$346,002

Total current liabilities

$???????

Fixed assets

$476,306

Long-term debt

$276,400

Common stock

$100,000

Retained earnings

$187,567

Liabilities and Total assets

$???????

stockholders’ equity

$???????

First, calculate total assets: $346,002 + $476,306 = $822,308 From Equation 3.1: $822,308 - $276,400 – 100,000 – 187,567 = $258,341 (total current liabilities) LO: 2 Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.3

What is the difference between a book-value balance sheet and a market-value balance sheet? Which provides better information to investors and management?

Solution: A book-value balance sheet is an accounting balance sheet in which asset values are listed at their historical cost. A market-value balance sheet reflects current asset values (what the assets are worth today). Market values provide better economic information for investors and managers than book values. Therefore, a market-value balance sheet provides better decision-making information. LO: 3

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Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Reporting

3.4

ACME Corporation had revenues of $867,030 in 2014. It also had expenses (excluding depreciation) of $356,240, depreciation of $103,456, and interest expense of $52,423. What was the company’s net income after taxes if its average tax rate was 40 percent?

Solution: Amount Revenues

$867,030.00

Expenses

356,240.00

EBITDA

$510,790.00

Depreciation

103,456.00

EBIT

$407,334.00

Interest

52,423.00

EBT

$354,911.00

Taxes (40%)

141,964.40

Net income

$212,946.60

LO: 4 Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.5

True Blue Company increased its investments in marketable securities by $323,370 and paid $1,220,231 for new fixed assets during 2014. The company also repaid $779,200 of existing long-term debt while raising $913,455 of new debt capital. In addition, True Blue had a net cash inflow of $345,002 from the sale of fixed assets, and repurchased

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stock in the open markets for a total of $56,001. What is the net cash used in long term investing activities by True Blue? What is the net cash provided by the company’s financing activities? Solution: Investing Activities Net property, equipment and other assets

$(1,220,231)

Net acquisitions and dispositions

345,002

Investments in marketable securities Net cash used in investing activities

$(875,229)

Financing Activities Long-term debt repayment

$(779,200)

Increase in long-term debt

913,455

Purchase of treasury stock

(56,001)

Net cash provided by financing activities

78,254

LO: 5 Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

3.6

Sun Devil Corporation reported EBITDA of $7,300,125 and net income of $3,328,950 for the fiscal year ended December 31, 2014. During the same period, the company had $1,155,378 in interest expense, $1,023,285 in depreciation and amortization expense, and an average corporate tax rate of 35 percent. What was the cash flow to investors from operating activity during 2014?

Solution: CFOA = EBIT – Current taxes + Noncash expenses CFOA = EBITDA – Current taxes CFOA = $7,300,125 – [0.35 × ($7,300,125 - $1,023,285 - $1,155,378)]

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= $5,507,613 LO: 7 Level: Intermediate Bloomcode: Analysis AACSB: Analytic IMA: Reporting AICPA: Measurement

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Chapter 4 Analyzing Financial Statements Before You Go On Questions and Answers Section 4.1 1.

Why is it important to look at a firm’s historical financial statements? When one does a ratio analysis on a firm, it is important to do the analysis over a three- to five-year period. Looking at the historical financial statements allows one to see the trends on the various ratios—whether they are improving, worsening, or staying the same.

What is the primary concern of a firm’s creditors? The creditors of a firm will want to know if the firm is generating enough cash flows to meet all of its required obligations, like employee wages and trade credit, and still has enough to meet the principal and interest payments due periodically. Their ultimate concern is being paid on time and being repaid in full.

Section 4.2 1.

Why does it make sense to standardize financial statements? Standardized, or common-size, financial statements allow you to make meaningful comparisons of financial statements between two firms that are dramatically different in size. They also make interpretation of data much easier. Standardized or common-size financial statements are those that are prepared with numbers that have been compiled using a common measure of the firm’s size.

What are common-size, or standardized, financial statements, and how are they prepared? Typically, balance sheets are standardized by dividing each asset and liability by total assets (or total deposits in the case of banks) and expressing it as a percentage of total assets. For income statements the scaling factor is sales or revenue, thus expressing each item as a percentage of sales.

Section 4.3 1.

What are the efficiency ratios, and what do they measure? Why, for some firms, is the total asset turnover more important than the fixed asset turnover?

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Efficiency ratios (also called turnover ratios) measure how efficiently a firm uses its assets to generate sales. The following ratios were discussed: • Inventory turnover/days’ sales in inventory—calculated as cost of goods sold divided by inventory; it shows how many times the inventory of a firm is sold and replaced over a specific period. • Accounts receivable turnover/days’ sales outstanding—computed as net sales divided by accounts receivable; it is a measure used to quantify a firm’s effectiveness in extending credit and success in collection of debts. • Total asset turnover—calculated as net sales divided by total assets; it gives us the amount of sales generated for every dollar’s worth of assets. • Fixed asset turnover—calculated by dividing sales by net fixed assets; it shows the amount of sales generated with each dollar of fixed assets. The fixed asset turnover is not very useful for service-oriented firms with little plant or equipment. Instead, the total asset turnover is more relevant. 2.

List the leverage ratios discussed in this section, and explain how they are related. Leverage ratios measure the extent to which a firm uses debt rather than equity financing and show the firm’s ability to meet its long-term financial obligations. The three leverage ratios discussed in this book are total debt ratio (plus its variations of debt-equity ratio and the equity multiplier), times interest earned, and cash coverage ratio. This is how all three ratios are linked together: the total debt ratio indicates what proportion of assets are financed from other sources than shareholders, and times interest earned measures how effectively the firm can meet the interest obligations on this financing based on operating earnings (EBIT). Cash coverage takes the analysis a step further, determining whether the firm has enough cash on hand to cover the interest payments.

List the profitability ratios discussed in this section, and explain how they differ from each other. The most commonly used profitability ratios are profit margin (gross profit margin, operating profit margin, and net profit margin), return on assets (ROA), and return on equity (ROE). The profit margin ratios examine the company’s profitability as a percentage of sales, whereas ROE and ROA help us analyze profitability as percentage of an investment, either in assets or in the firm’s equity. In other words, ROA tells us what earnings were generated from invested capital, and ROE indicates how well management is employing the investors’ capital invested in the company.

Section 4.4 1.

What is the purpose of the DuPont system of analysis? The purpose of the DuPont system of analysis is to determine a company’s financial health. It breaks down ROE into three parts: profit margin, total asset turnover, and

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financial leverage (equity multiplier). If ROE is unsatisfactory, the DuPont identity helps locate which part of the business is underperforming. 2.

What is the equation for ROA in the DuPont system, and how do the factors in that equation influence the ratio? In the previous section you learned that ROA is calculated as net income divided by total assets. Modifying the equation by dividing both the numerator and denominator by net sales and rearranging the terms, we can rewrite the equation as: ROA= Net income/Net sales x Net sales/Total assets or ROA = Net profit margin x Total asset turnover Therefore, based on the above equation, we can conclude that ROA is a combination of the firm’s ability to efficiently manage its operating expenses (operating efficiency) and efficient asset management (asset use efficiency). In order for the management to increase ROA, it can increase either the profit margin or asset turnover, or both. The strategies that companies choose to pursue to increase their ROA depend on their business type and long-term goals.

What are the three major shortcomings of ROE? The three major shortcomings of ROE are that it does not consider the size of the initial investment or the size of future cash payments, it ignores risk, and it does not directly consider the cash flow involved in the business decision-making process. However, despite the ratio’s drawbacks, it is a handy tool for measuring a company’s profitability and identifying industry leaders, as long as you know where the numbers are coming from.

Section 4.5 1.

In what three ways can a financial manager choose a benchmark? A financial manager can choose a benchmark based on either of the following methods: trend analysis, industry average analysis, or peer group analysis. Trend analysis uses history as its standard by evaluating the firm’s performance against itself over time. Industry average analysis compares the firm’s performance to the performance of sameindustry companies, and peer group analysis benchmarks the company’s performance to that of its competitors. Most of the time, a combination of all three methods is used when analyzing the company.

Explain what the SIC codes are, and discuss the pros and cons of using them in financial analysis. Standard Industrial Classification (SIC) codes are four-digit numbers that are used to categorize business activities. The first two digits determine the broad type of business,

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such as mining of metals, and then each additional digit narrows down the industry in greater detail. The advantage of using SIC codes in financial analysis is that the financial ratio data can be segmented into six size categories by asset size or by sales, which allows for more meaningful comparisons of like firms. The main drawback to using SIC codes is that companies with similar business lines, but not necessarily similar target markets, often have the same SIC codes (for example, Neiman Marcus and Wal-Mart). Therefore, using SIC codes as a basis for financial analysis requires more thought than just relying on the classification numbers.

Section 4.6 1.

Explain how the DuPont identity allows us to evaluate a firm’s performance. The DuPont identity, which leads to the measurement of a firm’s return on equity (ROE), allows one to break down the measure into three areas of performance. First, a firm’s operational efficiency is measured by the net profit margin; second, the firm’s efficiency in managing its assets is reflected in its asset turnover ratio; and finally, the impact of financial leverage is shown by the equity multiplier. One is then able to pinpoint areas of strengths and weaknesses by breaking down these measures, which are tied to either the balance sheet or the income statement.

What are the limitations on traditional financial statement analysis? The main problems with financial statement analysis are that since it is based on book values (historical data), it may not reflect a firm’s true economic condition, and there is a lack of economic underpinning for much of the decision rules. It is difficult to say a current ratio of 2.2 is good or that one ratio is more important than another.

List some of the problems that financial analysts confront when analyzing financial statements. Some of the problems that financial analysts run into when analyzing financial statements are: • Multiple business lines • Inflation adjustments • Globalization • Seasonality • Different accounting principles Therefore, a good analyst does not simply look at the numbers provided in the financial statements, but instead adjusts these numbers for all of the above factors to provide a meaningful and value-added analysis.

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Self Study Problems 4.1

The Abercrombie Supply Company reported the following information for 2014. Prepare a common-size income statement for the year ended June 30, 2014. Abercrombie Supply Company Income Statement for the Fiscal Year Ended June 30, 2014 ($ thousands)

Net sales Cost of goods sold Selling and administrative expenses Nonrecurring expenses

$2,110,965 1,459,455 312,044 27,215

Earnings before interest, taxes, depreciation, and amortization (EBITDA)

$ 312,251

Depreciation Earnings before interest and taxes (EBIT) Interest expense Earnings before taxes (EBT) Taxes (35%) Net income

112,178 $ 200,073 117,587 $ 82,486 28,870 $ 53,616

Solution: The common-size income statement for Abercrombie Supply Company should look like the following one: Abercrombie Supply Company Income Statement for the Fiscal Year Ended June 30, 2014 ($ thousands)

Net sales Cost of goods sold Selling and administrative expenses Nonrecurring expenses

$2,110,965 1,459,455 312,044 27,215

% of Net Sales 100.0 69.1 14.8 1.3

Earnings before interest, taxes, depreciation and amortization (EBITDA) Depreciation Earnings before interest and taxes (EBIT) Interest expense Earnings before taxes (EBT) Taxes (35%) Net income

$ 312,251 112,178 $ 200,073 117,587 $ 82,486 28,870 $ 53,616

14.8 5.3 9.5 5.6 3.9 1.4 2.5

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LO: 2 Level: Basic

4.2

Prepare a common-size balance sheet from the following information for Abercrombie Supply Company.

Assets: Cash and marketable securities Accounts receivable Inventory Other current assets Total current assets Net plant and equipment

Total assets

Abercrombie Supply Company Balance Sheet as of June 30, 2014 ($ thousands) Liabilities and Equity: $ 396,494 Accounts payable 708,275 Notes payable 1,152,398 Accrued income taxes 42,115 $2,299,282 Total current liabilities 1,978,455 Long-term debt Total liabilities Common stock Retained earnings Total common equity $4,277,737 Total liabilities and equity

$ 817,845 101,229 41,322 $ 960,396 1,149,520 $2,109,916 1,312,137 855,684 $2,167,821 $4,277,737

Solution: Abercrombie Supply Company Balance Sheet as of June 30, 2014 ($ thousands) Assets Cash and marketable sec. Accounts receivable Inventory Other current assets Total current assets Net plant and equipment

$ 396,494 708,275 1,152,398 42,115 $2,299,282 1,978,455

% of Assets 9.3 16.5 26.9 1.0 53.7 46.3

Total assets

$4,277,737

100.0

Liabilities and Equity: Accounts payable and accruals Notes payable Accrued income taxes

$ 817,845 101,229 41,322

% of Assets 19.1 2.4 1.0

Total current liabilities Long-term debt Total liabilities Common stock Retained earnings Total common equity Total liabilities and equity

$ 960,396 1,149,520 $2,109,916 1,312,137 855,684 $2,167,821 $4,277,737

22.5 26.9 49.3 30.7 20.0 50.7 100.0

LO: 2 Level: Basic

4.3

Using the 2014 data above for Abercrombie Supply Company calculate the following liquidity ratios: a. Current ratio b. Quick ratio

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Solution: a.

Current ratio =

Quick ratio =

$2,299,282 = 2.39 $960,396

$2,299,282 - $1,152,398 = 1.19 $960,396

LO: 3 Level: Basic

4.4

Refer above to the balance sheet and income statement for Abercrombie Supply Company for the year ended June 30, 2014. Calculate the following ratios: a. Inventory turnover b. Days’ sales outstanding c. Total asset turnover d. Fixed asset turnover e. Total debt ratio f. Debt-to-equity ratio g. Times interest earned h. Cash coverage

Solution: Ratio Inventory turnover Days’ sales outstanding Total asset turnover Fixed asset turnover Total debt ratio Debt-to-equity ratio Times-interest-earned Cash coverage LO: 3 Level: Basic

4.5

Calculation $1,459,455 / $1,152,398 $708,275 / ($2,110,965/365) $2,110,965 / $4,277,737 $2,110,965 / $1,978,455 $2,109,916 / $4,277,737 $2,109,916 / $2,167,821 $200,073 / $117,587 $312,251 / $117,587

Value 1.27 122.5 days 0.49 1.07 0.493 0.974 1.7 2.66

Refer to the balance sheet and income statement for Abercrombie Supply Company for the fiscal year ended June 30, 2014. Use the DuPont equation to calculate the return on equity (ROE). In the process, calculate the following ratios: profit margin, EBIT return on assets, equity multiplier, total asset turnover.

Solution: Following are the calculations for the ROE and associated ratios:

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Net Profit margin = Net income / Net Sales = $ 53,616 / $2,110,965 = 0.0254, or 2.54% EBIT ROA = EBIT / Total assets = $200,073 / $4,277,737 = 0.0468, or 4.68% Return on assets = Net income / Total assets = $ 53,616 / $4,277,737= 0.0125, or 1.25% Equity multiplier = Total assets / Total Equity = $4,277,737 / $2,167,821 = 1.97 Total asset turnover = Net Sales / Total assets = $2,110,965 / $4,277,737 = 0.49 DuPont identity: ROE = ROA × EM = Net profit margin × total assets turnover × equity multiplier Net income Net sales Total assets = × × Net sales Total assets Total equity = 0.0254 × 0.49 × 1.97 = 𝟎. 𝟎𝟐𝟒𝟓, 𝐨𝐫 𝟐. 𝟒𝟓% LO: 3 Level: Basic

Discussion Questions 4.1

What does it mean when a company’s return on assets (ROA) is equal to its return on equity (ROE)? When ROA equals ROE, it means that the firm does not use any leverage (debt financing). For firms that do use leverage, ROE will be higher than ROA.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.2

Why is too much liquidity not a good thing? Too much liquidity could mean that a firm is not putting its money to work as the shareholders would want it to. It could mean that the firm’s managers are being too conservative and investing in low-yield assets, or it could mean that the firm does not have enough investment opportunities and is therefore hanging onto its cash. Recently, several firms including Microsoft had several billions of dollars in cash on their books, and, ultimately, Microsoft paid a special dividend to its shareholders. Too much liquidity can also make it a takeover target for firms looking to utilize the debt capacity of the liquid firm.

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Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement 4.3

Inventory is excluded when the quick ratio or acid-test ratio is calculated because inventory is the most difficult current asset to convert to cash without loss of value. What types of inventory are likely to be most easily converted to cash without loss of value? For the quick ratio, one uses only the most liquid of all assets—that is, all current assets less inventory, which is not very liquid relative to cash or receivables. While the current ratio assumes that inventory could be sold at book value, the quick ratio assumes that inventory has no value. Hence, this gives a more conservative estimate of a firm’s liquidity than the current ratio, and gives a better estimate of the firm’s ability to meet its short-term obligations. Inventories of a raw material commodity, such as gold or crude oil, is more likely to be sold with little loss in value.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement 4.4

What does a very high inventory turnover ratio signify? This could mean a number of things, including that the firm is using up its inventory too fast and is unable to meet the demand for its products, or it has priced its products too low relative to its competitors, or worse, the firm is selling defective products that would eventually be returned.

LO: 3 Level: Basic

4.5

How would one explain a low receivables turnover ratio? A low receivables turnover implies a high DSO. This could mean that the firm’s customers are not paying on time, either because of an inefficient collection system or because of a slowdown in their customers’ business or even in the entire economy.

LO: 3 Level: Basic

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Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement 4.6

What additional information does the fixed asset turnover ratio provide over the total asset turnover ratio? For which industries does it carry greater significance? The total asset turnover ratio measures the level of sales per dollar invested in total assets. The higher the number, the more efficiently the management is using the firm’s assets. Too high a number relative to its peers could imply that the firm is reaching its full capacity and may require an additional investment in plant and equipment to generate additional sales. The fixed asset turnover ratio can be utilized to break down the performance of individual manufacturing facilities or a division. This ratio provides significant information for manufacturing firms that are capital-intensive, while it will be of much less significance for the service industry, where there is less reliance on plant and equipment.

LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.7

How does financial leverage help stockholders? Financial leverage implies the use of debt capital in addition to the owners’ capital to finance the firm. With the addition of debt, the owners’ capital can go a long way in acquiring assets for the firm. Given that creditors only get the fixed-interest payments and do not get any share of the gains from the company, the stockholders gain from the usage of debt. This is called the leverage multiplier effect. As the company’s revenues grow, stockholders get all the gain and the debt holders merely receive their interest payments.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.8

Why is ROE generally much higher than ROA for banks relative to other industries?

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Banks have a very small equity base relative to firms in most other industries. Thus, they are highly leveraged with borrowed funds. Since their equity base is small, this magnifies the return on equity, but the return on assets is relatively small for the large asset base. LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.9

Why is the ROE a more appropriate proxy (for stockholder value maximization) for some firms than for other firms? The basis on which any business or investment decisions are evaluated must include the size, timing, and uncertainty in the future cash flows. ROE considers neither the risk of the cash flows nor the size of the initial investment or future cash flows from that investment. While the ROE and shareholder wealth are correlated, this is still a problem in large, well-diversified companies with resources from multiple sources. Smaller firms have fewer resources and sources and can better correlate their ROE to shareholder wealth.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.10

Why is it not enough for an analyst to look at just the short-term and long-term debt on a firm’s balance sheet when assessing the firm’s fixed obligations? The amount of liabilities shown on a firm’s balance sheet is not the total obligation of a firm in any given period. To get a true picture, one needs to look at the financial footnotes that follow the financial statements. This is where you will be able to find the amount of debt repayment that the firm is responsible for in the coming years. In addition, off-balance sheet items could reflect certain future liabilities of the firm that do not have to be reported on the balance sheet. One also should look for lease obligations of the firm that are reported off the balance sheet but nevertheless remain a fixed obligation that the firm has to meet with its cash flows. Thus, it is important for an analyst to look beyond the short-term and long-term debt on the balance sheet to get a true measure of the firm’s true financial commitments in any given period. LO: 3, 5

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Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

Questions and Problems BASIC 4.1

Liquidity ratios: Explain why the quick ratio or acid-test ratio is a better measure of a firm’s liquidity than the current ratio. Solution: The quick ratio is a better or more conservative measure of liquidity than the current ratio. The difference in the measurement of the two is that for the quick ratio we exclude the inventory in accounting of the short- term assets. Thus the quick ratio is measured as: Current assets − Inventory Quick ratio = Current liabilities This measure includes only the most liquid of the current assets and hence gives a better measure of liquidity. LO: 4.3 Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.2

Liquidity ratios: Flying Penguins Corp. has total current assets of $11,845,175, current liabilities of $5,311,020, and a quick ratio of 0.89. How much inventory does it have? Solution: Current assets = $11,845,175 Current liabilities = $5,311,020 Quick ratio = 0.89 Current assets − Inventory Current liabilities $11,845,175 − Inventory 0.89 = $5,311,020 0.89 × $5,311,020 = $11,845,175 − Inventory Quick ratio =

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Inventory = $11,845,175 − (0.89 × $5,311,020) = $𝟕, 𝟏𝟏𝟖, 𝟑𝟔𝟕 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.3

Efficiency ratio: If Newton Manufacturers has an accounts receivable turnover of 4.8 times and net sales of $7,812,379, what would its receivables be? Solution: Accounts receivable turnover = 4.8 times Net sales = $7,812,379 Net sales Accounts receivable turnover = Accounts receivable 7,812,379 4.8 = Accounts receivable 7,812,379 Accounts receivable = = $𝟏, 𝟔𝟐𝟕, 𝟓𝟕𝟗 4.8 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.4

Efficiency ratio: Bummel and Strand Corp. has a gross profit margin of 33.7 percent, sales of $47,112,365, and inventory of $14,595,435. What is its inventory turnover ratio? Solution: Gross profit margin = 33.7% Sales = $ 47,112,365 Inventory = $14,595,435 Net sales-Cost of goods sold Gross Profit Margin = Net Sales

0.337 =

$47,112,365 − COGS 47,112,365

Cost of goods sold = $47,112,365 − (0.337  47,112,365) = 31, 235, 498

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Inventory Turnover Ratio =

Solutions Manual

Cost of goods sold Inventory

31,235,498 Inventory Turnover Ratio = = 𝟐. 𝟏𝟒 𝐭𝐢𝐦𝐞𝐬 14,595,435 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.5

Efficiency ratio: Sorenson Inc. has sales of $3,112,489, a gross profit margin of 23.1 percent, and inventory of $833,145. What are the company’s inventory turnover ratio and days’ sales in inventory? Solution: Sales = $3,112,489 Gross profit margin = 23.1% Inventory = $833,145 Sales-Cost of goods sold Gross profit margin = Sales

0.231 =

3,112, 489 − Cost of Goods Sold 3,112,489

Cost of goods sold = 3,112, 489 − (0.231  3,112, 489) = $2,393,504

Inventory turnover ratio =

Cost of goods sold $2,393,504 = Inventory $833,145

= 2.873 times

Day's sales in inventory =

365 365 = Inventory turnover ratio 2.873

= 127.1 days LO: 4.3

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.6

Leverage ratios: Breckenridge Ski Company has total assets of $422,235,811 and a debt ratio of 29.5 percent. Calculate the company’s debt-to-equity ratio and equity multiplier. Solution: Total assets = $422,235,811 Debt ratio = 29.5% Total debt = $422,235,811 × 0.295 = $124,559,564 Total equity = Total assets − Total debt = $422,235,811 − $124,559,564 = $297,676,247 $124,559,564 = 𝟎. 𝟒𝟐 $297,676,247 Total assets $422,235,811 Equity multiplier = = = 𝟏. 𝟒𝟐 Total equity $297,676,247 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement Debt to equity ratio =

4.7

Leverage ratios: Norton Company has a debt-to-equity ratio of 1.65, ROA of 11.3 percent, and total equity of $1,322,796. What are the company’s equity multiplier, debt ratio, and ROE? Solution: Debt-equity ratio = 1.65 ROA = 11.3% Total equity = $1,322,796

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Equity multiplier = 1 + Debt to equity ratio = 1 + 1.65 = 2.65 Total assets Equity multiplier = Total equity Total assets = Equity multiplier  Total equity = 2.65  $1,322,796 = $3,505,409

Net income Total assets Net income = ROA  Total assets = 0.113 3,505,409 = $396,111 ROA =

ROE =

Net income $396,111 = = 29.9% Equity $1,322,796

Debt ratio = 1 =1−

  Equity 1 = 1 − Total assets  Equity multiplier  1 = 0.623 2.65

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.8

DuPont Equation: The Rangoon Timber Company has the following ratios: Net sales/Total assets = 2.23; ROA = 9.69%; ROE = 16.4% What are Rangoon’s profit margin and debt ratios? Solution: Total assets turnover = 2.23 ROA = 9.69% ROE = 16.4% ROA = Profit margin × Total assets turnover ROA 0.0969 Profit margin = = = 0.04345 Total assets turnover 2.23

= 4.35% ROE = ROA x Equity multiplier

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ROE 0.164 = = 1.69 ROA 0.0969 Equity 1 Debt ratio = 1 − = 1− Total assets Equity multiplier Equity multiplier =

=1−

1 = 0.41 1.69

LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.9

DuPont Equation: Lemmon Enterprises has a total asset turnover of 2.1 and a net profit margin of 7.5%. If its equity multiplier is 1.90, what is the ROE for Lemmon Enterprises? Solution: Total Asset Turnover = 2.1 Net Profit Margin = 7.5% Equity Multiplier = 1.90 ROE = ROA × Equity multiplier ROA = Net profit margin × Total asset turnover = 7.5% × 2.1 = 15.75% ROE = 15.75% × 1.9 = 29.93% LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Benchmark analysis: List the ways a company’s financial manager can benchmark the company’s own performance. Solution: Financial managers can benchmark their firm’s performance by collecting data in three ways: through trend analysis, industry average analysis, and peer group analysis. LO: 4.5 4.10

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Bloomcode: Knowledge AASCB: Analytic IMA: FSA AICPA: Measurement

Benchmark analysis: Trademark Corp.’s financial manager collected the following information for its peer group to compare its performance against that of its peers. Ratios Trademark Peer Group DSO 33.5 days 27.9 days Total asset turnover 2.3 3.7 Inventory turnover 1.8 2.8 Quick ratio 0.6 1.3 a. Explain how Trademark is performing relative to its peers. b. How do the industry ratios help Trademark’s management? Solution: a. One can see that Trademark is not doing as well as its competitors. The asset turnover ratio indicates that the firm either needs to increase its sales relative to its level of assets or reduce its assets relative to its level of sales. In addition, the lower quick ratio indicates a lower level of liquidity, perhaps because of too much inventory. A reduction in the inventory would help Trademark improve its performance to a level that is comparable to its peer group. In addition, collection of receivables is longer, which could result in cash flow problems and nonpayments. b. Average industry ratios serve as benchmarks for the firm’s management to measure its own performance. While no two firms are identical in any industry, the average ratios across the industry are good target ratios for a firm. LO: 4.5 Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement 4.11

4.12

Market-value ratios: Rockwell Jewelers management announced that the company had net earnings of $6,481,778 for this year. The company has 2,543,800 shares outstanding, and the year-end stock price is $54.21. What are Rockwell’s earnings per share and P/E ratio? Solution: Net earnings = $6,481,778

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Shares outstanding = 2,543,800 Year-end stock price = $54.21 Net earnings $6,481,778 Earnings per share = EPS = = Shares outstanding 2,543,800

= $2.55 Price per share $54.21 Price - earnings ratio = = Earnings per share $2.55 = 21.26 times LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.13

Market-value ratios: Chisel Corporation has 3 million shares outstanding at a price per share of $3.25. If the debt-to-equity ratio is 1.7 and total book value of debt equals $12,400,000, what is the market-to-book ratio for Chisel Corporation? Solution: Shares outstanding = 3,000,000 Market Price per share = $3.25 Debt-to-Equity ratio = 1.7 Total book value of debts = $12,400,000 Market value of equity = 3,000,000 × $3.25 = $9,750,000 $12,400,000 Book value of equity = 1.7 = $7,294,117.65 $9,750,000 Market - to - book ratio = $7,294,117.65 = 1.34 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

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INTERMEDIATE 4.14

Liquidity ratios: Laurel Electronics has a quick ratio of 1.15, current liabilities of $5,311,020, and inventories of $7,121,599. What is the firm’s current ratio? Solution: Quick ratio = 1.15 Current liabilities = $5,311,020 Inventory = $7,121,599 Current asset - Inventory Current assets - 7,121,599 Quick ratio = = Current liabilities $5,311,020

= 1.15 =

Current asset - $7,121,599 $5,311,020

Current assets = (1.15  5,311,020) + 7,121,599 Current assets = $13,229,272

Current ratio =

Current assets $13,229,272 = = 𝟐. 𝟒𝟗 Current liabilities $5,311,020

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.15

Efficiency Ratio: Lambda Corporation has current liabilities of $450,000, a quick ratio of 1.8, inventory turnover of 5.0, and a current ratio of 3.5. What is the cost of goods sold for Lambda Corporation? Solution: Current Liabilities = $450,000 Quick Ratio = 1.8 Inventory Turnover ratio = 5.0 Current ratio = 3.5 Current assets = 3.5 × $450,000 = $1,575,000

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Quick ratio = 1.8 =

Solutions Manual

Current assets - Inventory Current liabilities $1,575,000 − Inventory $450,000

Inventory = $765,000 Inventory Turnover =

Cost of goods sold Inventory

Cost of goods sold = 5.0  $765,000 = $3,825,000 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.16

Efficiency ratio: Norwood Corp. currently has accounts receivable of $1,223,675 on net sales of $6,216,900. What are its accounts receivable turnover and days’ sales outstanding (DSO)? Solution: Accounts receivable = $1,223,675 Net sales = $6,216,900 Accounts receivables turnover =

DSO =

Net sales = Accounts receivables

$6,216,900 $1,223,675 ⬚ = 𝟓. 𝟎𝟖 𝐭𝐢𝐦𝐞𝐬

365 365 = = 71.8 days Accounts receivable turnover 5.08

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

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Efficiency ratio: If Norwood Corp.’s management wants to reduce the DSO from that calculated in Problem 4.16 to an industry average of 56.3 days and its net sales are expected to decline by about 12 percent, what would be the new level of receivables? Solution: Target DSO = 56.3 days New level of sales = $6,216,900 x 0.88 = $5,470,872 365 DSO = 56.3 Days = Net sales/Accounts receivable 4.17

Accounts receivable = =

DSO  Net sales 365 56.3  5, 470,872 365

= $843, 863 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.18

Coverage ratios: Nimitz Rental Company had depreciation expenses of $108,905, interest expenses of $78,112, and an EBIT of $1,254,338 for the year ended June 30, 2014. What are the times-interest-earned and cash coverage ratios for this company? Solution: Depreciation = $108,905 Interest expenses = $78,112 EDIT = $1,254,338 EBIT $1,254,338 Times interest earned = = Interest expense $78,112 = 16.1 times EBITDA EBIT + Depreciation Cash coverage ratio = = Interest expense Interest expense $1,363,243 = $78,112 = 17.5 times LO: 4.3

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Leverage ratios: Conseco, Inc., has a debt ratio of 0.56. What are the company’s debt-toequity ratio and equity multiplier? Solution: Debt ratio = 0.56 4.19

Equity multiplier =

Total assets 1 = Total equity Total equity/Total Assets

1 1−Debt/Total assets

1 1−0.56

=2.27 Equity multiplier = 1 + (Debt to equity ratio) Debt-to-equity ratio = Equity multiplier-1 =2.27-1 = 1.27 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.20

Profitability ratios: Cisco Systems has total assets of $35.594 billion, total debt of $9.678 billion, and net sales of $22.045 billion. Its net profit margin for the year is 20 percent, while the operating profit margin is 30 percent. What are Cisco’s net income, EBIT ROA, ROA, and ROE? Solution: Total assets = $35.594 billion Total debt = 9.678 billion Net sales = $22.045 billion Net profit margin = 20%

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Operating profit margin = 30% Net income Net profit margin = Sales

Net income = 0.2  $22.045 = $4.409 billion Operating profit margin =

EBIT SALES

EBIT = 0.3 × $22.045 =$6.614 billion EBIT $6.613 = = 18.6% Total assets $35.594 Net income $4.409 ROA = = = 12.4% Total assets $35.594 Total equity = Total assets – Total debt = $35.594 - $9.678 = $25.916 billion Total assets $35.594 Equity multiplier = = Total equity $25.916 = 1.37 ROE = ROA  EM = 0.124  1.37 = 17% LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement EBIT ROA =

4.21

Profitability ratios: Procter & Gamble reported the following information for its fiscal year end: On net sales of $51.407 billion, the company earned net income after taxes of $6.481 billion. It had cost of goods sold of $25.076 billion and EBIT of $9.827 billion. What are the company’s gross profit margin, operating profit margin, and net profit margin? Solution: Net sales = $51.407 billion Net income = $6.481 billion

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Solutions Manual

Cost of goods sold = $25.076 billion EBIT = $9.827 billion Net sales - Cost of goods sold Gross profit margin = Net sales $51.407 − $25.076 = = 51.2% $51.407 EBIT $9.827 Operating profit margin = = = 19.1% Net sales $51.407 Net income $6.481 Net profit margin = = = 12.6% Net sales $51.407 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.22

Profitability ratios: Wal-Mart, Inc., has net income of $9,054,000 on net sales of $256,329,812. The company has total assets of $104,912,112 and stockholders’ equity of $43,623,445. Use the extended DuPont identity to find the return on assets and return on equity for the firm. Solution: Net income = $9,054,000 Net sales = $256,329,812 Total assets = $104,912,112 Stockholders equity = $43,623,445 Net income $9,054,000 Profit margin = = = 3.53% Net sales $256,329,812 Total assets turnover =

Net sales $256,329,812 = = 2.44 times Total assets $104,912,112

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Solutions Manual

Return on assets = Profit margin  Total assets turnover = 0.0353  2.44 = 8.61% ROE = ROA  EM = 0.0861 

Total assets Total equity

= 0.0861 

$104,912,112 $43,623, 445

= 20.71% LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.23

Profitability ratios: Xtreme Sports Innovations has disclosed the following information: EBIT = $25,664,300 Net income = $13,054,000 Net sales = $83,125,336 Total debt = $20,885,753 Total assets = $71,244,863 Compute the following ratios for this firm using the DuPont Identity: debt-to-equity ratio, EBIT ROA, ROA, and ROE. Solution: EBIT = $25,664,300 Net income = $13,054,000 Net sales = $83,125,336 Total debt = $20,885,753 Total assets = $71, 244,863 Debt Debt = Equity (Total assets − Total debt $20,885,753 = = 𝟎. 𝟒𝟏 ($71,244,863 − $20,885,753 Equity multiplier = 1 + Debt to equity ratio = 1 + 0.41 = 𝟏. 𝟒𝟏 Debt to equity ratio =

EBIT $25,664,300 = Total assets $71,244,863 = 36.02%

EBIT ROA =

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Net income $13,054,000 = Total assets $71,244,863 = 18.32% ROE = ROA  EM

ROA =

= 0.1832  1.41 = 25.83% LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.24

Market-value ratios: Cisco Systems had net income of $4.401 billion and at year end 6.735 billion shares outstanding. Calculate the earnings per share for the company.

Solution: Net income = $4.401 billion Shares outstanding = 6.735 billion Net income $4.401 Earnings per share = = = $𝟎. 𝟔𝟓 𝐩𝐞𝐫 𝐬𝐡𝐚𝐫𝐞 Shares outstanding 6.735 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.25

Market-value ratios: Use the information for Cisco Systems in Problem 4.24. In addition, the company’s EBITDA was $6.834 billion and its share price was $22.36. Compute the firm’s price-earnings ratio and the price-EBITDA ratio. Solution: EBITDA = $6.834 billion Share price = $22.36 $22.36 Price - earnings ratio = = 34.4 times $0.65 $6.834 EBITA per share = = $1.015 per share 6.735

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Fundamentals of Corporate Finance, 3rd Edition

Price − EBITDA ratio =

Solutions Manual

$22.36 = 22.04 times $1.015

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.26

DuPont equation: Carter, Inc., a manufacturer of electrical supplies, has an ROE of 23.1 percent, a profit margin of 4.9 percent, and a total asset turnover ratio of 2.6 times. Its peer group also has an ROE of 23.1 percent, but has outperformed Carter with a net profit margin of 5.3 percent and a total asset turnover ratio of 3.0 times. Explain how Carter managed to achieve the same level of profitability as reflected by the ROE. Solution: Carter Inc: ROE = 23.1%, PM = 4.9%, TATO = 2.6 times ROA = PM  TATO

= 0.049  2.6 = 0.1274 ROE = 0.231 = ROA  EM 0.231 EM = = 1.81 times 0.1274 Peer Group: ROE = 23.1%, PM = 5.3%, TATO = 3 times ROE = 0.231 = PM  TATO  EM 0.231 EM = = 1.45 times 0.053  3 Carter matched its peer group’s ROE by using a higher degree of financial leverage as indicated by its higher equity multiplier. LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.27

DuPont equation: Grossman Enterprises has an equity multiplier of 2.6 times, total assets of $2,312,000, an ROE of 14.8 percent, and a total asset turnover ratio of 2.8 times. Calculate the firm’s sales and ROA. Solution: Copyright © 2015 John Wiley & Sons, Inc.

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Solutions Manual

EM = 2.6 times, TA = $2,312,000, ROE = 14.8%, TATO = 2.8 times

Sales Total assets Sales 2.8 = $2,312,000 Sales = 2.8  $2,312,000 = $6,473,600 ROE = ROA × EM ROE ROA = EM 0.148 = = 0.0569 = 𝟓. 𝟔𝟗% 2.6 LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement Total asset turnover =

ADVANCED 4.28

Complete the balance sheet of Flying Roos Corporation. Flying Roos Corporation Balance Sheet as of December 31, 2014

Assets: Cash and marketable securities Accounts receivable Inventory Total current assets

Liabilities and Equity: Accounts payable and accruals Notes payable Total current liabilities

Net plant and equipment Total assets

$8,000,000

Long-term debt Common stock Retained earnings Total liabilities and equity

$ 300,000

$2,000,000 $1,250,000

You have the following information: Debt ratio = 40% Current ratio = 1.5 Net Sales = $2.25 million DSO = 39 days Inventory turnover ratio = 3.375 Cost of goods sold = $1.6875 million Solution: Copyright © 2015 John Wiley & Sons, Inc.

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Total debt = 0.4  Total assets = 0.4  $8,000,000 = $3,200,000 Accounts payable = Total debt - (Long term debt + Notes payable)

= $3,200,000 - (2,000,000 + 300,000) = $900,000 Cost of goods sold Inventory turnover ratio = Inventory Cost of goods sold $1,687,500 Inventory = = ITO 3.375 = $500,000 Accounts receivables DSO = Sales/365 Sales 2,250,000 Accounts receivables = DSO  = 39  365 365

= $240,411 Current asset = Current ratio  Current liabilities = 1.5  $1,200,000 = $1,800,000 Net plant and equipment (Fixed assets) = Total assets – Total Current assets = $8,000,000 - $1,800,000 = $6,200,000 Cash = Current assets – (Accounts receivables + Inventory) = $1,800,000 – ($240,411 + $500,000) = $1,059,589 Common stock = Total liabilities and Equity – (Total liabilities + Retained earnings) = $8,000,000 – ($3,200,000 + $1,250,000) = $3,550,000

Flying Roos Corporation Balance Sheet as of December 31, 2014 Assets Cash and marketable securities Accounts receivable Inventories Total current assets

$1,059,589 240,411 500,000 $1,800,000

Net plant and equipment

6,200,000

Total assets

$8,000,000

Liabilities and Equity Accounts payable Notes payable

$ 900,000 300,000

Total current liabilities Long-term debt Common stock Retained earnings Total liabilities and equity

$1,200,000 2,000,000 3,550,000 1,250,000 $8,000,000

LO: 4.3

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.29

For the year ended June 30, 2014, Northern Clothing Company has total assets of $87,631,181, ROA of 11.67 percent, ROE of 21.19 percent, and a net profit margin of 11.59 percent. What are the company’s net income and net sales? Calculate the firm’s debt-to-equity ratio. Solution: Total assets = $87,631,181 ROA = 11.67%, ROE = 21.19%, PM = 11.59% NI = ROA  TA

= 0.1167  87,631,181 = $10, 226, 559 Net income $10,226,559 Net sales = = = $88,236,057 Profit margin 0.1159 Total equity = NI/ROE = $10,226,559 / 0.2119 = $48,261,251

Total debt = Total assets - Total equity = $87,631,181 - $48,261,251 = $39,369,931 Debt $39,369,931 = Equity $48,261,251 = 81.6%

Debt to equity ratio =

LO: 4.3, 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.30

Blackwell Automotive’s balance sheet at the end of its most recent fiscal year shows the following information: Blackwell Automotive Balance Sheet as of March 31, 2014

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Assets: Cash and marketable sec. Accounts receivable Inventory Total current assets

23,015 141,258 212,444 $ 376,717

Solutions Manual

Liabilities and Equity: Accounts payable and accruals Notes payable Total current liabilities

$ 163,257 21,115 $ 184,372

Long-term debt 168,022 Net plant and equipment 711,256 Total liabilities $ 352,394 Goodwill and other assets 89,879 Common stock 313,299 Retained earnings 512,159 Total assets $1,177,852 Total liabilities and equity $1,177,852 In addition, it was reported that the firm had a net income of $156,042 on net sales of $4,063,589. a. What are the firm’s current ratio and quick ratio? b. Calculate the firm’s days’ sales outstanding, total asset turnover ratio, and fixed asset turnover ratio. Solution:

Current ratio = a.

Current assets $376,717 = Current liabilities $184,372

= 2.04 times Current asset − Inventory $376,717 − $212,444 Quick ratio = = Current liabilities $184,372

= 0.89 times b.

DSO =

365 365 = Accounts receivables turnover Net sales/Accounts receivables

365  Accounts receivables 365  $141,258 = Net sales $4,063,589 = 12.69 days

Net sales $4,063,589 = Total assets $1,177,852 = 3.45 times Net sales $4,063,589 Fixed asset turnover = = Net fixed assets $711,256 = 5.71 times LO: 4.3 Total asset turnover =

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.31

The following are the financial statements for Nederland Consumer Products Company for the fiscal year ended September 30, 2014. Nederland Consumer Products Company Income Statement for the Fiscal Year Ended September 30, 2014 Net sales Cost of products sold Gross profit Marketing, research, administrative exp. Depreciation Operating income (loss) Interest expense Earnings (loss) before income taxes Income taxes Net earnings (loss)

$51,407 25,076 $26,331 15,746 758 $ 9,827 477 $ 9,350 2,869 $ 6,481

Nederland Consumer Products Company Balance Sheet as of September 30, 2014 Assets: Cash and marketable securities Investment securities Accounts receivable Inventory Deferred income taxes Prepaid expenses & other receivables Total current assets Property, plant, and equip., at cost Less: Accumulated depreciation Net property, plant, and equipment Net goodwill and other intangible assets Other noncurrent assets Total assets

$ 5,469 423 4,062 4,400 958 1,803 $17,115 25,304 11,196 $14,108 23,900 1,925 $57,048

Liabilities and Equity: Accounts payable Accrued and other liabilities Taxes payable Debt due within one year Total current liabilities Long-term debt Deferred income taxes Other noncurrent liabilities Total liabilities Convertible Class A preferred stock Common stock

$ 3,617 7,689 2,554 8,287 $22,147 12,554 2,261 2,808 $39,770 1,526 2,141

Retained earnings Total stockholders’ equity Total liabilities and equity

13,611 $17,278 $57,048

Calculate all the ratios for which industry figures are available below for Nederland and compare the firm’s ratios with the industry ratios. Ratio Industry Average

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Current ratio Quick ratio Gross margin Net profit margin Debt ratio Long-term debt to equity Interest coverage ROA ROE

Solutions Manual

2.05 0.78 23.9% 12.3% 0.23 0.98 5.62 5.3% 18.8%

Solution: Ratio Current ratio Quick ratio Gross margin Net Profit margin Debt ratio Long-term debt to equity Interest coverage ROA ROE

Industry Average 2.05 0.78 23.9% 12.3% 0.23 0.98 5.62 5.3% 18.8%

Nederland 0.77 0.57 51.2% 12.6% 0.70 0.73 20.6 11.4% 37.5%

LO: 4.3

4.32

Refer to the preceding information for Nederland Consumer Products Company. Compute the firm’s ratios for the following categories and briefly evaluate the company’s performance using these numbers. a. Efficiency ratios b. Asset turnover ratios c. Leverage ratios d. Coverage ratios Solution: Efficiency Ratios Inventory turnover ratio Days sales in inventory Accounts receivables turnover DSO Asset Turnover Ratios Total asset turnover Fixed assets turnover Leverage Ratios Total debt ratio

5.70 64.05 days 12.66 times 28.84 days

COGS/Inventory 365/ITO Sales/AR 365/AR turnover

0.90 times 3.64 times

Sales/TA Sales/FA

0.70

TD/TA

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Debt to equity ratio Equity multiplier Coverage Ratios Times interest earned Cash coverage

Solutions Manual

2.30 3.30

D/E TA/E

20.60 22.19

EBIT/Interest (EBIT + Depreciation)/Interest

LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.33

Refer to the earlier information for Nederland Consumer Products Company. Using the DuPont identity, calculate the return on equity for Nederland, after calculating the ratios that make up the DuPont identity. Solution: Net Profit margin Total assets turnover ratio Equity multiplier Return on assets Return on equity

12.61% 0.90 times 3.30 11.4% 37.5%

NI/Sales Sales/TA TA/E NI/TA PM×TATO×EM

LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.34

Nugent, Inc., has a gross profit margin of 31.7 percent on net sales of $9,865,214 and total assets of $7,125,852. The company has a current ratio of 2.7 times, accounts receivable of $1,715,363, cash and marketable securities of $315,488, and current liabilities of $870,938. a. What is Nugent’s total current assets? b. How much inventory does the firm have? What is the inventory turnover ratio? c. What is Nugent’s days’ sales outstanding? d. If management sets a target DSO of 30 days, what should Nugent’s accounts receivable be? Solution: Cash & marketable securities = $ 315,488; Accounts receivables = $1,715,363 Current liabilities = $870,938; Total assets = $7,125,852

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Fundamentals of Corporate Finance, 3rd Edition

Sales = $9,865,214; Current ratio = 2.7 a.

Current ratio = 2.7 =

Solutions Manual

Gross profit margin = 31.7%

Current assets Current liabilities Current assets $870,938

Current assets = 2.7  $870,938 = $2, 351, 533 Current assets = Cash + Accounts receivables + Inventory $2,351,533 = $315,488 + $1,715,363 + Inventory Inventory = $2,351,533– ($315,488 + $1,715,363) = $320,682 Cost of goods sold = Sales x (1 – Gross PM) = $9,865,214 × (1 – 0.317) = $6,737,941 Cost of goods sold Inventory turnover ratio = Inventory $6,737,941 = = 21.01 times $320,682

c. DSO =

365 365 × Accounts receivables = Net sales/Accounts receivables Net sales =

365 × $1,715,363 = 𝟔𝟑. 𝟓 𝐝𝐚𝐲𝐬 $9,865,214

Target DSO = 30 days

DSO =

30=

365 365  Accounts receivables = Net sales/Accounts receivables Net sales

365×Accounts receivables $9,865,214

30  $9,865,214 = $810, 840 365 The firm has to limit its accounts receivables to $810,840 at its current sales level to achieve its target DSO of 30 days. LO: 4.3 Accounts receivables =

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.35

Recreational Supplies Co. has net sales of $11,655,000, an ROE of 17.64 percent, and a total asset turnover of 2.89 times. If the firm has a debt-to-equity ratio of 1.43, what is the company’s net income? Solution: EM = 1 + D / E ratio = 1 + 1.43 = 2.43 ROE = PM  TATO  EM ROE 0.1764 PM = = TATO  EM 2.89  2.43

= 2.51% NI = Sales  PM = $11,655,000  0.0251

= $292, 540.50 LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.36

Nutmeg Houseware, Inc., has an operating profit margin of 10.3 percent on revenues of $24,547,125 and total assets of $8,652,352. a. Calculate the company’s total asset turnover ratio and its operating profit (EBIT). b. The company’s management has set a target for the total asset turnover ratio of 3.25 for next year. If there is no change in the total assets of the company, what will the new sales level have to be next year? Calculate the dollar change in sales necessary and the percentage change in sales necessary. c. If the operating profit margin declines to 10 percent, what will be the EBIT at the new level of net sales? Solution: Operating PM = 10.3% Sales = $24,547,125 Total assets = $8,652,352

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Solutions Manual

Sales $24,547,125 = Total assets $8,652,352 = 2.84 times Operating profit = EBIT = Op. PM  Sales TATO =

= 0.103  $24,547,125

= $2, 528, 354 New TATO = 3.25 times = New sales/TA New sales = TATO  TA = 3.25  $8,652,352 = $28,120,144 $ Change in Sales = $28,120,144 - $24,547,125

= $3,573,019 % Change in sales = $3,573,019/ $24,547,125 = 14.6% Operating PM = 10% Sales = $28,120,144 New EBIT = Profit margin  Sales

= 0.10  $28,120,144 = $2,812,014 LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.37

Modern Appliances Corporation has reported its financial results for the year ended December 31, 2014. Modern Appliances Corporation Income Statement for the Fiscal Year Ended December 31, 2014 Net Sales Cost of goods sold Gross profit Selling, general, and admin. expenses Depreciation Operating income Interest expense

$5,398,412,000 3,432,925,255 $1,965,486,745 1,036,311,231 299,928,155 $ 629,247,359 35,826,000

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EBT Income taxes Net earnings

Assets: Cash and cash equivalents Accounts receivable Inventory Other current assets Total current assets Net fixed assets Goodwill Other assets Total assets

$ 593,421,359 163,104,554 $ 430,316,805 Modern Appliances Corporation Balance Sheet as of December 31, 2014 Liabilities and Equity: $ 514,412,159 Short-term borrowings 1,046,612,233 Trade accounts payable 981,870,990 Other current liabilities 313,621,610 $2,856,516,992 Total current liabilities 754,660,275 Long-term debt 118,407,710 Common stock 665,058,761 Retained earnings $4,394,643,738 Total liabilities and equity

$ 117,109,865 466,937,985 994,289,383 $1,578,337,233 1,200,691,565 397,407,352 1,218,207,588 $4,394,643,738

Using the information from the financial statements, complete a comprehensive ratio analysis for Modern Appliances Corporation. a. Calculate these liquidity ratios: current and quick ratios. b. Calculate these efficiency ratios: inventory turnover, accounts receivable turnover, DSO. c. Calculate these asset turnover ratios: total asset turnover, fixed asset turnover. d. Calculate these leverage ratios: total debt ratio, debt-to-equity ratio, equity multiplier. e. Calculate these coverage ratios: times interest earned, cash coverage. f. Calculate these profitability ratios: gross profit margin, net profit margin, ROA, ROE. g. Use the DuPont identity after calculating the component ratios to compute ROE. Solution: a.

Liquidity Ratios Current ratio Quick ratio Efficiency Ratios Inventory turnover ratio Accounts receivables turnover DSO Asset Turnover Ratios Total asset turnover Fixed assets turnover Leverage Ratios Total debt ratio

1.81 Current assets/Current liabilities 1.19 (Current assets-Inventory)/Current liabilities 3.50 times 5.16 times 70.76 days

COGS/Inventory Net Sales/AR 365/AR turnover

1.23 times 7.15 times

Net Sales/Total assets Net Sales/Fixed assets

0.63

Total debt/Total assets

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Debt to equity ratio Equity multiplier Coverage Ratios Times interest earned Cash coverage Profitability Ratios Gross profit margin Net profit margin ROA ROE

Solutions Manual

1.72 2.72

Debt/Equity Total assets/Equity

17.56 25.94

EBIT/Interest (EBIT + Depreciation)/Interest

0.36 0.08 0.10 0.27

Gross profit/Net Sales Net income/Net Sales Net income/Total assets Net income/Equity

DuPont identity. ROE =

Net income Net Sales



Net Sales Total assets



Total assets Common equity

= 0.08  1.23  2.72 = 0.27 LO: 4.3, 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

CFA PROBLEMS 4.38

Common-size analysis is used in financial analysis to: a. evaluate changes in a company’s operating cycle over time. b. predict changes in a company’s capital structure using regression analysis. c. compare companies of different sizes or compare a company with itself over time. d. restate each element in a company’s financial statement as a proportion of the similar account for another company in the same industry.

Solution: c is correct. The most significant benefit of using common-size statements is scaling, whether for a given company or over time. Common-size analysis allows us to make comparisons of investments, financing, and profitability between companies of different sizes and over time for a single company. LO: 4.2 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

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4.39

The TBI Company has a number of days of inventory of 50. Therefore, the TBI Company’s inventory turnover is closest to: a. 4.8 times. b. 7.3 times. c. 8.4 times. d. 9.6 times. Solution: b is correct. We perform the calculations using the following relationship: Cost of goods sold Inventory × = 365 Inventory Cost of goods sold / 365 Inventory turnover  Number of days of inventory = 365

Inserting the given information, we have Inventory turnover × 50 = 365, and solving for Inventory turnover provides a turnover of 7.3 times. LO: 4.3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.40

DuPont analysis involves breaking return-on-assets ratios into their a. profit components. b. marginal and average components. c. operating and financing components. d. profit margin and turnover components. Solution: d is correct. This is the DuPont “triangle,” in which profit margins and

turnovers are used to explain returns. LO: 4.4 Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Measurement

4.41

If a company’s net profit margin is –5 percent, its total asset turnover is 1.5 times, and its equity multiplier is 1.2 times, its return on equity is closest to a. –9.0 percent.

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Solutions Manual

b. –7.5 percent. c. –3.2 percent. d. 1.8 percent. Solution: a is correct. Return on equity =

Net income Net income Net sales Average total assets = × × Average total equity Net sales Average total assets Average total equity

Return on equity = –5% × 1.5 × 1.2 = –9.0% LO: 4.4 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Sample Test Problems Greenfern Corporation recently filed the following financial statements with the SEC. Greenfern Corporation Income Statement for the Fiscal Year Ended July 31, 2014 Net sales $73,236 Cost of products sold 52,092 Gross profit $21,144 Selling, general, and administrative expenses 9,333 Depreciation 1,060 Operating income (loss) $ 10,751 Interest expense 649 Earnings (loss) before income taxes 10,102 Income taxes 3,536 Net earnings (loss) $ 6,566 Greenfern Corporation Balance Sheet as of July 31, 2014 Assets Liabilities and Stockholders’ Equity Cash and marketable securities $ 9,118 Accounts payable Accounts receivable 7,844 Accrued and other liabilities Inventory 8,900 Taxes payable Deferred income taxes 878 Debt due within one year

$ 6,379 5,663 4,821 10,778

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Fundamentals of Corporate Finance, 3rd Edition

Prepaid expenses & other receivables Total current assets Property, plant, and equipment Less: Accumulated depreciation Net property plant and equip.

2,803 $29,543 62,467 22,196 $40,271

Goodwill and other assets

16,270

Total assets

$86,084

Solutions Manual

Total current liabilities Long-term debt Deferred income taxes Other non-current liabilities Total liabilities Common stock Retained earnings Total stockholders’ equity (deficit) Total liabilities and stockholders’ equity

$27,641 24,280 6,903 5,608 $64,432 3,667 17,985 $21,652 $86,084

4.1

Refer to the preceding balance sheet and income statement for Greenfern Corporation for the fiscal year ended July 31, 2014. What are the company’s current ratio and quick ratio? What do these ratios tell us about Greenfern? Solution: Current assets $29,543 Current ratio = = =1.07 Current liabilities $27,641

Quick ratio =

Current assets − Inventory $29,543 − $8,900 = = 0.75 Current liabilities $27,641

The current ratio of just over 1 tells us that Greenfern’s cash and marketable securities, and other current assets, such as accounts receivable and inventory, if liquidated, will just provide enough proceeds to cover short-term liabilities. The quick ratio of Greenfern indicates that if we exclude inventory, which might be considerably less liquid than other current assets, the remaining current assets can cover just 75 percent of the short-term liabilities. LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

4.2

Refer to the preceding balance sheet and income statement for Greenfern Corporation for the fiscal year ended July 31, 2014. Calculate the following ratios: a. Inventory turnover

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Fundamentals of Corporate Finance, 3rd Edition

b. Days’ sales outstanding. c. Total asset turnover. d. Fixed asset turnover. e. Total debt ratio. f. Debt-to-equity ratio. g. Times interest earned ratio. h. Cash coverage ratio. Solution: Ratio a. Inventory turnover b. Days’ sales outstanding c. Total asset turnover d. Fixed asset turnover e. Total debt ratio f. Debt-to-equity ratio g. Times interest earned ratio h. Cash coverage ratio LO: 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

Solutions Manual

Calculation $52,092/$8,900 $7,844/($73,236/365) $73,236/$86,084 $73,236/$40,271 $64,432/$86,084 $64,432/$21,652 $10,751/$649 ($10,751 + $1,060)/$649

Value 5.85 39.1 days 0.85 1.82 0.75 2.98 16.57 18.20

4.3

Refer to the preceding balance sheet and income statement for Greenfern Corporation for the fiscal year ended July 31, 2014. Use the DuPont identity to calculate the return on equity (ROE). In the process, calculate the following ratios: net profit margin, total asset turnover, equity multiplier, EBIT return on assets (EROA), and return on assets. Solution: Net profit margin = Net income/Net sales = $ 6,566 / $73,236 = 0.0897 or 8.97% Total asset turnover = Net sales/Total assets = $73,236 / $86,084 = 0.85 Equity multiplier = Total assets/Total equity = $86,084 / $21,652 = 3.98 EROA = EBIT/Total assets = $10,751/$86,084 = 0.1249 or 12.49% Return on assets = Net income/Total assets = $ 6,566 / $86,084 = 0.0763 or 7.63% DuPont identity: ROE = ROA × Equity multiplier = Net profit margin × Total asset turnover × Equity multiplier = 0.0897 × 0.85 × 3.98 = 0.3033 = 30.35%

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LO: 3, 4 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.4

Last year Pontiff Enterprises reported net sales of $13,144,680, a gross profit $4,127,429, EBIT of $2,586,150, and net income of $867,555. Compute Pontiff’s cost of goods sold, gross profit margin, operating profit margin, and net profit margin? Solution: Cost of goods sold = Net sales − Gross profit

= $13,144,680 -$4,127,429 = $9,017,251 Gross profit margin = Grossprofit/Net sales = $4,127,429/$13,144,680 = 0.3140, or 31.40% Operating profit margin = EBIT/Net sales = $2,586,150/$13,144,680 = 0.1967, or19.67% Net profit margin = Net income/Net sales = $867,555/$13,144,680 = 0.0660, or 6.60% LO: 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Measurement

4.5

National City Bank has 646,749,650 shares of common stock outstanding that are currently selling for $37.55 per share on the New York Stock Exchange. If National City’s net income was $2,780,955,000 in the year that just ended, what was its earnings per share and what is its current price-earnings ratio? If the typical price-earnings ratio for a bank is currently 15, what does the price-earnings ratio for National City tell you about its prospects? Solution:

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Net income Shares outstanding

Earnings per share (EPS) = = Price-earnings ratio =

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$2,780,955,000 = $4.30 646,749,650

Share price EPS

$37.55 = 8.73 $4.30 The fact that the price-earnings ratio for National City of 8.73 is well below the typical value for a bank tells us that the market places a smaller value on each current dollar of earnings at National City than on each current dollar of earnings at the typical bank. This suggests that the market is less optimistic about National City’s prospects than it is about the prospects of the typical bank. =

LO: 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: FSA AICPA: Measurement

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Chapter 5 The Time Value of Money Before You Go On Questions and Answers Section 5.1 1.

Why is a dollar today worth more than a dollar one year from now? A dollar is worth more today than one year from now, due to its potential earning capacity. If you have the money in your hand today, you have the opportunity to invest it and earn interest or you can purchase goods and services for your immediate consumption. Given that people have a positive preference for consumption, time value of money holds true.

What is a time line, and why is it important in financial analysis? A time line is a horizontal line that starts at time zero (today) and shows cash flows as they occur over time. It is an important tool used to analyze cash flows over certain time periods, as timing of each cash flow has a big impact on the final figure, and therefore on the resulting investment decision.

Section 5.2 1.

What is compounding, and how does it affect the future value of an investment? Compounding is the process that refers to converting the initial (principal) amount into a future value. In order to obtain the future value of the principal amount, you calculate what the value at the end of the time period will be assuming the initial investment will earn interest, which is reinvested and will earn additional interest in the future periods.

What is the difference between simple interest and compound interest? The difference is the interest earned on interest.

How does changing the compounding period affect the amount of interest earned on an investment? The more frequent the compounding schedule, the higher the interest earned. For example, $100 invested for one year at 10 percent compounded annually will earn you $10 of interest at the end of the year, but if your bank compounded interest quarterly, your earnings from interest would increase to $10.38.

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Section 5.3 1.

What is the present value, and when is it used? Present value is the amount a future sum is worth today given a certain return rate. The present value concept should be used when calculating how much money you need today in order to reach your financial goal sometime in the future.

What is the discount rate? How does the discount rate differ from the interest rate in the future value equation? The discount rate is the compound interest rate used to determine the present value of future cash flows. Both discount and interest rates essentially represent the same concept. The only difference is the context in which they are used.

What is the relation between the present value factor and the future value factor? The present value factor is the reverse of the future value factor. To obtain the present value factor, you divide 1 by the future value factor (1 + i).

Explain why you would expect the discount factor to become smaller when based on the longer the time to payment. The discount factor will become smaller the longer the time to payment due to time value of money. The longer you have to wait to obtain the money, the less value it will have to you. Mathematically, the discount factor is calculated as 1/(1 + i)n. The longer the time to payment, the larger n gets, which will make the discount factor smaller.

Section 5.4 1.

What is the difference between the interest rate (i) and the growth rate (g) in the future value equation? The interest rate and the growth rate in the future value equation essentially represent the same concept. The growth rate is used when we deal with numerical values such as sales or change over time. When referring to money being invested, we use the term interest rate.

Self-Study Problems and Solutions 5.1

Amit Patel is planning to invest $10,000 in a bank certificate of deposit (CD) for five years. The CD will pay interest of 9 percent. What is the future value of Amit’s investment?

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Solution: Present value of the investment = PV = $10,000 Interest rate = i = 9% Number of years = n = 5. 0 1 2 3 4 5 Years ├───┼───┼───┼────┼───┤ -$10,000 FV5=?

FVn = PV(1 + i ) n FV5 = $10,000(1 + 0.09)5 = $15, 386.24

5.2

Megan Gaumer expects to need $50,000 for a down payment on a house in six years. How much does she need to invest today in an account paying 7.25 percent in order to have $50,000 in six years? Solution: Amount Megan will need in six years = FV6 = $50,000 Number of years = n = 6 Interest rate = i = 7.25% Amount needed to be invested now = PV = ? 0 1 2 3 4 5 6 Year ├───┼───┼───┼────┼───┼───┤ PV = ? FV6 = $50,000 FV

PV = (1+𝑖)𝑛 𝑛 =

$50,000 (1+0.0725)6

= $32,853.84 5.3

Kelly Martin has $10,000 that she can deposit into a savings account for five years. Bank A pays compounds interest annually, Bank B twice a year, and Bank C quarterly. Each

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bank has a stated interest rate of 4 percent. What amount would Kelly have at the end of the fifth year if she left all the interest paid on the deposit in each bank? Solution: Present value of Kelly’s deposit = PV = $10,000 Number of years = n = 5 Interest rate = i = 4% Compound period m: A=1 B=2 C=4 Amount at the end of 5 years = FV5 = ? 0 4% 1 2 3 4 5 Year ├───┼───┼───┼────┼───┤ -$10,000 FV5 = ? A:

FVn FV5

= PV × (1 + i/m)m x n = 10,000 × (1 + 0.04/1)1x5 = $12,166.53

FV5

= 10,000 × (1 + 0.04/2)2x5 = $12,189.94

FV5

= 10,000 × (1 + 0.04/4)4x5 = $12,201.90

5.4

You have an opportunity to invest $2,500 today and receive $3,000 in three years. What would be the return on your investment if you accepted this opportunity? Solution: Your investment today = PV = $2,500 Amount to be received = FV3= $3,000 Time of investment = n = 3 Return on the investment = i = ? 0i=? 1 2 3 Year ├───┼────┼───┤ -$2,500 $3,000 FV𝑛 = PV × (1 + 𝑖)𝑛

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$3,000 = $2,500 × (1 + 𝑖)3 $3,000 $2,500

= (1 + 𝑖)3

i = 6.27%

5.5

Emily Smith deposits $1,200 in her bank today. If the bank pays 4 percent simple interest, how much money will she have at the end of five years? What if the bank pays compound interest? How much of the earnings will be interest on interest? Solution: Emily’s deposit today= PV = $1,200 Interest rate = i = 4% Number of years = n = 5 Amount to be received = FV5 = ? 0 4% 1 2 3 4 5 Year ├───┼───┼───┼────┼───┤ -$1.200 FV5 = ? a. Future value with simple interest Simple interest per year = $1,200 × 0.04 = $48 Simple interest for 5 years = $48 × 5 = $240 FV5 = $1,200 + $240 = $1,440 b. Future value with compound interest FV5 = $1,200 × (1 + 0.04)5 = $1,459.98 Simple interest = ($1,440 – $1,200) = $240 Interest on interest = $1,459.98 – $1,200 – $240 = $19.98

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Discussion Questions 5.1

Explain the phrase “a dollar today is worth more than a dollar tomorrow.” The implication is that if one was to receive a dollar today instead of in the future, the dollar could be invested and will be worth more than a dollar tomorrow because of the interest earned during that one day. This makes it more valuable than receiving a dollar tomorrow.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.2

Explain the importance of a time line. Time lines are important tools used to analyze investments that involve cash flow streams over a period of time. They are horizontal lines that start at time zero (today) and show cash flows as they occur over time. Because of time value of money, it is crucial to keep track of not only the size, but also the timing of the cash flows.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.3

What are the two factors to be considered in time value of money? The factors that are critical in time value of money are the size of the cash flows and the timing of the cash flows.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.4

Explain the difference between future value and present value. Future value measures what one or more cash flows are worth at the end of a specified period, while present value measures what one or more cash flows that are to be received in the future will be worth today (at t = 0). LO: 2, 3 Level: Basic

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Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.5

Explain the difference between compounding and discounting. The process of converting an amount given at the present time into a future value is called compounding. It is the process of earning interest over time. Discounting is the process of converting future cash flows to what its present value is. In other words, present value is the current value of the future cash flows that are discounted at an appropriate interest rate. LO: 2, 3 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.6

Explain how compound interest differs from simple interest. Suppose I invest $100 for three years at a rate of 10 percent. Simple interest would imply that I will earn $10 for each of the three years for a total of $30 interest. At the end of three years I would have $130. Compound interest recognizes that the interest earned in years 1 and 2 will also earn interest over the remaining period. Thus, the $10 earned in the first year would earn interest at 10 percent for the next two years, and the $10 earned in the second year would earn interest for the third year. Thus the total amount that I would have at the end of three years would be: $100(1.10)3 = $133.10 . By compounding, I have earned an additional interest of $3.10. The total interest or compound interest is the $33.10 earned on the $100 invested, while the simple interest earned is equal to $30.

LO: 2 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.7

If you were given a choice between investing in a savings account that paid quarterly interest and one that paid monthly interest, which one should you choose if they both offered the same stated interest rate and why? The impact of compounding really dictates that one should pick the account that pays interest more frequently (as long as the interest rates are the same). This allows for the interest earned in the earlier periods to earn interest and the investment to grow more.

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LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.8

Compound growth is exponential over time. Explain. Growth rates, as well as interest rates, are not linear, but rather exponential over time. In other words, the growth rate of the invested funds is accelerated by the compounding of interest. Over time, the principal amount you receive interest on will get larger with compounding, thus generating higher interest payments.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.9

What is the Rule of 72? This is a rule of thumb to determine how fast an investment can double. It is a rule that allows you to closely approximate the time that it would take to double your money. It works well with interest rates between 5 and 20 percent, but varies more with higher rates. The Rule of 72 says that the time to double your money (TDM) approximately equals 72/i, where i is the rate of return expressed as a percentage.

LO: 4 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement 5.10

You are planning to take a spring break trip to Cancun your senior year. The trip is exactly two years away, but you want to be prepared and have enough money when the time comes. Explain how you would determine the amount of money you will have to save in order to pay for the trip. First, determine how much money you will need for the trip. Second, check how much you already have and how it translates into future value cash—how much it will be worth in two years. Next, determine how much you will have to deposit today, given the bank’s offered interest rate, to ensure that you will have saved up the difference when the time for your senior spring break comes.

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Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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Questions and Problems BASIC 5.1

Future value: Chuck Tomkovick is planning to invest $25,000 today in a mutual fund that will provide a return of 8 percent each year. What will be the value of the investment in 10 years?

Solution: 0 10 years ├────────────────────┤ PV = -$25,000 FV10 = ? Amount invested today = PV = $25,000 Return expected from investment = i = 8% Duration of investment = n = 10 years Value of investment after 10 years = FV10 FV10 = PV  (1 + i ) n = $25,000  (1.08)10

= $53,973.12

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.2

Future value: Ted Rogers is investing $7,500 in a bank CD that pays a 6 percent annual interest. How much will the CD be worth at the end of five years? Solution: 0 5 years ├────────────────────┤ PV = $7,500 FV5 = ? Amount invested today = PV = $7,500 Return expected from investment = i = 6% Duration of investment = n = 5 years Value of investment after 5 years = FV5 FV5 = PV  (1 + i ) n = $7,500  (1.06) 5

= $10,036.69

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LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.3

Future value: Your aunt is planning to invest in a bank CD that will pay 7.5 percent interest compounded semiannually. If she has $5,000 to invest, how much will she have at the end of four years? Solution: 0 4 years ├────────────────────┤ PV = $5,000 FV4 = ? Amount invested today = PV = $5,000 Return expected from investment = i = 7.5% Duration of investment = n = 4 years Frequency of compounding = m = 2 Value of investment after 4 years = FV4 i   FV4 = PV   1 +   m

 0.075  = $5,000   1 +  2  

24

= $5,000  (1.0375)8 = $6, 712.35

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.4

Future value: Kate Eden received a graduation present of $2,000 that she is planning on investing in a mutual fund that earns 8.5 percent each year. How much money will she have in three years? Solution: 0 3 years ├────────────────────┤ PV = $2,000 FV3 = ? Amount Kate invested today = PV = $2,000 Return expected from investment = i = 8.5% Copyright © 2015 John Wiley & Sons, Inc.

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Duration of investment = n = 3 years Value of investment after 3 years = FV3

FV3 = PV  (1 + i ) n = $2,000  (1.085) 3 = $2,554.58

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.5

Future value: Your bank pays 5 percent interest semiannually on your savings account. You don’t expect to add to the current balance of $2,700 over the next four years. How much money can you expect to have at the end of this period? Solution: 0 4 years ├────────────────────┤ PV = -$2,700 FV4 = ? Amount invested today = PV = $2,700 Return expected from investment = i = 5% Duration of investment = n = 4 years Frequency of compounding = m = 2 Value of investment after 4 years = FV4 mn

i    0.05  FV4 = PV  1 +  = $2,700  1 +  m 2    = $2,700  (1.025) 8 = $3,289.69

24

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.6

Future value: Your birthday is coming up and instead of other presents, your parents promised to give you $1,000 in cash. Since you have a part time job and thus don’t need the cash immediately, you decide to invest the money in a bank CD that pays 5.2 percent,

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compounded quarterly, for the next two years. How much money can you expect to earn in this period of time? Solution: 0 2 years ├────────────────────┤ PV = -$1,000 FV2 = ? Amount invested today = PV = $1,000 Return expected from investment = i = 5.2% Duration of investment = n = 2 years Frequency of compounding = m = 4 Value of investment after 2 years = FV2 mn

i    0.052  FV2 = PV  1 +  = $1,000  1 +  m 4    = $1,000  (1.013) 8 = $1,108.86

42

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.7

Multiple compounding periods: Find the future value of a five-year $100,000 investment that pays 8.75 percent and that has the following compounding periods: a. Quarterly. b. Monthly. c. Daily. d. Continuous. Solution: 0 5 years ├────────────────────┤ PV = -$100,000 FV5 = ? Amount invested today = PV = $100,000 Return expected from investment = i = 8.75% Duration of investment = n = 5 years a.

Frequency of compounding = m = 4

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Value of investment after 5 years = FV5 mn

45

125

3655

i    0.0875  FV5 = PV  1 +  = $100,000  1 +  m 4    = $100,000  (1.021875) 20 = $154,154.24 b.

Frequency of compounding = m = 12 Value of investment after 5 years = FV5

i    0.0875  FV5 = PV  1 +  = $100,000  1 +  m 12    = $100,000  (1.00729) 60 = $154,637.37 c.

Frequency of compounding = m = 365 Value of investment after 5 years = FV5

i    0.0875  FV5 = PV  1 +  = $100,000  1 +  m 365    = $100,000  (1.00024)1825 = $154,874.91 d.

Frequency of compounding = m = Continuous Value of investment after 5 years = FV5 FV5 = PV  e in = $100,000  e 0.08755

= $100,000  1.5488303 = $154,883.03

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.8

Growth rates: Joe Mauer, a catcher for the Minnesota Twins, is expected to hit 15 home runs in 2014. If his home-run-hitting ability is expected to grow by 12 percent every year for the following five years, how many home runs is he expected to hit in 2019? Solution: 0 5 years ├────────────────────┤ PV = -15 FV5 = ?

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Number of home runs hit in 2014 = PV = 15 Expected annual increase in home runs hit = i = 12% Growth period = n = 5 years Expected home runs in 2019 = FV5

FV5 = PV  (1 + g) n = 15  (1.12)5 = 26.4  26 home runs

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.9

Present value: Roy Gross is considering an investment that pays 7.6 percent, compounded annually. How much will he have to invest today so that the investment will be worth $25,000 in six years? Solution: 0 6 years ├────────────────────┤ PV = ? FV6 = $25,000 Value of investment after 6 years = FV6 = $25,000 Return expected from investment = i = 7.6% Duration of investment = n = 6 years Amount to be invested today = PV FVn $25,000 PV = = n (1 + i ) (1.076) 6 = $16,108.92

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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5.10

Present value: Maria Addai has been offered a future payment of $750 two years from now. If she can earn 6.5 percent, compounded annually, on her investment, what should she pay for this investment today? Solution: 0 2 years ├────────────────────┤ PV = ? FV2 = $750 Value of investment after 2 years = FV2 = $750 Return expected from investment = i = 6.5% Duration of investment = n = 2 years Amount to be invested today = PV FVn $750 PV = = n (1 + i ) (1.065) 2

= $661.24

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.11

Present value: Your brother has asked you for a loan and has promised to pay you $7,750 at the end of three years. If you normally invest to earn 6 percent per year, how much will you be willing to lend to your brother if you view this purely as a financial transaction (i.e. you don’t give your brother a special deal)? Solution: 0 3 years ├────────────────────┤ PV = ? FV3 = $7,750 Loan repayment amount after 3 years = FV3 = $7,750 Return expected from investment = i = 6% Duration of investment = n = 3 years Amount to be invested today = PV FVn $7,750 PV = = n (1 + i ) (1.06) 3

= $6,507.05

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LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.12

Present value: Tracy Chapman is saving to buy a house in five years. She plans to put 20 percent down at that time, and she believes that she will need $35,000 for the down payment. If Tracy can invest in a fund that pays 9.25 percent annually, how much will she need to invest today? Solution: 0 5 years ├────────────────────┤ PV = ? FV5 = $35,000 Amount needed for down payment after 5 years = FV5 = $35,000 Return expected from investment = i = 9.25% Duration of investment = n = 5 years Amount to be invested today = PV FVn $35,000 PV = = n (1 + i ) (1.0925) 5

= $22,488.52

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.13

Present value: You want to buy some bonds that will have a value of $1,000 at the end of seven years. The bonds pay 4.5 percent interest annually. How much should you pay for them today? Solution: 0 7 years ├────────────────────┤ PV = ? FV7 = $1,000 Copyright © 2015 John Wiley & Sons, Inc.

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Face value of bond at maturity = FV7 = $1,000 Appropriate discount rate = i = 4.5% Number of years to maturity = n = 7 years. Present value of bond = PV FVn $1,000 PV = = n (1 + i ) (1.045) 7 = $734.83

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.14

Present value: Elizabeth Sweeney wants to accumulate $12,000 by the end of 12 years. If the annual interest rate is 7 percent, how much will she have to invest today to achieve her goal? Solution: 0 12 years ├────────────────────┤ PV = ? FV12 = $12,000 Amount Ms. Sweeney wants at end of 12 years = FV12 = $12,000 Interest rate on investment = i = 7% Duration of investment = n = 12 years. Present value of investment = PV FVn $12,000 PV = = n (1 + i ) (1.07)12

= $5,328.14

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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5.15

Interest rate: You are in desperate need of cash and turn to your uncle, who has offered to lend you some money. You decide to borrow $1,300 and agree to pay back $1,500 in two years. Alternatively, you could borrow from your bank that is charging 6.5 percent interest annually. Should you go with your uncle or the bank? Solution: 0 2 years ├────────────────────┤ PV = -$1,300 FV2 = $1,500 Amount to be borrowed = PV = $1,300 Amount to be paid back after 2 years = FV2 = $1,500 Interest rate on investment = i = ? Duration of investment = n = 2 years. Present value of investment = PV FVn PV = (1 + i )n $1,500 $1,300 = (1 + i ) 2 $1,500 (1 + i) 2 = = 1.1538 $1,300

i = 1.1538 − 1 i = 7.42% You should borrow from the bank.

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.16

Number of periods: You invest $150 in a mutual fund today that pays 9 percent interest annually. How long will it take to double your money? Solution: 0 n years ├────────────────────┤ PV = -$150 FVn = $300 Value of investment today = PV = $150

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Interest on investment = n = 9% Future value of investment = FV = $300 Number of years to double investment = n

FVn = PV  (1 + i ) n $300 = $150  (1.09) n (1.09) n = $300 150 = 2.00 n  ln(1.09) = ln(2.00) n=

ln(2.00)  8 years ln(1.09)

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

INTERMEDIATE 5.17

Future value: Your finance textbook sold 53,250 copies in its first year. The publishing company expects the sales to grow at a rate of 20 percent each year for the next three years and by 10 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in years 3 and 4. Draw a time line to show the sales level for each of the next four years. Solution: Number of copies sold in its first year = PV = 53,250 Expected annual growth in the next 3 years = g = 20% Number of copies sold after 3 years = FV3 = FVn = PV  (1 + g ) n

= 53, 250  (1.20)3 = 92, 016 copies Number of copies sold in the fourth year = FV4 FVn = PV  (1 + g ) n = 92,016  (1.10) 0

= 101, 218 copies 4 years

SM 5-20

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

├───────────┼────────┤ PV = -53,250 92,016 101,218 copies

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.18

Future Value: CelebNav, Inc., had sales last year of $700,000, and the analysts are predicting a good year for the start-up, with sales growing 20 percent a year for the next three years. After that, the sales should grow 11 percent per year for two years, at which time the owners are planning to sell the company. What are the projected sales for the last year before the sale? Solution: 0 1 2 3 4 5 years ├───────┼────────┼───────┼────────┼───────┤ g1 = 20% g2 = 11% PV = -$700,000 FV5=? Sales of CelebNav last year = PV = $700,000 Expected annual growth in the next 3 years = g1 = 20% Expected annual growth in years 4 and 5 = g2= 11% Sales in year 5 = FV5 FV5 = PV  (1 + g1 )3  (1 + g 2 )2 = $700,000  (1.20)3  (1.11) 2

= $1, 490, 348.16

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.19

Future value: You decide to take advantage of the current online dating craze and start your own Web site. You know that you have 450 people who will sign up immediately and, through a careful marketing research and analysis, determine that membership can

SM 5-21

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

grow by 27 percent in the first two years, 22 percent in year 3, and 18 percent in year 4. How many members do you expect to have at the end of four years? Solution: 0 1 2 3 4 years ├───────┼────────┼───────┼────────┤ g1-2=27% g3=22% g4=18% PV = -450 FV4 = ? Number of Web site memberships at t = 0 = PV = 450 Expected annual growth in the next 2 years = g1-2 = 27% Expected annual growth in years 3 = g3= 22% Expected annual growth in years 4 = g4= 18% Number of members in year 4 = FV4 FV4 = PV(1 + g1 ) 2  (1 + g3 )  (1 + g 4 ) = 450  (1.27) 2  (1.22)  (1.18)

= 1, 045 members

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.20

Multiple compounding periods: Find the future value of an investment of $2,500 made today for the following rates and periods: a. 6.25 percent compounded semiannually for 12 years b. 7.63 percent compounded quarterly for 6 years c. 8.9 percent compounded monthly for 10 years d. 10 percent compounded daily for 3 years e. 8 percent compounded continuously for 2 years Solution: a.

 0.0625  FV12 = PV  1 +  2   = $5,232.09

FV6 = PV × (1 +

212

= $2,500  (2.0928)

0.0763 4×6 ) = $2,500 × (1.5738) 4

= $3,934.48

SM 5-22

Fundamentals of Corporate Finance, 3rd edition

0.089 12×10

FV10 = PV × (1 + 12 ) = $6,067.86

Solutions Manual

= $2,500 × (2.4271)

0.010 365×3 FV3 = PV × (1 + 365 ) = $2,500 × (1.3498) = $3,374.51

FV2 = PV × ein = $3,000 × e0.08 x 2 = $2,500 × 1.1735 = $2,933.78

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.21

Multiple compounding periods: Find the present value of $3,500 under each of the following rates and periods. a. 8.9% compounded monthly for five years. b. 6.6% compounded quarterly for eight years. c. 4.3% compounded daily for four years. d. 5.7% compounded continuously for three years. Solution: 0 n years ├────────────────────┤ PV = ? FVn = $3,500 a. Return expected from investment = i = 8.9% Duration of investment = n = 5 years Frequency of compounding = m = 12 Present value of amount = PV FV5 $3,500 PV = = mn 125 i  0.089    1 +  1 +  m 12    $3,500 = = $2,246.57 1.5579 b. Return expected from investment = i = 6.6% Duration of investment = n = 8 years Frequency of compounding = m = 4

SM 5-23

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Present Value of amount = PV PV =

FV8 mn

$3,500 48

i  0.066    1 +  1 +  m 4    $3,500 = = $2,073.16 1.6882 Return expected from investment = i = 4.3% Duration of investment = n = 4 years Frequency of compounding = m = 365 Present Value of amount = PV FV4 $3,500 PV = = mn 3654 i  0.043    1 +  1 +  m 365    $3,500 = = $2,946.96 1.1877 Return expected from investment = i = 5.7% Duration of investment = n = 3 years Frequency of compounding = m = Continuous Present value of amount = PV FV $3,500 PV = in 3 = 0.0573 e e

$3,500 = $2, 949.88 1.1865

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.22

Multiple compounding periods: Samantha plans to invest some money so that she has $5,500 at the end of three years. How much should she invest today given the following choices: a. 4.2 percent compounded daily b. 4.9 percent compounded monthly c. 5.2 percent compounded quarterly d. 5.4 percent compounded annually Solution:

SM 5-24

Fundamentals of Corporate Finance, 3rd edition

0 3 years ├────────────────────┤ PV = ? FV3 = $5,500 Return expected from investment = i = 4.2% Duration of investment = n = 3 years Frequency of compounding = m = 365 Present value of amount = PV FV3 $5,500 PV = = mn 3653 i  0.042    1 +  1 +  m 365    $5,500 = = $4,848.92 1.1343 Samantha should invest $4,848.92 today to reach her target of $5,500 in three years. Return expected from investment = i = 4.9% Duration of investment = n = 3 years Frequency of compounding = m = 12 Present value of amount = PV

PV =

Solutions Manual

FV3

$5,500

= 𝑖 mn 0.049 12 ×3 (1 + ) (1 ) + m 12 $5,500 1.1580

= $4,749.54

Samantha should invest $4,749.54 today to reach her target of $5,500 in three years. Return expected from investment = i = 5.2% Duration of investment = n = 3 years Frequency of compounding = m = 4 Present Value of amount = PV FV3 $5,500 PV = = mn 43 i  0.052    1 + 1 +     m 4    $5,500 = = $4,710.31 1.1677 Samantha should invest $4,710.31 today to reach her target of $5,500 in three years. Return expected from investment = i = 5.4% Duration of investment = n = 3 years Frequency of compounding = m = 1 Present value of amount = PV

SM 5-25

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

FV3 $5,500 = = $4,697.22 3 (1 + i ) (1.054) 3 Samantha should invest $4,697.22 today to reach her target of $5,500 in three years. Samantha should invest in choice D. PV =

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.23

Time to grow: Zephyr Sales Company has sales of $1.125 million. If the company’s management expects sales to grow 6.5 percent annually, how long will it be before sales doubles? Use a financial calculator to solve this problem. Solution: Enter 6.5% -$1.125 $2.250 N g% PMT PV FV Answer: 11 years

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.24

Time to grow: You are able to deposit $850 in a bank CD today, and you will withdraw the money only once the balance is $1,000. If the bank pays 5 percent interest, how long will it take for the balance to reach $1,000? Solution: Amount invested today = PV = $850 Expected amount in the future = FV = $1,000 Interest rate on CD = i = 5% To calculate the time needed to reach the target FV, we set up the future value equation.

SM 5-26

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

FVn = PV  (1 + i ) n $1,000 = $850  (1.05) n $1,000 (1.05) n = = 1.1764 $850 n  ln(1.05) = ln(1.1764) ln(1.1764) n= = 3.3 years ln(1.05)

LO 2, 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.25

Time to grow: Neon Lights Company is a private company with sales of $1.3 million a year. Management wants to take the company public but has to wait until the sales reach $2 million. If the sales are expected to grow 12 percent annually, when is the earliest that Neon Lights will go public? Solution: Current level of sales = PV = $1,300,000 Target sales level in the future = FV = $2,000,000 Projected growth rate = g = 12% To calculate the time needed to reach the target FV, we set up the future value equation. FV3 = PV × (1 + 𝑔)𝑛 $2,000,000 = $1,300,000 × (1.12)𝑛 $2,000,000 (1.12)𝑛 = = 1.5385 $1,300,000 n × ln(1.12) = ln(1.5385) n=

ln (1.5385) ln (1.12)

= 3.8 years

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

SM 5-27

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

5.26

Time to grow: You have just inherited $550,000. You plan to save this money and continue to live off the money that you are earning in your current job. If you can invest the money in a bond that pays 4.6 percent interest annually, how long will it be before your inheritance is worth $1 million? Solution: FV𝑛 = PV × (1 + 𝑖)𝑛 $1,000,000 = $550,000 × (1.046)𝑛 $1,000,000 $550,000

= (1.046)𝑛

$1,000,000 ) = n × ln(1.046) ln ( $550,000 $1,000,000

ln( $550,000 )

ln (1.046) $0.59784 $0.04497

n = 13.29 years

LO 2, 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.27

Growth rates: Xenix Corp had sales of $353,866 in 2014. If management expects its sales to be $476,450 in three years, what is the rate at which the company’s sales are expected to grow? Solution: Sales in 2014 = PV = $353,866

SM 5-28

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Expected sales three years from now = $476,450 To calculate the expected sales growth rate, we set up the future value equation. FV3 = PV  (1 + g)3

$476, 450 = $353,866  (1 + g)3 (1 + g)3 =

$476, 450 = 1.3464 $353,866 1

g = (1.3464) 3 − 1 = 10.42%

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.28

Growth rate: Infosys Technologies, Inc., an Indian technology company, reported net income of $419 million this year. Analysts expect the company’s earnings to be $1.468 billion in five years. What is the expected growth rate in the company’s earnings? Solution: Earnings in current year = PV = $419,000,000 Expected earnings five years from now = $1,468,000,000 To calculate the expected earnings growth rate, we set up the future value equation. FV5 = PV  (1 + g)5

$1, 468,000,000 = $419,000,000  (1 + g)5 (1 + g)5 =

$1, 468,000,000 = 3.5036 $419,000,000 1

g = (3.5036) 5 − 1 = 28.5%

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

SM 5-29

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

5.29

Present value: Caroline Weslin needs to decide whether to accept a bonus of $1,820 today or wait two years and receive $2,100 then. She can invest at 6 percent. What should she do? Solution: 0 2 years ├────────────────────┤ PV = -$1,820 FV2 = ? Amount to be received in 2 years = FV2 = $2,100 Return expected from investment = i = 6% Duration of investment = n = 2 years Present value of amount today PV = FV2 $2,100 PV = = n (1 + i ) (1.06) 2 = $1,868.99 Since $1,869 is greater than $1,820, Caroline should wait two years unless she needs the money sooner.

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.30. Present value: Congress and the President have decided to increase the federal tax rate in an effort to reduce the budget deficit. Suppose that Caroline Weslin, from problem 5.29, will pay 35 percent of her bonus to the federal government for taxes if she accepts the bonus today and 40 percent if she receives her bonus in two years. Will the increase in tax rates affect her decision? Solution: Yes. It will affect her decision. If Caroline accepts the bonus today, after paying the taxes, she will have $1,820 × (1 - 0.35) = $1,183.00 left over. If she waits two years and pays the high tax rate, the present value of what she will have left over is only $1,869 × (1 - 0.40) = $1,121.40.

SM 5-30

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

ADVANCED You have $2,500 that you want to invest in your classmate’s start-up business. You believe the business idea to be great and hope to get $3,700 back at the end of three years. If all goes according to the plan, what will be the return on your investment? Solution: 0 3 years ├────────────────────┤ PV = -$2,500 FV3 = $3,700 Amount invested in project = PV = $2,500 Expected return three years from now = FV =$3,700 To calculate the expected rate of return, we set up the future value equation. FV3 = PV  (1 + i ) 3 5.31

$3,700 = $2,500(1 + i ) 3 $3,700 (1 + i ) 3 = = 1.4800 $2,500 1

i = (1.4800) 3 − 1 = 0.1396 = 13.96%

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.32

Patrick Seeley has $2,400 to invest. His brother approached him with an investment opportunity that could double his money in four years. What interest rate would the investment have to yield in order for Patrick’s brother to deliver on his promise?

Solution: 0 4 years ├────────────────────┤ PV = -$2,400 FV4 = $4,800

SM 5-31

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Amount invested in project = PV = $2,400 Expected return three years from now = FV =$4,800 Investment period = n = 4 years To calculate the expected rate of return, we set up the future value equation. FV4 = PV × (1 + 𝑖)4 $4,800 = $2,400 × (1 + 𝑖)4 (1 + 𝑖)4 =

$4,800 $2,400

= 2.0000

i = (2.000)1/4 – 1 = 0.1892 = 18.92%

LO 2, 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.33

You have $12,000 in cash. You can deposit it today in a mutual fund earning 8.2 percent compounded semiannually, or you can wait, enjoy some of it, and invest $11,000 in your brother’s business in two years. Your brother is promising you a return of at least 10 percent on your investment. Whichever alternative you choose, you will need to cash in at the end of 10 years. Assume your brother is trustworthy and that both investments carry the same risk. Which one would yield the largest amount in 10 years? Solution: Option 1: Invest in account paying 8.2 percent semiannually for 10 years. 0 10 years ├────────────────────┤ PV = -$12,000 FV10 = ? Amount invested in project = PV = $12,000 Investment period = n = 10 years Interest earned on investment = i = 8.2% Frequency of compounding = m = 2 Value of investment after 10 years = FV10 210

 0.082  FV10 = PV  1 + = $12,000  (2.23365)  2   = $26,803.77 Option 2: Invest in brother’s business to earn 10 percent for eight years. 0 8 years

SM 5-32

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

├────────────────────┤ PV = -$11,000 FV8 = ? Amount invested in project = PV = $11,000 Investment period = n = 8 years Interest earned on investment = i = 10% Frequency of compounding = m = 1 Value of investment after 8 years = FV8

FV8 = PV  (1 + 0.10) = $11,000  (2.14359) 8

= $23,579.48 You are better off investing today in the mutual fund and earn 8.2 percent semiannually for 10 years.

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.34

When you were born your parents set up a bank account in your name with an initial investment of $5,000. You are turning 21 in a few days and will have access to all your funds. The account was earning 7.3 percent for the first seven years, but then the rates went down to 5.5 percent for six years. The economy was doing well from 2007 to 2009, and your account earned 8.2 percent three years in a row. Unfortunately, the next two years you earned only 4.6 percent. Finally, as the economy recovered, the return jumped to 7.6 percent for the last three years. a. How much money was in your account at the end of Year 16? b. How much money is in your account now, at the end of year 21? c. What would be the balance now if your parents made another deposit of $1,200 at the end of year 7? Solution: 0 1 7 13 14 15 16 21 years ├───┼∙∙∙∙∙∙∙∙∙∙┼∙∙∙∙∙∙∙∙∙∙∙∙────┼────┼───┼───∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙──┤ PV = -$5,000 FV21 = ? i1 = 7.3% i2 = 5.5% i3 = 8.2% i4 = 4.6% i5 = 7.6% a. Initial investment = PV = $5,000 Interest rate for first 7 years = i1 = 7.3% Interest rate for next 6 years = i2 = 5.5%

SM 5-33

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Interest rate for next 3 years = i3 = 8.2% Investment value at age 16 years = FV16 FV16 = PV  (1 + i1 ) 7  (1 + i2 ) 6  (1 + i3 ) 3 = $5,000  (1 + 0.073)  (1.055) 6  (1.082) 3 = $5,000  (1.6376)  (1.3788)  (1.2667) = $14,300.55 Interest rate for from age 17 to 18 = i4 = 4.6% Interest rate for next 3 years = i5 = 7.6% Investment at start of 16th year = PV = $14,300.95 Investment value at age 21 years = FV21 FV21 = FV16  (1 + i4 ) 2  (1 + i5 ) 3 7

= $14,300.55  (1 + 0.046)  (1.076) 3 = $14,300.55  (1.0941)  (1.2458)) = $19,492.38 Additional investment at start of 8th year = $1,200 Total investment for next 6 years = $8,187.82 + $1,200 = $9,387.82 Interest rate for next 6 years = i2 = 5.5% Interest rate for years 13 to 16 = i3 = 8.2% Interest rate for from age 17 to 18 = i4 = 4.6% Interest rate for next 3 years = i5 = 7.6% Investment value at age 21 = FV21 FV21 = FV7  (1 + i2 )6  (1 + i3 )3  (1 + i4 ) 2  (1 + i5 )3 2

= $9,387.82  (1.055)6  (1.082)3  (1.046 )  (1.076)3 2

= $9387.82  (1.3788)  (1.2667)  (1.0941)  (1.2458) = $22, 349.16 LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.35

Eric Fisher, a number 1 draft pick of the Kansas City Chiefs, and his agent are evaluating three contract options. Each option offers a signing bonus and a series of payments over

SM 5-34

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

the life of the contract. Fisher uses a 10.25 percent rate of return to evaluate the contracts. Given the cash flows for each option, which one should he choose? Year Cash Flow Type Option A Option B Option C 0 Signing Bonus $3,100,000 $4,000,000 $4,250,000 1 Annual Salary $ 650,000 $ 825,000 $ 550,000 2 Annual Salary $ 715,000 $ 850,000 $ 625,000 3 Annual Salary $ 822,250 $ 925,000 $ 800,000 4 Annual Salary $ 975,000 $1,250,000 $ 900,000 5 Annual Salary $1,100,000 $1,000,000 6 Annual Salary $1,250,000 Solution: To decide on the best contract from Eric Fisher’s viewpoint, we need to find the present value of each option. The contract with the highest present value should be the one chosen. Option A: Discount rate to be used = i= 10.25% Present value of contract = PVA $650,000 $715,000 $822,250 $975,000 $1,100,000 $1,250,000 PVA = $3,100,000 + + + + + + (1.1025)1 (1.1025) 2 (1.1025) 3 (1.1025) 4 (1.1025) 5 (1.1025) 6 = $3,100,000 + $589,569 + $588,232 + $613,576 + $659,918 + $675,305 + $696,047

= $6,922,647 Option B: Discount rate to be used = i= 10.25% Present value of contract = PVB $825,000 $850,000 $925,000 $1,250,000 PVB = $4,000,000 + + + + (1.1025)1 (1.1025) 2 (1.1025) 3 (1.1025) 4 = $4,000,000 + $748,299 + $699,297 + $690,249 + $846,049 = $6,983,894 Option C: Discount rate to be used = i= 10.25% Present value of contract = PVC $550,000 $625,000 $800,000 $900,000 $1,000,000 PVC = $4,250,000 + + + + + (1.1025)1 (1.1025) 2 (1.1025) 3 (1.1025) 4 (1.1025) 5 = $4,250,000 + $498,866 + $514,189 + $596,972 + $609,155 + $613,913 = $7,083,096 Option C is the best choice for Eric Fisher.

LO 3

SM 5-35

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

Surmec, Inc., reported sales of $2.1 million last year. The company’s primary business is the manufacture of nuts and bolts. Since this is a mature industry, analysts are confident that sales will grow at a steady rate of 7 percent per year The company’s net income equals 23 percent of sales. Management would like to buy a new fleet of trucks but can only do so once the net income reaches $620,000 a year. At the end of what year will Surmec be able to buy the trucks? What will sales and net income be in that year? Solution: Current level of sales for Surmec = PV = $2,100,000 Profit margin = 23% Net Income for the year = 0.23 x $2,100,000 = $483,000 Target profit level in the future = FV = $620,000 Projected growth rate of sales = g = 7% To calculate the time needed to reach the target FV, we set up the future value equation. 5.36

FV𝑛 = PV × (1 + g)𝑛 $620,000 = $483,000 × (1.07)𝑛 $620,000 (1.07)𝑛 = = 1.2836 $483,000 n × ln(1.07) = ln(1.2836) ln(1.2836) n= = 3.7 years ln (1.07) The company achieves its profit target during the fourth year. Sales level at end of year 4 = FV4 FVn = PV  (1 + g) n = $2,100,000  (1.07) 4 = $2,752,671.62

Profit for the year = $2,752,671.62 x 0.23 = $633,114.47

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

SM 5-36

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

5.37

You will be graduating in two years and are thinking about your future. You know that you will want to buy a house five years after you graduate and that you will want to put down $60,000. As of right now, you have $8,000 in your savings account. You are also fairly certain that once you graduate, you can work in the family business and earn $32,000 a year, with a 5 percent raise every year. You plan to live with your parents for the first two years after graduation, which will enable you to minimize your expenses and put away $10,000 each year. The next three years, you will have to live on your own, as your younger sister will be graduating from college and has already announced her plan to move back into the family house. Thus, you will be able to save only 13 percent of your annual salary. Assume that you will be able to earn 7.2 percent on the savings from your salary. At what interest rate will you need to invest the current savings account balance in order to achieve your goal? Hint: Draw a time line that shows all the cash flows for years 0 through 7. Remember, you want to buy a house seven years from now and your first salary will be in year 3. Solution: 0 1 2 3 4 5 6 7 ├─────┼──────┼─────┼─────┼──────┼─────┼──────┤ $10,000 $10,000 $4,586.40 $4,815,72 $5,056.48 Starting salary in year 3 = $32,000 Annual pay increase = 5% Savings in first 2 years = $10,000 Savings rate for years 3 to 7 = 13% Year 1 2 3 4 5 6 7 Salary $0 $0 $32,000 $33,600 $35,280 $37,044 $38,896 Savings $0 $0 $10,000 $10,000 $4,586.40 $4,815.72 $5,056.48 Investment rate = i = 7.2% Future value of savings from salary = FV7 FV7 = $0 + $0 + $10,000 × (1.072)4 + $10,000 × (1.072)3 + $4,586.40 x (1.072)2 = $4,815.72 X (1.072)1 + $5,056.48 x (1.072)0 = $13,206.24 + $12,319.25 + $5,270.62 + $5,162.45 + $5,056.48 = $41,015.07 Target down payment = $60,000 Amount needed to reach target = $60,000 - $41,015.07= FV = $18,984.93 Current savings balance = PV $8,000 Time to achieve target = n = 7 years.

SM 5-37

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

To solve for the investment rate needed to achieve target, we need to set up the future value equation: FV = PV × (1 + 𝑖)7 $18, 984.93 = $8,000 × (1 + 𝑖)7 $18,984.98 (1 + 𝑖)7 + $8,000 = 2.3731 1

i = (2.3731)7 − 1 = 1.1314 − 1 = 13.14%

LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

Sample Test Problems 5.1

Holding all else constant, what will happen to the present value of a future amount if you increase the discount rate? What if you increase the number of years? Solution: Holding all else constant, both increasing the discount rate and increasing the number of years, will decrease the present value.

LO 3 Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.2

Juliette Bronson anticipates needing $500,000 to start a business. If she can earn 4.5 percent compounded annually on her investments, how much money would Juliette have to invest today to have $500,000 in three years?

Solution:

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0 3 Year 1 2 4.5% ├────────────────────┤ PV = ? FV3 = $500,000 Amount required at end on investment period = FV3 = $500,000 Return expected from investment = i = 4.5% Duration of investment = n = 3 years Amount to be invested today = PV FV n $500,000 PV = = n (1 + i ) (1.045) 3 = $438,148.30

LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.3

Christopher Thompkins must decide how to invest $10,000 that he just inherited. What would be the future value of his investment after five years under each of the following three investment opportunities? a. 6.28% compounded quarterly. b. 6.20% compounded monthly. c. 6.12% compounded continuously.

Solution: a.

Interest rate on investment = i = 6.28% Frequency of compounding = m = 4 Value of investment after 5 years = FV5 mn

i    0.0628  FV5 = PV  1 +  = $10,000  1 +  4   m  = $10,000  (1.01570) 20 = $13,655.55 b.

4 x5

Interest rate on investment = i = 6.20% Frequency of compounding = m = 12 Value of investment after 5 years = FV5 mn

125

i    0.0620  FV5 = PV  1 +  = $10, 000  1 +  12   m  = $10, 000  (1.00517) 60 = $13, 623.37 c.

Interest rate on investment = i = 6.12%

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Frequency of compounding = m = Continuous Value of investment after 5 years = FV5 FV5 = PV  ein = $10, 000  e0.06125

= $10, 000 1.358 = $13, 579.82

LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

5.4.

Tina DeLeon deposited $2,500 today in an account paying 6 percent interest annually. What would be the simple interest earned on this investment in five years? With annual compounding, how much interest-on-interest would Tina earn in five years?

Solution: 0 5 years 3 2 1 4 ├────────────────────┤ PV = -$2,500 FV5 = ? Amount invested today = PV = $2,500 Return expected from investment = i = 6% Duration of investment = n = 5 years Frequency of compounding = m = 1 Value of investment after 5 years = FV5 FV5 = PV  (1 + i) n = $2,500(1.06) 5

= $3,345.56 Simple interest on investment = $2,500 × 0.06 × 5 = $750 Interest-on-interest = FV5 – PV – simple interest on investment Interest-on-interest = $3,345.56 – $2,500 – $750 = $95.56

LO 2 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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5.5

Solutions Manual

The state of Texas had 42,725 active patient care physicians in 2008 and by 2012 this number had grown to 47,663. What was the compound annual growth rate (CAGR) in the number of active care physicians during this period?

Solution: 0 4 years 2 3 1 ├────────────────────┤ PV = -42,725 FV4 = 47,663 Number of physicians in 2008 = PV = 42,725 Number of physicians in 2012 = FV4 = 47,663 Years to maturity = n = 4 years. growth rate = i FVn PV = n (1 + i )

47, 663 (1 + i ) 4 $47, 663 (1 + i ) 4 = = 1.1156 $42, 725

42, 725 =

i = (1.1156)1 4 − 1 i = 0.0277, or 2.77% The CAGR was 2.77 percent

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement

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Chapter 6 Discounted Cash Flows and Valuation Before You Go On Questions and Answers Section 6.1 1.

Explain how to calculate the future value of a stream of cash flows. It would helpful to first construct a time line so that we can identify the timing of each cash flow. Then you would calculate the future vale of each individual cash flow. Finally, you would add up the future values of all the individual cash flows to determine the future value of the cash flow stream.

Explain how to calculate the present value of a stream of cash flows. To calculate the present value of a stream of cash flows, you should first draw a time line so that you can see that each cash flow is placed in its correct time period. Then you simply calculate the present value of each cash flow for its time period, and finally you add up all the present values.

Why is it important to adjust all cash flows to a common date? When making economic decisions, we need to compare “apples to apples.” This is possible only when we bring all the cash flows to a common date, which can either be a present time or some future date. The reason is the time value of money: a dollar today is worth more than a dollar in the future. Thus, when cash flows are converted to the same time period, the time value of money concept holds true, and we can concentrate on the economic aspects of the decision.

Section 6.2 1.

How do an ordinary annuity, an annuity due, and a perpetuity differ? Ordinary annuity assumes that the cash flows occur at the end of a period. Most types of loans are ordinary annuities. On the other hand, annuity due is an annuity whose payment is to be made immediately (or at the beginning of a period) instead of at the end of the period. For example, in many leases the first payment is due immediately, and each successive payment must be made at the beginning of the month. Perpetuity is a special case of annuity, and it refers to a constant stream of identical cash flows with no end.

Give two examples of perpetuities. The text gives the example of British government bonds called consols that have no maturity and have been traded in the markets since the end of the Napoleonic wars.

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Another example could be a preferred stock of a company that has no maturity and will pay a constant dividend forever. 3.

What is the annuity transformation method? The annuity transformation method refers to the conversion of an ordinary annuity to annuity due. In this process, you first plot all the cash flows on a time line as if the cash flows were an ordinary annuity. Then you calculate the present or future value factor as you would with an ordinary annuity, and finally, you multiple your answer by (1 + i). Conveniently, this relationship works for both present and future value calculations.

Section 6.3 1.

What is the difference between a growing annuity and a growing perpetuity? A stream of cash flows that is growing at a constant rate over time can be called a growing annuity or growing perpetuity. If the cash flows extend over a finite length of time, then we call it a growing annuity and can use Equation6.5 to compute the present value. If the growth will continue for a very long time period and perhaps, forever, we refer to it as the growing perpetuity. We would then use Equation 6.6 to estimate the present value of this cash flow stream.

Section 6.4 1.

What is the APR, and why are lending institutions required to disclose this rate? APR, or the annual percentage rate, is the annualized interest rate using simple interest. It is defined as the simple interest charged per period multiplied by the number of compounding periods per year. Lending institutions are mandated by Federal Truth-inLending Act regulations to disclose this rate to essentially make it easier for consumers to be exposed to the same kind of rate by all businesses.

What is the correct way to annualize an interest rate in financial decision making? The correct way to annualize interest rates is by computing the effective annual interest rate (EAR). This is the annual growth rate that allows for compounding, which means you earn interest on interest. To calculate the EAR, take the quoted rate and divide it by the number of compounding periods (quoted rate/m). Then take the resulting interest rate, add 1 to it, and raise it to the power equal to m. Finally, subtract 1 and the result is EAR.

Distinguish between quoted interest rate, interest rate per period, and effective annual interest rate. Quoted interest rate, such as APR, is the interest rate that has been annualized by multiplying the rate per period by the number of compounding periods. Interest rate per period is the quoted rate per period. It can be stated in the form of an APR—in that case,

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just divide it by the number of compounding periods to obtain the interest rate per period. Finally, EAR is the annual rate of interest that accounts for the effects of compounding.

Self-Study Problems 6.1

Kronka, Inc., is expecting cash inflows of $13,000, $11,500, $12,750, and $9,635 over the next four years. What is the present value of these cash flows if the appropriate discount rate is 8 percent? Solution: The time line for the cash flows and their present value is as follows: 0 8% 1 2 3 4 Year ├─────────┼─────────┼─────────┼─────────┤ $13,000 $11,500 $12,750 $9,635 $13,000 $11,500 $12,750 $9,635 PV4 = + + + (1.08) (1.08) 2 (1.08) 3 (1.08) 4 = $12,037.03 + $9,859.40 + $10,121.36 + $7,082.01

= $39,099.80 LO: 4 Level: Basic

6.2

Your grandfather has agreed to deposit a certain amount of money each year into an account paying 7.25 percent annually to help you go to graduate school. Starting next year, and for the following four years, he plans to deposit $2,250, $8,150, $7,675, $6,125, and $12,345 into the account. How much will you have at the end of the five years? Solution: The time line for the cash flows and their future value is as follows: 0 7.25% 1 2 3 4 5 ├────────┼────────┼────────┼─────────┼────────┤ -$2,250 -$8,150 -$7,675 -$6,125 -$12,345

Year

FV5 = [$2,250 x (1.0725)4] + [$8,150 x (1.0725)3] + [$7,675 x (1.0725)2] + [$6,125 x 1.0725] + $12,345 = $2,976.95 + $10,054.25 + $8,828.22 + $6,569.06 + $12,345 = $40,773.48 LO: 2 Level: Basic Copyright ©2015 John Wiley & Sons, Inc.

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6.3

Mike White is planning to save up for a trip to Europe in three years. He will need $7,500 when he is ready to make the trip. He plans to invest the same amount at the end of each of the next three years in an account paying 6 percent. What is the amount he will have to save every year to reach his goal of $7,500 in three years? Solution: Amount Mike White will need in three years = FVA3 = $7,500 Number of years = n = 3 Interest rate on investment = i = 6.0% Amount needed to be invested every year = PMT = ? 0 6% 1 2 3 Year ├─────────┼──────┼───────┤ CF=? CF=? CF=? FVA3 = $7,500

FVA n = CF 

(1 + i ) n − 1 i

$7,500 = CF 

(1 + 0.06) 3 − 1 0.06

= CF  3.1836 CF =

$7,500 3.1836

= $2, 355.82 Mike will have to invest $2,355.82 every year for the next three years. LO: 5 Level: Basic

6.4

Becky Scholes has $150,000 to invest. She wants to be able to withdraw $12,500 every year forever without using up any of her principal. What interest rate would her investment have to earn in order for her to be able to do so? Solution: Present value of Becky Scholes’s investment = $150,000 Amount needed annually = $12,500 This is a perpetuity! CF PVP = 𝑖 CF $12,500 𝑖= = PVP $150,000 Copyright ©2015 John Wiley & Sons, Inc.

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𝒊 = 𝟖. 𝟑𝟑% LO: 6 Level: Basic

6.5

Dynamo Corp. is expecting annual payments of $34,225 for the next seven years from a customer. What is the present value of this annuity if the discount rate is 8.5 percent? Solution: The time line for Dynamo’s cash flows and their present value is as follows: 0 8.5% 1 2 3 4 5 6 7 Year

PVA = ?

$34,225

PVA 7 = CF 

$34,225 $34,225 $34,225

$34,225

1 − 1 (1 + i ) n i

= $34, 225 

1 − 1 (1.085)7 0.085

= $34, 225  5.1185 = $175,181.14 LO: 2 Level: Basic

Discussion Questions 6.1

Identify the steps involved in computing the future value when you have multiple cash flows. First, prepare a time line to identify the size and timing of the cash flows. Second, calculate the present value of each individual cash flow using an appropriate discount rate. Finally, add up the present values of the individual cash flows to obtain the present value of a cash flow stream. This approach is especially useful in the real world where the cash flows for each period are not the same.

LO: 1 Level: Basic

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Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.2

What is the key economic principle involved in calculating the present value or future value of multiple cash flows? Regardless of whether you are calculating the present value or the future value of a cash flow stream, the key idea is to discount or compound the cash flows to the same point in time.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.3

What is the difference between a perpetuity and an annuity? A cash flow stream that consists of the same amount being received or paid on a periodic basis for a limited time period is called an annuity. If the same payments are made periodically forever, the contract is called a perpetuity.

LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.4

Define annuity due. Would an investment be worth more if it were an ordinary annuity or an annuity due? Explain. When annuity cash flows occur at the beginning of each period, it is called an annuity due. Annuity due will result in a bigger investment than an ordinary annuity because each cash flow will accrue an extra interest payment.

LO: 2 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Raymond Bartz is trying to choose between two equally risky annuities, each paying $5,000 per year for five years. One is an ordinary annuity, the other is an annuity due. Which of the following statements is most correct? a. The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due. b. The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity. c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity. d. If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same. The answer is c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity.

LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.6

Which of the following investments will have the highest future value at the end of three years? Assume that the effective annual rate for all investments is the same. a. You earn $3,000 at the end of three years (a total of one payment). b. You earn $1,000 at the end of every year for the next three years (a total of three payments). c. You earn $1,000 at the beginning of every year for the next three years (a total of three payments). The answer is c. Earning $1,000 at the beginning of each year for the next three years will have the highest future value as it is an annuity due.

LO: 2 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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6.7

Explain whether or not each of the following statements is correct. a. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate. b. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent. Statement A is a true statement. The 15-year mortgage will have higher monthly payments since more of the principal will have to be paid each month than in the case of a 30-year mortgage. Statement B is true since the frequency of compounding is annual and hence the rate for a single period is the same as the rate for a year. LO: 2, 4 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.8

When will the annual percentage rate (APR) be the same as the effective annual rate (EAR)? The annual percentage rate (APR) will be the same as the effective annual rate only if the compounding period is annual, not otherwise.

LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.9

Why is the effective annual rate (EAR) superior to the annual percentage rate (APR) in measuring the true economic cost or return? Unlike the APR, which reflects annual compounding, the EAR takes into account the actual number of compounding periods. For example, suppose there are two investment alternatives that both pay an APR of 10 percent. Assume that the first pays interest annually and that the second pays interest quarterly. It would be a mistake to assume that both investments will provide the same return. The real return on the first one is 10 percent, but the second investment actually provides a return of 10.38 percent because of the quarterly compounding. Thus, this is the superior investment.

LO: 4

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Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.10

Suppose three investments have equal lives and multiple cash flows. A high discount rate tends to favor: a. The investment with large cash flows early. b. The investment with large cash flows late. c. The investment with even cash flows. d. None of the investments since they have equal lives. The correct answer is a. The investment with large cash flows early will be worth more compared to the one with the large cash flows late. The cash flows that come in later will have a heavier penalty when using a higher discount rate. Thus the investment with large cash flows early will be favored.

LO: 4 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Questions and Problems BASIC 6.1

Future value with multiple cash flows: Konerko, Inc., management expects the company to earn cash flows of $13,227, $15,611, $18,970, and $19,114 over the next four years. If the company uses an 8 percent discount rate, what is the future value of these cash flows at the end of year 4? Solution: 0 8% 1 2 3 4 ├───────┼────────┼───────┼────────┤ $13,227 $15,611 $18,970 $19,114 FV4 = [$13,227 × (1.08)3 ] + [$15,611 × (1.08)2 ] + [$18,970 × (1.08)1 ] + $19,114

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= $16,662.21 + $18,208.67 + $20,487.60 + $19,114 = $74,502.48

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.2

Future value with multiple cash flows: Ben Woolmer has an investment that will pay him the following cash flows over the next five years: $2,350, $2,725, $3,128, $3,366, and $3,695. If his investments typically earn 7.65 percent, what is the future value of the investment’s cash flows at the end of five years? Solution: 0 7.65% 1 2 3 4 5 Year ├───────┼────────┼───────┼────────┼───────┤ $2,350 $2,725 $3,128 $3,366 $3,695

FV5= $2,350  (1.0765)4  + $2,725  (1.0765)3  + $3,128  (1.0765)2  + $3,366  (1.0765)1  + $3,695 = $3,155.91 + $3,399.45 + $3,624.89 + $3,623.50 + $3,695 = $17, 498.75 LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.3

Future value with multiple cash flows: You are a freshman in college and are planning a trip to Europe when you graduate from college at the end of four years. You plan to save the following amounts annually, starting today: $625, $700, $700, and $750. If you can earn 5.75 percent annually, how much will you have at the end of four years? Solution: 0 5.75% 1 2 3 4 Year ├───────┼────────┼───────┼────────┤ $625 $700 $700 $750 ?

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FV4 = $625(1.0575) 4 + $700(1.0575) 3 + $700(1.0575) 2 + $750(1.0575) = $781.63 + $827.83 + $782.81 + 793.13 = $3,185.40

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.4

Present value with multiple cash flows: Saul Cervantes has just purchased some equipment for his landscaping business. For this equipment he must pay the following amounts at the end of each of the next five years: $10,450, $8,500, $9,675, $12,500, and $11,635. If the appropriate , what is the cost in today’s dollars of the equipment Saul purchased today? Solution: 0 10.875% 1 2 3 4 5 Year ├───────┼────────┼───────┼────────┼───────┤ $10,450 $8,500 $9,675 $12,500 $11,635 $10,450 $8,500 $9,675 $12,500 $11,635 + + + + 2 3 4 (1.10875) (1.10875) (1.10875) (1.10875) (1.10875) 5 = $9,425.03 + $6,914.35 + $7,098.23 + 8,271.33 + $6,943.82 = $38,652.76

PV =

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.5

Present value with multiple cash flows: Jeremy Fenloch borrowed some money from his friend and promised to repay him $1,225, $1,350, $1,500, $1,600, and $1,600 over the next five years. If the friend normally discounts investments at 8 percent annually, how much did Jeremy borrow? Solution: 0 8% 1 2 3 4 5 Year ├───────┼────────┼───────┼────────┼───────┤ $1,225 $1,350 $1,500 $1,600 $1,600

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$1,225 $1,350 $1,500 $1,600 $1,600 + + + + (1.08) (1.08) 2 (1.08) 3 (1.08) 4 (1.08) 5 = $1,134.26 + $1,157.41 + $1,190.75 + $1,176.05 + $1,088.93 = $5,747.40

PV =

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.6

Present value with multiple cash flows: Biogenesis Inc. management expects the following cash flow stream over the next five years. They discount all cash flows using a 23 percent discount rate. What is the present value of this cash flow stream?

1 2 3 4 5 Year ┼────────┼───────┼────────┼───────┤ -$1,133,676 -$978,452 $275,455 $878,326 $1,835,444 Solution: 0 23% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ -$1,133,676 -$978,452 $275,455 $878,326 $1,835,444

Year

− $1,133,676 − $978,452 $275,455 $878,326 $1,835,444 + + + + (1.23) (1.23) 2 (1.23) 3 (1.23) 4 (1.23) 5 = −$921,687.80 − $646,739.37 + $148,025.09 + $383,738.43. + $651,951.94 = −$384,711.72

PV =

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.7

Present value of an ordinary annuity: An investment opportunity requires a payment of $750 for 12 years, starting a year from today. If your required rate of return is 8 percent, what is the value of the investment to you today? Solution: 0 8% 1 2 3 11 12 Year ├───────┼────────┼───────┼………………┼───────┤

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$750

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$750

Annual payment = PMT = $750 No. of payments = n = 12 Required rate of return = 8% Present value of investment = PVA12 1 1− (1 + i ) n PVA n = PMT  i 1− = $750 

1 (1.08)12 = $750  7.5361 0.08

= $5, 652.06

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.8

Present value of an ordinary annuity: Dynamics Telecommunications Corp. has made an investment in another company that will guarantee it a cash flow of $22,500 each year for the next five years. If the company uses a discount rate of 15 percent on its investments, what is the present value of this investment? Solution: 0 15% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ $22,500 $22,500 $22,500 $22,500 $22,500 Annual payment = PMT = $22,500 No. of payments = n = 5 Required rate of return = 15% Present value of investment = PVA5

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1− PVA n = PMT 

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1 (1 + i ) n i 1−

= $22,500 

1 (1.15)5 = $22,500  3.3522 0.15

= $75, 423.49

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.9

Future value of an ordinary annuity: Robert Hobbes plans to invest $25,000 a year at the end of each year for the next seven years in an investment that will pay him a rate of return of 11.4 percent. How much money will Robert have at the end of seven years? Solution: 0 11.4% 1 2 3 6 7 Year ├───────┼────────┼───────┼………………┼───────┤ $25,000 $25,000 $25,000 $25,000 $25,000 Annual investment = PMT = $25,000 No. of payments = n = 7 Investment rate of return = 11.4% Future value of investment = FVA7 (1 + i ) n − 1 FVA n = PMT  i

(1.114)7 − 1 = $25,000  = $25,000  9.9044 0.114 = $247, 609.95 LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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6.10

Future value of an ordinary annuity: Cecelia Thomas is a sales executive at a Baltimore firm. She is 25 years old and plans to invest $3,000 every year in an IRA account, beginning at the end of this year until she reaches the age of 65. If the IRA investment will earn 9.75 percent annually, how much will she have in 40 years, when she turns 65? Solution: 0 9.75% 1 2 3 39 40 Year ├───────┼────────┼───────┼………………┼───────┤ $3,000 $3,000 $3,000 $3,000 $3,000 Annual investment = PMT = $3,000 No. of payments = n = 40 Investment rate of return = 9.75% Future value of investment = FVA40 (1 + i ) n − 1 FVA n = PMT  i

= $3,000 

(1.0975)40 − 1 = $3,000  413.5588 0.0975

= $1, 240, 676.41 LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.11

Future value of an annuity due: Refer to Problem 6.10. If Cecelia Thomas invests at the beginning of each year, how much will she have at age 65? Solution: 0 9.75% 1 2 3 39 40 Year ├───────┼────────┼───────┼………………┼───────┤ $3,000 $3,000 $3,000 $3,000 $3,000 Annual investment = PMT = $3,000 No. of payments = n = 40 Type of annuity = Annuity due Investment rate of return = 9.75% Future value of investment = FVA40

SM 6-15

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

(1 + i ) n − 1 FVA n = PMT   (1 + i ) i (1.0975)40 − 1 = $3,000   (1.0975) = $3,000  413.5588  1.0975 0.0975 = $1, 361, 642.36 LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.12

Computing annuity payment: Kevin Winthrop is saving for an Australian vacation in three years. He estimates that he will need $5,000 to cover his airfare and all other expenses for a week-long holiday in Australia. If he can invest his money in an S&P 500 equity index fund that is expected to earn an average annual return of 10.3 percent over the next three years, how much will he have to save every year if he starts saving at the end of this year? Solution: 0 10.3% 1 2 3 Year ├───────┼────────┼───────┤ PMT PMT PMT FVAn = $5,000 Future value of annuity = FVA = $5,000 Return on investment = i = 10.3% Payment required to meet target = PMT Using the FVA equation: (1 + i ) n − 1 FVA n = PMT  i $5,000 = PMT  PMT =

(1.103)3 − 1 0.103

$5,000 $5,000 = 3 (1.103) − 1 3.3196 0.103

= $1, 506.20 Kevin has to save $1,506.20 every year for the next three years to reach his target of $5,000.

SM 6-16

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.13

Computing annuity payment: The Elkridge Bar & Grill has a seven-year loan of $23,500 with Bank of America. It plans to repay the loan in seven equal installments starting today. If the rate of interest is 8.4 percent, how much will each payment be? Solution: 0 1 2 3 6 7 Year ├───────┼────────┼───────┼………………┼───────┤ PMT PMT PMT PMT PMT PMT PVAn = $23,500 n = 7; i = 8.4% Present value of annuity = PVA = $23,500 Return on investment = i = 8.4% Payment required to meet target = PMT Type of annuity = Annuity due Using the PVA equation: 1 1− (1 + i ) n PVA n = PMT   (1 + i ) i

PMT =

$23,500 $23,500 = 1 5.1359  1.084 1− 7 (1.084)  (1.084) 0.084

= $4, 221.07 Each payment made by Elkridge Bar & Grill will be $4,221.07, starting today. LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.14

Perpetuity: Your grandfather is retiring at the end of next year. He would like to ensure that his heirs receive payments of $10,000 a year forever, starting when he retires. If he can earn 6.5 percent annually, how much does your grandfather need to invest to produce the desired cash flow? Solution:

SM 6-17

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Annual payment needed = PMT = $10,000 Investment rate of return = i = 6.5% Term of payment = Perpetuity Present value of investment needed = PV PMT $10,000 PV of Perpetuity = = i 0.065 = $153,846.15 LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.15

Perpetuity: Calculate the annual cash flows for each of the following investments: a. $250,000 invested at 6% b. $50,000 invested at 12% c. $100,000 invested at 10% Solution: a. Annual payment = PMT Investment rate of return = i = 6% Term of payment = Perpetuity Present value of investment needed = PV = $250,000 PMT PV of Perpetuity = i PMT = PV  i = $250,000  0.06 b.

= $15,000 Annual payment = PMT Investment rate of return = i = 12% Term of payment = Perpetuity Present value of investment needed = PV = $50,000 PMT PV of Perpetuity = i PMT = PV  i = $50,000  0.12 = $6,000 Annual payment = PMT Investment rate of return = i = 10% Term of payment = Perpetuity Present value of investment needed = PV = $100,000

SM 6-18

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

PMT i PMT = PV  i = $100,000  0.10 = $10,000

PV of Perpetuity =

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.16. Effective annual interest rate: Marshall Chavez bought a Honda Civic for $17,345. He put down $6,000 and financed the rest through the dealer at an APR of 4.9 percent for four years. What is the effective annual interest rate (EAR) if the loan payments are made monthly? Solution: Loan amount = PV = $11,345 Interest rate on loan = i = 4.9% Frequency of compounding = m = 12 Effective annual rate = EAR m1

i   0.049  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.05 − 1 = 5% LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.17

Effective annual interest rate: Cyclone Rentals borrowed $15,550 from a bank for three years. If the quoted rate (APR) is 6.75 percent, and the compounding is daily, what is the effective annual interest rate (EAR)? Solution: Loan amount = PV = $15,550 Interest rate on loan = i = 6.75% Frequency of compounding = m = 365 Effective annual rate = EAR m1

i   0.0675 EAR = 1 +  − 1 = 1 + 365   m  = 1.0698 − 1 = 7%

365

−1

LO 5

SM 6-19

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.18

Growing perpetuity: You are evaluating a growing perpetuity investment from a large financial services firm. The investment promises an initial payment of $20,000 at the end of this year and subsequent payments that will grow at a rate of 3.4 percent annually. If you use a 9 percent discount rate for investments like this, what is the present value of this growing perpetuity? Solution: Cash flow at t = 1 = CF1 = $20,000 Annual growth rate = g = 3.4% Discount rate = i = 9% Present value of growing perpetuity = PVA∞ CF1 $20,000 PVA  = = (i − g) (0.09 − 0.034) = $357,142.86 LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

INTERMEDIATE 6.19

Future value with multiple cash flows: Trigen Corp. management will invest cash flows of $331,000, $616,450, $212,775, $818,400, $1,239,644, and $1,617,848 in research and development over the next six years. If the appropriate interest rate is 6.75 percent, what is the future value of these investment cash flows six years from today? Solution: 0 6.75% 1 2 3 4 5 6 ├───────┼────────┼───────┼────────┼───────┼────────┤ $331,000 $616,450 $212,775 $818,400 $1,239,644 $1,617,848

SM 6-20

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

FV6 = $331,000  (1.0675)5  + $616, 450  (1.0675) 4  + $212,775  (1.0675)3  + $818, 400  (1.0675) 2  + $1, 239,644  (1.0765)1  + $1,617,848 = $458,846.49 + $800,514.85 + $258,835.74 + $932,612.84 + $1,323,319.97 + $1,617,848 = $5, 391, 977.89 LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.20

Future value with multiple cash flows: Stephanie Watson plans to make the following investments beginning next year. She will invest $3,125 in each of the next three years and will then make investments of $3,650, $3,725, $3,875, and $4,000 over the following four years. If the investments are expected to earn 11.5 percent annually, how much will Stephanie have at the end of the seven years? Solution: Expected rate of return = i = 11.5% Investment period = n = 7 years Future value of investment = FV

FV7 = $3,125  (1.115)6  + $3,125  (1.115)5  + $616, 450  (1.115)4  + $3,650  (1.115)3  + $3,725  (1.115)2  + $3,875  (1.115)1  + $4,000 = $6,004.81 + $5,385.48 + $4,830.03 + $5,059.61 + $4,631.01 + $4,320.63 + $4,000 = $34, 231.57 LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.21

Present value with multiple cash flows: Carol Jenkins, a lottery winner, will receive the following payments over the next seven years. If she can invest her cash flows in a fund that will earn 10.5 percent annually, what is the present value of her winnings? 0 1 2 3 4 5 6 7 Year ├────┼─────┼─────┼──────┼─────┼──────┼─────┤ $200,000 $250,000 $275,000 $300,000 $350,000 $400,000 $550,000 Solution: Copyright ©2015 John Wiley & Sons, Inc.

SM 6-21

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Expected rate of return = i = 10.5% Investment period = n = 7 years Future value of investment = FV $200,000 $250,000 $275,000 $300,000 $350,000 $400,000 $550,000 FV7 = + + + + + + (1.105)1 (1.105) 2 (1.105) 3 (1.105) 4 (1.105) 5 (1.105) 6 (1.105) 7 = $180,995.48 + $204,746.01 + $203,819.56 + $201,220.46 + $212,449.96

+ $219,728.47 + $273,417.77 = $1,496,377.71 LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.22

Computing annuity payment: Gary Whitmore is a high school sophomore. He currently has $7,500 in a savings account that pays 5.65 percent annually. Gary plans to use his current savings plus what he can save over the next four years to buy a car. He estimates that the car will cost $12,000 in four years. How much money should Gary save each year if he wants to buy the car? Solution: Cost of car in four years = $12,000 Amount invested in money market account now = PV = $7,500 Return earned by investment = i = 5.65% Value of current investment in 4 years = FV4

FV4 = PV(1 + i ) 4 = $7,500(1.0565) 4 = $9,344.14 Balance of money needed to buy car = $12,000 – $9,344.14 = $2,655.86 = FVA Payment needed to reach target = PMT (1 + i ) n − 1 FVA = PMT  i PMT =

FVA $2,655.86 $2,655.86 = n = 4 1 − (1 + i ) (1.0565) − 1 4.351949 i 0.0565

= $610.27 LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 6-22

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

6.23

Growing annuity: Modern Energy Company owns several gas stations. Management is looking to open a new station in the western suburbs of Baltimore. One possibility that managers at the company are evaluating is to take over a station located at a site that has been leased from the county. The lease, originally for 99 years, currently has 73 years before expiration. The gas station generated a net cash flow of $92,500 last year, and the current owners expect an annual growth rate of 6.3 percent. If Modern Energy uses a discount rate of 14.5 percent to evaluate such businesses, what is the present value of this growing annuity? Solution: Time for lease to expire = n = 73 years Last year’s net cash flow = CF0 = $92,500 Expected annual growth rate = g = 6.3% Firm’s required rate of return = i = 14.5% Expected cash flow next year = CF1 = $92,500(1 + g) = $92,500(1.063) = $98,327.50 Present value of growing annuity = PVAn

  1 + g n    1.063  73  CF1 $98,327.50 PVA n =  1 −   1 −   =   (i − g)   1 + i   (0.145 − 0.063)   1.145   = $1,199,115.85  0.995593 = $1,193,831.54 LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.24

Future value of an annuity due: Jeremy Denham plans to save $5,000 every year for the next eight years, starting today. At the end of eight years, Jeremy will turn 30 years old and plans to use his savings toward the down payment on a house. If his investment in a mutual fund will earn him 10.3 percent annually, how much will he have saved in eight years when he buys his house? Solution: 0 10.3% 1 2 3 7 8 Year ├───────┼────────┼───────┼………………┼───────┤ $5,000 $5,000 $5,000 $5,000 $5,000 Annual investment = PMT = $5,000

SM 6-23

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

No. of payments = n = 8 Type of annuity = Annuity due Investment rate of return = 10.3% Future value of investment = FVA8

 (1 + i ) n − 1 FVA n = PMT   (1 + i ) i    (1.103) 8 − 1 = $5,000   (1.103) = $5,000  11.5612  1.103  0.103  = $63,760.19 LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.25

Present value of an annuity due: Grant Productions borrowed some money from the California Finance Company at a rate of 17.5 percent for a seven-year period. The loan calls for a payment of $1,540,862.19 each year beginning today. How much did Grant borrow? Solution: 0 17.5% 1 2 3 6 7 ├───────┼────────┼───────┼………………┼───────┤ PMT =$1,540,862.19 at the beginning of each year Annual payment = PMT = $1,540,862.19 Type of annuity = Annuity due No. of payments = n = 7 Required rate of return = 17.5% Present value of investment = PVA8 1 1− (1 + i ) n PVA n = PMT   (1 + i ) i

1− = $1,540,862.19 

1 (1.175)7  (1.175) = $1,540,862.19  3.8663  1.175 0.175

= $6, 999, 999.98  $7, 000, 000 LO 2

SM 6-24

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 6.26

Present value of an annuity due: Sharon Kabana has won a state lottery and will receive a payment of $89,729.45 every year, starting today, for the next 20 years. If she invests the proceeds at a rate of 7.25 percent, what is the present value of the cash flows that she will receive? Round to the nearest dollar. Solution: 0 7.25% 1 2 3 19 20 ├───────┼────────┼───────┼………………┼───────┤ PMT = $89,729.45 at the beginning of each year Annual payment = PMT = $89,729.45 Type of annuity = Annuity due No. of payments = n = 20 Required rate of return = 7.25% Present value of investment = PVA20 1 1− (1 + i ) n PVA n = PMT   (1 + i ) i

1− = $89,729.45 

1 (1.0725)20  (1.0725) = $89,729.45  10.3912  1.0725 0.0725

= $999, 999.95  $1, 000, 000 LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.27

Present value of an annuity due: You wrote a piece of software that does a better job of allowing computers to network than any other program designed for this purpose. A large networking company wants to incorporate your software into its systems and is offering to pay you $500,000 today, plus $500,000 at the begining of each of the following six years, for permission to do this. If the appropriate interest rate is 6 percent, what is the present value of the cash flow stream that the company is offering you? Solution:

SM 6-25

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

You are being offered a seven year annuity due. You can solve this problem several different ways. First, you can calculate the present value of each of the individual cash flows and then add the present values together. Second, you can use the annuity transformation method discussed in the chapter. Third, you can calculate the present value of an ordinary six-year annuity and then add $500,000 to that value. Of course you can also use your calculator or Excel to do the calculations for you. Below are the calculations for the annuity transformation method. PVA7 = CF × PV annuity factor = $500,000 × 5.5824 = $2,791,190.72 Annuity value due

= PVA7 × (1 + i) = $2,791,190.72 × 1.06 = $2,958,662.16

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.28

Present value of an annuity: Suppose that the networking company in problem 6.27 will not start paying you until the first of new systems that uses your software is sold in two years. What is the present value of that annuity? Assume that the appropriate interest rate is still 6 percent. Solution: Since the first cash flow will not be received for two years, the present value will be less than in problem 6.27. All you have to do to solve this problem is to discount the answer from problem 6.27 for two years. Annuity value = value of annuity value due/(1 + i)2 = $2,958,662/(1.06)2 = $2,633,198.79 This is also equal to the value of the regular annuity in problem 6.27, PVA7, discounted one year at 6 percent. LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 6-26

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

6.29

Perpetuity: Calculate the present value of the following perpetuities: a. $1,250 discounted to the present at 7percent b. $7,250 discounted to the present at 6.33percent c. $850 discounted to the present at 20 percent Solution: a. Annual payment = PMT =$1,250 Investment rate of return = i = 7% Term of payment = Perpetuity Present value of investment needed = PV PMT $1,250 PV of Perpetuity = = i 0.07 = $17,857.14 b. Annual payment = PMT =$7,250 Investment rate of return = i = 6.33% Term of payment = Perpetuity. Present value of perpetuity = PV PMT $7,250 PV of Perpetuity = = i 0.0633 = $114,533.97 c. Annual payment = PMT =$850 Investment rate of return = i = 20% Term of payment = Perpetuity. Present value of investment needed = PV PMT $850 PV of Perpetuity = = i 0.20 = $4,250 LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.30

Effective annual interest rate: Find the effective annual interest rate (EAR) on each of the following: a. 6 percent compounded quarterly. b. 4.99 percent compounded monthly. c. 7.25 percent compounded semiannually. d. 5.6 percent compounded daily.

SM 6-27

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Solution: a. Interest rate = i = 6% Frequency of compounding = m = 4 Effective annual rate = EAR m1

i   0.06  EAR = 1 +  − 1 = 1 + −1 4   m  = 1.06136 − 1 = 6.14% Interest rate = i = 4.99% Frequency of compounding = m = 12 Effective annual rate = EAR m1

m1

365

i   0.0499 EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0511 − 1 = 5.11% Interest rate = i = 7.25% Frequency of compounding = m = 2 Effective annual rate = EAR i   0.0725 EAR = 1 +  − 1 = 1 + −1 2   m  = 1.0738 − 1 = 7.38% Interest rate = i = 5.6% Frequency of compounding = m = 365 Effective annual rate = EAR i   0.056  EAR = 1 +  − 1 = 1 + 365   m  = 1.0576 − 1 = 5.76%

−1

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.31

Effective annual interest rate: Which of the following investments has the highest effective annual interest rate (EAR)? a. A bank CD that pays 8.25 percent compounded quarterly. b. A bank CD that pays 8.25 percent compounded monthly. c. A bank CD that pays 8.45 percent compounded annually. d. A bank CD that pays 8.25 percent compounded semiannually. e. A bank CD that pays 8 percent compounded daily (on a 365-day per year basis).

SM 6-28

Fundamentals of Corporate Finance, 3rd edition

Solution: a.

Solutions Manual

Interest rate on CD = i = 8.25% Frequency of compounding = m = 4 Effective annual rate = EAR m1

m1

i   0.0825 EAR = 1 +  − 1 = 1 + −1 4   m  = 1.08509 − 1 = 8.51% Interest rate on CD = i = 8.25% Frequency of compounding = m = 12 Effective annual rate = EAR

i   0.0825 EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0857 − 1 = 8.57% Interest rate on CD = i = 8.45% Frequency of compounding = m = 12 Effective annual rate = EAR i   0.0845 EAR = 1 +  − 1 = 1 + −1 1   m  = 1.0845 − 1 = 8.45% Interest rate on CD = i = 8.25% Frequency of compounding = m = 2 Effective annual rate = EAR i   0.0825 EAR = 1 +  − 1 = 1 + −1 2   m  = 1.0842 − 1 = 8.42% Interest rate on CD = i = 8% Frequency of compounding = m = 365 Effective annual rate = EAR m1

365

i   0.08  EAR = 1 +  − 1 = 1 + −1  m  365  = 1.0833 − 1 = 8.33% Investment b. (8.25% monthly) has the highest EAR. LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 6-29

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

6.32

Effective annual interest rate: You are considering three alternative investments: (1) a three-year bank CD paying 7.5 percent compounded quarterly; (2) a three-year bank CD paying 7.3 percent compounded monthly; and (3) a three-year bank CD paying 7.75 percent compounded annually. Which investment has the highest effective annual interest rate (EAR)? Solution: (1) Interest rate on CD = i = 7.5% Frequency of compounding = m = 4 Effective annual rate = EAR m1

m1

i   0.075 EAR = 1 +  − 1 = 1 + −1 4   m  = 1.0771 − 1 = 7.71% (2) Interest rate on CD = i = 7.3% Frequency of compounding = m = 12 Effective annual rate = EAR i   0.073 EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0755 − 1 = 7.55% (3) Interest rate on CD = i = 7.75% Frequency of compounding = m = 1 Effective annual rate = EAR m1

i   0.0775 EAR = 1 +  − 1 = 1 + −1 1   m  = 1.0775 − 1 = 7.75% Investment (3) The three-year bank CD paying 7.75 percent interest compounded annually has the highest effective yield. LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

ADVANCED 6.33

You have been offered the opportunity to invest in a project which is expected to provide you with the following cash flows: $4,000 in one year, $12,000 in two years, and $8,000 in three years. If the appropriate interest rates are 6 percent for the first year, 8 percent for the second year, and 12 percent for the third year, what is the present value of these cash flows?

SM 6-30

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Solution: The answer is $20,495.15. Calculated as follows: $4,000 $12,000 $8,000 PV = + + 1.06 (1.06)(1.08) (1.06 )(1.08)(1.12 )

= $3,773.58 + $10, 482.18 + $6, 239.39 = $20, 495.15 If the interest rate is different each year, then you must perform the calculation in this way. What you are effectively doing here is discounting each cash flow one year at a time using the appropriate rate. For example, you discount the year three cash flow of $8,000 for one year at 12 percent: $8,000/1.12 = $7,142.86 You then discount this result for one year at 8 percent: $7,142.86/1.08 = $6,613.76 Finally, you get the present value of the $8,000 by discounting the above result by 6 percent: $6,613.76/1.06 = $6,239.40 The one cent difference from the number above is due to rounding. LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.34

Tirade Owens, a professional athlete, currently has a contract that will pay him a large amount in the first year of his contract and smaller amounts thereafter. He and his agent have asked the team to restructure the contract. The team, though reluctant, obliged. Tirade and his agent came up with a counteroffer. What are the present values of each of the three alternatives below using a 14 percent discount rate? Which of the three has the highest present value? Year Current Contract Team’s Offer Counteroffer 1 $8,125,000 $4,000,000.00 $5,250,000.00 2 $3,650,000 $3,825,000.00 $7,550,000.00 3 $2,715,000 $3,850,000.00 $3,625,000.00 4 $1,822,250 $3,925,000.00 $2,800,000.00 Solution: Current Contract

SM 6-31

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

$8,125,000 $3,650,000 $2,715,000 $1,822,250 + + + (1.14) (1.14) 2 (1.14) 3 (1.14) 4 = $7,127,192.98 + $2,808,556.48 + $1,832,547.67 + $1,078,918.29 = $12,847,215.41 Team’s Offer $4,000,000 $3,825,000 $3,850,000 $3,925,000 PV = + + + (1.14) (1.14) 2 (1.14) 3 (1.14) 4 = $3,508,771.93 + $2,943,213.30 + $2,598,640.34 + $2,323,915.09 = $11,374,540.65 Counteroffer $5,250,000 $7,550,000 $3,625,000 $2,800,000 PV = + + + (1.14) (1.14) 2 (1.14) 3 (1.14) 4 = $4,605,263.16 + $5,809,479.84 + $2,446,771.75 + $1,657,824.78 = $14,519,339.52 The counteroffer has the best value for the player. PV =

LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.35

Gary Kornig will be 30 years old next year and wants to retire when he is 65. So far he has saved (1) $6,950 in an IRA account in which his money is earning 8.3 percent annually and (2) $5,000 in a money market account in which he is earning 5.25 percent annually. Gary wants to have $1 million when he retires. Starting next year, he plans to invest a fixed amount every year until he retires in a mutual fund in which he expects to earn 9 percent annually. How much will Gary have to invest every year to achieve his savings goal? Solution: Investment (1) Balance in IRA investment = PV = $6,950 Return on IRA account = i = 8.3% Time to retirement = n = 35 years Value of IRA at age 65 = FVIRA

FVIRA = PV  (1 + i ) n = $6,950  (1.083)35 = $113,235.03 Investment (2) Balance in money market investment = PV = $5,000

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Return on money market account = i = 5.25% Time to retirement = n = 35 years Value of money market at age 65 = FVMMA

FVMMA = PV  (1 + i ) n = $5,000  (1.0525)35 = $29,973.93 Target retirement balance = $1,000,000 Future value of current savings = $113,235.03 + $29,973.93 = $143,208.96 Amount needed to reach retirement target = FVA = $856,774.04 Annual payment needed to meet target = PMT Expected return from mutual fund = i = 9%

 (1 + i ) n − 1  FVA = PMT    i   PMT =

FVA $856,791.04 $856,791.04 = = n 215.711  (1 + i ) − 1   (1.09)35 − 1      i    0.09 

= $3, 971.94 LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.36 The top prize for the state lottery is $100,000,000. You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annual payment option. If you choose the annual payment option and win, you will receive $100,000,000 in 25 equal payments of $4,000,000─one payment today and one payment at the end of each of the next 24 years. If you choose the cash payment, you will receive a one-time lump sum payment of $59,194,567.18. If you can invest the proceeds and earn 6 percent, which option should you choose? Solution: You should choose the lump sum option. To see this, all you have to do is calculate the present value of the cash flows from the annual payment option using the 6 percent discount rate. Since the annual payment option is like a 25- year annuity due, this value is: PVA25 = CF × PV annuity factor

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= $4,000,000 × 12.7834 = $51,133,424.63Annuity value due = PVA25 × (1 + i) = $51,133,424.63 × 1.06 = $54,201,430.11 Since this is less than the $59,194,567.18 lump sum, you are better off taking the lump sum. LO 2 Bloomcode: Anlysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.37

At what interest rate would you be indifferent between the cash and annual payment options in problem 6.36? Solution: You would be indifferent if you could only earn 5 percent from your investments. With this discount rate, the present value of the cash flows from the annual payment option equals the $59,194,567.18 lump sum. PVA25 = CF × PV annuity factor = $4,000,000 × 14.0949 = $56,375,778.26 Annuity value due

= PVA25 × (1 + i) = $56,376,000 × 1.05 = $59,194,567.18 If you use your calculator or Excel to calculate the present value of the cash flows from the annual payment option you will get exactly $59,194,567.18. LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.38

Babu Baradwaj is saving for his son’s college tuition. His son is currently 11 years old and will begin college in seven years. Babu has an index fund investment of $7,500 that is earning 9.5 percent annually. Total expenses at the University of Maryland, where his son says he plans to go, currently total $15,000 per year, but are expected to grow at roughly 6 percent each year. Babu plans to invest in a mutual fund that will earn 11 percent annually to make up the difference between the college expenses and his current

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savings. In total, Babu will make seven equal investments with the first starting today and with the last being made a year before his son begins college. a. What will be the present value of the four years of college expenses at the time that Babu’s son starts college? Assume a discount rate of 5.5 percent. b. What will be the value of the index mutual fund when his son just starts college? c. What is the amount that Babu will have to have saved when his son turns 18 if Babu plans to cover all of his son’s college expenses? d. How much will Babu have to invest every year in order to have enough funds to cover all his son’s expenses? Solution: Annual cost of college tuition today (t = 0) = $15,000 Expected increase in annual tuition costs = g = 6% a. Four-year tuition costs (t = 7 to t = 10) Years from now Future value calculation Tuition costs 7 7 $15,000(1.06) $22,554.45 8 8 $15,000(1.06) $23,907.72 9 9 $15,000(1.06) $25,342.18 10 10 $15,000(1.06) $26,862.72 Discount rate = i = 5.5% Present value of tuition costs = PV $22,554.45 $23,907.72 $25,342.18 $26,862.72 PV = + + + (1.055) (1.055) 2 (1.055) 3 (1.055) 4 = $21,378.63 + $21,479.95 + $21,581.75 + $21,684.03 = $86,124.36 b. Future value of the index mutual fund at t = 7 Present value of index fund investment = PV = $7,500 Return on fund = i = 9.5% Future value of investment = FV

FV = PV  (1 + i ) n = $7,500  (1.095)7

= $14,156.64 Target savings needed at t = 7 PV of tuition costs – Future value of investment

= $86,124.36 – $14,156.64 = $71,967.72

Annual savings needed Return on fund = i = 11% Amount that needs to be saved = FVA = $71,967.72 Annuity payment needed = PMT

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FVA = PMT  PMT =

Solutions Manual

(1 + i ) n − 1  (1 + i ) i

FVA $71,967.72 $71,967.72 = = 7 (1 + i ) − 1 (1.11) − 1 9.7833  1.11  (1 + i )  (1.11) i 0.11 n

= $6, 627.21 LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.39

You are now 50 years old and plan to retire at age 65. You currently have a stock portfolio worth $150,000, a 401(k) retirement plan worth $250,000, and a money market account worth $50,000. Your stock portfolio is expected to provide annual returns of 12 percent, your 401(k) investment will earn 9.5 percent annually, and the money market account earns 5.25 percent, compounded monthly. a. If you do not save another penny, what will be the total value of your investments when you retire at age 65? b. Assume you plan to invest $12,000 every year in your 401(k) plan for the next 15 years (starting one year from now). How much will your investments be worth when you retire at age 65? c. Assume that you expect to live 25 years after you retire (until age 90). Today, at age 50, you take all of your investments and place them in an account that pays 8 percent (use the scenario from part b in which you continue saving). If you start withdrawing funds starting at age 66, how much can you withdraw every year (e.g., an ordinary annuity) and leave nothing in your account after a 25th and final withdrawal at age 90? d. You want your current investments, which are described in the problem statement, to support a perpetuity that starts a year from now. How much can you withdraw each year without touching your principal? Solution: a. Stock Portfolio Current value of stock portfolio = $150,000 Expected return on portfolio = i = 12% Time to retirement = n = 15 years Expected value of portfolio at age 65 = FVStock

FVStock = PV  (1 + i )15 = $150,000  (1.12)15 = $821,034.86

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410(k) Investment Current value of 410(k) portfolio = $250,000 Expected return on portfolio = i = 9.5% Time to retirement = n = 15 years Expected value of portfolio at age 65 = FV401k

FV401k = PV  (1 + i )15 = $250,000  (1.095)15 = $975,330.48 Money market account Current value of savings = $50,000 Expected return on portfolio = i = 5.25% Time to retirement = n = 15 years Frequency of compounding = m = 12 Expected value of portfolio at age 65 = FVMMA

i   FVMMA = PV   1 +   m

mn

1215

 0.0525  = $50,000   1 +  12  

= $50,000  2.1941 = $109,706.14 Total value of all three investments = $821,034.86 + $975,330.48 + $109,706.14 = $1,906,071.48 Planned annual investment in 401k plan = $12,000 Future value of annuity = FVA

 (1 + i ) n − 1 FVA n = PMT    i  

 (1.095)15 − 1 = $12,000    = $12,000  30.5402  0.095  = $366,482.77 Total investment amount at retirement = $1,906,071.48 + $366,482.77 = $2,272,554.25 Amount available at retirement = PVA = $2,272,554.25 Length of annuity = n = 25 Expected return on investment = i = 8% Annuity amount expected = PMT Using the PVA equation:

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1   1 − (1 + i ) n  PVA n = PMT    i     $2,272,554.25 $2,272,554.25 PMT = = 1  10.6748  1 − (1.08) 25    0.08     = $212,889.63 Each payment received for the next 25 years will be $212,889.63. Type of payment = Perpetuity Present value of perpetuity = PVA = $2,272,554.25 Expected return on investment = i = 8% PMT PV of Perpetuity = i PMT $2,272,553.75 = 0.08 PMT = $2,272,554.25  0.08

= $181,804.34 You could receive an annual payment of $181,804.34 forever. LO 1, LO 2, LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.40

Trevor Diaz wants to purchase a Mercedes Benz SL600 Roadster, which has an invoice price of $121,737 and a total cost of $129,482. Trevor plans to put down $20,000 and will pay the rest by taking on a 5.75 percent five-year bank loan. What is the monthly payment on this auto loan? Prepare an amortization table using Excel. Solution: Cost of new car = $129,482 Down payment = $20,000 Loan amount = $129,482 – $20,000 = $109,482 Interest rate on loan = i = 5.75% Term of loan = n = 5 years Frequency of payment = m = 12 Monthly payment on loan = PMT

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1− PVA n = PMT  PMT =

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1 (1 + i ) n i

$109, 482 $109, 482 = 1 52.0379 1− 125  0575  1 +  12   0.0575 12

= $2,103.89 LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.41

The Yan family buying a new 3,500-square-foot house in Muncie, Indiana, and will borrow $237,000 from Bank One at a rate of 6.375 percent for 15 years. What will be their monthly loan payment? Prepare an amortization schedule using Excel. Solution: Home loan amount = $237,000 Interest rate on loan = i = 6.375% Term of loan = n = 15 years Frequency of payment = m = 12 Monthly payment on loan = PMT 1 1− (1 + i ) n PVA n = PMT  i

PMT =

$237,000 1 1− 1215  0.06375  1 +  12   0.06375 12

$237,000 = $2, 048.27 115.7072

LO 2

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Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.42

Assume you will start working as soon as you graduate from college. You plan to start saving for your retirement on your 25th birthday and retire on your 65th birthday. After retirement, you expect to live at least until you are 85. You wish to be able to withdraw $40,000 (in today’s dollars) every year from the time of your retirement until you are 85 years old (i.e., for 20 years). The average inflation rate is likely to be 5 percent. a. Calculate the lump sum you need to have accumulated at age 65 to be able to draw the desired income. Assume that your annual return on your investment is likely to be 10 percent. b. What is the dollar amount you need to invest every year, starting at age 26 and ending at age 65 (i.e., for 40 years, to reach the target lump sum at age 65? c. Now answer questions a. and b. assuming the rate of return to be 8 percent per year, then again at 15 percent per year. d. Now assume you start investing for your retirement when you turn 30 years old and analyze the situation under rate of return assumptions of (i) 8 percent, (ii) 10 percent, and (iii) 15 percent. e. Repeat the analysis by assuming that you start investing only when you are 35 years old. Solution: RETIREMENT ANALYSIS SUMMARY INVESTMENT AGE = 25 INVESTMENT AGE = 30 Rate of Return Inflation rate Retirement Income Level Lump sum needed at age 65 Annuity payment needed

10%

15%

10%

INVESTMENT AGE = 35

15%

10%

15%

5% $40,000 $5,160,266

$4,353,087

$3,011,353

$5,160,266

$4,353,087

$3,011,353

$5,160,266

$4,353,087

$3,011,353

$19,919

$9,835

$1,693

$29,946

$16,062

$3,417

$45,552

$26,463

$6,927

LO 1, LO 2, LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Sample Test Problems 6.1

Freisinger, Inc., is expecting a new project to start paying off, beginning at the end of next year. It expects cash flows to be as follows: 0 7.8% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ $433,676 $478,452 $475,455 $478,326 $535,444

If Freisinger can reinvest these cash flows to earn a return of 7.8 percent, what is the future value of this cash flow stream at the end of five years? What is its present value? Solution: FV5= $433,676  (1.078) 4  + $478, 452  (1.078) 3  + $475, 455  (1.078) 2  + $478,326  (1.078)1  +$535, 444 = $585,653.08 + $599,369.52 + $552,518.65 + $515,635.43 + $535, 444 = $2, 788, 620.68

PV= $433, 676 /1.078 + $478, 452 / (1.078) 2  + $475, 455 / (1.078)3  + $478,326 / (1.078) 4  + [$535, 444 / (1.078)5 ] = $402, 296.85 + $411, 718.95 + $379,536.14 + $354, 200.32 + $367,807.22 = $1,915,559.47

LO: 1 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.2

Compare an annuity due with an ordinary annuity. The payments for both are made annually and are of the same dollar amounts. The two annuities also have the same duration in years and the same discount rate. Which of the following statements is /are correct? a. The present value of the ordinary annuity is greater. b. The present value of the annuity due is greater. c. The future value of the ordinary annuity is greater. d. The future value of the annuity due is greater.

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Solution: b and d are both correct The cash flows of the annuity due are received at the beginning of the period, resulting in less discounting and a higher PV and more compounding and a higher FV. LO: 2 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.3

You plan to set up an endowment at your alma mater that will fund $200,000 of scholarships each year indefinitely. If the principal (the amount you donate) can be invested at 5.5 percent, compounded annually, how much do you need to donate to the university today, so that the first scholarships can be awarded beginning one year from now? Solution: Annual payment needed = PMT = $200,000 Investment rate of return = i = 5.5% Term of payment = Perpetuity PMT $200,000 PV of Perpetuity = = Present value of investment needed = PV i 0.055 = $3,636,363.64 LO: 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.4

Annalise Genric wants to open a restaurant in a historic building. The property can be leased for 20 years, but not purchased. She believes her restaurant can generate a net cash flow of $76,000 the first year and expects an annual growth rate of 4 percent thereafter. If a discount rate of 15 percent is used to evaluate this business, what is the present value of the cash flows that it will generate? Solution: Length of lease = n = 20 years Next year’s net cash flow = CF1 = $76,000 Expected annual growth rate = g = 4% Required rate of return = i = 15%

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Present value of growing annuity = PVAn

PVAn =

 1 + g n    1.04  20  CF1 $76,000  1 −  =      1 −  (i − g )   1 + i   (0.15 − 0.04)   1.15  

= $690,909  0.86612 = $598,410.10 LO: 4 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.5

A credit card offers financing at an APR of 18 percent, with monthly compounding on outstanding charges. What is the effective annual rate (EAR)? Solution: Interest rate = i = 18% Frequency of compounding = m = 12 Effective annual rate = EAR m1

i    0.18  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.1956 − 1 = 0.1956, or19.56 percent

LO: 5 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

6.6

Thomas Nguyen currently has $10,000 in the bank earning interest of 6 percent per year, compounded monthly. If he needs $25,000 to purchase a car and can save an additional $100 a month stating at the end of this month, how long will it take him to accumulate the $25,000? Solution: months 0 5% 1 2 3 4 ? ├───────┼────────┼───────┼────────┤…………….

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$10,000

$100

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$100

$100 $25,000

Monthly payment = CF = $100 Present Value = PV = 10,000 Future Value = FV = 25,000 Annual rate of return = i = 6% Payments per year = m = 12 Type of annuity = Ordinary Annuity Using the FVA equation and the equation for the FV of a single amount: nm   i  nm  1 +  −1  i  m     FV = CF  + PV  1 +  = i    m   m  

  0.06 nm  nm  1 +  −1 12    + $ 10, 000  1 + 0.06  $25,000 = $100   0.06   12     12    0.06  $25, 000 = $20, 000  1 +  12  

n m

 0.06  − $20, 000 + $10, 000  1 +  12  

n m

 0.06  $45, 000 = $30, 000  1 +  12    $45, 000   0.06  ln  = n  m  ln 1 +   12    $30, 000  nm=

ln (1.5) = 81.3months ln (1.005 )

Solving for n × m yields: n × m = 81.3 months It will take Shannon 81.3 months or 6.8 years to save the $25,000. LO: 2 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Appendix: Deriving the Formula for the Present Value of an Ordinary Annuity In this chapter we showed that the formula for a perpetuity can be obtained from the formula for the present value of an ordinary annuity if n is set equal to ∞. It is also possible to go the other way. In other words, the present value of an ordinary annuity formula can be derived from the formula for a perpetuity. In fact, this is how the annuity formula was originally obtained. To see how this was done, assume that someone has offered to pay you $1 per year forever, beginning next year, but that, in return, you will have to pay that person $1 per year forever, beginning in year n + 1. Solution: In this problem, you will receive an annual payment that grows at a rate of g forever. In return, you will have to pay that person $1(1 + g)n each year forever, beginning in year n + 1. The cash flows that you will receive can be represented as in the following time line. 0 1 2 3 n-1 n n+1 n+2 ∞

Receive $1

$1(1+g) $1(1+g)2……$1(1+g)n-2 $1(1+g)n-1 $1(1+g)n

Pay $0 $0 $0 $0 $0 $1(1+g)n The first time line shows the cash flows for the perpetuity that you will receive. This perpetuity is worth: $1 CF PVRe ceive = = (i − g ) (i − g) The second time line shows the cash flows for the perpetuity that you will pay. The present value of what you owe is: $1  (1 + g) n CF  (1 + g) n (i - g) (i - g) PVOwe = = n (1 + i ) n (1 + i ) Notice that if you subtract, year-by-year, the cash flows you would pay from the cash flows you would receive, you get the cash flows for an n-year annuity. 0 1 2 3 n–1 n n+1 n+2 ∞

Difference $1 $1(1 + g) $1(1 + g)2………$1(1 + g)n-2 $1(1 + g)n-1 $0

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Therefore, the value of the offer equals the value of an n-year growing annuity. Solving for the difference between PVOwe from PVReceive ,we see that this is the same as Equation 6.5. CF(1 + g) n n CF CF   1 + g   i PVRe ceive − PVOwe = − =  1 −     (i - g) (1 + i ) n (i - g)   1 + i  

Problem 6A.1 In the chapter text, you saw that the formula for a growing perpetuity can be obtained from the formula for the present value of a growing annuity if n is set equal to ∞. It is also possible to go the other way. In other words, the present value of a growing annuity formula can be derived from the formula for a growing perpetuity. In fact, this is how Equation 6.5 was actually derived. Show how Equation 6.5 can be derived from Equation 6.6. Solution: LO: 4 Level:

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Chapter 7 Risk and Return Before You Go On Questions and Answers Section 7.1 Note to instructor: There are no questions for this section.

Section 7.2 1.

What are the two components of a total holding period return? Capital appreciation and income. This can be seen in Equation 7.1.

How is the expected return on an investment calculated? The expected return is calculated as a weighted-average of the possible returns on an investment (outcomes) where the weights are the probabilities that each of the possible returns will be realized.

Section 7.3 1.

What is the relation between the variance and the standard deviation? The standard deviation is the square root of the variance. Alternatively, the variance equals the standard deviation squared.

What relation do we generally observe between risk and return when we examine historical returns? Investments with higher risks tend to have higher returns. This is illustrated in Exhibit 6.3.

How would we expect the standard deviation of the return on an individual stock to compare with the standard deviation of the return on a stock index? We would expect the standard deviation of the return on an individual stock to be greater than the standard deviation of the return on a stock index. For an illustration, see Exhibit 6.4.

Section 7.4 1.

What does the coefficient of variation tell us, and how is it related to the Sharpe Ratio?

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The coefficient of variation is a measure of risk per unit of return. It tells us the amount of risk, defined as the standard deviation of returns, associated with each 1 percent of expected return for an asset. A larger coefficient of variation indicates greater risk for each 1 percent of return. The Sharpe ratio differs from the coefficient of variation in two ways. First, instead of using the total return in the calculation, with the Sharpe ratio we use the difference between the total return and the risk free rate. Second, the Sharpe ratio is the inverse of the coefficient of variation ratio that would be calculated using this adjusted return. Computing the inverse of the coefficient of variation yields a measure return per unit of risk, which some investors find more intuitive than a measure of risk for each 1 percent of return. 2.

What are the two components of total risk? The two components of total risk are unique risk and systematic risk. Unique risk is risk that is unique to a particular asset. This is the risk that can be eliminated through diversification. Systematic risk is risk that is common to all assets and cannot be diversified away.

Why does the total risk of a portfolio not approach zero as the number of assets in a portfolio becomes very large? Because the systematic risk associated with the individual assets cannot be diversified away. With a very large number of assets, the total risk of a portfolio will approach the weighted average (where the weights are the fractions of total portfolio value represented by each asset) of the systematic risks associated with each asset.

Section 7.5 1.

Why are returns on the stock market used as a benchmark in measuring systematic risk? Because the stock market portfolio is the most diversified portfolio for which good return data are available, it is the portfolio that both comes closest to eliminating all unique risk and has good return data. This makes the returns on the stock market a practical choice as a benchmark for measuring the systematic risk of individual assets.

How is beta estimated? Beta is estimated using regression analysis in which returns on an individual asset are regressed against returns on the market. Beta is the slope of the regression line. This is illustrated in Exhibit 6.11.

How would you interpret a beta of 1.5 for an asset? A beta of 0.75?

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A beta of 1.5 indicates that the asset has 1.5 times as much systematic risk as the market. A beta of 0.75 indicates that the asset has 75 percent as much systematic risk as the market.

Section 7.6 Note to instructor: There are no questions for this section.

Section 7.7 1.

How is the expected return on an asset related to its systematic risk? CAPM tells us that there is a linear relation between expected return and systematic risk. With zero systematic risk, the expected return equals the risk-free rate. For systematic risk greater than zero, the expected return on an asset increases as its systematic risk increases and this increase is linear. This relation is illustrated in Equation 7.9.

What name is given to the relation between risk and expected return implied by the CAPM? This plot is called the Security Market Line, or SML, and is illustrated in Exhibit 7.11.

If an asset’s expected return does not plot on the line in question 2 above, what does that imply about its price? If the expected return on an asset does not plot on the SML, then this indicates that the expected return on the asset is either too low or too high in view of its systematic risk. If the asset plots below the SML, the expected return is too low and the price is too high. If the asset plots above the SML, the expected return is too high and its price is too low.

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Self-Study Problems 7.1

Kaaran made a friendly wager with a colleague that involves the result from flipping a coin. If heads comes up, Kaaran must pay her colleague $15; otherwise, her colleague will pay Kaaran $15. What is Kaaran’s expected cash flow, and what is the variance of that cash flow if the coin has an equal probability of coming up heads or tails? Suppose Kaaran’s colleague is willing to handicap the bet by paying her $20 if the coin toss results in tails. If everything else remains the same, what are Kaaran’s expected cash flow and the variance of that cash flow? Solution: Part 1: E(cash flow) = (0.5 × –$15) + (0.5 × $15) = 0 σ2cash flow = [0.5 × (–$15 - $0)2] + [0.5 × ($15 – $0)2] = $225 Part 2: E(cash flow) = (0.5 × –$15) + (0.5 × $20) = $2.50 σ2cash flow = [0.5 × (–$15 – $2.50)2] + [0.5 × ($20 – $2.50)2] = $306.25

7.2

You know that the price of CFI, Inc., stock will be $12 exactly one year from today. Today the price of the stock is $11. Describe what must happen to the price of CFI, Inc., today in order for an investor to generate a 20 percent return over the next year. Assume that CFI does not pay dividends. Solution: The expected return for CFI based on today’s stock price is ($12 – $11)/$11 = 9.09 percent, which is lower than 20 percent. Since the stock price one year from today is fixed, then the only way that you will generate a 20 percent return is if the price of the stock drops today. Consequently, the price of the stock today must drop to $10. It is found by solving the following: 0.2 = ($12 – x)/ x, or x = $10.

7.3

The expected value of a normal distribution of prices for a stock is $50. If you are 90 percent sure that the price of the stock will be between $40 and $60, then what is the variance of the prices for the stock? Solution: Since you know that 1.645 standard deviations around the expected return captures 90 percent of the distribution, you can set up either of the following equations: $40 = $50 – 1.645σ or $60 = $50 + 1.645σ and solve for σ. Doing this with either equation yields σ = $6.079 and σ2 = 36.954

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7.4

You must choose between investing in stock A and stock B. You have already used CAPM to calculate the rate of return you should expect to receive for each stock given their systematic risk and decided that the expected return for both exceeds that predicted by CAPM by the same amount. In other words, both are equally attractive investments for a diversified investor. However, since you are still in school and do not have a lot of money, your investment portfolio is not diversified. You have decided to invest in the stock that has the highest expected return per unit of total risk. If the expected return and standard deviation of returns for stock A are 10 percent and 25 percent, respectively, and the expected return and standard deviation of returns for stock B are 15 percent and 40 percent, respectively, which should you choose? Assume that the risk free rate is 5 percent. Solution: A comparison of the Sharpe ratios for the two stocks will tell you which has the highest expected return per unit of total risk. E(R A ) - R rf 0.10 − 0.05 SA = = = 0.20 σRA 0.25

SB =

E(R B ) - R rf 0.15 − 0.05 = = 0.25 σRB 0.40

Stock B has the highest expected return per unit of risk.

7.5

CSB, Inc., has a beta of 1.35. If the expected market return is 14.5 percent and the risk-free rate is 5.5 percent, what is the appropriate required return of CSB (using the CAPM)? Solution: E(RCSB) = Rrf + CSB[E(RM) - Rrf] = 0.055 + 1.35 × (0.145 - 0.055)] = 0.1765 or, 17.65%

Discussion Questions 7.1

Suppose that you know the risk and the expected return for two stocks. Discuss the process you might utilize to determine which of the two stocks is a better buy. You may assume that the two stocks will be the only assets held in your portfolio. You should be looking to maximize your expected return on an investment given the level of risk that such an investment requires the investor to bear. Therefore, you should compare the expected return and risk associated with each of the two stocks. If the stocks

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have the same expected return, then choose the stock with the lower risk. If the stocks have the same risk, then choose the stock with the greatest expected return. If the expected return and risk of the two assets have no common level, perhaps you should compare the ratio of the risk/expected return to see which stock contains the least risk per unit of expected return. LO: 1 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 7.2

What is the difference between the expected rate of return and the required rate of return? What does it mean if they are different for a particular asset at a particular point in time? The required rate of return is the rate of return that investors require to compensate them for the risk associated with an investment. The expected return will not necessarily equal the required rate of return. The expected return can be lower, in which case the return will not be sufficient to compensate the investor for the risk associated with the investment if the expected return is realized. It can also be higher, in which case the expected return will be greater than that necessary to compensate the investor for the riskiness of the asset.

LO: 6 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 7.3

Suppose that the standard deviation of the returns on the shares of stock at two different companies is exactly the same. Does this mean that the required rate of return will be the same for these two stocks? How might the required rate of return on the stock of a third company be greater than the required rates of return on the stocks of the first two companies even if the standard deviation of the returns of the third company’s stock is lower? No. Because some risk can be diversified away, it is possible that two stocks with the same standard deviation of returns can have different required rates of return. One of these stocks can have a higher systematic risk than the other stock and, therefore, a higher required rate of return. The third stock can have a higher required rate of return if its systematic risk is greater than the systematic risk of the stock in the other two companies. LO: 4

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Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

7.4

The correlation between stocks A and B is 0.50, while the correlation between stocks A and C is –0.5. You already own stock A and are thinking of buying either stock B or stock C. If you want your portfolio to have the lowest possible risk, would you buy stock B or C? Would you expect the stock you choose to affect the return that you earn on your portfolio? You would buy stock C because it would result in your portfolio having a lower beta. If you buy stock C, the required return for your portfolio would be lower than the required return would be if you bought stock B. If the expected returns on stocks C and B equal their required returns, then you would expect your portfolio to earn less with stock C.

LO: 5 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

7.5

The idea that we can know the return on a security for each possible outcome is overly simplistic. However, even though we cannot possibly predict all possible outcomes, this fact has little bearing on the risk-free return. Explain why. The risk-free security delivers the same return in all states of the world. Even though we do not know all of the possible states of the world in future periods, we do know that the U.S. government will be able to repay its borrowing in every state of the world. Therefore, the shortcoming of the model does not affect the risk-free security’s return.

LO: 6 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 7.6

Which investment category included in Exhibit 7.3 has shown the greatest degree of risk in the United States since 1926? Explain why that makes sense in a world where

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the value of an asset in this investment category is likely to be more sensitive to changes in market conditions than is the price of a corporate bond. Small stocks have generally been riskier than large stocks, long-term corporate bonds, long-term government bonds, intermediate government bonds, and short-term government bonds. The explanation for this can be best understood if we realize that small stocks will be affected to a greater extent than the list of investments above by either good or bad states of the world. These good and bad effects translate into a distribution with greater spread or greater risk than the other investments. LO: 4 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Measurement 7.7

You are concerned about one of the investments in your fully diversified portfolio. You just have an uneasy feeling about the CFO, Iam Shifty, of that particular firm. You do believe, however, that the firm makes a good product and that it is appropriately priced by the market. Should you be concerned about the effect on your portfolio if Shifty embezzles a portion of the firm’s cash? The risk of Shifty embezzling is a nonsystematic risk that will most likely be offset by a more fortunate event affecting another holding in your portfolio. Therefore, Shifty’s actions should not affect the risk that you bear by investing in your diversified portfolio (systematic risk). LO: 5, 6 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Measurement 7.8

The CAPM is used to price the risk (estimate the expected return) for any asset. Our examples have focused on stocks, but we could also use CAPM to estimate the expected rate of return for bonds. Explain why. A firm’s ability to repay its debt obligations will be affected in a very similar, and yet lessened, way than the firm’s stock will be affected. That is, systematic and nonsystematic factors will also affect returns for debt securities. However, if held in a diversified portfolio, then only the systematic risk component will be borne and then compensated for bearing. Therefore, we can use the CAPM to price debt securities.

LO: 7 Level: Intermediate

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Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 7.9

In recent years, investors have agreed that the market portfolio consists of more than just a group of U.S. stocks and bonds. If you are an investor who invests in only U.S. stocks and bonds, describe the effects on the risk in your portfolio. If the market portfolio is composed of all assets, then the U.S.-only portfolio will probably have a small amount of nonsystematic risk that is not providing return compensation for that risk. Therefore, the portfolio is bearing too much risk given its expected returns. LO: 5, 6 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement 7.10

You may have heard the statement that you should not include your home as an asset in your investment portfolio. Assume that your house will comprise up to 75 percent of your assets in the early part of your investment life. Evaluate the implications of omitting it when calculating the risk of your overall investment portfolio. From a systematic risk measurement perspective, omitting the beta of your real estate investment, which does not have a beta equal to zero, could have a serious impact on your portfolio’s perceived systematic risk. In a volatile real estate market, you could be understating the risk in your portfolio, and in a flat real estate market, you could be overestimating the risk in your portfolio.

LO: 7 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Measurement

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Questions and Problems BASIC 7.1

Returns: Describe the difference between a total holding period return and an expected return. LO 2, LO3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decision AICPA: Measurement Solution: A holding period return is the total return over some investment or “holding” period. It consists of a capital appreciation component and an income component. A holding period return reflects past performance. An expected return is a return that is based on the probability-weighted average of the possible returns from an investment. It describes a possible return (or even a return that may not be possible) for a yet- to-occur investment period.

7.2

Expected returns: John is watching an old game show rerun on television called Let’s Make a Deal in which the contestant chooses a prize behind one of two curtains. Behind one of the curtains is a gag prize worth $150, and behind the other is a round-the-world trip worth $7,200. The producer of the game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is the expected value of the selection, and what is the standard deviation of that selection?

LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution: E(prize) = (0 .75 × $150) + (0.25 × $7,200) = $1,912.50 σ2prize = (0.75 × ($150 – $1,912.50)2) + (0.25 × ($7,200 – $1,912.50)2 ) = $9,319,218.75 σprize = ($9,319,218.75)1/2 = $3,052.74

7.3

Expected returns: You have chosen biology as your college major because you would like to be a medical doctor. However, you find that the probability of being accepted to

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medical school is about 10 percent. If you are accepted to medical school, then your starting salary when you graduate will be $300,000 per year. However, if you are not accepted, then you would choose to work in a zoo, where you will earn $40,000 per year. Without considering the additional years you would spend in school if you study medicine or the time value of money, what is your expected starting salary as well as the standard deviation of that starting salary? LO 3 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution: E(salary) = 0.9($40,000) + (0.1) ($300,000) = $66,000 σ2salary = 0.9($40,000 – $66,000)2 + (0.1) ($300,000 – $66,000)2 = $6,084,000,000 σsalary = ($6,084,000,000)1/2 = $78,000

7.4

Historical market: Describe the general relation between risk and return that we observe in the historical bond and stock market data. LO 3, LO4 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: The general axiom that the greater the risk, the greater the return describes the historical returns of the bond and stock market. If we look at Exhibit 6.3 in the text, we see that small stocks have averaged the greatest returns but that they also have the greatest standard deviation for the returns. When compared to large stocks, the average return and standard deviation of the small stocks are greater. Large stock average returns and standard deviation numbers are larger than those of long-term government bonds, which are larger than those of intermediate-term government bonds, which in turn are larger than those of U.S. Treasury bills. The comparison shows that the riskier the investment category, the greater the average return as well as standard deviation of returns.

7.5

Single-asset portfolios: Stocks A, B, and C have expected returns of 15 percent, 15 percent, and 12 percent, respectively, while their standard deviations are 45 percent, 30 percent, and 30 percent, respectively. If you were considering the purchase of each of these stocks as the only holding in your portfolio and the risk free rate is 0 percent, which stock should you choose?

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LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution: Since the holding will be made in a completely undiversified portfolio, then we can calculate the risk per unit of return for each stock, the coefficient of variation, and choose the stock with the lowest value. CV(RA) = 0.45/0.15 = 3.0 CV(RB) = 0.30/0.15 = 2.0===> Choose B CV(RC) = 0.30/0.12 = 2.5 Alternatively, we could have noted that the expected return for A and B was the same, with A having a greater degree of risk. B and C have the same degree of risk, but B has a greater expected return. This would lead you to the conclusion, just as our coefficient of variation calculations did, that Stock B is superior.

7.6

Diversification: Describe how investing in more than one asset can reduce risk through diversification.

LO 5 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Measurement Solution: An investor can reduce the risk of his or her investments by investing in two or more assets whose values do not always move in the same direction at the same time. This is because the movements in the values of the different investments will partially cancel each other out.

7.7 Systematic risk: Define systematic risk. LO 6 Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Measurement Solution: Risk that cannot be diversified away is systematic risk. It is the only type of risk that exists in a diversified portfolio, and it is the only type of risk that is rewarded in asset markets. Copyright © 2015 John Wiley & Sons, Inc.

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Measuring systematic risk: Susan is expecting the returns on the market portfolio to be negative in the near term. Since she is managing a stock mutual fund, she must remain invested in a portfolio of stocks. However, she is allowed to adjust the beta of her portfolio. What kind of beta would you recommend for Susan’s portfolio?

LO 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: If we confine our analysis to portfolios with positive beta values, and since beta describes how much and what direction our portfolio is expected to vary with the market portfolio, then Susan should construct a very low beta portfolio. In that case, Susan’s portfolio is not expected to have losses quite as large as that of the market portfolio. A large beta portfolio would have larger losses than that of the market portfolio. If Susan could construct a negative beta portfolio, then she would like to construct as negative a portfolio beta as possible.

7.9

Measuring systematic risk: Describe and justify what the value of the beta of a U.S. Treasury bill should be.

LO 6 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: Since the beta of any asset is the slope of the line of best fit for the plot of an asset against that of the market return, then we can use that logic to help us understand the beta of a Tbill. If we purchased a T-bill five years ago and held the same T-bill through each of the last 60 months, then the return for each of those 60 months would be exactly the same. Therefore, the vertical axis coordinates of each of the monthly returns would have the same value and the slope (beta) of the line of best fit would be zero. The meaning of a beta of zero means that our T-bill has no systematic risk. That is logically given that we know that a T-bill has no risk at all since it is a riskless asset.

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Measuring systematic risk: If the expected rate of return for the market is not much greater than the risk-free rate of return, what does this suggest about the general level of compensation for bearing systematic risk?

LO 6 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: Such a situation suggests that return compensation for investing in an asset is determined more by the risk-free return than by the market’s compensation for bearing systematic risk. This means that the price for bearing systematic risk is very low. This may be caused by a very low perceived level of risk in the market or by an abundance of funds in the market seeking to be invested in risky assets.

7.11 CAPM: Describe the Capital Asset Pricing Model (CAPM) and what it tells us. LO 7 Bloomcode: Knkowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: The CAPM describes the relation between systematic risk and the expected return. The model tells us that the expected return on an asset with no systematic risk equals the riskfree rate. As systematic risk increases, the expected return increases linearly with beta. The CAPM is written as E(Ri) = Rrf + β i(E(Rm) – Rrf) .

7.12

The Security market line: If the expected return on the market is 10 percent and the risk-free rate is 4 percent, what is the expected return for a stock with a beta equal to 1.5? What is the market risk premium?

LO 7 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: Following the CAPM prediction: E(Ri) = Rrf + β (E(Rm) – Rrf) = 0.04 + 1.5 × (0.1 – 0.04) = 0.13 The market risk premium is (E(Rm) – Rrf) = 0.06

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INTERMEDIATE 7.13

Expected returns: Jose is thinking about purchasing a soft drink machine and placing it in a business office. He knows that there is a 5 percent probability that someone who walks by the machine will make a purchase from the machine, and he knows that the profit on each soft drink sold is $0.10. If Jose expects a thousand people per day to pass by the machine and requires a complete return of his investment in one year, then what is the maximum price that he should be willing to pay for the soft drink machine? Assume 250 working days in a year, and ignore taxes and the time value of money.

LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Measurement Solution: E(Revenue) = 1,000 × 0.05 x $.10 × 250 days = $1,250 Therefore, the most Jose should pay for the machine is $1,250.

7.14

Interpreting the variance and standard deviation: The distribution of grades in an introductory finance class is normally distributed, with an expected grade of 75. If the standard deviation of grades is 7, in what range would you expect 95 percent of the grades to fall?

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution: 95% is 1.960 standard deviations from the mean. Thus, the range can be determined as: 75 ± (1.960 × (7)) So, the lower end is: 75 – (1.960 × (7)) = 61.28 And the upper end is: 75 + (1.960 × (7)) = 88.72 So, 95 percent of the grades should fall between 61.28 and 88.72.

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Calculating the variance and standard deviation: Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.4, 0.5, and 0.1, respectively, then what are the expected return and the standard deviation of the return on Kate’s investment?

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution: E(Ri) = (0.4)(0.3) + (0.5) (0.1) + (0.1) (–.25) = 0.145 σ2return = (0.4)(0.3 – 0.145)2 + (0.5) (0.1 – 0.145)2 + (0.1) (–0.25 – 0.145)2 = 0.02623 σreturn = (0.02623)1/2 = 0.16194 rounded to 0.162

7.16

Calculating the variance and standard deviation: Barbara is considering investing in a company’s stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below, find the expected return and the standard deviation of the return on Barbara’s investment. Probability Return Boom 0.1 25.00% Good 0.4 15.00% Level 0.3 10.00% Slump 0.2 -5.00%

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution: E(Ri) = 0.1 × (0.25) + (0.4) × (0.15) + (0.3) × (0.1) + (0.2) (–0.05) = 0.105 σ2return = 0.1 × (0.25 – 0.105)2 + (0.4) × (0.15 – 0.105)2 + (0.3) × (0.1 – 0.105)2 + (0.2) × (–0.05 – 0.105)2

= 0.00773

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σreturn = (0.00773)1/2 = 0.08789

7.17

Calculating the variance and standard deviation: Ben would like to invest in gold and is aware that the returns on such an investment can be quite volatile. Use the following table of states, probabilities, and returns to determine the expected return and the standard deviation of the return on Ben’s gold investment. Probability Return Boom 0.1 40.00% Good 0.2 30.00% OK 0.3 15.00% Level 0.2 2.00% Slump 0.2 -12.00%

LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution E(Ri) = 0.1 × (0.4) + (0.2) × (0.3) + (0.3) × (0.15) + (0.2) × (0.02) + (0.2) × (–0.12) = 0.125 σ2return = 0.1 × (0.4 – 0.125)2 + (0.2) × (0.3 – 0.125)2 + (0.3) × (0.15 – 0.125)2 + (0.2) × (0.02 – 0.125)2 + (0.2) × (–0.12 – 0.125)2 = 0.02809 σreturn = (0.02809)1/2 = 0.16759 rounded to 0.168

7.18

Single-asset portfolios: Using the information from Problems 7.15, 7.16, and 7.17, calculate the coefficient of variation for each of the investments in those problems. LO 3, LO 4 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution: Coefficient of variation = σReturn / E(Ri) Problem 15: 0.16194/0.145 = 1.11684 (using the exact values rather than the printed) Problem 16: 0.08789/0.105 = 0.83707 (using the exact values rather than the printed) Problem 17: 0.16759/0.125 = 1.34069 (using the exact values rather than the printed)

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Portfolios with more than one asset: Emmy is analyzing a two-stock portfolio that consists of a utility stock and a commodity stock. She knows that the return on the utility stock has a standard deviation of 40 percent and the return on the commodity stock has a standard deviation of 30 percent. However, she does not know the exact covariance in the returns of the two stocks. Emmy would like to plot the variance of the portfolio for each of three cases—covariance of 0.12, 0, and –0.12—in order to understand what the variance of the portfolio would be for a range of covariances. Do the calculation for all three cases (0.12, 0 and –0.12), assuming an equal proportion of each stock in the portfolio.

LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: Var ( R2 asset port ) = x12 12 + x 22 22 + 2 x1 x 2 1, 2 Case 1, σ1,2 = 0.12: (0.5)2 × (0.4)2 + (0.5)2 × (0.3)2 + 2 × (0.5) × (0.5) × (0.12) = 0.1225 Case 2, σ1,2 = 0.0: (0.5)2 × (0.4)2 + (0.5)2 × (0.3)2 + 2 × (0.5) × (0.5) × (0.0) = 0.0625 Case 3, σ1,2 = -0.12: (0.5)2 × (0.4)2 + (0.5)2 × (0.3)2 + 2 × (0.5) × (0.5) × (-0.12) = 0.0025

7.20 Portfolios with more than one asset: Given the returns and probabilities for the three possible states listed below, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 11.75 percent and 18 percent, respectively. Probability Return on A Return on B Good 0.35 0.30 0.50 OK 0.50 0.10 0.10 Poor 0.15 -0.25 -0.30 LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution:

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Cov(R A , R B ) = AB = 0.35  (0.3 − 0.1175)  (0.5 − 0.18) + 0.5  (0.1 − 0.1175)  (0.1 − 0.18) + 0.15  ( −0.25 − 0.1175)  ( −0.3 − 0.18) = 0.0476 7.21

Compensation for bearing systematic risk: You have constructed a diversified portfolio of stocks such that there is no unsystematic risk. Explain why the expected return of that portfolio should be greater than the expected return of a risk-free security.

LO 6 Bloomcode: Comprehension AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution: Your portfolio contains no unsystematic risk but it does contain systematic risk. Therefore, the market should compensate the holder of this portfolio for the systematic risk that the investor bears. A risk-free security has no risk and therefore requires no compensation for risk bearing. The expected return of your portfolio should therefore be greater than the return of the risk-free security.

7.22

Compensation for bearing systematic risk: Write out the equation for the covariance in the returns of two assets, Asset 1 and Asset 2. Using that equation, explain the easiest way for the two asset returns to have a covariance of zero.

LO 6 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution:

Cov(Return1 , Return 2 ) =  R12 n

(

=  p i  (Return1,i − E(Return1 )   (Return 2,i − E(Return 2 )  i =1

)

We know that all state probabilities must be greater than zero, and thus the source of a zero covariance cannot be from the state probabilities. The easiest way for the entire probability weighted sum to equal zero is for one of the assets, say Number 1(2), to have a value in all states j that is equal to the expected return of Number 1(2). Another way of saying that is for one of the assets to have a constant return in all states. If that occurs, then the second term in the equation will always be equal to zero, causing the sum, or covariance, to be zero.

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Compensation for bearing systematic risk: Evaluate the following statement: “By fully diversifying a portfolio, such as by buying every asset in the market, we can completely eliminate all types of risk, thereby creating a synthetic Treasury bill.”

LO 6 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: The statement is false. A portfolio of all assets would only eliminate unsystematic risk. The systematic risk would remain. If you could eliminate both systematic and unsystematic risk, the expected rate of return on the market portfolio would be equal to the risk-free rate of return, and we know that this is not true.

7.24

CAPM: Damien knows that the beta of his portfolio is equal to 1, but he does not know the risk-free rate of return or the market risk premium. He also knows that the expected return on the market is 8 percent. What is the expected return on Damien’s portfolio?

LO 7 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: Following the CAPM prediction: E(Ri) = Rrf + β (E(Rm) – Rrf) = Rrf + E(Rm) – Rrf = E(Rm) = 0.08 = 8.0%

7.25

CAPM: In February 2014 the risk free rate was 4.75 percent, the market risk premium was 6 percent and the beta for Twitter stock was 1.31. What is the expected return that was consistent with the systematic risk associated with the returns on Twitter stock?

LO 7 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: From Equation 7.10: E(RTwitter stock) = Rrf + βTwitter stock[E(Rm) - Rrf] E(RTwitter stock) = 0.0475 + 1.31[0.06] E(RTwitter stock) = 0.0475 + 0.0786 = 0.1261, or 12.61%

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CAPM: The market risk premium is 6 percent, and the risk-free rate is 5 percent. If the expected return on a bond is 6.5 percent, what is its beta?

LO 7 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: From Equation 7.10, we can calculate the beta of the bond as: E(Rbond) = Rrf + β bond × [E(Rm) - Rrf] 0.065 = 0.050 + β bond × 0.06 β bond = (0.065 – 0.050)/0.060 = 0.25

ADVANCED

7.27

David is going to purchase two stocks to form the initial holdings in his portfolio. Iron stock has an expected return of 15 percent, while Copper stock has an expected return of 20 percent. If David plans to invest 30 percent of his funds in Iron and the remainder in Copper, what will be the expected return from his portfolio? What if David invests 70 percent of his funds in Iron stock?

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: Part 1: E(Rport) = (0.3) × (0.15) + (0.7) × (0.2) = 0.185 = 18.5% Part 2: E(Rport) = (0.7) × (0.15) + (0.3) × (0.2) = 0.165 = 16.5%

Peter knows that the covariance in the return on two assets is –0.0025. Without knowing the expected return of the two assets, explain what that covariance means. LO 3, LO 5 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Measurement 7.28

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Solution: The covariance measure is dependent on the expected return of the two assets but in question without knowingthe expected return of the two assets, it is difficult to characterize the scale of the covariance. However, since the covariance is negative, we can say that generally the two assets move in opposite directions, with respect to their own means, from each other in given states of nature.

7.29

In order to expect that it will fund her retirement, Glenda needs her portfolio to have an expected return of 12 percent per year over the next 30 years. She has decided to invest in Stocks 1, 2, and 3, with 25 percent in Stock 1, 50 percent in Stock 2, and 25 percent in Stock 3. If Stocks 1 and 2 have expected returns of 9 percent and 10 percent per year, respectively, then what is the minimum expected annual return for Stock 3 that is likely to enable Glenda to achieve her investment requirement? LO 3, LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: The formula for the expected return of a three-stock portfolio is: E ( R3 asset port ) = x1 E ( R1 ) + x2 E ( R2 ) + x3 E ( R3 ) Therefore, we can solve as in the following: 0.12 = 0.25 × (0.09) + 0.5 × (0.1) + 0.25 × E(R3) E(R3) = 0.19 or 19.0%

7.30

Tonalli is putting together a portfolio of 10 stocks in equal proportions. What is the relative importance of the variance for each stock versus the covariance for the pairs of stocks in her portfolio? For this exercise, ignore the actual values of the variance and covariance terms and explain their importance conceptually. LO 4, LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: The variance of the portfolio will be composed of 10 (n = 10) individual stock variance terms and 45 ((n2 –n)/2) covariance terms (really 90). Therefore, the vast majority of the portfolio variance calculation will be determined by the covariance terms of the portfolio in most cases.

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7.31

Explain why investors who have diversified their portfolios will determine the price and, consequently, the expected return on an asset. LO 3, LO 5 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Measurement Solution: If all investors require returns that compensate them for the level of risk that they bear, then undiversified investors will require a greater return for a given investment than diversified investors will. In other words, diversified investors will be willing to pay a higher price for an asset than will undiversified investors. Therefore, a diversified investor is the marginal investor whose purchase will determine the price, and therefore the expected return for an asset.

7.32

Brad is about to purchase an additional asset for his well-diversified portfolio. He notices that when he plots the historical returns of the asset against those of the market portfolio, the line of best fit tends to have a large amount of prediction error for each data point (the scatter plot is not very tight around the line of best fit). Do you think that this will have a large or a small impact on the beta of the asset? Explain your opinion.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: It will have no effect on the beta of the asset. The beta measures only the systematic risk or variation in the returns of the asset. The prediction error reflects the nonsystematic risk inherent in the returns of the asset and will consequently not affect the beta of the asset.

7.33

Draw the Security Market Line (SML) for the case where the market risk premium is 5 percent and the risk-free rate is 7 percent. Now suppose an asset has a beta of –1.0 and an expected return of 4 percent. Plot it on your graph. Is the security properly priced? If not, explain what we might expect to happen to the price of this security in the market. Next, suppose another asset has a beta of 3.0 and an expected return of 20 percent. Plot it on the graph. Is this security properly priced? If not, explain what we might expect to happen to the price of this security in the market.

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LO 7 Bloomcode: Application AASCB: Analytic IMA: Quantitative Methods AICPA: Measurement Solution: The Security Market Line (SML) shows the relationship between an asset’s expected return and its beta. We know the market has a beta of one, and we know the risk-free rate has a beta of zero. The risk-free rate of return is 7 percent, and the market is expected to return 5 percent more than this. Therefore, the expected rate of return for the market (a beta one asset) is 12 percent. To draw this SML, we need only connect the dots:

Expected Return

18% 15% 12% 9% 6% 3% 0% 0

Beta

We can see from the following diagram that an asset with expected return of 4 percent and a beta of –1.0 is underpriced (its expected return is too high). As the market becomes aware of this underpricing, investors will purchase the asset, bidding up its price until its expected return falls on the SML. (Recall that as the initial purchase price of an asset increases, the expected return from purchasing the asset will decrease because you are paying a higher initial cost for the asset.)

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As we can see from the following diagram, an asset with a beta of 3.0 should have an 18%

Expected Return

15%

The investment will fall here in this plot

12%

0% -1

Beta

expected return of 7% + (3)(5%) = 22%. The asset only has an expected return of 20 percent. Therefore, this asset is overpriced. Demand for this asset will be low, driving down its market price, until the asset’s expected return falls on the SML. 23%

Expected Return

18%

14%

The investment will fall here in this plot

0% 0

Beta

7.34

If the CAPM describes the relation between systematic risk and expected returns, can both an individual asset and the market portfolio of all risky assets have negative expected real rates of return? Why or why not?

LO7 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: A negative expected real rate of return implies that the expected total rate of return is less than the risk-free rate.

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1) It is possible for the beta of an individual stock to be negative. Therefore, from CAPM, E[Ri] = Rrf + βi × [E(Rm) - Rrf)], it is also possible for a share of stock to have a negative expected real rate of return. 2) It is not possible for the market portfolio to have a negative expected real rate of return since the beta for the market equals 1.

7.35

You have been provided the following data on the securities of three firms and the market: Security E[Ri] σRi βi  Stock A 0.15 1.0 1.5 Stock B 0.15 0.18 0.5 Stock C 0.10 0.02 0.5 Market portfolio 0.10 0.04 Treasury bills 0.05 0 Assume the CAPM and SML are true and fill in the missing values in the table. Would you invest in the stock of any of the three firms? If so, which one(s) and why?

LO 7 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: 1) The missing values in the table are: A =  RA,M (RA )  RM = 1.0( RA ) (0.04)

RA = 0.06  B =  RB,M ( RB )  RM = 0.5(0.18) (0.04) = 2.25 C =  RC,M (RC )  RM =  RC,M ( 0.02 0.04 )

 RC,M = 1.00  R M ,M = 1.00;  M = 1.00

 R T − bill ,M = 0; T −bill = 0 2) Using Equation 7.10 you can calculate the expected returns for the different shares: E(RA) = 0.05 + [1.5 × (0.10 - 0.05)] = 0.125, or 12.5%

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E(RB) = 0.05 + [2.25 × (0.10 - 0.05)] = 0.1625, or 16.25% E(RC) = 0.05 + [0.5 × (0.10 - 0.05)] = 0.075, or 7.5% A comparison of the expected returns that are given in the table above,with the returns that CAPM predicts (which are calculated above), indicates that you should buy stocks A and C and avoid stock B.

Sample Test Problems INTERMEDIATE 7.1

Given the following information from Capstone Corporation, what price would CAPM predict that the company’s stock will trade for 1 year from today. Assume that the risk free rate is 3 percent and that the market risk premium is 8 percent? Beta: 0.65 Current stock price: $64.61 Annual dividend: $1.92 LO 2, LO 7 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: Using CAPM, we find: E(RCapstone) = Rrf + ßCapstone × (E(Rm) – Rrf) = 0.03 + (0.65 × 0.08) = 0.082 or 8.2 percent Using the total holding period return formula (Equation 7.1) we can solve for the stock price in one year:

RT =

7.2.

P1 − P0 + CF1 P − $64.61 + 1.92  0.082 = 1  P1 = $67.99 P0 $64.61

You are considering investing in a mutual fund. The fund is expected to earn a return of 15 percent in the next year. If its annual return is normally distributed with a standard deviation of 6.5 percent, what return can you expect the fund to beat 95 percent of the time?

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LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: Since the annual returns earned by the mutual fund are normally distributed, a 90 percent confidence level corresponds to 1.645 standard deviations from the mean. Therefore, 90 percent of the time you would expect the annual return for next year to be in the range: 0.15 + (1.645× 0.065). The lower end of this range is: 0.15 – (1.645 × 0.065) = 0.04308, or 4.31%, which is the return that you can expect the fund to beat 95 percent of the time.

7.3

You have just invested in a portfolio of three stocks. The amount of money that you invested in each stock and its beta are summarized below. Calculate the beta of the portfolio and use the capital asset pricing model (CAPM) to compute the expected rate of return for the portfolio. Assume that the expected rate of return on the market is 15 percent and that the risk-free rate is 7 percent. Stock Investment Beta A $ 200,000 1.50 B 300,000 0.65 C 500,000 1.25

LO 3, LO 7 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: N

Portfolio Beta =  p =  wi  i i =1

A $200,000 20% B $300,000 30% C $500,000 50% Total $1,000,000 100%  p = (0.20 × 1.50) + (0.30 × 0.65) + (0.50 × 1.25) = 1.12 E(RPortfolio) = Rrf + βPortfolio (E(RM) – Rrf) = 0.07 + [1.12 × (0.15 - 0.07)] = 0.1596, or 15.96% Copyright © 2015 John Wiley & Sons, Inc.

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What would you recommend to an investor who is considering making an investment in a stock which plots below the security market line (SML)? Explain.

LO 7 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement Solution: You should recommend that the investor not make this investment. An investment that plots below the SML has an expected return that is too low to fully compensate the investor for its systematic risk. In other words, its price is so high that it is not expected to yield a sufficiently high return to compensate for its risk. If investors in the market as a whole realize this, they will sell the stock in question and its price will be driven down by such sales to the point where the expected return fully compensates them for the risk. If the investor you are advising buys the stock now and its price subsequently declines, he or she will bear the cost of that decline.

7.5 Why does an investor want a diversified portfolio? Can an investor eliminate all risk? LO 5, LO 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decision AICPA: Measurement Solution: An investor of a diversified portfolio reduces total risk by investing in two or more assets whose values do not always move in the same direction at the same time. With enough diversification, the investor can eliminate unsystematic or unique risk, but, by definition, will not be able to eliminate systematic, or market risk

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CHAPTER 8 Bond Valuation and the Structure of Interest Rates

Before You Go On Questions and Answers Section 8.1 1.

What are the main differences between the bond markets and stock markets?

A corporate bond market is much larger than the stock market. The biggest investors in corporate bonds are mutual funds, life insurance companies, and pension funds, and given the size of these investors, the trades are conducted in much larger blocks than in the stock market. Also, while most stocks are traded in organized securities markets, most bond transactions take place through dealers in the OTC market.

A bond has a 7 percent coupon rate, a face value of $1,000, and a maturity of four years. On a time line, lay out the cash flows for the bond.

The annual payments for the bond will be $70 ($1,000 x 7%); thus the time line for cash inflows would be as follows: 0

_______3

$70

_____4 $1,070 ($1,000 + $70)

Explain what a convertible bond is.

Convertible bonds are bonds that can be converted into shares of common stock at some predetermined ratio at the discretion of the bondholder. The convertible feature allows the bondholder to take advantage of the firm’s prosperity if the share prices rises above a certain value.

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Section 8.2 1.

Explain conceptually how bonds are priced.

The current price of a bond is equal to the present value of all the cash flows that will be received from the investment. There are two sets of cash flows from a bond investment. First, there are the coupon payments to be received either annually or semiannually throughout the life of the bond. Second, there is the principal or face value of $1,000 that will be received when the bond matures. In order to find the price of the bond, we must find the present value of the coupons and the present value of the face value. We do this by discounting the entire cash flow stream at the current market rate and adding them up. This gives us the current price of the bond. Recognize that the coupons represent an annuity and that we can use the equation for the present value of an annuity from Chapter 6 to calculate the present value of this cash flow stream.

What is the compounding period for most bonds sold in the United States?

Most bonds sold in the United States pay interest semiannually, whereas European bonds typically only pay interest once a year.

What are zero coupon bonds, and how are they priced?

Zero coupon bonds are debt instruments that do not pay coupon interest but promise a single payment (interest earned plus principal) paid at maturity. The price of a zero coupon bond can be calculated using the same equation as used for coupon bonds, but setting the coupon payments to zero. The resulting formula is as follows: PB = Fmn/(1 + i/m)mn Because zero coupon bonds offer the entire payment at maturity, for a given change in interest rates, their price fluctuates more than coupon bonds with a similar maturity.

Section 8.3 1.

Explain how bond yields are calculated.

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A bond’s yield can be defined as the interest rate that equates a bond’s price to the present value of its interest payments and principal amount. The calculation of a bond’s yield, or its yield to maturity, takes into account the bond’s time to maturity, the coupon rate, and par.

Section 8.4 1.

What is interest rate risk?

Bond prices are negatively related to interest rate movements. As interest rates rise, bond prices fall, and vice versa. Interest rate risk simply recognizes the fact that bond prices fluctuate as interest rates change, and, if you sell a bond before maturity, you may sell the bond for a price other than what you paid for it. The greater the fluctuation in bond prices due to changes in interest rates, the greater the interest rate risk.

Explain why long-term bonds with zero coupons are riskier than short-term bonds that pay coupon interest.

According to bond theorems number two and three, for a given change in interest rates, longer-term bonds with low coupon rates have greater price changes than shorter-term bonds with higher coupon rates. Thus, long-term zero coupon bonds have greater interest rate risk—greater price swings—than short-term bonds that pay coupon payments.

Section 8.5 1.

What are default risk premiums, and what do they measure?

Default risk premiums are the amount of return that investors must be paid to purchase a security that possesses default risk compared to a similar risk-free investment. Default risk premiums, at any point in time, represent compensation for the expected financial injury for owning a bond plus some additional premium for bearing risk.

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Describe the three most prominent bond rating systems.

Default risk premiums tend to increase during periods of economic decline and to narrow during periods of economic expansion. This phenomenon is due to changes in investors’ willingness to own bonds with different credit ratings over the business cycle, the socalled flight to quality argument. Specifically, during periods of expansion when few defaults take place, investors are willing to invest in bonds with low credit quality to gain higher yields. In contrast, during tough economic times when many businesses fail, investors are concerned with safety. Accordingly, they adjust their portfolios to include more high-quality credits and sell off bonds with low credit ratings. The three most prominent credit rating agencies are Moody’s Investors Service (Moody’s), Standard & Poor’s (S&P) and Fitch. Exhibit 8.4 describes the corporate bond rating systems used by the three rating agencies.

What are the key factors that most affect the level and shape of the yield curve?

The key factors that most affect the shape of the yield curve are the real rate of interest, the expected rate of inflation, and interest rate risk. If the future real rate of interest is expected to rise, it will result in an upward slope of the real rate of interest and consequently in an upward bias to the market yield curve. Similarly, increasing the expected rate of inflation will result in an upward-sloping yield curve, because long-term interest rates will contain a larger inflation premium than short-term interest rates. If these two variables are expected to decline in the future, the result will be a downward bias to the yield curve. In contrast, the longer a bond’s maturity, the greater the bond’s interest rate risk. Thus, interest rate risk premium always adds an upward bias to the slope of the yield curve, since the longer the maturity of a security, the greater its interest rate risk.

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Self-Study Problems 8.1

Calculate the price of a five-year bond that has a coupon of 6.5 percent paid annually. The current market rate is 5.75 percent.

Solution: 0

5.75%

5 Year

├───────┼────────┼───────┼────────┼───────┤ $65

PB = =

$65

$1,065

C3 C +F C1 C2 C4 + + + + 5 55 2 3 4 1 + i (1 + i) (1 + i) (1 + i) (1 + i) $65 $65 $65 $65 ($65 + $1, 000) + + + + 1 2 3 4 (1 + 0.0575) (1.0575) (1.0575) (1.0575) (1.0575)5

= $61.47 + $58.12 + $54.96 + $51.95 + $805.28 = $1, 031.81

8.2

Bigbie Corp. issued a five-year bond a year ago with a coupon of 8 percent. The bond pays interest semiannually. If the yield to maturity on this bond is 9 percent, what is the price of the bond?

Solution: 0 9% 1

8 Semiannual Period

├───┼───┼───┼────┼───┼───┼───┼────┤ PB =? $40

$40

$1,040

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PB =

C3 / m C8 + F8 C1 / m C2 / m + + + .......... + 1 2 3 (1 + i / m) (1 + i / m) (1 + i / m) (1 + i / m)8

$80 / 2 $40 $40 ($40 + $1, 000) + + + ........ + 1 2 3 (1 + 0.09 / 2) (1.045) (1.045) (1.045)8

= $38.28 + $36.63 + $35.05 + $33.54 + $32.10 + $30.72 + $29.39 + $731.31 = $967.02 Alternatively, we can use the present value annuity factor (in Equation 5.5) and the present value equation (Equation 5.4) from Chapter 5 to solve for the price of the bond: 1   1   mn  1 − 1− 8  i  1+   (1 + 0.045 )  + $1, 000 Fn m PB = C   + = $40    mn m   (1.045 )8 i m 0.045   (1 + i m )        

(

)

= $263.84 + $703.19 = $967.03

8.3

Rockwell Industries has a three-year bond outstanding that pays a 7.25 percent coupon and is currently priced at $913.88. What is the yield to maturity of this bond? Assume annual coupon payments.

Solution: 0

├───────┼────────┼───────┤ PB = $913.88

$72.50

$1,072.50

Use the trial-and error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate. Try YTM = 10%.

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C1 C2 C3 + F3 + 2 + 3 1 + i (1 + i ) (1 + i ) $72.50 $72.50 $72.50 + $1, 000 + + 1.10 (1.10) 2 (1.10)3

= $65.91 + $59.92 + $805.79  $931.61

Try a higher rate, say YTM = 11%.

PB = =

C1 C2 C3 + F3 + 2 + 3 1 + i (1 + i ) (1 + i ) $72.50 $72.50 $72.50 + $1, 000 + + 1.11 (1.11) 2 (1.11)3

= $65.32 + $58.84 + $784.20  $908.36

Since this is less than the price of the bond, we know that the YTM is between 10 and 11 percent and closer to 11 percent. Try YTM = 10.75%.

PB = =

C1 C2 C3 + F3 + 2 + 3 1 + i (1 + i ) (1 + i ) $72.50 $72.50 $72.50 + $1,000 + + 2 1.1075 (1.1075) (1.1075)3

= $65.46 + $59.11 + $789.53  $914.09

Alternatively, we can use Equation 5.5 and the present value equation (Equation 5.4) from Chapter 5 to solve for the price of the bond:

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1   1 − (1 + i ) n  Fn PB = C   + n i   (1 + i)   1   1 − (1.1075)3  $1, 000 $913.88 = $72.50   + 3  0.1075  (1.1075)   = $177.94 + $736.15  $914.09

Thus, the YTM is approximately 10.75 percent. Using a financial calculator provided an exact YTM of 10.7594 percent.

8.4

Hindenberg, Inc., has a 10-year bond that is priced at $1,100.00. It has a coupon of 8 percent paid semiannually. What is the yield to maturity on this bond?

Solution: 0

├───┼────┼───┼───┼───┼────┼── $40

$40

─┼────┤

$40

$40 $1,000

The easiest way to calculate the yield to maturity is with a financial calculator. The inputs are as follows: Enter

20 N

Answer

−1,100

1,000

PMT

3.31

The answer we get is 3.31 percent, which is the semiannual interest rate. To obtain an annualized yield to maturity, we multiply this by two: YTM = 3.31%  2 YTM = 6.62%

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8.5

Solutions Manual

Highland Corp., a U.S. company, has a five-year bond whose yield to maturity is 6.5 percent. The bond has no coupon payments. What is the price of this zero coupon bond? Solution: You have the following information: YTM = 6.5% No coupon payments Most U.S. bonds pay interest semiannually. Thus m x n = 5 × 2 = 10 and i/2 = 0.065/2 = 0.0325. Using Equation 7.3, we obtain the following:

PB =

Fmn mn (1 + i m )

$1,000 (1.0325)10

= $726.27

Discussion Questions 8.1

Because the conversion feature in a convertible bond is valuable to bondholders, convertible bond issues have lower coupon payments than otherwise similar bonds that are not convertible. Does this mean that a company can lower its cost of borrowing by selling convertible debt? Explain.

No. The interest (coupon) payments can be reduced by the company but not the overall cost of borrowing by selling convertible debt. The reduction in the value of the interest payments is offset by the value of the conversion feature. If the company’s stock price goes above the price implied by the conversion ratio, the existing stockholders must share some of their gains with the bondholders. Investors are going to look for a required rate of return that compensates them for the risk that they are bearing. The only difference with a

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

convertible bond is that some of that compensation comes in the form of the ability to benefit from appreciation in the company’s stock price. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

What economic conditions would prompt investors to take advantage of a bond’s

8.2

convertibility feature? A bond’s convertibility feature becomes attractive when the company’s stock price rises above the bond’s price. This usually happens in times of economic expansion when the stock market is booming and interest rates are increasing, hence lowering the bond’s price. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.3

We know that a vanilla bond with a coupon rate below the market rate of interest will sell for a discount and that a vanilla bond with a coupon rate above the market rate of interest will sell for a premium. What kind of bond or loan will sell at its par value regardless of what happens to the market rate of interest?

A bond that pays a variable coupon rate that moves up and down with the market rate of interest. While corporate bonds in the U.S. do not have variable coupon payments, bank loans often have variable rates which adjust frequently enough so that the value of the loans remains relatively constant as interest rates move up and down over time. LO: 1 Level: Basic

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.4

Define yield to maturity. Why is it important?

Yield to maturity (YTM) is the rate of return earned by investors if they buy a bond today at its market price and hold it to maturity. It is important because it represents the opportunity cost to the investor or the discount rate that makes the present value of the bond’s cash flows (i.e., its coupons and its principal payments) equal to the market price. So, YTM is also referred to as the going market rate or the appropriate discount rate for a bond’s cash flows. It is important to understand that any investor who buys a bond and holds it to maturity will have a realized gain equal to the yield to maturity. If the investor sells before the maturity date, then realized gain will not be equal to the YTM, but will only be based on cash flows earned to that point. Similarly, for callable bonds, investors are guaranteed a gain to the point in time when the bond is first called, but they cannot be assured of the yield to maturity because the issuer could call the bond before maturity. LO: 3 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.5

Define interest rate risk. How can the CFOs manage this risk?

The change in a bond's prices caused by changes in interest rates is called interest rate risk. In other words, we can measure the interest rate risk to a bond’s investor by measuring the percentage change in the bond’s price caused by a 1 percent change in the market interest rates.

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

The key to managing interest rate risk is to understand the relationships between interest rates, bond prices, the coupon rate, and the bond’s term to maturity. Portfolio managers need to understand that as interest rates rise bond prices decline, and it declines more for low-coupon bonds and longer-term bonds than for the others. In such a scenario, bond portfolio managers can reduce the size and maturity of their portfolio to reduce the impact of interest rate increases. When interest rates decline, bond prices increase and rise more for longer-term bonds and higher coupon bonds. At such times, CFOs can increase the size and maturity of their portfolios to take advantage of the inverse relationship between interest rates and bond prices. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Risk Analysis

8.6

Explain why bond prices and interest rates are negatively related. What are the roles of the coupon rate and the term to maturity in this relation?

Bond prices and interest rates are negatively related because the market rate varies, while the coupon rate is constant over the life of the bond. Thus, as rates increase, demand and bond prices of existing bonds decline, while newer bonds with coupon rates at the current rate are in greater demand. o

For a given change in interest rates, longer-term bonds experience greater price changes (price volatility) than shorter-term bonds. Longer-term bonds have more of their cash flows farther in the future, and their present value of cash flows will be lower due to heavily discounted. In addition, the longer it takes for investors to receive the cash flows, the more uncertainty they have to deal with and hence the more price-volatile the bond will be.

Lower coupon bonds are more price volatile than higher coupon bonds. The same argument used above also explains this relationship. The lower the coupon on a bond, the greater the proportion of cash flows that investors receive at maturity.LO: 4 Level: Basic Copyright © 2015 John Wiley & Sons, Inc.

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.7

If interest rates are expected to increase, should investors look to long-term bonds or short-term securities? Explain.

As interest rates increase, bond prices decrease with longer-term bonds, experiencing a bigger decline than shorter-term securities. So, investors expecting an increase in interest rates should choose short-term securities over long-term securities and reduce their interest rate risk. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.8

Explain what you would assume the yield curve would look like during economic expansion and why.

At the beginning of an economic expansion, the yield curve tends to be rather steep as the rates begin to rise once the demand for capital is beginning to pick up due to growing economic activity. The yield curve will retain its positive slope during the economic expansion, which reflects the investors’ expectations that the economy will grow in the future and that the inflation rates will also rise in the future.

LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Fundamentals of Corporate Finance, 3rd edition

8.9

Solutions Manual

An investor holds a 10-year bond paying a coupon rate of 9 percent. The yield to maturity of the bond is 7.8 percent. Would you expect the investor to be holding a par-value, premium, or discount bond? What if the yield to maturity were 10.2 percent? Explain. Since the bond’s coupon of 9 percent is greater than the yield to maturity, the bond will be a premium bond. As market rates of interest drop below the coupon rate of the 9 percent bond, demand for the bond increases, driving up the price of the bond above face value. If the yield to maturity is at 10.2 percent, then the bond is paying a lower coupon than the going market rate and will be less attractive to investors. The demand for the 9 percent bond will decline, driving its price below the face value. This will be a discount bond.

LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.10 a. Investor A holds a 10-year bond, while investor B holds an 8-year bond. If interest rate increases by 1 percent, which investor has the higher interest rate risk? Explain.

Since A holds the longer-term bond, he or she will face the higher interest rate risk. Longer-term bonds are more price volatile than shorter-term bonds.

b. Investor A holds a 10-year bond paying 8 percent a year, while investor B also has a 10-year bond that pays a 6 percent coupon. Which investor has the higher interest rate risk? Explain.

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Investor B will have the higher interest rate risk since lower coupon bonds have a higher interest rate risk than higher coupon bonds of the same maturity. LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Questions and Problems BASIC 8.1

Bond price: BA Corp is issuing a 10-year bond with a coupon rate of 8 percent. The interest rate for similar bonds is currently 6 percent. Assuming annual payments, what is the value of the bond?

Solution: Years to maturity = n = 10 Coupon rate = C = 8% Annual coupon = $1,000 × 0.08 = $80 Current market rate = i = 6% Present value of bond = PB 0 6% 1

├───┼────┼───┼───┼───┼────┼── $80

$80

10 Years ─────┤ $80 + $1,000

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

C3 C + F 10 C1 C2 + + +  + 10 10 1 2 3 (1 + i ) (1 + i ) (1 + i ) (1 + i )

PB =

1  1    1− 1 − (1 + i ) n   Fn (1.06)10  $1,000 +  + =C = $ 80  n 10 i   (1 + i )  0.06  (1.06)     = $588.81 + $558.39 = $1,147.20

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.2

Bond price: Pierre Dupont just received a cash gift from his grandfather. He plans to invest in a five-year bond issued by Venice Corp. that pays an annual coupon rate of 5.5 percent. If the current market rate is 7.25 percent, what is the maximum amount Pierre should be willing to pay for this bond?

Solution: 0

7.25%

5 Years

├───────┼────────┼───────┼────────┼───────┤ $55

$55

$1,055

Coupon rate = C = 5.5% Annual coupon = $1,000 × 0.055 = $55 Current market rate = i = 7.25% Present value of bond = PB

1  1    1− 5  1 − (1 + i ) n   Fn $1,000 (1.0725) + + PB = C   = $55   n 5 i   (1 + i )  0.0725  (1.0725)     = $224.01 + $704.72 = $928.72 LO 2 Bloomcode: Application

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.3

Bond price: Knight, Inc., has issued a three-year bond that pays a coupon rate of 6.10 percent. Coupon payments are made semiannually. Given the market rate of interest of 5.80 percent, what is the market value of the bond?

Solution: Years to maturity = n = 3 Coupon rate = C = 6.1% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.061/2) = $30.50 Current market rate = i = 5.8% Present value of bond = PB 0 5.8% 1

Years

├───┼────┼───┼───┼───┼────┤ $30.50 $30.50 $30.50 $30.50 $30.50 $30.50 + $1,000

1   1   2n  1 − 1− i 6   1 +  2  + F 2 n = $30.50   (1.029)  + $1,000 PB = C    2n 6 2 i  0.029  (1.029)   1+ i 2 2       = $165.77 + $842.38 = $1,008.15

(

)

(

)

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.4

Bond price: Regatta, Inc., has seven-year bonds outstanding that pay a 12 percent coupon rate. Investors buying these bonds today can expect to earn a yield to maturity of

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

8.875 percent. What is the current value of these bonds? Assume annual coupon payments.

Solution: Years to maturity = n = 7 Coupon rate = C = 12% Annual coupon = $1,000 x 0.12 = $120 Current market rate = i = 8.875% Present value of bond = PB 08.875%1

Years

├───┼────┼───┼───┼───┼────┼───┤ $120

$120

$120+ $1,000

1  1    1− 7  1 − (1 + i ) n   Fn $1,000 (1.08875) + + PB = C   = $120   n 7 i   (1 + i )  0.08875  (1.08875)     = $606.50 + $551.44 = $1,157.94 LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.5

Bond price: You are interested in investing in a five-year bond that pays a 7.8 percent coupon rate with interest to be received semiannually. Your required rate of return is 8.4 percent. What is the most you would be willing to pay for this bond?

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Current market rate = i = 8.4% Present value of bond = PB

0 8.4% 1

├───┼────┼───┼───┼───┼────┼── $39

$39

10 Years ─────┤

$39

$39+ $1,000

1   1   2n  1 − 1− i 10   1 +  2  + F 2 n = $39   (1.042)  + $1,000 PB = C    2n 10 2 i  0.042  (1.042)   1+ i 2 2       = $313.20 + $662.71 = $975.91

(

)

(

)

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.6

Zero coupon bonds: Diane Carter is interested in buying a five-year zero coupon bond with a face value of $1,000. She understands that the market interest rate for similar investments is 9 percent. Assume annual coupon payments. What is the current value of this bond?

Solution: Years to maturity = n = 5 Coupon rate = C = 0% Current market rate = i = 9% 0 9%

5 Years

├───┼────┼───┼───┼───┤ $0

$0+ $1,000

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Fundamentals of Corporate Finance, 3rd edition

PB =

Solutions Manual

Fmn $1,000 = = $649.93 mn 5 ( ) i 1 . 09 1+ m

(

)

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.7

Zero coupon bonds: Ten-year zero coupon bonds issued by the U.S. Treasury have a face value of $1,000 and interest is compounded semiannually. If similar bonds in the market yield 10.5 percent, what is the value of these bonds?

Solution: Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 10.5% 010.5% 1

├───┼────┼───┼───┼───┼────┼── $0

Years

─────┤ $0 + $1,000

PB =

Fmn $1,000 = = $359.38 mn (1.0525)20 1+ i m

(

)

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.8

Zero coupon bonds: Northrop Real Estate Company management is planning to fund a development project by issuing 10-year zero coupon bonds with a face value of $1,000.

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Solutions Manual

Assuming semiannual compounding, what will be the price of these bonds if the appropriate discount rate is 14 percent?

Solution: Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 14% 014% 1

├───┼────┼───┼───┼───┼────┼── $0

20 Years ─────┤ $0 + $1,000

PB =

Fmn $1,000 = = $258.42 mn 20 ( ) i 1 . 07 1+ m

(

)

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.9

Yield to maturity: Ruth Hornsby is looking to invest in a three-year bond that makes semiannual coupon payments at a rate of 5.875 percent. If these bonds have a market price of $981.13, what yield to maturity and effective annual yield can she expect to earn?

Solution: Years to maturity = n = 3 Coupon rate = C = 5.875% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.05875/2) = $29.375 Yield to maturity = i Present value of bond = PB = $981.13 Copyright © 2015 John Wiley & Sons, Inc.

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Solutions Manual

Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate. Try YTM = 6%. 1   2n  1 − 1+ i   F2n 2 PB = C   +  2n 2 i   1+ i 2 2    

(

)

(

)

1   1 − 1 + 0.03 6  ( )  + $1, 000 $981.13  $29.375     (1.03)6 0.03      $159.13 + $837.48  $996.61

Try a higher rate, say YTM = 6.6%. 1   2n  1 − 1+ i   F2n 2 PB = C   +  2n 2 i   1+ i 2 2    

(

)

(

)

1   1 − 1 + 0.033 6  ( )  + $1, 000 $981.13  $29.375     (1.033)6 0.033      $157.56 + $823.00  $980.56

The YTM is approximately 6.6 percent. Using a financial calculator provided an exact YTM of 6.58 percent Enter

$29.375 -$981.13 $1,000 N

Answer

PMT

6.58%

The effective annual yield can be computed as:

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

EAY = (1 + Quoted rate m) m − 1 = (1 + 0.06578 2) − 1 2

= (1.03289) 2 − 1 = 0.06686 = 6.69%

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.10

Yield to maturity: Rudy Sandberg wants to invest in four-year bonds that are currently priced at $868.43. These bonds have a coupon rate of 6 percent and make semiannual coupon payments. What is the current market yield on this bond?

Solution: Years to maturity = n = 4 Coupon rate = C = 6% Frequency of payment = m = 2 Semiannual coupon = $1,000 × (0.06/2) = $30 Yield to maturity = i Present value of bond = PB = $868.43 Use the trial-and-error approach to solve for YTM. Since the bond is selling at a discount, we know that the yield to maturity is higher than the coupon rate. Try YTM = 10%.

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Solutions Manual

1   2n  1 − 1+ i   F2n 2 C PB =  = + 2n 2  i   1+ i 2 2    

(

)

(

)

1   1 − 1 + 0.05 8  ( )  + $1, 000 $868.43  $30     (1.05 )8 0.05      $193.90 + $676.84  $870.74

Try a higher rate, say YTM = 10.1%. 1   2n  1 − 1+ i   F2n 2 PB = C   + 2n 2 i   1+ i 2 2    

(

)

(

)

1   1 − 1 + 0.0505 8  ( )  + $1, 000 $868.43  $30*    (1.0505 )8 0.0505      $193.51 + $674.27  $867.78

The YTM is approximately 10.1 percent. Using a financial calculator provided an exact YTM of 10.08 percent. Enter

$30 N

Answer

PMT

-$868.43

$1,000

10.08%

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Fundamentals of Corporate Finance, 3rd edition

8.11

Solutions Manual

Realized yield: Josh Kavern bought 10-year, 12 percent coupon bonds issued by the U.S. Treasury three years ago at $913.44. If he sells these bonds, for which he paid the face value of $1,000, at the current price of $804.59, what is his realized yield on the bonds? Assume similar coupon-paying bonds make annual coupon payments.

Solution: Purchase price of bond = $913.44 Years investment held = n = 3 Coupon rate = C = 12% Frequency of payment = m = 1 Annual coupon = $1,000 × (0.12) = $120 Realized yield = i Selling price of bond = PB = $804.59 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has declined, market rates must have increased. So, the realized return is going to be less than the bond’s coupon. Try rates lower than the coupon rate. Try i = 10%.

1   1 − (1 + i ) n  Fn + PB = C   n i   (1 + i )   1   1 − (1.10) 3  $804.59 + $913.44 = $120   3  0.10  (1.10)   = $298.42 + $604.50  $902.92 Try a lower rate, i = 9.5%.

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Solutions Manual

1   1 − (1 + i ) n  Fn + PB = C   n i   (1 + i )   1   1 − (1.095) 3  $804.59 + $913.44 = $120   3  0.095  (1.095)   = $301.07 + $612.82 = $913.89 The realized rate of return is approximately 9.5 percent. Using a financial calculator provided an exact yield of 9.52 percent. Enter

3 N

Answer

$120

-$913.44

$804.59

PMT

9.52%

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.12

Realized yield: Four years ago, Lisa Stills bought six-year, 5.5 percent coupon bonds issued by the Fairways Corp. for $947.68. If she sells these bonds at the current price of $894.52, what will be her realized yield on the bonds? Assume similar coupon-paying bonds make annual coupon payments.

Solution: Purchase price of bond = $947.68 Years investment held = n = 4 Coupon rate = C = 5.5% Frequency of payment = m = 1 Annual coupon = $1,000 × (0.055) = $55 Realized yield = i

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Solutions Manual

Selling price of bond = PB = $894.52 To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has declined, market rates must have increased. So, the realized return is going to be less than the bond’s coupon. Try rates lower than the coupon rate. Try i = 5%.

1   1 − (1 + i ) n  Fn + PB = C   n i   (1 + i )   1   1 − (1.05) 4  $894.52 + $947.68 = $55   4  0.05  (1.05)   = $195.03 + $735.92  $930.95 Try a lower rate, i = 4.5%.

1   1 − (1 + i ) n  Fn + PB = C   n i   (1 + i )   1   1 − (1.045) 4  $894.52 + $947.68 = $55   4  0.045  (1.045)   = $197.31 + $750.11  $947.42 The realized rate of return is approximately 4.5 percent. Using a financial calculator provided an exact yield of 4.49 percent. Enter

$55 N

Answer

PMT

-$947.68

$894.52

4.49%

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

INTERMEDIATE 8.13

Bond price: The International Publishing Group is raising $10 million by issuing 15-year bonds with a coupon rate of 8.5 percent. Coupon payments will be made annually. Investors buying the bonds today will earn a yield to maturity of 8.5 percent. At what price will the bonds sell in the marketplace? Explain.

Solution: Years to maturity = n = 15 Coupon rate = C = 8.5% Annual coupon = $1,000 × 0.085 = $85 Current market rate = i = 8.5% Present value of bond = PB 0 8.5% 1

├───┼────┼───┼───┼─── $85

$85

Year

─────┤

$85

$85+ $1,000

n = 15;

C = 8.5%;

i = YTM = 8.5%

1  1    1− 15  1 − (1 + i) n   Fn $1,000 (1.085) + + PB = C   = $85   n 15 i   (1 + i)  0.085  (1.085)     = $705.86 + $294.14 = $1,000.00 This answer should have been intuitive. Since the bond is paying a coupon equal to the going market rate of 8.5 percent, the bond should be selling at its par value of $1,000.

Enter

8.5%

Answer

$85 PMT

$1,000 PV

-$1,000

LO 2

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Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.14

Bond price: Pullman Corp issued 10-year bonds four years ago with a coupon rate of 9.375 percent. At the time of issue, the bonds sold at par. Today bonds of similar risk and maturity must pay an annual coupon of 6.25 percent to sell at par value. Assuming semiannual coupon payments, what will be the current market price of the firm’s bonds?

Solution: Years to maturity = n = 6 Frequency of payment = m = 2 Coupon rate = C = 9.375% Semiannual coupon = $1,000 × (0.09375/2) = $46.875 Current market rate = i = 6.25% Present value of bond = PB 0 6.25% 1

├───┼────┼───┼───┼───

─────┤

$46.875 $46.875………

$46.875+ $1,000

n = 6; m = 2; C = 9.375%; i = YTM = 6.25% 1   1   1 − 1 − (1 + i 2 ) 2n   (1.03125)12  F $1,000 + PB = C   = $46.875   +  2n 12 2  i 2  (1 + i 2 )  0.03125  (1.03125)       = $463.13 + $691.25 = $1,154.38

Enter

3.125%

$46.875

PMT

Answer

$1,000 PV

- $1,154.38

LO 2

SM 8-29

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.15

Bond price: Marshall Company is issuing eight-year bonds with a coupon rate of 6.5 percent and semiannual coupon payments. If the current market rate for similar bonds is 8 percent, what will be the bond price? If company management wants to raise $1.25 million, how many bonds does the firm have to sell?

Solution: Years to maturity = n = 8 Frequency of payment = m = 2 Coupon rate = C = 6.5% Semiannual coupon = $1,000 × (0.065/2) = $32.50 Current market rate = i = 8% Present value of bond = PB

0 8% 1

├───┼────┼───┼───┼───

$32.50

Year

─────┤

$32.50………..$32.50

$32.50+ $1,000

1   1   mn  1 − 1− i 16   1 +  2  + F 2 n = $32.50   (1.04)  + $1,000 PB = C    mn 16 2 i  0.04  (1.04)   1+ i 2 2       = $378.70 + $533.91 = $912.61

(

)

(

)

To raise $1.25 million, the firm would have to sell: Number of bonds = $1,250,000 / $912.61 = 1,370 bond contracts Enter

$32.50

$1,000

SM 8-30

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

PMT

Answer

-$912.61

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.16

Bond price: Rockne, Inc., has outstanding bonds that will mature in six years and pay an 8 percent coupon semiannually. If you paid $1036.65 today and your required rate of return was 6.6 percent, did you pay the right price for the bond?

Solution: Years to maturity = n = 6 Frequency of payment = m = 2 Coupon rate = C = 8% Semiannual coupon = $1,000 × (0.08/2) = $40 Current market rate = i = 6.6% Present value of bond = PB 0 6.6%

├───────┼────────┼────────┼── $40

$40

─────────┤

$40

$40+ $1,000

1   1   mn  1 − 1− i 12   1 +  2  + F 2 n = $40   (1.033)  + $1,000 PB = C    mn 12 2 i  0.033  (1.033)   1+ i 2 2       = $391.12 + $677.32 = $1,068.45

(

)

(

)

You paid less than what the bond is worth. That was a good price. Enter

3.3%

$40

$1,000

SM 8-31

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

PMT

Answer

-$1,068.45

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.17

Bond price: Nanotech, Inc., has a bond issue maturing in seven years that is paying a coupon rate of 9.5 percent (semiannual payments). Management wants to retire a portion of the issue by buying the securities in the open market. If it can refinance at 8 percent, how much will Nanotech pay to buy back its current outstanding bonds?

Solution: Years to maturity = n = 7 Frequency of payment = m = 2Coupon rate = C = 9.5% Semiannual coupon = $1,000 × (0.095/2) = $47.50 Current market rate = i = 8%

Present value of bond = PB 0 8%

├───────┼────────┼────────┼── $47.50

$47.50

14 ──────┤

$47.50

$47.50 + $1,000

1   1 − 1   mn   1 − i 14   1+  2  + F 2 n = $47.50   (1.04)  + $1,000 PB = C    mn 14 2 i i  0.04  (1.04) 1 +   2 2       = $501.75 + $577.48 = $1,079.22

(

)

(

)

The firm will be willing to pay no more than $1,079.22 for their bond.

SM 8-32

Fundamentals of Corporate Finance, 3rd edition

Enter

Solutions Manual

$47.50 i%

$1,000

PMT

Answer

-$1,079.22

LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.18

Zero coupon bonds: Kintel, Inc., management wants to raise $1 million by issuing sixyear zero coupon bonds with a face value of $1,000. The company’s investment banker states that investors would use an 11.4 percent discount rate to value such bonds. At what price would these bonds sell in the marketplace? How many bonds would the firm have to issue to raise $1 million? Assume semiannual coupon payments.

Solution: Years to maturity = n = 6 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 11.4% Assume semiannual coupon payments. 0 11.4% 1

├───┼────┼───┼───┼───┼────┼── $0

Year

─────┤ $0 $1,000

PB =

Fmn $1,000 = = $514.16 mn 12 ( ) i 1 . 057 1+ m

(

)

= $1,000,000 / $514.16 = 1,945 bond contracts SM 8-33

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.19

Zero coupon bonds: Rockinghouse Corp. management plans to issue seven-year zero coupon bonds. It has learned that these bonds will sell today at a price of $439.76. Assuming annual coupon payments, what is the yield to maturity on these bonds?

Solution: Years to maturity = n = 7 Coupon rate = C = 0% YTM = i Present value of bond = PB = $439.76 0i=? 1

├───┼────┼───┼───┼───┼────┼───┤ $0

$0+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Try YTM = 10%.

PB =

(1 + i )

$1,000 (1.10)7

$439.76  $513.16 Try a higher rate, YTM = 12%.

PB =

(1 + i )

$1,000 (1.12)7

$439.76  $452.35 Try YTM=12.5%.

PB =

(1 + i )

$1,000 (1.125)7

$439.76  $438.46

SM 8-34

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

The YTM is approximately 12.5 percent. Enter

$0 N

Answer

-$439.76 $1,000

PMT

12.453%

LO 1, LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.20

Yield to maturity: Electrolex, Inc., has four-year bonds outstanding that pay a coupon rate of 6.6 percent and make coupon payments semiannually. If these bonds are currently selling at $914.89, what is the yield to maturity that an investor can expect to earn on these bonds? What is the effective annual yield?

Solution: Years to maturity = n = 4 Frequency of payment = m = 2Coupon rate = C = 6.6% YTM = i Semiannual coupon payments = $1,000 × (0.066/2) = $33 Present value of bond = PB = $914.89 0i=?

├───────┼────────┼────────┼── $33

$33

8 ─────────┤Yrs. $33+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Since this is a discount bond, the market rate should be higher than 6.6 percent. Try i = 8% or i/2 = 4%.

SM 8-35

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

1   1 − (1 + i ) n  Fn PB = C   + n i   (1 + i )   1   1 − (1.04)8  $1,000 $914.89 = $33   + 8  0.04  (1.04)   = $222.18 + $730.69  $952.87

Try a higher rate, i = 9%, i/2 = 4.5%. 1   1 − (1 + i ) n  Fn PB = C   + n i   (1 + i )   1   1 − (1.045)8  $1,000 $914.89 = $33   + 8  0.045  (1.045)   = $217.66 + $703.19  $920.85

Try a higher rate, i = 9.2%, i/2 = 4.6%. 1   1 − (1 + i ) n  Fn PB = C   + n i   (1 + i )   1   1 − (1.046)8  $1,000 $914.89 = $33   + 8  0.046  (1.046)   = $216.78 + $697.82  $914.60

The yield to maturity is approximately 9.2 percent. The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.046) − 1 = 0.0941 = 9.41% 2

SM 8-36

Fundamentals of Corporate Finance, 3rd edition

Enter

Solutions Manual

$33 N

Answer

-$914.89

$1,000

PMT

4.5954%

The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.045954) − 1 = 0.09399 = 9.4% 2

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.21

Yield to maturity: Serengeti Corp. has five-year bonds outstanding that pay a coupon of 8.8 percent. If these bonds are priced at $1,064.86, what is the yield to maturity on these bonds? Assume semiannual coupon payments. What is the effective annual yield?

Solution: Years to maturity = n = 5 Frequency of payment = m = 2 Coupon rate = C = 8.8% Current market rate = i Semiannual coupon payments = $1,000 x (0.088/2) = $44 Present value of bond = PB = $1,064.86 0 i=?

├───────┼────────┼────────┼── $44

$44

10 ─────────┤Yrs. $44+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Since this is a premium bond, the market rate should be lower than 8.8 percent. Try i = 7% or i/2 = 3.5%.

SM 8-37

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

1   1 − (1 + i ) n  FV PB = C   + n i   (1 + i )   1   1 − (1.035)10  $1,000 $1,064.86 = $44   + 10  0.035  (1.035)   = $365.93 + $708.92  $1,074.85 Try a higher rate, i = 7.2%, i/2 = 3.6%.

1   1 − (1 + i ) n  Fn + PB = C   n i   (1 + i )   1   1 − (1.036)10  $1,000 + $1,068.86 = $44   10  0.036  (1.036)   = $364.09 + $702.11  $1,066.20 The YTM is approximately 7.2 percent. The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.036) − 1 = 0.0733 = 7.33% 2

Enter

$44

Answer

-$1,064.86

$1,000

PMT

3.6156%

The effective annual yield can be computed as: EAY = (1 + Quotedrate m) m − 1 = (1.036156) − 1 = 0.0736 = 7.36% 2

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance

SM 8-38

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

AICPA: Measurement

8.22

Yield to maturity: Adrienne Dawson is planning to buy 10-year zero coupon bonds issued by the U.S. Treasury. If these bonds have a face value of $1,000 and are currently selling at $404.59, what is the expected return on them? Assume that interest compounds semiannually on similar coupon paying bonds.

Solution: Years to maturity = n = 10 Frequency of payment = m = 2Coupon rate = C = 0% Current market rate = i Assume annual coupon payments. Present value of bond = PB = $404.59 0 i=?

├───────┼────────┼────────┼── $0

20 Yrs. ─────────┤ $0+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Try YTM = 10%.

Fmn $1,000 = mn (1.05)20 1+ i m $404.59  $376.89 PB =

(

)

Try a lower rate, YTM = 9%.

Fmn $1,000 = mn (1.045)20 1+ i m $404.59  $414.64 PB =

(

)

Try YTM=9.25%.

SM 8-39

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Fmn $1,000 = mn (1.04625)20 1+ i m $404.59  $404.85 PB =

(

)

The YTM is approximately 9.25 percent. EAY = (1 + Quoted rate m) m − 1 = (1.04625) − 1 = 0.09464 = 9.46% 2

The expected return from this investment is 9.46 percent. Enter

N Answer

-$404.59

$1,000

PMT

4.63%

The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.046283) − 1 = 0.0947 = 9.47% 2

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.23

Realized yield: Brown & Co. issued seven-year bonds two years ago that can be called after two years. The bonds make semiannual coupon payments at a coupon rate of 7.875 percent. Each bond has a market value of $1,053.40, and the call price is $1,078.75. If an investor purchased the bonds at par value when they were originally issued and the bonds are called by the firm today, what is the investor’s realized yield?

Solution: Purchase price of bond = $1,000 Years investment held = n = 2 Coupon rate = C = 7.875%

SM 8-40

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Frequency of payment = m = 2 Annual coupon = $1,000 × (0.07875/2) = $39.375 Realized yield = i Call price of bond = CP = $1,078.75 Current market value = $1,053.40

To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has increased, market rates must have decreased. So, the realized return is going to be greater than the bond’s coupon. Try rates higher than the coupon rate. Try i = 10%, or i/2 = 5%.

1   1 − (1 + i ) mn  C CP + 2 PB =     i 2 (1 + i ) mn 2 2     1   1 − (1.05) 4  $1, 078.75 $1, 000 = $39.375   + (1.05) 4  0.05    = $139.62 + $887.49  $1, 027.11

Try a higher rate, i = 11.48% or i/2 = 5.74%.

1   1 − (1 + i ) mn  C CP 2 + PB =   i  (1 + i ) mn 2  2 2     1   1 − (1.0574) 4  $1,078.75 $1,000 = $39.375   + 4  0.0574  (1.0574)   = $137.25 + $862.91  $1,000.16

SM 8-41

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

EAY = (1+ Quoted rate m) m -1 = (1.0574 ) -1 2

= 0.11809 = 11.81% The realized rate of return is approximately 11.81 percent. Using a financial calculator provided an exact yield of 11.49 percent.

Enter

4 N

Answer

$39.375 i%

PMT

-$1,000 $1,078.75 PV

5.74%

The effective annual yield can be computed as:

EAY = (1+ Quoted rate m) m -1 = (1.0574 ) -1 2

= 0.1181 = 11.81% LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.24

Realized yield: Trevor Price bought 10-year bonds issued by Harvest Foods five years ago for $936.05. The bonds make semiannual coupon payments at a rate of 8.4 percent. If the current price of the bonds is $1,048.77, what is the yield that Trevor would earn by selling the bonds today?

Solution: Purchase price of bond = $936.05 Years investment held = n = 5 Coupon rate = C = 8.4% Frequency of payment = m = 2 Annual coupon = $1,000 × (0.084/2) = $42 Realized yield = i

SM 8-42

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Selling price of bond = PB = $1,048.77

Try i = 11%, or i/2 = 5.5%.

1   1 −  m  n i C  (1 + 2 )  F 2n PB =   +  i 2 (1 + i ) mn 2 2     1   1 − (1.055)10  $1,048.77 + $936.05 = $42   10  0.055  (1.055)   = $316.58 + $613.98  $930.56

Try a lower rate, i = 10.8% or i/2 = 5.4%.

1   1 −  m  n i C  (1 + 2 )  FV PB =   +  (1 + i ) mn i 2 2 2     1   1 − (1.054)10  $1,048.77 + $936.05 = $42   10  0.054  (1.054)   = $318.10 + $619.83  $937.94

EAY = (1 + Quoted rate m) m − 1 = (1.054) − 1 = 0.1109 = 11.09% 2

SM 8-43

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

The realized rate of return is approximately 11.09 percent. Using a financial calculator provided an exact yield of 11.14 percent.

Enter

$42

N Answer

-$936.05

PMT

$1,048.77 FV

5.425%

The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.05425) − 1 = 0.1114 = 11.14% 2

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.25

Realized yield: You bought a six-year bond issued by Runaway Corp. four years ago. At that time, you paid $974.33 for the bond. The bond pays a coupon rate of 7.375 percent, and coupon payments are made semiannually. Currently, the bond is priced at $1,023.56. What yield can you expect to earn on this bond if you sell it today?

Solution: Purchase price of bond = $974.33 Years investment held = n = 4 Coupon rate = C = 7.375% Frequency of payment = m = 2 Annual coupon = $1,000 × (0.07375/2) = $36.875 Realized yield = i Selling price of bond = PB = $1,023.56

SM 8-44

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

1   1 −  mn  i (1 + )  C F 2n 2 PB =   +   i 2 (1 + i ) mn 2 2     1   1 − (1.045) 8  $1,023.56 + $974.33 = $36.875   8  0.045  (1.045)   = $243.22 + $719.75  $962.98 Try a lower rate, i = 8.6% or i/2 = 4.3%.

1   1 −  mn i C  (1 + 2 )  F 2n PB =  +  (1 + i ) mn i 2  2 2     1   1 − (1.043)8  $1,023.56 + $974.33 = $36.875   8  0.043  (1.043)   = $245.22 + $730.87  $976.09 EAY = (1 + Quoted rate m) m − 1 = (1.043) − 1 = 0.08785 = 8.78% 2

The realized rate of return is approximately 8.78 percent. Using a financial calculator provided an exact yield of 8.84 percent.

Enter

8 N

Answer

$36.875

-$974.33

$1,023.56

PMT

4.327%

SM 8-45

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.04327) − 1 = 0.0884 = 8.84% 2

LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

ADVANCED 8.26

Lopez Information Systems management is planning to issue 10-year bonds. The going market yield for such bonds is 8.125 percent. Assume that coupon payments will be made semiannually. Management is trying to decide between issuing an 8 percent coupon bond or a zero coupon bond. Lopez needs to raise $1 million. a.

What will be the price of an 8 percent coupon bond?

How many 8 percent coupon bonds would have to be issued?

What will be the price of a zero coupon bond?

How many zero coupon bonds will have to be issued?

Solution: a.

Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 8.00% Semiannual coupon = $1,000 × (0.08/2) = $40 Current market rate = i = 8.125% Present value of bond = PB 0

8.125%

├───────┼────────┼────────┼── $40

$40

20 ─────────┤ $40+ $1,000

SM 8-46

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

1   1   mn  1 − 1− i 20   1 +  2  + F 2 n = $40   (1.040625)  + $1,000 PB = C    mn 20 2 i  0.040625  (1.040625)   1+ i 2 2       = $540.62 + $450.94 = $991.56

(

)

(

)

The firm can sell these bonds at $991.56.

Enter

4.0625%

$40

$1,000

PMT

Answer

-$991.55

Amount needed to be raised = $1,000,000 Number of bonds sold = $1,000,000 / $991.55 = 1,009 bond contracts

Years to maturity = n = 10 Coupon rate = C = 0% Current market rate = i = 8.125% 0 8.125%

├───── ┼────┼───┼───┼───┼────┼── $0

─────┤

$0+ $1,000

PB =

Fmn $1,000 = = $450.94 mn (1.040625)20 1+ i m

(

Enter

)

20 N

4.0625% i%

Answer

$0 PMT

$1,000 PV

-$450.94

At the price of $450.94, the firm needs to raise $1 million. To do so, the firm will have to issue:

SM 8-47

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Number of bonds sold = $1,000,000 / $450.94 = 2,218 bond contracts (Rounded) LO 1, LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.27

Showbiz, Inc., has issued eight-year bonds with a coupon of 6.375 percent and semiannual coupon payments. The market’s required rate of return on such bonds is 7.65 percent. a.

What is the market price of these bonds?

If the above bond is callable after five years at an 8.5 percent premium on the face value, what is the expected return on this bond?

Solution: a.

Years to maturity = n = 8 Frequency of payment = m = 2 Coupon rate = C = 6.375% Semiannual coupon = $1,000 × (0.06375/2) = $31.875 Current market rate = i = 7.65% Present value of bond = PB

0 7.65%

├───────┼────────┼────────┼── $31.875

$31.875

16 ─────────┤Yrs. $31.875+ $1,000

SM 8-48

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

1   1   mn  1 − 1− i 16   1 +  F 2n $1,000 (1.03825) 2 + + PB = C   = $31.875    mn 16 2 i  0.03825  (1.03825)   1+ i2 2       = $376.26 + $548.49 = $924.75

(

)

(

)

The firm can sell these bonds at $924.75.

Purchase price of bond = $924.75 Years investment held = n = 5 Coupon rate = C = 6.375% Semiannual coupon = $1,000 × (0.06375/2) = $31.875 Frequency of payment = m = 2 Realized yield = i Call price of bond = CP = $1,000 × (1.085) = $1,085.00 To compute the expected return, either the trial-and-error approach or the financial calculator can be used. Try rates higher than the coupon rate. Try i = 8%, or i/2 = 4%. 1   1m n   C CP (1 + i 2) PB =   + m n 2  i2  (1 + i 2)   1   1- (1.04)10  $1,085 $924.75 = $31.875   + 10  0.04  (1.04)   = $258.54 + $732.99  $991.53

Try a higher rate, i = 9.67% or i/2 = 4.835%.

SM 8-49

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

1   1− m n   C CP (1 + i 2) PB =   + m n 2  i 2  (1 + i 2)   1   1 −  (1.04835)10  $1,085 $924.75 = $31.875   + 10  0.04835  (1.04835)   = $248.11 + $676.65  $924.77

The realized rate of return is approximately 9.67% percent. Using a financial calculator provided an exact yield of 9.6705 percent.

Enter

10 N

Answer

$31.875 i%

-$924.75 $1,085

PMT

4.835%

The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.04835) − 1 2

= 0.0990 = 9.90%

LO 2, LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.28

Peabody Corp. has seven-year bonds outstanding. The bonds pay a coupon of 8.375 percent semiannually and are currently worth $1,063.49. The bonds can be called in three years at price of $1,075. a.

What is the yield to maturity of these bonds?

What is the effective annual yield?

What is the realized yield on the bonds if they are called?

If you plan to invest in one of these bonds today, what is the expected yield on the investment? Explain.

SM 8-50

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Solution: a.

Years to maturity = n = 7 Frequency of payment = m = 2 Coupon rate = C = 8.375% Current market rate = i Semiannual coupon payments = $1,000 × (0.08375/2) = $41.875 Present value of bond = PB = $1,063.49 0i=?

├───────┼────────┼────────┼── $41.875

$41.875

14 Yrs. ─────────┤ $41.875+ $1,000

To solve for the YTM, a trial-and-error approach has to be used. Since this is a premium bond, the market rate should be lower than 8.375 percent. Try i = 8% or i/2 = 4%. 1   1 − n  i (1 + )  F 2n 2 PB = C   +   i (1 + i ) mn 2 2     1   1 − (1.04)14  $1,000 + $1,063.49 = $41.875   14  0.04  (1.04)   = $442.33 + $577.48  $1,019.81

Try a lower rate, i = 7.2%, or i/2 = 3.6%.

SM 8-51

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

1   1 − (1 + i 2) n  F 2n + PB = C   i   (1 + i ) mn 2 2   1   1 − (1.036)14  $1,000 + $1,063.49 = $41.875  14  0.036  (1.036)   = $454.24 + $609.49  $1,063.73 The yield-to maturity is approximately 7.2 percent.

The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.036) − 1 = 0.073296 = 7.3% 2

Enter

$41.875

N Answer

PMT

-$1,063.49 $1,000 PV

3.602%

The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.036021) − 1 = 0.073340 = 7.3% 2

Purchase price of bond = $1,063.49 Years investment held = n = 3 Coupon rate = C = 8.375% Semiannual coupon payments = $1,000 x (0.08375/2) = $41.875 Frequency of payment = m = 2 Realized yield = i Selling price of bond = PB = $1,075

SM 8-52

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

To compute the realized return, either the trial-and-error approach or the financial calculator can be used. Since the price has increased, market rates must have decreased. So, the realized return is going to be higher than the bond’s coupon. Try rates higher than the coupon rate. Try i = 9%, or i/2 = 4.5%.

1   1 − m n   F2n C (1 + i 2) PB =   + m n 2  i2  (1 + i 2)   1   1 − (1.045)6  $1, 075 $1, 063.49 = $41.875   + 6  0.045  (1.045)    $215.99 + $825.49  $1, 041.48

Try a lower rate, i = 8.2% or i/2 = 4.1%.

1   1− m n   F2n C (1 + i 2) PB =   + m n 2  i 2  (1 + i 2)   1   1 − (1.041)6  $1, 075 $1, 063.49 = $41.875   + 6  0.041  (1.041)   = $218.80 + $844.70 = $1, 063.50

EAY = (1 + Quoted rate m) m − 1 = (1.041) − 1 2

= 0.08368 = 8.368%

SM 8-53

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

The realized rate of return is approximately 8.37 percent. Using a financial calculator provided an exact yield of 8.2 percent.

Enter

6 N

Answer

$41.875 -$1,063.49

$1075

PMT

4.1%

The effective annual yield can be computed as: EAY = (1 + Quoted rate m) m − 1 = (1.04100 ) − 1 2

= 0.08368 = 8.368%

Purchase price of bond = PB = $1,063.49 Years to maturity = n =7 Coupon rate = C = 8.375% Semiannual coupon payments = $1,000 × (0.08375/2) = $41.875 Frequency of payment = m = 2 Maturity value = FV = $1,000 Use the trial-and-error approach to compute the yield to maturity. Since we have a premium bond, market rates are lower than the bond’s coupon. Try i = 7%, or i/2 = 3.5%.

1   1 − (1 + i )mn  F2n C + 2 PB =     i 2 (1 + i )mn 2 2     1   1 − (1.035)14  $1, 000 $1, 063.49 = $41.875   + 14  0.035  (1.035)   = $457.30 + $617.78  $1, 075.08

SM 8-54

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Try a higher rate, i = 7.2%, or i/2 = 3.6%.

1   1 − (1 + i 2) n  F 2n + PB = C   i   (1 + i ) mn 2 2   1   1 − (1.036)14  $1,000 + $1,063.49 = $41.875  14  0.036  (1.036)   = $454.24 + $609.49  $1,063.73 The expected yield is approximately 7.2 percent which is the same as the yield to maturity obtained in (a). If the bond is not called and is held to maturity, then the expected yield is the yield to maturity.

EAY = (1 + Quoted rate m) m − 1 = (1.036 ) − 1 2

= 0.073296 = 7.33%

The expected yield is approximately 7.33 percent. Using a financial calculator provided an exact yield 7.334 percent.

Enter

$41.875 -$1,063.49 $1,000

N Answer

PMT

3.602%

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m) m − 1 = (1.03602 ) − 1 2

= 0.073337 = 7.33% LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-55

Fundamentals of Corporate Finance, 3rd edition

8.29

Solutions Manual

The Maryland Department of Transportation has issued 25-year bonds that make semiannual coupon payments at a rate of 9.875 percent. The current market rate for similar securities is 11 percent. a.

What is the current market value of one of these bonds?

What will be the bond’s price if rates in the market (i) decrease to 9 percent or (ii) increase to 12 percent?

Refer to your answers in part b. How do the interest rate changes affect premium bonds and discount bonds?

Suppose the bond were to mature in 12 years. How do the interest rate changes in part b affect the bond prices?

Solution: a.

Years to maturity = n = 25 Frequency of payment = m = 2 Coupon rate = C = 9.875% Semiannual coupon = $1,000 × (0.09875/2) = $49.375 Current market rate = i = 11% Present value of bond = PB 0 11%

├───────┼────────┼────────┼── $49.375

$49.375

50 Yrs. ─────────┤

$49.375

$49.375+ $1,000

1   1   2n  1 − 1− i 50   1 +  2  + F 2 n = $49.375   (1.055)  + $1,000 PB = C    mn 50 2 i  0.055  (1.055)   1+ i 2 2       = $835.99 + $68.77 = $904.76

(

)

(

)

The Maryland bonds will sell at $904.76.

SM 8-56

Fundamentals of Corporate Finance, 3rd edition

Enter

Solutions Manual

5.5% $49.375 N

PMT

Answer

(i)

$1,000 PV

-$904.76

Current market rate = i = 9%

1   1   2n  1 − 1− i 50   1 +  2  + F 2 n = $49.375   (1.045)  + $1,000 PB = C    mn 50 2 i  0.045  (1.045)   1+ i 2 2       = $975.75 + $110.71 = $1,086.46

(

)

(

)

The Maryland bonds will increase in price to sell at $1,086.46. Enter

4.5% $49.375 N

$1,000

PMT

Answer

(ii)

-$1,086.46

Current market rate = i = 12%

1   1   2n  1 − 1− i 50   1 +  2  + F 2 n = $49.375  (1.06)  + $1,000 PB = C    mn 50 2 i  0.06  (1.06)   1+ i 2 2       = $778.24 + $54.29 = $832.53

(

)

(

)

The Maryland bonds will drop in price to $832.53. Enter

6% $49.375 N

Answer

PMT

$1,000 PV

-$832.53

Bonds, in general, decrease in price when interest rates go up. When interest rates decrease, bond prices increase.

(i)

Current market rate = i = 9%

SM 8-57

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Term to maturity = 12 years

1   1   2n  1 − 1− i 24   1 +  2  + F 2 n = $49.375   (1.045)  + $1,000 PB = C    mn 24 2 i  0.045  (1.045)   1+ i 2 2       = $715.71 + $347.70 = $1,063.42

(

)

(

)

The Maryland bonds will increase in price to sell at $1,063.42. Enter

4.5%

$49.375 i

PMT

Answer

(ii)

$1,000 PV

-$1,063.42

Current market rate = i = 12%

1   1   2n  1 − 1− i 24   1 +  2  + F 2 n = $49.375  (1.06)  + $1,000 PB = C    mn 24 2 i  0.06  (1.06)   1+ i 2 2       = $619.67 + $246.98 = $866.65

(

)

(

)

The Maryland bonds will drop in price to $866.65. Enter

24 N

Answer

6% $49.375 i

PMT

$1,000 PV

-$866.65

With shorter maturity, bond prices react the same way as in part b, but to a lesser extent. When interest rates increase, the bond’s price declines; but the decline in price is less than that for a longer-term bond. When interest rates decrease, bond prices increase with longer-term bonds, increasing more than shorter-term bonds. LO 2, LO 3, LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-58

Fundamentals of Corporate Finance, 3rd edition

8.30

Solutions Manual

Rachette Corp. has 18-year bonds outstanding. These bonds, which pay interest semiannually, have a coupon rate of 9.735 percent and a yield to maturity of 7.95 percent.

a. Compute the current price of these bonds. b. If the bonds can be called in five years at a premium of 13.5 percent over par value, what is the investor’s realized yield? c. If you bought one of these bonds today, what is your expected rate of return? Explain.

Solution: a.

Years to maturity = n = 18 Frequency of payment = m = 2 Coupon rate = C = 9.735% Semiannual coupon = $1,000 × (0.09735/2) = $48.675 Current market rate = i = 7.95% Present value of bond = PB 0

├───────┼────────┼────────┼── $48.675

$48.675

─────────┤Yrs.

$48.675

$48.675+ $1,000

1   1   2n  1 − 1− 36  1+ i    F2n $1, 000 (1.03975) 2 PB = C   = $48.675   + + 2n 2 i 0.03975  (1.03975)36 i    1 + 2 2       = $923.56 + $245.79 = $1,169.34

(

)

(

)

The bond’s current price is at $1,169.34.

Enter

3.975%

$48.675

PMT

Answer

$1,000 PV

-$1,169.34

Purchase price of bond = $1,169.34 (value today);

SM 8-59

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Call price = $1,135

To compute the realized return, either the trial-and-error approach or the financial calculator can be used.

Try rates lower than the coupon rate.

Try i = 8%, or i/2 = 4%.

1   1 − (1 + i ) mn  F2n C + 2 PB =    (1 + i ) mn i 2  2 2     1   1 −  (1.04)10  $1,135 $1,169.34 = $48.675   + 10  0.04  (1.04)   = $394.80 + $766.77  $1,161.56

Try a lower rate, i = 7.8% or i/2 = 3.9%.

1   1 − (1 + i ) mn  F2n C + 2 PB =     i 2 (1 + i ) mn 2 2     1   1 − (1.039)10  $1,135 $1,169.34 = $48.675   + 10  0.039  (1.039)   = $396.77 + $774.18  $1,170.95

EAY = (1 + Quoted rate m) m − 1 = (1.039 ) − 1 2

= 0.07952 = 7.95% The realized rate of return is approximately 7.95 percent. Using a financial calculator provided an exact yield of 7.834 percent.

SM 8-60

Fundamentals of Corporate Finance, 3rd edition

Enter

Solutions Manual

$48.675 -$1,169.34 $1,135.00

N Answer

PMT

3.917%

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m) m − 1 = (1.03917 ) − 1 2

= 0.07987 = 7.99%

Purchase price of bond = PB = $1,169.34 Years to maturity = n = 18 Coupon rate = C = 9.735% Semiannual coupon = $1,000 × (0.09735/2) = $48.675 Frequency of payment = m = 2 Maturity value = FV = $1,000

Use the trial-and-error approach to compute the yield to maturity. Since we have a premium bond, market rates are lower than the bond’s coupon. Try i = 8%, or i/2 = 4.0%.

1   1 − (1 + i ) mn  F2n C + 2 PB =     i 2 (1 + i ) mn 2 2     1   1 − (1.04)36  $1, 000 $1,169.34  $48.675   + 36  0.04  (1.04)    $920.36 + $243.67  $1,164.03

Try i = 7.9%, or i/2 = 3.95%.

SM 8-61

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

1   1 − (1 + i ) mn  F2n C + 2 PB =    (1 + i ) mn i 2  2 2     1   1 − (1.0395)36  $1, 000 $1,169.34  $48.675   + 36  0.0395  (1.0395)    $926.77 + $247.92  $1,174.69

Thus the expected yield is between 7.9 percent and 8 percent. Using a financial calculator provided an exact yield of 7.95 percent.

Enter

$48.675

N Answer

PMT

-$1,169.34 $1,000 PV

3.975%

The effective annual yield can be computed as:

EAY = (1 + Quoted rate m) m − 1 = (1.03975) − 1 2

= 0.08108 = 8.11% LO 2, LO 3, LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.31

Zippy Corporation just sold $30 million of convertible bonds with a conversion ratio of 40. Each $1,000 bond is convertible into 25 shares of Zippy’s stock.

What is the conversion price of Zippy’s stock?

SM 8-62

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

If the current price of Zippy’s stock is $15 and the company’s annual stock return is normally distributed with a standard deviation of $5, what is the probability that investors will find it attractive to convert the bond into Zippy stock in the next year?

Solution: a.

The conversion price is $1,000/40 = $25.

The stock price would have to increase by approximately two standard deviations (2  $5 = $10) for the price to increase to $25 and for conversion to become attractive to the investors. From Chapter 7we know that 95% of possible outcomes fall within two standard deviations of the mean (average) value in a normal distribution. This means that there is a 5 percent chance that the stock price will move up or down by $10 or more. Since the normal distribution is symmetric, this means that there is only a 2.5 percent chance that Zippy’s stock price will increase enough for it to become attractive for the investors to exercise the conversion option in the next year.

LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-63

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Sample Test Problems 8.1

Seven years ago Eastern Corporation issued 20-year bonds that had a $1000 face value, paid interest annually, and that had a coupon rate of 7 percent. If the market rate of interest is 5.5 percent today, what is the current market price of an Eastern Corporation bond? Are these bonds selling at a premium or discount? (LO 2)

Solution: Years to maturity = n = 13 Coupon rate = C = 7% Annual coupon payment = $1,000 × 0.07 = $70 Current market rate = i = 5.5% Present value of bond = PB 0 1 2 3 4 ├───┼────┼───┼───┼─── $70 $70 $70 $70

13 ─────┤ $70 $1,000

1  1    1 − 1 − n 13   (1 + i )   (1.055) F $1,000 + + PB = C   = $70   n i   (1 + i )  0.055  (1.055)13         = $498.56 + $638.19 = $1,136.75 These bonds are selling at a premium. Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 8-64

Fundamentals of Corporate Finance, 3rd edition

8.2

Solutions Manual

You are considering investing in a 10-year zero coupon bond that compounds interest semiannually. If the current market rate is 5.65 percent, what is the maximum price you should have pay for this bond? (LO 2) Solution: Years to maturity = n = 10 Coupon rate = C = 0% Current market rate = i = 5.65% Frequency of payments = m = 2

0 1 2 3 4 5 6 ├───┼────┼───┼───┼───┼────┼── $0 $0 $0 $0 $0 $0

PB =

(

Fmn

1+ i

)

$1, 000

(1 + 0.0565 / 2 )

2 x10

20 ─────┤ $0 $1,000

= $572.83

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.3

Bigbox, Inc. has bonds outstanding that will mature in eight years. These bonds pay interest semiannually and have a coupon rate of 4.6 percent. If the bonds are currently selling at $888.92, what is the yield to maturity that an investor who buys them today can expect to earn? What is the effective annual yield? (LO 3) Solution: Years to maturity = n = 8 Coupon rate = C = 4.6% Current market rate = i Semiannual coupon payment = $1,000 × (0.046/2) = 23 Present value of bond = PB = $888.92 0 1 2 3 ├───────┼────────┼────────┼──

16 ─────────┤

SM 8-65

Fundamentals of Corporate Finance, 3rd edition

(888.92)

$23

$23 $1,000 To solve for the YTM, a trial-and-error approach has to be used. Since this bond is selling at a discount, we know that the market rate is higher than 4.6 percent.

$23

Solutions Manual

$23

SM 8-66

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Try i = 6% or i/2 = 3%. 1   1 − i n FV  (1 + 2 )  PB = C   +  i i n   (1 + 2 ) 2   1   1 − (1.03)16  $1,000 + = $23   0.03  (1.03)16      = $288.91 + $623.16 = $912.17  $888.92 Try a higher rate, i = 7%, i/2 = 3.5%.

1   1 − i n FV  (1 + 2 )  PB = C   +  i i n   (1 + 2 ) 2   1   1 − (1.035)16  $1,000 + = $23   0.035  (1.035)16      = $278.17 + $576.71 = $854.57  $888.92 Try a lower rate, i = 6.4%, i/2 = 3.2%.

1   1 − (1 + i ) n  FV PB = C   + n i   (1 + i )   1   1 − (1.032)16  $1, 000 $882.92 = $23   + 16  0.032  (1.032)   = $284.54 + $604.12 = $888.66  $888.92 The YTM is approximately 6.4 percent.

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Using a financial calculator provides an exact YTM of 6.395 percent Enter

16 N

Answer

i% 6.395%

$23 PMT

-$888.92 PV

$1,000 FV

The effective annual yield can be computed as:

EAY=(1 + Quoted rate m) m − 1 = (1 + 0.06395 2 ) − 1 2

= (1.03198) 2 − 1 = 0.064972 = 6.497% Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.4

Given a change in market interest rates, which will change more; the market price of a bond with 20 years until maturity or the market price of a bond with 5 years until maturity? Assume all the characteristics of these bonds are identical except the maturity dates. (LO 4) Solution: The price of the bond with 20 years to maturity will change more. The cash flows from the longer term bond are paid further in the future. As a result, these cash flows are more heavily discounted and therefore more sensitive to interest rate changes.

Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

8.5

Which of the following classes of securities is likely to have the lowest corporate borrowing cost? (LO 5) a. AAA rated bonds. b. A rated bonds. c. BB rated bonds. d. C rated bonds. e. All of the above will have the same corporate borrowing cost.

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Solution: a. The issuers of AAA rated bonds should have the lowest borrowing cost because their default risk premium is lower than issuers with weaker credit ratings. Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Chapter 9 Stock Valuation Before You Go On Questions and Answers

Section 9.1

1. What is NASDAQ?

The National Association of Securities Automatic Quotation (NASDAQ) system is one of the largest electronic stock markets in the world, listing over three thousand companies. It was created in 1971 by the National Assoc. of Securities Dealers

2. How do dealers differ from brokers?

A dealer differs from a broker in that a dealer takes ownership of assets and is exposed to inventory risk, while a broker only facilitates a transaction on behalf of a client. Unlike brokers, dealers are subject to capital risk, because they must finance their inventories of securities.

3. List the major stock market indexes, and explain what they tell us.

The major U.S. Stock market indexes are the Dow Jones Industrial Average, New York Stock Exchange, Standard & Poor’s 500 Index, and NASDAQ Composite Index. A stock market index is essentially a listing of stocks that bear some commonality, such as being traded on the same market exchange. They are used to measure the stock market performance and many are used to benchmark the performance of portfolios, such as mutual funds.

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4. What does the price-earnings ratio tell us? The price-earnings ratio is the firm’s current price divided by the current earnings. When valuing a company’s stock, it is useful to look at a company’s ratio and compare it to that of similar firms. In general, a high P/E ratio means high projected earnings in the future. In addition, it also tells us how much investors are willing to pay per dollar of earnings.

5. Why do some people view preferred stock as a special type of a bond rather than a stock?

Just like debt, preferred stock is often callable and may be convertible into common stock. Also, like debt, it has “credit” ratings that are similar to those issued to bonds. But most important, preferred stock has no voting rights and just like bonds pays fixed dividends. For these reasons, many analysts treat preferred stock as a special kind of debt rather than as an equity.

Section 9.2 1.

What is the general formula used to calculate the price of a share of a stock? What does it mean? The general formula developed to value a share of stock is as follows: P0 =

D3 D5 D1 D2 D4 + + + + +  2 3 4 (1 + R ) (1 + R ) (1 + R ) (1 + R ) (1 + R )5

It says that the price of a share of stock is the present value of all expected future dividends, or: Stock price = PV (all future cash dividends).

2. What are growth stocks, and why do they typically pay little on dividends?

Growth stocks are defined as equity in any company whose earnings are growing faster than the average firm and the higher growth rate is expected to continue for some time. Instead of

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paying dividends, these firms reinvest the earnings back into the firm to pursue other highreturn investment opportunities.

Section 9.3 1.

What three different models are used to value stocks based on different dividend patterns?

Based on dividend patterns, we can use the following three models to value stock: (1) zerogrowth dividend model, (2) constant-growth dividend model, or (3) supernormal dividend growth model.

2. Explain why the growth rate g must always be less than the rate of return R. For the valuation equation to have any meaning, the firm’s dividend growth rate g must be less than the rate of return R. It also makes intuitive sense, since no firm can in the long run grow faster than the rate of economy. If that was the case, this one firm would become 100 percent of the economy and that makes no sense.

Section 9.4 1. Why can skipping payment of a preferred dividend be a bad signal?

A preferred dividend is treated like an interest payment on debt by financial markets and investors. Although the firm will not be in default, any delay or failure to pay the dividends by the firm will be treated seriously by the financial markets and make them think that the firm is in financial difficulty.

2. How is a preferred stock with a fixed maturity valued?

Any preferred stock with a defined maturity date is similar to a bond with a fixed maturity date. This similarity allows for the preferred stock to be valued in a similar fashion after making adjustments for differences in the preferred stock relative to a bond. Using Equation 7.2, developed to value bonds, the coupons are replaced by the preferred dividends and the

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number of payments is adjusted to four a year to accommodate the fact that firms pay the dividends every quarter and not semiannually. This results in the model represented by Equation 8.7.

Self- Study Problems

9.1

Ted McKay has just bought the common stock of Ryland Corp. The company expects to grow at the following rates for the next three years: 30 percent, 25 percent, and 15 percent. Last year the company paid a dividend of $2.50. Assume a required rate of return of 10 percent. Compute the expected dividends for the next three years and also the present value of these dividends.

Solution: Expected dividends for Ryland Corp and their present value: 0

10%

├─────────┼─────────┼─────────┼─────────┼──────────› D0 = $2.50

g1 = 30%

g2 = 25%

D1 =

D0 × (1 + g1) = $2.50(1 + 0.30) = $3.25

D2 =

D1 × (1 + g2) = $3.25(1 + 0.25) = $4.06

D3 =

D2 × (1 + g3) = $4.06(1 + 0.15) = $4.67

g3 = 15%

R = 10%

Present value of the dividends = PV(D1) + PV(D2) + PV(D3) = $2.95 + $3.36 + $3.51 = $9.82 9.2

Merriweather Manufacturing Company has been growing at a rate of 6 percent for the past two years, and the CEO expects the company to continue to grow at this rate for the next several years. The company paid a dividend of $1.20 last year. If your required rate

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of return is 14 percent, what is the maximum price that you would be willing to pay for this company’s stock?

Solution: Present value of Merriweather stock: 0

14%

├─────────┼─────────┼─────────┼─────────┼──────────› D0 = $1.20

g = 6% R = 14% D1 = D0 × (1 + g) = $1.20(1 + 0.06) = $1.27

D1 $1.27 = ( R − g) (0.14 − 0.06) = $15.88

P0 =

The maximum price you should be willing to pay for this stock is $15.90.

9.3

Clarion Corp. has been selling electrical supplies for the past 20 years. The company’s product line has changed very little in the past five years, and the company’s management does not expect to add any new items for the foreseeable future. Last year, the company paid a dividend of $4.45 to its common stockholders. The company is not expected to increase its dividends for the next several years. If your required rate of return for such firms is 13 percent, what is the current value of this company’s stock?

Solution: Present value of Clarion Corp. stock: 0

13%

Year

├─────────┼─────────┼─────────┼─────────┼──────────›

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D0 = $4.45

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g = 0% R = 13% Since the company’s dividends are not expected to grow, D0 = D1 =D2=……..D∞ = $4.45 = D Current value of the stock

9.4

D/R

$4.45/0.13

$34.23

Barrymore Infotech is a fast -growing communications company. The company did not pay a dividend last year and is not expected to do so for the next two years. Last year the company’s growth accelerated, and management expects to grow the business at a rate of 35 percent for the next five years before growth slows to a more stable rate of 7 percent. In the third year, management has forecasted a dividend payment of $1.10. Dividends will grow with the company thereafter. Calculate the value of the company’s stock at the end of its rapid growth period (i.e., at the end of five years). The required rate of return for such stocks is 17 percent. What is the current value of this stock?

Solution: Present value of Barrymore Infotech stock: 0 17% 1

├────┼────┼────┼────┼────┼────┼────┼────┤ D0

g1 – g5 = 35%

g6 and beyond = 7%

R = 17% D0 = D1 =D2 = 0 D3 = $1.10 D4 = D3 × (1 + g4) = $1.10(1 + 0.35) =$1.485 D5 = D4 × (1 + g5) = $1.485(1 + 0.35) = $2.005 D6 = D5 × (1 + g6) = $2.005(1 + 0.07) = $2.145

Value of stock at t = 5 P5:

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D6 $2.145 = ( R − g) (0.17 − 0.07) = $21.45

P5 =

Present value of the dividends in years 1 to 5 = PV(D1) + PV(D2) + PV(D3) + PV(D4) + PV(D5) $1.10 $1.485 $2.005 + + (1.17)3 (1.17) 4 (1.17)5 = $0 + $0 + $0.69 + $0.79 + $0.91 = $2.39

= $0 + $0 +

Current value of stock = PV(Dividends) + PV(P5) = $2.39 + [$21.45/(1.17)5] = $2.39 + $9.78 = $ 12.18

9.5

You are interested in buying the preferred stock of a bank that pays a dividend of $1.80 every quarter. If you discount such cash flows at 8 percent, what is the value of this stock?

Solution: Present value of preferred bank stock: Quarterly dividend on preferred stock = D = $1.80 Required rate of return = 8% Current value of stock: = Po = =

D R $1.80  4 0.08

= $90.00

Discussion Questions

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9.1

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Why can the market price of a stock differ from its true (intrinsic) value?

Let us start by first defining the market price of a stock as the price that equates the demand for a stock with the supply of the stock. The role of the stock markets is to bring buyers and sellers together in the most efficient way such that stocks are bought and sold at the market price. In reality, however, barriers of various kinds including the geographic separation of the two parties, strong demand that leads to overvaluation and vice versa, make the market price of a security slightly different than its true (intrinsic) value. The more efficient the market place, the smaller the deviation between the two. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.2

Why are investors and managers concerned about stock market efficiency?

The role of secondary markets is to bring buyers and sellers together. Ideally, we would like stock markets to be as efficient as possible. Markets are efficient when current market prices of securities traded reflect all available information relevant to the security. If this is the case, security prices will be near or at their true value. The more efficient the market, the more likely this is to happen. This makes it easier for managers to price the stocks close to their intrinsic value. What investors are most concerned about is having complete information regarding a stock’s current price and where that price information can be obtained. Efficient markets allow them to trade at prices that are closer to the true value than otherwise possible. Thus, both investors who provide funds and managers (firms) who raise money are concerned when high transaction costs lead to inefficient markets. LO: 1 Level: Basic Bloomcode: Comprehension

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AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.3

Why are common stockholders considered to be more at risk than the holders of other types of securities?

In the hierarchy of lenders of funds to a firm, common stockholders have the most to lose. In the event of a firm becoming bankrupt, the law requires that creditors of different types, including bondholders, be paid off first. Next, preferred stockholders are paid off. Finally, common stockholders receive their investment if any funds are still available. Thus, common stockholders receive their money back last and are placed at most risk. This feature of common equity is referred to as residual claim. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.4

Under what conditions does it make sense to use the constant-growth dividend model to value a stock?

It only makes sense to use the constant-growth dividend model to value the stock of a company that is already paying a dividend and when that dividend can reasonably be expected to grow at a constant rate forever⎯in other words, the stock of a mature company. As discussed in the chapter, the growth rate of such a company will be less than the long term rate of inflation and the real growth rate of the economy. It must also be less than the required rate of return on the stock. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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What does it mean when a company has a very high P/E ratio? Give examples of industries in which you believe high P/E ratios are justified.

A high P/E ratio implies that investors believe that the firm has good prospects for earnings growth in the future. In fact, they believe that the firm will have higher growth potential than firms with lower P/E ratios. Companies in industries that are fast growing like biotech or any hi-tech industry have high P/E ratios. In the past, firms like Cisco and Intel had very high P/E ratios. As these firms matured and settled to annual growth rates of 15 percent or less, their P/E ratios have declined. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.6

Explain why preferred stock is considered to be a hybrid of equity and debt securities. The law considers preferred stock as equity. Thus, holders are treated as the firm’s owners. Also, like common stockholders, preferred stockholders have to pay taxes on their dividend income. However, preferred stockholders do not have any voting rights. In addition, they receive only a fixed dividend just like bondholders. If a firm is liquidated, then they receive a stated value (par value) similar to bondholders. Preferred stock is rated by credit rating agencies just like bonds. Some preferred issues are convertible to the firm’s common stock just as convertible bonds. Some preferred issues are not perpetual and have a fixed maturity just like bonds. Thus preferred stock is a hybrid security—like equity in some ways and like debt security in others.

LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Why is stock valuation more difficult than bond valuation?

Despite the availability of mathematical models to value stocks, it is more difficult to apply valuation techniques to stocks than to bonds. First, unlike bonds, firms are not in default if dividends are not declared. This makes it difficult to determine the size and timing of the cash flows. Second, common stock, unlike bonds, does not have a fixed maturity, and hence, it is difficult to determine a terminal value unlike bonds, which have a maturity value. Next, it is easier to calculate the present value of a bond because the required rate of return is observable. In the case of stocks, it is rather difficult to estimate a required rate of return for many stocks and classify them into different risk groups. LO: 2 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.8

You are currently thinking about investing in a stock valued at $25.00 per share. The stock recently paid a dividend of $2.25 and its dividend is expected to grow at a rate of 5 percent for the foreseeable future. You normally require a return of 14 percent on stocks of similar risk. Is the stock overpriced, underpriced, or correctly priced?

D0 = $2.25 Required rate of return (R) = 14% Growth rate (g) = 5% Using Constant-growth model, the price of stock is:

P0 =

D (1 + g ) D1 = 0 R−g R−g

$2.25(1.05) = $26.25 0.14 − 0.05

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This stock is underpriced at $25. Using the constant-growth model, we arrived at a price of $26.25 for this stock. This makes the stock underpriced, and it should be considered a good buy. LO: 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.9

Stock A and Stock B are both priced at $50 per share. Stock A has a P/E ratio of 17, while Stock B has a P/E ratio of 24. Which is the more attractive investment, considering everything else to be the same, and why?

Stock A is the more attractive investment because it has a lower P/E ratio. The lower the P/E ratio, the larger the amount of earnings supporting the stock price. This makes Stock A a more attractive investment than Stock B. LO: 1 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.10

Facebook does not pay dividends. How can it have a positive stock price?

Investors expect that Facebook will eventually start paying dividends and the value of its shares reflects the present value of these expected dividends. The fact that a company is not currently paying dividends does not mean that its stock is worthless. It is not uncommon for high growth firms not to pay dividends, since they often have to reinvest all of their earnings to maintain their high growth rate. However, if they are successful, as their growth rate slows over time they will begin to pay dividends. Examples of such companies that do not pay dividends include Apple, Microsoft, Dell, among many others. LO: 3, 4 Level: Intermediate

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Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

Questions and Problems

BASIC 9.1

Stock Market Index: What is a stock market index?

Solution: A stock market index is used to measure the performance of the stock market. These indexes reflect the value of the stocks in a particular market, such as the NYSE or the NASDAQ, or across markets, and increase and decrease as the values of the stocks go up and down. Examples of stock market indexes include the Dow Jones Industrial Average, the New York Stock Exchange Index, the Standard & Poor’s 500 Index, and the NASDAQ Composite Index. LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.2

Stock Market Index: What is the Dow Jones Industrial Average?

Solution: The Dow is the most widely published stock index and reflects the value of the stocks of 30 large companies. The value of the shares of these companies represents about 20 percent of the market value of all U.S. stocks. LO 1 Bloomcode: Knowledge

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AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

9.3

Stock Market Index: What does NASDAQ stand for? What is NASDAQ?

Solution: NASDAQ stands for National Association of Securities Dealers Automated Quotation system. NASDAQ is one of the largest electronic stock markets in the world, listing over three thousand companies. It is an OTC market and does not have any physical location. Companies listed on NASDAQ had market capitalization of $6.2 trillion as of December 2013.

LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

9.4

Dividend yield: What is a dividend yield? What does it tell us?

Solution: A dividend yield is the ratio of the annual dividend payout by the current market price of a stock. It tells us what percentage return we would earn from dividends alone if we purchased the stock at its current price. Alternatively, it tells us what percentage of the firm’s stock value is being distributed to stockholders each year. LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.5

Present value of dividends: Fresno Corp. is a fast-growing company whose management expects it to grow at a rate of 30 percent over the next two years and then slow down to a growth rate of 18 percent for the following three years. If the last

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dividend paid by the company was $2.15, estimate the dividends for the next five years. Compute the present value of these dividends if the required rate of return is 14 percent.

Solution: 0

├───────┼────────┼───────┼────────┼───────┤ D0 = $2.15

g1-2 = 30%;

g3-5 = 18%;

R = 14%

D1 = D0 × (1 + g1) = $2.15(1.30) = $2.795 D2 = D1 × (1 + g2) = $2.795(1.30) = $3.634 D3 = D2 × (1 + g3) = $3.634(1.18) = $4.288 D4 = D3 × (1 + g4) = $4.288(1.18) = $5.06 D5 = D4 × (1 + g5) = $5.06(1.18) = $5.97 $2.795 $3.634 $4.288 $5.06 $5.97 + + + + 1 2 3 4 (1.14) (1.14) (1.14) (1.14) (1.14)5 = $2.45 + $2.80 + $2.89 + $3.00 + $3.10 = $14.24

PV( Dividends ) =

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.6

Zero growth: Nynet, Inc., paid a dividend of $4.18 last year. The company’s management does not expect to increase its dividend in the foreseeable future. If the required rate of return is 18.5 percent, what is the current value of the stock?

Solution: D0 = $4.18; g = 0;

P0 =

R = 18.5%

D $4.18 = = $22.59 R 0.185

LO 4

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Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.7

Zero growth: Knight Supply Corp. has not grown for the past several years and management expects this lack of growth to continue. The firm last paid a dividend of $3.56. If you require a rate of return of 13 percent, what is the current value of this stock to you?

Solution: D0 = $3.56; g = 0;

P0 =

R = 13%

D $3.56 = = $27.38 R 0.13

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.8

Zero growth: Ron Santana is interested in buying the stock of First National Bank. While the bank’s management expects no growth in the near future, Ron is attracted by the dividend income. Last year the bank paid a dividend of $5.65. If Ron requires a return of 14 percent on such stocks, what is the maximum price he should be willing to pay for a share of the bank’s stock?

Solution: D0 = $5.65; g = 0; P0 =

R = 14%

D $5.65 = = $40.36 R 0.14

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance

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AICPA: Measurement

9.9

Zero growth: The current stock price of Largent, Inc., is $44.72. If the required rate of return is 19 percent, what is the dividend paid by this firm if the dividend is not expected to grow in the future?

Solution: P0 = $44.72; P0 =

R = 19%;

D = ?;

D R

D 0.19 D = $44.72  0.19 = $8.50

$44.72 =

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.10

Constant growth: Moriband Corp. paid a dividend of $2.15 yesterday. The company’s

dividend is expected to grow at a steady rate of 5 percent for the foreseeable future. If investors in stocks of companies like Moriband require a rate of return of 15 percent, what should be the market price of Moriband stock?

Solution: D0 = $2.15;

g = 5%;

P0 =

D1 D (1 + g ) = 0 R−g R−g

$2.15(1.05) = $22.58 0.15 − 0.05

R = 15%

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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Constant growth: Nyeil, Inc., is a consumer products firm that is growing at a constant rate of 6.5 percent. The firm’s last dividend was $3.36. If the required rate of return is 18 percent, what is the market value of this stock if dividends grow at the same rate as the firm?

Solution: D0 = $3.36;

P0 =

g = 6.5%;

R = 18%

D1 $3.36(1.065) = R − g 0.18 − 0.065

= $31.12 LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.12

Constant growth: Reco Corp. is expected to pay a dividend of $2.25 next year. The forecast for the stock price a year from now is $37.50. If the required rate of return is 14 percent, what is the current stock price? Assume constant growth.

Solution: D1 = $2.25;

P1 = $37.50;

R = 14%

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D2 D (1 + g ) = 1 R−g R−g $2.25(1 + g ) 0.14 − g

$37.50(0.14 − g ) = $2.25 + 2.25 g $5.25 − 37.5 g = 2.25 + 2.25 g $5.25 − $2.25 = 37.5 g + 2.25 g g=

$3.00 = 7.55% $39.75

P0 =

D1 R−g

$2.25 = $34.87 0.14 − 0.0755

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.13

Constant growth: Proxicam, Inc., is expected to grow at a constant rate of 7 percent. If the company’s next dividend, which will be paid in a year, is $1.15 and its current stock price is $22.35, what is the required rate of return on this stock?

Solution: D1 = $1.15;

P0 = $22.35;

g = 7%

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P0 =

D1 R−g

D1 +g P0

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$1.15 + 0.07 $22.35

= 0.0515 + 0.07 = 12.15% LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.14

Preferred stock valuation: X-Centric Energy Company has issued perpetual preferred stock with a stated (par) value of $100 and a dividend of 4.5 percent. If the required rate of return is 8.25 percent, what is the stock’s current market price?

Solution: D = 4.5% ($100) = $4.50; P0 =

R = 8.25%

D $4.50 = = $54.55 R 0.0825

LO 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.15

Preferred stock valuation: The First Bank of Flagstaff has issued perpetual preferred stock with a $100 par value. The bank pays a quarterly dividend of $1.65 on this stock. What is the current price of this preferred stock given a required rate of return of 11.6 percent?

Solution:

SM 9-20

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Quarterly dividend = $1.65 Required rate of return = R = 11.6% P0 =

(1.65  4) = $56.90 0.116

LO 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.16

Preferred stock valuation: The preferred stock of Axim Corp. is currently selling at $47.13. If the required rate of return is 12.2 percent, what is the dividend paid by this stock?

Solution: P0 = $47.13;

R = 12.2%

D 0.122 D = $47.13  0.122 = $5.75

P0 = $47.13 =

LO 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.17

Preferred stock valuation: Each quarter, Sirkota, Inc., pays a dividend on its perpetual preferred stock. Today the stock is selling at $63.37. If the required rate of return for such stocks is 15.5 percent, what is the quarterly dividend paid by Sirkota?

Solution: P0 = $63.37;

R = 15.5%

SM 9-21

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

D 0.155 D = $63.37  0.155 = $9.82

P0 = $63.37 =

Annual dividend = $9.82 Quarterly dividend = $9.82 /4 = $2.46 LO 6 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

INTERMEDIATE 9.18

Constant growth: Kay Williams is interested in purchasing the common stock of Reckers, Inc., which is currently priced at $37.45. The company is expected to pay a dividend of $2.58 next year and to increase its dividend at a constant rate of 7 percent. a. What should the market value of the stock be if the required rate of return is 14 percent? b. Is this a good buy? Why or why not?

Solution: D1 $2.58 = = $36.86 R − g 0.14 − 0.07

P0 =

The stock is overpriced and not a good buy.

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 9-22

Fundamentals of Corporate Finance, 3rd edition

9.19

Solutions Manual

Constant growth: The required rate of return is 23 percent. Ninex Corp. has just paid a dividend of $3.12 and is expected to increase its dividend at a constant rate of 5 percent. What is the expected price of the stock three years from now?

Solution: R = 23%;

D0 = $3.12;

g = 5%

D4 D0 (1 + g )4 P3 = = R−g R−g =

3.12(1.05)4 = $21.07 0.23 − 0.05

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.20

Constant growth: Jenny Banks is interested in buying the stock of Fervan, Inc., which is increasing its dividends at a constant rate of 6 percent. Last year the firm paid a dividend of $2.65. The required rate of return is 16 percent. What is the current value of this stock? What should be the price of the stock in year 5?

Solution: g = 6%,

D0 = $2.65,

R = 16%

P0 =

D1 $2.65(1.06) = = $28.09 R − g 0.16 − 0.06

P5 =

D6 $2.65(1.06)6 = = $37.59 R−g 0.16 − 0.06

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 9-23

Fundamentals of Corporate Finance, 3rd edition

9.21

Solutions Manual

Constant growth: You own shares of Old World DVD Company and are interested in selling them. With so many people downloading music these days, sales, profits, and dividends at Old World have been declining 6 percent per year. The firm just paid a dividend of $1.15 per share. The required rate of return for a stock this risky is 15 percent. If dividends are expected to decline at 6 percent per year, what is a share of the stock worth today?

Solution: R = 15%; P0 = =

D0 = $1.15;

g = -6%

D1 D (1 + g ) = 0 R−g R−g $1.15  (1 − 0.06) = $5.15 0.15 − ( −0.06)

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.22

Nonconstant growth: You own a company that competes with Old World DVD Company (in the previous problem). Instead of selling DVDs, however, your company sells music downloads from a web site. Things are going well now, but you know that it is only a matter of time before someone comes up with a better way to distribute music. Your company just paid a $1.50 per share dividend, and you expect to increase the dividend 10 percent next year. However, you then expect your dividend growth rate to begin going down – to 5 percent the following year, 2 percent the next year, and to -3 percent per year thereafter. Based upon these estimates, what is the value of a share of your company’s stock? Assume that the required rate of return is 12 percent.

Solution: g1 = 10%, g2 = 5%, g3 =2%, D1 = $1.50 × 1.1 = $1.65, $1.7672,

g = -3%,

D0 = $1.50

R = 12%

D2 = $1.65 × 1.05 = $1.7325, D3 = $1.7325 ×1.02 =

D4 = $1.7672 × 0.97 = $1.7141.

SM 9-24

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

P3 =

D4 $1.7141 = = $11.43 R − g 0.12 − (−0.03)

P0 =

D1 D2 D3 P3 + + + 2 3 1 + R (1 + R) (1 + R) (1 + R) 3

P0 =

$1.65 $1.7325 $1.7672 $11.43 + + + 1.12 (1.12) 2 (1.12) 3 (1.12) 3

P0 = $1.47 + $1.38 + $1.26 + $8.14 P0 = $12.25 LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.23

Nonconstant growth: Tre-Bien, Inc., is a fast-growing technology company. Management projects rapid growth of 30 percent for the next two years, then a growth rate of 17 percent for the following two years. After that, a constant-growth rate of 8 percent is expected. The firm expects to pay its first dividend of $2.45 a year from now. If dividends will grow at the same rate as the firm and the required rate of return on stocks with similar risk is 22 percent, what is the current price of the stock?

Solution: g1 = g2 = 30%,

g3 = g4 = 17%,

D1 = $2.45,

D2 = $2.45 × 1.30 = $3.19,

D4 = $3.73 × 1.17 = $4.36,

P4 =

g = 8%,

D1 = $2.45,

R = 22%

D3 = $3.19 × 1.17 = $3.73

D5 = 4.36 × 1.08 = $4.71

D5 $4.71 = = $33.63 R − g 0.22 − 0.08

SM 9-25

Fundamentals of Corporate Finance, 3rd edition

P0 =

D1 D2 D3 D4 P4 + + + + 2 3 4 1 + R (1 + R) (1 + R) (1 + R) (1 + R) 4

P0 =

$2.45 $3.19 $3.73 ($4.36 + 33.64) + + + 2 1.22 (1.22) (1.22)3 (1.22) 4

Solutions Manual

P0 = $2.01 + $2.14 + $2.05 + 17.15 P0 = $23.35 LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.24

Nonconstant growth: Management of ProCor, a biotech firm, forecasted the following growth rates for the next three years: 35 percent, 28 percent, and 22 percent. Management then expects the company to grow at a constant rate of 9 percent forever. The company paid a dividend of $1.75 last week. If the required rate of return is 20 percent, what is the value of this stock?

Solution: g1 = 35%; g2 = 28%; g3 = 22%; g4 = 9%; D0 = $1.75; R = 20%

SM 9-26

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

D1 = D0 (1 + g 1 ) = $1.75  1.35 = $2.36 D2 = D1 (1 + g 2 ) = $2.36  1.28 = $3.02 D3 = D2 (1 + g3 ) = $3.02  1.22 = $3.69 D4 = D3 (1 + g ) = $3.69  1.09 = $4.02

P3 =

D4 $4.02 = = $36.57 R − g 0.20 − 0.09

P0 =

D1 D2 D3 P3 + + + 2 3 1 + R (1 + R) (1 + R) (1 + R) 3

P0 =

$2.36 $3.02 $3.69 $36.57 + + + 2 1.20 (1.20) (1.20)3 (1.20)3

P0 = $1.97 + $2.10 + $2.14 + $21.16 P0 = $27.37 LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.25

Nonconstant growth: Revarop, Inc., is a fast- growth company that is expected to grow at a rate of 23 percent for the next four years. It is then expected to grow at a constant rate of 6 percent. Revarop’s first dividend, of $4.25, will be paid in year 3. If the required rate of return is 17 percent, what is the current value of the stock if dividends are expected to grow at the same rate as the company?

Solution: g1-4 = 23%;

g = 6%;

D3 = $4.25;

R = 17%

D4 = D3 × 1.23 = $4.25 × 1.23 = $5.23

SM 9-27

Fundamentals of Corporate Finance, 3rd edition

P4 =

D5 $5.23  (1.06) = = $50.37 R−g 0.17 − 0.06

P0 =

D3 D1 D2 D + P4 + + + 4 2 3 1 + R (1 + R) (1 + R) (1 + R) 4

P0 = 0 + 0 +

Solutions Manual

$4.25 ($5.23 + $50.37) + (1.17)3 (1.17) 4

P0 = $2.65 + $29.69 = $32.33

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.26

Nonconstant growth: Quansi, Inc., management expects to pay no dividends for the next six years. It has projected a growth rate of 25 percent for the next seven years. After seven years, the firm will grow at a constant rate of 5 percent. Its first dividend, to be paid in year 7, will be $3.25. If the required rate of return is 24 percent, what is the stock worth today?

Solution: g = 5%; R = 24%; D7 = $3.25; D1 – D6 = 0

P7 =

D8 $3.25  (1.05) = = $17.96 R−g 0.24 − 0.05

P0 =

D7 + P7 $3.25 + $17.96 = = $4.71 (1 + R)7 (1.24)7

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 9-28

Fundamentals of Corporate Finance, 3rd edition

9.27

Solutions Manual

Nonconstant growth: Staggert Corp. will pay dividends of $5.00, $6.25, $4.75, and $3.00 in the next four years. Thereafter, management expects the dividend growth rate to be constant at 6 percent. If the required rate of return is 18.5 percent, what is the current value of the stock?

Solution: D1 = $5;

D2 = $6.25;

D3 = 4.75;

D4 = $3;

g = 6%;

P0 =

D1 D2 D3 D4 P4 + + + + 2 3 4 1 + R (1 + R) (1 + R) (1 + R) (1 + R) 4

P4 =

D5 $3  (1.06) = = $25.44 R − g 0.185 − 0.06

P0 =

$5 $6.25 $4.75 ($3 + $25.44) + + + 2 3 1.185 (1.185) (1.185) (1.185)4

R = 18.5%;

P0 = $4.22 + $4.45 + $2.86 + $14.42 = $25.95

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.28

Nonconstant growth: Diaz Corp. is expected to grow rapidly at a rate of 35 percent for the next seven years. The company’s first dividend, to be paid three years from now, will be $5. After seven years, the company (and the dividends it pays) will grow at a rate of 8.5 percent. What is the value of Diaz stock with a required rate of return of 14 percent?

Solution: g1-7 = 35%; D3 = $5.00; g = 8.5%; R = 14% D1 = D2 = 0;

D3 = $5

D4 = $5 × 1.35 = $6.75 D5 = $6.75 × 1.35 = $9.11

SM 9-29

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

D6 =$9.11 × 1.35 = $12.30 D7 = $12.30 × 1.35 = $16.61 D8 = $16.61 × 1.085 = $18.02 P7 =

D8 $18.02 = = $327.64 R − g 0.14 − 0.085

P0 =

D1 D2 D3 D4 D5 D6 D + P7 + + + + + + 7 2 3 4 5 6 1 + R (1 + R) (1 + R) (1 + R) (1 + R) (1 + R) (1 + R) 7

= 0+0+

$5 $6.75 $9.11 $12.30 ($16.61 + $327.64) + + + + 3 4 (1.14) (1.14) (1.14)5 (1.14) 6 (1.14) 7

= $3.38 + $4.00 + $4.73 + $5.60 + $137.58 = $155.29

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.29

Nonconstant growth: Tin-Tin Waste Management, Inc., is growing rapidly. Dividends are expected to grow at rates of 30 percent, 35 percent, 25 percent, and 18 percent over the next four years. Thereafter, management expects dividends to grow at a constant rate of 7 percent. The stock is currently selling at $47.85, and the required rate of return is 16 percent. Compute the dividend for the current year (D0).

Solution: g1 = 30%; g2 = 35%; g3 = 25%; g4 = 18%; g = 7%; R = 16%; P0 = $47.85

SM 9-30

Fundamentals of Corporate Finance, 3rd edition

P0 = $47.85 =

Solutions Manual

D3 D1 D2 D4 P4 + + + + 2 3 4 (1 + R1 ) (1 + R2 ) (1 + R3 ) (1 + R4 ) (1 + R4 ) 4 D0  (1.30) D0  (1.30)  (1.35) D 0  (1.30)  (1.35)  (1.25) + + 1.16 (1.16) 2 (1.16)3

D  (1.30)  (1.35)  (1.25)  (1.18) + 0 + (1.16) 4

D0  (2.5886)  (1.07) 0.16 − 0.07 (1.16) 4

= D0  [1.12 + 1.30 + 1.41 + 1.43 + 17.00] D0 =

$47.85 = $2.15 $22.26

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

ADVANCED 9.30

Equation 9.4 shows the relation between a stock’s value and the dividend that is expected next year if dividends grow at a constant rate forever. If a firm pays all of its earnings as dividends, show how Equation 9.4 can be rearranged to calculate that firm’s P/E ratio. What does this tell us about the factors that determine a firm’s P/E ratio?

Solution: P0 =

D1 E1 , where, E1 is the earnings per share next year. = R−g R−g

Rearranging the formula:

P0 1 = E1 R − g This formula tells us that the P/E ratio is determined by both the risk of the dividend cash flows and the rate at which they are expected to grow. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance

SM 9-31

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

AICPA: Measurement

9.31

Riker Departmental Stores management has forecasted a growth rate of 40 percent for the next two years, followed by growth rates of 25 percent and 20 percent for the following two years. It then expects growth to stabilize at a constant rate of 7.5 percent forever. The firm paid a dividend of $3.50 recently. If the required rate of return is 18 percent, what is the current value of Riker’s stock?

Solution: g1-2 = 40%; g3 = 25%; g4 = 20%; g = 7.5%; D0 = $3.50; R = 18%

D1 = D0  (1 + g 1 ) = $3.50  1.40 = $4.90 D2 = D1  (1 + g 2 ) = $4.90  1.40 = $6.86 D3 = D2  (1 + g 3 ) = $6.86  1.25 = $8.575 D4 = D3  (1 + g 4 ) = $8.575  1.20 = $10.29 D5 = D4  (1 + g) = $10.29  1.075 = $11.06 P4 =

D5 $11.06 = = $105.35 R − g 0.18 − 0.075

P0 =

D1 D2 D3 D4 P4 + + + + 2 3 4 1 + R (1 + R) (1 + R) (1 + R) (1 + R) 4

P0 =

$4.90 $6.86 $8.575 $10.29 $105.35 + + + + 1.18 (1.18) 2 (1.18)3 (1.18) 4 (1.18) 4

P0 = $4.15 + $4.93 + $5.22 + $5.31 + $54.34 P0 = $73.94 LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 9-32

Fundamentals of Corporate Finance, 3rd edition

9.32

Solutions Manual

Courtesy Bancorp issued perpetual preferred stock a few years ago. The bank pays an annual dividend of $4.27 and your required rate of return is 12.2 percent. a.

What is the value of the stock given your required rate of return?

Should you buy this stock if its current market price is $34.41? Explain.

Solution: a.

D = $4.27; P0 =

R = 12.2%

D $4.27 = = $35.00 R 0.122

Since the stock is worth $35.00 but can be purchased for $34.41, you should buy this stock.

LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.33

Rhea Kirby owns shares in Ryoko Corp. Currently, the market price of the stock is $36.34. Management expects dividends to grow at a constant rate of 6 percent for the foreseeable future. Its last dividend was $3.25. Rhea’s required rate of return for such stocks is 16 percent. She wants to find out whether she should sell her shares or add to her holdings. a.

What is the value of this stock?

Based on your answer to part a, should Rhea buy additional shares in Ryoko Corp? Why or why not?

Solution: D1 $3.25  (1.06) = = $34.45 R−g 0.16 − 0.06

P0 =

No, she should not buy more shares. This stock is overpriced with the stock selling at a higher price than what it is worth. She should sell her shares.

LO 4 Bloomcode: Analysis

SM 9-33

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.34

Perry, Inc., paid a dividend of $2.50 yesterday. You are interested in investing in this company, which has forecasted a constant-growth rate of 7 percent for its dividends, forever. The required rate of return is 18 percent. a.

Compute the expected dividends D1, D2, D3, and D4.

Compute the present value of these four dividends.

What is the expected value of the stock four years from now (P4)?

What is the value of the stock today based on the answers to parts b and c?

Use the equation for constant growth (Equation 9.4) to compute the value of the stock today.

Solution: a.

D0 = $2.50 g = 7% R = 18% D1 = $2.50  (1.07) = $2.675 D2 = $2.50  (1.07)2 = $2.86 D3 = $2.50  (1.07)3 = $3.063 D4 = $2.50  (1.07)4 = $3.277

$2.675 $2.86 $3.063 $3.277 + + + (1.18)1 (1.18)2 (1.18)3 (1.18) 4 = $2.27 + 2.05 + $1.86 + $1.69 = $7.88

PV ( Dividends) =

D5 = D4 (1 + g ) = $3.277  (1.07) = $3.506

P4 =

D5 $3.506 = = $31.88 R − g 0.18 − 0.07

SM 9-34

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

$31.88 = $16.44 (1.18) 4 P0 = PV ( Dividends) + PV ( P4 )

PV ( P4 ) = d.

= $7.87 + $16.44 = $24.32

For a constant-growth stock: P0 =

D1 $2.675 = = $24.32 R − g 0.18 − 0.07

LO 4 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.35

Zweite Pharma is a fast -growing drug company. Management forecasts that in the next three years, the company’s dividend growth rates will be 30 percent, 28 percent, and 24 percent, respectively. Last week it paid a dividend of $1.67. After three years, management expects dividend growth to stabilize at a rate of 8 percent. The required rate of return is 14 percent. a.

Compute the dividends for each of the next three years, and calculate their present value.

Calculate the price of the stock at the end of year 3, when the firm settles to a constant-growth rate.

What is the current price of the stock?

Solution:

g1 = 30%; g2 = 28%; g3 = 24%; g = 8%; D0 = $1.67; R = 14%

SM 9-35

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

D1 = D0 (1 + g 1 ) = $1.67  (1.30) = $2.171 D 2 = D1 (1 + g 2 ) = $2.171  (1.28) = $2.779 D3 = D 2 (1 + g3 ) = $2.779  (1.24) = $3.446

a. PV(Dividends) =

D1 D2 D3 + + 2 1 + R (1 + R) (1 + R) 3

$2.171 $2.779 $3.446 + + 1.14 (1.14) 2 (1.14) 3

= $1.90 + $2.14 + $2.33 = $6.37

b. D4 = D3 (1 + g ) = $3.446  (1.08) = $3.722 P3 =

D4 $3.722 = = $62.02 R − g 0.14 − 0.08

$62.03 = $41.87 (1.14)3 P0 = PV ( Dividends) + PV ( P3 )

PV ( P3 ) = c.

= $6.37 + $41.87 = $48.23 LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.36

Triton Inc., is expected to grow at a rate of 22 percent for the next five years and then settle to a constant growth rate of 6 percent. The company recently paid a dividend of $2.35. The required rate of return is 15 percent. a.

Find the present value of the dividends during the rapid-growth period if dividends grow at the same rate as the company.

SM 9-36

Fundamentals of Corporate Finance, 3rd edition

What is the value of the stock at the end of year 5?

What is the value of the stock today?

Solutions Manual

Solution: g1-5 = 22%; g = 6%; D0 = $2.35; R = 15% a.

D1 = D0 (1 + g 1 ) = $2.35  (1.22) = $2.867 D 2 = D1 (1 + g 2 ) = $2.867  (1.22) = $3.498 D3 = D 2 (1 + g3 ) = $3.498  (1.22) = $4.267 D 4 = D3 (1 + g 4 ) = $4.267  (1.22) = $5.206 D5 = D 4 (1 + g ) = $5.206  (1.22) = $6.351

PV(Dividends) =

D3 D5 D1 D2 D4 + + + + 2 3 4 1 + R (1 + R) (1 + R) (1 + R) (1 + R)5

$2.867 $3.498 $4.267 $5.206 $6.351 + + + + 1.15 (1.15) 2 (1.15)3 (1.15) 4 (1.15) 5

= $2.49 + $2.65 + $2.81 + $2.98 + $3.16 = $14.09

D6 = D5 (1 + g ) = $6.351  (1.06) = $6.732

P5 =

D6 $6.732 = = $74.80 R − g 0.15 − 0.06

PV(P5 ) =

$74.80 = $37.19 (1.15)5

P0 = PV(Dividends) + PV(P5 ) = $14.09 + $37.19 = $51.28

SM 9-37

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.37

Ceebros Builders is expanding very fast and is expected to grow at a rate of 25 percent for the next four years. The company recently paid a dividend of $3.60 but is not expected to pay any dividends for the next three years. In year 4, management expects to pay a $5 dividend and thereafter to increase the dividend at a constant rate of 6 percent. The required rate of return on such stocks is 20 percent. a.

Calculate the present value of the dividends during the fast-growth period.

What is the value of the stock at the end of the fast-growth period (P4)?

What is the value of the stock today?

Would today’s stock value be affected by the length of time you intend to hold the stock?

Solution: a.

g1-4 = 25% g = 6% D0 = $3.60 D4 = $5.00 R = 20% PV( Dividends ) = 0 + 0 + 0 +

P4 =

D5 $5.00  (1.06) = = $37.86 R−g 0.20 − 0.06 P0 = $2.41 +

c. d.

$5 = $2.41 (1.20) 4

$37.86 = $20.67 (1.20) 4

No, the length of the holding period has no bearing on today’s stock price.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 9-38

Fundamentals of Corporate Finance, 3rd edition

Solutions Manual

Sample Test Problems

9.1

Which type of secondary market provides the most efficient market for financial securities? (LO 1) Solution: An auction market is the most efficient type of secondary market because the buyers and sellers in an auction market interact directly with each other and bargain over price.

Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

9.2

Is preferred stock a debt or an equity security? (LO 2) Solution: Preferred stock represents an ownership interest in a corporation and is legally a form of equity. However, it does have characteristics that are similar to those of debt, such as no voting rights, fixed payments (dividends), and credit ratings similar to those issued to bonds.

Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.3

Burnes, Inc. is a mature firm that is growing at a constant rate of 5.5 percent per year. The last dividend that the firm paid was $1.50 per share. If dividends are expected to grow at the same rate as the firm and the required rate of return on Burnes’s stock is 12 percent, what is the market value of the company’s stock? (LO 4) Solution: D0 = $1.50;

P0 =

g = 5.5%;

R = 12%

D1 $1.50 1.055 = = $24.35 R − g 0.12 − 0.055

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

SM 9-39

Fundamentals of Corporate Finance, 3rd edition

9.4

Solutions Manual

Abacus Corporation will pay dividends of $2.25, $2.95, and $3.15 in the next three years. After three years, the dividends are expected to grow at a constant rate of 4 percent per year. If the required rate of return is 14.5 percent, what is the current value of the Abacus common stock? (LO 4) Solution: gconstant = 4%; D1 = $2.25 D2 = $2.95 D3 = $3.15; R = 14.5%

P3 =

D4 $3.15 1.04 = = $31.20 R − g 0.145 − .04

$2.25 $2.95 $3.15 $31.20 + + + 2 3 (1.145) (1.145) (1.145) (1.145)3 = $1.97 + $2.25 + $2.10 + $20.78 = $27.10

P0 =

Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

9.5

The preferred stock of Wellcare Inc. is currently trading at $137.50 per share. If the required rate of return is 8 percent and this stock has no maturity date, what is the quarterly dividend paid by this stock? What is the quarterly dividend if the stock will mature in one year and it has a par value of $140? (LO 6) Solution: With no maturity date: PS0 = $137.5; R = 8.0% D PS0 = $137.50 = 0.08 D = $137.50  0.08 = $11.00

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Annual dividend = $11.00 Quarterly dividend = $11.00 /4 = $2.75

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We can use Equation 9.7 to solve for the dividend with a one year maturity date:

D/m + Pmn D/m D/m D/m + + + 2 3 (1 + i / m) (1 + i / m) (1 + i / m) (1 + i / m) 4 D/m D/m D/m D/m + $140 = $137.50 = + + + 2 3 (1 + 0.08 / 4) (1 + 0.08 / 4) (1 + 0.08 / 4) (1 + 0.08 / 4) 4 D/m D/m D/m D/m + $140 = $137.50 = + + + 2 1.02 (1.02) (1.02)3 (1.02) 4

PS0 =

Using a financial calculator to solve for PMT, we find that the quarterly dividend, D/m = $2.14. Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Measurement

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CHAPTER 10 The Fundamentals of Capital Budgeting

Before You Go On Questions and Answers Section 10.1 1.

Why are capital investments considered the most important decisions made by a firm’s management? Capital investments are the most important decisions made by a firm’s management, because they usually involve large cash outflows and once made are not easily reversed. These are usually long-term projects that will define the firm’s line of business and significantly contribute to the total revenue figure for years to come.

What are the differences between capital projects that are independent, mutually exclusive, and contingent?

A project is independent if the decision to accept or reject it does not affect the decision to accept or reject another project. On the other hand, projects are mutually exclusive if the acceptance of one implies rejection of the other. Contingent projects are those in which the acceptance of one project is dependent on another project.

Section 10.2 1.

What is the NPV of a project? NPV is simply the difference between the present value of a project’s expected future cash flows and its cost. It is the recommended technique used to value capital investments, as it takes into account both the timing of the cash flows and their risk.

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If a firm accepts a project with a $10,000 NPV, what is the effect on the value of the firm?

If a firm accepts a project with a $10,000 NPV, it will increase its value by $10,000.

What are the five steps used in NPV analysis? The five-step process used in the NPV analysis can be listed as follows: (1) Determine the cost of the project. (2) Estimate the project’s future cash flows over its expected life. (3) Determine the riskiness of a project and the appropriate cost of capital. (4) Compute the project’s NPV. (5) Make a decision.

Section 10.3 1.

What is the payback period? The payback period is defined as the number of years it takes to recover the project’s initial investment. All other things being equal, the project with the shortest payback period is usually the optimal investment.

Why does the payback period provide a measure of a project’s liquidity risk?

The payback period determines how quickly you recover your investment in a project. Thus, it serves as a good measure of the project’s liquidity.

What are the main shortcomings of the payback method?

The payback method does not account for time value of money, nor does it distinguish between high- and low-risk projects. In addition, there is no rationale behind choosing the cutoff criteria. For all these reasons, the payback method is not the ideal capital decision rule. Copyright © 2015 John Wiley & Sons, Inc.

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Section 10.4 1.

What are the major shortcomings of using the ARR method as a capital budgeting method?

The biggest shortcoming of using ARR as a capital budgeting tool is that it uses historical, or book value data rather than cash flows and thus disregards the time value of money principle. In addition, as in the payback method, it fails to establish a rationale behind picking the appropriate hurdle rate.

Section 10.5 1.

What is the IRR method?

The IRR, or the internal rate of return, is the discount rate that makes the net present value of the project’s future cash flows zero. The IRR determines whether the project’s return rate is higher or lower than the required rate of return, which is the firm’s cost of capital. As a rule, a project should be accepted if the IRR exceeds the firm’s cost of capital; otherwise the project should be rejected.

In capital budgeting, what is a conventional cash flow pattern?

A conventional project cash flow in capital budgeting is one in which an initial cash outflow is followed by one or more future cash inflows.

Why should the NPV method be the primary decision tool used in making capital investment decisions?

Given all the different methods to evaluate capital investment decisions, the NPV method is the preferred valuation tool as it accounts for both time value of money and the project’s risk. Furthermore, NPV is not sensitive to nonconventional projects, and

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therefore it is superior to the IRR technique and it gives a measure of the value increase/decrease to the firm by undertaking the project.

Section 10.6 1.

What decision criteria should managers use in selecting projects when there is not enough money to invest in all available positive-NPV projects?

When a firm does not have enough money to invest in all available positive NPV projects, managers should identify the bundle of positive NPV projects that creates the greatest total value for stockholders.

What might cause a firm to face capital constraints?

A firm might face capital constraints because it can be difficult for outside investors (new creditors, bondholders, or stockholders) to accurately assess the risks and returns associated with the firm’s projects. This might cause the investors to require returns for their capital that are so high that they make positive-NPV projects unattractive, because those projects cannot produce the high returns required by investors.

How can the PI help in choosing projects when a firm faces capital constraints? What are its limitations?

The basic principle is to select the projects that yield the largest NPV per dollar invested. The PI tells us the NPV per dollar invested for an individual project. In a single period, Copyright © 2015 John Wiley & Sons, Inc.

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the PI can be used to identify the bundle of projects that yields the largest NPV per dollar invested. However, as illustrated in Section 12.5, the PI will not necessarily help identify the most valuable bundle of projects if investments are being compared across more than one year and the timing of cash flows from early investments affects the firm’s ability to make subsequent investments.

Section 10.7 1.

What changes have taken place in the capital budgeting techniques used by U.S. companies?

Over the years, there has been a shift from using payback and ARR as the primary capital budgeting tools to using NPV and IRR instead. Managers today understand the importance of the time value of money and discounting and thus regard ARR as an inaccurate and obsolete decision tool.

Self-Study Problems 10.1

The Management of Premium Manufacturing Company is evaluating two forklift systems to use in its plant that produces the towers for a windmill power farm. The costs and the cash flows from these systems are shown below. If the company uses a 12 percent discount rate for all projects, determine which forklift system should be purchased using the net present value (NPV) approach.

Otis

Year 0

Year 1

Year 2

Year 3

−$3,123,450

$979,225

$1,358,886

$2,111,497

Forklifts

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Craigmore

−$4,137,410

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$875,236

$1,765,225

$2,865,110

Forklifts Solution: NPV for Otis Forklifts:

CFt t t = 0 (1 + k )

NPV = 

$979,225 $1,358,886 $2,111,497 + + (1 + 0.12)1 (1.12) 2 (1.12) 3 = −$3,123,450 + $874,308 + $1,083,296 + $1,502,922 = $337,075

= −$3,123,450 +

NPV for Craigmore Forklifts:

CFt t t = 0 (1 + k )

NPV = 

$875,236 $1,765,225 $2,865,110 + + (1 + 0.12)1 (1.12) 2 (1.12) 3 = −$4,137,410 + $781,461 + $1,407,229 + $2,039,227 = $90,606

= −$4,137,410 +

Premium should purchase the Otis forklift since it has a larger NPV.

10.2

Perryman Crafts Corp. management is evaluating two independent capital projects that together will cost the company $250,000. The two projects will provide the following cash flows:

Year

Project A

Project B

$80,750

$32,450

$93,450

$76,125

$40,325

$153,250

$145,655

$96,110

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Which project will be chosen if the company’s payback criterion is three years? What if the company accepts all projects as long as the payback period is less than five years?

Solution: Payback periods for Perryman projects A and B: Project A Cumulative Year

Cash Flow

Cash Flows

$(250,000)

80,750

(169,250)

93,450

(75,800)

40,235

(35,565)

145,655

110,090

Project B Cumulative Year

Cash Flow

Cash Flows

$(250,000)

32,450

(217,550)

76,125

(141,425)

153,250

11,825

96,110

107,935

Payback period for Project A:

Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$35,565 $145,655 per year = 3.24 years

= 3+

Payback period for Project B:

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Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$141, 425 $153, 250 per year = 2.92 years

=2+

If the payback period is three years, only project B will be chosen. If the payback criterion is five years, both A and B will be chosen.

10.3

Terrell Corp. management is considering purchasing a machine that will cost $117,250 and will be depreciated on a straight-line basis over a five-year period. The sales and expenses (excluding depreciation) for the next five years are shown in the following table. The company’s tax rate is 34 percent.

Year 1

Year 2

Year 3

Year 4

Year 5

Sales

$123,450

$176,875

$242,455

$255,440

$267,125

Expenses

$137,410

$126,488

$141,289

$143,112

$133,556

The company will accept all projects that provide an accounting rate of return (ARR) of at least 45 percent. Should the company accept this project?

Terrell will accept all projects that provide an accounting rate of return (ARR) of at least 45 percent. Should the company accept the project?

Solution: Year 1

Year 2

Year 3

Year 4

Year 5

Sales

$123,450 $176,875

$242,455

$255,440

$267,125

Expenses

137,410

141,289

143,112

133,556

126,488

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Depreciation

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23,450

EBIT

23,450

$ (37,410) $ 26,937

$ 77,716

$ 88,878

$110,119

9,159

26,423

30,219

37,440

$ (24,691) $ 17,778

$ 51,293

$ 58,659

$ 72,679

Taxes (34%)

12,719

Net Income Beginning Book Value

117,250

93,800

70,350

46,900

23,450

Less: Depreciation

(23,450)

Ending Book Value

$ 93,800 $ 70,350

$ 46,900

$ 23,450

Average net income

= (–$24,691 + $17,778 + $51,293 + $58,659 + $72,679) / 5 = $35,143.60

Average book value

= (1$117,250 + $93,800 + $70,350 + $46,900 + $23,450 + $02)/6 = $58,625

Accounting rate of return

= $35,143.6 / $58,625 = 0.599 or 59.9%

The company should accept the project.

10.4

Refer to Problem 9.1. Compute the IRR for each of the two systems. Is the investment decision different from the one determined by NPV?

Solution: IRR for two forklift systems: Otis Forklifts: First compute the IRR by the trial-and-error approach: NPV (Otis) = $337,075 > 0 Use a higher discount rate to get NPV = 0! At k = 15%, $979, 225 $1,358,886 $2,111, 497 + + (1 + 0.15)1 (1.15) 2 (1.15)3 = −$3,123, 450 + $851,500 + $1,027,513 + $1,388,344 = $143,907.

NPVOtis = −$3,123, 450 +

Try a higher rate. At k = 17%,

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NPVOtis = −$3,123,450 + $836,944 + $992,685 + $1,318,357 = $24,536. Try a higher rate. At k = 17.5%,

NPVOtis = −$3,123,450 + $833,383 + $984,254 + $1,301,598 = −$4,215 Thus the IRR for Otis is less than 17.5 percent. Using a financial calculator, you can find that the exact rate to be 17.43 percent.

Craigmore Forklifts: First compute the IRR by the trial-and-error approach: NPV (Craigmore) = $90,606 > 0 Use a higher discount rate to get NPV = 0! At k = 15%,

$875, 236 $1,765, 225 $2,865,110 + + (1.15)1 (1.12) 2 (1.12)3 = −$4,137, 410 + $761,075 + $1,334,764 + $1,883,856 = −$157,715

NPVCraigmore = −$4,137, 410 +

Try a lower rate. At k = 13%,

NPVCraigmore = −$4,137, 410 + $774,545 + $1,382, 430 + $1,985,665 = $5, 230 Try a higher rate. At k = 13.1%,

NPVCraigmore = −$4,137, 410 + $773,860 + $1,379,987 + $1,980, 403 = −$3,161 Thus the IRR for Craigmore is less than 13.1 percent. The exact rate is 13.06 percent. Based on the IRR, we would still pick Otis over Craigmore forklift systems. The decision is the same as that indicated by NPV

10.5

You are considering a project that has an initial outlay of $1 million. The profitability index of the project is 2.24. What is the NPV of the project?

Solution: You can use Equation 9.6 to solve for the NPV:

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NPV + Initial investment Initial investment NPV + $1,000,000 2.24 = $1,000,000 PI

Therefore: NPV = $2,240,000

Discussion Questions 10.1

Explain why the cost of capital is referred to as the “hurdle” rate in capital budgeting.

Solution The cost of capital is the minimum required return on any new investment that allows a firm to break even. Since we are using the cost of capital as a benchmark or “hurdle” to compare the return earned by any project, it is sometimes referred to as the hurdle rate. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.2

a. Sykes, Inc. management is considering two projects: a plant expansion and a new computer system for the firm’s production department. Classify these projects as independent, mutually exclusive, or contingent projects and explain your reasoning.

b. A company is building a new plant on the outskirts of Smallesville. The town has offered to donate the land, and as part of the agreement, the company will have Copyright © 2015 John Wiley & Sons, Inc.

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to build an access road from the main highway to the plant. How will the project of building the road be classified in the capital budgeting analysis?

c. Management of your firm is currently considering the upgrading of the operating systems of all the firm’s computers. One alternative is to choose the Linux operating system that a local computer services firm has offered to install and maintain. Microsoft has also put in a bid to install the new Windows operating system for businesses. How would these projects be classified?

Solution a. These two projects are independent projects. Accepting or rejecting one will not influence the decision on the other project. The cash flows of the two projects are unrelated.

b. This is a contingent project. Acceptance of the road-building project is contingent on the new plant being a financially viable project. If the new plant will not have a positive value, then the firm will not even consider this project. However, this project’s cost will have to be considered along with the cost of building the new plant in the capital budgeting analysis. c. These are two mutually exclusive projects. The company’s computers need only one operating system. Either the Linux or the Windows operating system needs to be installed, not both. Hence, the selection of one will eliminate the other from consideration. LO: 1 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.3

In the context of capital budgeting, what is “capital rationing”?

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Solution Capital rationing implies that a firm does not have the resources necessary to fund all of the available projects. In other words, funding needs exceed funding resources. Thus, the available capital will be allocated to the projects that will benefit the firm and its shareholders the most. Projects that create the largest increase in shareholder wealth will be accepted until all the available resources have been allocated. LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.4

Provide two conditions under which a set of projects might be characterized as mutually exclusive.

Solution When projects are mutually exclusive, acceptance of one project precludes the acceptance of others. Typically, mutually exclusive projects perform the same function and so only one of them needs to be accepted. A funding or resource constraint can also cause projects to be mutually exclusive. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.5

a. A firm invests in a project that is expected to earn a return of 12 percent. If the appropriate cost of capital is also 12 percent, did the firm make the right decision. Explain.

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Solution a. We would normally argue that a firm should only accept projects in which the project’s return exceeds the cost of capital. In other words, only if the net present value exceeds zero should a project be accepted. But in reality, projects with a zero NPV should also be accepted because the project earns a return that equals the cost of capital. For some firms like the one above, this could be the situation because they may not have projects that provide a return greater than the cost of capital for the firm. b. When a firm takes on positive NPV projects, the value of the firm increases. By the same token, when a project undertaken has a negative NPV, the value of the firm will decrease by the amount of the net present value. LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.6

Identify the weaknesses of the payback period method.

Solution There are several critical weaknesses in the payback period approach of evaluating capital projects. ▪

The payback period ignores the time value of money by not discounting future cash flows.

▪

When comparing projects, it ignores risk differences between the projects.

▪

A firm may establish payback criteria with no economic basis for that decision and thereby run the risk of losing out on good projects.

▪

The method ignores cash flows beyond the payback period, thus leading to nonselection of projects that may produce cash flows well beyond the payback period or more cash flows than accepted projects. This leads to a bias against longer-term

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projects. LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.7

What are the strengths and weaknesses of the accounting rate of return approach?

Solution The biggest advantage of Accounting Rate of Return (ARR) approach is that it is easy to compute since accounting data is readily available, whereas estimating cash flows is more difficult. However, the disadvantages outweigh this specific advantage. Similar to the payback, it does not discount cash flows, but merely averages net income over time. No economic rationale is used in establishing an ARR cutoff rate. Finally, the ARR uses net income to evaluate the project and not cash flows or market data. This is a serious flaw in this approach. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.8

Under what circumstances might the IRR and NPV approaches produce conflicting

results?

Solution IRR and the NPV methods of evaluating capital investment projects might produce dissimilar results under two circumstances. First, if the project’s cash flows are not conventional—that is, if the sign of the cash flow changes more than once during the life Copyright © 2015 John Wiley & Sons, Inc.

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of a project—then multiple IRRs can be obtained as solutions. We would be unable to identify the correct IRR for decision making. (See Learning by Doing Application 10.3.) The second situation occurs when two or more projects are mutually exclusive. The project with the highest IRR may not necessarily be the one with the highest NPV and thereby be the right choice. There is an important reason for this. IRR assumes that all cash flows received during the life of a project are reinvested at the IRR, whereas the NPV method assumes that they are reinvested at the cost of capital. Since the cost of capital is the better proxy for opportunity cost, NPV uses the better proxy, while the IRR may use an unrealistically higher rate as proxy. LO: 5 Level: Intermediate Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.9

The modified IRR (MIRR) alleviates two concerns with using the IRR method for evaluating capital investments. What are they?

Solution IRR assumes that the cash flows from a project are reinvested at the project’s IRR, while the NPV assumes that they are invested at the firm’s cost of capital. The NPV assumption is correct more often than not. The MIRR assumes that each operating cash flow is reinvested at the firm’s cost of capital.

The second appeal of MIRR is that under this method all of the compounded operating cash flow values are summed up to get the project’s terminal value. Since most projects generate positive total net operating cash flows, MIRR does not suffer from issues associated with unconventional cash flows. LO: 5 Level: Basic Copyright © 2015 John Wiley & Sons, Inc.

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Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.10 Elkridge Construction Company has an overall (composite) cost of capital of 12 percent. This cost of capital reflects the cost of capital for an Elkridge Construction project with average risk. However, the firm takes on projects of various risk levels. The company’s experience suggests that low-risk projects have a cost of capital of 10 percent and high-risk projects have a cost of capital of 15 percent. Which of the following projects should the company not select to maximize shareholder wealth?

Project

Expected Return

Risk

1. Single-family homes

13%

Low

2. Multifamily residential

Average

3. Commercial

High

4. Single-family homes

Low

5. Commercial

High

Required

Expected

Return

Solution Project

Risk

Decision

1. Single-family homes

Low

10%

13%

2. Multifamily residential

Average

Accept / Indifferent

3. Commercial

High

4. Single-family homes

Low

Reject

5. Commercial

High

Reject

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10.11 High Tech Monopoly Co. has plenty of cash to fund any conceivable positive NPV project. Can you describe a situation in which capital rationing could still occur?

Solution: Financial capital is not the only constrainable item within the firm. This might occur, for example, when human capital is in short supply, as is the case with most high-technology firms. Even if every positive NPV project could be funded, the firm might not have enough employees to manage the projects. Therefore, even with ample financial capital, firms will more than likely still be rationing projects. LO: 6 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.12 The profitability index is a tool for measuring a project’s benefits relative to its costs. How might this help to eliminate bias in project selection?

Solution: Since the profitability index is a modified pure-return-type measure, it offers a method to maximize the use of capital that is employed by the firm. This could help eliminate some types of bias if the measure were to be employed universally. However, it does not

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necessarily maximize the use of capital that is not employed, which could in some circumstances be problematic. LO: 6 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Questions and Problems BASIC 10.1

Net present value: Riggs Corp. management is planning to spend $650,000 on a newmarketing campaign. They believe that this action will result in additional cash flows of $325,000 over the next three years. If the discount rate is 17.5 percent, what is the NPV on this project?

Solution: Initial investment = $650,000 Annual cash flows = $325,000 Length of project = n = 3 years Required rate of return = k = 17.5% Net present value = NPV

NCFt $325,000 $325,000 $325,000 = −$650,000 + + + t (1.175)1 (1.175) 2 (1.175)3 t = 0 (1 + k ) = −$650,000 + 276,596 + $235,401 + $200,341 = $62,337 n

NPV = 

LO 2

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Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.2

Net present value: Kingston, Inc. management is considering purchasing a new machine at a cost of $4,133,250. They expect this equipment to produce cash flows of $814,322, $863,275, $937,250, $1,017,112, $1,212,960, and $1,225,000 over the next six years. If the appropriate discount rate is 15 percent, what is the NPV of this investment?

Solution: Cost of new machine = $4,133,250 Length of project = n = 6 years Required rate of return = k = 15% n

NCFt t t =0 (1 + k )

NPV = 

$814,322 $863,275 $937,250 $1,017,112 $1,212,960 $1,225,000 + + + + + (1.15)1 (1.15) 2 (1.15) 3 (1.15) 4 (1.15) 5 (1.15) 6 = −$4,133,250 + $708,106 + $652,760 + $616257 + $581,537 + $603,055 + $529,601

= −$4,133,250 + = −$441,933

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.3

Net present value: Crescent Industries management is planning to replace some existing machinery in its plant. The cost of the new equipment and the resulting cash flows are shown in the accompanying table. If the firm uses an 18 percent discount rate for projects like this, should management go ahead with the project? Year

Cash Flow

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−$3,300,000

875,123

966,222

1,145,000

1,250,399

1,504,445

Solution: Initial investment = $3,300,000 Length of project = n = 5 years Required rate of return = k = 18%

NCFt t t = 0 (1 + k ) n

NPV = 

$875,123 $966,222 $1,145,000 $1,250,399 $1,504,455 + + + + (1.18)1 (1.18) 2 (1.18)3 (1.18) 4 (1.18)5 = −$3,300,000 + $741,630 + $693,926 + $696,882 + $644,942 + $657,607 = $134,986

= −$3,300,000 +

Since the NPV is positive, the firm should accept the project. LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.4

Net present value: Management of Franklin Mints, a confectioner, is considering purchasing a new jelly bean-making machine at a cost of $312,500. They project that the cash flows from this investment will be $121,450 for the next seven years. If the appropriate discount rate is 14 percent, what is the NPV for the project?

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Annual cash flows = $121,450 Length of project = n = 7 years Required rate of return = k = 14%

NCFt t t = 0 (1 + k ) n

NPV = 

$121,450 $121,450 $121,450 $121,450 $121,450 + + + + (1.14)1 (1.14) 2 (1.14)3 (1.14) 4 (1.14)5 $121,450 $121,450 + + (1.14)6 (1.14)7 = −$312,500 + $106,535 + $93,452 + $81,975 + $71,908 + $63,077 + $55,331 + $48,536 = $208,315

= −$312,500 +

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.5

Net present value: Blanda Incorporated management is considering investing in two alternative production systems. The systems are mutually exclusive, and the cost of the new equipment and the resulting cash flows are shown in the accompanying table. If the firm uses a 9 percent discount rate for production system projects, in which system should the firm invest? Year 0 1 2 3

System 1 -15,000 15,000 15,000 15,000

System 2 -45,000 32,000 32,000 32,000

Solution The NPV of System 1 is $22,969.42 and the NPV of System 2 is $36,001.43. Since the NPV of the System 2 is larger than the NPV for System 1, and the investments are mutually exclusive, the firm should take System 2. LO 2 Bloomcode: Analysis AASCB: Analytic Copyright © 2015 John Wiley & Sons, Inc.

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IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.6

Payback: Refer to problem 10.5. What are the payback periods for Production Systems 1 and 2? If the systems are mutually exclusive and the firm always chooses projects with the lowest payback period, in which system should the firm invest?

Solution System 1 has a payback of exactly one year. System 2 has a payback of 1.41 years. Given the shorter payback period for system 1, the investment should be made in System 1 based on the payback criteria. LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.7

Payback: Quebec, Inc., is purchasing machinery at a cost of $3,768,966. The company’s management expects the machinery to produce cash flows of $979,225, $1,158,886, and $1,881,497 over the next three years, respectively. What is the payback period?

Solution: Cumulative Year

Cash Flow

$(3,768,966)

979,225

(2,789,741)

1,158,886

(1,630,855)

1,881,497

250,642

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 2 + ($1,630,855 / $1,881,497) = 2.87 years LO 3

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Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.8

Payback: Northern Specialties just purchased inventory-management computer software at a cost of $1,645,276. Cost savings from the investment over the next six years will produce the following cash flow stream: $212,455, $292,333, $387,479, $516,345, $645,766, and $618,325. What is the payback period on this investment?

Solution: Cumulative Year

Cash Flow

$(1,645,276)

212,455

(1,432,821)

292,333

(1,140,488)

387,479

(753,009)

516,345

(236,664)

645,766

409,102

618,325

1,027,427

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 4 + ($236,664 / $645,766) = 4.37 years LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.9

Payback: Nakamichi Bancorp has made an investment in banking software at a cost of $1,875,000. Management expects productivity gains and cost savings over the next

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several years. If, as a result of this investment, te firm is expected to generate additional cash flows of $586,212, $713,277, $431,199, and $318,697 over the next four years, what is the investment’s payback period? Solution: Cumulative Year

Cash Flow

$(1,875,000)

586,212

(1,288,788)

713,277

(575,511)

431,199

(144,312)

318,697

174,385

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($144,312 / $318,697) = 3.45 years LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective 10.10 Average accounting rate of return (ARR): Capitol Corp. management is expecting a project to generate after-tax income of $63,435 in each of the next three years. The average book value of the project’s equipment over that period will be $212,500. If the firm’s investment decision on any project is based on an ARR of 37.5 percent, should this project be accepted?

Solution: Annual after-tax income = $63,435 Average after-tax income = ($63,435 +$63,435 + $63,435) / 3 = $63,435 Average book value of equipment = $212,500

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Average after - tax income Average book value $63,435 = = 29.9% $212,500

Accounting rate of return =

Since the project’s ARR is below the acceptance rate of 37.5 percent, the project should be rejected. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.11 Internal rate of return: Refer to Problem 10.4. What is the IRR that Franklin Mints management can expect on this project?

Solution: Initial investment = $312,500 Annual cash flows = $121,450 Length of project = n = 7 years Required rate of return = k = 14% To determine the IRR, a trial-and-error approach can be used. Set NPV = 0. Since the project had a positive NPV of $208,315, try IRR > k. Try IRR = 25%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.25) 7   0  −$312,500 + $121,450    0.25     −$312,500 + $383,920  $71,420

Try a higher rate, IRR = 34%.

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NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.34) 7   0  −$312,500 + $121,450    0.34     −$312,500 + $311,161  −$1,339 Try a lower rate, IRR = 33.8%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 −  (1.338) 7   0 = −$312,500 + $121,450    0.338    = −$312,500 + $312,515 = $15  0 The IRR of the project is 33.8 percent. Using a financial calculator, we find that the IRR is 33.8 percent. LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.12 Internal rate of return: Hathaway, Inc., a resort management company, is refurbishing one of its hotels at a cost of $7.8 million. Management expects that this will lead to additional cash flows of $1.8 million for the next six years. What is the IRR of this project? If the appropriate cost of capital is 12 percent, should Hathaway go ahead with this project?

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Annual cash flows = $1,800,000 Length of project = n = 6 years Required rate of return = k = 12% To determine the IRR, a trial-and-error approach can be used. Set NPV = 0. Try IRR = 12%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.12) 6   0  −$7,800,000 + $1,800,000    0.12     −$7,800,000 + $7,400,533  −$399,467

Since NPV < 0, try a lower rate, IRR = 10%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.10) 6   0  −$7,800,000 + $1,800,000    0.10     −$7,800,000 + $7,839,469  $39,469 Try IRR = 10.2%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 −  (1.102) 6   0  −$7,800,000 + $1,800,000    0.102     −$7,800,000 + $7,793,735  −$6,265 Try IRR = 10.15%.

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NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1   1 − (1.1015) 6   0  −$7,800,000 + $1,800,000    0.1015     −$7,800,000 + $7,805,129  $5,129 The IRR of the project is between 10.15 percent and 10.2 percent. Using a financial calculator, we find that the IRR is 10.1725 percent. Since IRR < k, reject the project. LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.13 Profitability index: What is the profitability index, and why is it helpful in the capital rationing process?

Solution: The profitability index is computed as the ratio of NPV plus initial investment divided by initial investment. In the capital rationing process, we can calculate the profitability index for each potential investment and choose the projects with the largest indexes until we run out of capital. This follows the basic principle that we need to choose the set of projects that creates the greatest value given the limited capital available. LO 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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INTERMEDIATE 10.14 Net present value: Champlain Corp. management is investigating two computer systems. The Alpha 8300 costs $3,122,300 and will generate cost savings of $1,345,500 in each of the next five years. The Beta 2100 system costs $3,750,000 and will produce cost savings of $1,125,000 in the first three years and then $2 million for the next two years. If the company’s discount rate for similar projects is 14 percent, what is the NPV for the two systems? Which one should be chosen based on the NPV?

Solution: Cost of Alpha 8300 = $3,122,300 Annual cost savings = $1,345,500 Length of project = n = 5 years Required rate of return = k = 14%

1   1−  NCFt (1.14) 5    NPV =  = − $ 3 , 122 , 300 + $ 1 , 345 , 500  t  0.14  t = 0 (1 + k )   = −$3,122,300 + $4,619,210 = $1,496,910 n

Cost of Beta 2100 = $3,750,000 Length of project = n = 5 years Required rate of return = k = 14%

1   1−  NCFt (1.14) 3  $2,000,000 $2,000,000  + NPV =  = − $ 3 , 750 , 000 + $ 1 , 125 , 500  + t (1.14) 4 (1.14) 5  0.14  t =0 (1 + k )   = −$3,750,000 + $2,611,836 + $1,184,161 + 1,038,737 = $1,084,734 n

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Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.15 Net present value: Briarcrest Condiments is a spice-making firm. Recently, it developed a new process for producing spices. The process requires new machinery that would cost $1,968,450, have a life of five years, and would produce the cash flows shown in the following table. What is the NPV if the discount rate is 15.9 percent? Year

Cash Flow

$512,496

(242,637)

814,558

887,225

712,642

Solution: Cost of equipment = $1,968,450 Length of project = n = 5 years Required rate of return = k = 15.9%

NCFt t t =0 (1 + k )

NPV = 

$512,496 $242,637 $814,558 $887,225 $712,642 − + + + (1.159)1 (1.159) 2 (1.159) 3 (1.159) 4 (1.159) 5 = −$1,968,450 + $442,188 − $180,630 + $523,205 + 491,700 + 340,764 = −$351,223

= −$1,968,450 +

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.16 Net present value: Cranjet Industries is expanding its product line and its production capacity. The costs and expected cash flows of the two independent projects are given in the following table. The firm uses a discount rate of 16.4 percent for such projects. a.

What are the NPVs of the two projects?

Should both projects be accepted? Or either? Or neither? Explain your reasoning.

Product Line

Production Capacity

Year

Expansion

$(2,575,000)

$(8,137,250)

600,000

2,500,000

875,000

2,500,000

875,000

2,500,000

875,000

3,250,000

875,000

3,250,000

Solution: a.

Required rate of return = k =16.4% Product Line Expansion: Cost of product line expansion = $2,575,000 n

NCFt t t =0 (1 + k )

NPV = 

$600,000 $875,000 $875,000 $875,000 $875,000 + + + + (1.164)1 (1.164) 2 (1.164) 3 (1.164) 4 (1.164) 5 = −$2,575,000 + $515,464 + $645,806 + $554,816 + 476,646 + 409,490 = $27,222

= −$2,575,000 +

Production Capacity Expansion: Cost of production capacity expansion = $8,137,250

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NCFt t t =0 (1 + k )

NPV = 

1   1 − (1.164) 3  $3,250,000 $3,250,000 + = −$8,137,250 + $2,500,000   + (1.164) 4 (1.164) 5  0.164    = −$8,137,250 + $5,578,116 + $1,770,400 + $1,520,962 = $732,228 b.

Since they are independent, and both have NPV > 0, both projects should be accepted.

LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.17 Net present value: Emporia Mills management is evaluating two alternative heating systems. Costs and projected energy savings are given in the following table. The firm uses 11.5 percent to discount such project cash flows. Which system should be chosen?

Year

System 100

System 200

$(1,750,000)

$(1,735,000)

275,223

750,000

512,445

612,500

648,997

550,112

875,000

384,226

Solution: Required rate of return = k = 11.5% System 100: Cost of System 100 = $1,750,000

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NCFt $275,223 $512,445 $648,997 $875,000 = −$1,750,000 + + + + t (1.115)1 (1.115) 2 (1.115) 3 (1.115) 4 t =0 (1 + k ) = −$1,750,000 + $246,837 + $412,190 + $468,186 + 566,120 = −$56,667

NPV = 

System 200: Cost of System 200 = $1,735,000 n

NCFt $750,000 $612,500 $550,112 $384,226 = −$1,735,000 + + + + t (1.115)1 (1.115) 2 (1.115) 3 (1.115) 4 t =0 (1 + k ) = −$1,735,000 + $672,646 + $492,670 + $396,850 + 248,592 = $75,758

NPV = 

Since System 200 has a positive NPV, select that system. Reject System 100 as it has negative NPV. LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.18 Payback: Creative Solutions, Inc., has just invested $4,615,300 in new equipment. The firm uses a payback period criteria of not accepting any project that takes more than four years to recover its costs. Management anticipates cash flows of $644,386, $812,178, $943,279, $1,364,997, $2,616,300, and $2,225,375 over the next six years. Does this investment meet the firm’s payback criteria?

Solution: Cumulative Year

Cash Flow

$(4,615,300)

644,386

(3,970,914)

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812,178

(3,158,736)

943,279

(2,215,457)

1,364,997

(850,460)

2,616,300

1,765,840

2,225,375

3,991,215

Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$850, 460 $2,616,300 = 4.33 years

=4+

Since the project payback period exceeds the firm’s target of four years, it should not have been accepted. LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.19 Discounted payback: Timeline Manufacturing Co. management is evaluating two projects. The company uses payback criteria of three years or less. Project A has a cost of $912,855, and project B’s cost is $1,175,000. Cash flows from both projects are given in the following table. What are their discounted payback periods, and which will be accepted with a discount rate of 8 percent? Year

Project A

Project B

$ 86,212

$586,212

313,562

413,277

427,594

231,199

285,552

Solution: Project A

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Cumulative Year

$(912,855)

Cumulative PVCF

PVCF

$(912,855)

86,212

(826,643)

79,826

(833,029)

313,562

(513,081)

268,829

(564,200)

427,594

(85,487)

339,438

(224,762)

285,552

200,065

209,889

(14,873)

The payback period of Project A exceeds three years. Project B Cumulative Year 0

Cumulative

$(1,175,000) $(1,175,000)

PVCF

$(1,175,000)

586,212

(588,788)

542,789

(632,211)

413,277

(175,511)

354,318

(277,893)

231,199

55,688

183,533

(94,359)

The payback period of Project A exceeds three years. Since the firm’s acceptance criteria is three years, neither project will be accepted. LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.20 Payback: Regent Corp. management is evaluating three competing types of equipment. Costs and cash flow projections for all three are given in the following table. Which would be the best choice based on payback period? Year 0

Type 1

Type 2

Type 3

$(1,311,450)

$(1,415,888)

$(1,612,856)

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212,566

586,212

786,212

269,825

413,277

175,000

455,112

331,199

175,000

285,552

141,442

175,000

121,396

175,000

Solution: Type 1

Type 2

Cumulative

Type 3

Cumulative

Year

$(1,311,450)

$(1,415,888)

$(1,612,856)

($1,612,856)

212,566

(1,098,884)

586,212

(829,676)

786,212

(826,644)

269,825

(829,059)

413,277

(416,399)

175,000

(651,644)

455,112

(373,947)

331,199

(85,200)

175,000

(476,644)

285,552

(88,395)

141,442

56,242

175,000

(301,644)

121,396

33,001

175,000

(126,644)

175,000

48,356

Type 1:

Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$88,395 $121,396 = 4.73 years

=4+

Type 2:

Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$85, 200 $141, 442 = 3.6 years

= 3+

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Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$126,644 $175,000 = 5.72 years

= 5+

Select Type 2 because it has the lowest payback period. LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.21 Discounted payback: Nugent Communication Corp. is investing $9,365,000 in new technologies. The company’s management expects significant benefits in the first three years after installation (as can be seen by the following cash flows), and smaller constant benefits in each of the next four years. What is the discounted payback period for the project assuming a discount rate of 10 percent? Years

Cash flows

4–7

$2,265,433

$4,558,721

$3,378,911

$1,250,000

Solution: Discount rate = k = 10% Cumulative Year 0

$(9,365,000) $(9,365,000)

Cumulative PVCF

PVCF

$(9,365,000)

2,265,433

(7,099,567)

2,059,485

(7,305,515)

4,558,721

(2,540,846)

3,767,538

(3,537,977)

3,378,911

838,065

2,538,626

(999,352)

1,250,000

2,088,065

853,767

(145,585)

1,250,000

3,338,065

776,152

630,567

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1,250,000

4,588,065

705,592

1,336,159

1,250,000

5,838,065

641,448

1,977,607

Discounted PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 4 + ($145,585 / $776,152) = 4.19 years LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.22 Modified internal rate of return (MIRR): Morningside Bakeries recently purchased equipment at a cost of $650,000. Management expects the equipment to generate cash flows of $275,000 in each of the next four years. The cost of capital is 14 percent. What is the MIRR for this project?

Solution: PV of costs = $650,000 Length of project = n = 4 years Cost of capital = k = 14% Annual cash flows = CFt = $275,000

TV = CF1 (1 + k ) n −1 + CF2 (1 + k ) n − 2 +  + CFn (1 + k ) n − n = $275,000(1.14)3 + $275,000(1.14) 2 + $275,000(1.14)1 + $275,000(1.14)0 = $407,425 + $357,390 + $313,500 + $275,000 = $1,353,315 Now we can solve for the MIRR using Equation 9.5.

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TV (1 + MIRR) t $1,353,315 $650,000 = (1 + MIRR) 4 $1,353,315 (1 + MIRR) 4 = = 2.0820 $650,000 PVCosts =

(1 + MIRR) = (2.0820) 4 = 1.2012 MIRR = 0.2012 = 20.1% 1

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.23 Modified internal rate of return (MIRR): Management of Sycamore Home Furnishings is considering acquiring a new machine that can create customized window treatments. The equipment will cost $263,400 and will generate cash flows of $85,000 over each of the next six years. If the cost of capital is 12 percent, what is the MIRR on this project?

Solution: PV of costs = $263,400 Length of project = n = 6 years Cost of capital = k = 12% Annual cash flows = CFt = $85,000

TV = CF1 (1 + k ) n −1 + CF2 (1 + k ) n − 2 +  + CFn (1 + k ) n − n = $85,000(1.12)5 + $85,000(1.12) 4 + $85,000(1.12)3 + $85,000(1.12) 2 + $85,000(1.12)1 + $85,000(1.12)0 = $149,799 + $133,749 + $119,419 + $106,624 + $95,200 + $85,000 = $689,791 Now we can solve for the MIRR using Equation 9.5.

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TV (1 + MIRR) t $689,791 $263, 400 = (1 + MIRR)6 $689,791 (1 + MIRR)6 = = 2.6188 $263, 400 PVCosts =

(1 + MIRR) = (2.6188) 6 = 1.1740 MIRR = 0.1740 = 17.4% 1

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.24 Internal rate of return: Management of Great Flights, Inc., an aviation firm, is considering purchasing three aircraft for a total cost of $161 million. The company would lease the aircraft to an airline. Cash flows from the proposed leases are shown in the following table. What is the IRR of this project? Years

Cash Flow

1–4

$23,500,000

5–7

$72,000,000

8–10

$80,000,000

Years

Cash Flow

Initial investment =

1–4

$23,500,000

$161,000,000

Length of project =

5–7

$72,000,000

n = 10 years

Required rate of

8–10

$80,000,000

return = k =

Solution:

To determine the IRR, the trial-and-error approach can be used. Set NPV=0. Try a higher rate than k = 15%; try IRR = 22%.

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NCFt t t =0 (1 + IRR)

NPV = 0 = 

1  1    1 − (1.22) 4  1 − (1.22) 3  1  + $72,000,000    0  −$161,000,000 + $23,500,000   4  0.22   0.22  (1.22)     1   1 − (1.22) 3  1  + $80,000,000   7  0.22  (1.22)    −$161,000,000 + $58,600,552 + $66,374,346 + $40,614,233  $4,589,131 Try IRR = 23%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1  1    1 − (1.23) 4  1 − (1.23) 3  1  + $72,000,000    0  −$161,000,000 + $23,500,000   4  0.23   0.23  (1.23)     1   1 − (1.23) 3  1  + $80,000,000   7  0.23  (1.23)    −$161,000,000 + $57,534,386 + $63,271,035 + $37,778,708  −$2,415,871 Try IRR = 22.7%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1 1     1 − (1.227) 4  1 − (1.227) 3  1  + $72,000,000    0  −$161,000,000 + $23,500,000   4  0.227   0.227  (1.227)     1   1 − (1.227) 3  1  + $80,000,000   7  0.227  (1.227)    −$161,000,000 + $57,850,786 + $64,183,552 + $38,605,355  −$360,307

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The IRR of the project is between 22 and 23 percent. Using a financial calculator, we find that the IRR is 22.65 percent. LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.25 Internal rate of return: Refer to problem 10.5. Compute the IRR for both production System 1 and production System 2. Which has the higher IRR? Which production system has the higher NVP? Explain why the IRR and NPV rankings of Systems 1 and 2 are different?

Solution The IRR of system 1 is 83.93 percent and the IRR of system 2 is 50.07 percent. The NPV of system 1 is $22,969.42 and the NPV of system 2 is $36,001.43. System 1 delivers a higher IRR because it requires a lower initial investment and the cost is recovered the first year. Thus, even with lower cash inflows in the years after startup, system 1is able to deliver a higher return on the initial investment. System 2 has a higher initial investment but delivers a higher net cash flow for the firm. LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.26 Internal rate of return: Ancala Corporation management is considering investments in two new golf apparel lines for next season: golf hats and belts. Due to a funding constraint, these lines are mutually exclusive. A summary of each project’s estimated cash flows over its three -year life, as well as the IRR and NPV of each are outlined below. The CFO of the firm has decided to manufacture the belts; however, the CEO is Copyright © 2015 John Wiley & Sons, Inc.

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questioning this decision given that the IRR is higher for manufacturing hats. Explain to the CEO why the IRRs and NPVs of the belt and hat projects disagree? Is the CFO’s decision the correct? Year 0 1 2 3

Golf Belts -$1,000 1,000 500 500

Golf Hats -$500 500 300 300

NPV IRR

$697.97 54%

$427.87 61%

Solution The IRRs and NPVs of the belt and hat lines disagree because of the differences in the scale of the project. Golf hats deliver a higher IRR because they require a lower initial investment. Thus, even with lower cash inflows in the years after startup, the golf hat project is able to deliver a higher return on the initial investment. While the golf belts project does cost more, it delivers a higher net cash flow for Ancala’s investors. This NPV factors in the initial cost of the project, and reflects the total net cash flow for the firm’s shareholders. The CFO’s decision to choose the golf belts project is the right choice because it yields the higher net cash flows for Ancala’s investors. LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.27 Internal rate of return: Compute the IRR on the following cash flow streams: a.

An initial investment of $25,000 followed by a single cash flow of $37,450 in year 6.

An initial investment of $1 million followed by a single cash flow of $1,650,000 in year 4.

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An initial investment of $2 million followed by cash flows of $1,650,000 and $1,250,000 in years 2 and 4, respectively.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Solution: a.

Try IRR = 7%. n

NCFt t t = 0 (1 + IRR) $37,450 0  −$25,000 + (1.07) 6  −$25,000 + $24,955  −$45

NPV = 0 = 

Try IRR = 6.97%. n

NCFt t t =0 (1 + IRR) $37,450 0  −$25,000 + (1.0697) 6  −$25,000 + $24,997  −$3

NPV = 0 = 

The IRR of the project is approximately 6.97 percent. Using a financial calculator, we find that the IRR is 6.968 percent.

Try IRR = 12%. n

NCFt t t = 0 (1 + IRR) $1,650,000 0  −$1,000,000 + (1.12) 4  −$1,000,000 + $1,048,605  $48,605

NPV = 0 = 

Try IRR = 13%.

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NCFt t t =0 (1 + IRR) $1,650,000 0  −$1,000,000 + (1.13) 4  −$1,000,000 + $1,011,976  $11,976

NPV = 0 = 

Try IRR = 13.3%. n

NCFt t t = 0 (1 + IRR) $1,650,000 0  −$1,000,000 + (1.133) 4  −$1,000,000 + $1,001,300  $1,300

NPV = 0 = 

The IRR of the project is approximately 13.3 percent. Using a financial calculator, we find that the IRR is 13.337 percent.

Try IRR = 15%. n

NCFt t t =0 (1 + IRR) $1,650,000 $1,250,000 0  −$2,000,000 + + (1.15) 2 (1.15) 4  −$2,000,000 + $1,247,637 + $714,692  −$37,671

NPV = 0 = 

Try IRR = 14%. n

NCFt t t =0 (1 + IRR) $1,650,000 $1,250,000 0  −$2,000,000 + + (1.14) 2 (1.14) 4  −$2,000,000 + $1,269,621 + $740,100  $9,721

NPV = 0 = 

The IRR of the project is between 14 and 15 percent. Using a financial calculator, we find that the IRR is 14.202 percent.

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An initial outlay of $3,125,000 followed by annual cash flows of $565,325 for the next eight years.

An initial investment of $33,750 followed by annual cash flows of $9,430 for the next five years.

An initial outlay of $10,000 followed by annual cash flows of $2,500 for the next seven years.

Solution: a.

Initial investment = $3,125,000 Annual cash flows = $565,325 Length of investment = n = 8 years

Try IRR = 8%.

1   1−  NCFt (1.08) 8    NPV =  = − $ 3 , 125 , 000 + $ 565 , 325  t  0.08  t =0 (1 + k )   = −$3,125,000 + $3,248,719 = $123,719 n

Try a higher rate, IRR = 9%.

1   1−  NCFt (1.09) 8    NPV =  = − $ 3 , 125 , 000 + $ 565 , 325  t  0.09  t =0 (1 + k )   = −$3,125,000 + $3,128,972 = $3,972 n

The IRR of the project is approximately 9 percent. Using a financial calculator, we find that the IRR is 9.034 percent.

Initial investment = $33,750 Annual cash flows = $9,430

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Length of investment = n = 5 years Try IRR = 12%.

1   1−  NCFt (1.12) 5    NPV =  = − $ 33 , 750 + $ 9 , 430  t  0.12  t =0 (1 + k )   = −$33,750 + $33,993 = $243 n

Try IRR = 12.3%.

1   1− 5   NCFt (1.123)  NPV =  = −$33,750 + $9,430   t  0.123  t =0 (1 + k )   = −$33,750 + $33742 = −$8  0 n

The IRR of the project is approximately 12.3 percent. Using a financial calculator, we find that the IRR is 12.29 percent.

Initial investment = $10,000 Annual cash flows = $2,500 Length of investment = n = 7 years Try IRR = 16%.

1   1−  NCFt (1.16) 7    NPV =  = − $ 10 , 000 + $ 2 , 500  t  0.16  t =0 (1 + k )   = −$10,000 + $10,096 = $96 n

Try IRR = 16.3%.

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1   1− 7   NCFt (1.163)  NPV =  = −$10,000 + $2,500   t  0.163  t =0 (1 + k )   = −$10,000 + $10,008 = $8  0 n

The IRR of the project is approximately 16.3 percent. Using a financial calculator, we find that the IRR is 16.327 percent. LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

9.29

Profitability index: Suppose that you could invest in the following projects but have only $30,000 to invest. How would you make your decision and in which projects would you invest? Project

Cost

NPV

$ 8,000

$4,000

11,000

7,000

9,000

5,000

7,000

4,000

Solution: One would compute the Profitability index for each of the projects as follows:

PI =

NPV+Initial investment Initial investment

The profitability indexes of the projects are:

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PI A =

$4,000 + $8,000 = 1.50 $8,000

PI B =

$7,000 + $11,000 = 1.64 11,000

PI C =

$5,000 + $9,000 = 1.56 $9,000

PI D =

$4,000 + $7,000 = 1.57 $7,000

Solutions Manual

With $30,000, you should invest in B, D, and C. The total cost is $27,000, and the total NPV is $16,000. LO 6 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.30 Profitability index: Suppose that you could invest in the same projects as in the previous problem, but have only $25,000 to invest. Which projects would you chose?

Solution: The profitability indexes of the projects are: A: 1.50; B: 1.64; C: 1.56; D: 1.57 With $25,000, you cannot invest in all of B, D, and C, since the total cost is $27,000. You may think that you should then invest in only B and D, since they have the highest

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profitability indexes. This will yield a total NPV of $11,000, and you are left with $7,000 of idle capital. If you give up project B, however, which has the highest profitability index and highest cost, and invest instead in A, C, and D, which require less capital, you will get a total NPV of $13,000, and you are left with less idle capital ($1,000). From this example you can see that capital rationing with indivisible projects are sometimes complicated and require a careful thought of all possibilities (or linear/integer programming). LO 6 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

ADVANCED 10.31 Management of Draconian Measures, Inc., is evaluating two independent projects. The company uses a 13.8 percent discount rate for such projects. The costs and cash flows for the projects are shown in the following table. What are their NPVs? Year

Project 1

Project 2

$(8,425,375)

$(11,368,000)

3,225,997

2,112,589

1,775,882

3,787,552

1,375,112

3,125,650

1,176,558

4,115,899

1,212,645

4,556,424

1,582,156

1,365,882

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Solution: Project 1: Cost of Project 1 = $8,425,375 Length of project = n = 7 years Required rate of return = k = 13.8% n

NCFt t t =0 (1 + k )

NPV = 

$3,225,997 $1,775,882 $1,375,112 $1,176,558 $1,212,645 + + + + (1.138)1 (1.138) 2 (1.138) 3 (1.138) 4 (1.138) 5 $1,582,156 $1,365,882 + + (1.138) 6 (1.138) 7 = −$8,425,375 + $2,834,795 + $1,371,291 + $933,064 + 701,527 + $635,364 + $728,443 + $552,608 = −$668,283

= −$8,425,375 +

Since Project 1 NPV is negative, we reject this project.

Project 2: Cost of Project 2 = $11,368,000 Length of project = n = 5 years Required rate of return = k = 13.8% n

NCFt t t =0 (1 + k )

NPV = 

$2,112,589 $3,787,552 $3,125,650 $4,115,899 $4,556,424 + + + + (1.138)1 (1.138) 2 (1.138) 3 (1.138) 4 (1.138) 5 = −$11,368,000 + $1,856,405 + $2,924,651 + $2,120,868 + $2,454,119 + $2,387,332 = $375,375

= −$11,368,000 +

Since Project 2 NPV is positive, we accept this project. LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.32 Refer to Problem 10.31. a.

What are the IRRs for the projects?

Does the IRR criterion suggest a different decision than the NPV criterion?

Explain how you would expect the management of Draconian Measures to decide which project(s) to invest in.

Solution: a.

Project 1: At the required rate of return of 13.8 percent, Project 1 has a NPV of $(668,283). To find the IRR, try lower rates. Try IRR = 11%. n

NCFt t t =0 (1 + k )

NPV = 

$3,225,997 $1,775,882 $1,375,112 $1,176,558 $1,212,645 + + + + (1.11)1 (1.11) 2 (1.11) 3 (1.11) 4 (1.11) 5 $1,582,156 $1,365,882 + + (1.11) 6 (1.11) 7 = −$8,425,375 + $2,906,304 + $1,441,346 + $1,005,470 + $775,035 + $719,646 + $845,885 + $657,889 = −$73,801

= −$8,425,375 +

Try a lower rate, IRR=10.7%. n

NCFt t t =0 (1 + k )

NPV = 

$3,225,997 $1,775,882 $1,375,112 $1,176,558 $1,212,645 + + + + (1.107)1 (1.107) 2 (1.107) 3 (1.107) 4 (1.107) 5 $1,582,156 $1,365,882 + + (1.107) 6 (1.107) 7 = −$8,425,375 + $2,914,180 + $1,449,168 + $1,013,667 + $783,471+ $729,450 + $859,733 + $670,471 = −$5,235

= −$8,425,375 +

The IRR of the project is approximately 10.7 percent. Using a financial calculator, we find that the IRR is 10.677 percent.

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Project 2: At the required rate of return of 13.8 percent, Project 2 has a NPV of $ 375,375. To find the IRR, try higher rates. Try IRR = 15%. n

NCFt t t = 0 (1 + IRR) $2,112,589 $3,787,552 $3,125,650 $4,115,899 $4,556,424 0 = −$11,368,000 + + + + + (1.15)1 (1.15) 2 (1.15) 3 (1.15) 4 (1.15) 5 = −$11,368,000 + $1,837,034 + $2,863,933 + $ 2,055,166 + $ 2,353,279 + $ 2,265,348 = $6,760

NPV = 0 = 

Try IRR = 15.1%. n

NCFt t t = 0 (1 + IRR) $2,112,589 $3,787,552 $3,125,650 $4,115,899 $4,556,424 0 = −$11,368,000 + + + + + (1.151)1 (1.151) 2 (1.151) 3 (1.151) 4 (1.151) 5 = −$11,368,000 + $1,835,438 + $2,858,959 + $ 2,049,814 + $2,345,111 + $ 2,255,524 = −$23,154

NPV = 0 = 

The IRR of the project is between 15 and 15.1 percent. Using a financial calculator, we find that the IRR is 15.023 percent.

Based on the IRR, Project 1 will be rejected and Project 2 will be accepted. These decisions are identical to those based on NPV. (Given that Project 1 had a negative NPV, the IRR will always be less than the required rate of return 13.8%.)

Management would use the decision spelled out by NPV, although in this case the IRR has come up with the same decision.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.33 Management of Dravid, Inc., is currently evaluating three projects that are independent. The cost of funds can be either 13.6 percent or 14.8 percent depending on their financing plan. All three projects cost the same at $500,000. Expected cash flow streams are shown in the following table. Which projects would be accepted at a discount rate of 14.8 percent? What if the discount rate was 13.6 percent? Year

Project 1

Project 2

Project 3

$245,125

125,000

212,336

150,000

500,000

112,500

375,000

500,000

74,000

Solution: Cost of projects = $500,000 Length of project = n = 4 years Required rate of return = k = 14.8%

Project 1: n

NCFt $0 $125,000 $150,000 $375,000 = −$500,000 + + + + t 1 (1.148) (1.148) 2 (1.148) 3 (1.148) 4 t =0 (1 + k ) = −$500,000 + $0 + $94,848 + $99,144 + $ 215,906 = −$90,103

NPV = 

Project 2: n

NCFt $0 $0 $500,000 $500,000 = −$500,000 + + + + t 1 2 (1.148) (1.148) (1.148) 3 (1.148) 4 t =0 (1 + k ) = −$500,000 + $0 + $0 + $330,479 + $ 287,874 = $118,353

NPV = 

Project 3:

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NCFt $245,125 $212,336 $112,500 $74,000 = −$500,000 + + + + t (1.148)1 (1.148) 2 (1.148) 3 (1.148) 4 t =0 (1 + k ) = −$500,000 + $213,524 + $161,116 + $74,358 + $ 42,605 = −$8,397

NPV = 

At a discount rate of 14.8 percent, only project 2 will be accepted. At a discount rate of 13.6 percent, the NPVs of the three projects are -$75,645, $141,295, and $1,491 respectively. Both projects 2 and 3 have positive NPVs and will be accepted.

Year

Project 1

PVCF

Project 2

PVCF

Project 3

PVCF

$(500,000)

−

245,125

215,779

125,000

96,862

−

212,336

164,538

150,000

102,319

500,000

341,063

112,500

76,739

375,000

225,175

500,000

300,232

74,000

44,434

NPV

(75,645)

141,295

1,491

LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.34 Management of Intrepid, Inc., is considering investing in three independent projects. The costs and the cash flows are given in the following table. The appropriate cost of capital is 14.5 percent. Compute the project IRRs and identify the projects that should be accepted.

Year

Project 1

Project 2

Project 3

$(275,000)

$(312,500)

$(500,000)

63,000

153,250

212,000

85,000

167,500

212,000

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85,000

100,000

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112,000

212,000 212,000

Solution: Project 1: Cost of Project 1 = $275,000 Length of project = n = 4 years Required rate of return = k = 14.5% n

NCFt t t = 0 (1 + k )

NPV = 

$63,000 $85,000 $85,000 $100,000 + + + (1.145)1 (1.145) 2 (1.145) 3 (1.145) 4 = −$275,000 + 55,022 + $64,835 + $56,624 + $58,181 = −$40,338

= −$275,000 +

At the required rate of return of 14.5 percent, Project 1 has a NPV of $(40,338). To find the IRR, try lower rates.

Try IRR = 7.6%. n

NCFt t t =0 (1 + IRR) $63,000 $85,000 $85,000 $100,000 0 = −$275,000 + + + + (1.076)1 (1.076) 2 (1.076) 3 (1.076) 4 = −$275,000 + 58,550 + $73,417 + $68,231 + $74,602 = −$200  0

NPV = 0 = 

The IRR of the project is approximately 7.6 percent. Using a financial calculator, we find that the IRR is 7.57 percent.

Project 2: Cost of Project 2 = $312,500 Length of project = n = 3 years Required rate of return = k = 14.5%

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NCFt $153,250 $167,500 $112,000 = −$312,500 + + + t (1.145)1 (1.145) 2 (1.145) 3 t =0 (1 + k ) = −$312,500 + $ 133,843 + $127,763 + $74,611 = $23,717

NPV = 

At the required rate of return of 14.5 percent, Project 2 has a NPV of $23,717. To find the IRR, try higher rates. Try IRR =19%. n

NCFt t t =0 (1 + IRR) $153,250 $167,500 $112,000 0 = −$312,500 + + + (1.19)1 (1.19) 2 (1.19) 3 = −$312,500 + $128,782 + $118,283 + $66,463 = $1,027

NPV = 0 = 

Try IRR=19.2%. n

NCFt t t =0 (1 + IRR) $153,250 $167,500 $112,000 0 = −$312,500 + + + (1.192)1 (1.192) 2 (1.192) 3 = −$312,500 + $128,565 + $117,886 + $66,129 = $80  0

NPV = 0 = 

The IRR of the project is approximately 19.2 percent. Using a financial calculator, we find that the IRR is 19.22 percent.

Project 3: Cost of Project 3 = $500,000 Length of project = n = 4 years Required rate of return = k = 14.5%

1   1− 4   NCFt (1.145)  NPV =  = −$500,000 + $212,000   t  0.145  t =0 (1 + k )   = −$500,000 + $611,429 = $111,429 n

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At the required rate of return of 14.5 percent, Project 3 has a NPV of $111,429. To find the IRR, try higher rates. Try IRR =25%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.25) 4   0 = −$500,000 + $212,000    0.25    = −$500,000 + $500,659  $659 Try IRR=25.1%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.251) 4   0 = −$500,000 + $212,000    0.251    = −$500,000 + $500,659 = −$231  0 The IRR of the project is approximately 25.1 percent. Using a financial calculator, we find that the IRR is 25.07 percent. Only Projects 2 and 3 will be accepted as the IRRs exceed the required rate of return of 14.5 percent. Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.35 Jekyll & Hyde Corp. management is evaluating two mutually exclusive projects. The cost of capital is 15 percent. Costs and cash flows for each project are given in the following table. Which project should be accepted? Copyright © 2015 John Wiley & Sons, Inc.

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Year

Project 1

Project 2

$(1,250,000)

250,000

350,000

450,000

350,000

500,000

350,000

750,000

350,000

Solution: Project 1: Cost of project = $1,250,000 Length of project = n = 5 years Required rate of return = k = 15% n

NCFt t t =0 (1 + k )

NPV = 

$250,000 $350,000 $450,000 $500,000 $750,000 + + + + (1.15)1 (1.15) 2 (1.15) 3 (1.15) 4 (1.15) 5 = −$1,250,000 + $217,391+ $264,650 + $ 295,882 + $ 285,877 + $372,883 = $186,683

= −$1,250,000 +

At the required rate of return of 15 percent, Project 1 has an NPV of $186,683.Based on the positive NPV, Project 1 should be accepted.

To find the IRR, try higher rates.

Try IRR = 20%. n

NCFt t t =0 (1 + k )

NPV = 0 = 

$250,000 $350,000 $450,000 $500,000 $750,000 + + + + (1.20)1 (1.20) 2 (1.20) 3 (1.20) 4 (1.20) 5 = −$1,250,000 + $208,333 + $243,056 + $ 260,417 + $ 241,127 + $301,408  $4,340

0 = −$1,250,000 +

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Try IRR = 20.1%. n

NCFt t t =0 (1 + IRR) $250,000 $350,000 $450,000 $500,000 $750,000 0 = −$1,250,000 + + + + + (1.201)1 (1.201) 2 (1.201) 3 (1.201) 4 (1.201) 5 = −$1,250,000 + $208,160 + $242,651 + $ 259,767 + $ 240,324 + $300,155 = $1,057  0

NPV = 0 = 

The IRR of the project is approximately 20.1 percent. Using a financial calculator, we find that the IRR is 20.132 percent.

Project 2: Cost of project = $1,250,000 Length of project = n = 5 years Required rate of return = k = 15%

1   1−  NCFt (1.15) 5    NPV =  = − $ 1 , 250 , 000 + $ 350 , 000  t  0.15  t =0 (1 + k )   = −$1,250,000 + $1,173,254 = −$76,746 n

At the required rate of return of 15 percent, Project 2 has an NPV of $(76,746). Based on the negative NPV, Project 2 should be rejected.

To find the IRR, try lower rates. Try IRR = 12%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.12) 5   0 = −$1,250,000 + $350,000    0.12    = −$1,250,000 + $1,261,672 = $11,672

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Solutions Manual

Try IRR = 12.4%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.124) 5   0 = −$1,250,000 + $350,000    0.124    = −$1,250,000 + $1,249,269 = −$731  0

The IRR of the project is approximately 12.4 percent. Using a financial calculator, we find that the IRR is 12.376 percent.

Given a required rate of return of 15 percent, Project 1 will be accepted as the IRR of 20.1 percent exceeds the required rate of return. Project 2 will be rejected. LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.36 Management of Larsen Automotive, a manufacturer of auto parts, is considering investing in two projects. The company typically compares project returns to a cost of funds of 17 percent. Compute the IRRs based on the cash flows in the following table. Which project(s) will be accepted? Year

Project 1

Project 2

$(475,000)

$(500,000)

300,000

117,500

110,000

181,300

125,000

244,112

140,000

278,955

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Solutions Manual

Solution: Project 1: Cost of project = $475,000 Length of project = n = 4 years Required rate of return = k = 17% n

NCFt t t = 0 (1 + k )

NPV = 

$300,000 $110,000 $125,000 $140,000 + + + (1.17)1 (1.17) 2 (1.17) 3 (1.17) 4 = −$475,000 + $256,410 + $80,356 + $78,046 + $74,711 = $14,524

= −$475,000 +

At the required rate of return of 17 percent, Project 1 has an NPV of $14,524. To find the IRR, try higher rates.

Try IRR = 19%. n

NCFt t t = 0 (1 + k )

NPV = 

$300,000 $110,000 $125,000 $140,000 + + + (1.19)1 (1.19) 2 (1.19) 3 (1.19) 4 = −$475,000 + $252,101+ $77,678 + $74,177 + $69,814  −$1,230 = −$475,000 +

Try IRR = 18.8%. n

NCFt t t = 0 (1 + k )

NPV = 

$300,000 $110,000 $125,000 $140,000 + + + (1.188)1 (1.188) 2 (1.188) 3 (1.188) 4 = −$475,000 + $252,525 + $77,940 + $74,552 + $70,285 = $302  0

= −$475,000 +

The IRR of the project is approximately 18.8 percent. Using a financial calculator, we find that the IRR is 18.839 percent.

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Cost of project = $500,000 Length of project = n = 4 years Required rate of return = k = 17% n

NCFt t t =0 (1 + k )

NPV = 

$117,500 $181,300 $244,112 $278,955 + + + (1.17)1 (1.17) 2 (1.17) 3 (1.17) 4 = −$475,000 + $100,427 + $132,442 + $152,416 + $148,864 = $34,150

= −$500,000 +

At the required rate of return of 17 percent, Project 2 has an NPV of $34,150. To find the IRR, try higher rates.

Try IRR = 20%. n

NCFt t t =0 (1 + IRR) $117,500 $181,300 $244,112 $278,955 0 = −$500,000 + + + + (1.20)1 (1.20) 2 (1.20) 3 (1.20) 4 = −$475,000 + $97,917 + $125,903 + $141,269 + $134,527 = −$385  0

NPV = 0 = 

The IRR of the project is approximately 20 percent. Using a financial calculator, we find that the IRR is 19.965 percent. Both projects can be accepted since their IRRs exceed the cost of capital of 17 percent.

LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.37 Compute the IRR for each of the following projects: Year

Project 1

Project 2

Project 3

$(10,000)

4,750

1,650

800

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Solutions Manual

3,300

3,890

1,200

3,600

5,100

2,875

2,100

2,750

3,400

800

6,600

Solution: Project 1: Cost of project = $10,000 Length of project = n = 4 years n

NCFt t t =0 (1 + IRR) $4,750 $3,300 $3,600 $2,100 0 = −$10,000 + + + + (1.16)1 (1.16) 2 (1.16) 3 (1.16) 4 = −$10,000 + $4,095 + $2,452 + $ 2,306 + $1,160 = $13  0

NPV = 0 = 

The IRR of the project is approximately 16 percent. Using a financial calculator, we find that the IRR is 16.076 percent.

Project 2: Cost of project = $10,000 Length of project = n = 5 years n

NCFt t t =0 (1 + IRR) $1,650 $3,890 $5,100 $2,750 $800 0 = −$10,000 + + + + + 1 2 3 4 (1.137) (1.137) (1.137) (1.137) (1.137) 5 = −$10,000 + $1,451 + $3,009 + $3,470 + $1,645 + $421 = −$4  0

NPV = 0 = 

The IRR of the project is approximately 13.7 percent. Using a financial calculator, we find that the IRR is 13.685 percent.

Project 3:

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Solutions Manual

Cost of project = $10,000 Length of project = n = 5 years n

NCFt t t =0 (1 + IRR) $800 $1,200 $2,875 $3,400 $6,600 0 = −$10,000 + + + + + 1 2 3 4 (1.109) (1.109) (1.109) (1.109) (1.109) 5 = −$10,000 + $721 + $976 + $ 2,108 + $ 2,248 + $3,934 = −$13  0

NPV = 0 = 

The IRR of the project is approximately 10.9 percent. Using a financial calculator, we find that the IRR is 10.862 percent.

LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

9.38

Primus Corp. management is planning to convert an existing warehouse into a new plant that will increase its production capacity by 45 percent. The cost of this project will be $7,125,000. It will result in additional cash flows of $1,875,000 for the next eight years. The discount rate is 12 percent. a.

What is the payback period?

What is the NPV for this project?

What is the IRR?

Solution: a. Year

Project 1

Cumulative CF

$(7,125,000)

1,875,000

(5,250,000)

1,875,000

(3,375,000)

1,875,000

(1,500,000)

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1,875,000

375,000

1,875,000

2,250,000

1,875,000

4,125,000

1,875,000

6,000,000

1,875,000

7,875,000

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($1,500,000 / $1,875,000) = 3.80 years

Cost of this project = $7,125,000 Required rate of return = 12% Length of project = n = 8 years n

NCFt t t =0 (1 + k )

NPV = 

1   1 − (1.12) 8   = −$7,125,000 + $1,875,000    0.12    = −$7,125,000 + $9,314,325 = $2,189,325

To compute the IRR, try rates higher than 12 percent. Try IRR = 20%. n

NCFt t t =0 (1 + k )

NPV = 0 = 

1   1 − (1.20) 8   0 = −$7,125,000 + $1,875,000    0.20    = −$7,125,000 + $7,194,675 = $69,675

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NCFt t t =0 (1 + k )

NPV = 0 = 

1   1 − (1.203) 8   0 = −$7,125,000 + $1,875,000    0.203    = −$7,125,000 + $7,130,832 = $5,832

The IRR of the project is approximately 20.3 percent. Using a financial calculator, we find that the IRR is 20.328 percent. LO 2, LO 3, LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.39 Quasar Tech Co. management is investing $6 million in new machinery that will produce the next-generation routers. Sales to its customers will amount to $1,750,000 for the next three years and then increase to $2.4 million for three more years. The project is expected to last six years and operating costs, excluding depreciation, will be $898,620 annually. The machinery will be depreciated to a salvage value of $0 over 6 years using the straight-line method. The company’s tax rate is 30 percent, and the cost of capital is 16 percent. a.

What is the payback period?

What is the average accounting return (ARR)?

Calculate the project NPV.

What is the IRR for the project?

Solution: a.

Year

Net Income

Depreciation

Project 1

Cumulative

Cash Flows

$(6,000,000)

$(6,000,000) SM 10-68

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$(104,034)

$1,000,000

895,966

(5,104,034)

$(104,034)

$1,000,000

895,966

(4,208,068)

$(104,034)

$1,000,000

895,966

(3,312,102)

350,966

$1,000,000

1,350,966

(1,961,136)

350,966

$1,000,000

1,350,966

(610,170)

350,966

$1,000,000

1,350,966

740,796

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 5 + ($610,170 / $1,350,966) = 5.45 years b. Year 1 Sales

Year 2

Year 3

Year 4

Year 5

Year 6

$ 1,750,000 $ 1,750,000 $ 1,750,000 $ 2,400,000 $ 2,400,000 $ 2,400,000

Expenses

898,620

Depreciation

1,000,000

EBIT

$(1,48,620)

$ 501,380

Taxes (30%)

44,586

(150,414)

Net income

$ (104,034)

$ 350,966

Beginning BV

6,000,000

5,000,000

4,000,000

3,000,000

2,000,000

1,000,000

Less:

1,000,000

Depreciation Ending BV

$ 5,000,000 $ 4,000,000 $ 3,000,000 $ 2,000,000 $ 1,000,000

Average after-tax income = $123,466 Average book value of equipment = $3,000,000

Average after - tax income Average book value $123,466 = = 4.1% $3,000,000

Accounting rate of return =

Cost of this project = $6,000,000

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Required rate of return = k =16% Length of project = n = 6 years n

NCFt t t =0 (1 + k )

NPV = 

1  1    1 − (1.16) 3  1 − (1.16) 3  1  + $1,350,966    = −$6,000,000 + $895,966   3  0.16   0.16  (1.16)     = −$6,000,000 + $2,012,241 + $1,943,833 = −$2,043,927 d.

To compute the IRR, try rates lower than 16 percent. Try IRR = 3%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1  1    1 − (1.03) 3  1 − (1.03) 3  1  + $1,350,966    0 = −$6,000,000 + $895,966   3  0.03   0.03  (1.03)     = −$6,000,000 + $2,534,340 + $3,497,084 = $31,424 Try IRR = 3.1%. n

NCFt t t =0 (1 + IRR)

NPV = 0 − 

1 1     1 − (1.031) 3  1 − (1.031) 3  1  + $1,350,966    0 = −$6,000,000 + $895,966   3  0.031   0.031  (1.031)     = −$6,000,000 + $2,529,475 + $3,480,225 = $9,700 The IRR of the project is approximately 3.1 percent. Using a financial calculator, we find that the IRR is 3.145 percent.

SM 10-70

Fundamentals of Corporate Finance, 3rd edition

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AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.40 Management of Skywards, Inc., an airline caterer, is purchasing refrigerated trucks at a total cost of $3.25 million. After-tax net income from this investment is expected to be $750,000 for the next five years. Annual depreciation expense will be $650,000. The cost of capital is 17 percent. a.

What is the discounted payback period?

Compute the ARR.

What is the NPV on this investment?

Calculate the IRR.

Solution: a.

Year 0 1 2 3 4 5

CF $(3,250,000) 1,400,000 1,400,000 1,400,000 1,400,000 1,400,000

Cumulative CF $(3,250,000) (1,850,000) (450,000) 950,000 2,350,000 3,750,000

PVCF $(3,250,000) 1,196,581 1,022,719 874,119 747,110 638,556

Cumulative PVCF $(3,250,000) (2,053,419) (1,030,700) (156,581) 590,529 1,229,085

Discount payback period = Years before recovery + (Remaining cost / Next year’s CF) = 3 + ($156,581 / $747,110) = 3.21 years b. Net income Beginning BV Less: Depreciation Ending BV

Year 1 $ 750,000 3,250,000 650,000

Year 2 $ 750,000 2,600,000 650,000

Year 3 $ 750,000 1,950,000 650,000

Year 4 $ 750,000 1,300,000 650,000

Year 5 $ 750,000 650,000 650,000

$2,600,000

$1,950,000

$1,300,000

$ 650,000

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Average book value of equipment = $1,625,000

Average after - tax income Average book value $750,000 = = 46.2% $1,625,000

Accounting rate of return =

Cost of this project = $3,250,000 Required rate of return = k =17% Length of project = n = 5 years

1   1−  NCFt (1.17) 5    NPV =  = − $ 3 , 250 , 000 + $ 1 , 400 , 000  t  0.17  t =0 (1 + k )   = −$3,250,000 + $4,479,085 = $1,229,085 n

To compute the IRR, try rates much higher than 17 percent. Try IRR = 30%. n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.30) 5   0 = −$3,250,000 + $1,400,000    0.30    = −$3,250,000 + $3,409,798 = $159,798 Try IRR = 32.5%.

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NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.325) 5   0 = −$3,250,000 + $1,400,000    0.325    = −$3,250,000 + $3,252,904 = $2,904  0 The IRR of the project is approximately 32.5 percent. Using a financial calculator, we find that the IRR is 32.548 percent. LO 2, LO 3, LO 4, LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.41 Trident Corp. management is evaluating two independent projects. The costs and expected cash flows are given in the following table. The cost of capital is 10 percent. Year

$(312,500)

$(395,000)

121,450

153,552

121,450

158,711

121,450

166,220

121,450

132,000

121,450

122,000

Calculate the projects’ NPV.

Calculate the projects’ IRR.

Which project should be chosen based on NPV? Based on IRR? Is there a conflict?

If you are the decision maker for the firm, which project or projects will be accepted? Explain your reasoning.

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Solution: a.

Project A: Cost of this project = $312,500 Annual cash flows = $121,450 Required rate of return = k = 10% Length of project = n = 5 years

1   1−  NCFt (1.10) 5    NPV =  = − 312 , 500 + $ 121 , 450  t  0.10  t =0 (1 + k )   = −$312,500 + 460,391 = $147,891 n

Project B: Cost of this project = $395,000 Required rate of return = k = 10% Length of project = n = 5 years n

NCFt t t =0 (1 + k )

NPV = 

$153,552 $158,711 $166,220 $132,000 $122,000 + + + + (1.10)1 (1.10) 2 (1.10) 3 (1.10) 4 (1.10) 5 = −395,000 + $139,593 + $131,166 + $124,884 + 90,158 + 75,752 = $166,553

= −$395,000 +

Project A: Since NPV > 0, to compute the IRR, try rates higher than 10 percent. Try IRR = 27%.

SM 10-74

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NCFt t t = 0 (1 + IRR)

NPV = 0 = 

1   1 − (1.27) 5   0 = −312,500 + $121,450    0.27    = −$312,500 + 313,666  $1,166

Try IRR = 27.2%, n

NCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.272) 5   0 = −312,500 + $121,450    0.272    = −$312,500 + 312,418 = −$82  0 The IRR of Project A is approximately 27.2 percent. Using a financial calculator, we find that the IRR is 27.187 percent. Project B: Since NPV > 0, to compute the IRR, try rates higher than 10 percent. Try IRR = 26%. n

NCFt t t =0 (1 + IRR) $153,552 $158,711 $166,220 $132,000 $122,000 0 = −$395,000 + + + + + (1.26)1 (1.26) 2 (1.26) 3 (1.26) 4 (1.26) 5 = −$395,000 + $121,867 + $99,969 + $83,094 + $52,371 + $38,416  $717

NPV = 0 = 

Try IRR = 26.1%. n

NCFt t t =0 (1 + IRR) $153,552 $158,711 $166,220 $132,000 $122,000 0 = −$395,000 + + + + + (1.261)1 (1.261) 2 (1.261) 3 (1.261) 4 (1.261) 5 = −$395,000 + $121,770 + $99,811 + $82,897 + $52,205 + $38,263 = −$54  0

NPV = 0 = 

SM 10-75

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The IRR of Project B is approximately 26.1 percent. Using a financial calculator, we find that the IRR is 26.093 percent.

Since both projects have positive NPVs and they are independent projects, both should be accepted under the NPV decision criteria. Under the IRR decision criteria, since both projects have IRRs greater than the cost of capital, both will be accepted. Thus, there is no conflict between the NPV and IRR decisions.

Based on NPV, both projects will be accepted.

LO 2, LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.42 Management of Tyler, Inc., is considering switching to a new production technology. The cost of the required equipment will be $4 million. The discount rate is 12 percent. The cash flows that management expects the new technology to generate are as follows. Years

1-2

3–5

$845,000

6–9

$1,450,000

Compute the payback and discounted payback periods for the project.

What is the NPV for the project? Should the firm go ahead with the project?

What is the IRR, and what would be the decision based on the IRR?

SM 10-76

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Cumulative

Year

Cash Flows

PVCF

$(4,000,000)

(4,000,000)

845,000

601,454

(3,155,000)

(3,398,546)

845,000

537,013

(2,310,000)

(2,861,533)

845,000

479,476

(1,465,000)

(2,382,057)

1,450,000

734,615

(15,000)

(1,647,442)

1,450,000

655,906

1,435,000

(991,536)

1,450,000

585,631

2,885,000

(405,905)

1,450,000

522,885

4,335,000

116,979

Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$15,000 $1, 450,000 = 6.01 years

=6+

Discounted Payback period = Years before cost recovery +

Remaining cost to recover Cash flow during the year

$405,905 $522,885 = 8.8 years

=8+

Cost of this project = $4,000,000 Required rate of return = k = 12% Length of project = n = 9 years

SM 10-77

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1   1−  NCFt 1 (1.12) 3     000 , 845 $ + 0 + 0 + 000 , 000 , 4 $ − = NPV =  2 t  0.12  (1.12) t =0 (1 + k )   1   1 − (1.12) 4  1  + $1,450,000   5  0.12  (1.12)   n

= −$4,000,000 + 0 + 0 + $1,617,943 + $2,499,037 = $116,980 Since NPV > 0, the project should be accepted. c.

Given a positive NPV, to compute the IRR, one should try rates higher than 12 percent.

Try IRR = 12.5%.

1   1 − 3   NCFt 1 (1.125)  NPV =  = −$4,000,000 + 0 + 0 + $845,000   t 2  0.125  (1.125) t =0 (1 + k )   1   1 − (1.125) 4  1  + $1,450,000   5  0.125  (1.125)   n

= −$4,000,000 + 0 + 0 + $1,589,915 + $2,418,479 = $8,394 The IRR is approximately 12.5 percent. Using the financial calculator, we find that the IRR is 12.539 percent. Based on the IRR exceeding the cost of capital of 12 percent, the project should be accepted.

LO 2, LO 3, LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.43 You are analyzing two proposed capital investments with the following cash flows: Year 0

Project X $(20,000)

Project Y $(20,000)

13,000

7,000

6,000

7,000

6,000

7,000

2,000

7,000

The cost of capital for both projects is 10 percent. Calculate the profitability index (PI) for each project. Which project, or projects, should be accepted if you have unlimited funds to invest? Which project should be accepted if they are mutually exclusive?

Solution: The PI calculations are as follows: The NPV is needed first:

$13,000 $6,000 $6,000 $2,000 + + + = $2,650.78 (1.1)1 (1.1) 2 (1.1) 3 (1.1) 4 $7,000 $7,000 $7,000 $7,000 NPVy = −$20,000 + + + + = $2,189.06 (1.1)1 (1.1) 2 (1.1) 3 (1.1) 4

NPVx = −$20,000 +

NPV + Initial Investment $22, 650.78 = =1.1325 Initial Investment $20, 000 NPV + Initial Investment $22,189.06 PI y = = =1.1095 Initial Investment $20, 000

PI x =

Both methods rank Project X over Project Y. Therefore, both should be accepted if they are independent and sufficient resources are available. If the projects are mutually exclusive, we should choose the project with the higher PI at r = 10%, which in this case is Project X. Copyright © 2015 John Wiley & Sons, Inc.

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LO 6 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

CFA Problems 10.44 Given the following cash flows for a capital project, calculate the NPV and IRR. The required rate of return is 8 percent. Year

CASH FLOW

–50,000

15,000

20,000

10,000

5,000

NPV

IRR

$1,905

10.9%

$1,905

26.0%

$3,379

10.9%

$3,379

26.0%

SOLUTION: c is correct. NPV = −50, 000 +

15, 000 15, 000 20, 000 10, 000 5, 000 + + + + 1.08 1.082 1.083 1.084 1.085

NPV = –$50,000 + $13,888.89 + $12,860.08 + $15,876.64 + $7,350.30 + $3,402.92 NPV = –$50,000 + $53,378.83 = $3,378.83 The IRR, found with a financial calculator, is 10.88 percent. Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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10.45 Given the following cash flows for a capital project, calculate its payback period and discounted payback period. The required rate of return is 8 percent.

Year

CASH FLOW

–50,000

15,000

20,000

10,000

5,000

The discounted payback period is a.

0.16 year longer than the payback period.

0.80 year longer than the payback period.

1.01 years longer than the payback period.

1.85 years longer than the payback period.

SOLUTION: c is correct. YEAR

CASH FLOW

–$50,000

$15,000

$20,000

$10,000

$5,000

–50,000

–35,000

–20,000

10,000

15,000

–50,000

13,888.89

12,860.08

15,876.64

7,350.30

3,402.92

–

$36,111.11

$23,251.03

$7,374.38

CUMULATIVE CASH FLOW

DISCOUNTED CASH FLOW

CUMULATIVE DCF

–$50,000

$3,378.8 –$24.09

As the table shows, the cumulative cash flow offsets the initial investment in exactly three years. The payback period is 3.00 years. The discounted payback period is between four and five years. The discounted payback period is 4 years plus 24.09/3,402.92 = 0.007 of the fifth year cash flow, or 4.007 = 4.01 years. The Copyright © 2015 John Wiley & Sons, Inc.

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discounted payback period is 4.01 – 3.00 = 1.01 years longer than the payback period. LO 3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.46 An investment of $100 generates after-tax cash flows of $40 in Year 1, $80 in Year 2, and $120 in Year 3. The required rate of return is 20 percent. The net present value is closest to a.

$42.22

$58.33

$68.52

$98.95

SOLUTION: b is correct.

NCFt 40 80 120 = −$100 + + + = $58.33 t 2 1.20 1.20 1.203 t =0 (1 + k )

NPV =  LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions

AICPA: Industry/Sector Perspective

10.47 An investment of $150,000 is expected to generate an after-tax cash flow of $100,000 in one year and another $120,000 in two years. The cost of capital is 10 percent. What is the internal rate of return? Copyright © 2015 John Wiley & Sons, Inc.

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28.19 percent

28.39 percent

28.59 percent

28.79 percent

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SOLUTION: d is correct. The IRR can be found using a financial calculator or with trial and error. Using trial and error, the total PV is equal to zero if the discount rate is 28.79 percent. YEA

CASH FLOW

PRESENT VALUE 28.19%

28.39%

28.59%

28.79%

–150,000

100,000

78,009

77,888

77,767

77,646

120,000

73,025

72,798

72,572

72,346

1,034

686

338

–8

Total

A more precise IRR of 28.7855 percent has a total PV closer to zero. LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions

AICPA: Industry/Sector Perspective

10.48 An investment requires an outlay of $100 and produces after-tax cash flows of $40 annually for four years. A project enhancement increases the required outlay by $15 and the annual after-tax cash flows by $5. How will the enhancement affect the project’s NPV profile? The vertical intercept of the NPV profile of the project shifts: a.

up and the horizontal intercept shifts left.

up and the horizontal intercept shifts right.

down and the horizontal intercept shifts left.

down and the horizontal intercept shifts right.

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SOLUTION: a is correct. The vertical intercept changes from $60 to $65, and the horizontal intercept changes from 21.86 percent to 20.68 percent. LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Sample Test Problems 10.1

Testco Corporation is considering adding a new product line. The cost of the factory and equipment to produce this product is $1,780,000. Company management expects net cash flows from the sale of this product to be $450,000 in each of the next eight years. If Testco uses a discount rate of 12 percent for projects like this, what is the net present value of this project? What is the internal rate of return? (LO 2 & 5) Solution: Investment = $1,780,000 Annual net cash flow = NCF = $450,000 Discount rate = k = 12% Length of project = n = 8 years

1   1 −  (1.12)8  NCFt NPV=  = − $1, 780, 000 + $450, 000    t t = 0 (1 + k )  0.12    = −$1, 780, 000 + $2, 235, 438 NPV = $455, 437.90 n

Determine the IRR using trial and error: Since NPV > 0, try IRR > k. Try IRR = 20%

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1   1−  NCFt (1.20)8  NPV = 0 =  = −$1,500, 000 + $450, 000    t t = 0 (1 + IRR)  0.20    = −$1, 780, 000 + $1, 726, 722  −$53, 278 n

Try IRR = 19% n

NCFt = −$1, 780, 000 + $450, 000  t t = 0 (1 + IRR) = −$1, 780, 000 + $1, 779, 465 = −$535  0

NPV = 0 = 

1−

1 (1.19)8 0.19

The IRR is approximately 19 percent. Using the financial calculator, we find that the IRR is 18.99 percent. Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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10.2

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Flowers Unlimited is considering purchasing an additional delivery truck which will have a seven year useful life. The new truck will cost $42,000. Cost savings with this truck are expected to be $12,800 for the first two years, $8,900 for the following two years, and $5,000 for the last 3 years of the truck’s useful life. What is the payback period for this project? What is the discounted payback period for this project with a discount rate of 10 percent? (LO 3) Solution: Discount rate = k = 10% Year 0 1 2 3 4 5 6 7

NCF $(42,000) 12,800 12,800 8,900 8,900 5,000 5,000 5,000

Cumulative NCF $(42,000) (29,200) (16,400) (7,500) 1,400 6,400 11,400 16,400

PV(NCF) $(42,000) 11,636 10,579 6,687 6,079 3,105 2,822 2,566

Cumulative PV(NCF) $(42,000) (30,364) (19,785) (13,098) (7,019) (3,914) (1,092) 1,474

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($7,500 / $8,900) = 3.84 years Discounted PB = Years before cost recovery + (Remaining cost to recover/ PV Cash flow during the year) = 6 + ($1,092 / $2,566) = 6.43 years Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.3

What is the average accounting rate of return (ARR) on a piece of equipment that will cost $1.2 million and that will result in pretax cost savings of $380,000 for the first three years and then $280,000 for the following three years? Assume that the machinery will be depreciated to a salvage value of 0 over 6 years using the straight-line method and the company’s tax rate is 32 percent. If the acceptance decision is based on the project exceeding an ARR of 20 percent, should this machinery be purchased? (LO 4)

Solution: Cost savings Depreciation

Year 1 $ 380,000 200,000

Year 2 $ 380,000 200,000

Year 3 $ 380,000 200,000

Year 4 $ 280,000 200,000

Year 5 $ 280,000 200,000

Year 6 $ 280,000 200,000

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EBIT Taxes (32%) Net income

Solutions Manual

$ 180,000 57,600 $ 122,400

$ 80,000 25,600 $ 54,400

Beg. book value 1,200,000 Less:Depreciation 200,000 End. book value $ 1,000,000

5,000,000 200,000 $ 800,000

4,000,000 200,000 $ 600,000

3,000,000 200,000 $ 400,000

2,000,000 200,000 $ 200,000

1,000,000 200,000 $ 0

Average after-tax income (years 1 through 9) = $88,400 Average book value of equipment (years 0 through 6) = $600,000

Average after-tax income Average book value $88, 400 = = 14.7% $600, 000 Since the project’s ARR is below the acceptance rate of 20 percent, the machinery should not be purchased. Accounting rate of return =

Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.4

What do we know about that project’s IRR if we know that it has a positive NPV? (LO 2 & 5) Solution: If a project has a positive NPV, the IRR of that project is greater than the required rate of return. Since the IRR is the discount rate that makes the NPV equal zero, a positive NPV results from the project’s IRR being greater than the required rate of return.

Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.5

West Street Automotive is considering adding state safety inspections to their service offerings. The equipment necessary to perform these inspections will cost $557,000 and will generate cash flows of $195,000 over each of the next five years. If the cost of capital is 14

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percent, what is the MIRR on this project? (LO 5) Solution: Investment (cost) = $557,000 Annual net cash flow = NCFt = $195,000 Length of project = n = 5 years Cost of capital = k = 14% TV = NCF1 (1 + k ) n −1 + NCF2 (1 + k ) n −2 +

+ NCFn (1 + k ) n −n

= $195, 000  (1.14) 4 + $195, 000  (1.14)3 + $195, 000  (1.14)2 + $195, 000 1.14 + $195, 000 = $329,347 + $288,901 + $253, 422 + $222,300 + $195, 000 = $1, 288,970 Solve for the MIRR: TV PVCost = (1 + MIRR) n $1, 288,970 $557, 000 = (1 + MIRR)5 $1, 288,970 (1 + MIRR) 5 = = 2.3141 $557, 000

(1 + MIRR) = (2.3141)1/5 = 1.1827 MIRR = 0.1827 = 18.3% Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

10.6

You are chairperson of the investment committee at your fi rm. Five projects have been submitted to your committee for approval this month. The investment required and the project profitability index for each of these projects are presented in the following table: (LO 6) Project

Investment

A B C D E

$20,000 50,000 70,000 10,000 80,000

2.500 2.000 1.750 1.000 0.800

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If you have $500,000 available for investments, which of these projects would you approve? Assume that you do not have to worry about having enough resources for future investments when making this decision.

Solution: Definitely accept projects A, B, and C. They all have a positive NPV. Project D just returns the opportunity cost of capital, so you would be indifferent with regards to accepting this project. Do not accept project E; it has a negative NPV. Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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Chapter 11 Cash Flows and Capital Budgeting

Before You Go On Questions and Answers

Section 11.1 1. Why do we care about incremental cash flows at the firm level when we evaluate a project?

We care about incremental cash flows at the firm level because they reflect the impact of the project on the total cash flows that the firm produces. This is what the stockholders care about. The difference between the present value of the expected cash flows from the firm with the project and the present value of the expected cash flows from the firm without the project is precisely what the NPV of a project is. Our NPV estimate will be incorrect if we do not account for all of the incremental cash flows at the firm level.

2. Why is D&A first subtracted and then added back in FCF calculations?

By subtracting D&A, calculating the tax obligation, and then adding back D&A, we are accounting for the fact that D&A is a noncash charge that reduces the firm’s tax obligation by the

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product of D&A and the tax rate (D&A x t). If we did not do this, we would overstate the tax obligation and understate FCF.

3. What types of investments should be included in FCF calculations?

All investments directly associated with the project should be included in FCF calculations. These can include both investments in tangible and intangible assets. They can also include investments in additions to working capital, such as for the credit a firm extends to its customers and inventories.

Section 11.2 1. What are the five general rules for calculating FCF?

(1) Include cash flows and only cash flows in your calculations. (2) Include the impact of the project on cash flows from other product lines. (3) Include all opportunity costs. (4) Forget sunk costs. (5) Include only after-tax cash flows in the cash flow calculations.

2. What is the difference between nominal and real dollars? Why is it important not to mix them in an NPV analysis?

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When most people talk about dollar amounts, they are referring to nominal dollars. Nominal dollars do not take into account changes in purchasing power. Real dollars are dollar amounts that are adjusted for changes in purchasing power. For example, 100 real dollars have the same purchasing power whether they are received today or at some future date. It is important not to mix nominal and real dollars in an NPV analysis because the discount rate is either a nominal rate, which is used to discount nominal dollars, or a real rate, which is used to discount real dollars. Since the discount rate must be either a nominal rate or a real rate, if real and nominal dollars are mixed in an NPV analysis, the NPV will be calculated incorrectly.

3. What is a progressive tax system? What is the difference between a firm’s marginal and average tax rates?

A progressive tax system is one in which the marginal tax rate at low levels of income is lower than the marginal tax rate at high levels of income. A firm’s marginal tax rate is the rate that it pays on the last dollar earned while the average tax rate is the average rate paid on the firm’s total earnings (tax paid divided by taxable income).

4. How can FCF in the terminal year of a project’s life differ from FCF in the other years?

FCF in the terminal year can differ from FCF in other years in several ways. The terminal year cash flows can include cash flows from the asset sales, including the actual proceeds from the sales themselves and taxes due or received if there is a gain or loss on the sale. Terminal year cash flows can also include cash flows associated with recovery of working capital. Copyright © 2015 John Wiley & Sons, Inc.

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5. Why is it important to understand that cash flow forecasts in an NPV analysis are expected values?

It is important to recognize that we are forecasting expected cash flows in an NPV analysis because uncertainties regarding project cash flows that are unique to the project should be reflected in the cash flow forecasts.

Section 11.3 1. What is the difference between variable and fixed costs, and what are examples of each? Variable costs vary directly with unit sales. Fixed costs do not vary with unit sales. For an example of each, see the video game player scenario on page 379. Variable costs are those associated with purchasing the components for the player, the labor required, and sales and marketing. These costs will vary according to the number of units produced. Fixed costs are those associated with assembly space, and administrative expenses.

2. How are working capital items forecast? Why are accounts receivable typically forecast as a percentage of revenue and accounts payable, and inventories as percentages of the cost of good sold? Working capital items are forecast using 1) cash and cash equivalents, 2) accounts receivable, 3) inventories, and 4) accounts payable. Inventories are forecast as a percentage of the cost of goods sold because the COGS represent a measure of the amount of money invested in inventories. Accounts payable are forecast this way because the COGS is a measure of the amount of money actually owed to suppliers. Copyright © 2015 John Wiley & Sons, Inc.

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Section 11.4 1. When can we not simply compare the NPVs of two mutually exclusive projects?

If we expect to replace at least one of the projects at the end of its life, we cannot simply compare the NPVs. Doing so would ignore the subsequent investment(s). You can only directly compare the NPVs of mutually exclusive projects under one condition—that is, if you expect to terminate the project that is chosen (e.g., sell the lawn mower) on or before the end of the life of the shorterlived project.

2. How do we decide when to harvest an asset?

We choose the harvest date that maximizes the NPV of the asset. To identify this date, we compare the NPVs expected from harvesting the asset for each of the feasible harvest dates. The best date to harvest the asset is the date that produces the largest NPV, once the NPVs for all of the alternative harvest dates have been discounted to the same point in time.

3. Under what circumstance would you replace an old machine that is still operating with a new one?

You should replace the old machine when the EAC of the new machine is lower than the EAC of the old machine (if revenues are the same for both machines) or when the annualized cash inflow from the replacement is greater. Copyright © 2015 John Wiley & Sons, Inc.

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Self-Study Problems

11.1

Explain why the announcement of a new investment is usually accompanied by a change in the firm’s stock price.

Solution: A firm’s investments cause changes in its future after-tax cash flows and stockholders are the residual claimants (owners) of those cash flows. Therefore, the stock price should increase when stockholders expect an investment to have a positive NPV, and decrease when it is expected to have a negative NPV.

11.2

In calculating the NPV of a project, should we use all of the after-tax cash flows associated with the project, or incremental after-tax cash flows from the project? Why?

Solution: We should use incremental cash flows of the project. Incremental cash flows reflect the amount by which the firm’s total cash flows will change if the project is adopted. In other words, incremental cash flows represent the net difference in cash revenues, costs, and investment outlays (in net working capital and capital expenditures) at the firm level with and without the project, which is precisely what the stockholders care about.

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11.3

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You are considering opening another restaurant in the TexasBurgers chain. The new restaurant will have annual revenue of $300,000 and operating expenses of $150,000. The annual depreciation and amortization for the assets used in the restaurant will equal $50,000. An annual capital expenditure of $10,000 will be required to offset wear-and-tear on the assets used in the restaurant, but no additions to working capital will be required. The marginal tax rate will be 40 percent. Calculate the incremental annual free cash flow for the project

Solution: The incremental annual free cash flow is calculated as:

FCF = ($300,000 − $150,000 − $50,000)  (1 − 0.4) + $50,000) − $10,000 = $100,000

11.4

Sunglass Heaven, Inc., is launching a new store in a shopping mall in Houston. The annual revenue of the store depends on the weather conditions in the summer in Houston. The annual revenue will be $240,000 in a sizzling summer, with probability of 0.3; $80,000 in a cool summer, with probability of 0.2; and $150,000 in a normal summer, with probability of 0.5. What is the expected annual revenue of the store?

Solution: The expected annual revenue is: (0.3 × $240,000) + (0.2 × $80,000) + (0.5 × $150,000) = $163,000

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11.5

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Sprigg Lane Manufacturing, Inc., needs to purchase a new central air-conditioning system for a plant. There are two choices. The first system costs $50,000 and is expected to last 10 years, and the second system costs $72,000 and is expected to last 15 years. Assume that the opportunity cost of capital is 10 percent. Which air-conditioning system should Sprigg Lane purchase?

Solution: The equivalent annual cost for each system is:

(1.1)10 EAC1 = (0.1)($50,000) = $8,137.27 (1.1)10 − 1

EAC2 = (0.1)($72,000)

(1.1)15 = $9,466.11 (1.1)15 − 1

Therefore Sprigg Lane should purchase the first one.

Discussion Questions 11.1

Do you agree or disagree with the following statement given the discussion in this chapter? We can calculate future cash flows precisely and obtain an exact value for the NPV of an investment.

The statement is not true. The nature of the real business world includes those risks which cannot be forecasted or foreseen such as changes in nation’s economic policy, fluctuation in inflation and interest rates and likes. Given this, it is almost certain that the cash flows generated by a project will differ from the forecasts used to decide whether to proceed with Copyright © 2015 John Wiley & Sons, Inc.

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the project. However, techniques discussed in this chapter provide an important and useful framework that helps minimize errors and ensures that forecasts are internally consistent. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.2

What are the differences between cash flows used in capital budgeting calculations and past accounting earnings?

Cash flows used in capital budgeting calculations are forward looking; they are incremental after-tax cash flows based on forecast. Accounting earnings are backward looking; they represent a record of past performance and may not accurately reflect cash flows. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.3

Suppose that FRA Corporation already has divisions in both Dallas and Houston. FRA is now considering setting up a third division in Austin. This expansion will require that

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one senior manager from Dallas and one from Houston relocate to Austin. Ignore relocation expenses. Is their annual compensation relevant to the decision to expand?

The annual compensations of existing senior managers are not incremental to the new investment and therefore are not relevant for capital budgeting analysis. This is consistent with our Rule 1 for incremental cash flow calculations: Include cash flows and only cash flows; do not include allocated costs unless they reflect cash flows. LO: 1, 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.4

MusicHeaven,Inc., is a producer of media players which currently have either 20 gigabytes or 30 gigabytes of storage. Now the company is considering launching a new production line making mini media players with 5 gigabytes of storage. Analysts forecast that MusicHeaven will be able to sell 1 million such mini media players if the investment is made. In making the investment decision, discuss what the company should consider other than the sales of the mini media players.

The company’s launch of the new mini media players may reduce its current sales of media players of bigger storage. This impact has to be considered. This is consistent with our Rule 2

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for incremental cash flow calculations: Include the impact of the project on cash flows from other product lines. LO: 1, 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.5

QualityLiving Trust is a real estate investment company that builds and remodels apartment buildings in northern California. It is currently considering remodeling a few idle buildings that it owns in San Jose into luxury apartment buildings. The company bought those buildings eight months ago. How should the market value of the buildings be treated in evaluating this project?

Although the buildings are not currently in use, the company can sell them at their market value rather than remodel them into apartments. Therefore, the market value of the buildings is the opportunity cost of the project and should be considered as cash outflow in the investment decision. This is consistent with our Rule 3 for incremental cash flow calculations: Include all opportunity costs. LO: 1, 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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11.6

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High-End Fashions, Inc., bought a production line of ankle-length skirts last year at a cost of $500,000. This year, however, miniskirts are in and ankle-length skirts are completely out of fashion. High-End has the option to rebuild the production line and use it to produce miniskirts with an annual operating cost of $300,000 and expected revenue of $700,000. How should the company treat the $500,000 cost of the old production line in evaluating the rebuilding plan?

The cost of the old production line occurred in the past. It cannot be changed whether or not the company rebuilds it into the miniskirt production line. Therefore, High-End should not consider the cost of $500,000. This is consistent with our Rule 4 for incremental cash flow calculations: Forget sunk costs. LO: 1, 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.7

How is the MACRS depreciation method under IRS rules different from the straightline depreciation allowed under GAAP rules? What is the implication on incremental after-tax free cash flows from firms’ investments?

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GAAP allows the straight-line depreciation method. In contrast, an “accelerated” method of depreciation, Modified Accelerated Cost Recovery System (MACRS), has been used for U.S. federal tax calculations. The advantage of MACRS, relative to straight-line depreciation, is that it enables a firm to deduct depreciation changes sooner, thereby realizing the tax saving sooner and increasing the present value of the tax savings. LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.8

Explain the difference between marginal and average tax rates, and identify which of these rates is used in capital budgeting and why?

The marginal tax rate is the rate paid on the next dollar earned. The average tax rate is the dollar value of total taxes paid divided by total income. The marginal tax rate is the appropriate rate to use in capital budgeting analysis because this is the tax rate that will be paid on the incremental income earned by the project. LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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11.9

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Under what circumstances will the sale of an asset result in a taxable gain? How do you estimate the taxes or tax benefits associated with the sale of an asset?

The sale of an asset results in a taxable gain when the selling price of the asset exceeds its book value. Tax on the sale of an asset = (Selling price of asset – Book value of asset) × Tax rate (t) LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.10 When two mutually exclusive projects have different lives, how can an analyst determine which is better? What is the underlying assumption in this method?

When we choose from mutually exclusive projects with different lives, instead of electing the project with higher NPV or lower net present value of costs, we should choose the project with higher Equivalent Annual Revenue or lower Equivalent Annual Cost. The underlying assumption is that we will continue to operate with the same equivalent annual revenue or equivalent annual cost in the future. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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11.11 What is the opportunity cost of using an existing asset? Give an example of the opportunity cost of using the excess capacity of a machine.

The opportunity cost of using an existing asset in a project is the present value of the change in the firm’s cash flows that is attributed to the fact that this asset is being used in the project. For example, by using the excess capacity of a machine, you may accelerate the wear-andtear of the machine and hence will need to replace it sooner. The present value of the added annualized costs is the opportunity cost of using the excess capacity. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.12 You are providing financial advice to a shrimp farmer who will be harvesting his last crop of farm-raised shrimp. His current shrimp crop is very young and will, therefore, grow and become more valuable as their weight increases. Describe how you would determine the appropriate time to harvest the entire crop of shrimp.

Assuming that the price of shrimp is directly (and linearly) related to the weight of the shrimp, then the optimal point in time to harvest the shrimp would be where the rate of weight increase is no longer greater than the opportunity cost of capital for the shrimp farmer. Copyright © 2015 John Wiley & Sons, Inc.

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Alternatively, the appropriate time is when the value increase of the shrimp is no longer greater than the opportunity cost of capital. LO: 5 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Questions and Problems

BASIC 11.1 Calculating project cash flows: Why do we use forecasted incremental after-tax free cash flows instead of forecasted accounting earnings in estimating the NPV of a project?

Solution: Accounting earnings can differ from cash flows for a number of reasons, making accounting earnings an unreliable measure of the costs and benefits of a project. For example, ease of manipulating earnings components such as accounts receivable and depreciation may result in distorted estimation of capital budgeting; using forecasted cash flows eliminates such Copyright © 2015 John Wiley & Sons, Inc.

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possibilities. In addition, because there is time value of money, cash flows better reflect the actual available funds to be distributed to shareholders at each point in time. LO 1 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.2 The FCF calculation: How do we calculate incremental after-tax free cash flows from forecasted earnings of a project? What are the common adjustment items?

Solution: We need to adjust for the depreciation and amortization tax shield, capital expenditures, and changes in working capital (including receivables and payables). LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.3 The FCF calculation: How do we adjust for depreciation when we calculate incremental aftertax free cash flow from EBITDA? What is the intuition for the adjustment?

Solution:

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There are two ways to adjust for depreciation: (1) subtract depreciation from EBITDA, multiply it by (1 – tax rate), and then add depreciation back; (2) add the tax shield from depreciation (depreciation multiplied by tax rate) to revenue. These two methods yield the same results. The intuition is that although depreciation itself is not a cash inflow or outflow, increase in depreciation will result in a decrease in taxable income. This saving on tax is treated as cash inflow in calculating incremental after-tax free cash flows. LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.4

Nominal versus real cash flows: What is the difference between nominal and real cash flows? Which rate of return should we use to discount each type of cash flow?

Solution: Nominal cash flows are cash flows stated as we usually think of them. They represent the actual cash flow that we expect a project to generate in the future, without any adjustment, for changes in purchasing power over time. Real cash flows are cash flows stated so that their purchasing power remains constant. We should use nominal rate of return to discount future nominal cash flows and real rate of return to discount future real cash flows. By doing this, we will get meaningful present values of cash flows and purchasing power. LO 2 Bloomcode: Analysis Copyright © 2015 John Wiley & Sons, Inc.

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11.5

Taxes and depreciation: What is the difference between average tax rate and the marginal tax rate? Which one should we use in calculating incremental after-tax cash flows?

Solution: In a progressive tax system, the marginal tax rate is different from the average tax rate. The average tax rate is the total amount of tax divided by total amount of money earned, while the marginal tax rate is the rate paid on the last dollar earned. Since a firm already pays taxes, the appropriate tax rate used for the firm’s new project is the tax rate that the firm will pay on any additional profits that are earned because the project is adopted. Therefore, we use the marginal tax rate in calculating incremental after-tax cash flows. LO 2 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.6

Computing terminal-year FCF: Healthy Potions, Inc., a pharmaceutical company, bought a machine at a cost of $2 million five years ago that produces pain-reliever medicine. The machine has been depreciated over the past five years, and the current book value is $800,000. The company decides to sell the machine now at its market price of $1 million. The

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marginal tax rate is 30 percent. What are the relevant cash flows? How do they change if the market price of the machine is $600,000 instead?

Solution: The relevant cash flows include the sale price of the machine, as well as the tax on the capital gain: $1,000,000 – 0.3 × ($1,000,000 – $800,000) = $940,000 When the market price of the machine is changed to $600,000, the relevant cash flows include the sale price and tax saving on capital loss: $600,000 + 0.3 × ($800,000 – $600,000) = $660,000 LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.7

Cash flows from operations: What are variable costs and fixed costs? What are some examples of each? How are these costs estimated in forecasting operating expenses?

Solution: Variable costs vary directly with unit sales, while fixed costs do not. Variable costs are those associated with purchasing the components for the product, the labor required, and sales and marketing. These costs will vary according to the number of units produced. Fixed costs are those associated with assembly space, and administrative expenses. Copyright © 2015 John Wiley & Sons, Inc.

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LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

11.8

Cash flows from operations: When forecasting operating expenses, explain the difference between a fixed cost and a variable cost.

Solution: While forecasting operating expenses, Fixed costs are based on cost of manufacturing space, administrative expenses required for administration of the project, and so forth. While variable costs vary directly with the number of units sold, they can be forecasted by multiplying the variable cost per unit (that has been estimated to be produced) by the number of units expected to be sold each year. LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.9

Investment cash flows: Zippy Corporation just purchased computing equipment for $20,000. The equipment will be depreciated using a five-year MACRS depreciation schedule. If the equipment is sold at the end of its fourth year for $12,000, what are the after-tax proceeds from the sale, assuming the marginal tax rate is 35 percent.

Solution: The 5-year depreciation schedule allows us to depreciate 20 percent of the value of the equipment in year 1, 32 percent in year two, 19.20 percent in year 3, and 11.52 percent in year Copyright © 2015 John Wiley & Sons, Inc.

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four after the purchase. The associated depreciation charges in years 1 through 4 in order are $4,000, $6,400, $ 3,840, and $2,304 respectively. Total depreciation at the end of year 4 $16,544, so the book value of the equipment when sold is $3,456. Since the equipment is sold for $12,000 the tax on the sale of the asset is equal to ($12,000-$3,456) × 0.35 = $2,990.40. The total after tax proceeds are $12,000 - $2,990.40 = $9,009.60 LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.10 Investment cash flows: Six Twelve, Inc., is considering opening up a new convenience store in downtown New York City. The expected annual revenue at the new store is $800,000. To estimate the increase in working capital, analysts estimate the ratio of cash and cashequivalents to revenue to be 0.03 and the ratios of receivables, inventories, and payables to revenue to be 0.05, 0.10, and 0.04, respectively, in the same industry. What is the expected incremental cash flow related to working capital when the store is opened?

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AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.11 Investment cash flows: Keswick Supply Company wants to set up a division that provides copy and fax services to businesses. Customers will be given 20 days to pay for such services. The annual revenue of the division is estimated to be $25,000. Assuming that the customers take the full 20 days to pay, what is the incremental cash flow associated with accounts receivable?

Solution: The average accounts receivable balance will be (20days/365days/year) ×100% ×25,000 = 5.48% × 25,000 = $1,370.

Alternatively, the average daily credit sale = $25,000 / 365 = $68.49, and it takes 20 days, on average, to collect the sale.

Therefore, the incremental cash flow related to working capital when the store is opened: 20 × $68.49 = $1,369.86, or about $1,370. LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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11.12 Expected cash flows: Define expected cash flows, and explain why this concept is important in evaluating projects.

Solution: Expected cash flows are probability-weighted averages of the future cash flows generated by a project under alternative scenarios. In the real business world there are a lot of uncertainties. Future cash flows may vary across different states of the world. It is not possible to estimate a unique number of cash flow for all states. We can estimate the expected cash flows across different states and use that as an estimation of future cash flows. The cash flows that are discounted in an NPV analysis are the expected incremental cash flows the project will produce. LO 2 Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.13 Projects with different lives: Explain the concept of equivalent annual cost and how it is used to compare projects with different lives.

Solution: The equivalent annual cost (EAC) is the annualized cost of an investment stated in nominal dollars. In other words, it is the annual payment from an annuity with a life equal to that of a project that has the same NPV as the project. Since it is a measure of the annual cost or cash Copyright © 2015 John Wiley & Sons, Inc.

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inflow from a project, the EAC for one project can be compared directly with the EAC from another project, regardless of the lives of those two projects. LO 4 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.14. Replace an existing asset: Explain how we determine the optimal time to replace an existing asset with a new one.

Solution: The optimal time to replace an existing asset with a new one is if the benefits of replacing the machine exceed the costs. LO 4 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.15. Projects with different lives: If you had to choose between one project with an expected life of five years and a second project with an expected life of six years, how could you do this without using the equivalent annual cost concept?

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Solution: When we choose from mutually exclusive project with different lives, instead of electing the project with higher NPV or lower net present value of costs, we should choose the project with higher Equivalent Annual Revenue or lower Equivalent Annual Cost. The underlying assumption is that we will continue to operate with the same equivalent annual revenue or equivalent annual cost in the future. LO 4 Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

INTERMEDIATE

11.16 Nominal versus real cash flows: You are buying a sofa. You will pay $200 today and make three consecutive annual payments of $300 in the future. The real rate of return is 10 percent, and the expected inflation rate is 4 percent. What is the actual price of the sofa?

Solution: We can calculate it in two different ways: (1)

Use nominal dollars and nominal rate of return: Nominal rate of return = (1 + 10%) × (1 + 4%) - 1 = 14.4% Price = 200 + 300 / (1 + 14.4%) + 300/(1 + 14.4%)2 + 300 / (1 + 14.4%)3 = $891.84

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(2)

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Use real dollars and a real rate of return: Real annual payments are: 300 / (1 + 4%) = 288.46, 300 / (1 + 4%)2 = 277.37, and 300 / (1 + 4%)3 = 266.70 Price = 200 + 288.46/(1 + 10%) + 277.37/(1 + 10%)2+266.7 / (1+10%)3 =891.84

Note that we get identical results as long as we are consistent in using nominal or real cash flows and corresponding discount rates. LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.17 Nominal versus real cash flows: You are graduating in two years. You want to invest your current savings of $5,000 in bonds and use the proceeds to purchase a new car when you graduate and start to work. You can invest the money in either Bond A, a two-year bond with a 3 percent annual interest rate, or Bond B, an inflation-indexed two-year bond paying 1 percent real interest above the inflation rate (assume this bond makes annual interest payments). The inflation rate over the next two years is expected to be 1.5 percent. Assume that both bonds are default free and have the same market price. Which bond should you invest in?

Solution:

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The nominal interest rate is 3 percent for bond A, and (1 + 1%) × (1 +1.5%) – 1 = 2.52% for the inflation-indexed bond B. You should invest in bond A. LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.18 Marginal and average tax rates: Given the U.S. Corporate Tax Rate Schedule in Exhibit 11.6, what was the marginal tax rate and average tax rate of a corporation that had a taxable income of $12 million in 2013? Solution: The marginal tax rate is 35 percent. The total tax payable is 3,400,000 + (12,000,000-10,000,000) ×35% = $4,100,000 Therefore the average tax rate = 4,100,000 / 12,000,000 = 34.2% LO 2 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.19 Investment cash flows: Healthy Potions, Inc., is considering investing in a new production line for eye drops. Other than investing in the equipment, the company needs to increase its cash and cash equivalents by $10,000, increase the level of inventory by $30,000, increase accounts receivable by $25,000, and increase accounts payable by $5,000 at the beginning of Copyright © 2015 John Wiley & Sons, Inc.

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the project. Healthy Potions will recover these changes in working capital at the end of the project 10 years later. Assume the appropriate discount rate is 12 percent. What are the present values of the relevant investment cash flows?

Solution: The relevant cash flow related to working capital at the beginning of the project is: $10,000 +$30,000+$25,000 - $5,000 = $60,000 The present value of relevant cash flow related to working capital at the end of the project is: $60,000 / (1 + 0.12)10 = $19,318.39 LO 1 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.20 Cash flows from operations: Given the soaring price of gasoline, Ford is considering introducing a new production line of gas-electric hybrid sedans. The expected annual unit sales of the hybrid cars is 30,000; the price is $22,000 per car. Variable costs of production are $10,000 per car. The fixed overhead including salary of top executives is $80 million per year. However, the introduction of the hybrid sedan will decrease Ford’s sales of regular sedans by 10,000 cars per year; the regular sedans have a unit price of $20,000, a unit variable cost of $12,000, and fixed costs of $250,000 per year. Depreciation costs of the production plant are

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$50,000 per year. The marginal tax rate is 40 percent. What is the incremental annual cash flow from operations?

Solution: Step One: Revenue: $22,000 × 30,000 cars =$660,000,000 Step Two: Op Exp: $10,000 × 30,000 cars = $300,000,000, plus lost net revenue from regular sedans = ($20,000 – $12,000) × 10,000 cars = $80,000,000; total Op Exp = $380,000,000 Step Three: D&A: $50,000 Step Four: Plug information into the text book template as below.

= = x = + = =

ΔNR ΔOpEx ΔEBITDA ΔD&A ΔEBIT (1-t) ΔNOPAT ΔD&A ΔCFO ΔCapEx ΔAWC ΔFCF

660,000,000 -380,000,000 280,000,000 -50,000 279,950,000 0.60 167,970,000 50,000 168,020,000 0 0 168,020,000

Alternatively, the incremental annual cash flow from operations is: (($22,000-$10,000) ×30,000-($20,000-$12,000) ×10,000) ×(1-0.4) + $50,000 ×0.4 = $168,020,000 Note that the fixed costs are not included in the incremental cash flows calculations, since they exist regardless of the hybrid sedan investment. LO 3 Copyright © 2015 John Wiley & Sons, Inc.

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Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.21 FCF and NPV for a project: Archer Daniels Midland Company is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $12 million. This investment will consist of $2 million for land and $10 million for trucks and other equipment. The land, all trucks, and all other equipment are expected to be sold at the end of 10 years for a price of $5 million, which is $2 million above book value. The farm is expected to produce revenue of $2 million each year, and annual cash flow from operations equals $1.8 million. The marginal tax rate is 35 percent, and the appropriate discount rate is 10 percent. Calculate the NPV of this investment.

Solution: Cash flow of investment in year 0 is: $(12,000,000) Annual cash flows from operations = $1,800,000 Present value of free cash flows:

PV(FCF1−10 ) = Annual CF  PV Annuity factor  1- 1  (1.10)10   =$1,800,000    0.10   = $11,060220.79 Book value of asset = $3,000,000 Sale price of asset = $5,000,000 Copyright © 2015 John Wiley & Sons, Inc.

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Tax on sale of an asset = (Selling price of asset - Book value of asset) × t = $2,000,000 × 0.35 = $700,000 PV of after-tax salvage value in year 10 is:

($5,000,000 − $700,000) 

1 = $1,657,836.15 (1.10)10

NPV = −$12,000,000 + $11,060,220.79 + 1,657,836.15 = $718,056.94 Since NPV > 0, project should be accepted. LO 1 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.22 Projects with different lives: You are trying to choose between purchasing one of two machines for a factory. Machine A costs $15,000 to purchase and has a three-year life. Machine B costs $17,700 to purchase but has a four year life. Regardless of which machine you purchase, it will have to be replaced at the end of its operating life. Which machine should you choose? Assume a marginal tax rate of 35percent and a discount rate of 15percent

Solution Since the machines have difference purchase costs and different operating lives, you should choose the machine that has the lowest equivalent annual cost (EAC).  (1 + k )t  EACA = kNPVA   t  (1 + k ) − 1  = (0.15)(−$15, 000) 

(1.15)3 = −$6,569.65 (1.15)3 − 1

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EACB = (0.15)(−$17, 700)

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(1.15)4 = −$6,199.70 (1.15)4 − 1

You should choose machine B because it has the lower equivalent annual cost. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.23 Projects with different lives: You are starting a family pizza parlor and need to buy a motorcycle for delivery orders. You have two models in mind. Model A costs $9,000 and is expected to run for 6 years; Model B is more expensive, with a price of $14,000, and has an expected life of 10 years. The annual maintenance costs are $800 for Model A and $700 for Model B. Assume that the opportunity cost of capital is 10 percent. Which one should you buy? Solution: You need to first calculate the NPV of costs for each of the motorcycles:

1   1−  (1.10)6  NPVA = −$9,000 + ( −$800)   = −$12, 484.21 0.10    

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 (1 + k )t  EACA = kNPVA   t  (1 + k ) − 1  = (0.10)(−$12, 484.21) 

(1.10)6 = −$2,866.47 (1.10)6 − 1

EACB = (0.10)( −$18,301.20) 

(1.10)10 = −$2,978.44 (1.10)10 − 1

Since EAC is lower for Model A, you should buy Model A. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.24 When to harvest an asset: Predator LLC, a leveraged-buyout specialist, recently bought a company and wants to determine the optimal time to sell it. The partner in charge of this investment has estimated the after-tax cash flows from a sale at different times to be as follows: $700,000 if sold one year later; $1,000,000 if sold two years later; $1,200,000 if sold three years later; and $1,300,000 if sold four years later. The opportunity cost of capital is 12 percent. When should Predator sell the company? Why?

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NPV4 = $1,300,000 / (1.12)4 = $826,174 Selling the company in 3 years provides the highest NPV. LO 5 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.25 Replace an existing asset: Bell Mountain Vineyards is considering updating its current manual accounting system with a high-end electronic system. While the new accounting system would save the company money, the cost of the system continues to decline. The Bell Mountain’s opportunity cost of capital is 10 percent, and the costs and values of investments made at different times in the future are as follows: Year

Cost

Value of Future Savings (at time of purchase)

$5,000

$7,000

4,500

7,000

4,000

7,000

3,600

7,000

3,300

7,000

3,100

7,000

When should Bell Mountain buy the new accounting system?

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NPV0 = Future savings – Cost = $7,000 - $5,000 = $2,000 NPV1 = $2,500 / (1.1)1 = $2,275 NPV2 = $3,000 / (1.1)2 =$ 2,479 NPV3 = $3,400 /(1.1)3 =$2,554 NPV4 = $3,700 / (1.1)4 = $2,527 NPV5 = $3,900 / (1.1)5 = $2,422 Therefore the company should purchase the system in year 3. LO 4 Bloomcode: AAnalysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.26 Replace an existing asset: You have a 2000 Nissan that is expected to run for another three years, but you are considering buying a new Hyundai before the Nissan wears out. You will donate the Nissan to Goodwill when you buy the new car. The annual maintenance cost is $1,500 per year for the Nissan and $200 for the Hyundai. The price of your favorite Hyundai model is $18,000, and it is expected to run for 15 years. Your opportunity cost of capital is 3 percent. Ignore taxes. When should you buy the new Hyundai?

Solution: NPV of cost of the new car is:

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1   1−  (1.03)15  NPVHyundai = −$18,000 + ( −$200)   = −$20,387.59 0.03     EAC of the new car is:  (1 + k )t  EACHyundai = kNPVt   t  (1 + k ) − 1  (1.03)15 = (0.03)( −$20,387.59)  = −$1,707.80 (1.03)15 − 1

Since the EAC of the new car is $1,707.8 and exceeds that of the Nissan( $1,500), you should drive the 2000 Nissan for three more years and then buy a new Hyundai. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.27 Replace an existing asset: Assume that you are considering replacing your old Nissan with a new Hyundai, as in the previous problem. However, the annual maintenance cost of the old Nissan increases as time goes by. It is $1,200 in the first year, $1,500 in the second year, and $1,800 in the third year. When should you replace it with the new Hyundai in this case?

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The EAC of the Hyundai remains at $1,707.80, as calculated above. Comparing this amount with the annual maintenance costs of the Nissan and you will see that in year 2 it is cheaper to drive the Nissan, but in year 3 it is cheaper to drive the Hyundai. Therefore, the optimal time to replace the old car is at the end of year 2. LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.28 When to harvest an existing asset: Anaconda Manufacturing Company currently own a mine that is known to contain a certain amount of gold. Since Anaconda does not have any goldmining expertise, the company plans to sell the entire mine and base the selling price on a fixed multiple of the spot price for gold at the time of the sale. Analysts at Anaconda have forecast the spot price for gold and have determined that the price will increase by 14 percent, 12 percent, 9 percent, and 6 percent during the next one, two, three, and four years, respectively. If Anaconda’s opportunity cost of capital is 10 percent, what is the optimal time for Anaconda to sell the mine?

Solution: The rate of gold price appreciation is greater than the opportunity cost of capital for the next two years and then it drops below the opportunity cost of capital. Therefore, Anaconda should sell the gold at the beginning of the third year (or at the end of the second year). LO 5 Copyright © 2015 John Wiley & Sons, Inc.

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Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.29 Replace an existing asset: You are thinking about delivering pizzas in your spare time. Since you must use your own car to deliver the pizzas, you will wear out your current car one year earlier, which is one year from today, than if you did not take on the delivery job. You estimate that when you purchase a new car, regardless of when that occurs, you will pay $20,000 for the car and it will last you five years. If your opportunity cost of capital is 7 percent, what is the opportunity cost of using your car to deliver pizzas?

Solution:

 (1 + 0.07)5  EAC New Car = 0.07  −$20, 000    = −$4,877.81 5  (1 + 0.07) − 1  Therefore, the opportunity cost of wearing out your car a year earlier is

NPVUsin g your car = −$4,877.81 / (1.07)1 = −$4,558,70 LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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ADVANCED

11.30 You are the CFO of SlimBody, Inc., a retailer of the exercise machine Slimbody6 and related accessories. Your firm is considering opening up a new store in Los Angeles. The store will have a life of 20 years. It will generate annual sales of 5,000 exercise machines, and the price of each machine is $2,500. The annual sales of accessories will be $600,000, and the operating expenses of running the store, including labor and rent, will amount to 50 percent of the revenues from the exercise machines. The initial investment in the store will equal $30 million and will be fully depreciated on a straight-line basis over the 20-year life of the store. Your firm will need to invest $2 million in additional working capital immediately, and recover it at the end of the investment. Your firm’s marginal tax rate is 30 percent. The opportunity cost of opening up the store is 10 percent. What are the incremental free cash flows from this project at the beginning of the project as well as in years 1-19 and 20? Should you approve it?

Solution: Step One: Initial outlay = $30,000,000 + $2,000,000 (WC requirement) = $32,000,000 Step Two: ΔNR for years 1- 20: $2,500 × 5,000 machines = $12,500,000 plus $600,000 = $13,100,000 Step Three: ΔOpExp for years 1- 20: $1,250 × 5,000 machines = $6,250,000 Step Four: ΔD&A for years 1- 20: $30,000,000 / 20 years = $1,500,000 / year Step Five: Plug information into the text book template as below. Step Six: Yr 20 recapture of WC requirements that were funded in year 0. Copyright © 2015 John Wiley & Sons, Inc.

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Yrs 1-19 ΔNR Δ

(

Yr 20

)

Therefore the NPV of the project is:

1    1 − (1.10)19  1 NPV = −$32,000,000 + $5, 245,000    + 7, 245,000  0.10  (1.10)20      = $12,950,928.97

You should approve the project since it has a positive NPV. Alternative Solution: Incremental cash flows in year 0 is: FCF0 = -$30,000,000-$2,000,000= -$32,000,000 Annual incremental cash flows through the life of the investment are: FCFt = ($2,500 ×2,500+$600,000) × (1-0.3)+0.3 ×$1,500,000 = $5,245,000 Additional incremental cash flows at the end of the project are: $2,000,000 Therefore the NPV of the project is:

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You should approve the project since it has a positive NPV. LO 1, 3, 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.31 Merton Shovel Corporation has decided to bid for a contract to supply shovels to the Honduran Army. The Honduran Army intends to buy 1,000 shovels per year for the next three years. To supply these shovels, Merton will have to acquire manufacturing equipment at a cost of $150,000. This equipment will be depreciated on a straight-line basis over its five-year lifetime. At the end of the third year, Merton can sell the equipment for exactly its book value ($60,000). Additional fixed costs will be $36,000 per year, and variable costs will be $3.00 per shovel. An additional investment of $25,000 in net working capital will be required when the project is initiated. This investment will be recovered at the end of the third year. Merton Shovel has a 35 percent marginal tax rate and a 17 percent required rate of return on the project. What is the lowest possible per shove price that Merton can offer for the contract and still create value for its stockholders? Solution Year 0 cash flow = Cap Exp + Add WC = -$150,000 – $25,000 = -$175,000 Year 3: Cap Exp + Add WC = $60,000 + $25,000 = $85,000 We can’t directly solve for CF Opns since revenue depends on what we are going to charge per shovel. Since CF Opns must be the same in years 1, 2, and 3 of the project this is a three year annuity and we can solve for the total value of CF Opns as: Present value of CF Opns = CF Opns × [(1-1/(1.17)3)/0.17] NPV of the shovel contract = -$175,000 + $85,000/(1.17)3 + OCF [(1-1/(1.17)3)/0.17] Set NPV = 0 and solve for CF Opns: CF Opns = $55,181 Now solve CF Opns formula for the price of each shovel (P): Copyright © 2015 John Wiley & Sons, Inc.

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CF Opns = [Revenue – OpEx – D&A) × (1 – t)] + D&A $55,181 = [(P × 1000) – ($3.00 × 1000) – $36,000 - $30,000] × (1-0.35) + $30,000 P = $107.74 This is the minimum bid price for a shovel. If Merton Shovel charges less than this price per shovel, the NPV of the contract will be less than zero. LO 1,3 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.32 Rocky Mountain Lumber, Inc., is considering purchasing a new wood saw that costs $50,000. The saw will generate revenues of $100,000 per year for five years. The cost of materials and labor needed to generate these revenues will total $60,000 per year, and other cash expenses will be $10,000 per year. The machine is expected to sell for $1,000 at the end of its five-year life and will be depreciated on a straight-line basis over five years to zero. Rocky Mountain’s tax rate is 34 percent, and its opportunity cost of capital is 10 percent. Should the company purchase the saw? Explain why or why not?

Solution: Step One: Initial outlay = $50,000 Step Two: ΔNR for years 1- 5: $100,000 Step Three: ΔOpExp for years 1- 5: $60,000 + $10,000 = $70,000 Step Four: ΔD&A for years 1- 5: $50,000 / 5 years = $10,000 / year Step Five: Plug into the text book template as below. Step Six: Yr 5: Capital recovery = $1,000 – (0.34 × $1,000 gain on sale) = $660.

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Yrs 1-4 ΔNR Δ

(

Yr 5 ,

)

Therefore, NPV of investment is:

NPV = −$50,000 +

$23,200 $23,200 $23,200 $23,200 $23,860 + + + + (1.10) (1.10)2 (1.10)3 (1.10)4 (1.10)5

= $38,356 Since NPV > 0, the company should buy the machine.

Alternatively: The annual operating cash flows from year 1 to 5 are: ($100,000-$60,000-$10,000) ×(1-0.34) + 0.34 ×10,000=$23,200 The after-tax terminal value in year 5 is: $1,000 - (0.34)($1,000-$0) = $660 Therefore, NPV of investment is:

NPV = −$50,000 +

$23,200 $23,200 $23,200 $23,200 $23,860 + + + + (1.10) (1.10)2 (1.10)3 (1.10)4 (1.10)5

= $38,356 Therefore the company should buy the machine. LO 1,3,4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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11.33 A beauty product company is developing a new fragrance named Happy Forever. There is a probability of 0.5 that consumers will love Happy Forever, and in this case, annual sales will be 1 million bottles; a probability of 0.4 that consumers will find the smell acceptable and annual sales will be 200,000 bottles; and a probability of 0.1 that consumers will find the smell unpleasant and annual sales will be only 50,000 bottles. The selling price is $38, and the variable cost is $8 per bottle. Fixed production costs will be $1 million per year, and depreciation will be $1.2 million. Assume that the marginal tax rate is 40 percent. What are the expected annual incremental after-tax free cash flows from the new fragrance?

Solution: Step One: Expected sales units: (0.5) ×1,000,000 + (0.4) ×200,000 + (0.1) ×50,000 = 585,000 units Step Two: ΔNR: 585,000 units × $38 = $22,230,000 Step Three: ΔOpExp: 585,000 units x $8 + $1,000,000 = $5,680,000 Step Four: ΔD&A: $1,200,000 Step Five: Plug into the text book template as below.

= = x = + = =

ΔNR ΔOpEx ΔEBITDA ΔD&A ΔEBIT (1-t) ΔNOPAT ΔD&A ΔCFO ΔCapEx ΔAWC ΔFCF

22,230,000 -5,680,000 16,550,000 -1,200,000 15,350,000 0.60 9,210,000 1,200,000 10,410,000 0 0 10,410,000

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Alternatively, the expected annual incremental cash flows are:

(((0.5 ×1,000,000+0.4 ×200,000+0.1 ×50,000) × ($38-$8)) -1,000,000) × (1 - 0.4) +1,200,000 ×0.4 = $10,410,000 LO 1,3,4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.34 Great Fit, Inc., is a company that manufactures clothing. The company has a production line that produces women’s tops of regular sizes. The same machine could be used to produce petite sizes as well. However, the remaining life of the machines will be reduced from four years to two years if the petite size production is added. The cost of identical machines with a life of eight years is $2 million. Assume the opportunity cost of capital is 8 percent. What is the opportunity cost of adding petite sizes?

Solution: The opportunity cost is the incremental costs of the machine in year 3 and year 4 if petite sizes are in production. The EAC of the machine is:  (1 + k )t  EACA = kNPVA   t  (1 + k ) − 1  = (0.08)(−$2, 000, 000) 

(1.08)8 = −$348, 029.52 (1.08)8 − 1

The present value of such cost in year 3 and year 4 is:

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$348,029.52 $348,029.52 + (1.08)3 (1.08)4 = $532,089.14

NPV =

LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.35 Biotech Partners LLC has been farming a new strain of radioactive-material-eating bacteria that the electrical utility industry can use to help dispose of its nuclear waste. Two opposing factors affect Biotech’s decision of when to harvest the bacteria. The bacteria are currently growing at a 22 percent annual rate, but due to known competition from other top firms, Biotech analysts estimate that the price for the bacteria will decline according to the schedule below. If the opportunity cost of capital is 10 percent, then when should Biotech harvest the entire bacteria colony at one time? Year

Change in Price Due to Competition (5)

-2

-8

-10

-15

-25

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Solution: Change in revenue: Yr 1

(1.05)(1.22) = 1.2810 or 28.1%

Yr 2

(0.98)(1.22) = 1.1956 or 19.56%

Yr 3

(0.92)(1.22) = 1.1224 or 12.24%

Yr 4

(0.9)(1.22) = 1.0980 or 9.80%

Yr 5

(0.85)(1.22) = 1.037 or 3.70%

Yr 6

(0.75)(1.22) =- 0.9150 or -8.50%

Since the change in revenue is higher than the 10% opportunity cost of capital for the first three years, Biotech should sell its bacteria colony at the beginning of the third year or at the end of the second year. LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.36 ACME Manufacturing is considering replacing an existing production line with a new line that has a greater output capacity and operates with less labor than the existing line. The new line would cost $1 million, have a five-year life, and be depreciated using MACRS over three years. At the end of five years, the new line could be sold as scrap for $200,000 (in Year 5 dollars). Because the new line is more automated, it would require fewer operators, resulting in a savings of $40,000 per year before tax and unadjusted for inflation (in today’s dollars). Copyright © 2015 John Wiley & Sons, Inc.

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Additional sales with the new machine are expected to result in additional net cash inflows, before tax, of $60,000 per year (in today’s dollars). If ACME invests in the new line, a onetime investment of $10,000 in additional working capital will be required. The tax rate is 35 percent, the opportunity cost of capital is 10 percent, and the annual rate of inflation is 3 percent. What is the NPV of the new production line?

Solution: t=

0.35

rate =

0.1

NPV of the New Line 0

Op Exp)(1-t)

$66,950

$68,959

$71,027

$73,158

plus Tax x Deprec

$116,655

$155,575

$51,835

$25,935

(Revenue -

minus Cap Exp

$1,000,000

$75,353

$(200,000)

plus tax on Salvage

$(70,000)

minus Add WC

$10,000

Net Cash Flows

$(1,010,000)

$183,605

$224,534

$122,862

$99,093

$215,353

PV of Net Cash Flows

$(1,010,000)

$166,914

$185,565

$92,308

$67,682

$133,717

Net Present Value

$(10,000)

$(363,814)

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LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.37 The alternative to investing in the new production line in Problem 11.36 is to overhaul the existing line, which currently has both a book value and a salvage value of $0. It would cost $300,000 to overhaul the existing line, but this expenditure would extend its useful life to five years. The line would have a $0 salvage value at the end of five years. The overhaul outlay would be capitalized and depreciated using MACRS over three years. Should ACME replace or renovate the existing line?

0.35

rate =

0.1

Renovate Old Line 0

$34,997

$46,673

$15,551

$7,781

(Revenue Op Ex)(1-t)

plus Tax × Deprec

minus Cap Exp

$300,000

plus tax on Salvage

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minus Add WC

Net Cash Flows

$(300,000)

$34,997

$46,673

$15,551

$7,781

PV of Net Cash Flows

$(300,000)

$31,815

$38,572

$11,683

$5,314

Net Present Value

$(212,615)

NPVnew - NVPold

$(151,199)

Renovating the old line is less costly. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

CFA Problems 11.38. FITCO is considering the purchase of new equipment. The equipment costs $350,000, and an additional $110,000 is needed to install it. The equipment will be depreciated straight-line to zero over a five-year life. The equipment will generate additional annual revenues of $265,000, and it will have annual cash operating expenses of $83,000. The equipment will be sold for $85,000 after five years. An inventory investment of $73,000 is required during the life of the investment. FITCO is in the 40 percent tax bracket, and its cost of capital is 10 percent. What is the project NPV? Copyright © 2015 John Wiley & Sons, Inc.

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$47,818

$63,658

$80,189

$97,449

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Solution:

d is correct. Outlay = FCInv + NWCInv – Sal0 + T × (Sal0 – B0) Outlay = (350,000 + 110,000) + 73,000 – 0 + 0 = $533,000 The installed cost is $350,000 + $110,000 = $460,000, so the annual depreciation is $460,000/5 = $92,000. The annual after-tax operating cash flow for Years 1–5 is CF = (S – C – D)(1 – T) + D = (265,000 – 83,000 – 92,000)(1 – 0.40) + 92,000 CF = $146,000

The terminal year after-tax non-operating cash flow in Year 5 is TNOCF = Sal5 + NWCInv – T(Sal5 – B5) = 85,000 + 73,000 – 0.40(85,000 – 0) TNOCF = $124,000 The NPV is 5

146, 000 124, 000 + t 1.105 = $97,449 t=1 1.10

NPV = −533, 000 +  LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions

AICPA: Industry/Sector Perspective

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11.39 After estimating a project’s NPV, the analyst is advised that the fixed capital outlay will be revised upward by $100,000. The fixed capital outlay is depreciated straight-line over an eight-year life. The tax rate is 40 percent, and the required rate of return is 10 percent. No changes in cash operating revenues, cash operating expenses, or salvage value are expected. What is the effect on the project NPV?

$100,000 decrease

$73,325 decrease

$59,988 decrease

No change

Solution:

b is correct. The additional annual depreciation is $100,000/8 = $12,500. The depreciation tax savings is 0.40 ($12,500) = $5,000. The change in project NPV is 8

5, 000 = −100, 000 + 26, 675 = −$73,325 t t =1 (1.10)

−100, 000 +  LO 4 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions

AICPA: Industry/Sector Perspective

11.40. When assembling the cash flows to calculate an NPV or IRR, the project’s after-tax interest expenses should be subtracted from the cash flows for:

The NPV calculation, but not the IRR calculation.

The IRR calculation, but not the NPV calculation.

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Both the NPV calculation and the IRR calculation.

Neither the NPV calculation nor the IRR calculation.

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Solution: D is correct. Financing costs are not subtracted from the cash flows for either the NPV or the IRR. The effects of financing costs are captured in the discount rate used. LO 1 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

Sample Test Problems

11.1

You purchased 100 shares of stocks of an oil company, Texas Energy, Inc., at $50 per share. The company has 1 million shares outstanding. Ten days later, Texas Energy announced an investment in an oil field in east Texas. The probability of the investment being successful and generating NPV of $10 million is 0.2; the probability of the investment will be a failure and generate a negative NPV of negative $1 million is 0.8. How would you expect the stock price to change upon the company’s announcement of the investment?

Solution: The expected change in the stock price should be equal to the expected NPV of the project divided by the number of shares outstanding. The expected NPV of the project is (0.2 × $10,000,000) + (0.8 × –$1,000,000) = $1,200,000 Copyright © 2015 John Wiley & Sons, Inc.

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Therefore, the change in Texas Energy’s stock price should equal $1,200,000 / 1,000,000 shares = $1.2 per share when the investment is announced. The total value of your shares should increase by 100 shares × $1.20 per share = $120. Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.2

A division of Virginia City Highlands Manufacturing is considering purchasing for 1,500,000 a machine that automates the process of inserting electronic components onto computer motherboards. The annual cost of operating the machine will be $50,000, but it will save the company $370,000 in labor costs each year. The machine will have a useful life of 10 years, and its salvage value in 10 years is estimated to be $300,000. Straight-line depreciation will be used in calculating taxes for this project, and the marginal corporate tax rate is 32 percent. If the appropriate discount rate is 12 percent, what is the NPV of this project?

Solution: The incremental after-tax free cash flow (FCF) in year 0 is: FCF0 = –$1,500,000 The FCF in years 1 through 9 is: Annual Depreciation = ($1,500,000 – $300,000) / 10 = $120,000 per year FCFt = [($370,000 – $50,000) × (1 – 0.32)] + [ 0.32 × $120,000] = $256,000 The FCF in year 10 is: Copyright © 2015 John Wiley & Sons, Inc.

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FCF10 = $256,000 + $300,000 – [(Salvage Value – Book Value) × 0.032] = $556,000 Therefore, the NPV of the project is:

 1   1 –  9  ( 1 . 12 )   + $556,000  1  NPV = –$1,500,000 + $256,000   0.12    (1.12)10         = –$1,500,000 + $1,346,032 + $179,017 = $43,049 Virginia City Highlands Manufacturing should approve the project since it has a positive NPV. Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.3

After examining the NPV analysis for a potential project that would increase the firm’s output by 5 percent, an analyst’s manager tells the analyst to increase the initial fixed capital outlay in the analysis by $480,000. The initial fixed capital outlay would be fully depreciated on a straight-line basis over a 12-year life, regardless of whether it is increased. If the firm’s average tax rate is 28 percent, its marginal tax rate is 35 percent, and the required rate of return is 10 percent, what is the effect of the adjustment on the project NPV?

Solution: The additional annual depreciation is $480,000 / 12 = $40,000.

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For a project such as this we would use the marginal tax rate. Therefore, the annual depreciation tax savings is 0.35 × $40,000 = $14,000. The change in the overall NPV of the project is:

 1   1−  12  (1.10)  Change in NPV = – $480,000 + $14,000    0.10         = –$480,000 + $95,392 = –$384,608 The NPV will be reduced by $384,608 Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.4

Which of the following are relevant cash flows in the evaluation of a proposal to produce a new product? a. Decrease in the cash flows of a substitute product. b. Alternative of leasing an existing building that will be used for manufacturing this product. c. The cost of a new machine required to produce this product. d. Salvage value of the new machine at the end of its useful life. e. Increase in net working capital at the beginning of the project’s life. f. Cost to develop a product prototype last year.

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a, b, c, d, and e are all relevant cash flows. f is a sunk cost and is therefore not relevant. Bloomcode: Application AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

11.5

Managers of Central Embroidery have decided to purchase a new monogram machine and are considering two alternative machines. The first machine costs $100,000 and is expected to last five years. The second machine costs $160,000 and is expected to last eight years. Assume that the opportunity cost of capital is 8 percent. Which machine should Central Embroidery purchase?

Solution: The equivalent annual cost for each system is:

 (1.08)5  EACMachine 1 = 0.08 × $100,000×   = $25,045.65 5  (1.08) – 1   (1.08)8  EACMachine 2 = 0.08 × $160,000×   = $27,842.37 8  (1.08) – 1 Central Embroidery should purchase the first machine because it has a lower EAC. Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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You have inherited an apple orchard and want to sell it in the next four years. An expert in apple orchard valuation has estimated the after-tax cash flow you would receive if you sold at the end of each of the next four years as follows: $1,000,000 if you sell in one year; $1,300,000 if you sell in two years; $1,500,000 if you sell in three years; and $1,600,000 if you sell in four years. Your opportunity cost of capital is 10 percent. When should you sell the orchard?

Solution: The NPV in today’s dollars for each alternative is: NPV1 = $1,000,000 / (1.10)1 = $909,091 NPV2 = $1,300,000 / (1.10)2 = $1,074,380 NPV3 = $1,500,000 / (1.10)3 = $1,126,972 NPV4 = $1,600,000 / (1.10)4 = $1,092,822 You should sell the orchard in 3 years because the present value of the NPV is highest in year three. After year three, the value of the orchard is expected to increase at a rate that is less than your opportunity cost of capital. Therefore it is better for you to sell the orchard after three years and invest the proceeds elsewhere. Bloomcode: Analysis AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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Chapter 12 Evaluating Project Economics

Before You Go On Questions and Answers

Section 12.1 1.

Why do analysts care about how sensitive EBITDA and EBIT are to changes in revenue?

Comparing the sensitivity of EBITDA to changes in revenue can help you better understand risks and returns associated with alternative options. For example, if we assume that the sensitivity of EBITDA to changes in revenue is higher for one alternative than for the other. This means that EBITDA for the more sensitive alternative will decline more when revenue is lower than expected. A larger decline in EBITDA reduces the value of the project more and has a greater impact on the amount of cash the firm has available to fund other positive NPV projects. Conversely, EBITDA will increase more when revenue is greater than expected if the level of sensitivity is higher.

How is the proportion of fixed costs in a project’s cost structure related to the sensitivity of EBITDA and EBIT to changes in revenue?

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The greater the proportion of fixed costs, the more sensitive EBITDA and EBIT will be to changes in revenue.

Section 12.2 1.

How does operating leverage change when there is an increase in the proportion of a project’s costs that are fixed?

An increase in the proportion of a project’s costs that are fixed increases the operating leverage of the project.

What do the degree of pretax cash flow operating leverage (Cash Flow DOL) and the degree of accounting operating leverage (Accounting DOL) tell us?

Cash Flow DOL provides us with a measure of how sensitive pretax operating cash flows are to changes in revenue. Cash Flow DOL changes with the level of revenue. Accounting DOL is a measure of how sensitive accounting operating profits (EBIT) are to changes in revenue. Accounting DOL focuses on EBIT, whereas Cash Flow DOL focuses on EBITDA.

Section 12.3

How is the per-unit contribution related to the accounting operating profit breakeven point?

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The per unit contribution is how much is left from the sale of a single unit after paying the variable costs associated with that unit. This is the amount that is available to help cover FC and D&A for the project. When we calculate the accounting operating profit break-even point, we divide the sum of FC and D&A by the per unit contribution to determine how many units must be sold to cover FC and D&A.

What is the difference between the pretax operating cash flow break-even point and the accounting operating profit break-even point?

The pretax operating cash flow break-even point is the number of units that must be sold in a particular year for cash inflows to exactly equal cash outflows. The accounting operating profit break-even point is the number of units that must be sold in a particular year for the project to have operating profits of $0—in other words, to break even on an accounting operating profit basis.

Section 12.5 1.

How is a sensitivity analysis used in project analysis?

Sensitivity analysis is used to examine the sensitivity of a project’s NPV to changes in an individual assumption.

How does a scenario analysis differ from a sensitivity analysis?

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Scenario analysis recognizes that variables typically do not change one at a time. A change in economic or market conditions will usually cause several assumptions to change. Scenario analysis recognizes this by examining a project under alternative scenarios in which each assumption can change under each scenario.

What is a simulation analysis, and what can it tell us?

Simulation analysis is like scenario analysis which enables the analyst to evaluate the effects of different scenarios. A key difference is that simulation analysis uses computers to enable the analyst to examine a large number of scenarios in a short period of time.

Self-Study Problems

12.1

The Yellow Shelf Company sells all of its shelves for $100 per shelf, and incurs $50 in variable costs to produce each. If the fixed costs for the firm are $2,000,000 per year, what will the EBIT for the firm be if it produces and sells 45,000 shelves next year? Assume that depreciation and amortization is included in the fixed costs.

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Revenue

$100 per unit × 45,000 units =

$4,500,000

$50 per unit × 45,000 units =

2,250,000

FC + D&A

2,000,000

EBIT

$ 250,000

Hydrogen Batteries sells its specialty automobile batteries for $85 each, while its current variable cost per unit is $65. Total fixed costs (including depreciation and amortization expense) are $150,000 per year. Management expects to sell 10,000 batteries next year, but is concerned that variable cost will increase next year due to material cost increases. What is the maximum variable cost per unit increase that will keep the EBIT from becoming negative?

Solution: The forecasted EBIT for Hydrogen Batteries is: Revenue

$85 per unit × 10,000 units = $850,000

$65 per unit × 10,000 units = 650,000

FC + D&A

150,000

EBIT

$ 50,000

Therefore, total variable cost may increase by $50,000, which means that if the firm produces and sells 10,000 batteries, then the variable cost per unit may increase by $5 ($50,000 / 10,000 units = $5 per unit).

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12.3

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The Vinyl CD Co. is going to take on a project that is expected to increase its EBIT by $90,000, its fixed cost cash expenditures by $100,000, and its depreciation and amortization by $80,000 next year. If the project yields an additional 10 percent in revenue, what percentage increase in the project’s EBIT will result from the additional revenue?

Solution:

FC + D & A EBIT $100, 000 + $80, 000 = 1+ $90, 000 =3

Accounting DOL = 1+

Therefore, a 10 percent additional increase in revenue should result in approximately a 30 percent increase in EBIT.

12.4

You are considering investing in a business that has monthly fixed costs of $5,500 and sells a single product that costs $35 per unit to make. This product sells for $90 per unit. What is the annual pretax operating cash flow break-even point for this business?

Solution: You can solve for the monthly pretax operating cash flow break-even point using Equation 12.4:

EBITDA Break-Even =

FC $5,500 = =100 units per month Price − Unit VC $90 − $35

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Solutions Manual

Belt Bottoms, Inc. is considering a five-year project with an initial investment of $20,000. What annual free cash flow (FCF) would be required for this project to have an NPV of $0 if the opportunity cost capital is 11 percent?

Solution: If the FCF is equal in each of the five years, then we can solve for FCF using the present value of an ordinary annuity formula: 𝑭𝑪𝑭

𝟏

$20,000 = .𝟏𝟏 𝒕 × (𝟏 − (𝟏.𝟏𝟏)𝟓 ) → FCF = $5,411.41

Discussion Questions 12.1

You are involved in the planning process for a firm that is expected to have a large increase in sales next year. Which type of firm would benefit the most from that sales increase: a firm with low fixed costs and high variable costs or a firm with high fixed costs and low variable costs?

Solution: Under the circumstances described, the firm with the high fixed costs would incur lower total future costs associated with the increased sales than the firm with the low fixed costs due to the higher variable cost per unit of sales. Therefore, the firm with the high fixed costs structure would benefit the most. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic Copyright © 2015 John Wiley & Sons, Inc.

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12.2

You own a firm with a single new product that is about to be introduced to the public for the first time. Your marketing analysis suggests that the annual demand for this product could be anywhere between 500,000 units and 5,000,000 units. Given such a wide range, discuss the safest cost structure alternative for your firm.

Solution: Since there is a great deal of variability concerning the demand for the product, then the safest alternative would be to create a cost structure that limits the variability of the firm’s EBIT. This means that you would create a cost structure that is composed of high unit variable costs with low fixed costs. Although this would not enable the firm to maximize earnings if the 5,000,000 unit forecast occurs, it limits the downside profitability for the firm in the event that the 500,000 unit forecast occurs. LO: 1 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.3

Discuss the interpretation of the degree of accounting operating leverage and degree of pretax cash flow operating leverage.

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Solution: While the degree of accounting operating leverage is defined as: Accounting DOL = 1 + (FC + D&A) / (EBIT) it is used to interpret the percentage change in EBIT that will be driven by a given percentage change in net revenue. Similarly, the degree of pretax cash flow operating leverage is defined as: Cash Flow DOL = 1 + FC / (EBIT + D&A) but it is used to interpret the percentage change in EBITDA (or pretax operating cash flow) that will be driven by a given percentage change in net revenue. LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.4

Explain how EBITDA differs from incremental after-tax free cash flows (FCF) and discuss the types of businesses for which this difference would be especially small or large.

Solution:

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Depreciation and amortization, taxes, capital expenditures, and working capital are not reflected in EBITDA. If any of these is not equal to zero, then EBITDA is likely to differ from FCF, which is equal to EBIT(1-T) + depreciation—increases in working capital— capital expenditures. The type of businesses that require large capital expenditures (and therefore have large depreciation expenses per year) such as heavy manufacturing, are likely to have substantial differences between EBITDA and FCF. Conversely, smaller firms that have smaller capital expenditures, such as firms in retail sales, will likely have small differences between FCF and EBITDA for. Setting aside depreciation and special tax subsidies, taxes will always create a difference between EBITDA and FCF for a profitable firm. LO: 2 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.5

Describe how the pretax operating cash flow break-even point is related to the economic break-even point.

Solution: The pre-tax operating cash flow break-even point establishes the number of units that must be sold in a given year to break even for a particular year. The economic break-even Copyright © 2015 John Wiley & Sons, Inc.

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calculation looks at cash flows over the course of an entire project and tells us how many units must be sold to achieve an NPV of $0. The NPV calculation is useful when deciding whether to undertake a project in an economic sense. The cash flow break-even calculation is useful when considering whether to abandon a project or to make changes to a project’s cost structure. LO: 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.6

Is it possible to have a crossover point where the accounting break-even point is the same for two alternatives - that is, above the break-even point for a low-fixed-cost alternative but below the break-even point for a high-fixed-cost alternative? Explain.

Solution: No. Above the low fixed cost break-even sales level implies that income is positive. Below the high fixed cost break-even sales level implies that income is negative. However, the cross-over point is defined as the sales level at which the income level for both alternatives is the same. Therefore, it cannot occur. LO: 3 Level: Basic Bloomcode: Comrpehension Copyright © 2015 John Wiley & Sons, Inc.

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12.7

What is the fundamental difference between a sensitivity analysis and a scenario analysis?

Solution: A sensitivity analysis is a form of “what if” analysis that is very useful for identifying key individual assumptions in models used for financial analysis such as an NPV calculation. Scenario analysis identifies relationships across several key individual assumptions, and is therefore a good way of estimating how project values might vary under different economic scenarios. LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.8

The economics break-even calculation assumes that the number of units sold is the same each year during the life of the project. It is possible for the NPV of a project to be negative if unit sakes are not the same each year and the average unit sales are higher than that estimated using the economic break-even calculation.

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Solution: Yes. This is possible, if, for example, actual unit sales are lower than the average in the early years of a project’s life and higher than the average in the latter years of a project’s life. This is due to the time value of money. Unit sales in early years have a greater present value than unit sales in later years. Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.9

How does the pretax operating cash flow for a project differ from the economic profit for that project?

Solution: The pretax operating cash flow is a measure of the extent to which revenues exceed cash operating expenses. It does not account for taxes or the opportunity cost of the capital that is invested in the project. Economic profit is a measure of the extent to which revenues exceed cash operating expenses, taxes, and the opportunity cost of the capital invested in a project. Economic profit accounts for all of the costs associated with producing a project’s revenue. Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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12.10 What is the advantage of using a simulation analysis instead of a scenario analysis to assess the risk of a project? Solution: Simulation analysis is like a scenario analysis except that in simulation analysis an analyst uses a computer to examine a large number of scenarios in a short period of time. This description from the text suggests that simulation analysis allows for more efficient use of the analyst’s time. In addition, since an analyst can examine a very large number of scenarios (typically in the thousands) in a simulation analysis, this analytical tool can enable the analyst to get a more complete picture of the risks associated with a project. Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

Questions and Problems

BASIC 12.1

Fixed and variable costs: Define variable costs and fixed costs, and give an example of each.

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Solution: Fixed costs are costs that in the short term cannot be changed regardless of how much output the project produces. One example is the in-home technical computer support business (discussed in Learning by Doing Application 12.1). Regardless of the number of house calls the technical support firm makes, it will incur the full cost of advertising. Variable costs are costs that depend on the number of units of output produced by the project. An example is the gas that the technical support firm uses to make house calls. The cost to keep the vehicles gassed up is directly related to the number of service calls the firm makes. LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.2

EBIT: Describe the role that the mix of variable versus fixed costs has in the variation of earnings before interest and taxes (EBIT) for the firm.

Solution: By definition, variable costs do not occur unless matching sales or matching revenues also occur, whereas fixed costs are not a function of the level of sales. Therefore, a large mix of fixed costs within a firm’s cost structure will make the firm’s EBIT very reactive Copyright © 2015 John Wiley & Sons, Inc.

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to a change in the level of sales for the firm. The greater the proportion of fixed costs, (compared to variable costs), the greater the variability in EBIT for the firm. LO 1 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.3

EBIT: The Generic Publications Textbook Company sells all of its books for $100 per book, and it currently costs $50 in variable costs to produce each text. The fixed costs, which include depreciation and amortization for the firm, are currently $2 million per year. The firm is considering changing its production technology, which will increase the fixed costs for the firm by 50 percent but decrease the variable costs per unit by 50 percent. If the firm expects to sell 45,000 books next year, should the firm switch technologies?

Solution: The current EBIT for the firm is: Revenue

$100 per book × 45,000 books

$4,500,000

$50 per book × 45,000 books

2,250,000

FC + D&A

2,000,000

EBIT

$250,000

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If the fixed costs increase by 50 percent, then they will be $2,000,000 × 1.5 = $3,000,000, while the unit variable costs would be 0.5 × $50 = $25. The new EBIT for the firm would then be: Revenue

$100 per book × 45,000 books

$4,500,000

$25 per book × 45,000 books

1,125,000

FC + D&A

3,000,000

EBIT

$ 375,000

Since the EBIT after the technology change is $125,000 higher, the firm should adopt the new production technology. LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.4

EBIT: WalkAbout Kangaroo Shoe Stores forecasts that it will sell 9,500 pairs of shoes next year. The firm buys its shoes for $50 per pair from the wholesaler and sells them for $75 per pair. If the firm will incur fixed costs plus depreciation and amortization of $100,000, then what is the percent increase in EBIT if the actual sales next year equal 11,500 pairs of shoes instead of 9,500?

Solution: The forecasted EBIT for the firm is: Revenue

$75 per pair × 9,500 pairs

$712,500 SM 12-17

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$50 per pair × 9,500 pairs

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475,000

FC + D&A

100,000

EBIT

$137,500

The actual EBIT for the firm is: Revenue

$75 per pair × 11,500 pairs

$862,500

$50 per pair × 11,500 pairs

575,000

FC + D&A

100,000

EBIT

$187,500

Therefore, the percent increase in EBIT would be ($187,500 – $137,500) / $137,500 = 0.3636 = 36.36%. LO 1 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.5

Cash Flow DOL: The law firm of Dewey, Cheatem, and Howe has monthly fixed costs of $100,000, EBIT of $250,000, and depreciation charges on its office furniture and computers of $5,000. Calculate the Cash Flow DOL for this firm.

Solution:

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Cash Flow DOL = 1 +

Solutions Manual

FC $100,000 =1+ = 1.392 EBITDA $250,000 +$5,000

LO 2

12.6. Cash Flow DOL: The degree of pretax cash flow operating leverage at Rackit Corporation is 2.7 when it sells 100,000 units of its new tennis racket and its EBITDA is $95,000. Ignoring the effects of taxes, what are the fixed costs for Rackit Corporation?

Solution: Cash Flow DOL = 1 + FC/EBITDA 2.7 = 1 + FC / ($95,000) FC = $161,500 LO 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.7

Accounting DOL: Explain how the value of accounting operating leverage can be used.

Solution:

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Accounting operating leverage gives us the ratio by which the firm can convert revenues into EBIT. That is, if the firm’s operating leverage is 3, then a 15 percent increase will convert to a 45 percent (15% x 3) increase in EBIT for the firm. LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.8

Accounting DOL: Caterpillar, Inc. is a manufacturer of large earth-moving and mining equipment. This firm, and other heavy equipment manufacturers, have accounting degrees of operating leverage that are relatively high. Explain why.

Solution: Caterpillar and other heavy equipment manufacturers are heavily dependent on assets in place, like manufacturing equipment and facilities, for production. These investments result in relatively high fixed costs compared to variable costs of production, leading to a high degree of operating leverage. To illustrate, in 2009, CAT saw a 37% decrease in revenue and an 88% drop in operating income relative to their 2008 results. However, for the third quarter of 2010, CAT saw a 53% increase in sales and a 329% jump in operating profit. LO 2 Bloomcode: Comprehension AASCB: Analytic Copyright © 2015 John Wiley & Sons, Inc.

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12.9

Break-even analysis: Why is the per-unit contribution important in a break-even analysis?

Solution: Per-unit contribution is critical to break-even analysis in order for a firm to determine how many units are required to be sold to cover the firm’s fixed costs. The underlying known variable is the dollar amount of the contribution margin the firm will generate from each unit sold in order to make the above calculation. EBITDA Break-even = FC / (Price – Unit VC) and EBIT break-even = (FC + D&A) / (Price – Unit VC) demonstrate the calculation for EBITDA and EBIT break-even points respectively. The term in the denominator (Price-Unit VC) represents the per-unit cash flow contribution. LO 3 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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12.10 Break Even: Calculate the accounting operating profit break-even point and pretax operating cash flow break-even point for each of the three production choices outlined below. Choice

Price

Unit VC

D&A

A B C

$250 $55 $10

$160 $10 $1.50

$15,000 $1,100 $100

$3,000 $200 $100

Solution:

Choice

Unit price

Unit VC

Fixed costs

D&A

A B C

$250 $55 $10

$160 $10 $1.50

$15,000 $1,100 $100

$3,000 $200 $100

EBIT breakeven* 200 29 24

Pretax operating cash flow breakeven** 167 24 12

* EBIT breakeven = (Fixed Costs + D&A) / (Price – Unit VC) ** Pretax operating cash flow breakeven = Fixed Costs / (Price – Unit VC) LO 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.11 Economic break-even point: The accounting operating profit break-even point tells us the number of units that must be sold for a firm to break-even in a given year from an accounting operating profit perspective. What measure tells us the number of units that must be sold each year during the life of a project in order for the project to break-even with regards to its opportunity cost of capital? Copyright © 2015 John Wiley & Sons, Inc.

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Solution: The economic break-even point tells us the number of units that must be sold each year during the life of a project in order for the project to break even with regards to its opportunity cost of capital. Because the economic break-even point calculation accounts for all cash flows over the life of a project, it enables us to compute the annual level of unit sales that will result in an NPV of $0. This is, by definition, the break-even point with regards to a project’s opportunity cost of capital. Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.12 Simulation analysis: What is simulation analysis, and how is it used?

Solution: Simulation analysis is like scenario analysis except that in simulation analysis an analyst typically uses a computer to examine a large number of scenarios in a short period of time. Rather than selecting individual values for each of the assumptions—such as unit sales, unit price, and unit variable costs—the analyst assumes that those assumptions can be represented by statistical distributions. The computer then draws upon the distribution of each variable in order to generate an observation for a single scenario. After repeating the number of computer-generated scenarios, a distribution of cash flow outcomes will be generated, thereby offering the analyst the ability to perform a probability-based analysis on the cash flow distribution. LO 4 Copyright © 2015 John Wiley & Sons, Inc.

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Bloomcode: Knowledge AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

INTERMEDIATE 12.13 EBIT: If a manufacturing firm and a service firm have identical cash fixed costs, but the manufacturing firm has much higher depreciation and amortization, then which firm is more likely to have a large discrepancy between its FCF and its EBIT?

Solution: Since depreciation and amortization are noncash items, the manufacturing firm would have the greatest discrepancy between FCF and EBIT. LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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and amortization, are currently $220,000 per year. How much can either the fixed costs or the variable cost per unit increase in order to keep the company from having a negative EBIT. Solution: The forecasted EBIT for the firm is: Revenue

$110 per ball × 15,000 balls

$1,650,000

$80 per ball × 15,000 balls

1,200,000

FC + D&A EBIT

220,000 $ 230,000

Therefore, the fixed costs could increase by $230,000 and still keep the EBIT from being negative. If we focus on the variable costs, we know that total variable costs could increase by $230,000. If that cost is spread over 15,000 units, then the variable cost per unit could increase by ($230,000 / 15,000) = $15.33 and still keep the EBIT from being negative. Note that the analysis assumes that increases in either the fixed cost or the variable cost per unit will not change the other. This is probably not a realistic assumption. LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.15 EBIT: Specialty Light Bulbs anticipates selling 3,000 light bulbs this year at a price of $15 per bulb. It costs Specialty $10 in variable costs to produce each light bulb, and the Copyright © 2015 John Wiley & Sons, Inc.

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fixed costs for the firm are $10,000. Specialty has an opportunity to sell an additional 1,000 bulbs next year at the same price and variable cost, but by doing so the firm will incur an additional fixed cost of $4,000. Should Specialty produce and sell the additional bulbs?

Solution: The forecasted EBIT (Additional production) for the firm is: Revenue

$15 per bulb × 1,000 bulbs

$15,000

$10 per bulb × 1,000 bulbs

10,000

4,000

EBIT

$ 1,000

Since the EBIT is positive, then Specialty should produce and sell the additional bulbs. LO: 1 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.16. Cash Flow DOL: The pretax operating cash flow of Memphis Motors declined so much during the recession of 2008 and 2009 that the company almost defaulted on its debt. The owner of the company wants to change the cost structure of his business so that this does not happen again. He has been able to reduce fixed costs from $500,000 to $300,000 and, in doing so, reduce the Cash Flow DOL for Memphis Motors from 3.0 to 2.2 with sales Copyright © 2015 John Wiley & Sons, Inc.

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of $1,000,000 and pretax operating cash flow of $250,000. If sales declined by 20 percent from this level, how much more pretax operating cash flow would Memphis Motors have with the new cost structure than under the old?

Solution: With the old cost structure, pretax operating cash flow would decline by 3.0 × 20% = 60% to $100,000 ($250,000 × (1 – 0.6)). With the new cost structure, pretax operating cash flow would decline by 2.2 × 20% = 44% to $140,000 ($250,000 × (1 – 0.44)).

Memphis Motors would have $40,000 more pretax operating cash flow under the cost new structure.

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.17 Cash Flow DOL: For the Vinyl CD Co. in Self-Study Problem 12.3, what percentage increase in pretax operating cash flow will be driven by the additional revenue? Solution: Cash flow DOL

= 1 + (FC) / (EBIT + D&A) =1 + ($100,000) / ($90,000 + $80,000) = 1.59

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Therefore, a 10 percent additional increase in revenue should drive a 15.9 percent increase in pretax operating cash flow. LO 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

Use the following information for Problems 12.18, 12.19, and 12.20: Dandle’s Candles will be producing a new line of dripless candles in the coming years and has the choice of producing the candles in a large factory with a small number of workers or a small factory with a large number of workers. Each candle will be sold for $10. If the large factory is chosen, the cost per unit to produce each candle will be $2.50. The cost per unit will be $7.50 in the small factory. The large factory would have fixed cash costs of $2 million and a depreciation expense of $300,000 per year, while those expenses would be $500,000 and $100,000, respectively, in the small factory.

12.18 Accounting operating profit break-even: Calculate the accounting operating profit break-even point for both factory choices for Dandle’s Candles.

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For the large factory: EBIT break-even = ($2,000,000

$300,000) / ($10 – $2.50) = 306,667 units

For the small factory: EBIT break-even = ($500,000

$100,000) / ($10 – $7.50) = 240,000 units

LO 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.19. Crossover level of unit sales: Calculate the number of candles for which the accounting operating profit at Dandle's Candles is the same regardless of the factory choice.

Solution: The formula for the crossover level of units sales (CO) is:

COEBIT =

( FC + D & A) Alternative1 − ( FC + D & A) Alternative 2 Unit Contribution Alternative1 − Unit Contribution Alternative 2

$2,300, 000 − $600, 000 = 340, 000 units ($10 − $2.5) − ($10 − $7.5)

LO 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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12.20 Pretax operating cash flow break-even: Calculate the pretax operating cash flow break-even point for both factory choices for Dandle’s Candles.

Solution: The formula for the pretax operating cash flow break-even is: EBITDA Break-even = FC / (Price – Unit VC) and so the EBITDA break-even for the large factory is: EBITDA Break-even = $

/ ($10 – $2.5) = 266,667 units

and the EBITDA break-even for the small factory is: EBITDA Break-even = $

/ ($10 – $7.5) = 200,000 units

LO 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.21 Accounting and cash flow break-even: Your analysis tells you that at a projected level of sales, a project your firm is considering will be below accounting break-even but above cash flow break-even. Explain why this might still be a viable project for your firm.

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While the business may show an accounting loss, our focus should be on the cash flow gain or loss. The reason that the project will produce an accounting loss but cash flow income is that the depreciation and amortization charges do not apply to the cash flow calculations as they are noncash expenses that help to reduce the tax liability. Therefore, the project is viable if it does not show a cash flow loss. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.22 Economic break-even point: Management of March and Dine Inc. has estimated that the firm’s new TV dinner project must generate $10,200 in FCF during each of the next six years to have an NPV of $0. Management anticipates that depreciation and amortization charges will equal $3,000, capital expenditures will equal $2,000, and additions to working capital will equal $500 during each of those years. What level of EBIT corresponds to an annual FCF of $10,200 if the firm is subject to the 30 percent marginal tax rate?

Solution: From step 2 of the economic break-even point calculations described in the text, we can calculate the EBIT as follows: EBIT = (FCF – D&A + Cap Exp + Add WC)/(1 – t) EBIT = ($10,200 - $3,000 + $2,000 + $500)/(1 – 0.3) = $13,857.14 Copyright © 2015 John Wiley & Sons, Inc.

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Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.23 Economic break-even point: RoseWeiser Company Management is considering a project that will require an initial investment of $50,000 and will last for 10 years. No other capital expenditures or increases in working capital are anticipated during the life of the project. What is the annual EBIT that will make project economically viable if the cost of capital for the project is 9 percent and the firm will depreciate the investment using straight-line depreciation and a salvage value of $0? Assume that the marginal tax rate is 40 percent.

Solution: If the FCF are expected to be equal in each of the ten years, we can solve for FCF using the present value of an ordinary annuity formula: 𝟏

𝟏

$50,000 = FCF × 𝟎.𝟎𝟗 × (𝟏 − (𝟏.𝟎𝟗)𝟏𝟎 ) → FCF = $7,791.00 EBIT = (FCF – D&A + Cap Exp + Add WC)/(1 – t) EBIT = ($7,791 - $5,000 + $0 + $0)/(1 – 0.4) = $4,651.67

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IMA: Business Economics AICPA: Industry/Sector Perspective

12.24 Economic break-even point: The BowGus Archery Company management estimates that its new Galactically Flexible Bow project will have to generate EBIT of $20,000 each year to be viable. The project’s fixed cash expenses are expected to equal $8,000 and its depreciation and amortization expenses are expected to be $5,000 each year. If the Galactically Flexible bows are expected to sell for $150 each and the variable cost to produce each bow is expected to be $100, then how many of these bows must the firm produce and sell each year to generate annual EBIT of $20,000?

Solution

Using step 3 of the economic break-even point calculations described in the text, we can compute what the total contribution for the project must be:

Revenue – VC = EBIT + D&A + FC

= $20,000 + $5,000 + $8,000 = $33,000.

From step 4, we know that we can divide this value by the contribution margin per unit to obtain the required number of units:

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Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.25 Sensitivity and scenario analyses: Sensitivity analysis and scenario analysis are somewhat similar. Describe which is a more realistic method of analyzing the impact of different scenarios on a project. Solution: Sensitivity analysis captures the effect of a change in a single item such as unit selling price or a change in the number of units sold on a specific item such as EBIT. However, it is unlikely that a change in the selling price of an item will not affect the demand, and consequently the number of units sold, for the product in question. Scenario analysis analyzes the multiple effects of a scenario on an item such as EBIT by changing a number of interrelated variables at the same time to measure the effect of an entire scenario change. Therefore, scenario analysis is a much more practical tool for stresstesting a project. LO 5 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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12.26 Sensitivity analysis: Describe the circumstances under which sensitivity analysis might be a reasonable basis for determining changes to a firm’s EBIT or FCF.

Solution: Since sensitivity analysis assumes independence among variables (otherwise the analysis is too superficial), then that is the time when the analysis can yield the most meaningful results. One time when that might occur is if the sales level and product price are completely unaffected by movements in the other as with an industry monopoly. In a competitive market, such an assumption could yield disastrous results if they are followed without caution. LO 5 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.27 Scenario analysis: Chip’s Home Brew Whiskey management forecasts that if the firm sells each bottle of Snake-Bite for $20, then the demand for the product will be 15,000 bottles per year, whereas sales will be 90 percent as high if the price is raised 10 percent. Chip’s variable cost per bottle is $10, and the total fixed cash cost for the year is $100,000. Depreciation and amortization charges are $20,000, and the firm has a 30 percent marginal tax rate. Management anticipates an increased working capital need of Copyright © 2015 John Wiley & Sons, Inc.

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$3,000 for the year. What will be the effect of the price increase on the firm’s FCF for the year?

Solution: If the firm increases its price to $22 per bottle, then it will sell 0.9 × 15,000 = 13,500 units next year. We can now find the effect of the change in price. Normal

Price Hike

Revenue

$300,000

$297,000 ($22 per bottle × 13,500)

Less: VC

150,000

135,000 ($10 per bottle × 13,500)

Less: FC

100,000

EBITDA

$ 50,000

$ 62,000

Less: D&A

20,000

$ 30,000

$ 42,000

9,000

12,600

NOPAT

$ 21,000

$ 29,400

Add: D&A

20,000

CF Operations

$ 41,000

$ 49,400

Less: Add WC

3,000

$ 38,000

$ 46,400

EBIT Less: Tax (30%)

FCF

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IMA: Business Economics AICPA: Industry/Sector Perspective

12.28 Sensitivity, scenario, and simulation analysis: If you were interested in calculating the probability that your project will have a positive FCF, what type of risk analysis tool will you most likely use?

Solution: Sensitivity analysis can only manage a single movement in a modeled variable and can therefore only show the net impact of that movement. Scenario analysis is much more flexible and can quantify the impact of moving many interdependent variables at once, but it cannot produce confidence intervals for a given level of FCF. Simulation analysis begins with a distribution for the range of possible values for each variable. All of these modeled variables are then “freed up” to randomly move, all at the same time, within the modeled range in order to produce an individual observation. If this process is repeated a large number of times, then a distribution of observations is generated for the FCF value (or EBIT or a whole host of other calculations) in order to be able to make statistical inferences about the probability of achieving a given level of FCF.

LO 5

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AICPA: Industry/Sector Perspective

ADVANCED 12.29 Mick’s Soft Lemonade is starting to develop a new product for which the cash fixed costs are expected to be $80,000. The projected EBIT is $100,000, and the Accounting DOL is expected to be 2.0. What is the Cash Flow DOL for the firm?

Solution: Accounting DOL = 1 + (FC + D&A) / (EBIT) = 1 + ($80,000 + D&A) / $100,000 = 2 => D&A = $20,000 Cash flow DOL = 1 + (FC) / (EBIT + D&A) = 1 + ($80,000) / ($100,000 + $20,000) = 1.67 LO 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.30 If a firm has a fixed asset base, meaning that its depreciation and amortization for any year is positive, discuss the relation between its Accounting DOL and its Cash flow DOL. Copyright © 2015 John Wiley & Sons, Inc.

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Solution: By comparing the equations for the Accounting DOL and Cash Flow DOL: Accounting DOL = 1 + (FC + D&A) / (EBIT) Cash flow DOL = 1 + (FC) / (EBIT + D&A) We find that the denominator of the Cash Flow DOL will always be greater than the denominator of the Accounting DOL if depreciation and amortization is greater than zero. In addition, the numerator of the Cash Flow DOL will always be less than the denominator of the Accounting DOL if depreciation and amortization is greater than zero. Therefore, if depreciation and amortization is positive, then Cash Flow DOL must be less than Accounting DOL. LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.31 Silver Polygon, Inc., has determined that if its revenues were to increase by 10 percent, then EBIT would increase by 25 percent to $100,000. The fixed costs (cash only) for the firm are $100,000. Given the same 10 percent increase in revenues, what would be the corresponding change in EBITDA?

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Solution: Since a 10 percent increase in revenue will drive a 25 percent corresponding increase in EBIT, then we know that Accounting DOL = 2.5. The new EBIT would be $100,000, after the 25 percent increase, so the original EBIT was$ 100,000 / (1 + 0.25) = $80,000. Therefore, Accounting DOL = 1 + (FC + D&A) / (EBIT) = 2.5 = 1 + ($100,000 + D&A) / ($80,000) = 2.5 ==> D&A = $20,000 Cash Flow DOL = 1 + (FC) / (EBIT + D&A) = = 1 + ($100,000) / ($80,000 + $20,000) = 2.0 A 10 percent increase in revenue will drive a 20 percent increase in EBITDA. LO 2 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.32 If a firm’s costs (both variable as well as fixed) are known with certainty, then what are the only two sources of volatility for the firm’s operating profits or its operating cash flows?

Solution: If the cost structure is known, then costs will only vary according to the firm’s unit sales. Therefore, one source of volatility would be net revenue uncertainty. The second source Copyright © 2015 John Wiley & Sons, Inc.

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of volatility is based on the mix of variable and fixed costs within the firm’s cost structure. A higher mix of fixed costs would increase the operating leverage for a firm (both accounting and cash flow) and therefore increase the accounting profit and cash flow volatility for the firm. LO 1 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.33 In most circumstances, given the choice between a higher fixed cost structure and a lower fixed cost structure, which of the two would generate a larger contribution margin?

Solution: The firm with the higher fixed cost should have a lower variable cost per unit, assuming that there is a trade-off. A lower variable cost per unit would then create a higher contribution margin for that firm. LO 1 Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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12.34 Using the same logic as with the accounting break-even calculation in Problem 12.19, adapt the formula for crossover level of unit sales to find the number of units sold where the pretax operating cash flow is the same whether the firm chooses the large or small factory.

Solution:

The formula for the cross-over level of unit sales, based on accounting EBIT, is as follows:

COEBIT=

( FC+D&A )Alternative1 - ( FC+D&A )Alternative2 Unit Contribution Alternative1 - Unit Contribution Alternative2

Eliminating D&A, since D&A are non-cash charges, gives us COEBITDA =

COEBITDA =

( FC )Alternative1 - ( FC )Alternative2 Unit Contribution Alternative1 - Unit Contribution Alternative2 $2,000,000 -$500,000 $1,500, 000 = = 300, 000 ($10 -$2.5) - ($10 − $7.5) $7.5 − $2.5

LO 3 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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12.35 You are the project manager for Eagle Golf Corporation. You are considering manufacturing a new golf wedge with a unique groove design. You have put together the estimates in the following table about the potential demand for the new club, and the associated selling and manufacturing prices. You expect to sell the club for five years. The equipment required for the manufacturing process can be depreciated using straight line depreciation over five years and will have a zero salvage value at the end of the project’s life. No additional capital expenditures are required. No new working capital is needed for the project. The required return for projects of this type is 12 percent and the company has a 35 percent marginal tax rate. You estimate that there is a 50 percent chance the project will achieve the expected sales and a 25 percent chance of achieving either the weak or strong sales outcomes. Should you recommend the project?

Strong Sales

Expected Sales

Weak Sales

Units sold

15,000

10,000

7,000

Selling price per unit

$130

$120

$110

Variable costs per unit

$70

$65

$60

Fixed Costs

$1,290,000

Initial Investment

$1,400,000

Solution (Excel Model with Solution in Separate File): Expected unit sales = (0.25 × 15,000) + (0.50 × 10,000) + (0.25 × 7,000) = 10,500 units Expected unit price = (0.25 × $130) + (0.50 × $120) + (0.25 × $110) = $120 Expected unit variable cost = (0.25 × $70) + (0.50 × $65) + (0.25 × $60) = $65 Based on the expect values outlined below, the NPV of the project is -$279,365.20 so it should not be accepted. Copyright © 2015 John Wiley & Sons, Inc.

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12%

Opportunity cost of capital Expected unti sales

10,500

Expected unit price

$120 $65

Expected unti variable cost Initial investment

$1,400,000

D&A

$280,000 5

$1,260,000

- VC

(682,500)

($682,500)

- FC

($258,000)

EBITDA

$319,500

- D&A

($280,000)

$250,000

Fixed costs

Revenue

EBIT

$39,500

- Taxes (35%)

($13,825)

$25,675

280,000 $

280,000

$305,675

$305,675 $0

NOPAT $

+ D&A CF Opns - Cap Exp.

($1,400,000)

- Add. WC

FCF

($1,400,000)

$305,675

NPV @ k = 12%

($298,110.03)

LO 5 Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.36 Economic break-even point: Commodore Motors management is considering a project to produce toy cars. The project would require an initial outlay of $100,000 and have an expected life of 10 years. Management estimates that each year during the life of the project depreciation and amortization would be $8,000, capital expenditures would be $4,000, additions to working capital would be $2,000, and fixed costs would be $3,000. Also, each toy car would sell for $15 and cost $7 to produce. Finally, the cost of capital for the project would be 12 percent, cash flows from the project would be taxed at a 25 percent rate, and the assets would be depreciated to a salvage value of $0. How many units must be sold each year in order for this project to break-even from an economic standpoint?

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Step one: The required annual FCF is: 1

$100,000 = FCF × 0.12 × (1 − (1.12)10) → FCF = $17,698.42 Step two: The required EBIT is: EBIT = (FCF – D&A + Cap Exp + Add WC)/(1 – t) EBIT = ($17,698.42 - $8,000 + $4,000 + $2,000)/(1 – 0.25) = $20,931.23 Step three: The required contribution is: Revenue – VC = EBIT + D&A + FC = $20,931.22 + $8,000 + $3,000 = $31,931.23 Step four: Economic break-even level of unit sales is: = $31,931.22/($15 – 7) = 3,991.4, or 3,992 cars Bloomcode: Analysis AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

CFA PROBLEMS

12.37. Operating leverage is a measure of the: a.

Sensitivity of net earnings to changes in operating earnings.

Sensitivity of net earnings to changes in sales.

Sensitivity of fixed operating costs to changes in variable costs.

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Sensitivity of earnings before interest and taxes to changes in the number of units produced and sold.

Solution: d is correct. Operating leverage is the sensitivity of earnings before interest and taxes to changes in the number of units produced and sold. The degree of operating leverage is the elasticity of operating earnings with respect to the number of units produced and sold. LO 2 Bloomcode: Knowledge AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.38. The Fulcrum Company produces decorative swivel platforms for home televisions. If Fulcrum produces 40 million units, it estimates that it can sell them for $100 each. The variable production costs are $65 per unit, whereas the fixed production costs are $1.05 billion. Which of the following statements is true? a.

The Fulcrum Company produces a positive operating income if it produces and sells more than 25 million swivel platforms.

The Fulcrum Company’s degree of operating leverage is 1.333.

If the Fulcrum Company increases production and sales by 5 percent, its operating earnings are expected to increase by 20 percent.

Increasing the fixed production costs by 10 percent will result in a lower sensitivity of operating earnings to changes in units produced and sold.

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Solution:

c is correct. DOL =

40 million($100 − $65)  40 million($100 − $65)  − $1.05 billion

$1.400 billion $1.400 billion − $1.05 billion $1.4 = $0.35 =4

Operating breakeven =

$1.05 billion = 30 million units $35

Fulcrum produces positive operating income if it produces more than 30 million units. If it produces and sells fewer than 30 million, it will generate a loss. The DOL is 4. If unit sales increase by 5 percent, Fulcrum’s operating earnings are expected to increase by 4 × 5% = 20%. Increasing fixed production costs will increase the sensitivity of Fulcrum’s operating earnings to changes in sales. LO 1 Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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Sample Test Problems 12.1. Retro Inc. sells vintage football jerseys for $72 each. Variable costs are $58 per unit and total fixed costs (including depreciation and amortization expense) are $84,000 per year. If sales for next year are expected to equal 8,000 jerseys, how much can variable costs per unit increase without EBIT becoming negative? (LO 1) Solution: The values in the problem statement indicate that the expected EBIT for Retro Inc. next year is: Revenue

$72 × 8,000 =

$576,000

$58 × 8,000 =

464,000

FC + D&A

84,000

EBIT

$28,000

Therefore, total variable cost could increase by $28,000 without EBIT becoming negative. If the firm sells 8,000 jerseys, then the variable cost per unit could increase by as much as $3.50 ($28,000/8,000 units = $3.50 per unit). Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.2

How would a capital intensive company fare during good and poor economic times as compared with other companies? Explain. (LO 1) Solution: A capital intensive company has a higher proportion of fixed costs and therefore higher operating leverage than less capital intensive companies. High operating leverage causes the pretax operating cash flows and accounting profits to be more sensitive to changes in revenues. As a result, during good economic times these cash flows and profits will increase more and during poor economic times periods they will fall more than the corresponding measures at companies that have less operating leverage.

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Bloomcode: Comprehension AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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The manager of Roy’s Restaurant has determined that if revenues were to increase by 20 percent, then EBIT would increase by 45 percent to $87,000. What would be the corresponding change in EBITDA if revenues increased 20 percent and cash fixed costs are $35,000? (LO 2) Solution: If a 20 percent increase in revenue causes a 45 percent increase in EBIT, Accounting DOL must equal 2.25. Also, since EBIT would be $87,000 after the 45 percent increase, the original EBIT was $87,000/(1 + 0.45) = $60,000. Therefore: Accounting DOL = 2.25 = 1 + (FC + D&A)/EBIT = 2.25 = 1 + ($35,000 + D&A)/$60,000 => D&A = $40,000 Cash Flow DOL = 1 + FC/(EBIT + D&A) = 1 + $35,000/($60,000 + $40,000) = 1.35

Which tells us that a 20 percent increase in revenues will result in a 27 percent (20 percent × 1.35 = 27 percent) increase in EBITDA. Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

12.4

Luminosity Inc. produces modern light fixtures that sell for $150 per unit. The firm’s management is considering purchasing a high-capacity manufacturing machine. If the high-capacity machine is purchased, then the firm’s annual cash fixed costs will be $60,000 per year, variable costs will be $55 per unit, and annual depreciation and amortization expenses will equal $30,000. If the machine is not purchased, annual cash fixed costs will be $25,000, variable costs will be $105 per unit, and annual depreciation and amortization expenses will equal $10,000. What is the minimum level of unit sales necessary in order for EBIT with the high-capacity machine will be higher than EBIT without that machine? (LO 3)

Solution: This question is asking for the crossover level of unit sales for EBIT, COEBIT. Using Equation 12.7 we find that:

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CO EBIT =

COEBIT =

( FC + D&A )High capacity - ( FC+D&A ) No highcapacity Unit contribution Highcapacity - Unit contribution No highcapacity

Solutions Manual

, and so

$90,000-$35,000 =1,100 units ($150-$55) -($150-$105)

Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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Paper Christmas Trees Inc. is considering introducing a new line of inexpensive Christmas trees. The initial outlay for the project is $175,000, and the company will have to invest $5,000 in working capital and $10,000 in fixed assets each year during the six year life of the project. The initial outlay will be depreciated assuming a salvage value of $0. Annual depreciation and amortization charges for the project will be $15,000 and cash-related fixed costs will be $6,000 per year. The firm will sell each tree for $75, and the variable cost to produce each tree will be $40. Calculate the number of trees that the firm must produce and sell in order to break even economically. Assume that the appropriate cost of capital for the project is 15 percent and that the marginal tax rate for the firm is 40 percent. (LO 4) Solution: Step one: The required annual FCF is:

$175,000 = FCF 

1  1   1  FCF = $46,241.46 0.15  (1.15)6 

Step two: The corresponding EBIT is: EBIT = (FCF – D&A + Cap Exp + Add WC)/(1 - t) EBIT = ($46,241.46 – $15,000 + $10,000 + $5,000)/(1 - 0.4) = $77,069.10

Step three: Therefore, the total contribution is: Revenue - VC = EBIT + D&A + FC = $77,069.10 + $5,000 + $6,000 = $88,069.10

Step four: Finally, the economic break-even level of sales is: $88,069.10 / ($75 – $40) = 2,516.26 or 2,516 trees.

Bloomcode: Application AASCB: Analytic IMA: Business Economics AICPA: Industry/Sector Perspective

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Chapter 13 The Cost of Capital Before You Go On Questions and Answers Section 13.1 1. Why does the market value of the claims on the assets of a firm equal the market value of the assets? The investors who own the debt and equity claims on the assets of a firm have the right to receive all of the after-tax cash flows that the assets of the firm produce. Since the market value of the assets equals the present value of the cash flows the assets produce, the market value of the assets must equal the value of the claims on those assets. 2. How is the WACC for a firm calculated? The WACC is calculated as the weighted average of the different types of claims on the firm’s assets. The weights in this calculation are the fractions of the total value of the financing that is represented by each individual type of financing. Equation 11.2 is the general form of the WACC calculation. n

k firm =  xi ki = x1k1 + x2 k2 + x3k3 + ... + xn kn i =1

3. What does the WACC for a firm tell us? The WACC tells us the average cost of the money that has been used to finance the firm.

Section 13.2 1. Why do analysts care about the current cost of long-term debt when estimating a firm’s cost of capital? Managers care about the current cost of long-term debt because the opportunity cost of capital that is relevant when discounting future cash flows is the opportunity cost of capital as of today. Managers focus on long-term debt because firms generally use it to finance their long-term assets, and it is the long-term assets that they are concerned about when they think about the value of a firm’s assets. 2. How do you estimate the cost of debt for a firm with more than one type of debt?

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When a firm has more than one type of debt, its overall cost of debt is estimated as a weighted average of the costs of each type of debt. The weights in this calculation are the fractions of the total value of the debt represented by each individual type of debt. 3. How do taxes affect the cost of debt? In the United States, the ability of firms to deduct interest payments when they compute their taxes actually reduces the cost of using debt. The after-tax cost of debt equals the pretax cost of debt times one minus the firm’s marginal tax rate. Section 13.3 1. What information is needed to use the CAPM to estimate kcs or kps? In order to use the CAPM to estimate kcs or kps, you need to know the risk-free rate, the market risk premium, and the beta for the stock. 2. Under what circumstances can you use the constant-growth dividend formula to estimate kcs? The constant-growth dividend formula can be used to estimate kcs if you can observe the current market price of the common stock and you can estimate the dividend that stockholders will receive next period, D1, and the rate at which the market expects dividends to grow over the long run, g. Of course, it only makes sense to use this model if dividends are expected to grow at a constant rate for the foreseeable future and this growth rate is not greater than the long-term growth rate of the economy. 3. What is the advantage of using a multistage-growth dividend model, rather than the constantgrowth dividend model, to estimate kcs? A multistage model allows dividends to grow at different rates over time, while the constantgrowth model allows for only a single growth rate in perpetuity. Section 13.4 1. Do analysts use book values or market values to calculate the weights when they use Equation 11.7? Why? Analysts use market values because this is what the theory underlying the calculation says they should use. Book values are relevant only if they just happen to equal the market values. 2. What kinds of errors can be made when the WACC for a firm is used as the discount rate for evaluating all projects in the firm?

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Using the WACC to discount cash flows for projects that are less risky than the firm can result in managers rejecting positive-NPV projects. Using the WACC to discount cash flows for projects that are more risky than the firm can result in managers accepting negative-NPV projects. 3. Under what conditions is the WACC the appropriate discount rate for a project? The WACC is the appropriate discount rate for a project when the project has the same level of systematic risk as the firm and when the project will be financed with the same proportion of debt, preferred shares, and common shares that have been used to finance the assets of the firm.

Self-Study Problems 13.1 The market value of a firm’s assets is $3 billion. If the market value of the firm’s liabilities is $2 billion, what is the market value of the stockholders’ investment and why? Solution: Since the identity that Assets = Liabilities + Equity holds for market values as well as book values, we know that the market value of the firm’s equity is $3 billion—$2 billion, or $1 billion.

13.2 Berron Comics, Inc., has borrowed $100 million and is required to pay its lenders $8 million in interest this year. If Berron is in the 35 percent marginal tax bracket, then what is the after-tax cost of debt (in dollars as well as in annual interest) to Berron. Solution: Because Berron enjoys a tax deduction for its interest charges, the after-tax interest expense for Berron is $8 million × (1 – 0.35) = $5.2 million, which translates into an annual interest expense of $5.2/$100 = 0.052, or 5.2 percent.

13.3 Explain why the after-tax cost of equity (common or preferred) does not have to be adjusted by the marginal income tax rate for the firm. Solution:

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The U.S. tax code allows a deduction for interest expense incurred on borrowing. Preferred and common shares are not considered debt and, thus, do not benefit from an interest deduction. As a result, there is no distinction between the before-tax and after-tax cost of equity capital.

13.4 Mike’s T-Shirts, Inc., has debt claims of $400 (market value) and equity claims of $600 (market value). If the after-tax cost of debt financing is 11 percent and the cost of equity is 17 percent, then what is Mike’s weighted average cost of capital? Solution: Mike’s T-Shirts’ total firm value = $400 + $600 = $1,000. Therefore, Debt = 40 percent of financing Equity = 60 percent of financing WACC = xDebtkDebt(1-t) + xpskps + xcskcs WACC = (0.4 × 0.11) + (0.6 × 0.17) = 0.146, or 14.6%

13.5 You are analyzing a firm that is financed with 60 percent debt and 40 percent equity. The current cost of debt financing is 10 percent, but due to a recent downgrade by the rating agencies, the firm’s cost of debt is expected to increase to 12 percent immediately. How will this change the firm’s weighted average cost of capital if you ignore taxes? Solution: The pretax debt contribution to the cost of capital is xDebt × kDebt, and since the firm’s pretax cost of debt is expected to increase by 2 percent, we know that the effect on WACC (pretax) will be 0.6 × 0.02 = 0.012, or 1.2 percent. Incidentally, if we assume that the firm is subject to the 40 percent marginal tax rate, then the after-tax contribution to the cost of capital for the firm would be 0.012 × (1 – 0.4) = 0.0072, or 0.72 percent.

Discussion Questions 13.1

Explain why the required rate of return on a firm’s assets must be equal to the weighted average cost of capital associated with its liabilities and equity.

Solution: In order to conceptualize the answer to this question, it helps to think of the case in which the firm has raised all of its capital needs from a single source who owns all of the liability and all of the equity claims on the firm. Assume that this source has no other

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investments. If we were to measure the rate of return on the combined portfolio of investments for this source, we would find that it is exactly equal to the return on the total assets of the firm since that is the ultimate source of the returns. The weighted return of that portfolio, which is the weighted average cost of capital for the firm (if for the time being we abstract away tax effects), is the return on the assets of the firm. LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.2

Which is easier to calculate directly, the expected rate of return on the assets of a firm or the expected rate of return on the firm’s debt and equity? Assume that you are an outsider to the firm.

Solution: As an outsider to the firm, you will not be privy to the complete information about the projected cash flows of each of the firm’s assets, and so that is a somewhat difficult proposition. However, the collective market has made an inference concerning the expected cash flows of each of the financing claims of the firm, and by pricing those cash flows has given us an expected return for each of those claims. Therefore, finding the expected return on the debt and equity claims of the firm is much easier than finding the expected return on the assets of the firm, although that return can then be calculated from the expected return on the financing claims of the firm. LO: 1 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.3

With respect to the level of risk and the required return for a firm’s portfolio of projects, discuss how the market and a firm’s management can have inconsistent information and expectations.

Solution:

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Firm management will be fully informed concerning the firm’s project risks, but their ability to accurately predict the required return for the firm’s projects depends on the market’s assessment of those project risks. Alternatively, the collective market is not fully informed (as outsiders) concerning the firm’s project risks and yet uses its incomplete information set to dictate a required return for the firm’s projects. This suggests that if the firm were able to better inform the market, and thereby reduce the market’s perceived risk on the firm’s projects, then the firm might be able to reduce the required rate of return on the firm’s projects. LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.4

Your friend has recently told you that the federal government effectively subsidizes the use of debt financing (vs. equity financing) for corporations. Do you agree with that statement? Explain.

Solution: Your friend is correct. Because interest expense on debt is tax deductible, whereas dividend payments on equity are not, the firm effectively gets a rebate on interest paid through a lowered tax bill. Two firms with identical EBIT amounts with different interest expenses will have different cash flow available to its collective set of investors. The firm with greater interest expense (assuming it is less than the EBIT amount) will have greater cash flow available to all of its investors. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.5

Your firm will have a fixed interest expense for the next 10 years. You recently found out that the marginal income tax rate for the firm will change from 30 percent to 40 percent next year. Describe how the change will affect the cash flow available to investors.

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Solution: Let’s compare our firm to the firm with no interest expense. In order to make a concrete example, assume that our firm has interest expense of $100 per year. Since the after-tax cost of debt for the firm is equal to kDebt pretax × (1 – t), then we can calculate the tax benefit to using debt to be kDebt pretax × t. In order to calculate that benefit in dollar terms, we would just multiply (interest expense) × t. Therefore, the current dollar benefit to the interest expense is $100 × 0.3 = $30. Next year, the dollar benefit is $100 × 0.4 = $40. The net benefit of interest expense from the increased marginal corporate tax rate is $10, and that is a positive benefit. Note that the analysis isolates the effect on debt and does not consider the lower operating earnings figure caused by the increased tax rate. Overall, the increase in tax rate will result in less cash flows available to investors, but for the leveraged (debt holding) firm the reduction in cash flow is mitigated by the benefit from being able to deduct interest expenses. LO: 2 Level: Intermediate Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.6

Describe why it is not usually appropriate to use the coupon rate on a firm’s bonds to estimate the pretax cost of debt for the firm.

Solution: The pretax cost of debt for the firm is the current annual economic cost of borrowing for the firm (before any tax effects). That cost is better measured by the current yield to maturity on the firm’s debt than by the coupon rate that is currently paid on that debt. Since most firms try to issue new bonds very close to par, the coupon rate on a bond is an indication of the yield to maturity on the bond issue at the time of issue. Unless the market-determined borrowing rate for the firm is the same as when the bond was issued, then the current yield to maturity of a bond will not be equal to the current coupon rate on the bond. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Maltese Falcone, Inc., has not checked its weighted average cost of capital for four years. Firm management claims that since Maltese has not had to raise capital for new projects in four years, they should not have to worry about their current weighted average cost of capital. They argue that they have essentially locked in their cost of capital. Critique management’s statements.

Solution: That is a false statement. Maltese is assuming that since it does not have to raise capital for new projects, then it has essentially locked in its cost of capital. However, in a liquid capital market every firm competes for capital every day since the firm’s investors have the opportunity to sell their investments to other investors. If a firm does not provide investors with an ample return, then the investors will sell their investments in the firm, which, in aggregate, will have the effect of actually raising the cost of capital for the firm (since the current price of the securities will move down). Therefore, a firm that ignores its current cost of capital by thinking that it has locked in a cost of capital might even be raising its cost of capital by making that incorrect assumption. LO: 1 Level: Intermediate Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.8

Ten years ago, the Edson Water Company issued preferred stock at a price equal to the par value of $100. If the dividend yield on that issue was 12 percent, explain why the firm’s current cost of preferred capital is not likely to equal 12 percent.

Solution: Since the price of the preferred shares at issue was $100 and the dividend yield was 12 percent, then we know that the annual dividend on the shares is $12. We also then know that the required rate of return at the time of issue was 12 percent. If during the last 10 years, the required rate of return on Edson’s preferred shares has changed at all, the current required rate of return will not be 12 percent. This will, in turn, change the price of the shares to some amount other than $100. LO: 3 Level: Intermediate Bloomcode: Appllication

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13.9

Discuss under what circumstances you might be able to use a model that assumes constant growth in dividends to calculate the current cost of equity capital for a firm.

Solution: In order to be completely correct, a firm must grow its dividends at a constant rate into the indefinite future. If one expects the growth in dividends to change in the future, then using a constant-growth dividend assumption is incorrect and only an estimation. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.10 Your boss just finished computing your firm’s weighted average cost of capital. He is relieved because he says that he can now use that cost of capital to evaluate all projects that the firm is considering for the next four years. Evaluate that statement. Solution: Your boss is incorrect. A firm is always subject to revisions to its cost of capital due to current market and firm conditions. In addition, the firm could also be making an error by using the same cost of capital for all of its future projects. For that particular error to not be made, two conditions must be met. That is, future projects must be financed with the same mix of capital (debt, preferred shares, and common shares) with which the entire firm is currently financed. In addition, the future projects must contain the same level of systematic risk as that of the average project that the firm is currently operating. LO: 4 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Questions and Problems BASIC 13.1

Finance balance sheet: KneeMan Markup Company has total debt obligations with book and market values equal to $30 million and $28 million, respectively. It also has total equity with book and market values equal to $20 million and $70 million, respectively. If you were going to buy all of the assets of KneeMan Markup today, how much should you be willing to pay?

Solution: The price you should be willing to pay for all of the assets of the firm is the market value of those assets. Using the market price version of the balance sheet identity, we can add the market price of the debt obligations and the equity to find the market price of the assets. That is, $28 million + $70 million = $98 million. LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.2

WACC: What is the weighted average cost of capital for a firm?

Solution: The weighted average cost of capital (WACC) is the weighted average of the costs to the different sources of capital used to fund a firm that is the cost of each type of capital is weighted by the proportion of the total capital that it represents. The WACC is often used as an estimate of the cost of financing a new project given the firm’s current mix of debt and equity. LO 1 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.3

Taxes and the cost of debt: How are taxes accounted for when we calculate the cost of debt?

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Solution: When we calculate the cost of debt for a U.S. firm, we must take into account the tax subsidy given in the United States for interest payments on debt. For every dollar the firm pays in interest, the firm’s tax bill will decline by ($1 * t), where t is the firm’s marginal tax rate. We adjust for this tax benefit by multiplying the pretax cost of debt by (1 - t). This calculation gives us the after-tax cost of debt. We use the after-tax cost of debt for cost of capital calculations such as when we calculate the WACC. LO 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.4

Cost of common stock: List and describe each of the three methods used to calculate the cost of common stock.

Solution: 1) The Capital Asset Pricing Model (CAPM) formula for the cost of common stock, given in Equation 13.4 (kcs = Rrf + (βcs × Market risk premium), can be used to calculate the return investors will demand on investment in the company’s common stock. Read Chapter 7 for further discussion of the CAPM. 2) The constant-growth dividend model can be used to calculate the cost of equity implied by the firm’s current stock price. In an efficient market, the current price of the company’s stock should reflect the cash flows (dividends) that investors will receive in the future from holding equity in the firm, discounted by an appropriate rate (the cost of equity). By knowing the current dividend paid by the firm and the expected growth rate of dividends, we can use Equation 13.5 [(kcs = D1 / P0) + g] to compute the cost of capital that is implied in the firm’s current stock price. The constant-growth dividend model is only appropriate when there is a reasonable expectation that the firm’s dividend will continue growing at approximately the same rate forever. For example, it might be used to calculate the cost of equity for a mature company whose growth rate is similar to that of the economy. 3) The multistage-growth dividend model is very similar to the constant-growth dividend model, but the multistage-growth dividend model can be applied in situations when the growth rate is expected to change in the near term followed by a constant long term growth rate—for example, a small, fast growing company whose growth will certainly slow as the company becomes larger. See Section 13.3 for discussion of the calculation of cost of equity using the multistage-growth dividend model. Copyright © 2015 John Wiley & Sons, Inc.

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LO 3 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.5

Cost of common stock: Whitewall Tire Co. just paid an annual dividend of $1.60 on its common shares. If Whitewall is expected to increase its annual dividend by 2 percent per year into the foreseeable future and the current price of Whitewall’s common shares is $11.66, what is the cost of common stock for Whitewall?

Solution: The cost of common equity for Whitewall can be found using the constant-growth assumption equation: D1 D ×(1+ g ) $1.60×(1+ 0.02) Pcs = = 0 = = $11.66 kcs - g kcs - g kcs - 0.02 Solving for kcs, we find it is equal to 0.16 or 16 percent. LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.6

Cost of common stock: Seerex Wok Co. is expected to pay a dividend of $1.10 one year from today on its common shares. That dividend is expected to increase by 5 percent every year thereafter. If the price of Seerex common stock is $13.75, what is the cost of its common equity capital?

Solution: We can use the formula to find the cost of common equity assuming constant growth. D $1.10 kcs = 1 + g = + 0.05 = 0.13, or 13% Pcs $13.75 LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Cost of common stock: Two-Stage Rocket paid an annual dividend of $1.25 yesterday, and it is commonly known that the firm’s management expects to increase its dividend by 8 percent for the next two years and by 2 percent thereafter. If the current price of TwoStage’s common stock is $17.80, what is the cost of common equity capital for the firm?

Solution:

Pcs =

D0(1 + g1 ) D0(1 + g1 ) 2 D0(1 + g1 ) 2 (1 + g 2 ) + + 2 2 1 + kcs (1 + kcs ) ( kcs − g2 )(1 + kcs )

$17.80 =

$1.25  (1 + 0.08) $1.25  (1 + 0.08)2 $1.25  (1 + 0.08)2  (1 + 0.02) , + + 2 2 1 + kcs (1 + kcs ) ( kcs − 0.02)(1 + kcs )

Using a spreadsheet to solve for the value of kcs, we find that the cost of common equity capital is 10 percent. LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.8

Cost of preferred stock: Fjord Luxury Liners has preferred shares outstanding that pay an annual dividend equal to $15 per year. If the current price of Fjord preferred shares is $107.14, what is the after-tax cost of preferred stock for Fjord?

Solution: Using the equation for finding the cost of preferred equity, we have

kps =

Dps $15 = = 0.14, or 14% Pps $107.14

LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.9

Cost of preferred stock: Kresler Autos has preferred shares outstanding that pay annual dividends of $12, and the current price of the shares is $80. What is the after-tax cost of new preferred shares for Kresler if the flotation (issuance) costs for preferred shares are 5 percent?

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Solution: Kresler will only receive 95 percent of the proceeds, so we know that we can use the equation to solve for the cost of preferred equity by adjusting the denominator for the reduced proceeds from the sale of new equity. We then have:

k ps =

Dps $12 $12 = = = 0.158, or 15.8% Pps (1- F) $80(1 − 0.05) $76

LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.10 WACC: Describe the alternatives to using a firm’s WACC as a discount rate when evaluating a project. Solution: There are two major reasons why WACC may not be used to discount new projects: 1. It is not appropriate to use a firm’s WACC to discount a project’s free cash flows if the systematic risk of the project is very different from the systematic risk of the firm. To account for this potential problem, some firms estimate discount rates that directly reflect the risk involved in the project’s cash flows. For example, a risky project might be assigned a discount rate that is significantly higher than the firm’s WACC. 2. It is not appropriate to use a firm’s WACC when a project that has the same systematic risk as the firm is not being financed using the same mix of debt and equity as the firm— for example, if a project will be financed entirely with equity. The project’s cash flows should be discounted using the cost of equity rather than the firm’s WACC. These two rates will be the same only if the firm has no debt. LO 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.11 WACC: Capital Co. has a capital structure, based on current market values, that consists of 50 percent debt, 10 percent preferred stock, and 40 percent common stock. If the returns required by investors are 8 percent, 10 percent, and 15 percent for the debt, preferred equity, and common stock, respectively, what is Capital’s after-tax WACC? Assume that the firm’s marginal tax rate is 40 percent. Copyright © 2015 John Wiley & Sons, Inc.

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Solution: WACC = xdebt k debt (1 − t ) + x ps k ps + xcs k cs = WACC = 0.5×0.08×(1-0.4) + 0.1×0.10 + 0.4×0.15= 0.094, or 9.4%

LO 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.12 WACC: What are direct out-of-pocket costs? Solution: Direct out-of-pocket costs are the actual out-of-pocket costs that a firm incurs when it raises capital. They include such things as fees paid to investment bankers and legal and accounting expenses. LO 4 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 13.13 Finance balance sheet: Explain why the total value of all of the securities used to finance a firm must be equal to the value of the firm. Solution: The value of the firm’s assets is equal to the present value of the future cash flows expected to be generated by those assets. The cash flow claim on those assets is prioritized by the financing of those assets. Therefore, the financing claims on the assets of the firm fully account for the entire value of the assets, and the value of the financing claims must equal the value of the assets that are carved up by those claims. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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13.14 Finance balance sheet: Explain why the cost of capital for a firm is equal to the expected rate of return to the investors in the firm. Solution: If we view the firm as a conduit for the cash flows provided by the assets of the firm, then it is easy to see that the cash flows provided by the assets of the firm must equal the cash flows provided to the aggregate investor group of the firm. We also know that the capital invested in the firm must equal the capital invested by the firm. Therefore, we then know that the rate of return for the investors of the firm must equal the cost of capital provided to the firm. The expected return to investors will also equal the expected cost of capital for the firm. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.15 Current cost of a bond: You know that the after-tax cost of debt capital for Bubbles Champagne Company is 7 percent. If the firm has only one issue of five-year bonds outstanding, what is the current price of the bonds if the coupon rate on those bonds is 10 percent? Assume the bonds make semiannual coupon payments and the marginal tax rate is 30 percent. Solution: We know the after-tax cost of debt, and from that we can find the pretax cost of debt by dividing by 1 minus the tax rate. This becomes 0.07 / (1 – 0.3) = 0.10 or 10%. Since the YTM on the bonds is equal to the coupon rate, then we know the bonds are priced at par, or $1,000. LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.16 Current cost of a bond: Perpetual Ltd. has issued bonds that never require the principal amount to be repaid to investors. Correspondingly, Perpetual must make interest payments into the infinite future. If the bondholders receive annual payments of $75 and the current price of the bonds is $882.35, what is the after-tax cost of this debt for Perpetual if the firm is subject to a 40 percent marginal tax rate?

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Solution: Since the bonds represent a perpetuity, we know that the pretax cost of debt can be solved using the following: Coupon Payment $75 kdebt = = = 0.085 Bond Price $882.35 And the after-tax cost is 0.085 × (1 - 0.4) = 0.051, or 5.1% LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.17 Current cost of a bond: You are analyzing the cost of debt for a firm. You know that the firm’s 14-year maturity, 8.5 percent coupon bonds are selling at a price of $823.48. The bonds pay interest semiannually. If these bonds are the only debt outstanding, what is the after-tax cost of debt for this firm if it is subject to a 30 percent marginal and average tax rate? Solution: The current YTM for the bonds can be calculated as follows. $823.48 = $42.50 × PVIFA(28, YTM/2) + $1,000 × PVIF(28, YTM/2) Solving, we find that YTM = 0.11, and therefore the after-tax cost of debt is equal to: 0.11 × (1 – 0.3) = 0.077, or 7.7% LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.18 Taxes and the cost of debt: Holding all other things constant, does a decrease in the marginal tax rate for a firm provide incentive for the managers of a firm to increase or decrease its use of debt? Solution: The after-tax cost of debt for the firm is equal kDebt pretax x (1 – t). We can then calculate the tax benefit of using debt to be kDebt pretax x t. Therefore, the value of the tax benefit to debt increases with the marginal tax rate. If the marginal tax rate decreases, then the tax

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benefit to debt decreases as well. Therefore, the incentive to borrow actually decreases with a decrease in the marginal tax rate. LO 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.19 Cost of debt for a firm: You are analyzing the after-tax cost of debt for a firm. You know that the firm’s 12-year maturity, 9.5 percent semiannual coupon bonds are selling at a price of $1,200. If these bonds are the only debt outstanding for the firm, what is the after-tax cost of debt for this firm if it has a marginal tax rate of 34 percent? What if the bonds are selling at par? Solution: The current YTM for the bonds can be calculated as follows. 1   1 − (1 + i ) n  Fn PB = C   + n i   (1 + i )  

1   1 −  (1 + i ) 24  $1, 000 $1, 200 = $47.50   + 24 i   (1 + i )   Solving, we find that YTM = 0.07008 or 7.008% and therefore the after-tax cost of debt is equal to 0.07008 × (1 – 0.34) = 0.046253, or 4.63% If the bonds are priced at par, then the YTM on the bonds is 9.5 percent and then the after-tax cost of debt would be 6.27%. LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.20 Cost of common stock: Underestimated Inc.’s common shares currently sell for $36 each. The firm’s management believes that its shares should really sell for $54 each. If the firm just paid an annual dividend of $2 per share and management expects those

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dividends to increase by 8 percent per year forever (and this is common knowledge to the market), what is the current cost of common equity for the firm and what does management believe is the correct cost of common equity for the firm? Solution: The current cost of equity for the firm is D $2.00  1.08 kcs = 1 + g = + 0.08 = 0.14, or 14% Pcs $36.00 But the firm believes that its cost of capital is more appropriately D $2.00  1.08 kcs = 1 + g = + 0.08 = 0.12, or 12% Pcs $54.00 LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.21 Cost of common stock: Write out the general equation for the price of the stock for a firm that will grow dividends very rapidly at a constant rate for the four years after the next dividend is paid and will grow dividends thereafter at a constant, but lower rate. Discuss the problems in estimating the cost of equity capital for such a stock. Solution:

Pcs =

D1 D (1 + g1 ) D1 (1 + g1 ) 2 D1 (1 + g1 ) 3 D1(1 + g1 ) 4 D1(1 + g1 ) 4 (1 + g2 ) + 1 + + + + 3 4 5 1 + k cs (1 + kcs )2 (1 + kcs )5 (1 + kcs ) (1 + kcs ) ( kcs − g2 )(1 + kcs )

It is easy to see that in order to solve for a cost of capital, kcs, you must have a good idea of what g1 and g2 are. If those growth rates are poor estimates, then the calculation for kcs, will also be a poor estimate. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.22 Cost of common stock: You have calculated the cost of common stock using all three methods described in this chapter. Unfortunately, all three methods have yielded different answers. Describe which answer (if any) is most appropriate.

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Solution: Two of the methods involve an estimate of the growth rate in dividends for the firm. If you are confident in your estimate of the growth rate, then those methods might be most appropriate. Otherwise, utilizing the CAPM, which does not involve any dividend growth rate estimates, would probably be the best. You may choose to average the results of all three methods. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.23 WACC: The managers of a firm financed entirely with common stock are evaluating two distinct projects. The first project has a large amount of unsystematic risk and a small amount of systematic risk. The second project has a small amount of unsystematic risk and a large amount of systematic risk. Which project, if taken, is more likely to increase the firm’s cost of capital? Solution: Markets adjust the cost of capital according to the level of systematic risk in a project. Therefore, the project with the greatest level of systematic risk will have the greatest positive impact on the cost of capital for the firm, even if it has the lowest level of unsystematic risk. LO 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.24 WACC: The Imaginary Products Co. currently has debt with a market value of $300 million outstanding. The debt consists of 9 percent coupon bonds (semiannual coupon payments) which have a maturity of 15 years and are currently priced at $1,440.03 per bond. The firm also has an issue of 2 million preferred shares outstanding with a market price of $12.00 per share. The preferred shares pay an annual dividend of $1.20. Imaginary also has 14 million shares of common stock outstanding with a price of $20.00 per share. The firm is expected to pay a $2.20 common dividend one year from today, and that dividend is expected to increase by 5 percent per year forever. If Imaginary is subject to a 40 percent marginal tax rate, then what is the firm’s weighted average cost of capital?

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Solution: Step 1: Total amount of debt, common equity, and preferred equity: Debt = $300,000,000 (given) Preferred equity = $12 × 2,000,000 = $24,000,000 Common equity = $20 × 14,000,000 = $280,000,000 Total capital = $604,000,000 xDebt = 300 million/604 million = 0.4967 xps = 24 million/604 million = 0.0397 xcs = 280 million/604 million= 0.4636 Step 2: Cost of capital components: Cost of debt: $1,440.03 = $45 × PVIFA (30, YTM / 2) + $1,000 × PVIF (30, YTM / 2) Solving, we find that YTM = 0.0484 (this is a pretax number). Cost of preferred equity: D $1.20 kps = = = 0.10 Pps $12.00 Cost of common equity: D $2.20 kcs = 1 + g = + 0.05 = 0.16 Pcs $20.00 Step 3: Combine using the WACC formula. WACC = xdebt k debt (1 − t ) + x ps k ps + xcs k cs =

WACC = ( 0.4967  0.0484  (1 − 0.4) ) + ( 0.0397  0.10 ) + ( 0.4636  0.16 ) = 0.0926, or 9.26% LO 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.25 Choosing a discount rate: For the Imaginary Products firm in Problem 13.24, calculate the appropriate cost of capital for a new project that is financed with the same proportion of debt, preferred shares, and common shares as the firm’s current capital structure. Also assume that the project has the same degree of systematic risk as the average project that the firm is currently undertaking (the project is also in the same general industry as the firm’s current line of business). Solution:

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Since Imaginary will be financing the project with the same mix of capital that the firm is currently utilizing for its projects, we will have met the first restriction concerning financing mix. In addition, the new project will have the same degree of systematic risk (in addition to being in the same general line of business). Therefore, Imaginary can use the 9.26 percent cost of capital to evaluate its project. LO 1 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.26 Choosing a discount rate: If a firm’s management anticipates financing a project with a capital mix that is different from its current capital structure, describe how the firm is subjecting itself to a calculation error if its historical WACC is used to evaluate the project. Solution: Since the firm is financing the project with a different capital mix than it has historically used, we know that the weights and rates for debt, preferred, and common shares in the WACC formula will be different. We know that the cost of capital for each component is a function of the individual weights and rates, and that the WACC will be different for the overall firm versus that of the individual project. Therefore, using its historical WACC can result in an error in the NPV estimate for the project. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED 13.27 You are analyzing the cost of capital for MacroSwift Corporation, which develops software operating systems for computers. The firm’s dividend growth rate has been a very constant 3 percent per year for the past 15 years. Competition for the firm’s current products is expected to develop in the next year, and MacroSwift is currently expanding its revenue stream into the multimedia industry. Evaluate the appropriateness of continuing to use a 3 percent growth rate in dividends for MacroSwift in your cost of capital model.

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Solution: While the growth in dividends has been extremely constant for Macroswift over the last 15 years, it is appropriate to assume a constant-growth rate only if that same rate will continue in the future. Two factors will act to alter that growth in the future. MacroSwift will have competition for its current product list in the near future, and that could alter the firm’s growth rate. In addition, the firm is expanding its product line into an area that will probably not yield the same level of growth. It is therefore, unlikely that MacroSwift’s dividend growth rate will continue at a 3 percent annual rate. This suggests that we should consider something other than constant growth in our modeling. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.28 You are an external financial analyst evaluating the merits of a stock. Since you are using a dividend discount model approach to evaluate a cost of equity capital, you need to estimate the dividend growth rate for the firm in the future. Describe how you might go about doing this. Solution: One source for this data would be to measure the firm’s dividend growth rate in recent history. If we could assume that such a growth in dividends will continue into the future, then our measure would be reasonable. One additional source would be to read a financial analyst’s report in which the author of the report may have a better estimate of the firm’s future prospects. LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.29 You know that the return of Momentum Cyclicals common shares is 1.6 times as sensitive to macroeconomic information as the return of the market. If the risk-free rate of return is 3.72 percent and the market risk premium is 5.71 percent, what is Momentum Cyclicals’ cost of common equity capital? Solution:

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We know that the beta for Momentum Cyclicals is 1.6, and we can use the remaining information in the CAPM as follows: 𝐸(𝑅𝐶𝑆 ) = 𝑅𝑟𝑓 + 𝛽(𝐸(𝑅𝑚 ) − 𝑅𝑟𝑓 ) = 0.0372 + 1.6(0.0.0571) = 0.12856 = 12.86% LO 3 Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.30 In your analysis of the cost of capital for a common stock, you calculate a cost of capital using a dividend discount model that is much lower than the calculation for the cost of capital using the CAPM model. Explain a possible source for the discrepancy. Solution: Comparing the two formulas for the two methods, we have: D E(R cs ) = R rf + β E(R m ) - R rf and k cs = 1 + g Pcs

(

)

Given these two sources of information, we see that the only variable that we are not able to get directly from the market is the growth rate in dividends (note that future dividends are also a function of this growth rate), which is an estimate. Since our dividend discount method provided a lower cost of capital than the CAPM, it seems likely that we estimated the growth rate lower than what the aggregate market has assumed. Of course, this assumes that the market is efficiently pricing the stock. If the market price of the stock is mispriced, then this might lead to a difference. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.31 RetRyder Hand Trucks has a preferred share issue outstanding that pays a dividend of $1.30 per year. The current cost of preferred equity for RetRyder is 9 percent. If RetRyder issues additional preferred shares that pay exactly the same dividend and the investment banker retains 8 percent of the sale price, what is the cost of new preferred shares for RetRyder? Solution: The current cost of preferred shares for RetRyder is Copyright © 2015 John Wiley & Sons, Inc.

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D $1.30 = = $14.44 kps 0.09

and then RetRyder would receive 92 percent of the proceeds. We could then adapt the cost of preferred equity to the following: D $1.30 $1.30 k ps = = = =0.0978, or 9.78% Pps (1- F) $14.44(1-0.08) $13.29 LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.32 Enigma Corporation’s management believes that the firm’s cost of capital (WACC) is too high because the firm has been too secretive with the market concerning its operations. Evaluate that statement. Solution: The WACC is a function of the perceived risk involved in the cash flows of the projects that the firm is currently operating. If the market perceives that risk to be higher than the actual risk due to a lack of information concerning those projects, then the firm might be able to lower that perceived risk by sharing more information with the market. That could have the effect of lowering the firm’s WACC. LO 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.33 Discuss what valuable information would be lost if you decided to use book values in order to calculate the cost of each of the capital components within a firm’s capital structure. Solution: Market returns are impounded in market prices. If those prices are ignored, then the efficiency of the market’s information process is essentially thrown away. Since the market adjusts securities prices according to the expected return for investing in a security, then ignoring that information is the same as ignoring what the market deems to be an appropriate cost of capital for the firm.

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LO 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.34 Hurricane Corporation is financed with debt, preferred equity, and common equity with market values of $20 million, $10 million, and $30 million, respectively. The betas for the debt, preferred stock, and common stock are 0.2, 0.5, and 1.1, respectively. If the riskfree rate is 3.72 percent, the market risk premium is 5.71 percent, and Hurricane’s average and marginal tax rates are both 30 percent, what is the company’s weighted average cost of capital? Solution: The fractions of the total financing represented by debt, common equity, and preferred equity are: Debt = $20 million Preferred equity = $10 million Common equity = $30 million Total capital = $60 million xdebt = $20/$60 = 0.3333 xps = $10/$60 = 0.1667 xcs = $30/$60 = 0.5000 The costs of debt, common equity, and preferred equity are: E(RDebt) = Returnrf + βDebt (E(ReturnM) – Returnrf) = 0.0372 + (0.2 × 0.0571) = 0.04862, or 4.862% E(Rps) = Returnrf + βps (E(ReturnM) – Returnrf) = 0.0372+ (0.5 × 0.0571) = 0.06575, or 6.575% E(Rcs) = Returnrf + βcs (E(ReturnM) – Returnrf) = 0.0372+ (1.1 × 0.0571) = 0.10001 or 10.001% WACC = (0.3333 x 0.04862 x (1-0.3)) + (0.1667 x0.06575) + (0.5 x 0.10001) = 0.072308, or 7.2308% LO 4 Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

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13.35 You are working as an intern at Coral Gables Products, a privately owned manufacturing company. Shortly after you read Chapter 13 in this book, you got into a discussion with the Chief Financial Officer (CFO) at Coral Gables about weighted average cost of capital calculations. She pointed out that, just as the beta of the assets of a firm equals a weighted average of the betas for the individual assets, as shown in Equation 7.11: n

n Asset portfolio =  xi i = x11 + x2  2 + x3 3 + . . . + xn  n i =1

the beta of the assets of a firm also equals a weighted average of the betas for the debt, preferred stock, and common stock of a firm: n

 n Asset portfolio =  xi i = xDebt  Debt + xps  ps + xcs  cs i =1

Why must this be true? Solution: Since, collectively, the debt and equity holders are entitled to receive all of the cash flows that the assets of the firm are expected to produce, the systematic risk of the cash flows that they are entitled to receive must be the same as the systematic risk of the cash flows the assets are expected to produce. LO 1 Bloomcode: Analysis AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.36 The CFO described in Problem 13.35 asks you to estimate the beta for Coral Gables’s common stock. Since the common stock is not publicly traded, you do not have the data necessary to estimate the beta using regression analysis. However, you have found a company with publicly traded stock that has operations exactly like those at Coral Gables. Using stock returns for this pure-play comparable firm, you estimate the beta for the comparable company’s stock to be 1.06. The market value of that company’s common equity is $45 million, and it has one debt issue outstanding with a market value of $15 million and an annual pretax cost of 4.85 percent. The comparable company has no preferred stock. a. If the risk-free rate is 3.72 percent and the market risk premium is 5.71 percent, what is the beta of the assets of the comparable company?

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b. If the total market value of Coral Gables’s financing consists of 35 percent debt and 65 percent equity (this is what the CFO estimates the market values to be) and the pretax cost of its debt is 5.45 percent, what is the beta for Coral Gables’s common stock? Solution: You can solve this problem using the equation: n

 n Asset portfolio =  xi i = xDebt  Debt + xps  ps + xcs  cs i =1

Since neither company has preferred stock, the equation in this case has only two terms: n Asset portfolio = xDebt  Debt + xcs cs a. To calculate the beta of the assets of the comparable company, you must first estimate the beta of the comparable firm’s debt and the fractions of the total market value of the comparable firm’s financing which is represented by the debt and equity. The beta of the comparable firm’s debt can be estimated using the CAPM formula (Equation 7.10): E(Ri) = Rrf + βi[E(Rm) – Rrf] Since this formula can be used to calculate the expected return on debt, it can be written as: E(RDebt) = Rrf + βDebt[E(Rm) – Rrf] If we assume that the market is pricing the debt correctly, the pretax cost of debt equals the expected return on debt in this equation. Therefore, substituting the information from the problem statement into this equation yields: 4.85% = 3.72 % + βDebt[5.71 %] and the beta of the debt equals: βDebt = (4.85% - 3.72 %) / 5.71% = 0.198

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The fractions of the total financing represented by debt and common equity are: Debt = $15 million Common equity = $45 million Total capital = $60 million xDebt = $15/$60 = 0.25 xcs = $45/$60 = 0.75

Finally, the beta of the assets of the comparable company is: βnAsset portfolio = xDebtβDebt + xcsβcs = (0.25 x 0.198) + (0.75 x 1.06) = 0.8445

b. Since the comparable company is in exactly like Coral Gables, this is a good estimate of asset beta for Coral Gables. To calculate the beta for Coral Gables’s common equity, you use the following equation with the beta of the assets for the comparable company and the beta of debt and financing fractions for Coral Gables.

n Asset portfolio = xDebt  Debt + xcs cs The beta of the Coral Gables debt is: E(RDebt) = Rrf + βDebt[E(Rm) – Rrf] 5.45% = 3.72% + βDebt[5.71%] βDebt = (5.45% - 3.72%) / 5.71% = 0.3030 and the beta of the firm’s equity is: βn Asset portfolio = xDebtβDebt + xcsβcs 0.8445 = (0.35 x 0.3030) + (0.65 x βCS) βcs =

0.8445 − (0.35 𝑥 0.3030) 0.65

0.7384 0.65

= 1.136

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AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.37 Estimate the weighted average cost of capital for Coral Gables using your estimated beta and the information in the problem statement in Problem 13.36? Assume that the average and marginal tax rates for Coral Gables are both 25 percent. Solution: The cost of equity is: E(Rcs) = Rrf + βcs[E(Rm) – Rrf] E(Rcs) = 3.72% + (1.136 × 5.71%) = 10.21% The weighted average cost of capital is: WACC = (0.35 x 5.45% x (1-0.25)) + (0.65 x 10.21%) = 0.080651 = 8.07% LO 3, LO 4 Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

CFA Problems 13.38 The cost of equity is equal to the: a. Expected market return. b. Rate of return required by stockholders. c. Cost of retained earnings plus dividends. d. Risk the company incurs when financing. Solution: b is correct. The cost of equity is defined as the rate of return required by stockholders. LO 1 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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13.39 Dot.Com has determined that it could issue $1,000 face value bonds with an 8 percent coupon paid semiannually and a five-year maturity at $900 per bond. If Dot.Com’s marginal tax rate is 38 percent, its after-tax cost of debt is closest to: a. 6.2 percent. b. 6.4 percent. c. 6.6 percent. d. 6.8 percent. Solution: c is correct. FV = $1,000; PMT = $40; N = 10; PV = $900 Solve for i. The six-month yield, i, is 5.3149% YTM = 5.3149%  2 = 10.6298% kDebtpretax (1 – t)= 10.6298% × ( 1 – 0.38) = 6.5905% LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.40 Morgan Insurance Ltd. issued a fixed-rate perpetual preferred stock three years ago and placed it privately with institutional investors. The stock was issued at $25.00 per share with a $1.75 dividend. If the company were to issue preferred stock today, the yield would be 6.5 percent. The stock’s current value is: a. $25.00. b. $26.92. c. $37.31. d. $40.18.

Solution: b is correct. The company can issue preferred stock at 6.5%. Pps= $1.75/0.065 = $26.92 Note: Dividends are not tax deductible so there is no adjustment for taxes. LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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13.41 The Gearing Company has an after-tax cost of debt capital of 4 percent, a cost of preferred stock of 8 percent, a cost of equity capital of 10 percent, and a weighted average cost of capital of 7 percent. Gearing intends to maintain its current capital structure as it raises additional capital. In making its capital-budgeting decisions for the average-risk project, the relevant cost of capital is: a. 4 percent. b. 7 percent. c. 8 percent. d. 10 percent. Solution: b is correct. The weighted average cost of capital, using weights derived from the current capital structure, is the best estimate of the cost of capital for the average-risk project of a company. LO 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.42 Suppose the cost of capital of the Gadget Company is 10 percent. If Gadget has a capital structure that is 50 percent debt and 50 percent equity, its before-tax cost of debt is 5 percent, and its marginal tax rate is 20 percent, then its cost of equity capital is closest to: a. 10 percent. b. 12 percent. c. 14 percent. d. 16 percent. LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Solution: c is correct. re = ra + (ra – rd) (D/E) x (1-t) Note: If D/(D + E) = 0.50, then D/E = 1.0 re = 0.10 + (0.10 – 0.05)(1.0)(1 – 0.2)

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re = 0.10 + [0.05(0.80)] = 0.10 + 0.04 = 0.14, or 14%

Sample Test Problems 13.1

Howard Power and Telecommunications Corporation has three divisions. The names of these divisions, along with the after-tax cost of capital for each division and the market value of the assets in each division are as follows: (LO 1) Division Name Infrastructure development Power Telecommunications

Cost of Capital 8.75 7.50 8.25

MV of Assets $250,000,000 $325,000,000 $675,000,000

What is the overall after-tax cost of capital for Howard Power and Telecommunications? (LO 1)

Solution: The overall after-tax cost of capital for a firm is a value-weighted average of the after-tax cost of capital for the projects (assets) in that firm. We can calculate the overall after-tax cost of capital using Equation 13.2 as follows: n

kFirm =  xi ki = x1k1 + x2 k2 + x3k3 + ... + xn kn . i =1

$250,000,000 + $325,000,000 + $675,000,000 = $1,250,000 x1 = $250,000 / $1,250,000 = 0.20 x2 = $325,000 / $1,250,000 = 0.26 x1 = $675,000 / $1,250,000 = 0.54 (0.20 × 0.0875) + (0.26 × 0.0750) + (0.54 × 0.0825) = 0.0816, or 8.16% Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.2

Quarri Industries has eight percent coupon bonds outstanding. These bonds have a market price of $954.41, pay interest semiannually, and will mature in 6 years. If the tax rate is 35 percent, what are the pre-tax cost and after-tax cost of this debt? (LO 2)

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Solution:

   $40 1 $1,000    + $954.41= × 112 12  kDebt pretax  1+ k   (1+ k ( ) ) Debt pretax Debt pretax     kDebt pretax = 0.045, or 4.5% The annualized pretax cost is: kDebt pretax = (1 + 0.045) -1= 0.0920, or 9.20% 2

and the after-tax cost is: kDebt after-tax = 0.0920×(1-0.035) = 0.0598, or 5.98% Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.3

Quarri Industries has a beta of 1.6. If the market risk free rate is 4 percent and the expected return on the market 9 percent, what is Babbitt’s cost of common stock? (LO 3) Solution: kcs = Rrf + βcs (E(RM) – Rrf) kcs = 0.04 + 1.6 × (0.09 - 0.04) = 0.12, or 12%

Bloomcode: Application AASCP: Analytic IMA: Quantitative Methods AICPA: Industry/Sector Perspective

13.4

Miron’s Copper Corp. management expects its common stock dividends to grow 1.5 percent per year for the indefinite future. The firm’s shares are currently selling for $18.45, and the firm just paid a dividend of $3.00 yesterday. What is the cost of common stock for this firm? (LO 3)

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D (1+ g ) D1 D  kcs = 1 + g = 0 +g kcs − g P0 P0

 kcs =

$3.00  (1 + 0.015 ) + 0.015 = 0.18, or18% $18.45

Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.5

Use the information in questions 13.2 and 13.3 as well as the following information to compute the WACC for Quarri Industries. In addition to common stock, Quarri has 500,000 preferred shares outstanding that pay a quarterly dividend of $0.50 per share and are currently trading for $20.00 a share. The company’s outstanding bonds have a face value of $209,553,546. There are 2 million shares of common stock outstanding with a current market price of $98.00 per share. (LO 3 and LO 4)

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Solution: The total value of the outstanding debt, preferred stock and common stock are as follows: Debt = $209,553,546 × 0.95441 = $200,000,000 Preferred stock = $20 × 500,000 = $10,000,000 Common stock = $98 × 2,000,000 = $196,000,000 Total capital = $406,000,000 xDebt = $200/$406 = 0.4926 xps = $10/$406 = 0.0246 xcs = $196/$406 = 0.4828

The costs for the individual types of capital are: After-tax cost of debt (from problem 13.2): kDebt after-tax = 5.98% Cost of preferred stock: kps =

D Pps

4  $0.50 = 0.10, or 10% $20

Cost of common equity (from problem 13.3): kcs = 12%

WACC calculation:

WACC = xDebt kDebt after-tax + xps kps + xcs kcs WACC = (0.4926 × 0.0598) + (0.0246 × 0.10) + (0.4828 × 0.12) WACC = 0.0899, or 8.99% Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.6

Staunton Energy Corporation managers are considering a capital budgeting project to replace some machinery used in one of the company’s oil refineries. Is the company’s WACC the appropriate discount rate to use in the NPV analysis of this project? (LO 4)

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Solution: If the systematic risk of the individual project is the same as the systematic risk of the portfolio of projects that comprise the company as a whole, and the project is likely to be financed with the same financing mix as the company, then company’s WACC is the appropriate discount rate to use. However, since a project involving replacement of machinery is probably less risky than the overall company, the company’s WACC might be too high of a discount rate. If so, using the WACC as the discount rate could cause the company managers to underestimate the NPV of this project. They should probably use a lower discount rate to more accurately reflect the systematic risk of the project. Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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CHAPTER 14 Working Capital Management Before You Go On Questions and Answers Section 14.1 1.

How do you calculate net working capital, and why is it important? Net working capital is calculated as the difference between the current assets and current liabilities. It is important for a firm to keep a positive net working capital balance, as these funds are used to cover the day-to-day expenses and short-term liabilities as they come due.

What are some of the trade-offs required in the management of working capital accounts? When managing working capital accounts, a financial manager is looking to delay paying accounts payable as long as possible without suffering any penalties, maintain minimal finished goods inventories without losing sales, and collect cash payments on accounts receivable as fast as possible to close the loop, among other things.

Section 14.2 1.

What is the operating cycle, and how is it related to the cash conversion cycle? The operating cycle starts with the receipt of raw materials and ends with the collection of cash from customers for the sale of finished goods. The operating cycle can be described in terms of two components: days’ sales in inventory and days’ sales outstanding. The cash conversion cycle is the length of time between the actual cash outflow for materials and the actual cash inflow from sales. To calculate it, we need all of the information used to calculate the operating cycle plus one additional measure: days’ payables outstanding.

Section 14.3 1.

What are the two general current asset management strategies discussed in this section, and how do they differ? Typically, the two main current asset investment strategies are flexible and restrictive strategies. The flexible strategy prompts management to keep large balances of cash,

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marketable securities, and inventory. This strategy is perceived to be a relatively low-risk and low-return course of action for management to follow. The restrictive strategy, on the other hand, prompts management to keep the usage of current assets to a minimum and is perceived to be high risk and high return. 2.

What are the types of costs associated with each of these strategies? The flexible strategy is associated with a high level of carrying costs because of a firm’s high levels of inventory and providing liberal credit for customers. The restrictive strategy is associated with shortage costs, which can be either financial or operating in nature.

Section 14.4 1.

What does “4/15, net 30” mean? If a company declares a “4/15, net 30” means of sale, it signifies that it will grant the customer a 4 percent discount if the customer pays the full amount within 15 days of the invoice date. Otherwise the customer has 30 days from the date of the delivery to pay the full amount.

What is an aging schedule, and what is its purpose? The aging schedule for a firm lists the accounts receivable broken down by the number of days until they are due or past due. Firms use aging schedules to keep track of their accounts receivables and to assess how effective they are collecting on these accounts.

Section 14.5 1.

What is the economic order quantity model? The economic order quantity model is an inventory management tool that mathematically determines the minimum total inventory cost, taking into account reorder costs and inventory-carrying costs. The main objective of the model is to find the trade-off between the two costs.

Why can cash investment in inventory be costly? Investment in inventory is considered costly, because inventory must be stored, which results in rental and maintenance costs. Furthermore, inventory on hand is subject to loss and theft, and faces the possibility of becoming obsolete. Finally, investment in inventory provides no return unlike an investment in financial or real assets would.

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Section 14.6 1.

What is float? The collection time, which is the time between when a customer makes a payment and the time the cash becomes available is to the firm, is also referred to as float.

Explain how lockboxes are used. Lockboxes are post office boxes set up by the firm for its customers to deliver their payments to these boxes instead of the firm’s business address. The post office then collects these payments and delivers them to the bank. The main purpose of lockboxes is to minimize collection time for firms through cutting down on postal time and through processing the payments directly at the bank.

Section 14.7 1.

List and briefly describe the three main short-term financing strategies. The three main short-term financing strategies are (1) self-liquidating strategy, in which the maturity of the liabilities is matched with that of assets; (2) conservative strategy, which relies more heavily on long-term financing; and (3) restrictive strategy, which relies primarily on short-term financing.

What are the advantages and disadvantages of short-term financing? Short-term financing offers companies greater flexibility and usually a lower cost of capital. On the other hand, short-term financing often comes with some illiquidity problems as well as uncertainty due to increased exposure to interest rate fluctuations.

Give some examples of sources of short-term financing. Examples of short-term financing include accounts payable, short-term bank loans, informal lines of credit, formal lines of credit, or commercial paper. The two main current asset investment strategies are (1) flexible strategy, which encourages management to keep large balances of current assets, and (2) restrictive strategy, which keeps the usage of current assets to a minimum.

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Self-Study Problems 14.1

You are provided the following working capital information for the Blue Ridge Company: Account Beginning Balance Ending Balance Inventory $ 2,600 $2,890 Accounts receivable 3,222 2,800 Accounts payable 2,500 2,670 Net sales 24,589 Cost of goods sold 19,630 If all sales are made on credit, what are the firm’s operating and cash conversion cycles?

Solution: We calculate the operating and cash conversion cycles for Blue Ridge as follows: Inventory = $2,890 Accounts receivable = $2,800 Accounts payable = $2,670 Net sales = $24,589 Cost of goods sold = $19,630 Inventory $2,890 DSI = = = 53.7 days COGS 365 $19,630 365

DSO =

Accounts receivable $2,800 = = 41.6 days Credit sales 365 $24,589 365

Accounts payable $2,670 = = 49.6 days COGS 365 $19,630 365 Operating cycle = DSI + DSO = 53.7 days + 41.6 days = 95.3 days Cash conversion cycle = DSI + DSO – DPO = 53.7 days + 41.6 days – 49.6 days = 45.7 days DPO =

14.2

Merrifield Cosmetics calculates that its operating cycle for last year was 76 days. The company had $230,000 in its accounts receivable account and had sales of $1.92 million. Approximately how many days does it take from the time the raw materials are received at Merrifield until the finished products they are used to produce are sold?

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Solution: Merrifield’s days sales in inventory is calculated as follows: Operating cycle = 76 days Accounts receivables = $230,000 Net sales = $1,920,000 Accounts receivables $230,000 DSO = = = 43.7 days Credit sales 365 $1,920,000 365 Operating cycle = DSI + DSO 76 days = DSI + 43.7 days DSI = 32.3 days Merrifield Cosmetics takes 32.3 days to turn its inventory into sales.

14.3

Below is a partial aging of accounts receivable for Bitar Roofing Services. Fill in the rest of the information and determine Bitar’s days’ sales outstanding. How does it compare to the industry average of 40 days? Age of Accounts (in days) Value of Account ($) % of Total Account 0-10 $211,000 11-30 120,360 31-45 103,220 46-60 72,800 Over 60 23,740 Total $531,120

Solution: The missing information for Bitar Roofing and its days’ sales outstanding are as follows: Bitar Roofing Age of Accounts (in days) Value of Account ($) % of Total Account 0-10 $211,000 39.7% 11-30 120,360 22.7 31-45 103,220 19.4 46-60 72,800 13.7 Over 60 23,740 4.5 Total $531,120 100%

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Effective DSO = (0.397  10 days) + (0.227  30 days) + (0.194  45 days) + (0.137  60 days) + (0.045  3 = 3.97 days + 6.81 days + 8.73 days + 8.22 days + 16.43 days = 44.2 days

Bitar takes about 4 days more than the industry average of 40 to collect on its receivables. The firm should focus collection efforts on all credit sales that take 60 days or more to collect.

14.4

By obtaining a lockbox, Nizam’s Manufacturing was able to reduce its total cash collection time by two days. The firm has annual sales of $570,000 and can earn 4.75 percent annual interest. Assuming that the lockbox costs $50 per year, calculate the savings that can be attributed to the lockbox.

Solution: The savings that can bed attributed to Nizam’s lockbox are: Annual sales = $570,000 Annual interest rate = 4.75% Annual cost of lockbox = $50 Collection time saved = 2 days $570,000 Average daily sales = = $1,561.64 365 Savings = $1,561.64  0.0475  2 − $50 = $98.36 The firm can save $98.36 each year by using the lockbox.

14.5

Rockville Corporation is going to borrow $250,000 from its bank at an APR of 8.5 percent. The bank requires its customers to maintain a 10 percent compensating balance. What is the effective interest rate on this bank loan?

Solution: The effective rate on Rockville Corporation’s loan is calculated as follows: Rockville Corporation’s loan information is as follows: Amount to be borrowed = $250,000 Stated annual interest rate = 8.5% Compensating balance = 10% Amount deposited as compensating balance = $250,000 × 0.10 = $25,000 Effective borrowing amount equal to $250,000 − $25,000 = $225,000 Interest expense = $250,000 × 0.085 = $21,250

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Interest expense $21,250 = = 9.44% Effective borrowing amount $225,000 By setting aside a compensating balance of 10 percent or $25,000 on the loan, the firm increases its interest rate effectively to 9.44 percent. Effective interest rate =

Discussion Questions 14.1

What factors must a financial manager consider when making decisions about accounts receivable?

When dealing with accounts receivable, important decisions for the financial manager include the amount of credit offered to various customers and the term of the credit. Financial managers should keep close track of both the aging schedule and the effective DSO. If either or both show consistent deterioration, it may be time to reconsider the firm’s credit policy or the characteristics of its customers. In addition, in some industries, sales vary by season. Managers must be aware of seasonal patterns and make the necessary adjustments before drawing any conclusions about firm’s receivables. LO: 4 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Decision Analysis AICPA: Industry/Sector Perspective

14.2

List some of the working capital management practices you would expect to see in a manufacturing company following just-in-time inventory practices. Manufacturing companies like Dell are likely to do an exceptional job of managing their inventory and collecting on their receivables. Dell employs a strategy similar to just-intime management where they maintain just sufficient inventory to meet the needs for a very short time. This saves the firm a huge investment in inventory. Thus their days’ sales in inventory (DSI) will be very low compared to other industries. Similar to Dell, firms will have a short collection period, and their operating cycle will be much lower than firms in other industries. If other computer manufacturing firms follow the Dell operating philosophy, they will extend their days’ payable outstanding (DPO) to the point that their cash conversion cycle is negative. In other words, instead of having to invest in

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its working capital, these firms will end up taking more time to pay their suppliers than the time taken to produce, sell, and collect on the receivables. LO: 5 Level: Basic Bloomcode: Knowledge AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.3

What costs would a firm following a flexible current asset management strategy consider, and why?

The strategy’s downsides can include the high carrying costs associated with owning a high level of inventory and providing liberal credit terms to customers. By investing in current assets, management foregoes the higher rate of return it could have earned by investing in long-term assets. Therefore, there is an opportunity cost involved when investing in current assets. Furthermore, large investments in some types of inventory can require significant storage, tax, and insurance costs, which can be expensive. LO: 3 Level: Intermediate Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.4

How are customers and suppliers affected by a firm’s working capital management decisions? Customers want firms to maintain large finished goods inventories because when they go to make a purchase, the item they want will likely be in stock. In general, large inventory helps stimulate sales and increase customer satisfaction, but that can be a costly item on a firm’s balance sheet. Management’s decisions on the firm’s receivables policy is driven by the industry type. Companies selling perishable products, such as food companies, might ask for payment in full in less than 10 days. On the other hand, if the firm is selling durable goods, the terms of credit are likely to be more generous. The terms of sale are

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also affected by the creditworthiness of the customer. If the firm is confident that it will be paid, it is far more likely to extend credit than if there was some doubt about payment. If the customer is a particularly large firm or if there is a likelihood of repeat business, then extending credit may be part of the marketing effect to secure the order. Thus, when the financial manager makes a decision to increase working capital, good things are likely to happen to the firm—sales should increase, relationships with vendors and suppliers should improve, and work or manufacturing stoppages should be less likely. LO: 4 Level: Intermediate Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.5

A beverage bottling company in Vermont has days’ sales outstanding of 23.7 days. Is this good? Explain.

In general, a lower DSO reflects the fact that the firm is managing its receivables very well. However, it is not possible to decide whether a DSO of 23.7 days is good or bad unless you have a basis for comparison. That basis of comparison could be a peer group, historical data for the firm itself, or targets set by the management. LO: 2 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.6

How do the following circumstances affect the cash conversion cycle: (a) favorable credit terms allow the firm to pay its accounts payable slower, (b) inventory turnover increases, and (c) accounts receivable turnover decreases? (a) (b)

Favorable credit terms from suppliers allow the firm to use the suppliers’ funds to finance their working capital. It also reduces the firm’s cash conversion cycle. An increase in the inventory turnover results into decrease in DSI, which reduces both the firm’s operating cycle and the cash conversion cycle.

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As the accounts receivable turnover or Day Sales Outstanding (DSO) decreases, the firm improves its receivables management and reduces its operating cycle and hence, its cash conversion cycle.

LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.7

What are some industries in which the use of lockboxes would especially benefit companies? Explain.

Lockboxes are a useful tool to speed up collection of receivables when the customer base is dispersed across a large geographical area. Normally, this would mean customer payments would have to be mailed in, consolidated, and then deposited at the firm’s bank. The alternative of setting up a lockbox system allows the firm to redirect customer payments to regional locations for quicker consolidation and cashing of payments. This is typical in the retail industry where each store of a chain is located in a different city or state. LO: 6 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.8

Suppose you are a financial manager at a big firm and you expect interest rates to decline in the near future. What current asset investment strategy would you recommend that the company pursue? At a big firm, management would have access to the commercial paper market, which can provide cheaper funding than short-term bank financing. To borrow in the commercial paper market, a firm has to be financially strong. Thus, all or a portion of the working capital needs can be funded through short-term funds that can be rolled over as long as interest rates are declining. LO: 7

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Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Decision Analysis AICPA: Industry/Sector Perspective

14.9

Why is the commercial paper market available only to the most creditworthy companies?

Commercial paper is available only to the companies that are financially strong for two reasons. First, there is no secondary market for investors to liquidate prior to maturity. Consequently, investors must hold it to maturity and have the confidence that the issuer would pay them back at that time. Second, this type of debt is not secured by any real assets of the issuing firm. Thus, the companies that are the most creditworthy are able to raise funds in this market at costs that are lower than bank loans. LO: 7 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Decision Analysis AICPA: Industry/Sector Perspective

14.10 Explain what a negative cash conversion cycle means. Recognizing the cash conversion cycle is a function of a firm’s receivables turnover, inventory turnover, and payables turnover. Firms that are highly efficient in managing their inventory and receivables will have a short operating cycle and do not need a large investment in working capital. A large payables turnover implies that the firm is making use of their suppliers’ funds to fund their working capital needs. The difference between the operating cycle and the payables turnover is the cash conversion cycle. A negative cash conversion cycle means that the time taken by the firm to meet its payables exceeds its operating cycle. In other words, the amount of time to manage their inventory and the time taken to collect its receivables is less than the time taken to pay its suppliers. LO: 2 Level: Basic Bloomcode: Comprehension Copyright © 2015 John Wiley & Sons, Inc.

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Questions and Problems BASIC 14.1 Cash conversion cycle: Wolfgang’s Masonry management estimates that it takes the company 27 days on average to pay its suppliers. Management also knows that the company has days’ sales in inventory of 64 days and days’ sales outstanding of 32 days. How does Wolfgang’s cash conversion cycle compare with the industry average of 75 days? Solution: DPO = 27 days DSI = 64 days DSO = 32 days Industry average for cash conversion cycle = 75 days. Wolfgang’s cash conversion cycle: Cash conversion cycle = DSO + DSI − DPO = 32 days + 64 days − 27 days = 69 days

Since the firm’s Cash conversion cycle is less than the industry average of 75 days, the firm is more efficient than other firms in the industry in managing its working capital. LO 2 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.2 Cash conversion cycle: Northern Manufacturing Company management found that during

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the last year it took an average of 47 days to pay its suppliers, whereas it took 63 days to collect its receivables. The company’s days’ sales in inventory was 49 days. What was Northern’s cash conversion cycle? Solution: DPO = 47 days DSI = 49 days DSO = 63 days Northern's Cash conversion cycle = DSO + DSI − DPO = 63 days + 49 days − 47 days = 65 days

LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.3

Cash conversion cycle: Devon Automotive management estimates that it takes the company 62 days to collect cash from customers on finished goods from the day it receives raw materials, and it takes 65 days to pay its suppliers. What is the company’s cash conversion cycle? Interpret your answer.

Solution: DPO = 65 days Operating cycle = 62 days Devon’s cash conversion cycle = Operating cycle – DPO = 62 days – 65 days = -3 days This firm has a negative cash conversion cycle. The amount of time to manage its inventory and the time taken to collect its receivables is less than the time taken to pay its suppliers. LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning Copyright © 2015 John Wiley & Sons, Inc.

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AICPA: Industry/Sector Perspective

14.4

Operating cycle: Lilly Bakery distributes its products to more than 75 restaurants and delis. The company’s average collection period is 27 days, and it keeps its inventory for an average of four days. What is Lilly’s operating cycle?

Solution: DSI = 4 days DSO = 27 days Lilly's Operating cycle = DSO + DSI = 27 days + 4 days = 31 days

LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.5

Operating cycle: NetSpeed Technologies is a telecom component manufacturer. The firm typically has a collection period of 44 days and days’ sales in inventory of 29 days. What is the operating cycle for NetSpeed?

Solution: DSI = 29 days DSO = 44 days NetSpeed's Operating cycle = DSO + DSI = 44 days + 29 days = 73 days

LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning

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AICPA: Industry/Sector Perspective

14.6

Current asset management strategy: Describe the risks that are associated with a restrictive current asset management strategy.

Solution: The risk of a restrictive current asset management strategy comes from an exposure to shortage costs, which can be either financial or operating costs. Financial costs are associated with a sudden and unforeseen loss of liquidity that makes it difficult for a firm to repay its current liabilities. In this condition, firms may be forced to rely on costly external emergency borrowing, or if such funds can’t be secured, firms may have to default on their loan obligations. Operating shortage costs result from lost production or sales that occur if a firm does not have sufficient raw material or finished goods. Operating shortage costs may also occur if a firm’s credit policies are too restrictive and deter a significant number of sales to potential customers. LO 3 Bloomcode: Cmoprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.7

Cost of trade credit: Sybex Corp. sells its goods with terms of 2/10 EOM, net 30. What is the implicit cost of the trade credit?

Solution: Credit terms = 2/10 EOM, net 30

  Discount  Effective annual rate of accounts receivable = 1 +  Discounted price  = (1 + 2/98)365/20 – 1 = (1.0204)18.2500 – 1 = 1.4459 – 1 = 0.4459, or 44.59 percent

365 / days credit

−1

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Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective 14.8

Cost of trade credit: Mill Street Corporation sells its goods with terms of 4/10 EOM, net 60. What is the implicit cost of the trade credit?

Solution:

  Discount  Effective annual rate of accounts receivable = 1 + Discounted price   365/50 = (1 + 4/96) –1 7.3 = (1.0417) – 1 = 1.3472 – 1 = 0.3472, or 34.72%

365 / days credit

−1

LO 4 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.9

Lockbox: Rosenthal Design has daily sales of $59,000. The financial management team has determined that a lockbox would reduce the collection time by 1.6 days. Assuming the company can earn 5.2 percent interest per year, what are the savings from the lockbox?

Solution: All sales are assumed to be credit sales. Annual interest rate = 5.2% Collection time saved = 1.6 days Average daily sales = $59,000

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14.10 Lockbox: Pacific Traders has annual sales of $1,895,000. The firm’s financial manager has determined that using a lockbox will reduce collection time by 2.3 days. If the firm’s opportunity cost on savings is 5.25 percent, what are the savings from using the lockbox? Solution: Annual sales = $1,895,000 Annual interest rate = 5.25% Collection time saved = 2.3 days $1,895,000 Average daily sales = = $5,191.78 365 Savings = $5,191.78  0.0525  2.3 days = $626.91 The firm can save $626.91 with the use of lockbox.

LO 6 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.11 Effective interest rate: The Kellogg Bank requires borrowers to keep an 8 percent compensating balance. Gorman Jewels borrows $340,000 at a 7 percent stated APR. What is the effective interest rate on the loan? Solution: Amount borrowed = $340,000 Stated annual interest rate = 7% Compensating balance = 8% Amount deposited as compensating balance = $340,000 × 0.08 = $27,200 Effective borrowing amount = $340,000 − $27,200 = $312,800 Interest expense = $340,000 × 0.07 = $23,800

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Interest expense $23,800 = = 7.61% Effective borrowing amount $312,800 By setting aside a compensating balance of 8 percent or $27,200 on the loan, the firm increases its interest rate effectively to 7.61 percent. Effective interest rate =

LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.12 Effective interest rate: Morgan Contractors borrowed $1.75 million at an APR of 10.2 percent. The loan called for a compensating balance of 12 percent. What is the effective interest rate on the loan? Solution: Amount to be borrowed = $1,750,000 Stated annual interest rate = 10.2% Compensating balance = 12% Amount deposited as compensating balance = $1,750,000 × 0.12 = $210,000 Effective borrowing amount equal to $1,750,000 − $210,000 = $1,540,000 Interest expense = $1,750,000 × 0.102 = $178,500 Interest expense $178,500 Effective interest rate = = = 11.6% Effective borrowing amount $1,540,000 By setting aside a compensating balance of 12 percent or $210,000 on the loan, the firm increases its interest rate effectively to 11.6 percent. LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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14.13 Factoring: Maltz Landscaping has an average collection period of 38 days for its accounts receivable. Currently, Maltz factors all of its receivables at a 2 percent discount. What is the effective annual interest rate on the financing from the factor? Solution: The terms of this factor indicate that for every dollar of receivables sold to the factor today, the firm receives 98-cents today and 38-days later the factor receives the dollar in receivables. The cost to Maltz in percentage terms is 2.04 percent over a 38 day period. There are 9.61 periods (m) during a 365 day year. Effective annual rate = (1+0.0204)365/38 – 1 = .2142 or 21.42 percent. LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.14 Formal line of credit: Winegartner Cosmetics management is setting up a line of credit at the company’s bank for $5 million for up to two years. The interest rate is 5.875 percent and the loan agreement calls for an annual fee of 40 basis points on any unused balance for the year. If the firm borrows $2 million on the day the loan agreement is signed, what is the effective rate for the line of credit? Solution: Line of credit limit = $5,000,000 Loan rate = 5.875% Annual fee on used balance = 0.4% Amount borrowed = $2,000,000 Unused balance = $3,000,000 Annual fee = $3,000,000 × 0.004 = $12,000 Interest expense = $2,000,000 × 0.05875 = $117,500 Interest expense + Annual fee Effective interest rate = Borrowed amount ($117,500 + $12,000) = = 6.48% $2,000,000 The effective borrowing rate for the firm is 6.48% with the annual fee of 40 basis points.

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LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 14.15 Cash conversion cycle: Your boss asks you to compute your company’s cash conversion cycle. Looking at the financial statements, you see that the average inventory for the year was $26,300, accounts receivable averaged $17,900, and accounts payable averaged $15,100. You also see that the company had sales of $154,000 and that cost of goods sold was $122,000. Calculate and interpret your firm’s cash conversion cycle. Solution: All sales are assumed to be credit sales. Accounts receivable = $17,900 Accounts payable = $15,100 Sales = $154,000 Average inventory = $26,300 Cost of goods sold = $122,000 Accounts receivable $17,900 DSO = = = 42.4 days Credit sales 365 $154,000 365

DSI =

Inventory $26,300 = = 78.7 days COGS 365 $122,000 365

Accounts payable $15,100 = = 45.2 days COGS 365 $122,000 365 Cash conversion cycle = DSO + DSI − DPO DPO =

= 42.4 days + 78.7 days − 45.2 days = 75.9 days

The firm takes nearly 76 days from the time it pays for its raw materials to the time it realizes cash from its credit sales. By taking a couple of more days to pay it suppliers relative to the time it takes to collect on its receivables, it reduces the cash conversion cycle. LO 2 Bloomcode: Application Copyright © 2015 John Wiley & Sons, Inc.

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14.16 Cash conversion cycle: Blackwell Automotive, Inc., reported the following financial information for the last fiscal year. Blackwell Automotive, Inc. Assets Liabilities and Equity Cash and marketable securities $ 23,015 Accounts payable and $163,257 accruals Accounts receivable $141,258 Notes payable $21,115 Inventories $212,444 Total current liabilities $184,372 Other current assets $ 11,223 Sales and Costs Total current assets $387,940 Net sales $912,332 Cost of goods sold $547,400 Calculate the firm’s cash conversion cycle and operating cycle. Solution: All sales are assumed to be credit sales. Accounts receivable = $141,258 Accounts payable = $163,257 Net sales = $912,332 Inventory = $212,444 Cost of goods sold = $547,400 Accounts receivable $141,258 DSO = = = 56.5 days Credit sales 365 $912,332 365

DSI =

Inventory $212,444 = = 141.7 days COGS 365 $547,400 365

Accounts payable $163,257 = = 108.9 days COGS 365 $547,400 365 Operating cycle = DSO + DSI DPO =

= 56.5 days + 141.7 days = 198.2 days

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Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.17 Cash conversion cycle: Elsee, Inc., has net sales of $13 million, and 75 percent of these are credit sales. Its cost of goods sold is 65 percent of annual net sales. The firm’s cash conversion cycle is 41.3 days. The inventory balance at the firm is $1,817,344, while its accounts payable balance is $2,171,690. What is the firm’s accounts receivable balance? Solution: Net sales = $13,000,000 Credit sales = (0.75 × Sales) = (0.75 × $13,000,000) = $9,750,000 Accounts payable balance = $2,171,690 Inventory balance = $1,817,344 Cost of goods sold = (0.65 × Sales) = (0.65 × $13,000,000) = $8,450,000 Cash conversion cycle = 41.3 days Accounts payable $2,171,690 DPO = = = 93.8 days COGS 365 $8,450,000 365

Inventory $1,817,344 = = 78.5 days COGS 365 $8,450,000 365 Cash conversion cycle = DSO + DSI − DPO DSI =

41.3 days = DSO + 78.5 days − 93.8 days DSO = 56.6 days

Using the DSO equation, we can solve for the accounts receivable. Accounts receivable AR DSO = = = 56.6 days Credit sales 365 $9 , 750 , 000 365

Accounts receivable = 56.6  $26,712.33 = $1, 511, 917.81 The firm has accounts receivable of $1,511,918. LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning Copyright © 2015 John Wiley & Sons, Inc.

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AICPA: Industry/Sector Perspective 14.18 Cash conversion cycle: Joanna Handicrafts, Inc., has net sales of $4.23 million with 50 percent being credit sales. Its cost of goods sold is $2.54 million. The firm’s cash conversion cycle is 47.9 days and its operating cycle is 86.3 days. What is the firm’s accounts payable? Solution: Net sales = $4,230,000 Credit sales = (0.5 × $4,230,000) = $2,115,000 Cash conversion cycle = 47.9 days Operating cycle = 86.3 days Cost of goods sold = $2,540,000 Cash conversion cycle = (DSO + DSI) − DPO 47.9 days = 86.3 days − DPO DPO = 38.4 days DPO =

Accounts payable Accounts payable = = 38.4 days COGS 365 $2,540,000 365

Accounts payable = 38.4×$6,958.90 = $267, 221.92

The firm has accounts payable of $267,222. LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.19 Operating cycle: Aviva Technology’s operating cycle is 81 days. Its inventory was $134,000 at the end of last year, and the company had cost of goods sold of $1.1 million. How long does it take Aviva to collect its receivables on average? Solution: Operating cycle = 81 days Inventory = $134,000 Cost of goods sold = $1,100,000

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Inventory $134,000 = = 44.5 days COGS 365 $1,100,000 365

Operating cycle = DSO + DSI 81 days = DSO + 44.5 days DSO = 36.5 days

It takes Aviva 36.5 days to collect its receivables. LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.20 Operating cycle: Premier Corp. has net sales of $812,344, and cost of goods sold equal to 70 percent of net sales. Assume all sales are credit sales. If the firm’s accounts receivable total $113,902 and its operating cycle is 81.6 days, how much inventory does the firm have? Solution: All sales are assumed to be credit sales. Credit sales = $812,344 Operating cycle = 81.6 days Cost of goods sold = (0.7 × $812,344) = $568,641 Accounts receivable = $113,902 Accounts receivable $113,902 DSO = = = 51.2 days Credit sales 365 $812,344 365 Operating cycle = DSO + DSI 81.6 days = 51.2 days + DSI DSI = 30.4 days

Inventory Inventory = = 30.4 days COGS 365 $568,641 365 Inventory = $47,360.78 DSI =

The firm has inventory of $47,361. LO 2 Bloomcode: Application

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14.21 Operating cycle: Telecraft Enterprises carries 45 days of inventory in its stores. Last year Telecraft reported net sales of $1,400,000 and the company had receivables of $325,000 at the end of the year. What is the operating cycle at Telecraft? Solution: All sales are assumed to be credit sales. Accounts receivable $325,000 DSO = = = 84.7 days Credit sales 365 $1, 400,000 365 DSI = 45 days Operating cycle = DSO + DSI = 84.7 days + 45 days = 129.7 days

LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective 14.22 Operating Cycle: Given the data for Telecraft Enterprises in problem 14.21, re-estimate the firm’s operating cycle if days’ sales outstanding decreased to 75 days. For the same level of net sales, what is the implied dollar value of receivables with 75 days’ sales outstanding? Solution: Operating cycle = DSO + DSI = 75 days + 45 days = 120 days If the DSO is 75 days: DSO = 365 days / (credit sales / accounts receivable) 75 days = 365 days / ($1,400,000/accounts receivable) 75 days × $1,400,000 = 365 days × accounts receivable Accounts receivables = $1,400,000 × 75 days / 365 days Accounts receivables = $287,671.23 The value of receivables with 75 days’ sales outstanding is $287,671.

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LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective 14.23 Economic order quantity: Longhorn Traders is one of the largest RV dealers in Austin, Texas, and sells about 2,800 recreational vehicles a year. The cost of placing an order with Longhorn’s supplier is $800, and the inventory carrying costs are $150 for each RV. Management likes to maintain safety stock of 12 RVs. Most of its sales are made in either the spring or the fall. How many orders should the firm place this year? Solution: Annual sales = 2,800 units Cost of placing an order = $800 Inventory carrying cost per RV = $150 Safety stock = 12 RVs EOQ =

2  Reorder costs  Sales per period Carrying cos ts

2  $800  2,800 = 172.8 $150 Economic order quantity = 173 RVs Number of orders the firm needs to place = 2,800 / 173 = 16 LO 5 Bloomcode: Application =

AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.24 Effective interest rate: The Clarkson Designer Company Management wants to borrow $750,000.The bank will provide the loan at an APR of 6.875 percent. Since the loan calls for a compensating balance, the effective interest rate is actually 9.25 percent. What is the compensating balance on this loan? Solution: Amount to be borrowed = $750,000 Stated annual interest rate = 6.875% Copyright © 2015 John Wiley & Sons, Inc.

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Compensating balance = ? Effective interest rate = 9.25% Interest expense = $750,000 × 0.06875 = $51,562.50 Interest expense Effective interest rate = Effective borrowing amount $51,562.50 9.25% = Effective borrowing amount $51,562.50 Effective borrowing amount = = $557,432.43 0.0925 Effective borrowing amount = $750,000 − compensating balance deposit = $557,432.43 Compensating balance deposit = $750,000 - $557,432.43 = $192,567.57 Compensating balance = $192,567.57 / $750,000 = 25.6% By setting aside a compensating balance of 25.6% on the loan, the firm increases its interest rate effectively from 6.875 to 9.25 percent. LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.25 Effective interest rate: The Colonial Window Treatments Company is borrowing $1.5 million. The loan requires a 10 percent compensating balance, and the effective interest rate on the loan is 9.75 percent. What is the stated APR on this loan? Solution: Amount to be borrowed = $1,500,000 Stated annual interest rate = ? Compensating balance = 10% Effective interest rate = 9.75% Compensating balance = (0.10 × $1,500,000) = $150,000 Effective borrowing amount = $1,500,000 − $150,000 = $1,350,000 Interest expense Effective interest rate = Effective borrowing amount Interest expense 9.75% = Effective borrowing amount Interest expense = 0.0975  $1,350,000 = $131,625 Stated interest rate = $131,625 / $1,500,000 = 8.775%

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LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.26 Formal line of credit: Gruppa, Inc., has just set up a formal line of credit of $10 million with First Community Commercial Bank. The line of credit is good for up to five years. The bank will charge Gruppa an interest rate of 6.25 percent on any amount borrowed, and the firm will pay an annual fee of 60 basis points on the unused balance. The firm borrowed $7.5 million on the first day the credit line became available. What is the effective interest rate on this line of credit? Solution: Line of credit limit = $10,000,000 Interest rate = 6.25% Annual fee on used balance = 0.6% Amount borrowed = $7,500,000 Unused balance = $10,000,000 – $7,500,000 = $2,500,000 Annual fee = $2,500,000 × 0.006 = $15,000 Interest expense = $7,500,000 × 0.0625 = $468,750 Interest expense + Annual fee Effective interest rate = Borrowed amount ($468,750 + $15,000) = = 6.45% $7,500,000 The effective interest rate on the line of credit is 6.45% LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.27 Formal line of credit: Lansdowne Electronics has a formal line of credit of $1 million for up to three years with HND Bank. The interest rate on the loan is 5.3 percent, and under the agreement, Lansdowne has to pay an annual fee of 50 basis points on the unused amount.

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Suppose the firm borrows $675,000 the first day of the agreement. What is the fee the company must pay on the unused balance? What is the effective interest rate? Solution: Line of credit limit = $1,000,000 Interest rate = 5.3% Annual fee on used balance = 0.5% Amount borrowed = $675,000 Unused balance = $1,000,000 - $675,000 = $325,000 Annual fee = $325,000 × 0.005 = $1,625 Interest expense = $675,000 × 0.053 = $35,775 Interest expense + Annual fee Effective interest rate = Borrowed amount ($35,775 + $1,625) = = 5.54% $675,000 The effective interest rate is 5.54% LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

14.28 Lockbox: Jennifer Electrical is evaluating whether a lockbox it is currently using is worth keeping. Management estimates that the lockbox reduces the mail float by 1.8 days and the processing by half a day. The remittances average $50,000 a day for Jennifer Electrical, with the average check being for $500. The bank charges $0.34 per processed check. Assume that there are 270 business days in a year and that the firm’s opportunity cost for these funds is 6 percent. What will the firm’s savings be from using the lockbox? Solution: Average daily sales = $50,000 No. of business days = 270 Opportunity cost of funds = 6% Average check amount = $500 No. of checks processed per day = $50,000 / $500 = 100 Collection time saved = 1.8 days Processing time saved = 0.5 days Per check processing fee = $0.34

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The annual cost of a lockbox = 100 checks  $0.34 per check  270 days = $9,180 Savings from mail float = 1.8 days  $50,000 = $90,000 Savings from processing float = 0.5 days  $50,000 = $25,000 Total savings = (Savings from mail float + Savings from processing float) = $90,000 + $25,000 = $115,000 Savings from lockbox = $115,000 × 0.06= $6,900 Since the savings from the lockbox is less than the cost of the lockbox, it is not worth keeping the lockbox for Jennifer Electricals. LO 6 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.29 Lockbox: Hazel Corp. has just signed up for a lockbox. Management expects the lockbox to reduce the mail float by 2.1 days. Hazel Corp.’s remittances average $37,000 a day, and the average check is $125. The bank charges $0.37 per processed check. Assume that there are 270 business days in a year. What will the firm’s savings be from using the lockbox if the opportunity cost for these funds is 12 percent? Solution: Average daily sales = $37,000 No. of business days = 270 Average check amount = $125 No. of checks processed per day = $37,000 / $125 = 296 Collection time saved = 2.1 days Per check processing fee = $0.37 The annual cost of a lockbox = 296 checks  $0.37 per check  270 days = $29,570.40 Savings from mail float = 2.1 days  $37,000 = $77,700 Opportunity cost of funds = 12% Savings from lockbox = $77,700 × 0.12= $9,324 Since the savings from the lockbox is less than the cost of the lockbox, it is not worth keeping the lockbox for Hazel Corp. LO 6 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning

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14.30 Aging schedule: Ginseng Company collects 50 percent of its receivables in 10 days or fewer, 31 percent in 11 to 30 days, 7 percent in 31 to 45 days, 7 percent in 46 to 60 days, and 5 percent in more than 60 days. The company has $1,213,000 in accounts receivable. Prepare an aging schedule for Ginseng Company. Solution: Accounts receivables = $1,213,000 Age of Account (days) Value of Account 0-10 $ 606,500 11-30 376,030 31-45 84,910 46-60 84,910 Over 60 60,650 Total $1,213,000

% of Total Value 50% 31 7 7 5 100%

LO 4 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective 14.31 Aging schedule: A partial aging of accounts receivable for Lincoln Cleaning Services is given in the accompanying table. What percent of receivables are in the 45-day range? Determine the firm’s effective days’ sales outstanding. How does it compare with the industry average of 35 days? Age of Account (days) Value of Account % of Total Value 10 $271,000 30 145,220 45 60 53,980 75 31,245 Total $589,218 100.0% Solution: Accounts receivable = $589,218

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Age of Account (days) 10 30 45 60 75 Total

Value of Account $271,000 145,220 87,773 53,980 31,245 $589,218

Solutions Manual

% of Total Value 46.0% 24.6 14.9 9.2 5.3 100.0%

Effective DSO = Age of the account category  Percent of AR for the account category = (10 × 0.46 + 30 × 0.246 + 45 × 0.149 + 60 × 0.092 + 75 × 0.053) = 28.2 days The firm is more efficient than other firms in the industry as its effective DSO is lower. LO 4 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective 14.32 Aging schedule: Keswick Fencing Company collects 45 percent of its receivables in 10 days or fewer, 34 percent in 11 to 30 days, 12 percent in 31 to 45 days, 5 percent in 46 to 60 days, and 4 percent in more than 60 days. The company has $937,000 in accounts receivable. Prepare an aging schedule for Keswick Fencing. Solution: Accounts receivable = $937,000 Age of Account (days) Value of Account 0-10 $421,650 11-30 318,580 31-45 112,440 46-60 46,850 Over 60 37,480 Total $937,000

% of Total Value 45% 34 12 5 4 100%

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IMA: Strategic Planning AICPA: Industry/Sector Perspective 14.34 Factoring: Zenex, Inc., sells $250,000 of its accounts receivable to factors at a 3 percent discount. The firm’s average collection period is 90 days. What is the dollar cost of the factoring service? What is the simple annual interest cost of the factors loan? Solution: Accounts receivable sold = $250,000 Factor discount = 3% Average collection period = 90 days Dollar cost of factoring per month = $250,000 × 0.03 = $7,500 Dollar cost over 90 days = $7,500 × 90/30 = $22,500 Simple monthly interest cost of factoring = 3/97 or 0.03 / (1-0.03) = 0.03093 Simple annual interest cost of factoring = 0.03093 × 12 months = 37.1% LO 4 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.34 Factoring: A firm sells $100,000 of its accounts receivable to factors at a 2 percent discount. The firm’s average collection period is one month. What is the dollar cost of the factoring service? Solution: Accounts receivable sold = $100,000 Factor discount = 2% Average collection period = 30 days Dollar cost of factoring service per month = $100,000 × 0.02 = $2,000 LO 7 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

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14.35 What impact would the following actions have on the operating and cash conversion cycles? Would the cycles increase, decrease, or remain unchanged? a. More raw material than usual is purchased. b. The company enters into an off season, and finished goods inventory builds up. c. Better terms of payment are negotiated with suppliers. d. The cash discounts offered to customers are decreased. e. All else remaining the same, an improvement in manufacturing technique decreases the cost of goods sold. Solution: Situation a. More raw material than usual is purchased. b. The company enters into an off season, and finished goods inventory builds up. c. Better terms of payment are negotiated with suppliers. d. The cash discounts offered to customers are decreased. e. All else remaining the same, an improvement in manufacturing technique decreases the cost of goods sold. LO 2 Bloomcode: Comprehension

Operating cycle

Cash conversion cycle

Increase

No change

Decrease

Increase

Unchanged

AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.36 What impact would the following actions have on the operating and cash conversion cycles? Would the cycles increase, decrease, or remain unchanged? a. Less raw material than usual is purchased. b. The company encounters unseasonable demand, and inventory declines rapidly. c. Tighter terms of payment are demanded by suppliers. d. The cash discounts offered to customers are increased. Copyright © 2015 John Wiley & Sons, Inc.

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e. All else remaining the same, due to labor turnover and poor efficiency, the cost of goods sold increases. Solution: Situation a. Less raw material than usual is purchased. b. The company encounters unseasonable demand, and inventory declines rapidly. c. Tighter terms of payment are demanded by suppliers. d. The cash discounts offered to customers are increased. e. All else remaining the same, due to labor turnover and poor efficiency, the cost of goods sold increases.

Operating cycle

Cash conversion cycle

Decrease

No change

Increase

Decrease

Unchanged

LO 2 Bloomcode: Comprehension AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.37 Morgan Sports Company just reported the following financial information. Morgan Sports Equipment Company Assets Liabilities and Equity Cash $ 677,423 Accounts payable $1,721,669 Accounts receivable 1,845,113 Notes payable 2,113,345 Inventories 1,312,478 Total current liabilities $3,835,014 Total current assets $3,835,014 Sales and Costs

a. b. c.

Net sales Cost of goods sold Calculate the firm’s days’ sales outstanding. What is the firm’s days’ sales in inventory? What is the firm’s days’ payables outstanding?

$9,912,332 $5,947,399

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What is the firm’s operating cycle? How does it compare with the industry average of 72 days? What is the firm’s cash conversion cycle? How does it compare with the industry average of 42 days?

Solution: All sales are assumed to be credit sales. a.

DSO =

DSI =

DPO =

Accounts receivable $1,845,113 = = 67.9 days Credit sales 365 $9,912,332 365

Inventory $1,312,478 = = 80.6 days COGS 365 $5,947,399 365 Accounts Payable $1,721,669 = = 105.7 days COGS 365 $5,947,399 365

Operating cycle = DSO + DSI = 67.9 days + 80.6 days

= 148.5 days

The firm is very inefficient in managing its receivable and inventory as its operating cycle exceeds the industry average of 72 days by about 77 days. Cash conversion cycle = DSO + DSI − DPO = (67.9 days + 80.6 days) − 105.7 days

= 42.8 days

The firm’s cash conversion cycle is on a par with the industry average of 42 days thanks to its suppliers’ very generous credit policy. LO 2 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

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14.38 Jackson Electrical, one of the largest generator dealers in Phoenix, sells about 2,000 generators a year. The cost of placing an order with its supplier is $750, and the inventory carrying costs are $170 for each generator. Jackson likes to maintain safety stock of 15 generators at all times. a. What is the firm’s EOQ? b. How many orders will the firm need to place this year? c. What is the average inventory for the season? Solution: Annual sales = 2,000 generators Cost of placing an order = $750 Inventory carrying cost per generator = $170 Safety stock = 15 generators EOQ =

2  Reorder costs  Sales per period Carrying cos ts

2  $750  2,000 = 132.8 $170 Economic order quantity = 133 generators No. of orders the firm needs to place = 2,000 / 133 = 15 orders Average inventory = ((133 – 0)/2) + 15 = 82 generators =

b. c.

LO 5 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective 12.39 Tanzaniqe, Inc., sells $200,000 of its accounts receivable to factors at a 5 percent discount. The firm’s average collection period is 90 days. a. What is the dollar cost of the factoring service? b. What is the simple annual interest cost of the loan? c. What is the effective annual interest cost of the loan? Solution: Accounts receivable sold = $200,000 Factor discount = 5% Average collection period = 90 days a. Dollar cost of factoring per month = $200,000 × 0.05 = $10,000 Dollar cost over 90 days = $10,000 × 3 or $10,000 × 90 / 30 = $30,000 Copyright © 2015 John Wiley & Sons, Inc.

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Simple monthly interest cost of factoring = 5/95 OR 0.05 / (1-0.05) = 0.0526 Simple annual interest cost of factoring = 0.0526 × 12 = 63.2% m

 Quoted rate  EAR = 1 +  −1 m   12 = (1 + 0.0526) − 1 = 0.8506 = 85.06%

LO 7 Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

CFA PROBLEMS 12.40 A company increasing its credit terms for customers from 1/10, net 30 to 1/10, net 60 will likely experience: a. An increase in cash on hand. b. An increase in the average collection period. c. Higher net income. d. A higher level of uncollectible accounts. LO 6 Bloomcode: Application AASCP: Analytic IMA: Decision Analysis

AICPA: Industry/Sector Perspective Solution: b is correct.

14.41 Suppose a company uses trade credit with the terms of 2/10, net 50. If the company pays its account on the 50th day, the effective borrowing cost of skipping the discount on Day 10 is closest to a. 14.6percent. b. 14.9percent. c. 15.0percent. d. 20.2percent. Copyright © 2015 John Wiley & Sons, Inc.

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LO 4 Bloomcode: Application AASCP: Analytic IMA: Decision Analysis AICPA: Industry/Sector Perspective Solution: d is correct. 

Cost = 1+ 

365/ 40

0.02   0.98 

−1 = 20.24 percent

The following information relates to Problems 14.42 through 14.44. Mary Gonzales is evaluating companies in the office supply industry and has compiled the following information: 2013 2014 Average Average Company Credit Sales Receivables Credit Sales Receivables Balance Balance A $5.0 million $1.0 million $6.0 million $1.2 million B $3.0 million $1.2 million $4.0 million $1.5 million C $2.5 million $0.8 million $3.0 million $1.0 million D $0.5 million $0.1 million $0.6 million $0.2 million Industry $25.0 million $5.0 million $28.0 million $5.4 million

12.42 Which of the companies has the lowest accounts receivable turnover in 2014? a. Company A. b. Company B. c. Company C. d. Company D. LO 4 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

Solution: b is correct.

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Company A: $6.0 million/$1.2 million = 5.00 Company B: $4.0 million/$1.5 million = 2.67 Company C: $3.0 million/$1.0 million = 3.00 Company D: $0.6 million/$0.2 million = 3.00

14.43 The industry average receivables collection period: a. Increased from 2013 to 2014. b. Decreased from 2013 to 2014. c. Did not change from 2013 to 2014. d. Increased along with the increase in the industry accounts receivable turnover. LO 4 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective Solution: b is correct.

2013: 73 days 2014: 70.393 days Note: If the number of days decreased from 2013 to 2014, the receivable turnover has increased.

14.44 Which of the companies reduced the average time it took to collect on accounts receivable from 2013 to 2014? a. Company A. b. Company B. c. Company C. d. Company D. LO 4 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective Solution: b is correct. Copyright © 2015 John Wiley & Sons, Inc.

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Company B increased its accounts receivable (A/R) turnover and reduced its number of days of receivables between 2013 and 2014. 2013 Company

A/R turnover

A B C D

5.000 2.500 3.125 5.000

2014 Number of days of receivable 73.000 146.000 116.800 73.000

AR turnover 5.000 2.667 3.000 3.000

Number of days of receivable 73.000 136.875 121.667 121.667

Sample Test Problems 14.1

The Whole Foods Market, Inc. balance sheet for the fiscal year ending September 29, 2013 included the following: total current assets of $1,980 million, total assets of $5,538 million, total current liabilities of $1,088 million, and total liabilities of $1,660 million. What was the company’s net working capital on September 29, 2013? What does this tell us? (LO 1) Solution: Net Working Capital = Total Current assets – Total Current Liabilities = $1,980,000,000 - $1,088,000,000 = $892,000,000

This tells us that Whole Foods could pay off all its current liabilities (those that will come due in the next year) with the cash and other assets that could reasonably be expected to be converted to cash within the next year and still have $892 million left over. Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.2

Last year Perpetual Plastics Company took an average of 46 days to pay suppliers and 38 days to collect its receivables. The company’s average days’ sales in inventory was 52

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days. What was Perpetual’s operating cycle and cash conversion cycle last year? (LO 2) Solution: DPO = 46 days DSO = 38 days DSI = 52 days Perpetual’s operating cycle = DSO + DSI = 38 days + 52 days = 90 days Perpetual’s cash conversion cycle = DSO + DSI – DPO = 38 days + 52 days – 46 days = 44 days Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.3

Montrose, Inc. sells its products with terms of 3/15 EOM, net 30. What is the cost of the trade credit it provides its customers? (LO 4) Solution: Credit terms = 3/15 EOM, net 30

  Discount Effective annual rate (EAR) = 1+   Discounted price 

365/days credit

-1

= (1 + 3/97)365/15 – 1 = (1.030928)24.333333 – 1 = 2.0984 – 1 = 1.0984, or 109.84%

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Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.4

FRA Manufacturing Company purchases 9,000 units of Part 3BX each year. The cost of placing an order is $5 and the cost of carrying one part in inventory for a year is $1. What is the Economic Order Quantity (EOQ) for part 3BX if the company carries a safety stock of 200 units? How many orders will the company need to place this year? (LO 5)

Solution: Annual purchases = 9,000 units Cost of placing an order = $5 Inventory carrying cost per part = $1 Safety stock = 200 parts EOQ = =

2×Reorder costs×Sales (or purchases)per period Carrying costs 2×$5×9,000 = 300parts $1

The number of orders that the firm should to place each year is 300/9,000 = 30 Bloomcode: Analysis AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

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Solutions Manual

Rosemary Corporation has daily sales of $139,000. The financial manager at the firm has determined that a lockbox would reduce collection time by 2.2 days. Assuming the company can earn 5.5 percent interest per year, what are the potential annual savings from the lockbox? (LO 6) Solution: Average daily sales = $139,000 Collection time saved = 2.2 days Savings from mail float = 2.2 days × $139,000 = $305,800 Annual savings if invested = $305,800 × 0.055 = $16,819

Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

14.6

Sunny Way Landscaping has a formal line of credit of $500,000 with First Commerce Bank. The interest rate on the loan is 6 percent, and under the agreement, Sunny Skies must pay an annual fee of 75 basis points on the unused amount. The amount currently outstanding on the loan is $325,000. What is the annual fee the company must pay on the current unused balance? What is the effective interest rate? (LO 7)

Solution: Line of credit limit = $500,000 Interest rate = 6% Annual fee on unused balance = 0.75% Amount borrowed = $325,000 Unused balance = $175,000 Annual fee = $175,000 × 0.0075 = $1,312.50

Interest expense for amount borrowed = $325,000 × 0.06 = $19,500.00

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Interest expense + Annual fee Borrowed amount ($19,500.00 + $1,312.50) = = 0.0640, or 6.40% $325,000.00

Effective interest rate =

Bloomcode: Application AASCP: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

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CHAPTER 15 How Firms Raise Capital Before You Go On Questions and Answers Section 15.1 1.

Explain bootstrapping, and list the most common sources of seed money. Bootstrapping refers to the securing of initial funding by entrepreneurs to start a new business. It alludes to the idea of an individual or small group of entrepreneurs who keep their business idea barely alive by securing money to keep it going. The initial “seed” money usually comes from the entrepreneur or other founders. Other cash may come from personal savings, the sale of assets such as cars and boats, loans from family members and friends, and loans secured from credit cards.

Section 15.2 1.

Who are venture capitalists, and what do they do? Venture capitalists are individuals or groups of people that help new businesses to get started and provide much of their early financing. They pool money from various sources, such as wealthy individuals, insurance companies, pension funds, or large corporations and invest in start-up ventures. The primary types of businesses seeking the services of venture capitalists are high-tech firms.

How do venture capitalists reduce the risk of their investments? Venture capitalists reduce the risk of their investments in two ways: (1) stage funding, which gives the investors a chance to periodically reassess the project, the management team, and the firm’s financial performance, and to make necessary corrections throughout the duration of the project, and (2) personal investment by the entrepreneurs. Requiring the entrepreneurs to make a substantial personal investment in the business is to make sure that they are highly motivated to succeed.

Explain the venture capital funding cycle. The venture capital funding cycle starts with the development of a detailed business plan by the start-up company. Once a venture capitalist (VC) that will fund the project is

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selected, they state their terms of funding—how much money will they supply in what stages, criteria of success, and so on. Finally, exit strategy is developed. Since VCs are not long-term investors, it is important that a clear understanding of how the VC can exit the deal is part of the initial agreement. This can involve taking the firm public or sometimes selling the new firm to another business.

Section 15.3 1.

What is a seasoned offering, and why are seasoned securities valued more highly than securities sold in an IPO? A seasoned offering is a sale of securities by a firm that already has publicly traded securities outstanding. These are usually more expensive as they are viewed to be less risky than IPO securities; since they are sold by firms that already established a reputation for quality with the investing public, many investors prefer them to new issues.

Explain the two ways a security issue can be underwritten. A security can be underwritten in two ways: (1) firm-commitment basis—in this case the banker guarantees the issuer a fixed amount of money from the security sale, and (2) best-effort basis—whereby the banker makes no guarantee to sell the securities at a particular price, but instead promises to sell as much of the issue as possible above a certain price. The main difference between these two types of underwriting is who bears the risk. With the firm-commitment basis, it is the banking firm that buys the securities first before selling them to public. On the other hand, in a best-effort type of deal, the issuer is the risk bearer.

List the steps in the IPO process. The IPO process involves the following steps: (1) selection of the investment bank, (2) preparation of the registration paperwork and SEC process, (3) determination of the structural features of the offering, (4) valuation, (5) marketing of the IPO, and (6) sale of the securities.

Section 15.4 1.

What is underpricing, and why is it a cost to the stockholders? Underpricing is defined as the offering of new securities for sale at an offer price below the true value of the security. It is considered to be a cost to a firm, because if the stock sells at a low price, the issuer is essentially losing money, which goes in the pockets of investors that bought the issues for less than they are worth.

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What are the components of the cost associated with an IPO? The cost of issuing an IPO includes the following: (1) underwriting spread, (2) out-ofpocket expenses, and (3) underpricing.

Section 15.5 1.

Explain why firms generally sell their equity and complicated debt issues through negotiated sales. Negotiated sales allow the investment bankers to form a closer relationship with the issuer and develop a better understanding of the firm. This enables them to form more effective selling teams. As a result, this should allow the bankers to reduce uncertainty surrounding the issue, resulting in a lower issue cost.

Explain the importance of shelf registration. Shelf registration allows firms to register the inventory of securities for a two-year period. During this time the firm can take the securities and sell them as needed. This process simplifies the sale, as there are no flotation costs involved after the initial registration statement. The firm can also sell as many or as few securities at a time as it needs to, taking advantage of favorable market conditions. There is no penalty if authorized securities are not issued.

Section 15.6 1.

What are the disadvantages of a private placement sale compared with a public sale? Private placement has three main disadvantages compared to public sale. First, because of the lack of liquidity, nominal yields are higher. Second, since private placement securities are not registered, the covenants are stricter. And finally, compared to public securities, private placement securities are more difficult to sell in the secondary market.

Why do companies engage in PIPE transactions? Small and midsize companies can find it difficult or costly to raise money in the public markets. In these circumstances, it can be more efficient or cost effective to sell stock privately, even if the company’s stock is already publicly traded. PIPE transactions bring several advantages to the issuing firm. They give the firm faster access to capital and a lower funding cost than a registered public offering. A PIPE

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transaction can be completed in as short a time as two weeks, whereas a typical public offering underwritten by an investment bank takes several months. PIPE transactions involving a healthy firm can also be executed without the use of an investment bank, resulting in a cost saving of 7 to 8 percent of the proceeds. A PIPE transaction can be the only way for a small financially distressed company to raise equity capital.

Self-Study Problems 15.1

Management of Oakley, Inc., is planning to raise $1 million in new equity through a private placement. If the sale price is $18 per share, how many shares does the company have to issue?

Solution: To raise $1million, Oakley has to issue 55,556 shares: ($1,000,000 / $18 per share = 55,556 shares).

15.2

Suppose a firm is doing an IPO and the investment bank offers to buy the securities for $39 per share with an offering price of $42. What is the underwriter’s spread? Assume that the underwriter’s cost of bringing the security to the market is $5 per share. What is the net profit?

Solution: Underwriter’s spread: $42 – $39 = $3, or 7.1% ($3 / $42 = 0.071, or 7.1%) Net profit per share : $3 – $1 = $2

15.3

Management of The Stride Rite Corporation, designer and marketer of athletic apparel, is planning an expansion into foreign markets and needs to raise $10 million to finance this move. Management anticipates raisig the money through a general cash offering for $13 a share. If the underwriters charge a 5 percent spread, how many shares will the company have to sell to achieve its goal?

Solution: Underwriter’s spread = 5% Price per share for the firm = [$13 × (1-0.05)] = $12.35 To raise $10 million, the company needs to issue: ($10,000,000 / $12.35) = 809,717 new shares

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Dean Foods Co. needs to borrow $23 million for a factory equipment upgrade. Management decides to sell 10-year bonds. They determine that the 3-month Treasury bill yields 4.32 percent, the firm’s credit rating is AA, and the yield on 10-year Treasury bonds is 1.06 percent higher than for 3-month bills. Right now, AA bonds are selling for 1.35 percent above the 10-year Treasury bond rate. What is the borrowing cost for this transaction?

Solution: The borrowing cost for Dean Foods can be calculated as follows: kl = 4.32% + 1.35% + 1.06% = 6.73% The approach used here is similar to that used in the bank loan pricing model.

15.6

You are considering starting a new online dating service, but you lack the initial capital. What are your options for financing?

Solution: Possible sources of capital include your own savings, family and friends, wealthy individuals, venture capital firms, and financial institutions such as banks.

Discussion Questions 15.1

Assume you work for a venture capital firm and have been approached by a couple of recent college graduates with a request to fund their new business. If you are interested in the idea, what process will you follow? After setting up the initial meeting, we should carefully review their business plan and make sure that it contains all the important information a business plan should, such as industry and market analysis, vision and mission statements, management team description, and cost analysis along with the proposed budget. Providing we like the plan and decide to fund the project, we will try to minimize our risk of investing and only fund the project in stages. In addition, we will require some personal investment from the candidates to ensure their serious interest in the project. Finally, we will draft an exit strategy, outlining the timing and calculation of the exit price. LO: 2 Level: Basic

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15.2

Identify the three basic services investment bankers provide to help firms bring new security issues to the market. During which stage of the typical IPO does the investment banker take on the risk of the offering? Is there an alternative in which the risk remains with the company going public?

The three services provided by an investment banker in an initial public offering are origination, underwriting, and distribution. The underwriter takes on the risk during the second stage of the IPO process that is underwriting, providing a firm-commitment underwriting deal is in place. Under this scenario, the banker actually buys the securities from the firm at a fixed price and resells them to the public. Hence, the underwriter bears the risk that the securities may be sold for less than the underwriter paid for it. An alternative arrangement is the best-effort underwriting, where the investment banking firm makes no guarantee to sell the securities at a particular price, but instead promises only to make its “best effort” to sell as much of the issue as possible at a certain price. In this scenario, the risk stays with the offering firm. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.3

Define underpricing, and explain why the majority of IPOs are underpriced. What role do investment banks play in the price-setting process? Underpricing is defined as offering new securities for sale at a price below their true value. It is the loss that the issuer incurs from selling below its true market value. Asymmetric information plays a big role in an IPO underpricing, since both the bankers and the public know less about private companies going public than they do about already publicly traded firms. The lower offering price is to compensate the investors for taking on the risk of buying into a company for which not a lot of information is available. One way for companies to reduce underpricing is to choose a well-known investment bank to take them public. This will send a signal to the potential investors that the bank has done its due diligence and considers the firm to be creditworthy.

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LO: 4 Level: Intermediate Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.4

Explain why the owners of a company might choose to keep it private.

By remaining private, a company effectively avoids being subjected to SEC regulations. Many of the large private companies are family owned with a long history and prefer not to be subjected to public scrutiny. In addition, the management of the company is not pressured by Wall Street to report short-term earnings, but can concentrate their efforts on long-term growth and strategy realization. LO: 6 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.5

Identify the three cost components that make up the total cost of issuing securities for a company. Briefly describe each.

The total cost for a firm to issue securities is equal to the sum of the underwriting spread, out-of-pocket expenses, and underpricing. The underwriting spread is the difference between the proceeds the issuer receives and the total amount raised in the offering. Outof-pocket expenses are usually administrative costs such as investment banking fees, legal fees, accounting expenses, SEC filing fees, and so on. Finally, the total amount of underpricing is determined as the difference between the offering price and the closing price on the first day of trading in the public market. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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What are the characteristics of a public bond? (Think in terms of comparing it to private placement and bank term loans.)

A public bond is usually the most suitable securities for a large firm looking for a large loan. It tends to have the lowest interest costs as well as the lowest default risk, but usually has a long maturity. While it has very few restrictive covenants, it is also very difficult to renegotiate. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.7

Discuss the advantages of shelf registration. What kinds of securities are most likely to be registered this way?

Shelf registration allows the company to register an inventory of securities for a two year period, and thus the company can sell the securities when market conditions are most favorable. The company can take the securities “off the shelf” and sell them within minutes. They can also sell securities on a periodic basis, whenever cash is needed. Plain vanilla bonds are most likely to be sold by shelf registration through competitive bidding. LO: 5 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.8

Identify whether each of the following factors implies a lower or higher price for a bond. a. Low marketability of the security. b. Short term to maturity. c Low credit rating of the issuer. d. No call Bond yield Bond Price provision.Factor a. Low marketability of Increase Decrease the security

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b. Short term to maturity Decrease c. Low credit rating of the Increase issuer c. No call provision Decrease LO: 6 Level: Intermediate Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Increase Decrease Increase

15.9

Explain why time might play a significant role during low-interest periods in a decision of whether to choose a private placement or public sale. Solution:

Private placement deals tend to be much quicker than public sales. Since there is uncertainty about the future behavior of interest rates in the market, a firm might decide to go with private deal in order to lock in the favorable interest rates. LO: 6 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.10 Managers at a large firm are looking for a medium-size loan with a long term to maturity and low liquidity. Which of the following types of debt would be the most appropriate? a. Public bond. b. Private placement. c. Bank term loan. A large firm can have its pick of the three alternatives. A public offering of debt would be helpful to raise large amounts, but the terms of the bond contract may not be easily negotiated. Private placements have a number of advantages, relative to public offerings, for certain issuers. These include lower cost of funds, ability to negotiate changes to a bond contract, speed of private placement deals, and flexibility in issue size. Bank term loans are preferable when the loan term is short to medium term. A large firm may

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choose a bank loan only if it cannot raise funds publicly or through private placement. Bank loans offer some similar advantages as private placements. LO: 7 Level: Intermediate Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Questions and Problems BASIC 15.1

Venture capital: What items in a business plan does a venture capitalist look for in deciding whether to provide initial financing?

Solution: Every business plan should contain the following information: • A description of the business and industry trends. • Vision and key strategies for the business. • Principal products or services and any innovative features or patents. • The management team and their experience. • Market analysis and sales forecast. • How the products will be marketed and sold. • Production costs such as materials and labor. • Facilities needed and estimated costs. • Capital required and the use of the proceeds. • Detailed budget with six years of projected financial statements. LO 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Venture capital: You finally decide to act on your brilliant idea and start an online textbook rental company. You develop a detailed business plan and calculate that you will need about $350,000 of initial funding to get the business going. Luckily for you, you have lined up two venture capital firms offering to supply the funding. What criteria should guide your decision to select one firm over the other?

Solution: Criteria include in-depth knowledge of the business, industry and technology, references, chemistry, access to additional capital, networking, exit strategy, and proximity. LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 15.3

Venture capital: What are some viable exit strategies for a start-up company?

Solution: A firm can choose to either sell the business at some period, take it public, or in some instances remain a private company with few shareholders. LO 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.4

IPO: Briefly describe the IPO process.

Solution: The IPO process has three phases: origination, which is financial advising and getting the issue ready to sell; underwriting, which involves the investment banker buying the securities from the firm; and distribution, which is when the investment banker resells the securities to the public. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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IPO: Based on your knowledge from this and previous chapters, what are some methods an investment banker uses to determine an IPO price? What factors will play a significant role in the calculation?

Solution: In order to determine the price of a new security, the investment banker can look at comparable companies and see what they are trading for. Another approach is to do a discounted cash flow analysis, which is just like determining the price of a stock. You forecast future cash flows of the company, usually for a time horizon of 5 to 10 years, and discount them back to the present in order to get the firm value. The discount rate will be a factor of both the cost of debt and cost of equity (WACC). LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.6

IPO: A majority of firms choose a firm-commitment underwriting arrangement rather than a best-effort arrangement for their IPO. Explain why.

Solution: With a firm-commitment arrangement, the issuing firm is guaranteed to receive a specific amount of money from proceeds of the IPO. The underwriter bears the price risk of the issue. Price risk is the risk that the resale price to the market might be lower than that of agreed price to the issuing firm. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.7

Competitive versus negotiated sale: Why might a negotiated sale be the lowest cost means of issuing a complex debt security?

Solution: Debt issues that are complex in nature and/or issued at times of uncertainty often tend to be brought to the market by negotiated sales. This approach allows the underwriter to

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better control the uncertain situation and better explains the firm to potential investors, thereby leading to lower issue costs. LO 5 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.8

IPO pricing: Trajax, Inc., a high-technology firm in Portland, raised a total of $90 million in an IPO. The company received $27 of the $30 per share offering price. The firm’s legal fees, SEC registration fees, and other out-of-pocket costs were $450,000. The firm’s stock price increased 17 percent on the first day of trading. What was the total cost to the firm of issuing the securities?

Solution: The total costs to issue the securities are as follows: 1. Underwriting Spread: Underwriter’s spread ($30 per share - $27 per share) =$3 per share. Number of shares outstanding = ($90 million/$30 per share) = 3,000,000 shares. Underwriting cost = ($3 per share × 3,000,000 shares) = $9,000,000. 2. Out-of-Pocket Expenses: Out-of-pocket expenses are $450,000. 3. Underpricing: Stock price at end of first day = $30 per share (1.17) = $35.10 per share. First-day underpricing = ($35.10 per share - $30.00 per share) = $5.10 per share. Total underpricing = ($5.10 per share × 3,000,000 shares) = $15,300,000. Total cost to the firm of selling the IPO = $9,000,000 + $450,000 + $15,300,000 = $24,750,000 LO 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.9

IPO pricing: Myriad Biotech management plans a $114 million IPO in which the offering price to the public will be $51 per share. The company will receive $47.50 per share. The firm’s legal fees, SEC registration fees, and other out-of-pocket costs will

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total $525,000. If the stock price increases 14 percent on the first day of trading, what will be the total cost of issuing the securities? Solution: The total costs to issue the securities are as follows: 1. Underwriting Spread: Underwriter’s gross spread ($51per share - $47.50 per share) =$3.50 per share. Number of shares outstanding = ($114 million/$51 per share) = 2,235,294 shares. Underwriting cost = ($3.50 per share × 2,235,294 shares) = $7,823,529. 2. Out-of-Pocket Expenses: Out-of-pocket expenses are $525,000. 3. Underpricing: Stock price at end of first day = ($51per share × 1.14) = $58.14 First-day underpricing = ($58.14 per share - $51per share) = $7.14 per share. Total underpricing = ($7.14 per share × 2,235,294 shares) = $15,959,999. Total cost to the firm of selling the IPO = $7,823,529 + $525,000 + $15,959,999 = $24,308,528 LO 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.10 Shelf registration: Are the following statements true or false? a. Shelf registration allows firms to register an inventory of securities for an unlimited time. b. The securities can be taken off the shelf at any time within 2 years of such registration and sold to the public. c. Shelf registration reduces flotation and other expenses associated with registration. d. There is a large penalty if the authorized securities are not issued. e. A shelf registration can cover multiple securities. Solution: a. False b. True c. True d. False e. True LO 5 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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15.11 General cash offer: What are the steps in a general cash offering? Explain each of them. Solution: (1) Type of security and amount to be raised. (2) Approvals. (3) Registration statement. (4) Offer price and (5) Closing. LO 5 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 15.12 General Cash Offer: Explain the difference between a competitive and negotiated cash sale. Which method of sale is likely to yield the lowest funding cost for firms selling plain vanilla bonds in stable markets? Solution: In a competitive offer, an investment bank does the origination work for the securities to be issued and then invites underwriters to competitively bid for the issue. The investment banking firm that pays the highest price for the securities wins the bid. The winning underwriter then pays for the securities and makes them available to individual investors at the offer price. In a negotiated offer, an underwriter works with the issuing firm to both originate and sell the firm’s securities to individual investors. It is generally assumed that competitive offers yield the lowest cost of funding for firms issuing plain vanilla bonds. This is because the terms of the loans are standardized and well-known to the market participants. LO 5 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.13 Issuing securities: Explain what is meant by economies of scale in issuing securities. Solution: The economies of scale in issuing securities means that as the size of the issue increases, the total issue cost, as a percentage of the amount raised, declines. High fixed costs get spread out over a larger sum.

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LO 5 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.14 Bank term lending: Explain how term to maturity affects the price of a bank loan. Solution: Term to maturity (MAT) will essentially increase the borrowing rate. It is defined as the difference between the yield on a Treasury security with the same maturity as the term loan and the yield on 3-month Treasury bill rate. Thus, the longer the loan, the higher the borrowing rate will be. LO 7 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.15 Private placement versus public debt offering: Nalco Holding is an international company that operates in 130 countries, has a market capitalization (market value of equity) of $2.3 billion, and reported net income of $45 million on $3.3 billion in revenues last year. The company needs to raise $200 million in debt, and management is deciding between private placement and public offering. What are the advantages and disadvantages of the two alternatives, and which is likely to be the best choice? Solution: Public market allows for higher security since SEC is involved, it offers more liquidity, which might be important for a large issue, and most of the times to earn higher yield. Private placement, on the other hand, offers faster speed to market, lower issuance cost, and ease of restructuring. Given the size of the Nalco Holdings, the company should is better off choosing to raise debt in public market. LO 6 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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15.16 Prime-rate lending: Suppose two firms want to borrow money from a bank for a period of one year. Firm A has excellent credit, whereas Firm B’s credit standing is such that it would pay prime + 2 percent. The current prime rate is 6.75 percent, the 30-year Treasury bond yield is 4.35 percent, the three-month Treasury bill yield is 3.54 percent, and the 10year Treasury note yield is 4.22 percent. What are the appropriate loan rates for each firm? Solution: Firm A = Prime rate = 6.75% Firm B = Prime rate + 2% = 8.75% LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.17 Prime-rate lending: Now suppose that Firm B from Problem 15.16 decides to get a term loan for 10 years. How does this affect the company’s borrowing cost? Solution: Maturity risk premium = k10-year – kT-bill = 4.22% - 3.54% = 0.68% Borrowing rate for firm B = k = PR + DRP + MAT = 6.75% + 2% + 0.68% = 9.43% LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.18 Prime-rate lending: Cartco needs to borrow $5 million for an upgrade to its headquarters and manufacturing facility. Management has decided to borrow using a five-year term loan from its existing commercial bank. The prime rate is 3.25 percent, and Cartco’s current rating is prime + 2.48 percent. The yield on a five-year U.S. Treasury note is 2.01 percent, and the three-month U.S. Treasury bill rate is 0.09 percent. What is the estimated loan rate for the five-year bank loan? Solution:

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kl = PR + DRP + MAT MAT = y5-year - y3-mo = 2.01% – 0.09% = 1.92% PR = 3.25% DRP = 2.48% = 3.25% + 2.48% + 1.92% = 7.65% LO 7 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 15.19 Venture capital: You work for a venture capital firm and are approached to finance a new high-tech start-up. While you believe in the business idea, you also believe it is very risky. What strategies can help to mitigate the risk to your firm? Explain how these measures would work. Solution: You can fund the project in stages. This will allow you to review the project’s profitability before you commit to further financing. You may also require the entrepreneurs to invest some of their own capital in the new start-up, which will tie them to the project and make it harder for them to simply abandon the idea. LO 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.20 IPO: On August 19, 2004, Google completed its IPO of 19.6 million shares to the initial investors at $85.00 per share. The closing price of the stock that same day was $100.34. What was the dollar value of the underpricing associated with the Google IPO? Solution: With a closing price of $100.34 per share, the market value of Google shares was $1.97 billion after the issue. The shares issued at $85 yielded proceeds of $1.67 billion for Google, therefore total underpricing was $300 million. LO 4

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Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.21 IPO: Deere and Bros. is a broker that brings new issues of small firms to the public market. Its most recent deal for Dextra, Inc., had the following characteristics: Number of shares: 1,000,000 Price to public: $15 per share Proceeds to Dextra: $13,500,000 The legal fees were $150,000, printing costs were $56,000, and all the other expenses were $72,000. What is the profit or loss for Deere and Bros.? Solution: Total proceeds from offer = $15 × 1,000,000 shares = $15 million Proceeds to Dextra = $13.5 million Gross underwriting spread to Deere = $15 million - $13.5 million = $1.5 million Underwriting costs = $150,000 + 56,000 + $72,000 = $278,000 Net profit to underwriter = $1,500,000 - $278,000 = $1,222,000 LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.22 IPO: When Global Partners went public in September 2013, the offer price was $22.00 per share and the closing price at the end of the first day was $23.90. The firm issued 4.9 million shares. What was the loss to the company due to underpricing? Solution: Change in price on first day = $23.90 - $22.00 = $1.90 Number of shares outstanding = 4.9 million Loss due to underpricing = $1.90 × 4,900,000 = $9,310,000 LO 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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15.23 IPO: Bellex Technologies agreed to complete its IPO on a best-effort basis. The company’s investment bank demanded a spread of 17 percent of the offer price, which was set at $30 per share. Three million shares were issued; however, the bank’s management was overly optimistic and eventually was able to sell all of the stock for only $28 per share. What were the proceeds for the issuer and the underwriter? Solution: Gross proceeds from offer = $30.00 × 3,000,000 = $90,000,000 Underwriting spread = $90,000,000 × 0.17 = $15,300,000 Proceeds to issuer = ($28 × 3,000,000) − $15,300,000 = $68,700,000 LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.24 IPO: Suppose a biotech company in Boston, Massachusetts, completes an $85 million IPO priced to the public at $75 per share. The firm receives $72 per share, and the out-ofpocket expenses are $340,000. The stock’s closing price at the end of the first day is $84. What is the total cost to the firm of issuing the securities? Solution: The total cost to issue the securities is calculated as follows: Underwriter’s spread = $75 per share – $72 per share = $3 per share No. of shares outstanding = $85,000,000 / $75 = 1,133,333 shares Underwriting cost = $3 per share × 1,133,333 = $3,399,999 First-day underpricing per share = $84 – $75 = $9.00 Total underpricing on day 1 = $9.00 × 1,133,333 shares = $10,199,997 Total cost to the firm = $10,199,997 + $3,399,999 + $340,000 = $13,939,996 LO 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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15.25 IPO: An online medical advice company just completed an IPO with an investment bank on a firm-commitment basis. The firm issued five million shares of common stock, and the underwriting fees were $1.90 per share. The offering price was $26 per share. a. What were the total proceeds from the common-stock sale? b. How much money did the company receive? c. How much money did the investment bank receive in fees? Solution: a. Total proceeds from issue = $26.00 per share × 5,000,000 = $130,000,000 b. Net proceeds to firm = ($26 per share - $1.90 per share) x 5,000,000 = $120,500,000 c. Underwriting spread = $1.90 per share x 5,000,000 = $9,500,000 LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.26 IPO underpricing: Suppose that a biotech firm in Pittsburgh raised $120 million in an IPO. The firm received $23 per share, and the stock sold to the public for $25 per share. The firm’s legal fees, SEC registration fees, and other out-of-pocket costs were $270,000. The firm’s stock price increased 17.5 percent on the first day. What was the total cost to the firm of issuing the securities? Solution: The total cost to issue the securities is calculated as follows: a. Underwriting Cost: Underwriter’s spread = $25per share - $23 per share = $2 per share No. of shares outstanding = $120,000,000 / $25 = 4,800,000 shares Underwriting cost = $2 × 4,800,000 = $9,600,000 b. Underpricing: Price of stock at end of first day = $25 per share × (1.175) = $29.375 Underpricing per share = $29.375 - $25 = $4.375 Total underpricing on day 1= $4.375 × 4,800,000 = $21,000,000 Total cost to the firm= $21,000,000 + $9,600,000 + $270,000 = $30,870,000 LO 4 Bloomcode: Application AASCP: Analytic

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IMA: Corporate Finance AICPA: Industry/Sector Perspective

13.27 Long-term corporate debt: The 20-year Treasury rate is 4.67 percent, and a firm’s credit rating is BB. Suppose management of the firm decides to raise $20 million by selling 20-year bonds. Management determines that since it has plenty of experience, it will not need to hire an investment banker. At present, 20-year BB bonds are selling for 185 basis points above the 20-year Treasury rate, and it is forecast that interest rates will not stay this low for long. What is the cost of borrowing? What role does timing play in this situation? Solution: Cost of borrowing = 4.67% + 1.85% = 6.52% Cost of borrowing is 6.52 percent. Since the economy is supposed to improve, the interest rates are expected to go up in the near future, which could make the cost of borrowing more expensive. Time is of essence in this case. LO 5 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Sample Test Problems

15.1

Why are traditional sources of funding not usually available for new or emerging businesses? (LO 2)

Solution: There are three reasons such businesses often have little or no access to traditional funding: 1) The high degree of risk associated with them. 2) Their primary assets are often intangible assets that are not as well understood by lenders or other potential investors as tangible assets

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3) Potential investors often have limited knowledge of highly specialized technologies or new business areas and therefore find it difficult to assess the quality of their management teams or their prospects. Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.2

A firm is making an initial public offering. The investment bankers agree to a firm underwriting commitment for 500,000 shares that would be priced to the public at $36 a share. The underwriter’s spread is 7 percent. What were the proceeds for the issuer and the underwriter? (LO 3)

Solution:

Gross proceeds from offer = $36 × 500,000 = $18,000,000 Underwriting spread = Proceeds to Underwriter = $18,000,000 × 0.07 = $1,260,000 Proceeds to issuer = ($36 × 500,000) − $1,260,000 = $16,740,000 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.3

Hilton Worldwide Holdings Inc. completed an initial public offering on December 12, 2013. The offer price was $20.00 per share and the closing price at the end of the first day was $21.50. The firm issued

117.6 million shares. What was the loss to Hilton due to underpricing? Who received this value? (LO 4)

Solution:

Change in price on first day of trading = $21.50 - $20.00 = $1.50 Number of shares outstanding = 117.6 million Loss due to underpricing = $1.50 × 117.6 million = $176.4 million

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The initial investor, who purchased the shares allocated by the underwriters of the IPO received this value. Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

15.4

SMA Inc. is considering issuing the following securities. For which security would a competitive sale be less costly than a negotiated sale under stable market conditions? Why? (LO 5) a) Plain vanilla bonds. b) IPO of common stock. c) Secondary offering of common stock. d) Convertible bonds.

Solution:

a) Plain vanilla bonds. A competitive sale will be the least costly for bonds with standardized features in a stable market. In a stable market investors better understand the risks associated with these securities and are more comfortable purchasing them. The other three securities are more complex and these complexities are better handled through negotiated sales in which the underwriter can address investor uncertainty concerning the securities and better explain the firm’s situation. This will result in a lower funding cost for complex securities.

Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Management of Southern Parts Company has decided to sell 10-year bonds to finance expansion into the Pacific Northwest. The loan rate on these bonds is 8 percent and the 3month Treasury bill rate is 2.1 percent. The firm’s credit rating is B, and the yield on 10year Treasury bonds is 2.5 percent higher than that on 3-month Treasury bills. How much of a premium over the 10-year Treasury bond are these Southern Parts bonds selling for? (LO 7)

Solution:

kl = PR + DRP + MAT 8.0% = 2.1% + DRP + 2.5% DRP = 3.4% Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Chapter 16 Capital Structure Policy Before You Go On Questions and Answers Section 16.1 1.

What is the optimal capital structure for a firm? The optimal capital structure for a firm is the combination of debt and equity financing, which minimizes the overall cost of financing the firm’s real activities (projects). Minimizing the overall cost of financing a firm’s real activities maximizes the value of its cash flows.

What is M&M Proposition 1? M&M Proposition 2? Modigliani-Miller Proposition 1: The capital structure of a firm does not affect the firm’s value if the following three assumptions hold: a. There are no taxes. b. There are no information or transaction costs. c. A firm’s capital structure does not affect the firm’s real investment policy. Modigliani-Miller Proposition 2: The required rate of return on a firm’s equity (cost of equity) increases as the firm’s debt-to-equity ratio increases.

What is the difference between business risk and financial risk? Business risk reflects the uncertainty associated with the underlying assets of the firm. The level of business risk is reflected in the required rate of return associated with these assets. Financial risk represents the uncertainty that fixed debt payments introduce to the cash flows to the stockholders. The total risk faced by stockholders is affected by both the business risk of the firm and its financial risk.

How can the three conditions specified by M&M help us understand how the capital structure of a firm affects its value? M&M identify the three conditions under which the capital structure of a firm would not affect its value. By examining the three conditions specified by M&M, and how they are

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violated in the real world, we can better understand why capital structure does affect firm value.

Section 16.2 1.

What are some benefits of using debt financing? The benefits of using debt financing are: • The interest tax shield (interest is tax deductable, dividends are not). • The cost of issuing debt (underwriting spreads and out-of-pocket costs) are lower than the cost of issuing equity. • With more debt, managers have greater incentives to work hard to produce larger cash flows and thus avoid bankruptcy. • Increased debt limits the manager’s flexibility to spend money on wasteful, negative NPV projects.

What are bankruptcy costs, and what are the two types of bankruptcy costs? Bankruptcy costs are costs that firms face when they are in financial distress. Direct bankruptcy costs are out-of-pocket costs, such as the payments that are made to lawyers, accountants, and consultants, as well as court costs, when a firm gets into financial distress. Indirect bankruptcy costs result from changes in the behavior of the people that contract with the firm when they learn that it is in distress. For example, there may be less demand for a distressed firm’s product because of the concern that the firm will not exist to provide customer support in the future or suppliers might demand cash on delivery out of concern that the firm will not be able to pay for supplies.

What are agency costs, and how are they related to the use of debt financing? Agency costs are costs that are incurred when someone delegates decision-making authority to someone who has different objectives. Agency costs might arise in relationships between stockholders and the managers they hire because managers do not have the same incentives as stockholders. For example, when a firm has debt, managers can have incentives to invest in low-risk projects that do not maximize stockholder value. Agency costs also arise between stockholders and debt holders. Stockholders, through the managers they hire, can have incentives to engage in asset substitution, turn down positive-NPV projects (underinvestment), or pay out excess cash in the form of dividends.

Section 16.3 1.

What is the trade-off theory of capital structure?

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The trade-off theory of capital structure postulates that managers set a specific target for the capital structure of a firm in which they try to achieve the mix of debt and equity that will minimize the cost of financing the firm’s projects and thereby maximize its value. 2.

What is the pecking order theory of capital structure? The pecking order theory says that, instead of trying to achieve a specified target capital structure, firms use the cheapest form of capital available at any given time, until it is used up. According to this theory, the cost of capital from least expensive to most expensive is: 1. Internally generated funds 2. Debt issue 3. Equity issue

What does the empirical evidence tell us about the two theories? The empirical evidence provides some support for both theories. Studies find that industries with significant tangible assets tend to have more debt. This is consistent with the trade-off theory. These companies can generally borrow at a lower rate using their tangible assets as collateral. There is also evidence that more profitable firms hold less debt. This is consistent with the pecking order theory. These companies are capable of financing more projects with internal funds before taking on debt. The trade-off theory would suggest that more profitable companies should carry more debt, because they have more to benefit from the tax shelter of interest payments.

Section 16.4 1.

Why is financial flexibility important in the choice of a capital structure? The choice of capital structure may limit the ability of managers to take advantage of unexpected opportunities or to deal appropriately with unexpected problems. For example, suppose the firm learns of a positive-NPV project that is available for only a short period of time. If the firm already holds significant amounts of debt, lenders may be unwilling to loan more money to the firm. Raising funds though issuing equity is often a slow process, and the window of opportunity to accept the project may have passed. A firm that holds cash or can quickly issue debt (e.g., through a line of credit) has more flexibility in financing new projects.

How can capital structure decisions affect the risk associated with net income?

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The more debt a firm carries, the more risk will be associated with the firm’s net income. This occurs because given a certain level of fluctuating operating income, a larger fixed debt payments will magnify the effects of the fluctuations on net income. 3.

How can capital structure decisions affect the control of a firm? Issuing new equity reduces the control of the firm’s existing stockholders (assuming the existing stockholders do not purchase the new issues). In some cases firms may issue debt rather than equity to prevent the control of existing stockholders from being diluted. For example, if a firm is 51 percent owned by the founders, the founders may require the company to issue debt rather than equity to finance a new project. This will prevent the founder’s ownership from falling to less than 50 percent.

Appendix A16 1.

What is a lease? What are the two types of leases? A lease is an alternative way of financing the acquisition of an asset. In a lease agreement the lessee pays for the right to use the asset during the term of the lease while the lessor, who owns the asset, receives the lease payments in return for giving up the right to use the asset during the term of the lease. The lessor retains the right to use the asset after the term of the lease. The two types of leases that the IRS recognizes are: (1) leases which are truly rentals called operating leases, and (2) leases that have the key elements of an outright sale, known as capital leases.

What is the primary motivation for leasing? The primary motivation for leasing an asset is that leasing is a less expensive way of obtaining the use of an asset for a period of time than purchasing the asset.

What types of conflicts arise with leases and why? The two conflicts that arise with leases are the (1) intensity of use and (2) maintenance conflicts. These conflicts arise because a lease separates the right to use an asset during the term of a lease from the right to use the asset afterwards. Since two different parties own these rights (the lessee and the lessor) conflicts of interest are bound to arise.

Self Study Problems

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If any of the three assumptions in Modigliani and Miller Proposition 1 are relaxed, which has the most predictably quantifiable impact on the value of the firm?

Solution: The assumption with the most measurable impact is that involving taxes. We can calculate the present value of the tax shield generated by the interest costs of borrowing. The impacts of the other two assumptions, though real, are more difficult to predict.

16.2

If we assume that the cash flows for a firm with financial leverage are equal to the cash flows for the same firm without financial leverage, what can we say about the value of this firm if its cost of capital also does not vary with the degree of leverage utilized?

Solution: If the firm’s cash flows and cost of capital are the same, regardless of the amount of leverage utilized, then we can say that the value of the firm is also unchanged by the amount of financial leverage.

16.3

Are taxes necessary for the cost of debt financing to be less than the cost of equity financing?

Solution: The deduction for interest expense does make debt borrowing more attractive than it would otherwise be. However, even without the interest deduction benefit, the cost of debt is less than the cost of equity, because equity is a riskier investment than debt. This means that the pretax cost to the firm for debt is still lower than the cost of equity.

16.4

You are offered jobs with identical responsibilities by two different firms in the same industry. One has no debt in its capital structure, and the other has 99 percent debt in its capital structure. Will you require a higher level of compensation from one firm than from the other? If so, which firm will have to pay you more?

Solution: The firm with the large amount of debt financing (the 99 percent debt firm) has a higher probability of becoming financially distressed. Therefore, you should require greater compensation from that firm because your income is less certain and working at that firm poses a greater risk to your career..

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You are valuing two otherwise identical firms in the same industry. One firm has a corporate jet for every executive at the vice president level and above, while the other does not have a single corporate jet. More than likely, which firm has the greatest stockholder-manager agency costs?

Solution: While corporate jets can make economic sense because they enable managers to use their time more efficiently, one jet per vice president is certainly not cost effective. The multijet firm has higher stockholder-manager agency costs than the no-jet fi rm. It is spending too much on jets. The cash that is being spent on excess jets could be invested in positive NPV projects or returned to the firm’s stockholders.

Discussion Critical Thinking Questions 16.1

List and briefly describe the three key assumptions in Modigliani and Miller’s Proposition 1 that are required for total firm value to be independent of capital structure. 1. There are no taxes. This assumption is necessary in order to avoid creating a tax benefit when using debt instead of equity to finance firm assets. 2. There are no information or transactions costs for the firm. a. There are no bankruptcy costs (financial distress) to the firm associated with increased supplier, employee, and customer expenses, due to the firm having a higher likelihood of not being able to meet its debt obligations. Note that one interpretation of this assumption is that, the firm has a zero probability of not being able to meet its debt obligations. b. There are no agency costs. There are no costs associated with the conflict of interest between managers and stockholders, and there are no costs associated with the conflict between the interest between stockholders and debt holders of the firm. c. There are no market frictions. This means that individuals may borrow and lend at the same rate that the firm can borrow and lend. 3. The real investment policy of the firm is not affected by its capital structure. decisions. Without this, the assumption that an individual investor could replicate the actions of the firm, does not hold because the actual investment policy of the firm would be affected by the capital structure decision. Investors cannot replicate real investments.

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Level: Basic Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.2

Evaluate the statement that the weighted average cost of capital (WACC) for a firm (assuming that all three assumptions of Modigliani and Miller’s propositions hold) is always less than or equal to the cost of equity for the firm. If we look at the following WACC formula for a firm (without taxes): WACC = [Vcs/(VDebt+Vcs)] × kcs + [VDebt/(VDebt+Vcs )] × kDebt We see that with 100 percent equity financing, the WACC = kcs. A firm cannot be 100 percent debt-financed, even so as D/V approaches 1, then the WACC approaches kDebt. Since we know that debt is less risky than equity, we know that the WACC in that instance, must be greater than kDebt but less than kcs. Therefore, the WACC must be greater than kDebt but less than or equal to kcs .

LO: 1 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.3

If the value of the firm remains constant as a function of its capital structure and the three Modigliani and Miller assumptions apply, why might the overall cost of capital change or not change as capital structure changes? If the cash flow produced by a firm is unchanged, and the value of the firm producing that cash flow is unchanged by a firm’s capital structure changes, we can use a perpetual cash flow valuation model as follows: VFirm = CF/i If we know that VFirm and CF are unchanged due to capital structure changes; then kAssets must also remain unchanged.

LO: 1 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Consider the WACC for a firm that pays taxes. Explain what a firm’s best course of action would be to minimize its WACC and thereby maximize the firm value. Use the WACC formula for your explanation. WACC = (1 – t) × kDebt × [VDebt/(VDebt+Vcs)] + kcs × [Vcs/(VDebt+Vcs)] If kcs > kDebt, then it would make sense to increase debt relative to equity, in order to raise as much financing as possible with borrowing, rather than the more expensive equity. Therefore, by blindly following the WACC formula, we are led to believe that more debt will increase the value of the firm from its current valuation. This highlights the effect of taxes without taking into account the other M&M assumptions.

LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.5

The Modigliani and Miller propositions, when the no-tax assumption is relaxed, suggest that the firm should finance itself with as much debt as possible. Taking this suggestion to the extreme, is it even possible to finance a firm with 100 percent debt and no equity? Why or why not? Even with the list of assumptions required to get this result, a 100 percent debt firm is not practical. While we might think that there is no residual claimant for the firm’s cash flows, even this is not true. In fact, a 100 percent debt-financed firm is really a 100 percent equity-financed firm since the debt holders themselves must then be the residual claimants.

LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.6

Crossler Automobiles sells autos in a market where the standard auto comes with a 10-year/100,000-mile warranty on all parts and labor. Describe how an increased probability of bankruptcy could affect sales of autos by Crossler. In a market, where a warranty is a significant portion of the cost of an automobile, purchasing a car where the seller might not be able to completely perform on that

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warranty,due to increased probability of bankruptcy of Crossler, would have negative impact on the firm’s future automobile sales. This would decrease the amount of cash flow available to the investors of the firm, which would lower the value of the firm. LO: 2 Level: Basic Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.7

Agency problems occur because the nonowner managers and stockholders of a firm have different interests. Propose a capital structure change that might help better align these different interests. The managers of a firm would rather work as little as possible, given a set level of compensation, whereas stockholders would rather compensate the manager for a high level of effort, with a low effort receiving very little compensation. Increasing the proportion of debt in the capital structure would increase the probability of the firm falling into bankruptcy. This increased probability of bankruptcy, and therefore the increased chance that the manager will lose his job, would then help to align the interests of the manager and stockholders by giving the manager an additional incentive to work harder for the stockholders.

LO: 2 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.8

If a firm increases its debt to a very high level, then the positive effect of debt in aligning the interests of management with those of stockholders tends to become negative. Explain why this occurs. Increasing the debt level for a firm tends to catch management’s attention and force the managers to work harder; therefore, a very high level of debt can be detrimental. That is, at very high levels of debt, risk-averse managers begin to minimize the risks that a firm takes on, for the managers’ own job preservation needs. This risk minimization can deter managers from taking risky, but positive-NPV projects, which are needed to help the firm meet the very debt obligations that are causing the problem. In addition, the financially risky firm may also bear costs not previously borne in relationships with employees, suppliers, and customers.

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LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.9

Using the Modigliani and Miller framework but excluding the assumptions that there are no taxes and no information or transaction costs, describe the value of the firm as a function of the proportion of debt in its capital structure. With taxes included, we would predict that the firm would take on greater proportions of debt. Agency costs (part of the information and transactions cost) are actually reduced when adding moderate portions of debt. This would also predict that the firm value increases as we add moderate levels of debt to the firm. However, agency costs once again become positive (in total) as very high levels of debt are incurred. This suggests that at very high levels of debt the value of the firm could be dropping. Bankruptcy costs (which are also part of the information and transactions cost) are probably immaterial at low debt levels, but can become very high at higher levels of debt. Therefore, we should predict that by including dropping the three assumptions in the question, the value of the firm should be increase with additional debt for moderate debt levels while decreasing for high levels of debt.

LO: 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.10 When we observe the capital structure of many firms, we find that they tend to utilize lower levels of debt than that predicted by the trade-off theory. Offer an explanation for this.

This empirical result is consistent with a firm maintaining a reserve level of debt or high cash levels in order to have ample internally generated funds for new projects. One explanation would be that, firms like to have this “reserve” financing available for new projects when they are identified. Another explanation is that, firms do not have to offer an explanation to the new investors for the use of these funds and that makes it less expensive on an information basis to keep this reserve, compared to having to issue new

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securities for the financing of the new projects. Both of these explanations are in line with the pecking order theory. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Questions and Problems BASIC 16.1

M&M Proposition 1: The Modigliani and Miller theory suggests that the value of the firm’s assets is equal to the value of the claims on those assets and is not dependent on how the asset claims are divided. The common analogy to the theorem is that the total amount of pie available to be eaten (the firm) does not depend on the size of each slice of pie. If we continue with that analogy, then what if we cut up the pie with a very dull knife such that the total amount of pie available to be eaten is less after it is cut than before it was cut. Which of the three Modigliani and Miller assumptions, if relaxed, is analogous to the dull knife? Hint: Think about the process by which investors could undo the effects of a firm’s capital structure decisions.

Solution: The inability of individual investors to borrow and lend and at the same rate as firms, is analogous to the dull knife. This friction is part of the no information or transactions costs assumption. Since the process of rearranging the claims on the firm’s assets is similar to carving up the firm into different pieces, it is easy to see that such a market friction is similar to the dull knife in our pie example. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.2

M&M Proposition 1: Describe what exactly is meant when someone is describing the value of the firm versus the value of the equity of the firm.

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The value of the firm can be described as either the total market value of all the assets owned by the firm, or the total market value of all the claims of all the investors in the firm. In that case, it means that we are valuing all of the equity claims (shares) in the firm in addition to all of the debt claims (bonds, bank borrowing, etc.) of the firm. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.3

M&M Proposition 1: Under Modigliani and Miller’s Proposition 1, where all three of the assumptions remain in effect, explain how the value of the firm changes due to changes in the proportion of debt and equity utilized by the firm.

Solution: Under Modigliani and Miller’s Proposition 1, the value of the firm is independent of the proportion of debt and equity utilized by the firm. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.4

M&M Proposition 1: Cerberus Security Company produces a cash flow of $200 per year and is expected to continue doing so in the infinite future. The cost of equity capital for Cerberus is 20 percent, and the firm is financed entirely with equity. Management would like to repurchase $100 in shares by borrowing $100 at a 10 percent rate (assume that the debt will also be outstanding into the infinite future). Using Modigliani and Miller’s Proposition 1, what is the value of the firm today, and what will be the value of the claims on the firm’s assets after the stock repurchase? What will be the rate of return on common stock required by investors after the share repurchase?

Solution: Using the 20 percent cost of equity capital, the value of the firm today is $200/0.2 = $1,000, keeping in mind that the cash flow is expected to be produced into the infinite future. Note that, using M&M Proposition 1, this must be the value of the firm after the repurchase. The value of the debt claim must be $100 at the time of the borrowing, so we know that the value of the outstanding equity after the repurchase must be $1,000 – $100

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= $900. Since $10 in cash flow must be paid to the debt holders each year, $190 will be available to the stockholders on an annual basis. This implies that the new cost of equity capital for the firm must be such that $900 = $190 / kcs, or kcs = 21.11%. LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.5

M&M Proposition 1: A firm that is financed completely with equity currently has a cost of capital equal to 15 percent. If Modigliani and Miller’s Proposition 1 holds and the firm’s management is thinking about changing its capital structure to 50 percent debt and 50 percent equity, then what will be the cost of equity after the change if the cost of debt is 10 percent?

Solution: It is easy to see that the current cost of capital (also the cost of equity in this case) is 15 percent. Given the proposition, we know that the cost of capital (or WACC) for the firm must be constant at 15 percent. If we know that the firm can borrow at a 10 percent cost of capital, with a 50–50 percent debt-equity mix, then we can use the WACC formula to solve for the new cost of equity capital as follows:

WACC = xDebt kDebt + xcs kcs 0.15 = 0.5 × (0.10) + 0.5 × (kcs) kcs = 0.20, or 20% LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 16.6

M&M Proposition 1: Swan Specialty Cycles is currently financed with 50 percent debt and 50 percent equity. The firm pays $125 each year to its debt investors (at a 10 percent cost of debt), and the debt has no maturity date. What will be the value of the equity if the firm repurchases all of its debt and raises the funds to do this by issuing equity? Assume that all of the assumptions in Modigliani and Miller’s Proposition 1 hold.

Solution: Since the debt has no maturity date, we can find the value of the current debt claims: Value = $125 / 0.10 = $1,250. Since debt is 50 percent of the capital structure, then the

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value of the entire firm must be 2 x Value of debt = $2,500, which must be the value of the equity in an all-equity firm. LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.7

M&M Proposition 1: The weighted average cost of capital for a firm, assuming all three Modigliani and Miller assumptions hold, is 10 percent. What is the current cost of equity capital for the firm if the cost of debt for the firm is 8 percent, and the firm is 80 percent financed with debt?

Solution: Using the formula given in the text: kcs = kAssets + (VDebt /Vcs) x (kAssets – kDebt) kcs = 0.10 + (0.8 / 0.2) × (0.10 – 0.08) = 0.18, or 18% LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.8

Interest tax shield benefit: Legitron Corporation has $350 million of debt outstanding at an interest rate of 9 percent. What is the dollar value of the tax shield on that debt, just for this year, if Legitron is subject to a 35 percent marginal tax rate?

Solution: Legitron will pay $31,500,000 ($350,000,000 × 0.09) in interest this year, which will shield Legitron from paying a tax amount equal to: VTax-savings debt = D × t = ($31,500,000 × 0.35) = $11,025,000 Therefore, the amount of this year’s tax shield, due to debt issuance, for Legitron is $11,025,000. LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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Interest tax shield benefit: FAJ, Inc. has $500 million of debt outstanding at an interest rate of 9 percent. What is the present value of the tax shield on that debt if it has no maturity and if FAJ is subject to a 30 percent marginal tax rate?

Solution: The present value of FAJ’s tax shield is: t × D = 0.30 x $500,000,000 = $150,000,000 An alternative calculation would be: (t × D × kDebt ) / kDebt = (0.30 × $500,000,000 × 0.09) / 0.09 = $150,000,000 LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.10 Interest tax shield benefit: Springer Corp. has $250 million of debt outstanding at an interest rate of 11 percent. What is the present value of the debt tax shield if the debt has no maturity and if Springer is subject to a 40 percent marginal tax rate? Solution: The present value of Springer’s tax shield is: t × D = 0.40 × $250,000,000 = $100,000,000 LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.11 Interest tax shield benefit: Structural Corp. currently has an equity cost of capital equal to 15 percent. If the Modigliani and Miller Proposition 1 assumptions hold, with the exception of the assumption that there are no taxes, and the firm’s capital structure is made up of 50 percent debt and 50 percent equity, what is the weighted average cost of capital for the firm if the cost of debt is 10 percent and the firm is subject to a 40 percent marginal tax rate? Solution:

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WACC = xDebt kDebt + xcs kcs = (0.5) × (0.10) × (1-0.4) + 0.5 × (0.15) = 0.105, or 10.5% LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.12 Practical considerations in capital structure choice: List and describe three practical considerations that concern managers when they make capital structure decisions. Solution: 1.

2. 3.

Financial flexibility: Managers must minimize the firm’s cost of capital while also ensuring that the firm has the flexibility to raise new capital quickly to deal with unexpected problems or to take advantage of unexpected opportunities. Net income risk: Increasing the leverage of a firm increases the risk associated with firm’s net income, and the risk of default. Earnings impact: When a project is financed with debt, the interest payments reduce the accounting dollar value of net income. However, when debt is used, no new shares of equity are issued, so the company’s earnings per share would be expected to increase (given a positive NPV project). Although financial theory suggests that neither of these effects should matter, managers often take them into account when making financing decisions.

LO 4 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 16.13 M&M Proposition 1: Keyboard Chiropractic Clinics produces $300,000 of cash flow each year. The firm has no debt outstanding, and its cost of equity capital is 25 percent. The firm’s management would like to repurchase $600,000 of its equity by borrowing a similar amount at a rate of 8 percent per year. If we assume that the debt will be perpetual, find the cost of equity capital for Keyboard after it changes its capital structure. Assume that Modigliani and Miller Proposition 1 holds. Copyright © 2015 John Wiley & Sons, Inc.

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Solution: Using the 25 percent cost of equity capital, the value of the firm today is $300,000/0.25 = $1,200,000 This must be the value of the firm after the repurchase. The value of the debt claim must be $600,000 at the time of the borrowing, so the value of the outstanding equity after the repurchase must be $1,200,000 – $600,000 = $600,000 Since $48,000 ($600,000 × 0.08) in cash flow must be paid to the debt holders each year, $252,000 ($300,000 – $48,000) will be available to the stockholders on an annual basis. This implies that the new cost of equity capital for the firm must be such that $600,000 = $252,000 / kcs, or kcs = 0.42, or 42.00% LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.14 M&M Proposition 1: Marx and Spender Corp. currently has a WACC of 21 percent. If the cost of debt capital for the firm is 12 percent and the firm is currently financed with 25 percent debt, then what is the current cost of equity capital for the firm? Assume that the assumptions in Modigliani and Miller’s Proposition 1 hold. Solution: Using the WACC formula we can solve for the cost of equity capital for the firm:

WACC = xDebt kDebt + xcs kcs 0.21 = 0.25 × (0.12) + 0.75(kcs) kcs = 0.24, or 24% Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.15 M&M Proposition 1: What is the effect on Modigliani and Miller’s Proposition 1 of relaxing the assumption that there are no information or transaction costs? Solution:

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No information or transaction costs means, for example, that individuals may borrow and lend at the same rate that the firm can borrow and lend. If an investor were unable to sell (or buy) shares by investing (or borrowing) without transaction costs, then some of the value conserved in the Modigliani and Miller arguments through personal trading would be dissipated by transaction costs. This dissipation would then negate the conservation of value proposed by M&M. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.16 M&M Proposition 1: The weighted average cost of capital for a firm (assuming all three Modigliani and Miller assumptions apply) is 15 percent. What is the current cost of equity capital for the firm if its cost of debt is 10 percent and the proportion of debt to total firm value for the firm is 0.5? Solution: Since VDebt /VFirm = 0.5, VDebt /Vcs = 0.5 / 0.5 = 1 Using the formula given in the text, kcs = kAssets + (VDebt /Vcs) × (kAssets – kDebt) = 0.15 + (1) × (0.15 – 0.10) = 0.2, or 20% LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.17 M&M Proposition 2: Mikos Processed Foods is currently valued at $500 million. Mikos will be repurchasing $100 million of its equity by issuing a nonmaturing debt issue at a 10 percent annual interest rate. Mikos is subject to a 30 percent marginal tax rate. If all of the Modigliani and Miller assumptions apply, except the assumption that there are no taxes, what will be the value of Mikos after the recapitalization? Solution: Mikos will be worth $500,000,000 plus the present value of the tax shield. The present value of the tax shield is $100,000,000 × 0.3 = $30,000,000.

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Therefore, Mikos will be worth $530,000,000 after the recapitalization. Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.18 M&M Proposition 2: Backwards Resources Company has a WACC of 12.6 percent, and it is subject to a 40 percent marginal tax rate. Backwards has $250 million of debt outstanding at an interest rate of 9 percent and $750 million of equity (at market value) outstanding. What is the expected return on the equity with this capital structure? Solution: Using the WACC formula when taxes are included: WACC = (1-t) × kDebt × (VDebt/VFirm) + kcs × (Vcs/VFirm) We can solve for the missing variable: 0.126 = (1-0.4) × 0.09 × [250 million / (250 million + 750 million)] + kcs × (750 million/ [250 million + 750 million]) kcs = 0.15, or 15% LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.19 The costs of debt: Briefly discuss costs of financial distress to a firm that may arise when employees believe it is highly likely that the firm will declare bankruptcy. Solution: If the employees of a firm understand that the firm has a significant chance of filing for bankruptcy, then costs to the firm could be manifested in a number of ways, including: 1. Lower productivity due to lower morale and job hunting. This could be as simple as employees spending time gossiping about what is going to happen to them as well as employees actively pursuing other jobs while on the payroll of the troubled firm. 2. Higher recruiting costs. Understanding that working for the firm is a risky venture, new employees will seek compensation for this additional risk. Therefore, recruiting employees will become more expensive due to greater recruiting efforts as well as greater compensation expense when a new employee is finally located and hired. LO 2

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Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.20 The costs of debt: Santa’s Shoes is a retailer that has just begun having financial difficulty. Santa’s suppliers are aware of the increased possibility of bankruptcy. What might Santa’s suppliers do based on this information? Solution: Santa’s Shoes is not certain to go into bankruptcy, so its suppliers would still like to do business with Santa’s Shoes as long as it is profitable to do so. Therefore, the suppliers would still make sales to Santa’s Shoes as long as payment for the sales was made at the time of purchase rather than on credit. This would require Santa’s Shoes to maintain a higher cash balance. This requirement to hold additional cash could be viewed as a cost of financial distress to Santa’s Shoes. LO 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.21 Stockholder-manager agency costs: Deficit Corp. management has determined that they will be $50 million short of being able to pay the firm’s debt obligations at the end of this year. Management has identified a positive NPV project that will require a great deal of effort on their part. However, this project is expected to generate only $40 million at the end of the year. Assume that all the members of Deficit’s management team will lose their jobs if the firm goes into bankruptcy at the end of the year. How likely is management to take the positive NPV project? If management declines the project, what kind of cost will Deficit’s stockholders incur? Solution: Managers expect to lose their jobs in one year whether they work hard or not and take the project or not. Although, there may be a slim chance that the firm will not declare bankruptcy, management has no incentive to take on the difficult project. This makes the shortage to the debt holders, as well as the stockholders, greater than it would be if the firm followed the rule of always accepting positive NPV projects. This is another example of agency costs that can arise from financial distress.

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LO 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.22 Two theories of capital structure: Use the information in the following table to make a suggestion concerning the proportion of debt that the firm should utilize in its capital structure. Benefit or (Cost) No Debt Tax shield $0 Agency cost −$10 Financial distress cost −$ 1

25% Debt $10 −$ 5 −$ 3

50% Debt $20 −$ 5 −$10

75% Debt $30 −$20 −$10

Solution: By totaling the cost and benefits for each proportion of debt we find: Benefit or (Cost) Total cost/benefit

No Debt -$11

25% Debt $2

50% Debt $5

75% Debt $0

Therefore, this firm can maximize firm value by choosing a 50 percent debt capital structure. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.23 Two theories of capital structure: Problem 16.22 introduces taxes and information and transaction costs to the simplified Modigliani and Miller model. If the marginal tax rate for the firm were to suddenly increase by a material amount, would the capital structure that maximizes the firm’s value include less or more debt? Solution: If we hold all others things equal, then the value of the tax shield would become more valuable in the scenarios with positive debt amounts. While we cannot say for certain,

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given the information in the question, an increase in the tax rate will increase the value of the tax shield and should increase the amount of debt in the optimal capital structure. Therefore, it would appear that an increase in the tax rate should motivate firms to increase their debt levels. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.24 Two theories of capital structure: Describe the order of financial sources for managers who subscribe to the pecking order theory of financing. Evaluate that order by observing the costs of each source relative to the costs of other sources. Solution: According to the pecking order theory, the costs, from lowest to highest, are: 1. Internally generated funds (this is essentially retained earnings)—This will actually be the cheapest source in this list. 2. New issue debt—This will be the costlier than internally generated funds cheapest, but relatively inexpensive but relatively inexpensive costlier than internally generated funds, but relatively inexpensive source in this list. 3. New issue equity—This will be the most expensive source in this list. It appears that the managers who subscribe to the pecking order theory, choose the cheapest sources of financing before moving on to more expensive sources. Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.25 Two theories of capital structure: The pecking order theory suggests that managers prefer to first use internally generated equity to finance new projects. Does this preference mean that these funds represent an even cheaper source of funds than debt? Justify your answer. Solution: The internally generated equity is utilized first as a source of financing, but it does not mean that the internally generated funds are cheaper than debt. Internally generated funds belong to stockholders and, therefore, are really equity financing, which is more

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expensive than debt. However, using internally generated funds enables the firm to avoid the costs associated with borrowing or selling stock (including the costs associated with the signals that financing announcements send investors), which, in turn, can make internal funds most attractive. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.26 The costs of debt: Discuss how the legal costs of financial distress may increase with the probability that a firm will formally declare bankruptcy, even if the firm has not reached that point yet. Solution: If a firm is anticipating bankruptcy to a greater extent, then it will increase its legal efforts to protect the firm from creditors or if the firm reaches that point. Therefore, the legal costs of bankruptcy will increase with financial distress even if the firm has not yet declared bankruptcy. LO 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED 16.27 Operating a firm without debt is generally considered to be a conservative practice. Discuss how such a conservative approach to a firm’s capital structure is good or bad for the value of the firm in the absence of information or transaction costs and any effect of debt on the real investment policy of the firm. Solution: In the absence of information or transaction costs and any effect of debt on the real investment policy of the firm, value of the firm is increasing in proportion to debt in the firm’s capital structure, due to the present value of the tax shield on the debt. Therefore,

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although operating without debt may be a safer play for investors, it does not maximize stockholder value, which should be the goal of managers. LO 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.28 Finite Corp. has $250 million of debt outstanding at an interest rate of 11 percent. What is the present value of the debt tax shield if the debt will mature in five years (and no new debt will replace the old debt), assuming that Finite is subject to a 40 percent marginal tax rate? Solution: Finite will pay $27,500,000 ($250,000,000 × 0.11) in interest each year, which will shield Finite from paying a tax amount equal to $11,000,000 ($27,500,000 × 0.4). The tax shield will last for five years, so the present value of receiving this amount for the next five years is: $11,000,000 × PVIFA (11%, 5) = $11,000,000 × 3.695897 = $40,654,867.19 LO 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.29 The Boring Corporation is currently valued at $900 million, but management wants to completely pay off its perpetual debt of $300 million. Boring is subject to a 30 percent marginal tax rate. If Boring pays off its debt, what will be the total value of its equity? Solution: Boring will be worth $900 million less the present value of the tax shield on its current debt. The present value of the tax shield is $300,000,000 × 0.3 = $90,000,000 Therefore, Boring will be worth $810 million after the recapitalization, and since it will be an all-equity firm, that will be the value of the equity. LO 2 Bloomcode: Application AASCP: Analytic Copyright © 2015 John Wiley & Sons, Inc.

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IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.30 If we drop the assumption that there are no information or transaction costs, in addition to dropping the no-tax assumption, then will the Modigliani and Miller model still suggest that the firm should take on greater proportions of debt in its capital structure? Explain. Solution: If we only drop the no-tax assumption, then it is evident that the firm should always increase its use of debt within a firm’s capital structure. However, if we drop the no information or transaction costs assumption, then we are effectively introducing the possibility that the firm will default on its debt obligations. The higher the level of debt, the greater the possibility of defaulting and then the greater the interest costs on the debt. Given this increasing cost of debt, relative to the increased use of debt within a firm’s capital structure, then we are introducing the possibility that the firm’s overall cost of capital will increase at some high-debt level capital structure, thereby reducing the value of the firm. Therefore, by dropping the no information or transaction costs assumption, the firm will not always increase its use of debt. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.31 PolyAna Corporation has an abundant cash flow. It is so high that the managers take Fridays off for a weekly luncheon in Cancun using the corporate jet. Describe how altering the capital structure of the firm might make the management of this firm stay in the office on Fridays in order to work on new positive NPV projects. Solution: The root of the problem is that the firm’s management is too comfortable, because their weekly trip to Cancun is not costly enough to the managers of the firm. PolyAna could drastically increase the proportion of debt in the firm’s capital structure. This would decrease the amount of “free” cash that PolyAna’s management could spend on their weekly outings. If enough debt is placed on this firm, then a cash shortage, or lack of a

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large cash surplus, would necessitate that the managers of the firm work on new positive NPV projects rather than spend their Fridays in Cancun. LO 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

CFA PROBLEMS 16.32 Consider two companies that operate in the same line of business and have the same degree of operating leverage: the Basic Company and the Grundlegend Company. The Basic Company has no debt in its capital structure, but the Grundlegend Company has a capital structure that consists of 50 percent debt. Which of the following statements is true? a. The Grundlegend Company has a degree of total leverage that exceeds that of the Basic Company by 50 percent. b. The Grundlegend Company has the same sensitivity of net earnings to changes in earnings before interest and taxes as the Basic Company. c. The Grundlegend Company has the same sensitivity of earnings before interest and taxes to changes in sales as the Basic Company. d. The Grundlegend Company has the same sensitivity of net earnings to changes in sales as the Basic Company. Solution: c is correct. The degree of total leverage of the Grundlegend Company exceeds that of the Basic Company, but the extent of the difference depends on the amount of interest expense, not the amount of debt. In the case of financial leverage, it is the interest that acts as a fulcrum. LO 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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New equity is preferable to internally generated funds. New debt is preferable to internally generated funds. New equity is always preferable to other sources of capital.

Solution:

a is correct. According to pecking order theory, internally generated funds are preferable to both new equity and new debt. But new debt is preferable to new equity as it has lower cost. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.34 According to the trade-off theory: a. The amount of debt a company has is irrelevant. b. Debt should be used only as a last resort. c. Debt will not be used if a company’s tax rate is high. d. Companies have an optimal level of debt. Solution: d is correct. The static trade-off theory indicates that there is a trade-off between the tax shield from interest on debt and the costs of financial distress, leading to an optimal range of debt for a company. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Sample Test Problems

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Central Grocers Inc. produces annual cash flows of $175,000, which are expected to continue indefinitely. The company is financed entirely with equity capital at an annual cost of 12 percent. Management is considering borrowing $400,000 at an annual interest rate of 6 percent to repurchase $400,000 of the company’s outstanding stock (You can assume that the debt will be outstanding into the indefinite future.). What is the total value of Central Grocers’ stock before the stock repurchase? Under Modigliani and Miller’s Proposition 1, what would be the value of the total claims on the company’s assets after the stock repurchase? What will be the rate of return on common stock required by investors after the repurchase? (LO 1) Solution: Using the perpetuity formula, we can compute the value of Central Grocers’ stock before the repurchase to be $175,000/0.12 = $1,458,333 if the cash flow is expected to be produced into the infinite future. Under M&M Proposition 1, the value of the firm will be the same before and after the repurchase. Therefore, since the value of the debt claim will be $400,000 at the time of the transaction, the value of the outstanding equity after the repurchase must be $1,458,333 – $400,000 = $1,058,333. Since interest of $400,000 × 0.06 = $24,000 must be paid to the debt holders each year, the amount that will be available for the stockholders each year will equal $175,000 $24,000 = $151,000. This implies that the new cost of equity capital for the firm will be $1,058,333 = $151,000/kcs, or kcs = 0.1427, or 14.27%.

Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.2

The required rate of return on the assets of a firm is 12 percent, the firm has a debt-tocommon-stock ratio of 40 percent, and the cost of debt is 6 percent. If the firm has no

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preferred stock and the three conditions specified by M&M hold, what is the expected rate of return on the firm's common stock? (LO 1) Solution: Using the equation for M&M Proposition 2, Equation 16.3, we get: kcs = kAssets + (VDebt /Vcs) × (kAssets – kDebt) = 0.12 + [(0.4) × (0.12 – 0.06)] = 0.144, or 14.4% Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.3

Your boss at Box and Freight Company asks you how much additional debt the company would have to add through a capital restructuring in order to create $9 million in present value from the resulting interest tax shields. What would you tell him if the debt will have no maturity and if Box and Freight is subject to a 32 percent marginal tax rate? (LO 2) Solution: The present value of Box & Freight’s additional tax shield will be: tc × D = 0.32 × D = $9,000,000 Therefore: D = $28,125,000

Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Southwest Airlines has substantial cash reserves and an investment-grade bond rating. How would the trade-off theory predict that managers of Southwest would raise capital and choose the company’s capital structure if they were planning an expansion into Mexico? What would the pecking order theory suggest? (LO 3) Solution: The trade-off theory would predict that Southwest would raise additional funds by first issuing more debt. The additional debt would provide tax savings, and as long as the incremental tax savings exceeded any added financial distress or agency costs, Southwest’s managers would increase the debt in the company’s capital structure. The pecking order theory would suggest that internally generated funds, specifically, cash on hand, would be the cheapest source of capital, and therefore used first to fund the expansion. Only after exhausting the internal funds would Southwest managers seek to add more debt to the company’s capital structure.

Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

16.5

What control implications do a firm’s capital structure decisions have? (LO 4) Solution: Issuing debt does not change the ownership and therefore control of the firm, unless it is so much debt as to cause financial distress and the stockholders lose control to creditors. Issuing more common stock could dilute existing shareholders’ ownership if they do not purchase a proportionate amount of the new shares, thereby reducing their control.

Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Chapter 17 Dividends, Stock Repurchases, and Payout Policy Before You Go On Questions and Answers Section 17.1 1.

How does a dividend affect the size of a stockholder’s investment in a firm? A dividend reduces the size of the stockholder’s investment in a firm. After a dividend is issued, the shareholder owns the same percentage of the company, which is worth less than it did before the dividend. The shareholder can use the dividend as he or she sees fit (after paying taxes).

List and define four types of dividends. 1. Regular Cash Dividend — Paid out regularly, usually quarterly. This dividend is usually set at a level that the board expects to be sustainable in the long run. 2. Extra Dividend — Usually paid at the same time as a regular dividend. Often used to pay out extra earnings that will not be maintainable over the long run and/or to ensure that a certain percentage of earnings are returned to shareholders as dividends. 3. Special Dividend — One-time dividend usually resulting from a special event such as the sale of an asset or a large cash balance. For example, Microsoft’s special dividend of $3 per share at the beginning of the chapter. 4. Liquidating Dividend — Dividend resulting from the sale of assets of a company being liquidated (dissolved). This is the value left over for shareholders after the claims of other investors, such as bondholders, have been paid.

What are the key events and dates in the dividend payment process? • •

Board Vote — The firm’s board votes to issue a dividend, specifying the amount and key dates of the issue. Public Announcement Date — The firm releases the information regarding the dividend payment. Often the stock price will move on the dividend announcement date because investors use this dividend information as a signal regarding the future prospects of the firm.

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•

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Ex-Dividend Date — This is the first date on which purchasing the stock will not result in receiving a dividend. Record Date — This is the date on which one must be a stockholder of record to receive a dividend. This date is set by the board and is used by the exchange to set the ex-dividend day. The difference between the ex-dividend date and the record date reflects the time needed to compile and update the records of stock ownership. Payable Date — This is the date the dividend will actually be paid.

Section 17.2 1.

What is a stock repurchase? A stock repurchase takes place when a company purchases some of its own stock from shareholders. Shareholders who choose to participate receive payment in exchange for their shares.

How do stock repurchases differ from dividends? There are four major ways in which stock repurchases differ from dividends. First, the payments are not made on a pro-rata basis. Some stockholders choose to take the repurchase offer, whereas others choose to hold on to their shares. Second, stock repurchases reduce the number of outstanding shares. This can change the liquidity of the shares and ownership control of the firm. Third, stock repurchases are taxed differently, often resulting in a smaller tax burden for investors. Finally, accounting for stock repurchases and dividends is different. When a dividend is issued, the retained earnings account decreases on the liability and stockholder’s equity side of the balance sheet. For a stock repurchase, the treasury stock account on the right side of the balance sheet becomes more negative. Both stock repurchases and dividends reduce the cash account on the asset side of the balance sheet.

In what ways can a company repurchase its stock? Open-Market Repurchase — The company purchases shares at the exchange in the same manner as normal trades. This is convenient for small ongoing repurchases. Regulations meant to prevent price manipulation limit the amount that a company can purchase at the exchange in a day. These regulations make an open-market repurchase cumbersome for large share repurchases. Tender Offer Repurchases — The company makes an open offer to buy shares. There are two types of tender offers. In a fixed-price offer, the company offers a fixed price to investors who agree to sell their shares. In a Dutch auction offer, the company seeks bids

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for the number of shares investors would sell at a series of prices. The company may then choose the price in the series that will result in the desired number of shares being repurchased. Targeted Stock Repurchase — A company repurchases shares directly from one or more large stockholders. This is sometimes used to negotiate with a large stockholder who is attempting to gain control of the company.

Section 17.3 1.

What are the benefits and costs associated with dividends? The benefits associated with dividends are as follows: a. Dividends may attract investors who prefer to receive income directly from their investments. However, the tax costs of dividends may drive away other investors. b. Dividends can function as a signal to investors that the company is performing well and has higher then expected cash flows. c. Dividends can help align manager and stockholder incentives. By issuing dividends and raising capital through equity issues (rather than internal funds), managers are subject to more scrutiny. This increases the incentives for managers to perform well. d. Dividends reduce equity claims on the company; this can help managers achieve the target capital structure suggested by the trade-off theory. Some costs associated with dividends include: a. Taxes. Dividends have historically taxed at a higher rate than other forms of income. b. Reinvestment costs. Investors who don’t intend to spend the cash must pay the transactions costs associated with reinvesting (brokerage fees, etc.). c. Increased cost of debt. By reducing the amount of equity through a dividend issue, the firm becomes more leveraged. If the increase is significant, this could increase the risk associated with the company and increase the cost of debt should the company desire to borrow.

How do stock prices react to dividend announcements? Stock prices generally react favorably to announcements of higher than expected dividends and negatively to announcements of lower than expected dividends. This is consistent with the theory that dividends act as signals that convey to investors positive or negative changes to the firm’s fundamentals.

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Why might stock repurchases be preferred to dividends? Stock repurchases might be preferred to dividends because they result in lower taxes for investors and allow management more flexibility in distributing value. If the company has excess cash flow that is uncertain to continue in the future, it may be beneficial for management to initiate a stock repurchase, which can be quietly halted without sending a negative signal to investors.

Section 17.4 1.

What is a stock dividend? A stock dividend is a distribution of shares of stock to existing stockholders in proportion to the fraction of shares they own.

How does a stock dividend differ from a stock split? A stock dividend usually occurs on a regular basis, and the number of new shares is usually small compared to the number of existing shares. Stock splits are infrequent and involve a large number of new shares. For example, in a 2-for-1 split the number of newly created shares is equal to the number of existing shares, and the total number of shares is doubled.

How does a stock dividend differ from other types of dividends? Unlike other dividends, a stock dividend does not distribute anything of value, as the stockholders’ claim on the assets of the firm is unchanged. A stockholder may own more shares, but each share is worth less. The effects must exactly offset each other.

Section 17.5 1.

How are dividend payouts affected by expected earnings? Managers tend to set dividend policies that are achievable with expected long-run sustainable earnings. Because of the negative effect of a dividend reduction, managers are hesitant to increase dividends if they are concerned that the increase may have to be undone in the future.

What did the 2005 study conclude about how managers view stock repurchases?

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The study concluded that managers tend to view repurchases as the preferred option for returning extra cash left over after investment spending. The study also found that managers prefer the flexibility of share repurchase plans, repurchasing shares when they believe the companies’ stock is undervalued. Finally, managers believe that the decision between share repurchases and dividend payments has little effect on what type of investor is likely to own the company’s stock. 3.

List three practical considerations that managers should take into account when setting a dividend policy? • • • • •

The level of earnings (cash flows from operations) in excess of a company’s investment requirements over the long run and how certain this level is. Whether the firm has sufficient financial reserves to maintain the dividend payout during periods when earnings are down or investment opportunities are up. Whether the firm has sufficient financial flexibility to maintain dividends if unforeseen circumstances wipe out its financial reserves when earnings are down. Whether the firm is able to quickly raise enough capital if necessary. The control (voting) implications if a firm chooses to finance dividends by selling equity.

Self-Study Problems 17.1

You would like to own a common stock that has a record date of Friday, September 6, 2013. What is the last date that you can purchase the stock and still receive the dividend?

Solution: The ex-dividend date is the first day that the stock will be trading without the rights to the dividend, and that occurs two days before the record date, or on September 4, 2013. Therefore, the last day that you can purchase the stock and still receive the dividend will be the day before the ex-dividend date, or Thursday, September 3, 2013.

17.2

You believe that the average investor is subject to a 20 percent tax rate on dividend payments. If a firm is going to pay a $0.30 dividend, by what amount would you expect the stock price to drop on the ex-dividend date?

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If the tax rate of the average investor is reflected in the stock price change, we would expect investors to receive 80 percent (1.0 − 0.20 = 0.80 or 80 percent) of the dividend after paying taxes. This would necessitate a $0.24 (0.80 × $0.30 = $.24 drop in the stock price of the firm on the ex-dividend date.

17.3

The Veil Acts Company just announced that instead of a regular dividend this quarter, it will be repurchasing shares using the same amount of cash that would have been paid in the suspended dividend. Should this be a positive or negative signal from the firm?

Solution: Veiled Acts has replaced a committed cash flow with one that is stated but does not have to be acted on. Therefore, the firm’s actions should be greeted with suspicion, and the signal is not a positive one.

17.4

The Bernie Rubbel Company has just declared a three-for-one stock split. If you own 12,000 shares before the split, how many shares do you own after the split? What if it were a one-for-three reverse stock split?

Solution: You will own three shares of Bernie Rubbel for every one share that you currently own. Therefore, you will own 3 × 12,000 = 36,000 shares of the company. In the case of the reverse split, you will own 1/3 × 12,000 = 4,000 shares of the company.

1717.5 Two publicly traded companies in the same industry are similar in all respects except one. Where Publicks has issued debt in the public markets (bonds), Privicks has never borrowed from any public source. In fact, it always uses private bank debt for its borrowing. Which firm might be marginally more inclined to have a more aggressive regular dividend payout than the other? Explain. Solution: If all other things are the same about the two companies, then Publicks could be expected to have a more aggressive dividend payout. Since Publicks has issued debt in the past, while Privicks has not, Publicks is likely to have greater access to the capital markets than Privicks. Firms with greater access to capital markets can be more aggressive in their dividend payouts to the extent that they can raise capital more easily (cheaply) if necessary. Copyright © 2015 John Wiley & Sons, Inc.

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Discussion Questions 17.1

Suppose that you live in a country where it takes 10 days to settle a stock purchase. By how many days will the ex-dividend date precede the record date? The ex-dividend date is the first day that a stock will trade without the right to a dividend. In the United States, where it takes three days for a stock purchase to settle, the exdividend date is two days before the record date. Therefore, if it takes ten days for a stock purchase to settle, then the ex-dividend date will be nine days before the record date.

LO 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.2

The price of a share of stock is $15.00 on Tuesday, November 11, 2014. The record date for a $0.50 dividend is Friday, November 14, 2014. If there are no taxes on dividends, what would you expect the price of a share to be on each day from November 11 through 14 if no other information relevant to the price of the shares becomes public? Since we are excluding all nondividend related information, the price of the shares will remain constant until the ex-dividend date, when the price will drop by $0.50 per share. November 11—$15.00 November 12—$15.00 November 13—$14.50 November 14—$14.50

LO 1 Level: Basic Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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You find that you are the only investor in a particular stock who is subject to a 15 percent tax rate on dividends (all other investors are subject to a 5 percent tax rate on dividends). Is there greater value to you in holding the stock beyond the exdividend date or selling the stock and then repurchasing it on or after the exdividend date? Assume that the stock is currently selling for $10.00 per share and the dividend will be $0.25 per share. All other investors (who we can assume will be dictating the market equilibrium price) expect to pay 5 percent tax rate on their dividend receipt. Therefore, they expect to keep $0.25 × (1 – 0.05) = $0.2375 of the dividend after taxes are paid. Then, you would expect the price of the shares to be $9.7625 ($10.00 – $0.2375) on the ex-dividend date. However, you believe the correct price (based on your tax situation) to be $10.00 – (0.25 × (1 – 0.15)) = $9.7875. Therefore, by holding on to the stock, you would find that the share price dropped by $0.025 more than what you expected. Therefore, if we ignore transactions costs, it would be beneficial for you to sell your shares before the exdividend date and then repurchase them on the ex-dividend date. This argument, of course, ignores any taxes that might have to be paid by selling the shares at $10.00.

LO 1 Level: Intermediate Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.4

Discuss why the dividend payment process is so much simpler for private companies than for public companies. Since private companies have greater access to their shareholders than their public counterparts, the process of paying a dividend is not complicated by having to constantly monitor who owns the companies’ shares at any given time. In fact, the shares are bought and sold less frequently in private companies. This makes the dividend process much easier for private companies than for the public ones.

LO 1 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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You are the CEO of a firm that appears to be the target of a hostile takeover attempt. Thibeaux Piques has been accumulating the shares of your stock and now holds a substantial percentage of the outstanding shares. You would like to purchase the shares that he owns. What method of stock repurchase will you opt for? Since Mr. Piques is hostile to your firm, it will probably not help you to use an openmarket purchase. You could announce a tender offer, but unless he is willing to sell his shares for purely economic gain (and ignore the benefits of control of your firm), then a tender offer would probably not work very well either. You could negotiate directly with Mr. Piques for his shares and therefore isolate the shares that you need to purchase using a targeted share repurchase. However, this direct negotiation might not be advantageous to your remaining shareholders, and it may require a premium price to convince Mr. Piques to sell his shares.

LO 2 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.6

You have accumulated stock in a firm that does not pay cash dividends. You have read that, according to Modigliani and Miller, you can create a “homemade” dividend should you require cash. Discuss why this choice may not be very good for the value of your position. You could sell a portion of your shares to generate a cash dividend for yourself. However, if no other investors take that course of action, then you would be the only investor liquidating a portion of your holdings. If 20 percent of the voting interest in this firm helps you maintain a certain level of control of the firm, then dropping below that threshold might be enough for your diluted voting interest to lose whatever control of the firm you had maintained.

LO 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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You have just read a press release in which a firm claims that it will be able to generate a higher level of cash flows for its investors going forward. Justify the choice of a dividend payout that could credibly convey that information to the market. Either an extra or a special dividend is signaling a higher level of cash flow but without sustainability. The best way to convey to the market that this new level of cash flow is permanent is to increase (or commence) a regular cash dividend since a regular dividend comes with the expectation that it will not be reduced without unforeseen events occurring in the future.

LO 5 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.8

Some people argue that a high tax rate on dividends creates incentives for managers to go about their business without credibly convincing investors that the firm is doing well, even when it is. Discuss why this may be true. A credible signal is usually interpreted as a signal that is costly. Paying a regular dividend is costly, and we know that it credibly signals that the firm expects to maintain the current level of cash flow. If dividends are taxed at a rate high enough to discourage firms from paying them (discouraged because a very small portion of the cash sent to investors reaches them after the effects of taxes), the government is discouraging a credible signal that the firm’s prospects are still good. Without that costly signal, managers may continue about their normal routine without finding other ways to convey a firm’s prospects to investors.

LO 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Fled Flightstone Mining’s management does not like to pay cash dividends due to the volatility of the company’s cash flows. Fled management has found, however, that when it does not pay dividends, its stock price becomes too high for individual investors to afford round lots. What course of action could Fled take to get its stock price down without dissipating firm value for stockholders? Fled Flightstone Mining can double, triple, quadruple, etc., the number of shares outstanding without taking any meaningful economic steps. That is, it can take a 2-for-1, 3-for-1, or 4-for-1 stock split. This would increase the number of shares outstanding and decrease the value of each share outstanding proportionately. Since each shareholder would continue owning his or her prior pro-rata share of the firm, shareholders would not see any of their value dissipated by the firm’s actions.

LO 5 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.10 Lintner found that firms are reluctant to make dividend changes that might have to be reversed. Discuss the rationale for that behavior. The simplest reason is that the markets look to dividends for the information that the dividends convey as well as for their economic benefit. That is, an increase in the dividend rate tells the market that the cash flow that the firm produces, above and beyond that needed for projects, is anticipated to remain high. If the firm were to quickly reverse the increased dividend rate, then that might convey to the firm that the firm’s fortunes either were not that good to begin with or have changed drastically. Such a reversal could convey that the firm is riskier than what investors anticipated before the series of events described above. Therefore, firm management would naturally want to keep from having to quickly reverse its dividend decisions. LO 5 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Questions and Problems BASIC 17.1

Dividends: The Poseidon Shipping Company has paid a $0.25 dividend per quarter for the past three years. Poseidon just lowered its declared dividend to $0.20 for the next dividend payment. Discuss what this new information might convey concerning Poseidon management’s belief about the future of the company.

Solution: Since dividends convey information concerning the future prospects of the firm, any change in dividend levels is also believed to convey a change in management’s forecast of the firm’s prospects. That is, lowering the dividend from $0.25 to $0.20 suggests that the firm’s future cash flow may be reduced. This reduction could be because of a general reduced level of profitability, because the firm’s projects are winding down, or even because of an increased need to invest in new positive NPV projects for the future. LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.2

Dividends: Marx Political Consultants has decided to discontinue all of its business operations. The firm has total debt of $7 million, and the liquidation value of its assets is $10 million. If the book value of the firm’s equity is $5 million, then what will be the amount of the liquidating dividend when the firm liquidates all of its assets?

Solution: The liquidating value of the firm’s assets is $10 million while the firm owes $7 million. Therefore, $3 million will remain after complete liquidation for the shareholders. The firm will be able to pay a $3 million dividend to its shareholders. LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Dividends: Place the following in the proper chronological order, and describe the purpose of each: ex-dividend date, record date, payment date, and declaration date.

Solution: 1. Declaration date: the day the dividend payment was announced. 2. Ex-dividend date: the first day you can buy shares and not receive the dividend. 3. Record date: the day shareholders of record receive the dividend when it is paid. 4. Payment date: the date when the dividend is actually paid. LO 1 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 17.4

Dividends and firm value: Explain how the issuance of new securities by a firm can produce useful information about the issuing firm. How can this information make the shares of the firm more valuable, even if it only confirms existing information about the firm? Solution: When issuing new securities, the issuing firm must submit to a process that amounts to a special audit by outsiders such as investment bankers and other experts. This additional production of information increases the level of monitoring concerning the firm’s actual financial status. In a sense, it reduces the variability in the information that the firm may already have released. If the production of this information reduces the level of risk borne by investors, then the issue of new securities could actually increase the value of the securities issued by the firm and, in turn, the total value of the firm. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.5

Dividends: Explain why holders of a firm’s debt should insist on a covenant that restricts the amount of cash dividends the firm pays.

Solution: We have to remember that any cash paid to shareholders reduces the amount that is available to bondholders in the event of bankruptcy. Because bondholders are aware of this potential problem, they should then restrict the amount of cash that can be paid to Copyright © 2015 John Wiley & Sons, Inc.

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shareholders to at least a level where bondholders will still be able to generate their expected rate of return. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.6

Stock splits and stock dividends: Explain why managers of firms might prefer that their firms’ shares trade in a moderate per-share price range rather than in a high per-share price range. How do managers of firms keep their shares trading in a moderate price range?

Solution: Historically, the transactions and liquidity costs to trade 100 shares were lower than the cost to trade a smaller number of shares. Therefore, if small investors could not afford to trade 100 shares, then they might refrain from purchasing the shares. In that event, the high per-share price of the shares might eliminate potential investors for those shares. Consequently, firms preferred that their shares trade in an affordable range rather than at an expensive price per share. Note that no conclusive empirical evidence supports that notion. LO 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.7

Dividends: Scintilla, Inc., stock is trading for $10.00 per share on the day before the exdividend date. If the dividend is $0.25 and there are no taxes, what should the price of the shares be on the ex-dividend date?

Solution: Since there are no taxes, the value of the shares should drop by the amount of the dividend. Therefore, the shares should trade for $9.75 on the ex-dividend date. LO 1 Bloomcode: Application AASCP: Analytic Copyright © 2015 John Wiley & Sons, Inc.

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IMA: Corporate Finance AICPA: Industry/Sector Perspective 17.8

Dividends: A company’s management announces a $1.00 per share dividend payment. Assuming all investors are subject to a 15 percent tax rate on dividends, how much should the company’s share price drop on the ex-dividend date?

Solution: Investors will be able to capture 85 percent of the amount of any dividend paid. Therefore, the price on the ex-dividend date should go down by $0.85 [$1.00 x (1 – 15%)] per share. LO 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 17.9

Dividends and firm value: Explain how a stock repurchase is different from a dividend payment.

Solution: A share repurchase, if followed through by management, will place the same amount of cash in the hands of its shareholders. However, since shareholders have the option of selling their shares or holding on to their shares, the repurchase leaves it up to the individual shareholders whether or not they would like to receive the cash. The dividend payment method will effectively force the shareholders to receive the cash. LO 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.10 Dividends and firm value: You have just encountered two identical firms with identical investment opportunities, as well as the ability to fund these opportunities. One of the

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firms has just announced that it will pay a dividend, while the other has continued to pay no dividend. Which of the two firms is worth more? Explain. Solution: If we begin with a world described by the Modigliani and Miller paper in 1961, which assumes that (1) investors incur no taxes, (2) there are no information or transactions costs, and (3) the dividend payout rates have no effect on the firm’s real investment policy, then both firms will be worth exactly the same. That is because investors who want dividends but own a no-dividend stock can liquidate their appreciated value shares to create a homemade dividend, and shareholders who do not want dividends but own a dividend-paying stock can use their “unwanted” dividends to purchase additional shares of that stock. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.11 Dividends and firm value: Explain what the introduction of transaction costs does to the Modigliani and Miller assumption that dividends are irrelevant. Start with a firm that pays dividends to investors that do not want to receive dividend payments. Do not consider taxes. Solution: The no-transaction costs assumption is required for investors to create their own homemade dividends or for investors to “undo” their unwanted dividend payments by purchasing additional shares of the company stock. Therefore, by relaxing the no transaction cost assumption, we would increase the cost of producing the homemade dividend or the cost of undoing the unwanted dividends, which would then make dividend policy a relevant factor when valuing shares. For instance, receiving an unwanted dividend would now make it more costly to convert that dividend into new shares, in as much as part of that dividend would be dissipated to transaction costs. In that situation, the investor would value a non-dividendpaying share at a higher value than a dividend-paying share. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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17.12 Dividends and firm value: CashCo increased its cash dividend each quarter for the past eight quarters. While this may signal that the firm is financially very healthy, what else could we conclude from these actions? Solution: If we rule out the possibility that the firm is just producing a high level of cash, then we must conclude that the firm has more cash than it has investment opportunities to utilize that cash. In short, we might conclude that the firm’s growth rate will be slowing down in the future. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.13 Dividends and firm value: At the end of 2012 the maximum tax rate on dividends increased from 15 percent to 23.8 percent. How would you expect this increase to affect the prices of dividend-paying stocks versus those of nondividend-paying stocks? Solution: The value of a dividend received, after taxes are included, will be less than before. Therefore, we would expect the value of dividend-paying stocks to decrease relative to non-dividendpaying stocks. LO 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 17.14 Dividends: Undecided Corp. has excess cash on hand right now, although management is not sure about the level of cash flows going forward. If management would like to put cash in stockholders’ hands, what kind of dividend should the firm pay, and why? Solution: Since this is a one-time increase in cash flow, the firm would not want to commit to an ongoing higher dividend rate. If the firm went that route but then later had to reduce the dividend back to current dividend levels, then the market could interpret that action as indecision on the part of management, or worse. Therefore, an increase in the regular Copyright © 2015 John Wiley & Sons, Inc.

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dividend would not be appropriate. A more appropriate choice would be to declare an extra dividend. Note that it would be called a special dividend if the extra cash flow came from something other than the firm’s regular operations or if the cash were an unusually large amount. LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 17.15 Dividends and firm value: A firm can deliver a negative signal to stockholders by increasing the level of dividends or by reducing the level of dividends. Explain why this is true. Solution: When a firm reduces its dividend, the firm is telling the market that it does not have sufficient cash, which is of course a bad or negative signal. However, by increasing the dividend, the firm is telling its investors that it has greater cash than it has investment uses for that cash. If the firm is currently viewed as a growth firm, then the market could interpret an increase in the dividend as a slowdown in the growth rate of the firm precipitated by the firm’s lower investment rate. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 17.16 Dividends and firm value: A commentator on a financial talk show on TV says that “On average, firms pay out too little to stockholders. This is why stock prices go up with dividend increases and down with dividend decreases.” Is the commentator right? Solution: No. It is true that stock prices do tend to increase with dividend increases and to decrease with dividend decreases. However, this does not necessarily mean that firms are paying out too little to stockholders on average. The price of a company’s stock might increase when a firm increases its dividend because the increase signals to investors that the company’s management is optimistic about future cash flows or is willing to distribute excess cash rather than keep it and invest in negative NPV projects. The stock price might decrease when a firm reduces its dividend because investors might be concerned that a firm’s cash flows will decrease in the future or that management will invest excess Copyright © 2015 John Wiley & Sons, Inc.

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cash that is not being distributed in negative NPV projects. These arguments do not require that the firm be paying out too little at that time that the dividend is increased or decreased. The stock price reaction to the announcement of a dividend change reflects a change in investor expectations about what the announcement tells them about the cash flows they can expect to receive in the future. As the cash flow identity suggests, there are a number of reasons besides those above that might cause stock prices to increase with dividend increases and to decrease with dividend decreases. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.17 Dividends and firm value: You own shares in a firm that has extra cash on hand to distribute to stockholders. You do not want the cash. What course of action would you prefer the firm take? Solution: You would prefer that the firm initiate a share repurchase. You can opt not so sell your shares to the firm but still participate in the increased value of the firm’s shares since your pro-rata share of the expected future cash flows generated by the firm will increase. You would not like a dividend payment since you would then be required to receive the cash if you owned the shares at the time of the record date. LO 4 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.18 Dividends and firm value: Stock repurchases, once announced, do not actually have to occur in total or in part. From a signaling perspective, why would a special dividend be better than a stock repurchase? Solution: If we ignore the preferences of individual shareholders, then a special dividend is preferred to a share repurchase. Although dividends are binding, once declared by the firm’s board of directors, a share repurchase is not binding. Therefore, a special dividend is considered a stronger signal than a share repurchase. Copyright © 2015 John Wiley & Sons, Inc.

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LO 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.19 Dividends and firm value: Consider a firm that repurchases shares from its stockholders in the open market, and explain why this action might be detrimental to the stockholders from whom the firm buys shares. Solution: To understand this argument, we have to consider two points. First, the firm should be managed for the benefit of its shareholders. Second, the firm is the ultimate insider concerning the value of its shares. Given the above points, we must realize that any time the firm is purchasing its shares; it must be doing so because the firm’s management believes that the firm’s shares are undervalued. Therefore, by purchasing its shares, the firm is utilizing its inside information to purchase shares and ultimately to take advantage of the current owner of those shares in order to benefit the remaining shareholders of the firm. It is then not doing something in the interest of all of its shareholders since those who sell will be selling at a price lower than what they could have realized had they held their shares until the repurchase was complete. LO 3 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.20 Dividends and firm value: You read that a number of public companies have been financing their dividend payments in recent years entirely through equity issues. A colleague of yours argues that this only increase taxes paid by individual stockholders and boosts underwriting and other transactions costs for the company. He says that such a policy cannot make sense. What do you say? Solution: Such a policy can make sense. While there are costs associated with doing this, financing dividends with equity issues can help control agency conflicts by forcing managers to periodically submit to the scrutiny associated with the equity issuance process. It can Copyright © 2015 John Wiley & Sons, Inc.

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ultimately lead to better company performance and the willingness of investors to pay a higher price for the company’s stock. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.21 Stock repurchases: Briefly discuss the methods available for a firm to repurchase its shares and explain why you might expect the stock price reaction to the announcement of each of these methods to differ. Solution: 1. Open-market purchase — the firm simply purchases the shares in the market. 2. Tender offer — the firm makes an offer through a general announcement, offering to buy up to a certain number of shares from anyone who wishes to sell. Note that either the fixed-price or Dutch auction method can be used for a tender offer. 3. Targeted share repurchases — the firm directly negotiates with an individual shareholder to buy shares from that individual. LO 2 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.22 Stock repurchases: What is the advantage of a Dutch auction over a fixed-price tender offer? Solution: If the firm that is trying to purchase its own shares believes that there may be some variability in the supply curve for those shares, then a Dutch auction would essentially provide the firm with the necessary information to make the tender offer successful. In those same circumstances, a fixed-price tender offer might leave the firm paying too much for the shares or unable to purchase the desired number of shares given the fixedprice offer. LO 2 Bloomcode: Analysis Copyright © 2015 John Wiley & Sons, Inc.

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED 17.23 In the early 1990s, the amount of time that elapsed between purchasing a stock and actually obtaining that stock was five business days. This period was known as the settlement period. The settlement period for stock purchases is now two business days. Describe what should have happened to the number of days between the ex-dividend date and the record date at the time of this change. Solution: The purpose of setting the number of days between the ex-dividend date and the record date is to allow for a sale of securities to clear in order to determine which “owner” is entitled to the dividend. Since the settlement period was reduced from five days to two days, we should have seen the number of days between the ex-dividend date and the record date to be reduced from four days to two. LO 1 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.24 Dividend reinvestment programs (DRIPs) sometimes sell shares at a discount to stockholders who reinvest their dividends through such plans. Your boss tells you that such plans are just a scheme to transfer wealth from nonparticipating to participating stockholders and that they should be stopped. Do you agree? Why or why not? Solution: Disagree. It is true that the cost of a DRIPs (including any discount) is borne by all stockholders. However, it is not necessarily true that DRIPs are bad for non-participating stockholders. DRIPs help firms attract investors who might not otherwise invest in a dividend-paying stock. Being able to attract these investors can help improve the liquidity Copyright © 2015 John Wiley & Sons, Inc.

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of the shares and benefit all stockholders. Even without this benefit, it can make sense to sell shares at a discount. If DRIPs reduces the amount of capital that the firm has to raise in the future, it also reduces the issuance costs that the firm incurs in raising that capital. These cost savings can more than offset the cost of a discount offered to participating stockholders. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.25 WeAreProfits, Inc., has not issued any new debt securities in 10 years. It will begin paying cash dividends to its stockholders for the first time next year. Explain how a dividend might help the firm get closer to its optimal capital structure of 50 percent debt and 50 percent equity. Solution: If the firm has been successful over the last 10 years, then the value of its equity has increased but the total value of its debt has not increased accordingly. Therefore, the debtto-equity ratio of the firm has been dropping. By paying a dividend, the value of the equity, after the dividend is paid, will drop relative to that of the debt. This will help the firm to balance out its debt-equity ratio and get closer to a 50 percent-50 percent mix (assume that the debt was below the 50 percent level to begin with). LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.26 Shadows, Inc., had shares outstanding that were valued at $120 per share before a twofor-one stock split. After the stock split, the shares were valued at $62 per share. If we accept that the firm’s financial maneuver did not create any new value, then why might the market be increasing the total value of the firm’s equity? Solution: We know that the stock split did not create value for investors by itself. Therefore, there must be information in the split that accounts for the $4 increase in value to shareholders. Generally speaking, firms have a tendency to increase their dividend rate after a stock Copyright © 2015 John Wiley & Sons, Inc.

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split. Therefore, since a stock split is generally followed by dividend rate increases, the increase tends to generate information for investors that there is a potential increase in cash flow to investors of the firm’s equity. LO 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.27 Saguaro Company currently has 30,000 shares outstanding. Each share has a market value of $20. If the firm pays $5 per share in dividends, what will each share be worth after the dividend payment? Ignore taxes. Solution: The current value of all of the shares is 30,000 × $20 = $600,000. If the firm pays $5 per share, then the total cash paid out will be 30,000 × $5 = $150,000. Therefore, the value of all of the shares will be worth $150,000 less or $450,000, and the price of each share will be $450,000 / 30,000 = $15 per share. However, it seems logical that if shares were worth $20 before the dividend payout, then they should be worth $5 less after the dividend payout or $15 just as we have calculated. LO 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.28 Cholla Company currently has 30,000 shares outstanding. Each share has a market value of $20. If the firm repurchases $150,000 worth of shares, then what will be the value of each share outstanding after the repurchase? Ignore taxes. Solution: The current value of all of the shares is 30,000 × $20 = $600,000. If the firm repurchases $150,000 worth of shares, then it will repurchase $150,000 / $20 = 7,500 shares. Therefore, the value of all of the shares not purchased will be worth $150,000 less, or $450,000, and the price of each share will be $450,000 / (30,000 – 7,500) = $20 per share. It seems logical, however, that if shares were worth $20 before the repurchase, then they should be worth $20 after the repurchase since investors should be indifferent between selling their shares to the firm and retaining shares. Copyright © 2015 John Wiley & Sons, Inc.

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LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.29 You purchased 1,000 shares of Koogal stock five years ago for $30 per share. Today Koogal is repurchasing your shares through a fixed-price tender offer for $80 per share. What are the after-tax proceeds to you if only your capital gain is taxed at a 15 percent rate? Solution: The tax on the stock would be 1,000 × ($80 – $30) × 0.15 = $7,500. Therefore, the aftertax proceeds would equal (1,000 × $80) – $7,500 = $72,500. LO 1 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.30 You purchased 1,000 shares of Zebulon Copper Co. five years ago for $50 per share. Today Zebulon management is trying to decide whether to repurchase shares for $70 per share through a fixed-price tender offer or pay a $70 cash dividend per share. If capital gains are taxed at a 15 percent rate, then at what rate must dividends be taxed for you to be indifferent between receiving the dividend and selling your shares back to Zebulon? Solution: The tax on the stock would be 1,000 × ($70 – $50) × 0.15 = $3,000. Therefore, the tax on the dividend must be equal to $3,000 for you to be indifferent between the two choices. Therefore, $3,000 = 1,000 × $70 × Dividend Tax rate  Dividend Tax rate = 4.29% If dividends are taxed at any rate higher than 4.29 percent, then you would prefer the share repurchase. Note that the point of indifference is partially a function of the ratio of capital gains to the cash dividend. LO 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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17.31 Llama Wool Company management is doing some financial planning for the coming year. Llama plans to raise $10,000 in new equity this year and wants to pay a dividend to stockholders of $30,000. The firm must pay $20,000 of interest during the year and will also pay down principal on its debt obligations by $10,000.Its capital budgeting plan calls for $100,000 of capital expenditures during the year. Given the above information, how much cash must be provided from operations for the firm to meet its plan? Solution: Using the equation given in the text: CFOAt + Equityt + Debtt = Divt + Repurchasest + Interestt + Principalt + Invt CFOAt + $10,000 = $30,000 + $20,000 + $10,000 + $100,000 CFOAt = $150,000 LO 3 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.32 You are the Chief Financial Officer (CFO) of a large publicly traded company. You would like to convey positive information about the firm to the market. If you agree with the conclusions from the Lintner study, will you keep paying your currently high dividend or raise that dividend by a small amount? Explain. Solution: Although the current high level of dividends certainly suggests that the firm has the ability to sustain a high payout to investors, that high payout does not convey any positive information to the market. However, by increasing the dividend, the CFO would be telling the market that the firm will be able to support an even higher level of cash payout in the future. Therefore, it would be better to increase the dividend by a small amount. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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17.33 You are the CFO of a public company that advises distressed companies about how to manage their businesses. Your company has been performing extremely well. In fact, it has earned so much money that the increase in its retained earnings has resulted in a decline in the firm’s debt to total capital ratio from 30 percent to 15 percent. Much of the retained earnings is sitting in a cash account because your firm does not need the money to fund investments. You would like to increase the debt-to-total capital ratio to 30 percent, which you view as optimal for your firm. How would you recommend doing this if you want to complete the adjustment as soon as possible? Solution: You can do this by paying out some of the cash that the firm has accumulated using either a special dividend or a stock repurchase. A special dividend can be completed quickly, but would subject your stockholders to taxes if they are not tax-exempt organizations or stockholders who wanted to retain the same dollar investment in your firm. LO 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Sample Test Problems 17.1

Shares of Convoy West, Inc. are trading for $55.45 on the day before the ex-dividend date. If the quarterly dividend is $0.16 per share and there are no taxes, how will the share price change on the ex-dividend date?

Solution: Since there are no taxes, the value of the shares drop by the $0.16, the amount of the dividend. Therefore, the shares should trade for $55.29 ($55.45 – $0.16 = $55.29) on the ex-dividend date if no other information relevant to the price of the stock becomes public. Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.2

Three years ago, you purchased 4,000 shares of Metwa Inc. for $17 per share. Today Metwa is repurchasing its shares through a fixed-price tender offer at a price of $45 per share. What are the after-tax proceeds that you will receive if capital gains are taxed at a rate of 20 percent?

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Solution: The tax on the stock would be 4,000 × ($45 – $17) × 0.20 = $22,400. Your after-tax proceeds would equal (4,000 × $45) – $22,400 = $157,600. Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.3

Why does an ongoing stock repurchase program offer management greater flexibility in distributing value to stockholders than a regular cash dividend?

Solution: An ongoing stock repurchase program, such as that announced by DuPont in the chapter opener, is less perceived in the stock market as being less of a commitment than a regular cash dividend. The actual amount of cash being distributed through such a program is also less visible than the amount of money being distributed through dividends. If management decides to decrease the amount of cash being distributed to stockholders through a repurchase program, it can cut back or even terminate the program without causing the negative stock price reaction that typically accompanies reductions in regular cash dividends. Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

17.4

Why would management of a company undertake a reverse stock split?

Solution: Often, a reverse stock split is undertaken to satisfy exchange requirements. A reverse stock split can be used to increase the share price to a level above the required threshold at an exchange such as the NYSE or NASDAQ. Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Mastercard, Inc. completed a 10-for-1 stock split on January 22, 2014. Immediately before the stock split there were 120.38 million shares outstanding at a price of $826.00 per share. After the split how many shares were outstanding, and at what price would you expect them trade? Did the stock split cause any substantial change for Mastercard or the investors? Why would Mastercard management choose to split the company’s stock?

Solution: Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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CHAPTER 18 Business Formation, Growth, and Valuation

Before You Go On

Section 18.1 1. What are three general reasons that new businesses fail? Businesses fail for a variety of reasons. In some cases, a firm’s product(s) may find no demand among consumers. For others, the founding management may lack a clearly thought out strategy or lack the skills to move the firm forward. In addition, a lot of firms fail because they run out of money to operate the business and are unable to raise more.

2. How do financing considerations affect the choice of organizational form?

Of all the different forms of organizations, the sole proprietor takes the least amount of money to set up and is only dependent on the founder’s money. Forming a partnership is more involved and costs more. Setting up as a corporation is the most expensive and calls for a more active role by attorneys to set up the organization.

How does a cash budget help an entrepreneur?

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The cash budget is a very useful planning tool for entrepreneurs. It summarizes the cash flows into and out of a firm over a period of time. Cash budgets often present the inflows and outflows on a monthly basis but can be prepared for any period, including daily or weekly. Preparing a cash budget helps an entrepreneur better understand where money is coming from, where it is going, and how much external financing is likely to be needed and when. Understanding where the money is coming from and where it is going helps an entrepreneur maintain control of the company’s finances. Knowing how much external financing is likely to be needed and when helps the entrepreneur plan fund-raising efforts before it is too late.

Section 18.2 1. Why is a business plan important in raising capital for a young company?

A well-prepared business plan makes it easier for an entrepreneur to communicate to potential investors precisely what he or she expects the business to look like in the future, how he or she expects to get it to that point, and what returns an investor might expect to receive. This allows potential investors to get a feel for the strategic plan of the firm and also allows them to gauge the management ability of the entrepreneur.

What else can a business plan be used for?

A business plan is a tool that ▪

can help raise capital

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can help an entrepreneur set the goals and objectives for the company ▪

serve as a benchmark for evaluating and controlling the company’s performance,

▪

communicate the entrepreneur’s ideas to managers, outside directors, customers, suppliers, and others.

Why is it important to discuss the qualifications of the management team in a business plan?

The discussion of the qualification of the management team is especially important when it comes to raising capital. Investors in young businesses invest in the key people as much as in the business idea itself.

Section 18.3 1. Why is it important to specify a valuation date when you value a business?

The value of a business changes over time. This can be caused by changes in general economic conditions, industry conditions, and decisions that are made by the managers— all affect the value of the cash flows that a business is expected to generate in the future. Actions by competitors also affect the value of a business. The investment, operating, and financing decisions made by managers also affect the value of a business. Given this, it is important to specify a valuation date while valuing a business. This is the date as of which the value estimate applies.

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2. What is the difference between investment value and fair market value?

A strategic investor is one who has an interest in acquiring the business. The investment value of the firm to a strategic investor will take into consideration the benefits that can accrue from the acquisition and hence is likely to carry a higher value. In contrast, the fair market value is the valuation arrived by an investor who is only interested in the financial performance of the firm and not in acquiring the business. The fair market value can differ considerably from the investment value of the business.

What are the two market approaches that can be used to value a business, and how do they differ?

The two market approaches that are commonly used to value a business are multiples analysis and transactions analysis. Multiples analysis uses stock price or other value multiples that are observed for public companies to estimate the value of a company’s stock or an entire business. In transaction analysis, analysts use the information from transactions involving a merger or an acquisition of similar companies to estimate the value of a company or its stock.

What is a nonoperating asset, and how are such assets accounted for in business valuation?

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Nonoperating assets (NOA) are assets like cash or other assets that are not essential to support the operations of a business. As Equation 18.3 shows, when valuing a business, the net operating assets are included in the cash flows that are discounted to arrive at the present value of a firm.

What are three income approaches used to value a business?

The three income approaches to valuing a business are free cash flow from the firm (FCFF), free cash flow to equity (FCFE), and dividend discount model (DDM). In the free cash flow from the firm (FCFF) approach, an analyst values the discounted value of free cash flows that the assets of the firm are expected to produce in the future to estimate the value of the enterprise. The free cash flow to equity (FCFE) approach uses the discounted value of the portion of the cash flows that are available for distribution to stockholders to estimate the value of the enterprise. The dividend discount model (DDM) approach estimates the value of an enterprise using the discounted value of the dividends to be distributed to stockholders in the future.

What is the difference between FCFE and dividends?

The FCFE is an estimate of all cash flows available for distribution to shareholders of the firm. Recognize that not all of this will be distributed to stockholders as dividends. Thus, FCFE includes both dividends and retained earnings, the portion not distributed to shareholders but reinvested in the firm.

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Section 18.4 1. How might financial statements for private companies differ from those for public companies?

•

Some private companies have complete, audited financial statements, while others have incomplete financial statements that are not prepared in accordance with the GAAP. All public companies are required to file audited financial statements with the Securities and Exchange Commission (SEC).

•

In contrast to the financial statements of publicly held company, private company financials often include personal expenses of the owner and excess compensation expenses.

2. Why is marketability an important issue in business valuation?

The shareholders of a publicly held company have an easier time of liquidating their holdings if they so desire. Since a market and the value for their holdings are already established, a simple call to a broker will take care of it. In contrast, the shareholders of a privately held firm will have to spend a lot more time and money to liquidate their shares. This additional time and effort is a reflection of a lower level of marketability of such firms and will result in a discount in the value of the firm.

What is a key person?

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If the cash flows that a business is expected to generate depend heavily on the retention of a particular individual or group of individuals, then that individual or group can be referred to as key people. The survival of the firm is dependent on the continued employment of this individual or group.

Self-Study Problems 18.1

Your sister wants to open a store that sells antique-style jewelry and accessories. She has $15,000 of savings to invest, but opening the store will require an initial investment of $20,000. Net cash inflows will be −$2,000, −$1,000, and $0 in the first three months. As the store becomes better known, net cash inflows will become +$500 in the fourth month and grow at a constant rate of 5 percent in the following months. You want to help your sister by providing the additional money that she needs. How much money do you have to invest each month to start and to keep the store operating with a minimum cash balance of $1,000?

Solution: You will have to invest in $5,000 initially for her business to start (the difference between $20,000 and $15,000). You will then need to invest an additional $3,000 during the first month to cover the cash flow of -$2,000 and to establish a cash balance of $1,000. Another $1,000 will be required in the second month to cover the negative cash flow during that month. Since cash flows will be positive beginning in the third month, you will not have to invest any additional funds after the second month.

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You have the following information for a company you are valuing and for a comparable company: Comparable company:

Company you are valuing:

Stock price = $23.45

Value of debt = $3.68 million

Number of shares outstanding = 6.23 million

Est. EBITDA next year = $4.4 million

Value of debt = $18.45 million

Est. income next year = $1.5 million

Est. EBITDA next year = $17.0 million Est. income next year = $5.3 million Estimate the enterprise value of the company you are evaluating using the P/E and enterprise value/EBITDA multiples.

Solution: The P/E and enterprise value/EBITDA multiples for the comparable company are:

  Stock price P =     E Comparable  Earnings per share Comparable =

$23.45 per share $5.3 million 6.23 million shares

= 27.6  V + VE   Enterprise value  = D    EBITDA  Comparable  EBITDA Comparable =

$18.45 million + ($23.45 per share  6.23 million shares) $17.0 million

= 9.68

Using the P/E multiple, we can calculate the value of the equity as:

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P VE =    Net incomecompany being valued  E Comparable = 27.6  $1.5 million = $41.4 million which suggests an enterprise value of: VF = VE + VD = $41.4 million + $3.68 million = $45.08 million

Using the enterprise/EBITDA multiple, we obtain:

 Enterprise value  VF =   EBITDA Company being valued  EBITDA  Comparable = 9.68  $4.4 million = $42.59 million

18.3

How do the cash flows that are discounted when the WACC approach (FCFF approach) is used to value a business differ from those that are discounted when the free cash flow to equity (FCFE) approach is used to value the equity in a business?

Solution: The cash flows that are discounted when the WACC approach is used to value a business are calculated in the same way that the cash flows are calculated for a project analysis. These cash flows represent the total cash flows that the business is expected to generate from operations. The cash flows that are discounted when the FCFE approach is used are the portion of the total cash flows from the business that are available for distribution to the stockholders. In other words, they equal the total cash flows that the business is expected to generate less the net cash flows to the debt holders. The net cash flows to the Copyright © 2015 John Wiley & Sons, Inc.

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debt holders is equal to the interest and principal payments that the firm makes less any proceeds for the sale of new debt. 18.4

You are valuing a company using the WACC approach and have estimated that the free cash flows from the firm (FCFF) in the next five years will be $36.7, $42.6, $45.1, $46.3, and $46.6 million, respectively. Beginning in year 6, you expect the cash flows to decrease at a rate of 3 percent per year for the indefinite future. You estimate that the appropriate WACC to use in discounting these cash flows is 10 percent. What is the value of this company?

Solution: The present value of the cash flows expected over the next five years is:

PV(FCFF5 ) =

$36.7 million $42.6 million $45.1 million $46.3 million $46.6 million + + + + 2 3 4 5 1+ 0.1 (1+ 0.1) (1+ 0.1) (1+ 0.1) (1+ 0.1)

= $163.01million. The terminal value is:

TV5 =

FCFF5 × (1+ g ) $46.6 million × (1-0.03) = = $347.71million WACC- g 0.1+ 0.03

and the present value of the terminal value is:

PV(TV5 ) =

TV5

(1+ WACC )

$347.71

(1+ 0.1)

= $215.90 million.

Therefore, if there are no nonoperating assets, the value of the firm is: VF = $163.01 million + $215.90 million = $378.91 million

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You want to estimate the value of a local advertising firm. The earnings of the firm are expected to be $2 million next year. Based on expected earnings next year, the average price-to-earnings ratio of similar firms in the same industry is 48. Therefore, you estimate the value of the firm you are valuing to be $96 million. Further investigation shows that a large portion of the firm’s business is obtained through connections that John Smith, a senior partner of the firm, has with various advertising executives at customer firms. Mr. Smith only recently started working with his junior partners to establish similar relationships with these customers. Mr. Smith is approaching 65 years of age and might announce his retirement at the next board meeting. If he does retire, revenues will drop significantly and earnings are estimated to shrink by 30 percent. You estimate that the probability that Mr. Smith will retire this year is 50 percent. If he does not retire this year, you expect that Mr. Smith will have sufficient time to work with his junior partners so his departure will not affect earnings when he departs. How does this information affect your estimate of the value of the firm?

Solution: Mr. Smith is a key person in this firm. An adjustment should be made to the valuation to account for his potential departure this year. Taking the possibility that Mr. Smith will retire into account, the expected earnings next year will be: (2,000,000 × 0.5) + [$2,000,000 × (1 – 0.30) × 0.5] = $1,700,000

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Therefore, the adjusted value for the firm is: $1.7 million × 48 = $81.6 million. We can see that this implies a 15 percent key person discount from the original estimate of $96 million [($81.6 million ─ $96.0 million)/$96.0 million = ─ 0.15, or ─15 percent].

Discussion Questions 18.1

Given that many new businesses fail in the first few years after they are established, how should an entrepreneur think about the risk of failure associated with a new business? From what you have learned in this chapter, what can an entrepreneur do to increase the chance of success?

First of all, it is important for an entrepreneur to understand why many new businesses fail. Common reasons include poor products, poor business strategy, poor management skills, and wrong financing decisions. However, the risk of failure should not stop the start of a new business if the entrepreneur believes that he or she has a great business idea and is capable of implementing the idea. The entrepreneur should be careful and realistic in assessing the opportunities and taking risks into consideration. From what we have learned in this chapter, the entrepreneur should consult an attorney and choose the right organizational form according to the business’s operating and financing needs. In addition, he or she should carefully prepare a business plan that incorporates the main aspects of the business and facilitates the raising of external capital. The entrepreneur can use several tools to assess the financing needs of the new business: cash flow break-even analysis and cash budget. To value the new business, the

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entrepreneur can use one or more of the following methods: cost approach, market approach, or income approach. LO 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.2

Explain how the taxation of a C-corporation differs from the taxation of the other forms of business organization discussed in this chapter. With the exception of C-corporations, all profits flow through to the owners in proportion to their ownership interests. These owners pay taxes on the business profits only when they file their personal tax returns. In contrast, profits earned in C-corporations are taxed at the corporate tax rate, and the after-tax profits are taxed a second time when they are distributed to stockholders in the form of dividends. On the bright side, because profits are taxed in the corporation, certain benefits like health insurances that are paid to stockholders who work in a C-corporation are tax deductible. These benefits are not generally deductible with the other forms of organization. LO 1 Level: Basic

Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.3

What is a business plan? Explain how a business plan can help an entrepreneur succeed in building a business.

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A business plan is a document that describes the details of how a business will be developed over time. A well-prepared business plan helps an entrepreneur raise external capital. It makes it easier for an entrepreneur to communicate to potential investors precisely what he or she expects the business to look like in the future, how he or she expects to get it to that point, and what returns an investor might expect to receive. In addition, a business plan is a tool that can help an entrepreneur set the goals and objectives for the company, serve as a benchmark for evaluating and controlling the company's performance, and communicate the entrepreneur’s ideas to managers and stakeholders. LO 2 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.4

You are entering negotiations to purchase a business and are trying to formulate a negotiating strategy. You want to determine the minimum price you should offer and the maximum you should be willing to pay. Explain how the concepts of fair market value and investment value can help you do this.

An estimate of the fair market value of a business would provide you with an idea of the price that the seller could probably get from someone else. Since this is an indication of the alternatives available to the seller, it is a useful benchmark for determining the minimum price you should offer. The investment value of the business to you represents the maximum price that you should pay. If you pay more than the investment value, the acquisition will be a negative NPV project. LO 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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You have just received a business valuation report that is dated six months ago. Describe the factors that might have changed during the past six months and, therefore, caused the value of the business today to be different from the value six months ago. Which of these changes affect the expected cash flows, and which affect the discount rate that you would use in a discounted cash flow valuation of this company?

A lot might have changed in the last six months. For example, there might have been changes in general economic conditions, capital market conditions, the competitive environment in the industries in which the company competes, and in company characteristics such as the products it sells, the geographic markets it competes in, and management quality. Changes in all of these areas can affect expected cash flows through their impact on demand for the company’s products, the prices of these products, production costs, and investment requirements. Changes in capital market conditions can affect the company’s cost of capital and therefore the discount rate. LO 3 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.6

Is the replacement cost of a business generally related to the value of the cash flows that the business is expected to produce in the future? Why or why not? Illustrate your answer with an example.

The replacement cost of a business is an estimate of what it would cost to replace the tangible and intangible assets of an on-going business rather than a reflection of the value of the expected future cash flows of the business. Let us say that you are planning to start up a new coffee shop. You have a choice of either buying an existing coffee shop or starting up one entirely from scratch. The replacement cost of the coffee shop business should include the cost of all tangible assets, such as property, plant, and equipment, and all Copyright © 2015 John Wiley & Sons, Inc.

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intangible assets, such as brand names, customer lists, and the cost of hiring the people necessary to run the business and the time that it would take to build the business. This provides you a fair value of what you would pay for an existing business. If you can start up a business from start at a lower cost than that estimated value, then you should not buy up the existing business. It does not reflect the cash flows that the existing coffee shop will produce in the future, but only what it is worth now. LO 3 Level: Intermediate Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.7

You want to estimate the value of a company that has three very different lines of business. It manufactures aircraft, is in the data-processing business, and manufactures automobiles. How could you use an income approach to value a company such as this—one with three very distinct businesses that will have different revenue growth rates, profit margins, investment requirements, discount rates, and so forth?

In using an income approach like the free cash flow from the firm (FCFF) to value an entire firm, one would first estimate the expected future cash flows from each of the three distinct lines of business. If all three lines of businesses are financed the same way, then one would add up the cash flows across all the different lines of businesses and discount them using the firm’s WACC to estimate the value of the firm. If, however, the three distinct businesses have been financed differently, then each of the business’s value should be estimated independently and then finally added up to determine the value of the firm. LO 3 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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Your boss has asked you to estimate the intrinsic value of the equity for Google, which does not currently pay any dividends. You are going to use an income approach and are trying to choose between the free cash flow to equity (FCFE) approach and the dividend discount model (DDM) approach. Which would be more appropriate in this instance? Why? What concerns would you have in applying either of these valuation approaches to a company such as this?

Google is a fast growing, young firm that is unlikely to pay dividends in the near future. The dividend discount model (DDM) approach typically uses the constant-growth model to determine the intrinsic value of the firm’s equity. This model will not be applicable to firms like Google until it has settled down to a steady growth pattern at some point in the future. In contrast, the FCFE approach values cash flows that are available for distribution to stockholders. It allows for the firm to not distribute all available cash flows as dividends in any particular year. Hence, it would be more appropriate to use the FCFE approach to determine the intrinsic value of Google’s equity. LO 3 Level: Intermediate Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.9

Explain how the financial statements of a private company might differ from those of a public company. What does this imply for valuing a private company?

Financial statements of many private companies are not as complete and reliable as those of public companies. One needs to take caution in valuing a private business based on its financial statements. For example, private company financials often include personal expenses of the owner and extremely high compensation expenses. Excess

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compensations for the owners benefit them by voiding double taxation. To value a private firm more precisely, adjustments for excess expenses and compensations should be made. LO 4 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.10 Explain why it is difficult to value a young, rapidly growing company.

It is difficult to value a young, rapidly growing company for several reasons. First, such a company has less reliable historical information available; second, the future of such a company is often less certain than a matured company; third, such a company is usually not yet profitable, and therefore it is difficult to apply earnings multiples; and finally, such a company usually invests. LO 4 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

Questions and Problems BASIC

18.1

Organizational form: List some common forms of business organization, and discuss how access to capital differs across these forms of organization.

Solution:

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The forms of organizations discussed in this chapter include: sole proprietorship, partnership (general partnership and limited partnership), limited liability company (LLC), and corporations (S-corporation and C-corporation). The closer the type of organization is to the end of the list above, the better is its access to capital. Sole proprietorships must rely on equity contribution from the proprietor and debt or lease financing. In contrast, partnerships can turn to all of the partners for additional capital, and corporations can sell shares to both insiders and outsiders. Limited partnerships and limited liability companies (LLCs) are less constrained than general partnerships because they can raise money from limited partners or “members,” as outside investors in LLCs are called, who are not directly involved in running the business. C-corporations can have virtually an unlimited number of stockholders. LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.2

Starting a business: What are some of the things that the founder of a company must do to launch a new business?

Solution: The founder of a company needs to decide on its products, market, and business strategy. Then, he or she needs to estimate the company’s financing needs and raise the money to develop the products, acquire assets, and hire employees. As the business is being built, the founder must also manage the day-to-day operations. LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.3

Organizational form: Explain how financial liabilities differ among different forms of business organization.

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Solution: Sole proprietorships, general partnerships, and limited partnerships all are at a disadvantage. Sole proprietors and general partnerships face the possibility that their personal assets can be taken from them to satisfy claims on their businesses. In contrast, the liabilities of investors in limited partnerships, LLCs, and corporations are limited to the money that they have invested in the business. LO 1 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.4

Cash requirements: List two useful tools to help an entrepreneur to understand the cash requirements of a business and to estimate the financing needs of his or her business.

Solution: An entrepreneur can use cash flow break-even analysis and cash budget to estimate the cash requirement and financing needs of his or her business. The cash flow break-even analysis is used to compute the level of unit sales that is necessary to break even on operations from a pretax operating cash flow perspective. The cash budget presents the cash inflows and outflows as well as additional financing needs, usually on a monthly basis but can be prepared for any period, including daily or weekly. LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.5

Cash requirements: You believe you have a great business idea and want to start your own company. However, you do not have enough savings to finance it. Where can you get the additional funds you need?

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Solution: You can try to raise additional equity financing from your friends and family, from venture capitalists, or from other potential investors that you know. Debt financing might be obtained through bank loans, cash advances on credit cards, or loans from other local individual investors or other businesses. Of course, if a company is large enough, equity and debt financing can be obtained in the public markets. LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.6

Raising capital: Why is it especially difficult for an entrepreneur with a new business to raise capital? What tool can help him or her to raise external capital?

Solution: To raise external capital, an entrepreneur must convince potential investors that purchasing debt or equity from the firm will yield attractive returns, given the risks they will bear. It is especially difficult for an entrepreneur with a new business to do this, because the business does not have a well-established record and its future is typically very uncertain. A well-written business plan can be very helpful in convincing potential investors to put their money in the business. LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.7

Replacement cost: What is the replacement cost of a business?

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The replacement cost is the cost of duplicating the assets of a business in their present form, consisting of tangible and intangible assets as of the valuation date. LO 3 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.8 Multiples analysis: It is April 4, 2015, and your company is considering the possibility of purchasing the Chrysler automobile manufacturing business. Managers of Fiat, the Italian automobile manufacturer that owns Chrysler, have hinted that they might be interested in selling the firm. Since Chrysler does not have publicly traded shares of its own, you have decided to use Ford Motor Company as a comparable company to help you determine the market value of Chrysler. This morning Ford’s common stock was trading at $16.69 per share, and the company had 3.47 billion shares outstanding. You estimated that the market value of all of the company’s other outstanding securities (excluding the common stock but including special shares owned by the Ford family) is $100 billion and that its revenues from auto sales were $133.4 billion last year. Chrysler’s revenue in 2014 was $50.0 billion. Based on the enterprise value/revenue ratio, what is the total value of Chrysler that is implied by the Ford market values?

Solution: The enterprise value of Ford is:

VF = VE + VOther outstanding securities = ($16.69 per share × 3.47 billion shares) + $100 billion = $157.91 billion

and the enterprise value/revenue ratio is:

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This suggests that the value of the Chrysler business is 1.18 × $50.0 billion = $59.0 billion. (Note that in this example we used the enterprise value/revenue ratio because EDITDA was unclear for Chrysler.) LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.9

Nonoperating assets: Why is excess cash a nonoperating asset (NOA)? Why does it make sense to add the value of excess cash to the value of the discounted cash flows when we use the WACC or FCFE approach to value a business?

Solution: Excess cash is a nonoperating asset because, by definition, this cash can be distributed to stockholders without affecting the operations of the business and therefore the value of the expected future cash flows. It makes sense to add back the value of excess cash because it represents value over and above that which the business is expected to produce. LO 3 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.10 Dividend discount approach: You want to estimate the total intrinsic value of a large gas and electric utility company. This company has publicly traded stock and has been paying a regular dividend for many years. You decide that, due to the predictability of the dividend that this company pays, you can use the dividend discount valuation approach. The company is expected to pay a dividend of $1.25 per share next year, and the dividend is expected to grow at a rate of 3 percent per year thereafter. You estimate that the appropriate rate for discounting future dividends is 12 percent. In addition, you know that the company

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has 46 million shares outstanding and that the market value of its debt is $350 million. What is the total enterprise value of the company?

Solution: The value of a share of stock can be calculated using the constant-growth dividend model as:

P0 =

D1 $1.25 = = $13.89. kcs - g 0.12 − 0.03

Multiplying the price per share by the number of shares outstanding gives us the value of the equity: VE = $13.89 × 46 million = $638.94 million Therefore, the total value of the firm is: VF = VE + VD = $638.94 million + $350 million = $988.94 million LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.11 Public versus private company valuation: You are considering investing in a private company that is owned by a friend of yours. You have read through the company’s financial statements and believe that they are reliable. Multiples of similar publicly traded companies in the same industry suggest that the value of a share of stock in your friend’s company is $12. Should you be willing to pay $12 per share?

Solution: Shareholders in a private company may have to spend considerable resources in money and time to sell their shares. This additional transaction cost will make value derived from similar publicly traded company an overestimated figure. Therefore, you will most likely not be willing to pay for $12 a share. You can apply an appropriate marketability discount to this price as a fair price for this private equity.

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LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.12 Control: Does the expected rate of return that is calculated using CAPM, with a beta estimated from stock returns in the public market, reflect a minority or a controlling ownership position? How is it likely to differ between a minority and a controlling position?

Solution: The estimates we obtain using public market data with CAPM are based on small stock transactions. To the extent that having control would enable an investor to better manage the systematic risk associated with a business, a discount rate for a controlling transaction is likely to be lower than that implied by CAPM (this generates a higher value and therefore a premium price for control). LO 4 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE

18.13 Organizational form: Compare the characteristics of an LLC with those of a partnership and a C-corporation.

Solution:

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An LLC is a hybrid of a limited partnership and a corporation. Like a corporation, an LLC provides limited liability for the people who make the business decisions in the firm while enabling all investors to retain the tax advantages of a limited partnership. LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.14 Organizational form: Discuss the pros and cons of an S-corporation compared with a C-corporation.

Solution: An S-corporation is a variation of the C-corporation. The advantage of an S-corporation compared to a C-corporation is that all of its profits are passed directly to the stockholders, and therefore double taxation is avoided while it still offers the protection of limited liability for shareholders. The disadvantage of an S-corporation is the limitation on stock ownership. Currently, an S-corporation can have no more than 100 stockholders and have only one class of common stock, and all stockholders must be individuals who are U.S. citizens or residents. As a result, access to capital is less limited, and cost to transfer ownership is much higher for an S-corporation than for a C-corporation. LO 1 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.15 Break-even: You have started a business that sells a home gardening system that allows people to grow vegetables on the countertop in their kitchens. You are considering two options for marketing your product. The first is to advertise on local TV. The second is to distribute flyers in the local community. The TV option, which costs $50,000 annually, will promote the product more effectively and create a demand for 1,200 units per year. The flyer advertisement option costs only $6,000 annually but will create a Copyright © 2015 John Wiley & Sons, Inc.

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demand for only 250 units per year. The price per unit of the indoor gardening system is $100, and the variable cost is $60 per unit. Assume that the production capacity is not limited and that the marketing cost is the only fixed cost involved in your business. What are the break-even points for both marketing options? Which one should you choose?

Solution: The break-even point for TV advertisement = $50,000/$40 = 1,250 units. However, the demand is only 1,200 units with TV advertisement. Therefore you cannot break even. The break-even point for flyers = $6,000/$40 = 150 units. With a market demand of 250, you will make a profit. Therefore you should choose the flyer option. LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.16 Going-concern value: Aggie Motors is a chain of used car dealerships that has publicly traded stock. Using the adjusted book value approach, you have estimated the value of Aggie Motors to be $45,646,000. The company has $40.5 million of debt outstanding. Its stock price is $5.5 per share, and there are 1,378,000 shares outstanding. What is the going concern value of Aggie Motors?

Solution: The going-concern value equals the difference between the market value of the business (the present value of the expected cash flows) and its adjusted book value. The market value of the business can be calculated as: VF = VD + VE = $40,500,000 + ($5.5 × 1,378,000) = $48,079,000 Therefore, the going concern value is $48,079,000 – $45,646,000 = $2,433,000 LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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Use the following information concerning Johnson Machine Tool Company in Problems 18.17, 18.18, and 18.19. Johnson’s income statement from the fiscal year that ended this past December is: Revenue

$995

Cost of goods sold

652

Gross profit

$343

Selling, general, & administrative expenses

135

Operating profit (EBIT)

$208

Interest expense Earnings before taxes Taxes Net income

48 $160 64 $ 96

All dollar values are in millions. Depreciation and amortization expenses last year were $42 million, and the company has $533 million of debt outstanding.

18.17 Multiples analysis: You are an analyst at a private equity firm that buys private companies, improves their operating performance, and sells them for a profit. Your boss has asked you to estimate the fair market value of the Johnson Machine Tool Company. Billy’s Tools is a public company with business operations that are virtually identical to those at Johnson. The most recent income statement for Billy’s Tools is as follows:

Revenue

$1,764

Cost of goods sold

1,168

Gross profit

$ 596

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$ 226

All dollar values are in millions. Billy’s had depreciation and amortization expenses of $71 million last year and had 200 million shares and $600 million of debt outstanding as of the end of the year. Its stock is currently trading at $12.25 per share. Using the P/E multiple, what is the per share value of Johnson’s stock? What is the total value of Johnson Machine Tool Company?

Solution: The P/E multiple for Billy’s Tools is: P / E = ($12.25  200 million shares) / $226 = 10.84

which implies a value of 10.84 × $96 = $1,040.64 million for the equity of Johnson Machine Tools Company. Therefore, the implied total value of Johnson is: VF = VE + VD = $1,040.64 + $533.00 = $1,573.64 million LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.18 Multiples analysis: Using the enterprise value/EBITDA multiple, what is the total value of Johnson Machine Tool Company? What is the per share value of Johnson’s stock?

Solution: The enterprise value/EBITDA multiple for Billy’s is: EV/EBITDA = (($12.25 × 200 million shares) + $600 million debt) / ($385 million EBIT+ $71 million D&A) = 6.69 Therefore, the implied total value of Johnson is: VF = 6.69 × ($208 million EBIT + $42 million D&A) = $1,672.50 And the value of its stock is: Copyright © 2015 John Wiley & Sons, Inc.

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VE = VF – VD = $1,672.50 million - $533.00 million = $1,139.50 million LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.19 Multiples analysis: Which of the above multiples analyses do you believe is more appropriate?

Solution: While the value estimates in the previous questions are reasonably similar, the enterprise value/EBITDA multiple is more appropriate for this analysis. The reason is that the capital structures of Johnson and Billy’s differ considerably and the enterprise value/EBITDA multiple is less sensitive to differences in leverage. The debt/total capital ratio for Billy’s is $600 million /(($12.25 × 200 million shares) + $600 million debt) = 0.196 The debt/total capital ratio for Johnson is: $533 million / $1,672.50 million = 0.319 LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.20 Income approaches: You are using the FCFF approach to value a business. You have estimated that the FCFF for next year will be $123.65 million and that it will increase at a rate of 8 percent for each of the following four years. After that point, the FCFF will increase at a rate of 3 percent forever. If the WACC for this firm is 10 percent and it has no NOA, what is it worth?

Solution:

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You can value the FCFF for the first five years using the growing annuity formula from Chapter 6 (Equation 6.5).   1+ g  n  $123.65   1.08 5  CF1 PVAn = × 1-  × 1-   =   (WACC - g )   1+ WACC   0.10- 0.08   1.1   = $541.98 million

The present value of the terminal value is 𝐹𝐶𝐹𝐹1 × (1 + 𝑔1 )4 × (1 + 𝑔2 ) $123.65 × (1 + 0.08)4 × (1 + 0.03) ] [ ] 𝑊𝐴𝐶𝐶 − 𝑔2 0.1 − 0.03 𝑃𝑉(𝑇𝑉5 ) = = (1 + 𝑊𝐴𝐶𝐶)5 (1 + 0.1)5 [

= $1,536.97 million and the value of the firm is therefore: VF = $541.98 million + $1,536.97 million = $2,078.95 million LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.21 Valuing a private business: You want to estimate the value of a privately owned restaurant that is financed entirely with equity. Its most recent income statement is as follows:

Revenue Cost of goods sold

$3,000,000 600,000

Gross profit

$2,400,000

Salaries and wages

1,400,000

Selling expenses

100,000

Operating profit (EBIT) Taxes Net income

$ 900,000 315,000 $ 585,000

You note that the profitability of this restaurant is significantly lower than that of comparable restaurants, primarily due to high salary and wage expenses. Further investigation reveals Copyright © 2015 John Wiley & Sons, Inc.

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that the annual salaries for the owner and his wife, the firm’s accountant, are $900,000 and $300,000, respectively. These salaries are much higher than the industry median salaries for these two positions of $100,000 and $50,000, respectively. Compensation for other employees ($200,000 in total) appears to be consistent with the market rates. The median P/E ratio of comparable restaurants with no debt is 10. What is the total value of this restaurant?

Solution: The owner is paying himself and his wife salaries that are above normal for this industry, probably to avoid double taxation (assuming that the restaurant is organized as a C corporation). You should adjust the income statement to reflect the market rates of compensation for these positions. The adjusted income statement is as follows:

Revenue Cost of goods sold Gross profit

$3,000,000 600,000 $2,400,000

Salaries and wages

350,000

Selling expenses

100,000

Operating profit (EBIT) Taxes Net income

$1,950,000 682,500 $1,267,500

Therefore you estimate the company’s value to be: $1,267,500 × 10 = $12,675,000. The value of the company will be underestimated if no adjustment for excess compensation is made. LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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18.22 Valuing a private business: A few years ago, a friend of yours started a small business that develops gaming software. The company is doing well and is valued at $1.5 million based on multiples for comparable public companies after adjustments for their lack of marketability. With 300,000 shares outstanding, each share is estimated to be worth $5. Your friend, who has been serving as CEO and CTO (chief technology officer), has decided that he lacks sufficient managerial skills to continue to build the company. He wants to sell his 160,000 shares and invest the money in an MBA education. You believe you have the appropriate managerial skills to run the company. Would you pay $5 each for these shares? What are some of the factors you should consider in making this decision?

Solution: You should consider at least two additional factors in valuing these equity shares. First, note that since the company has a total 300,000 shares of equity outstanding, you will be purchasing a majority of the shares and will gain control of the company. Second, while you might be able to use your excellent managerial skills to create new value for the firm, if your friend is a key person, you must consider the impact of his departure on the development and sales of the company’s products. Your valuation of the equity could be higher or lower than $5 per share, based on adjustments for both potential control premium and key person discount. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED 18.23 You plan to start a business that sells waterproof sun block with a unique formula that reduces the damage of UVA radiation 30 percent more effectively than similar products on the market. You expect to invest $50,000 in plant and equipment to begin the business. The targeted price of the sun block is $15 per bottle. You forecast that unit sales will total 1,500 bottles in the first month and will increase by 20 percent in each of the following months Copyright © 2015 John Wiley & Sons, Inc.

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during the first year. You expect the cost of raw materials to be $3 per bottle. In addition, monthly gross wages and payroll are expected to be $13,000, rent is expected to be $3,000, and other expenses are expected to total $1,000. Advertising costs are estimated to be $35,000 in the first month, but to remain constant at $5,000 per month during the following eleven months. You have decided to finance the entire business at one time using your own savings. Is an initial investment of $75,000 adequate to avoid a negative cash balance in any given month? If not, how much more do you need to invest up front? How much do you need to invest up front to keep a minimum cash balance of $5,000? What is the break-even point for the business?

Solution: The monthly cash budget is as follows: Monthly Cash Budget Month

Beginning cash balance

$ 75,000

$ (9,000)

$ (9,400)

$ (5,480)

22,500

27,000

32,400

38,880

$ 97,500

$ 18,000

$ 23,000

$ 33,400

Raw material

4,500

5,400

6,480

7,776

Gross wages and payroll

13,000

Advertising

35,000

5,000

Rent

3,000

Cash receipts Cash sales Total cash available Operations

Other expenses

1,000

Operations total

$ 56,500

$ 27,400

$ 28,480

$ 29,776

---

Financing and investments Capital expenditures

50,000

Total cash payments

$106,500

$ 27,400

$ 28,480

$ 29,776

Ending cash balance

$ (9,000)

$ (9,400)

$ (5,480)

$ 3,624

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With $75,000 of capital invested in the initial period, the company will have negative cash balances during each of the first three months and positive cash balances in the following months. Additional capital investment totaling $9,400 will be needed to avoid negative cash balances in month 2. In other words, you will have to invest $84,400 of capital in total at the beginning of the business just to avoid negative cash balances. To maintain a minimum cash balance of $5,000, you will need to make an initial capital investment of $89,400 ($84,000 + $5,000). Break-even: Fixed costs in the initial month will equal: $13,000 + $35,000 + $3,000 + $1,000 = $52,000 Fixed monthly costs in the following months will be: $13,000 + $5,000 + $3,000 + $1,000 = $22,000. Since variable costs per bottle are $3, the monthly break-even points for the firm are: $52,000 / ($15 – $3) = 4,333.3 bottles in the initial month and $22,000 / ($15 – $3) =1,833.3 bottles in the following months. The sales of the company are 1,500, 1,800, 2,160, and 2,592 bottles in the first four months. Therefore, the firm will start to make a profit in the third month. This can be seen from the cash budget analysis above. Month 3 is the first month the firm’s cash balance is increasing (becoming less negative). LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.24 For the previous question, assume that you do not have sufficient savings to cover the entire amount required to start your sun-block business. You are going to have to get external financing. A local banker whom you know has offered you a six-month loan of $20,000 at an APR of 12 percent. You will pay interest each month and repay the entire principal at the end of six months. Assume that instead of making a single up-front investment, you are going to finance the business by making monthly investments as cash is needed in the business. If the proceeds from the loan go directly into the business on the first day and are therefore Copyright © 2015 John Wiley & Sons, Inc.

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available to pay for some of the capital expenditures, how much money do you need to pull out of your savings account every month to run the business and keep the cash balances positive?

Solution: The monthly payment of the loan is $20,000 ×1% = $200. The cash budget without your investment is as follows: Monthly Cash Budget Month

Beginning

cash $ 20,000

$(64,200) $(64,800) $(61,080) $(52,176) $(37,051)

balance Cash receipts Investments

owner Cash sales

22,500

Total cash available

27,000

32,400

38,880

46,656

55,987

$ 42,500

$(37,200) $(32,400) $(22,200) $(5,520)

$ 18,936

4,500

5,400

6,480

7,776

9,331

11,197

Gross wages and 13,000

13,000

Cash payments Operations Raw material

payroll Advertising

35,000

5,000

Rent

3,000

Other expenses

1,000

Operations total

$ 56,500

$ 27,400

$ 28,480

$ 29,776

$ 31,331

$ 33,197

50,000

---

Financing

and

investments Capital expenditures

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200

20, 200

Total cash payments

$106,700

$ 27,600

$28,680

$ 29,976

$ 31,531

$ 53,397

Ending cash balance

$(64,200) $(64,800) $(61,080) $(52,176) $(37,051) $(34,461)

payment

Therefore, you need to put in $64,200 initially, and $600 ($68,400–64,200) in the next month. You don’t need to invest in more money afterward, because the cash balance is increasing afterward. LO 1 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.25 Your friend is starting a new company. He wants to write a business plan to clarify the company’s business outlook and raise venture capital. Knowing that you have taken this course, he has asked you, as a favor, to help him prepare a template for a business plan. Prepare a template that includes the key elements of a business plan.

Solution: Business varies and so does a business plan. Here is a template for an intermediate-level business plan, which could be tailored to specific industry and company situations: 1. Executive Summary 1.1 Objectives 1.2 Mission 1.3 Keys to Success 2. Company Overview 3. Product Description 4.

Market Analysis 2.1 Market Segmentation 2.2 Target Market Segment Strategy 2.3 Market Needs

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2.4 Competitions and Buying Patterns 5. Marketing and Sales 5.1 Competitive Edge 5.2 Sales Strategy 6. Operations 6.1 Production 6.2 Distribution 6.3 Supply 7. Management and Ownership 7.1 Organizational Structure 7.2 Management Team 7.3 Ownership 8. Financial Plan 8.1 Break-even Analysis 8.2 Projected Profit and Loss 8.3 Projected Cash Flow 9. Appendices: Tables and charts LO 2 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.26 A friend of yours is trying to value the equity of a company and, knowing that you have read this book, has asked for your help. So far she has tried to use the FCFE approach. She estimated the cash flows to equity to be as follows:

Sales

$800.0

− CGS

−450.0

− Depreciation

−80.0

− Interest

−24.0

Earnings before taxes (EBT)

$246.0

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− Taxes (0.35 × EBT)

−86.1

= Cash flow to equity

$159.9

She also computed the cost of equity using CAPM as follows: kE = kF +

E(Risk premium) = 0.06 + (1.25 × 0.084) = 0.165 or 16.5%

where the beta is estimated for a comparable publicly traded company. Using this cost of equity, she estimates the discount rate as WACC = xDebtkDebt pretax(1 − t) + xcs kcs =[ 0.20 × 0.06 × (1 − 0.35)] + (0.80 × 0.165) = 0.14, or 14% Based on this analysis, she concludes that the value of equity is $159.9 million/0.14 = $1,142 million. Assuming that the numbers used in this analysis are all correct, what advice would you give your friend regarding her analysis?

Solution: There are a number of potential problems with your friend’s analysis. First, she has calculated FCFF incorrectly. She is assuming that net income equals FCFE. Once she obtains net income she should add back depreciation, subtract capital expenditures and additions to working capital, and subtract any net repayment of debt principal. Second, she is using the incorrect discount rate. She should be using the cost of equity to discount the FCFE. Finally, since your friend is using the perpetuity formula, she is assuming that the expected future FCFE will be constant forever. You should inquire whether this is really what she expects. LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.27 Forever Youth Technology is a biochemical company that is two years old. Its main product, an antioxidant drink that is supposed to energize the consumer and delay aging, is still under development. The company’s equity consists of $5 million invested by its Copyright © 2015 John Wiley & Sons, Inc.

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founders and $5 million from a venture capitalist. The company has spent $3 million in each of the past two years, mostly on lab equipment and R&D costs. The company has had no sales so far. What are the challenges associated with valuing such a young and uncertain company?

Solution: As discussed in the chapter, it is very difficult to value such a young firm with many uncertainties. The company has a short history, high investments, no sales, and highly uncertain cash flows in the future. The cost approach is not valid for such a young biochemical company. It is hard to value the company using multiples analysis because of the lack of sales and negativity of earnings, and because of lack of comparable companies of the same business. The transaction analysis approach is also hard to apply. Despite the many uncertainties, we should try to estimate the future cash flows and risks associated with these cash flows. First of all, we need to estimate the probability and time length to achieve success in developing the product. In addition, we need to find out what happens in case the firm’s capital is used up before the product is developed. We need to decide whether, based on the company’s future prospects, it is possible to raise additional external capital at that point of time, and if not, we need to decide whether the business has any liquidation value. Then, we need to estimate the market demand and shares as well as target price of the product, in case it is developed successfully. We also need to estimate the short-term and long-term growth rate of the company based on market, industry, and firm-specific conditions. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.28 Mad Rock Inc. is a company that sells mp3 music online. It is expected to generate earnings of $1 per share this year after its Web site is upgraded and online marketing is stepped up. Given the popularity of the iPod and iPad devices, the stock price of Mad Rock has rocketed

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from $8 to $95 per share in the past 12 months. The cost of capital for the company is 18 percent. Of course, the future of a young Internet company such as Mad Rock is highly uncertain. Nevertheless, using the very limited information provided in this problem, do you think $95 per share could be a fair price for its stock? Support your argument with a simple analysis.

Solution: Assume that the earnings of $1 will be realized. To simplify the problem, assume that all earnings will be paid out as dividends. Using the dividend growth model, $95 = $1/(0.18 – g), which implies that g = 16.9%. We know that it is not possible for a firm to grow at this rate forever because G is a growth rate that must be sustainable in perpetuity. No firm can grow indefinitely at such a high rate, which is many times the average growth rate of the world economy. Therefore, this analysis suggests that Mad Rock’s stock is overpriced. On the other hand, it is possible that Mad Rock could grow very rapidly for a few years and then grow at a sustainable rate that justifies the $95 price. For example, if we assume that a sustainable rate is 6 percent, we can solve for the earnings per share that would be required to justify a $95 stock price. This value is $95 = D/(0.18 – 0.06) which implies D = $11.4. Therefore, if the earnings per share increased rapidly to a value above $11.4, it is possible that a price of $95 could be justified. How much above $11.4 it would have to be, would depend on how quickly it increased. One other consideration here is that, as the business matures, its cost of capital is likely to decrease because its risk will decline. This will tend to increase the value of the equity. LO 4 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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18.29 At the end of 2014 the value of the S&P 500 Index divided by the estimated 2014 earnings for S&P 500 firms (the S&P 500 P/E multiple) was 18.66. Assume that the long term Treasury bond yield was 3.72 percent, the market risk premium was 5.17 percent, and firms in the S&P 500 were expected to pay out an average of 37.6 percent of their earnings as dividends in the future. At what rate were dividends paid by S&P 500 firms expected to grow in the future?

Solution: The equation of Price/earnings multiple based on constant-growth model can be used to answer this question.

P0 b = E1 kcs − g

Recognizing that E1 = E0 × (1 + g) we can rewrite this equation as:

P0 (1+ g )b = E 0 kcs − g

Since we know that P0/E0 = 18.66, and b = 37.6%, all that we have to do is calculate kcs in order to use the above equation to solve for g.

We can use CAPM to estimate kcs: kcs = Rrf + (βcs × Market risk premium)

From the problem statement we know that Rrf = 3.72 percent and that the market risk premium equals 5.17 percent. Therefore, we only need a value for βcs in order to calculate kcs.

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Since The S&P 500 represents more than 70 percent of the market capitalization of all stocks traded in the U.S. (see Chapter 9), we know that the beta for the S&P will be relatively close to 1. Using this value in CAPM we estimate that kcs equals:

kcs = 0.0372 + (1 × 0.0517) = 0.0889.

We can now write the formula for the P/E as follows:

P0 (1 + g )  0.376 =18.66 = E0 0.0889 − g

Solving for g yields g = 0.0674, or 6.74 percent. The S&P 500 index value at the end of 2014 implied that the market expected the dividends paid by firms in the S&P 500 to increase at an average annual rate of 6.74 percent forever. LO 3 Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.30 The S&P 500 P/E multiple of 18.66 at the end of 2014 was higher than its historical average of approximately 15. Some financial commentators argued that this meant that the firms in the S&P 500 were, on average, overvalued at the end of 2014. Based on your analysis in problem 18.29 and the concepts covered in this book, do you think that these commentators are right or wrong? Why or why not?

Solution: There is no way to know for sure whether the commentators are right or wrong. If the market is semi-strong form efficient, as this term is defined in Chapter 2, then all public information should be reflected in the prices of S&P 500 shares. This implies that there is

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no way for an outsider to know for sure whether the firms in the S&P 500 were, on average, over- or undervalued.

However, we can make some observations. First, with regards to the analysis in problem 18.29, if the constant growth perpetuity model (which was used to derive Equation 18.1) is an appropriate model for the dividends paid by S&P 500 firms, then the implied growth rate of 7.9 percent suggests that the market might be over-valuing the shares of S&P 500 firms. Recall from Chapter 9 that g cannot be greater than the sum of the expected real growth rate in the economy and the expected rate of inflation. This sum has historically been less than 7 percent. If g turns out to be less that 7 percent in the future, then the value of the S&P 500 index will decline⎯meaning that the firms in the S&P 500 would have been overvalued on average at the end of 2014.

On the other hand, if the mixed (supernormal) dividend growth model discussed in Chapter 9 is a more appropriate model for dividend growth at S&P 500 firms, then it is possible that the firms in the S&P 500 were not, on average, overvalued at the end of 2014. For example, since the U.S. economy was just emerging from a severe recession in 2010 it might have been perfectly reasonable to expect relatively large increases in 2011 and 2012 earnings as the economy recovered. As can be seen from the following table, which shows estimated earnings for S&P 500 firms for the 2004 to 2010 period, the 2010 earnings estimate was still considerably below the 2007 earnings.

S&P 500 Year

Earnings

2010

67.46

2009

12.65

2008

66.60

2007

88.70

2006

78.16

2005

67.86

2004

58.87

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A multiple of 18.66 would be justified if the earnings of S&P 500 firms were expected to return to the 2007 level in two years (e.g in 2012) and then grow at 4.2 percent per year afterwards. LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.31 You own a company that produces and distributes course packets for classes at local universities via the Internet. You have asked a friend to invest $35,000 in the business. Your friend wants to know what the business is worth so that he can determine how much of the equity (e.g., what percentage) he should expect to receive for his investment. You offer to help him value the business.

The business is expected to generate revenue of $110,000 and incur cash operating expenses of $70,000 next year. Over the following three years, revenue and cash operating expenses are expected to increase 15 percent, 10 percent, and 7 percent. After year 4 they are expected to grow 2 percent per year forever. Depreciation and amortization, capital expenditures, and additions to working capital are expected to equal 5 percent, 6 percent, and 1 percent of revenue, respectively, in the future. You have determined that a target capital structure of 10 percent is reasonable for this business. With this capital structure, the pretax cost of debt will be 6 percent and the beta for the equity will be 1.30. The average tax rate for the business is 10 percent, and the marginal rate is 20 percent. The risk-free rate is 4.25 percent and the market risk premium is 6.01 percent. What is a 100 percent equity interest in the business worth? What percentage of the equity should your friend get for his investment?

Solution: We can value the equity of this business using the FCFF Income approach. We will first estimate the WACC using Equation 13.7. To do this we calculate kcs using Equation 13.4: Copyright © 2015 John Wiley & Sons, Inc.

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kcs = Rrf + (βcs × Market risk premium) = 0.0425 + (1.30)(0.0601) = 0.1206, or 12.06% and substitute into Equation 13.7:

WACC = xDebt kDebt pretax (1- t ) + x ps k ps + xcs kcs = (0.10)(0.06)(1-.10) + (0)(0) + (0.9)(0.1206) = 0.1140 or11.40%

Note that we use the average tax rate in this calculation because we are assuming that the company will continue to operate on a stand-alone basis and that its average tax rate will continue to be 10 percent.

We next forecast the FCFF and discount them to the present using the WACC to obtain the enterprise value. There is no mention of NOA in the problem statement and so we assume that there are none. Since we are assuming that the firm will have 10 percent debt, the value of the equity equals 90 percent of the enterprise value.

The spreadsheet below shows the forecasted FCFF for the next five years and the calculation of the equity value.

The trickiest part of the calculations in the spreadsheet is in estimating the additions to working capital. Unlike depreciation and amortization and capital expenditures, we do not simply multiply the 1percent value given in the problem statement by revenue in the same year to obtain additions to working capital. The 1percent value is for the total working capital that the business has. Since it already has working capital in the previous year, we multiply the change in revenue in the upcoming year by 1 percent. This tells us how much must be invested in working capital at the beginning of that year in order to have enough working capital to support the forecasted revenue. For example, the additions to working capital for Year 1 (remember that this is also the beginning of Year 2) equals:

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YEARS Revenues Operating costs Depreciation and amortization Operating profit Taxes (10%) NOPAT Depreciation and amortization Capital expenditures Additions to working capital FCFF Terminal Value with 2% growth FCFF + TV PV(FCFF) @ 11.40% Enterprise Value Less: 10% debt Equity value

1 $110,000 70,000 5,500 34,500 3,450 31,050 5,500 6,600 165 $29,785

2 $126,500 $80,500 6,325 39,675 3,968 35,708 6,325 7,590 127 $34,316

3 $139,150 $88,550 6,958 43,643 4,364 39,278 6,958 8,349 97 $37,789

$29,785 $26,738

$34,316 $27,654

$37,789 $27,337

4 $148,891 $94,749 7,445 46,697 4,670 42,028 7,445 8,933 30 $40,509 $439,721 $480,230 $311,860

$393,588 $39,359 $354,230

The equity value that we have calculated does not take into account any adjustments for control, lack of marketability (remember that it is a private firm), or key people. Since there is no information in the problem statement we do not consider them here. With this caveat, we can calculate the percentage of the equity that your friend should receive as:

$35,000/$354,230 = 0.988, or 9.88% LO 3 Bloomcode: Analysis AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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5 $151,86 $96,64 7,59 47,63 4,76 42,86 7,59 9,11 3 $41,31

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Sample Test Problems

18.1

You plan to start a business to produce and sell custom kitchen cabinets. The targeted price for each order of cabinets is $10,000. You estimate that you will receive orders for cabinets for eight kitchens in each of the first two months, nine kitchens in the third month, and ten kitchens in the fourth month. The cost of the equipment necessary to produce the cabinets is $105,000. You expect the cost of raw materials to be $3,000 per order. In addition, you expect monthly gross wages and payroll to be $27,000, rent to be $8,000, and other expenses to total $4,000. You also expect advertising costs to be $10,000 in the first month, but to remain constant at $1,000 per month during the following three months. How much will you have to initially invest ensure that you have a cash balance of $10,000 at the beginning of the second month? If you invest this amount, what will be your cash balance at the end of the fourth month?

Solution: Ending cash balance of Month 1 = Beginning cash balance of Month 2 = $10,000 Ending cash balance of Month 1 = Beginning cash balance of Month 1 + Cash receipt – Cash payment $10,000 = Beginning cash balance of Month 1 + $80,000 – $178,000 Beginning cash balance of Month 1 = $108,000

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Cash Budget for 4 months:

Beginning cash balance Cash receipts: Cash sales Total cash receipts Total cash available Cash payments: Equipment Raw material cost Gross wages Rent Other expenses Advertising cost Total cash payments Ending cash balance

Month 1 $108,000

Month 2 $10,000

Month 3 $ 26,000

Month 4 $ 49,000

80,000 $ 80,000 $188,000

80,000 $80,000 $90,000

90,000 $ 90,000 $116,000

100,000 $100,000 $149,000

$105,000 24,000 27,000 8,000 4,000 10,000 $178,000 $ 10,000

0 24,000 27,000 8,000 4,000 1,000 $64,000 $26,000

0 27,000 27,000 8,000 4,000 1,000 $ 67,000 $ 49,000

0 30,000 27,000 8,000 4,000 1,000 $ 70,000 $ 79,000

We have to initially invest $108,000 to ensure that we have a cash balance of $10,000 at the beginning of the second month. If we invest $108,000, our cash balance at the end of the fourth month will be $79,000. Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.2

Which of the following is/are usually included in an entrepreneur’s business plan? a. Detailed description of the company’s products and services. b. Discussion of the management team, including organizational structure. c. A listing of the types of securities that have been issued and who owns them. d. A market analysis. e. All of the above are typically included in a business plan.

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Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.3

Sessler Corporation is a private company that had EBIT of $186 million and depreciation and amortization of $22 million in the most recent fiscal year. At the end of that year, a similar, public firm has an Enterprise Value/EBITDA multiple of 4.3. What is the implied enterprise value of Sessler?

Solution: We can estimate the enterprise value for the Sessler Corporation as:

 Enterprise value   EBITDA Company being valued VF =   EBITDA   Comparable EBITDA = EBIT + DA = $186 million + $22 million = $208 million VF = 4.3 × $208 million VF = $894.40 million Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.4

Winters Inc. management estimates that the company will generate after-tax free cash flows from the firm (FCFF) of $12.5 million, $16.8 million and $19.7 million, respectively, over the next three years. After that, FCFF are expected to grow at a constant five percent per year forever. The company has $5 million in non-operational assets. If the appropriate WACC is 8 percent, what is the enterprise value of this business?

Solution: We can calculate the enterprise value of Winters Inc. using following equation: VF = PV(FCFT) + PV(TVT) + NOA The present value of the free cash flows is: Copyright © 2015 John Wiley & Sons, Inc.

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PV(FCFF3) =

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$12.5 million $16.8 million $19.7 million = $41.62 million + + 1 + 0.08 (1 + 0.08)2 (1 + 0.08)3

We can then estimate the cash flows for the remainder of the business’s life (the terminal value) using two simple steps: (1) calculating the present value of all cash flows after the final (third) year of the detailed forecast using the formula for a growing perpetuity (2) discounting this value to the present

TV3 =

FCFF3  (1 + g) $19.7 million  (1 + 0.05) = = $689.50 million WACC – g 0.08 – 0.05

PV(TV3 ) =

TV3 $689.50 million = = $547.35 million 3 (1 + WACC) (1 + 0.08)3

The total value of Winters Inc.: VF = PV(FCFT) + PV(TVT) + NOA VF = $41.62 million + $547.35 + $5 million VF = $593.97 million Enterprise value of Winters Inc. is $593.97 million. Bloomcode: Application AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

18.5

Do private companies have audited financial statements prepared in accordance with GAAP?

Solution: There is no requirement that the financial statements of private companies be audited. Some private companies have complete, audited financial statements, whereas others have incomplete financial statements that are not prepared in accordance with the generally accepted accounting principles (GAAP). Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance Copyright © 2015 John Wiley & Sons, Inc.

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Chapter 19 Financial Planning and Forecasting Before You Go On Questions and Answers Section 19.1 1.

What are the four planning documents on which the financial plan is based? The four important planning documents are: (1) the strategic plan, which describes where the firm is headed and articulates the strategies that will be used to get it there; (2) the investment plan, which identifies the capital assets needed to execute the strategies; (3) the financing plan, which explains how the firm will raise the money to buy the assets; and (4) the cash budget, which determines whether the firm will have sufficient cash to pay its bills. These four planning documents provide the foundation for the firm’s financial plan, which consolidates the documents into a single scheme.

What is the strategic plan? The strategic plan is developed to communicate the firm’s long term goals from a very high conceptual level. It is extremely important as the strategy of the firm ultimately drives all other decisions at the firm.

How are the investment decision and financing decision related? When a firm makes a decision to invest in some asset, it must also identify a source of funding to pay for it. Thus, these two decisions are intertwined and must be made together.

Section 19.2 1.

Why is the sales forecast the key component of a financial model? Sales forecast is the key component in a financial model as the majority of data used are calculated as a percentage of sales. Hence, it is important to get as accurate a sales forecast as possible in order to build a meaningful model.

What are pro forma financial statements, and why are they an important part of the financial planning process?

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Pro forma financial statements are hypothetical statements that are projected into the future. They are then evaluated to determine which investment and under what conditions will be the most beneficial for the firm. 3.

What is the plug factor in a financial model? The plug factor in a financial model is the source of external financing needed to bring the balance sheet into balance.

Section 19.3 1.

How are historical financial data used to determine the forecasted values of balance sheet accounts? To forecast balance sheet values, the financial manager prepares a table that shows several years of historical accounting data as a percentage of sales. Then some simple trend lines are fitted to the data to see if there are any trends. This allows the forecaster to decide which financial accounts can safely be estimated as a percent of sales and which must be forecasted using other information.

Why might you expect accounts receivable to vary with sales? Accounts receivable can be expected to vary with sales since higher sales mean more money coming in, and hence increased level of receivables.

Section 19.4 1.

Why is it that some working capital accounts may not vary proportionately with sales? Working capital takes into account current assets and current liabilities, and in many instances inventories and cash balances do not proportionately change with sales. The working capital ratio often increases at a decreasing rate as sales increase.

What are lumpy assets, and how do these assets vary with sales? In most instances, fixed assets do not vary directly with sales, but are rather periodically added in large increments or lumps, hence the name “lumpy assets”.

Section 19.5 1.

What two factors determine the amount of EFN?

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The amount of EFN is determined by the difference between the total amount of new assets the firm needs to finance less the amount of internal financing available. 2.

What is IGR, and why is it of interest to management? IGR stands for internal growth rate and is defined as the maximum growth rate a firm can achieve without external financing. IGR is of management interest, as firms that can generate a high volume of retained earnings and/or use fewer assets can sustain a higher growth rate without raising more capital

If a firm continually exceeds its SGR, what problems may it face in the future? If the firm’s actual growth rate consistently exceeds its sustainable growth, the firm will have a cash shortage problem if it is unwilling to change its targeted capital structure or sell equity. If the firm has a high credit rating and its use of leverage is not excessive, the firm may have no problem going to the market and securing additional funds.

Self-Study Problems 19.1

The Starlight, Inc. financial statements for the fiscal year ended June 30, 2013, are presented below. The firm’s sales are projected to grow at a rate of 20 percent next year, and all financial statement accounts will vary directly with sales. Based on that projection, develop a pro forma balance sheet and income statement for the fiscal year ending June 30, 2014. Starlight, Inc., Balance Sheet as of June 30, 2013

Assets: Cash Accounts receivables Inventories Total current assets Net fixed assets Other assets Total assets

$ 25,135 43,758 167,112 $236,005 325,422 13,125 $574,552

Liabilities and Stockholders’ Equity: Accounts payables $ 67,855 Notes payables 36,454 Total current liabilities

$104,309

Long-term debt Common stock Retained earnings Total liabilities and equity

223,125 150,000 97,118 $574,552

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Starlight, Inc. Income Statement for the Fiscal Year Ended June 30, 2013 Net Sales Costs EBITDA Depreciation EBIT Interest EBT Taxes (35%) Net income

$1,450,000 812,500 $ 637,500 175,000 $ 462,500 89,575 $ 372,925 130,524 $ 242,401

Solution: The pro forma statements for Starlight are as follows: Starlight, Inc. Balance Sheet as of June 30, 2014 Assets: Liabilities and Stockholders’ Equity: Cash $ 30,162 Accounts payables Accounts receivables 52,510 Notes payables Inventories 200,534 Total current assets $283,206 Total current liabilities Net fixed assets Other assets Total assets

390,506 Long-term debt 15,750 Common stock Retained earnings $689,462 Total liabilities and equity

$ 81,426 43,745 $125,171 267,750 180,000 116,542 $689,462

Starlight, Inc. Income Statement for the Fiscal Year Ended June 30, 2014

Net Sales Costs EBITDA Depreciation EBIT Interest EBT Taxes (35%) Net income

19.2

$1,740,000 975,000 $ 765,000 210,000 $ 555,000 107,490 $ 447,510 156,629 $ 290,882

Use the financial information for Starlight from Problem 16.1. Assume now that equity accounts do not vary directly with sales but change when retained earning change or new

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equity is issued. The company pays 45 percent of its income as dividends every year. In addition, the company plans to expand production capacity by building a new facility that will cost $225,000. The firm has no plans to issue new equity this year. Any funds that need to be raised will be in the form of long-term debt. Prepare a pro forma balance sheet using this information. Solution: The pro forma income statement is the same as that shown in the solution to Problem 16.1. We now have to accommodate payment of dividends. Since the company pays 45 percent of its net income as dividend, the amount of retained earnings is calculated as follows: Retained earnings from 2014 income statement = $290,882 × (1 - 0.45) = $159,985 ▪ This is the amount by which retained earnings will increase by in 2014, from $97,118 to $257,103. ▪ No new equity is added. ▪ The increase in assets is financed externally through the sale of long-term debt. The pro forma balance sheet is as follows: Starlight, Inc. Balance Sheet as of June 30, 2014 Assets: Liabilities and Stockholders’ Equity: Cash $ 30,162 Accounts payables $ 81,426 Accounts receivables 52,510 Notes payables 43,745 Inventories 200,534 Total current assets $283,206 Total current liabilities $125,171 Net fixed assets Addition to fixed assets Other assets Total assets

19.3

390,506 Long-term debt 225,000 Common stock 15,750 Retained earnings $914,462 Total liabilities and equity

382,188 150,000 257,103 $914,462

Use the financial statements from Problem 16.1 and the information from Problem 16.2 to calculate the company’s retention(plowback) ratio, external funds needed (EFN), internal growth rate (IGR) and sustainable growth rate (SGR).

. Solution: The retention (plowback) ratio, external funds needed, internal growth rate, and sustainable growth rate are calculated as follows:

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Retention (plowback) ratio =

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Addition to retained earnings Net income $159,985 = $290,882 = 0.55, or 55%

= (Growth rate × Initial assets) – Addition to retained earnings = (0.20 × $574,552) ─ $159,985 = ─ $45,075 Thus, without considering the investment of $225,000 for the new facility, the firm will not need any external financing. However, if you add that in, then, EFN

= New investments – Addition to retained earnings = (0.20 × $574,552) + $225,000 ─ $159,985 = $179,925 Additions to retained earnings IGR = Initial assets $159,985 = $574,552 = 0.278 or 27.8% SGR = Plowback ratio × ROE Addition to retained earnings Net income = × Net income Total equity = 0.55×0.715 = 0.393 or 39.3%

EFN

19.4

Northwood Corp. has a dividend payout ratio of 60 percent, return on equity of 14.5 percent, total assets of $11,500,450, and equity of $4,652,125. Calculate the firm’s internal rate of growth (IGR).

Solution: We calculate Northwood’s internal growth rate as follows: IGR = Plowback ratio × ROE × Measure of leverage $4,652,125 = 0.40×0.145× $11,500, 450 = 0.235 or 2.35%

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Renewal Company has net income of $1.25 million and a dividend payout ratio of 35 percent. It currently has equity of $2,875,223. What is the firm’s sustainable growth rate?

Solution: Renewal’s sustainable growth rate is: SGR = Plowback ratio × ROE $1, 250,000 = 0.65× $2,875, 223 = 0.283 or 28.3%

Discussion Questions 19.1

What is financial planning? What four types of plans/budgets are involved in financial planning? Financial planning is the process by which a company’s management identifies the best investment opportunities from a strategic perspective and determines how to finance these investments. The end result is referred to as a financial plan. The four plans in financial planning are the strategic plan, the investment plan or capital budget, the financing plan, and the cash budget.

LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

19.2

Why is the capital budget an important part of a firm’s financial planning? The investment plan, also known as the capital budget, lays out the firm’s proposed spending on capital assets for the year. The capital budget describes in detail all the firm’s planned spending on productive assets like plant and equipment, a new production line, etc.

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AICPA: Industry/Sector Perspective

19.3

Why do financing and investment decisions have to be made concurrently? Any investment decision has to be linked to a source of funds to pay for the investment or any capital expenditures, and hence the investment decision and the financing decision have to be made concurrently.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

19.4

Explain how sales can be used to develop pro forma financial statements. For most financial planning models, the principal input variable is a forecast of the firm’s sales or sales growth rate. The forecasted sales can be the basis for a financial planning model because so many items on the income statement and balance sheet vary with changes in the level of sales.. Sales forecasts are given for some time period, such as a quarter or a year, and are often expressed as percent change in sales: % S = (St+1 –St)/ St

LO: 2 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Budget Preparation AICPA: Industry/Sector Perspective

19.5

Why is sales not always a good measure to use in forecasting fixed assets? When a percent of sales method is used to prepare pro forma financial statements, the issue of whether or not a firm is operating at full capacity is ignored. Only if the firm is

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operating at full capacity does fixed assets vary directly with sales. If a firm has excess capacity, then sales can increase without a need to invest in additional fixed assets. . LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Budget Preparation AICPA: Industry/Sector Perspective

19.6

List all the accounts that can be affected by the “plug” value. How does this value help managers? The plug value relates to the amount of external funds needed based on a given level of sales. Thus, all the various sources of funds for a firm like short-term and long-term debt, common equity, and retained earnings are affected by the plug value.

LO: 2 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

19.7

Explain why the fixed asset account may or may not vary with sales. Generally, companies invest in fixed assets in large discrete amounts rather than in small, continuous amounts. Thus, each investment in fixed assets can accommodate a further growth in sales without calling for additional investment in plant and equipment. Only after each level of sales is accomplished at full production capacity would management have to consider another increase in fixed assets.

LO: 3 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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Solutions Manual

How does the dividend payout ratio affect the amount of funds needed to finance growth? Any change in the dividend payout ratio directly affects the amount of funds retained by the company. The higher the firm’s ratio for a given level of net income, the lower the amount of retained earnings, and hence the larger will be the amount of external debt financing needed by the firm by holding the growth rate constant.

LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.9

Define internal growth rate (IGR). Identify the characteristics of a high-growth firm that has no external funds needed. Internal growth rate (IGR) is the maximum growth rate a firm can sustain without needing any external financing. Such firms have a high enough retention ratio to fund growth, generate a high level of net income for every dollar of equity than other firms, and use low amounts of leverage or debt financing.

LO: 5 Level: Basic Bloomcode: Knowledge AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.10 What is the sustainable growth rate? Why is it important? Sustainable growth rate (SGR) is the maximum growth rate a firm can sustain without needing any external equity financing, holding leverage constant. Holding the firm to a sustainable growth rate allows the firm to avoid costly equity issues, thus reducing the dilution of earnings. Whenever firms grow faster than the SGR, the firm is going to need external financing and may have to resort to debt financing, which increases the company’s risk. LO: 5 Copyright © 2015 John Wiley & Sons, Inc.

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Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

Questions and Problems BASIC 19.1

Strategic plan: Explain the importance of the strategic plan.

Solution: The strategic plan is the blueprint for a company’s management that determines the firm’s long-term goals, identifies the strategies to achieve these goals, and determines the company’s ability to be competitive. It drives all decision making within the firm and covers all areas of a firm’s operations. LO 1 Bloomcode: Comprehension AASCB: Analytic IMA: Strategic Planning AICPA: Industry/Sector Perspective

19.2

Capital budget: What are the various steps in preparing a capital budget?

Solution: First, management identifies all strategically acceptable investment opportunities and ranks them based on their contribution to shareholder wealth. Next, the senior management reviews the capital budget plan and may revise it, if necessary, based on need and the amount they can finance. LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Investment Decisions AICPA: Industry/Sector Perspective

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Financing plan: What are the elements of a financing plan?

Solution: First, the financing plan identifies the amount of external financing needed and where the funds could be obtained from. Second, the plan identifies the firm’s target capital structure. Last, the plan identifies the firm’s dividend policy, which directly affects the amount of funds available for new investment projects, the more funds the firm payout as cash dividends, the more the external funding needed for its investment. LO 1 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

19.4

Financial planning: Identify the steps in the financial planning process.

Solution: o o o o o

Establish a set of financial goals. Identify the investment opportunities and financing alternatives. Employ a financial planning model. Evaluate the investment and financing choices and decide on the ones that are the best fit for the firm. Prepare contingency plans for future use.

LO 1 Bloomcode: Knowledge AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

19.5

Financial modeling: List the various elements of financial modeling.

Solution: The important elements of financial modeling are the sales forecast, economic assumptions, pro forma statements, investment decisions, financing requirements, and the “plug factor” that determines the source of the external funds needed. LO 2 Bloomcode: Comprehension AASCB: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective Copyright © 2015 John Wiley & Sons, Inc.

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Payout ratio: Define the retention (plowback) ratio and the dividend payout ratio.

Solution: The dividend payout ratio tells us how much of a firm’s earnings are paid to the shareholders as dividends. The retention ratio is complementary to the payout ratio and tells us how much of the firm’s earnings are retained in the firm. Thus, the retention ratio equals: Retention ratio = (1 − Dividend payout ratio) LO 3 Bloomcode: Knowledge AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.7

Addition to retained earnings: Northwood, Inc., has revenue of $455,316, costs of $316,487, and a tax rate of 31 percent. If the firm pays out 45 percent of its earnings as dividends every year, how much earnings are retained and what is the firm’s retention ratio?

Solution: Revenue = $455,316 Costs = $316,487 Tax rate = 31% Payout ratio = 45% Net income = ($455,316 - $316,487)  (1 - 0.31) = $95,792 Retained earnings = 95,792 × (1 ─ 0.45) = $52,686 Retention ratio = (1 - Dividend payout ratio)

Retention ratio = (1 − 0.45) = 55% LO 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.8

Payout and retention ratio: Goodwin Corp. has revenues of $12,112,659, costs of $9,080,545, interest payments of $412,375, and a tax rate of 34 percent. It paid dividends

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of $1,025,000 to its stockholders. What are the firm’s dividend payout ratio and retention ratio? Solution: Goodwin Corp.

Revenues Costs EBIT Interest EBT Taxes (34%) Net income

$12,112,659 9,080,545 $ 3,032,114 412,375 $ 2,619,739 890,711 $1,729,028

Dividends paid = $1,025,000 Dividends $1, 025, 000 Dividend payout ratio = = = 59.28% Net income $1, 729, 028 Retention ratio = (1 - Dividend Payout ratio) = (1 – 0.5928) = 40.72%

LO 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.9

Percent of sales: Cattail Corporation’s financial statements for the fiscal year just ended are shown below: Cattail Corporation Financial Statements for Fiscal Year Just Ended ($ thousands) Income Statement Balance Sheet Net sales $1,500 Assets $700 Debt $600 Costs 350 Equity 100 Net income $1,150 Total $700 Total $700 Cattail management expects sales to increase by 14 percent next year. Assume that the financial statement accounts vary directly with changes in sales and that management has no financing plan at this time. Given this information, develop a pro forma income statement for Cattail for the next fiscal year.

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Projected costs = $350,000 × 1.14 = $399,000 Cattail Corporation Pro Forma Income Statement ($ thousands) Net sales $1,710 Costs 399 Net income $1,311 LO 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.10 Percent of sales: Given the data for Cattail Corporation in Problem 19.9, if you assume that all balance sheet items also vary with the change in sales, develop a pro forma balance sheet for Cattail for the next fiscal year. Assuming that the firm did not sell or repurchase stock, what is the cash dividend implied by the pro forma income statement and balance sheet? Solution: Projected assets = $700,000 × 1.14 = $798,000 Projected debt = $600,000 × 1.14 = $684,000 Projected equity = $100,000 × 1.14 = $114,000 Cattail Corporation Pro Forma Income Statement ($ thousands) Balance Sheet Assets $798 Debt $684 Equity $114 Total $798 Total $798 Pro forma net income is $1,311,000 and the change in the equity account is $14,000, therefore the difference ($1,311,000 - $14,000 = $1,297,000) is the amount of the cash dividends that must have been paid. LO 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

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19.11 Capital intensity ratio: Define capital intensity ratio, and explain its significance. Solution: The capital intensity ratio measures the amount of assets needed to generate one dollar in sales. The higher the ratio, the more assets are needed to generate every dollar of sales, and hence, the more capital intense is the firm and vice versa. LO 3 Bloomcode: Knowledge AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.12 Capital intensity ratio: Tantrix Confectioners has total assets of $3,257,845 and net sales of $5,123,951. What is the firm’s capital intensity ratio? Solution: Total assets = $3,257,845 Sales = $5,123,951 Total assets Capital intensity ratio = Net sales $3,257,845 = = 63.6% $5,123,951 LO 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.13 Capital intensity ratio: McDonald Metal Works has been able to generate net sales of $13,445,196 on assets of $9,145,633. What is the firm’s capital intensity ratio? Solution: Sales = $13,445,196 Total assets = $9,145,633

Total assets Net sales $9,145, 633 = = 0.6802 or 68.02% $13, 445,196

Capital intensity ratio =

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.14 Capital intensity ratio: For McDonald Metal Works in Problem 19.13, how much must net sales grow if the capital intensity ratio has to drop to 60 percent? State your answer as both a percent of sales and a dollar sales increase. Solution: Target capital intensity ratio = 60% Total assets Capital intensity ratio = Net sales $9,145,633 0.60 = Net sales $9,145,633 Net sales = = $15,242,721.67 0.60 Growth in net sales needed = New sales – Old sales = $15,242,722 – $13,445,196 = $1,797,526 Percentage change in net sales needed = $1,797,526 / $13,445,196 = 13.37% LO 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.15 Internal growth rate: Swan Supply Company has net income of $1,212,335, assets of $12,522,788 and retains 70 percent of its income every year. What is the company’s internal growth rate? Solution: Net income = $1,212,335 Total assets = $12,522,788 Plowback ratio = 70%

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Internal growth rate (IGR) = Plowback ratio  ROE  Measure of Leverage Net income Equity = Plowback ratio   Equity Total assets Net income = Plowback ratio  Total assets $1,212,335 = 0.70  $12,522,788 = 6.8% IGR = Addition to retained earnings/Initial total assets Addition to retained earnings= 70% × $1,212,335=$ 848,634.5 So, IGR = $ 848,634.5/$12,522,788 = 6.8% LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.16 Sustainable growth rate: If Newell Corp. has a ROE of 13.7 percent and a dividend payout ratio of 32 percent, what is its sustainable growth rate?

Solution: ROE = 13.7% Payout ratio = 32% Plowback ratio = (1 − Payout ratio) = (1 − 0.32) = 68%

SGR = Plowback ratio  ROE = 0.68  0.137 = 9.3% LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

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Growth _Rate_ (%) 0% 5 9.6 10 15 20

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__EFN_ ($ millions)_ -$4.8 -2.3 0.0 0.2 2.7 5.2

Check the calculations and plot the line to replicate the graph in Exhibit 19.11. Solution: Exhibit 19.11 gives you the plot. LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

INTERMEDIATE 19.18 Retention ratio: Refer to Problem 19.7. Northwood expects to increase its sales by 15 percent next year. All costs vary directly with sales. If Northwood wants to retain $65,000 of earnings next year, will it have to change its dividend payout ratio? If so, what will be the new dividend payout and retention ratios for the firm? Solution: Expected increase in sales = 15% All costs vary directly with sales Revenues next year = $455,316  (1.15) = $523,613 Costs = $316, 487  (1.15) = $363,960 EBT = $159, 653 Net income = $159, 653  (1- 0.31) = $110,161

Targeted retained earnings = $65,000 Retention ratio = $65,000/$110,161 = 59.0% Dividend payout ratio = (1 - 0.59) = 41% So, the dividend payout ratio declines from 45 percent to 41 percent. LO 3 Bloomcode: Application Copyright © 2015 John Wiley & Sons, Inc.

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AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.19 Capital intensity: Identify two industries (other than airlines) that are capital intensive. Using online or other data sources, compute the capital intensity ratio for the largest firm in each of the chosen industries. Solution: Two industries that may be considered to be capital intensive are the electric utilities industry and the aluminum processing industry. LO 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.20 Percent of sales: Tomey Supply Company’s financial statements for the most recent fiscal year are shown below. The company management projects that sales will increase by 20 percent next year. Assume that all costs and assets increase directly with sales. The company has a constant 33 percent dividend payout ratio and has no plans to issue new equity. Any financing needed will be raised through the sale of long-term debt. Prepare pro forma financial statements for the coming year based on this information, and calculate the EFN for Tomey. Tomey Supply Company Income Statement and Balance Sheet Income Statement Balance Sheet Net sales $1,768,121 Assets: Costs 1,116,487 Current assets $280,754 EBT $651,634 Net fixed assets 713,655 Taxes (35%) 228,072 Total assets $994,409 Net income $ 423,562 Liabilities and Equity: Current liabilities $167,326 Long-term debt 319,456 Common stock 200,000 Retained earnings 307,627 Total liabilities and equity $994,409

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Solution: Tomey Supply Company Net sales Costs EBT Taxes (35%) Net income Dividends paid Addition to retained earnings

Solutions Manual

Sales Change $1,768,121 1.2 1,116,487 1.2 $ 651,634 228,072 $ 423,562

Pro Forma $2,121,745 1,339,784 $ 781,961 273,686 $ 508,275 167,731 $340,544

Assets: Current assets Net fixed assets Total assets

$ 280,754 713,655 $ 994,409

1.2 1.2

$ 336,905 856,386 $1,193,291

Liabilities and Equity: Current liabilities Long-term debt Common stock Retained earnings Total liabilities & equity

$ 167,326 319,456 200,000 307,627 $ 994,409

1.2

$ 200,791 144,329 200,000 648,171 $1,193,291

EFN = (Initial assets  Growth rate) − Addition to retained earnings = ($994, 409  0.20) - $340,544 = −$141,662 Addition to current liabilities = $33,465 So, actual EFN = -$141,662 - $33,465 = -$175,127 LO 3 Bloomcode: Application AASCB: Analytic IMA: Budget Preparation AICPA: Industry/Sector Perspective

19.21 Internal growth rate: Using the pro forma financial statements for Tomey Supply Company developed in Problem 19.20, find the internal growth rate for Tomey. Solution:

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IGR = Addition to retained earnings / Initial assets = $340,543 / $994, 409 = 0.3425 or 34.25% LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.22 Sustainable growth rate: Use the following pro forma information for Tomey Supply Company for next year: net income = $508,275; addition to retained earnings = $340,544; common equity = $848,171; net sales = $2,121,745. Assume that management does not want the ratio of long-term debt to equity to exceed the current long-term debtto-equity ratio of 63 percent and also does not want to issue new equity. What level of sales growth can Tomey Supply Company sustain? Calculate the new sales level. Solution: Current debt to equity ratio = 63% Sustainable growth rate (SGR) = Plowback ratio  ROE Addition to retained earnings Net income SGR = × Net income Total equity

$340,544 $508, 275 × $508, 275 $848,171 = 40.2% New sales level = Old sales  (1 + SGR) =

= $2,121,745  (1.402) = $2, 974, 686 LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective 19.23 Sustainable growth rate: Rowan Company has a net profit margin of 8.3 percent, debt ratio of 45 percent, total assets of $4,157,550, and sales of $6,852,654. If the company has a dividend payout ratio of 67 percent, what is its sustainable growth rate? Solution: Net profit margin = 8.3% Copyright © 2015 John Wiley & Sons, Inc.

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Debt ratio = 45% Total assets = $4,157,550 Sales = $6,852,654 Dividend payout ratio = 67% Plowback ratio = (1- 0.67) = 33% Net income Net profit margin = Sales Net income = Sales × Net profit margin

= $6,852,654 × 0.083 = $568,770 Measure of Leverage = 1- Debt ratio = (1- 0.45) = 55% Total equity = 0.55  $4,157,550 = $2, 286, 653

Net income × Plowback ratio Total equity $568, 770 = × 0.33 $2, 286, 653 = 8.2%

SGR =

LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.24 Sustainable growth rate: Refer to the information for Rowan Company in Problem 19.23. The firm’s management desires a sustainable growth rate (SGR) of 10 percent but does not wish to change the company’s level of debt or its payout ratio. What will the firm’s new profit margin have to be in order to achieve the desired growth rate? Solution: Target SGR = 10% Plowback ratio = 33% Debt ratio = 45%

Equity multiplier = EM =

1 1 = = 1.82 Equity (1- 0.45)

Total assets turnover ratio = TATO =

Sales $6,852,654 = == 1.65 Times Total assets $4,157,550 SM 19-23

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ROE =

Solutions Manual

SGR 0.10 = = 30.3% Plowback ratio 0.33

ROE = PM ×TATO× EM ROE 0.303 Net profit margin = PM = = = 10.1% TATO× EM (1.65×1.82) LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.25 Sustainable growth rate: Rocky Sales, Inc., has current sales of $1,215,326 and net income of $211,253. It also has a debt ratio of 25 percent and a dividend payout ratio of 75 percent. The company’s total assets are $712,455. What is its sustainable growth rate? Solution: Sales = $1,215,326 Net income = $211,253 Debt ratio = 25% Dividend payout ratio = 75% Total assets = $712,455 Plowback ratio = (1 - 0.75) = 25%

Equity ratio or Measure of leverage = (1 - 0.25) = 75% Total equity = 0.75  Total assets = 0.75  $712,455 = $534,341 Net income $211, 253 ROE = = = 39.5% Total equity $534,341 SGR = Plowback ratio  ROE = 0.25  0.395 = 9.9% LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

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19.26 Sustainable growth rate: Ellicott Textile Mills management has reported the following financial information for the year ended September 30, 2014. The company generated a net income of $915, 366 on a net profit margin of 6.4 percent. It has a dividend payout ratio of 50 percent, a capital intensity ratio of 62 percent, and a debt ratio of 45 percent. What is the company’s sustainable growth rate? Solution: Net income = $915,366 Net profit margin = 6.4% Dividend payout ratio = 50% Capital intensity ratio = 62% Debt ratio = 45% Net income $915,366 Sales = = = $14,302,594 Profit margin 0.064 Total assets Sales Total Assets = Capital intensity ratio ×sales

Capital intensity ratio =

= 0.62 ×$14,302,594 = $8,867,608 Equity = (1- Debt ratio) × Total assets (1- 0.45) ×$8,867,608 = $4,877,184 Net income $915,366 ROE = = = 18.8% Total equity $4,877,184

SGR = Plowback ratio  ROE = 0.50  0.188 = 9.4% LO 3, LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.27 Internal growth rate: Given the information in Problem 19.26, what is the internal growth rate of Ellicott Textile Mills? Solution:

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IGR = Plowback ratio  ROA $915,366 = 0.50  = 5.2% $8,867,608 LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.28 Internal growth rate: Fantasy Travel Company has a return on equity of 17.5 percent, a total equity/total assets ratio of 65 percent, and a dividend payout ratio of 75 percent. What is the company’s internal growth rate? Solution: ROE = 17.5% Equity ratio = 65% Dividend payout ratio = 75% Plowback ratio = (1 - 0.75) = 25% IGR = Plowback ratio  ROE  Measure of Leverage

= 0.25  0.175  0.65 = 2.8% LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.29 EFN: Maryland Micro Brewers generated revenues of $12,125,800 with a 72 percent capital intensity ratio during the year ended September 30, 2014. Its net income was $873,058. With the introduction of a half dozen new specialty beers, management expects to grow sales by 15 percent next year. Assume that all costs vary directly with sales and that the firm maintains a dividend payout ratio of 70 percent. What will be the EFN needed by this firm? If the company wants to raise no more than $750,000 externally and is not averse to adjusting its payout policy, what will be the new dividend payout ratio? Solution: Total sales = $12,125,800 Capital intensity ratio = 72% Copyright © 2015 John Wiley & Sons, Inc.

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Total assets = Capacity intensity ratio×Sales = 0.72×$12,125,800 = $8,730,576 Net income = $873,058 Projected net income =$873,058 x 1.15 =$1,004,017 Dividend payout ratio = 70% Addition to retained earnings = $1,004,017(1-0.7) = $301,205

EFN = (Growth rate×Total assets) - Addition to retained earnings = (0.15×$8, 730,576) − $301, 205 = $1, 008,381 Target EFN = $750,000 Addition to retained earnings = (Growth rate  Total assets) - EFN = (0.15  $8,730,576) − $750,000 = $559,586

Plowback ratio =

$559,586 = 55.73% $1, 004 , 017

Dividend payout ratio = (1- Plowback ratio) = (1- 0.5573) = 44.27%

LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.30 EFN: Ritchie Marble Company has total assets of $12,899,450, sales of $18,174,652, and net income of $4,589,774. Management expects sales to grow by 25 percent next year. All assets and costs (including taxes) vary directly with sales, and management expects to maintain a payout ratio of 65 percent. Calculate Ritchie’s EFN. Solution: Total assets = $12,899,450 Sales = $18,174,652 Net income = $4,589,774 Copyright © 2015 John Wiley & Sons, Inc.

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Expected growth rate = 25% Projected net income = $4,589,774 (1.25) = $5,737,217.50 Payout ratio = 65% Addition to retained earnings = Net income × (1- Payout ratio)

= $5,737,217.50 × 0.35 = $2,008, 026.13 EFN = (Growth rate × Total assets) - Addition to retained earnings = (0.25×$12,899,450) - $2,008,026 = $1, 216,836 LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.31 EFN: Norton Group, Inc., expects to add $1,213,777 to retained earnings and currently has total assets of $23,159,852. If the company has the ability to borrow up to $1 million, how much growth can the firm support if it is willing to borrow to its maximum capacity? Solution: Addition to retained earnings = $1,213,777 Total Assets = $23,159,852 EFN = $1,000,000 EFN = (Growth rate  Total assets) - Addition to Retained earnings

(EFN + Addition to Retained earnings) = Growth rate  Total assets EFN + Addition to retained earnings Total assets $1,000,000 + $1, 213,777 = = 9.6% $23,159,852

Growth rate =

LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.32 EFN: Capstone Marketing Group has total assets of $5,568,000, sales of $3,008,725, and net income of $822,000. The company expects its sales to grow by 12 percent next year. Copyright © 2015 John Wiley & Sons, Inc.

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All assets and costs (including taxes) vary directly with sales, and the firm expects to maintain a payout ratio of 55 percent. Calculate Capstone’s EFN. Solution: With a growth rate in sales of 12 percent, if all costs increase at the same rate, then pro forma net income will be: $822,000 × 1.12 = $920,640. Addition to retained earnings = (1 ─ 0.55) × $920,640 = $414,288 EFN = (0.12 × $5,568,000) – $414,288 = $253,872 LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.33 Maximum sales growth: Given the data for Capstone Marketing Group in Problem 19.32, what would Capstone’s payout ratio have to be for the firm’s EFN to be zero? Solution: EFN will be equal to zero if the change in assets is equal to the change in retained earnings. Projected net income = $822,000 × 1.12 = $920,640 Projected change in assets = 0.12 × $5,568,000 = $668,160 $668,160 = $920,640 × (1 – payout ratio) Payout ratio = 0.274, or 27.4% LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.34 Maximum sales growth: Rockville Consulting Group expects to add $271,898 to retained earnings this year. The company has total assets of $3,425,693 and wishes to add no new external funds for the coming year. If assets and costs vary directly with sales, how much sales growth can the company support while retaining an EFN of zero? What is the firm’s internal growth rate? Solution: Addition to retained earnings = $271,898 Total assets = $3,425,693 Copyright © 2015 John Wiley & Sons, Inc.

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EFN = 0

(EFN + Addition to retained earnings) Total assets (0 + $271,898) = = 7.9% $3, 425,693)

Maximum growth rate =

Addition to retained earnings $271,898 = = 7.9% Initial assets $3, 425,693 With no external financing, the maximum possible growth equals the internal growth rate. IGR =

LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

ADVANCED 19.35 The financial statements for the year ended June 30, 2014, are given below for Morgan Construction Company. The firm’s sales are projected to grow at a rate of 25 percent next year, and all financial statement accounts will vary directly with sales. Based on that projection, develop a pro forma balance sheet and an income statement for the 2015 fiscal year. Morgan Construction Company Balance Sheet as of June 30, 2014 Assets: Liabilities and Stockholders’ Equity: Cash $ 3,349,239 Accounts payable $ 9,041,679 Accounts receivable 5,830,754 Notes payable 4,857,496 Inventories 22,267,674 Total current assets $31,447,667 Total current liabilities $13,899,175 Net fixed assets Other assets Total assets

Net sales

43,362,482 Long-term debt 1,748,906 Common stock Retained earnings $76,559,055 Total liabilities and equity

29,731,406 19,987,500 12,940,974 $76,559,055

Morgan Construction Company Income Statement for the Fiscal Year Ended June 30, 2014 $193,212,500

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Costs EBITDA Depreciation EBIT Interest EBT Taxes (35%) Net income

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145,265,625 $ 47,946,875 23,318,750 $ 24,628,125 11,935,869 $ 12,692,256 4,442,290 $ 8,249,966

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Solution:

Cash Accounts receivable Inventories Total current assets

Morgan Construction Company—Pro Forma Balance Sheet for Year Ended June 30, 2015 2014 2015 2014 $ 3,349,239 1.25 $ 4,186,549 Accounts payable $ 9,041,679 5,830,754 1.25 7,288,443 Notes payable 4,857,496 22,267,674 1.25 27,834,593 $31,447,667 $39,309,584 Total current liabilities $13,899,175

Net fixed assets Other assets

43,362,482 1,748,906

Total assets

$76,559,055

1.25 1.25

54,203,103 2,186,133 $95,698,819

Long-term debt Common stock Retained earnings Total liabilities & equity

Pro Forma Income Statement for Year Ended June 30, 2015 2014 Revenues $193,212,500 1.25 Costs 145,265,625 1.25 EBITDA $ 47,946,875 Depreciation 23,318,750 1.25 EBIT $ 24,628,125 Interest 11,935,869 1.25 EBT $ 12,692,256 Taxes (35%) 4,442,290 1.25 Net income $ 8,249,966 LO 3 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

29,731,406 19,987,500 12,940,974 $76,559,055

1.25 1.25

2015 $11,302,099 6,071,870 $17,373,969

1.25 1.25 1.25

37,164,258 24,984,375 16,176,218 $95,698,819

2015 $241,515,625 181,582,031 $ 59,933,594 29,148,438 $ 30,785,156 14,919,836 $ 15,865,320 5,552,862 $ 10,312,458

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19.36 Use the financial information for Morgan Construction Company from Problem 19.35. Assume now that equity accounts do not vary directly with sales but change when retained earnings change or new equity is issued. The company pays 75 percent of its income as dividends every year. In addition, the company plans to expand production capacity by expanding the current facility and acquiring additional equipment. This will cost the firm $10 million. The firm has no plans to issue new equity this year. Prepare a pro forma balance sheet using this information. Any funds that need to be raised (in addition to changes in current liabilities) will be in the form of long-term debt. What is the external funding needed in this case? Solution: Retention ratio = 25% Net income in 2015 = $10,312,458 Addition to retained earnings = $2,578,114.50 or $2,578,115

Cash Accounts receivable Inventories Total current assets Net fixed assets Addition to fixed assets Other assets Total assets

1.25

1,748,906 $76,559,055

1.25

54,203,102 10,000,000 2,186,133 $105,698,819

Long-term debt Common stock Retained earnings Total liabilities & equity

29,731,406 19,987,500 12,940,974 $76,559,055

1.25 1.25

2015 $11,302,099 6,071,870 $ 17,373,969 $52,818,261 19,987,500 15,519,089 $105,698,819

EFN = (Growth rate  Total assets)-Addition to Retained earnings = (0.25  $76,559,055) − $2,578,115 = $16,561,649 Thus, without considering the investment of $10,000,000 for the new facility, the firm will not need any external funding. However, if you add the investment, then, EFN= New investment – Addition to retained earnings (0.25 ×$76,559,055) + $10,000,000 – $2,578,115 = $26,561,649 LO 3, LO 5 Copyright © 2015 John Wiley & Sons, Inc.

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Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

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19.37 Using the information for Morgan Construction Company in the preceding problem, calculate the firm’s internal growth rate and sustainable growth rate. Solution:

IGR =

Addition to retained earnings $2,578,115 = = 3.37% Initial assets $76,559, 055

Net Income $ 10,312,458 = = Equity $ 41,160,593 SGR = Plowback ratio  ROE ROE =

25.05%

= 0.25  0.2505 = 6.26% LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.38 Use the information for Morgan Construction Company from Problems 19.35 and 19.36. Assume that equity accounts do not vary directly with sales, but change when retained earnings change or new equity is issued. The company’s long-term debt-toequity ratio is approximately 90 percent, and its equity-to-total assets ratio is about 43 percent. The company management wishes to increase its equity-to-total assets ratio to at least 50 percent. Management is willing to reduce the company’s payout ratio, but will retain no more than 40 percent of earnings. The company will raise any additional funds needed, including funds for expansion, by selling new equity. No new long-term debt will be issued. Prepare pro forma statements to reflect this new scenario. a. What is the external funding needed to accommodate the expected growth? b. What is the firm’s internal growth rate? c. What is the firm’s sustainable growth rate? d. How much new equity will the firm have to issue? e. What is the firm’s new equity ratio and debt- to- equity ratio? Copyright © 2015 John Wiley & Sons, Inc.

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Solution: a. Retention ratio = 40% EFN = (Growth rate×Total assets) - Addition to retained earnings

= (0.25×$76,559,055) - (0.40×$10,312, 458) = $15,014,780.55 EFN including expansion = $25,014,781

b. c. d.

Addition to retained earnings $4,124,983 = = 5.39% Initial assets $76,559, 055 SGR = Plowback ratio× ROE = 0.40×0.2505 = 10.02% Retained earnings in 2015 = $12,940,974 + $4,124,983 = $17,065,957 Total liabilities and equity = $105,698,819 Current liabilities = $17,373,969 Common equity = $105,698,819 – ($17,373,969+$29,731,406+$17,065,957) = $41,527,487 Common equity in 2014 = $19,987,500 New common equity issued = $41,527,487 - $19,987,500 = $21,539,987 Equity ($41,523, 487 + $17, 069,957) New equity ratio = = Total assets $105, 698,818 = 55.43% Debt $29, 731, 406 Debt - to - equity ratio = = = 50.74% Equity $58,593, 444 IGR =

Morgan Construction Company—Pro Forma Balance Sheet for Year Ended June 20, 2015 2014 2015 2014

2015

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Cash

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$ 3,349,239

1.25

$ 4,186,549

5,830,754

1.25

7,288,443

22,267,674 $31,447,667

1.25

27,834,593 $ 39,309,584

Net fixed assets Addition to fixed assets Other assets

43,362,482

1.25

Total assets

$76,559,055

Accounts receivable Inventories Total current assets

54,203,103 10,000,000

1,748,906

1.25

2,186,133 $105,698,819

Accounts payable Notes payable

$ 9,041,679

1.25

$11,302,099

4,857,496

1.25

6,071,870

Total current liabilities

$13,899,175

$ 17,373,969

Long-term debt Common stock Retained earnings Total liabilities & equity

29,731,406

29,371,406

19,987,500

41,527,487

12,940,974

17,065,957

$76,559,055

$105,698,819

LO 5 Bloomcode: Application AASCB: Analytic IMA: Budget Preparation AICPA: Industry/Sector Perspective

19.39 Munson Communications Company has just reported earnings for the year ended June 30, 2014. Below are the firm’s income statement and balance sheet. The company had a 55 percent dividend payout ratio for the last 10 years and management does not plan to change this policy. Based on internal forecasts, Management expects sales growth in 2015 to be 20 percent. Assume that equity accounts and long-term debt do not vary directly with sales, but change when retained earnings change or additional capital is issued.

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Munson Communications Company Balance Sheet as of June 30, 2014 Assets: Cash Accounts receivable Inventories Total current assets

Liabilities and Stockholders’ Equity: $ 1,728,639 Accounts payable 3,009,421 Notes payable 11,492,993 $16,231,053 Total current liabilities

Net fixed assets Other assets

22,380,636 Long-term debt 1,748,906 Common stock Retained earnings $40,360,595 Total liabilities and equity

Total assets

$ 4,666,673 2,507,094 $ 7,173,767 13,345,242 10,165,235 9,676,351 $40,360,595

Munson Communications Company Income Statement for the Fiscal Year Ended June 30, 2014 Net sales Costs EBITDA Depreciation EBIT Interest EBT Taxes (35%) Net income a. b. c.

$79,722,581 59,358,499 $20,364,082 7,318,750 $13,045,332 3,658,477 $ 9,386,855 3,285,399 $ 6,101,456

What is the firm’s internal growth rate (IGR)? What is the firm’s sustainable growth rate (SGR)? What is the external funding needed (EFN) to accommodate the expected growth? Copyright © 2015 John Wiley & Sons, Inc.

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Construct the firm’s 2015 pro forma financial statements under the assumption that long-term debt will provide all external funding.

Solution: a. Retention ratio = 45.0% Net income in 2014 = $ 6,101,456 Expected net income in 2015 = $6,101,456 (1.20) = $7,321,747 Addition to retained earnings = $ 3,294,786 ROE = 30.8% Growth rate = 20% IGR =

b. c.

Addition to retained earnings Initial assets

$ 3,294,786 $ 40,360,595

8.16%

SGR = Plowback ratio× ROE = 0.45×0.308 = 13.84% EFN = (Growth rate×Total assets) - Addition to retained earnings

= (0.20×$40,360,595) - (0.45×$7,321,747) = $4, 777, 333

Cash Accounts receivable Inventories Total current assets

Munson Communications Company—Pro Forma Balance Sheet as of June 20, 2015 2014 2015 2014 $ 1,728,639 1.20 $ 2,074,367 Accounts payable 4,666,673 3,009,421 1.20 3,611,305 Notes payable 2,507,094 11,492,993 1.20 13,791,592 $16,231,053 $19,477,264 Total current liabilities $ 7,173,767

1.20 1.20

Net fixed assets Other assets

22,380,636 1,748,906

1.20 1.20

Total assets

$40,360,595

1.20 1.20

26,856,763 2,098,687 $48,432,714

Long-term debt Common stock Retained earnings Total liabilities & equity

13,345,242 10,165,235 9,676,351 $40,360,595

2015 $ 5,600,008 3,008,513 $ 8,608,521 16,687,821 10,165,235 12,971,137 $48,432,714

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Pro Forma Income Statement for the Fiscal Year Ended June 30, 2015 2014 Revenues $79,722,581 1.20 Costs 59,358,499 1.20 EBITDA $20,364,082 Depreciation 7,318,750 1.20 EBIT $13,045,332 Interest 3,658,477 1.20 EBT $ 9,386,855 Taxes (35%) 3,285,399 1.20 Net income $ 6,101,456

2015 $95,667,097 71,230,199 $24,436,898 8,782,500 $15,654,398 4,390,172 $11,264,226 3,942,479 $ 7,321,747

LO 5 Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

Sample Test Problems 19.1 Mars Company had net sales of $18 million in the year that just ended. Next year, the company’s management expects a 15 percent increase in sales. If cost of goods sold is 60 percent of sales and inventory is 25 percent of sales, what would you estimate sales, inventory, and cost of goods sold to be next year? Solution: Net sales (St) = $18 million % change in net sales (%ΔS) = 15% Expected net sales (St +1) = (0.15 × $18 million) + $18 million = $20.7 million Expected inventory (I t+1) = $20.7 million × 0.25 Copyright © 2015 John Wiley & Sons, Inc.

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= $5.175 million Expected cost of goods sold (COGS t+1) = $20.7 million × 0.60 = $12.42 million 19.2 Lavaca Inc. management expects net sales to be $855,000, total costs to be $647,000, and to pay taxes at an average rate of 32 percent this year. If the Lavaca pays out 38 percent of its earnings as dividends, what is its retention ratio? How much will Lavaca’s retained earnings increase? Solution: Lavaca Inc. Pro Forma Income Statement Net sales $855,000 Total costs 647,000 Taxable income $208,000 Taxes (32%) 66,560 Net income $141,440 Dividends (38%) $ 53,747 Addition to retained earnings $ 87,693 Retention ratio = (1 − Dividend payout ratio)

= (1 – 0.38) = 0.62 or 62% Increase in Lavaca’s retained earnings = Net income – Dividends = ($141,440 – $53,747) = $87,693

19.3 Spurlock Inc. had net income of $266,778 in its most recent fiscal year and total assets of $1,833,400 at the end of the year. The company’s total debt ratio (total debt to total assets) is 35 percent, and Spurlock retains 60 percent of its income every year. What is Spurlock’s internal growth rate? What is its sustainable growth rate? Copyright © 2015 John Wiley & Sons, Inc.

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Solution: Addition to retained earnings Initial total assets As Spurlock retains 60 percent of its income every year, its retention ratio = 0.60, or 60%. Spurlock’s addition to retained earnings = Retention ratio × Net income = 0.60 × $266,778 = $160,066.80 Initial total assets = $1,833,400 $160,066.80 Internal Growth Rate (IGR) = = 0.0873, or 8.73% $1,833,400.00

Internal Growth Rate (IGR) =

Sustainable growth rate (SGR) = Retention ratio × ROE Total debt = Total debt ratio × Total assets = 0.35 × $1,833,400 = $641,690 Total equity = Total assets – Total debt = $1,833,400 – $641,690 = $1,191,710 Net income ROE = Total equity ROE =

$266,778 = 0.2239, or 22.39% $1,191,710

Sustainable growth rate (SGR) = 0.60 × 0.2239 = 0.1343, or 13.43% 19.4 Using the information in Sample Test Problem 19.3, what is Spurlock’s capital intensity ratio if the company has net sales of $3,557,100? What does this ratio tell us? Solution: Total assets Net sales $1,833,400 = $3,557,100

Capital intensity ratio =

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= 0.5154, or 51.54% Capital intensity ratio tells us something about the amount of assets the firm needs to generate $1 in sales. The higher the ratio, the more capital the firm needs to generate sales—that is, the more capital intensive the firm. Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

19.5 Edgefield Excavation Company has total assets of $4,976,456, sales of $1,225,700, and net income of $587,000. The company’s management expects sales to grow by 9 percent next year. All costs (including taxes) and assets vary directly with sales, and the firm expects to maintain a payout ratio of 35 percent. Calculate the external funds needed (EFN) by Edgefield. What would Edgefield’s payout ratio have to be in order for the company’s EFN to equal zero? Solution: External funds needed (EFN) = New investments – Addition to retained earnings New investments = Growth rate × Initial total assets New investments = 0.09 × $4,976,456 = $447,881.04 Addition to retained earnings = Retention ratio × Net income = (1 – Dividend payout ratio) × Net income = (1 – 0.35) × $587,000 = $381,550 External funds needed (EFN) = $447,881.04 – $381,550 = $66,331.04 So external funds needed (EFN) by Edgefield is $66,331.04. The company’s EFN will be zero if new investments is equal to the addition to retained earnings. Edgefield’s addition to retained earnings = New investments = $447,881.04 Dividend payout ratio = 1 – Retention ratio

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Addition to retained earnings Net income $447,881.04 = = 0.763, or 76.3% $587,000 Dividend payout ratio = (1 – 0.763) = 0.237, or 23.7% Therefore, to be in order for Edgefield’s EFN to equal zero, the company’s payout ratio would be 0.237, or 23.7%. Bloomcode: Application AASCB: Analytic IMA: FSA AICPA: Industry/Sector Perspective

Retention ratio =

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Chapter 20 Options and Corporate Finance Before You Go On Section 20.1 1.

What is a call option, and what do the payoff functions for the owner and seller of a call option look like?

A call option gives the owner the right to buy or “call” the underlying asset at a prespecified price. The payoff for the owner of a call option is zero when the value of the underlying asset is below the exercise price, and increases dollar for dollar with the price of the underlying asset once the asset price goes above the exercise price. The payoff for the seller of a call option is 0 when the value of the underlying asset is below the exercise price, and decreases dollar for dollar with the price of the underlying asset once the asset price goes above the exercise price.

What is a put option, and what do the payoff functions for the owner and seller of a put option look like?

A put option gives the owner the right to sell the underlying asset at a pre-specified price. The payoff for the owner of a put option is 0 when the value of the underlying asset is above the exercise price, and increases dollar for dollar with decrease of the price of the

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underlying asset when the asset price drops below the exercise price. The payoff for the seller of a put option is 0 when the value of the underlying asset is above the exercise price, and decreases dollar for dollar with decrease of the price of the underlying asset once the asset price drops below the exercise price.

Why does the payoff function for an option have a kink in it?

The payoff function for an option has a “kink” at the exercise price. This kink exists because the owner of the option has a right, not an obligation, to buy or sell the underlying asset. If it is not in the owner’s interest to exercise the option, he or she can simply let it expire.

Section 20.2 1.

What are the limits on the value of a call option prior to its expiration date?

The value of a call option can never be less than zero since the owner of the option can always decide not to exercise it if doing so is not beneficial. A second limit on the value of a call option is that it can never be greater than the value of the underlying asset. It would not make sense to pay more for the right to buy an asset than you would pay for the asset itself. The third limit is that the value of a call option prior to expiration will never be less than the value of that option at expiration. Because of the time value of money, the final limit is that the value of a call option prior to expiration will never be

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less than the difference between the current value of the underlying asset and the present value of the exercise price.

What variables affect the value of a call option?

The following five variables affect the value of a call option prior to expiration: (1) Current value of the underlying asset (2) Exercise price (3) Volatility of the value of the underlying asset (4) Time until the expiration of the option (5) Risk-free rate of interest

Why are the variables that affect the value of a put option the same as those that affect the value of a call option?

Given the value of a call option, the value of a put option can be calculated using the putcall parity: P = C + Xe-rt – V. where "P" is the value of the put option, "C" is the value of the call option, "X" is the exercise price, "r" is the risk-free rate, "t" is the amount of time before the option expires, and "V" is the current value of the underlying asset. The term "e–rt" is the exponential function that you can calculate using the “ex” key on your calculator; it is simply a discount factor that assumes continuous compounding.

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We can see that the formula does not include any variables other than the five factors in valuation of a call option.

Section 20.3

What is a real option?

Real options are options on real assets. In some cases, the value of real options can be incorporated into an investment analysis by valuing the option separately using valuation methods similar to those used to value financial options, and then adding this value to the value estimated by traditional NPV analysis.

What are four different types of real options commonly found in business?

(1) Options to defer investment. (2) Options to make follow-on investments. (3) Options to change operations. (4) Options to abandon projects.

Is it always possible to estimate the value of a real option? Why or why not?

In some instances, it is not possible to estimate the value of a real option because we do not have enough information or because the necessary analysis is too complex. Although Copyright © 2015 John Wiley & Sons, Inc.

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it might not even be possible to directly estimate the value of the real options associated with a project, it is important to recognize that they exist when you perform a project analysis.

Section 20.4 1.

What do the payoff functions for stockholders and lenders look like?

The payoff function for the stockholders looks exactly like that for the owner of a call option where the exercise price is the amount owed on the loan and the underlying asset is the firm itself. The payoff function for the lenders looks like that for the seller of a put option, where the exercise price is the amount of the loan and the underlying asset is the firm itself.

What does the payoff function for a typical manager look like?

When a company defaults on its debt, the payoff function for the manager will look something like that for the lender—it will slope downward as the value of the firm decreases. On the positive side, a manager’s payoff will increase with the value of the firm when this value is above the amount that the company owes to its lenders.

Section 20.5 1.

What is hedging?

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Hedging is a method of reducing financial risks faced by a firm. Options, along with other derivative instruments, such as forwards, futures, and swaps, are commonly used in hedging.

What types of risks can options be used to manage?

Options can be used to manage risks associated with commodity prices, interest rates, foreign exchange rates, and equity prices.

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Self-Study Problems

20.1

Of the two parties to an option contract, the buyer and the seller, who has a right and who has an obligation?

Solution: The buyer (owner) of the option has the right to exercise the option but is not required to do so. The seller (or writer) of the option is obligated to take the other side of the transaction if the option owner decides to exercise it.

20.2

The stock of Augusta Light and Power is currently selling at $12 per share. Over the next year the company is undertaking a new electricity production project. If the project is successful, the company’s stock is expected to rise to $24 per share. If the project fails, the stock is expected to fall to $8 per share. The risk free rate is 6 percent. Calculate the value today of a one year call option on one share of Augusta Light and Power with an exercise price of $20.

Solution: First determine the payoffs for the stock, a risk-free loan, and the call option under the two possible outcomes. In one year, the stock price is expected to be either $8 or $24. The loan will be worth $1.06 regardless of whether the project is successful. If the project fails, the stock price will be less than the exercise price of the call option. The option will

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not be exercised, and will be worth $0. If the project is successful, the stock price will be higher than the exercise price of the call option. The option will be exercised and its value will be the difference between the stock price and the exercise price, $4. Stock (x) Today

$12

Expiration

Risk-Free Loan (y) $1

$24

$1.06

Call Option ?

$1.06

$0 $24 – $20 = $4

The stock and loan can be used to create a replicating portfolio which has the same payoff as the call option: ($8 × x) + (1.06 × y) = $0 ($24 × x) + (1.06 × y) = $4 Solving the two equations yields: x = 0.25, y = –1.887 The value of the call option is the same as the current value of this portfolio: ($12 × 0.25) + ($1 × -1.887) = $1.11

20.3

ADCAP International is a U.S.-based company which sells its products primarily in overseas markets. The company’s stock is currently trading at $50 per share. Depending on the outcome of U.S. trade negotiations with the countries to which ADCAP exports its products, the company’s stock price is expected to be either $65 or $30 in six months. The risk free rate is 8 percent per year. What is the value of a put option on ADCAP stock that has an exercise price of $40 per share?

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Solution: Here we solve directly for the value of the put option. First we determine the payoffs for the stock, a risk free bond, and the put option under the two possible outcomes. To determine payoff of the bond six months from now, we must calculate the six-month risk free interest rate given the one year risk free rate in the problem statement. Six month risk free rate = (1 + 0.08)1/2 – 1 = 1.039, or 3.9% The payoffs are therefore: Stock (x) Today

$50

Expiration

$30

Risk-Free Loan (y)

Put Option

$65

$1.039

$40 – $30 = $10

Now we can use the stock and bond to create a replicating portfolio, which will give the same payoff as the put option: ($30 × x) + (1.039 × y) = $10 ($65 × x) + (1.039 × y) = $0 Solving the two equations we determine x = –0.286, y = 17.87 The value of the put option is the same as the current value of this portfolio: ($50 × –0.286) + ($1 × 17.87) = $3.58 Alternatively, you could solve this problem by calculating the value of a call option with an exercise price of $40 per share and then using the put-call parity relation. The value of the call option is $15.09 and the value of the associated put option calculated using the Copyright © 2015 John Wiley & Sons, Inc.

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put-call parity relation is $3.52. The difference ($3.58 vs. $3.52) is due to rounding and the compounding assumption for the discount rate.

20.4

Your company is considering opening a new factory in Europe to serve the growing demand for your product there. What real options might you want to consider in your capital budgeting analysis of the factory?

Solution: Several significant real options might be associated with the factory. First, by having a factory in Europe, and the employees and management associated with it, your company might be better positioned to introduce products to the European markets. In addition, you will have options to change operations, to sell the factory, or to simply abandon the project.

20.5 Your firm, which uses oil as an input to its production processes, hedges its exposure to changes in the price of oil by buying call options on oil at today’s price. If the price of oil goes down by the time the contract expires, what effect will that have on your company?

Solution: The effect on your company of the decline in the price of oil will be to increase earnings. This is because the oil is an input to your production process, and a drop in prices will reduce your expenses. If the price of oil goes down, you would let the call option expire

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without exercising it. Of course, the benefit your company receives from the drop in oil prices would be reduced by the amount that you paid to purchase the option. .

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Discussion Questions

20.1

Options can be combined to create more complicated payoff structures. Consider the combination of one put option and one call option with the same expiration date and the same strike price. Draw the payoff diagram and describe what the purchaser of such a combination thinks will happen before expiration.

The payoff diagram will be in the shape of a V centered at the strike price:

Buy Put

Value

and Call

Stock Price

This combination is called a straddle. Its purchaser thinks that the value of the underlying asset will change significantly, but he is unsure in which direction it will move. If he is correct, one of his options will expire worthless, but the other will be exercised (and have value). If he is wrong, the payoff from the option that ends up being exercised will not be enough to cover the expense of buying the options in the first place. LO: 1 Copyright © 2015 John Wiley & Sons, Inc.

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Level: Basic Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective 20.2

A writer (seller) of a call option may or may not actually own the underlying asset. If he or she owns the asset, and therefore will have the asset available to deliver should the option be exercised, he or she is said to be writing a covered call. Otherwise, he or she is writing a naked call and will have to buy the underlying asset on the open market should the option be exercised. Draw the payoff diagram of a covered call (including the value of the owned underlying asset) and compare it with the payoff of other options.

Value

Covered Call

Stock Price

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A covered call has the same payoff shape as a put option, but it is shifted upward by the value of the strike price. This is equivalent to the combination of a put option and a riskfree bond. LO: 1 Level: Basic Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.3

An American option will never be worth less than a European option. Evaluate this statement.

This statement is true. An American option has all the rights that a European option has. In addition, it can be exercised on any date prior to the exercise date. Since these additional rights can never have a negative value, an American option will always be worth at least as much as a corresponding European option. LO: 1 Level: Basic Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Solutions Manual

Explain why, in the binomial pricing theory, the probabilities of an upward move versus a downward move are not important.

The replicating portfolio calculated to value the option in this model will have the same value as the option whether the stock goes up or down. The probability of an up move could be 99 percent or 1 percent, and that would not change. The replicating portfolio is not determined by the likelihood of the two possibilities—only the option value in those two cases. That said, the value of the replicating portfolio (and therefore the option) is affected by the current stock price, which, presumably, would change with the probabilities of up or down stock price moves. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.5

Like all other models, the binomial pricing model is a simplification of reality. In this model, how do we represent high volatility or low volatility of the value of the underlying asset?

The difference between the high and low possible future prices represents volatility. If these two numbers are relatively close together, that represents low volatility of the value

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of the underlying asset. The further apart they are, the higher the volatility the model represents. LO: 2 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.6

What kinds of real options should be considered in the following situations? a. Wingnuts R Us is considering two sites for a new factory. One is just large enough for the planned facility, while the other is three times larger. b. Carousel Cruises is purchasing three new cruise ships to be built sequentially. The first ship will commence construction today and will take one year to build. The second will then be started. Carousel can cancel the order for a given cruise ship at any time before construction begins.

a. Wingnuts R Us should consider the option to expand operations. b. Carousel should consider the option to abandon their order and not take delivery of the additional ships. LO: 3 Level: Basic Bloomcode: Analysis AASCP: Analytic Copyright © 2015 John Wiley & Sons, Inc.

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IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.7

Future Enterprises is considering building a factory that will include an option to expand operations in three years. If things go well, the anticipated expansion will have a value of $10 million and will cost $2 million to undertake. Otherwise, the anticipated expansion will have a value of only $1 million and will not take place. What information would we need in order to analyze this capital budgeting problem using the traditional NPV approach that we would not need using option valuation techniques?

In order to use traditional NPV techniques, we need to know the probability of “things going well” so that we can estimate the expected cash flows. We will also need to know how the performance of the overall economy affects these probabilities so that we can estimate an appropriate discount rate for the expected expansion cash flows. LO: 3 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.8

Corporations frequently include employee stock options as a part of the compensation for their managers and sometimes for all of their employees. These

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options allow the holder to buy the stock of the company for a preset price like any other option, but they are usually very long lived, with maturities of 10 years. The goal of stock option plans is to align the incentives of employees with those of stockholders. What are the implications of these compensation plans for current stockholders?

Such plans have the effect of diluting the value of any gains in stock price. When the value of the firm goes up, the options will be exercised and the result will be more people with a claim on the same underlying assets. The value of each claim will be reduced. At the same time, the objective of the plans is to mitigate the agency problems associated with managers’ and employees’ incentives. Managers and employees who have been granted stock options have more to gain when the company does well. They are less likely to be too conservative when deciding which projects the company will pursue. If the stock option plans achieve their objective, the firm will be worth more than it would have been without the plan, and so there will be more wealth to split up. Finding a good trade-off between these effects is a challenge. LO: 1 Level: Intermediate Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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You are a bond holder of ABC Corp. Using option pricing theory, explain what agency concerns you would have if ABC were in danger of bankruptcy.

The equity of a firm can be thought of as a call option on the assets of the firm. If the firm is close to bankruptcy, you as a bondholder should be concerned that the company will take actions to increase the volatility of the assets by investing in highly risky projects, turn down positive-NPV projects, and, possibly, try to increase the dividend payouts. All of these actions can increase the value of the equity at the expense of the value of the debt holders. LO: 4 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.10 A bond covenant is a part of a bond contract that restricts the behavior of the firm, barring it from taking certain actions. Using the terminology of options, explain why a bond contract might include a covenant preventing the firm from making large dividend payments to its stockholders.

Cash on hand reduces the total volatility of the value of the firm. If any cash on hand is paid out to stockholders in the form of a large dividend payment, the volatility of the firm

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will increase and the value of the debt will decrease. In order to prevent this, bonds often feature covenants restricting the firm to dividend payments no larger than some fraction of current earnings. LO: 4 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.11 How can the insurance policy on a car be viewed as an option?

The insurance policy on a car can be viewed as a put option. In the extreme case, where your car is totaled, you have the right to put the car to the insurance company for its market value prior to the accident. LO: 5 Level: Basic Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Questions and Problems

BASIC 20.1

Option characteristics: What is an option? Solution: An option is the right to buy or sell an asset at a pre-specified price on or before a prespecified date. LO: 1

Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.2

Option characteristics: Explain how the payoff functions differ for the owner (buyer) and the seller: (1) of a call option; (2) of a put option.

Solution: (1) Call option: When the value of the underlying asset is below the exercise price, the payoffs for both the buyer and seller of a call option are 0. Once the asset price goes above the exercise price, the payoff for the buyer increases dollar for dollar with the price of the underlying asset, while the payoff for the seller decreases dollar for dollar with the price of the

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underlying asset. The sum of the payoffs of the buyer and seller of a call option is always 0. (2) Put option: When the value of the underlying asset is above the exercise price, the payoffs for both the buyer and seller of a put option are 0. Once the asset price drops below the exercise price, the payoff for the buyer increases dollar for dollar with decrease of the price of the underlying asset, while the payoff for the seller decreases dollar for dollar with decrease of the price of the underlying asset. The sum of the payoffs of the buyer and seller of a put option is always 0. LO: 1 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.3

Option payoffs: What is the payoff for a call option with a strike price of $50 if the stock price at expiration is $40? What if the stock price is $65?

Solution: If the stock price is $40, then the option will not be exercised and the option is worthless. (Why buy for $50 what you can buy in the market for $40?) If the stock price is $65, then the option is worth the difference between the price and the strike price: $65 – $50 = $15. LO: 1

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Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.4

Option payoffs: What is the payoff for a put option with a strike price of $50 if the stock price at expiration is $40? What if the stock price is $65? Solution: If the stock price is $40, then the option is worth the difference between the strike price and the stock price: $50 – $40 = $10. If the stock price is $65, then the option is worthless. LO: 1

Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.5

Option valuation: What are the five variables that affect the value of an option, and how do changes in each of these variables affect the value of a call option?

Solution: The value of a call option increases as: (1) Current value of the underlying asset increases; (2) Exercise price decreases;

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(3) Volatility of the value of the underlying asset increases; (4) Time until the expiration of the option increases; or (5) Risk-free rate of interest increases. LO: 2 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.6

Option valuation: Assuming nothing else changes, what happens to the value of an option as time passes and the expiration date gets closer? Solution: The value of an option declines as time passes. LO: 2

Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.7

Option valuation: What does the seller of a put option hope will happen? Solution: He hopes the option will not be exercised. In this case, the option will be exercised if the asset value at expiration is lower than the strike price, so he hopes the asset value will rise (or at least will remain above the strike price).

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LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.8

Option valuation: What is the value of a call option if the stock price is zero? What if the stock price is extremely high (relative to the strike price)? Solution: If the stock price is zero, then there is no possibility that the stock will have positive value. Thus the option to buy the stock in the future is worthless. If the stock price is extremely high compared to the strike price, then there is essentially zero probability that the stock price will be below the strike price at expiration. The option will always be exercised, and the value of the option is the difference between the current stock price and the present value of the strike price. LO: 2

Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.9

Option valuation: Like owners of stock, owners of options can lose no more than the amount they invested. They are far more likely to lose that full amount, but they cannot lose more. Do sellers of options have the same limitation on their losses?

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Solution: No. The seller of a call option can lose a theoretically unlimited amount of money because the value of the underlying asset can go arbitrarily high. The seller of a put option is limited to losing the amount of the strike price (since that is how much they would lose if the stock price went to zero). LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.10 Option valuation: What is the value at expiration of a call option with a strike price of $65 if the stock price is $1? $50? $65? $100? $1,000?

Solution: The value of the option for any stock price less than $65 (including $1 and $50) is zero because the option would not be exercised. When the stock price is equal to the strike price ($65 in this case), the option owner does not care whether or not he exercises the option. He gains (or loses) nothing. Again, the option is worth zero. If the stock price is higher than the strike price, the option is worth the difference. If the stock is worth $100, the option is worth $35. If the stock is worth $1,000, the option is worth $935. LO: 2

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Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.11 Option valuation: Suppose you have an option to buy a share of ABC Corp. stock for $100. The option expires tomorrow, and the current price of ABC Corp. is $95. How much is your option worth?

Solution: Your option is worth very slightly more than zero. There is little chance that the stock price will move above $100 by tomorrow, but the chance is not zero, so the option still has some value. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.12 Option valuation: You hold an American option to sell one share of Zyther Co. stock. The option expires tomorrow. The strike price of the option is $50, and the current stock price is $49. What is the value of exercising the option today? If you wanted to sell the option instead, about how much would you expect to receive?

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Solution: The value of exercising today is the difference between the strike price and the stock price: $50 – $49 = $1. If you sold the option, you should expect to receive slightly more than that. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.13 Real options: What is the difference between a financial option and a real option?

Solution: The underlying asset of a financial option is a financial asset, while the underlying asset of a real option is a real asset like investment projects. LO: 3 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.14 Real options: List and describe four different types of real options that are associated with investment projects.

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Solution: Four types of real options are associated with investment projects: (1)

Options to defer investment: the ability to defer an investment decision until information on its future cash flows is less uncertain.

(2)

Options to make follow-on investments: the possibility to exploit future business opportunities that will not otherwise be available if the investment is not taken.

(3)

Options to change operations: the flexibility in changing operations as business conditions change if the investment is taken.

(4)

Options to abandon projects: the ability to terminate the project at a smaller loss if things do not go as well as anticipated.

LO: 3 Bloomcode: Knowledge AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.15 Agency costs: How are options related to the agency costs of debt and equity?

Solution: Agency costs arise since the incentives of shareholders are different from those of the debt holders. Equity and debt claims are like different types of options on the firm. The payoff function for the stockholders looks exactly like that for the owner of a call option where the exercise price is the amount owed on the loan and the underlying asset is the

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firm itself. The payoff function for the lenders looks like that for the seller of a put option, where the exercise price is the amount of the loan and the underlying asset is the firm itself. The different payoff functions create different incentives for shareholders and debt holders. For example, shareholders are likely to pursue more risky projects. The increased volatility of cash flows increases the expected payout for the holder of a call option, the shareholder, and decreases the expected payout for the seller of a put option, the debt holder. LO: 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

INTERMEDIATE 20.16 Option valuation: Suppose that you own a call option and a put option on the same stock and that these options have the same exercise price. Explain how the relative values of these two options will change as the stock price increases or decreases.

Solution: When stock prices increase, the value of the call option increases and the value of the put option decreases; when stock prices decrease, the value of the call option decreases and the value of the put option increases. The further the stock price is from the exercise price, the more valuable the combination of these options becomes.

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LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.17 Other options: A callable bond is a bond that can be bought back by the bond issuer before maturity for some pre-specified price (normally a small amount above face value) at the discretion of the bond issuer. How would you go about finding the value of such a bond? Would the bond be worth more or less than an equivalent noncallable bond?

Solution: The purchaser of a callable bond is simultaneously selling the issuer a call option on that bond. The value would be equal to the value of the straight bond minus the value of the option. This is clearly less than the value of the (noncallable) bond by itself. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.18 Other options: A convertible bond is a bond that can be exchanged for stock at the discretion of the bondholder. How would you go about finding the value of such a bond? Would the bond be worth more or less than an equivalent nonconvertible bond?

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Solution: A convertible bond is equivalent to a combination of a nonconvertible bond and a call option on the stock, where the strike price of the option is the value of the bond. Because the value of the bond may change along with the value of the stock, this is not a straightforward problem, but the value would be equal to the value of the straight bond plus the value of the option. This is clearly more than the value of the (nonconvertible) bond by itself. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.19 Option valuation: The seller of an option can never make any money from a change in the value of the underlying asset; he or she can only hope that the option will not be exercised and that he or she will not lose any money. Given that this is the case, why do people sell options?

Solution: Option writers receive the value of the option up front. The money the seller receives by selling the bond is referred to as the bond premium. This payment compensates them for the obligation they are taking on.

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. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.20 Option valuation: The stock of Socrates Motors is currently trading for $40 and will either rise to $50 or fall to $35 in one month. The risk-free rate for one month is 1.5 percent. What is the value of a one-month call option with a strike price of $40?

Solution:

Today

Expiration

Stock (X)

Risk-Free (Y)

Option

$40

???

$35

$50

$1.015

$10

These two equations define our portfolio: $10 = ($50 × X) + ($1.015 × Y) $0 = ($35 × X) + ($1.015 × Y) and the solution is X = 2/3 and Y = -$22.99. That is, we borrow $22.99 and buy twothirds of a share of Socrates Motors at a cost of $40.00 per share. The total net cost of this portfolio is $40.00 × (2/3) – 22.99 = $3.68 and this is the value of the option.

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LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.21 Option valuation: Again assume that the price of Socrates Motors stock will either rise to $50 or fall to $35 in one month and that the risk-free rate for one month is 1.5 percent. How much is an option with a strike price of $40 worth if the current stock price is $45 instead of $40?

Solution: The replicating portfolio of X = 2/3 and Y = -$22.99 does not depend on the current stock price and so would not change. The value of that portfolio would now be $45 × (2/3) – $22.99 = $7.01 and this is the value of the option. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.22 Option valuation: Assume that the stock of Socrates Motors is currently trading for $40 and will either rise to $50 or fall to $35 in one month. The risk-free rate for one month is 1.5 percent. What is the value of a one-month call option with a strike price of $25?

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Solution:

Today

Expiration

Stock (X)

Risk-Free (Y)

Option

$40

???

$35

$50

$1.015

$10

$25

These two equations define our portfolio: $25 = ($50 × X) + ($1.015 × Y) $10 = ($35 × X) + ($1.015 × Y) and the solution is X = 1 and Y = -$24.63. That is, we borrow $24.63 and buy 1 share of Socrates Motors at a cost of $40. The total net cost of this portfolio is $40 – $24.63 = $15.37, and this is the value of the option. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.23 Option valuation: You are considering buying a three-month put option on Wing and a Prayer Construction stock. The company’s stock currently trades for $10 per share and its

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price will either rise to $15 or fall to $7 in three months. The risk-free rate for three months is 2 percent. What is the appropriate price for a put option with a strike price of $9?

Solution: If the stock rises to $15, then the option will not be exercised and its payoff will be $0. If the stock falls to $7, the option will be exercised and its value will be the difference between the strike price and the stock price, $2.

Today

Expiration

Stock (X)

Risk-Free (Y)

Option

$10

???

$15

$1.02

The formulas that define the replicating portfolio are: $2 = ($7 × X) + ($1.02 × Y) $0 = ($15 × X) + ($1.02 × Y) and the solution is X = -$0.25 and Y = $3.68. That is, we will short sell one-fourth of a share of the stock, receiving $2.5, and we will lend $3.68 at the risk-free rate. (Short selling is the process of borrowing an asset that you do not own and selling, with the promise that at some time in the future you will buy it back and return it to its owner.) The net cost is $3.68 – $2.50 = $1.18. This is the value of the option. LO: 2 Copyright © 2015 John Wiley & Sons, Inc.

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Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.24 Option valuation: You hold a European put option on Tubes, Inc., stock, with a strike price of $100. Things haven’t been going too well for Tubes. The current stock price is $2, and you think that it will either rise to $3 or fall to $1.50 at the expiration of your option. The appropriate risk-free rate is 5 percent. What is the value of the option? If this were an American option, would it be worth more?

Solution: Note that this option will be exercised regardless.

Stock (X)

Risk-Free (Y)

Option

$2.0

???

Today

Expiration

$1.5

$3.0

$1.05

$98.5

$97

The formulas that define the replicating portfolio are: $98.5 = ($1.5 × X) + ($1.05 × Y) $97 = ($3 × X) + ($1.05 × Y)

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and the solution is X = –1 and Y = $95.24. That is, we will short sell 1 of a share of the stock, receiving $2, and we will lend $95.24 at the risk-free rate. The net cost is $95.24 – $2.00 = $93.24. This is the value of the (European) option. If this were an American option, we could exercise today if we wanted. We would want to do so if the value of exercising today was greater than the value of the option. Exercising today would allow us to sell for $100 something worth $2, a gain of $98. This is more than $93.24. The American option is worth more. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.25 Other options: A golden parachute is a part of a manager’s compensation package that makes a large lump-sum payment in the event that the manager is fired (or loses his or her job in a merger, for example). Providing such payouts to managers seems ill advised to most people first hearing about it. Explain how a golden parachute can help reduce agency costs between stockholders and managers.

Solution: Managers have incentives to avoid bankruptcy or even underperformance because the personal cost to them is quite high. As a result they may choose to avoid high risk

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investments even if those investments are highly positive NPV. The costs to the manager if the project goes badly outweigh the benefits if it goes well. However, stockholders want the manager to take positive-NPV projects, even if they are risky. Golden parachutes help to solve this problem by reducing the costs to the manager associated with poor performance or bankruptcy. The manager faces a payoff structure like the seller of an option. Golden parachutes serve to reduce the volatility of that option and therefore to reduce the value of that option. LO: 4 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

ADVANCED 20.26 Consider the following payoff diagram.

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Covered Call

Value

$10

$40 $50 Stock price

$60

Find a combination of calls, puts, risk-free bonds, and stock that has this payoff. (You need not use all of these instruments, and there are many possible solutions.)

Solution: One possible solution would consist of four options: (a) Buy a call with a strike of $50. (b) Buy a put with a strike of $50. (c) Sell a put with a strike of $40. (d) Sell a call with a strike of $60. If the stock price at expiration is below $40, then neither call will be exercised, but both puts will be. We will be forced to buy the stock for $40 because of option c, but we will be able to sell it for $50, using option b. Our net gain will be $10. Copyright © 2015 John Wiley & Sons, Inc.

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If the stock price is between $40 and $50, the only option to be exercised will be option b, and we will gain the difference between $50 and the stock price. If the stock price is between $50 and $60, the only option to be exercised will be a call option and we will gain the difference between the stock price and $50. If the stock price is above $60, then neither put will be exercised, but both calls will be. We will be able to buy the stock for $50 using option a, but we will be forced to sell it for $60 by the owner of option d. Our net gain will be $10. LO: 1 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.27 Consider the payoff structures of the following two portfolios: a. Buying a one month call option on one share of stock at a strike price of $50 and saving the present value of $50 (so that at expiration it will have grown to $50 with interest). b. Buying a one month put option on one share of stock at a strike price of $50 and buying one share of stock. What conclusion can you draw about the relation between call prices and put prices from a comparison of these two portfolios?

Solution:

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The payoff of these two portfolios is identical. In the first case, if the stock price is below $50 at expiration, you will not exercise and you will be left with $50. If it is above $50, you will exercise and you will have a share of stock (whatever it is worth). In the second case, if the price is below $50, you will exercise your put option and get $50 for your share of stock. If it is above $50, you will not exercise and you will retain your share of stock (whatever it is worth). From this, we can see that the value of the two portfolios today must be the same. That is: P = C + Xe-rt – V where P is the value of the put option, C is the value of the call option, X is the exercise price, r is the risk-free rate, t is the amount of time before the option expires, and V is the current value of the underlying asset. Th e term e2rt is the exponential function that you can calculate using the “ex” key on your calculator; it is simply a discount factor that assumes continuous compounding. If we know the value of a call (and the current stock price and interest rate), we can calculate the value of a put. This relation is call put-call parity. Note that this relation is not dependent on any option pricing model. LO: 2 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.28 One way to extend the binomial pricing model is by including multiple time periods. Suppose Splittime, Inc., is currently trading for $100 per share. In one month, the price

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will either increase by $10 (to $110) or decrease by $10 (to $90). The following month will be the same. The price will either increase by $10 or decrease by $10. Notice that in two months, the price could be $120, $100, or $80. The risk-free rate is 1 percent per month. Find the value today of an option to buy one share of Splittime in two months for a strike price of $105. (Hint: To do this, first find the value of the option at each of the two possible one-month prices. Then use those values as the payoffs at one month and find the value today.)

Solution: If the price of Splittime goes from $100 to $90 during the first month, then this option will never be exercised because the highest price to which Splittime could rise by two months is $100, which is lower than the strike price of $105. Therefore, the value of the option in the “down case” is $0. If the price rises to $110 in the first month, then the payoff of the option will be either $15 (if the price continues to rise to $120) or $0 (if the price falls back to $100).

One month

Expiration

Stock (X)

Risk-Free (Y)

Option

$110

???

$100

$120

$1.01

$15

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$15 = $120 × X + $1.01 × Y $0 = $100 × X + $1.01 × Y The solution is X = 0.75 shares and Y = -$74.26. The value of this portfolio, and therefore the value of the option at this point, is $8.24. (0.75 × $110 – $74.26). Now we are ready to calculate the value of the option today using $0 and $8.24 as the one-month option “payoffs.”

Today

One month

Stock (X)

Risk-Free (Y)

Option

$100

???

$90

$110

$1.01

$8.24

Now the equations that define our portfolio are $8.24 = $110 × X + $1.01 × Y $0 = $90 × X + $1.01 × Y The solution is X = 0.412 and Y = -$36.72. The portfolio value is$4.49, and this is the value of the option. LO: 2 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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20.29 SpinTheWheel Co. has assets currently worth $10 million in the form of one-year riskfree bonds that will return 10 percent. The company has debt with a face value of $5.5 million due in one year. (No interest payments will be made.) The stockholders decided to sell $8 million of the risk-free bonds and to invest the money in a very risky venture. This venture consists of giving Mr. William Kid the money now and, in one year, flipping a coin. If it comes up heads, Mr. Kid will pay SpinTheWheel $17.6 million. If it is tails, SpinTheWheel gets nothing. This investment has an NPV of zero. a. What is the value of the debt and equity before the stockholders make this “investment”? b. Using the binomial pricing model, with the payoff to the equity holders representing the option and the assets of the company representing the underlying asset, estimate the value of the equity after the stockholders make the investment. c. What is the new value of the debt after the investment?

Solution: a. The firm is certain to have the $5.5 million owed to the debt holders in one year, so the correct discount rate for the debt is the risk-free rate, 10 percent. Thus the value today of the debt is the present value of the debt at the risk-free rate: $5.5 million / 1.1 = $5 million. The value of the equity is therefore $10 million – $5 million = $5 million. b. The payoffs of the option (the equity), the underlying (the firm), and the risk-free bond are:

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Firm

Risk-Free (Y)

Equity

$10 million

???

$2.2 million $19.8 million $1.1

$1.1

$14.3

Note that the payoff of $14.3 for the option in the up case comes from the $19.8 million less the $5.5 million they will pay the bondholders. In the down case, there is not enough money to pay the bondholders what they are owed, so the bondholders will receive the entire $2.2 million value of the firm and the equity holders get nothing. The equations are:

$14.3 = $19.8 × X + $1.1 × Y $0 = $2.2 × X + $1.1 × Y and the solution is X = 0.8125 and Y = -$1.625. The value of this portfolio is $6.5 million. This is the new value of the equity. c. The current value of the firm did not change (this was a zero NPV project) and remains at $10 million. If the equity has increased in value to $6.5 million, the debt has decreased in value to $3.5 million. LO: 4 Bloomcode: Application AASCP: Analytic

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IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.30 The price of a stock that does not pay dividends is currently $35, and the risk-free rate is 4 percent. A European call option on the stock, with a strike price of $35 and which expires in six months, sells for $3.04. A European put option on the same stock with the same strike price sells for $2.35. Is there an arbitrage opportunity here? If so, what is it?

Solution: To check whether there is an arbitrage opportunity, substitute the values into the put-call parity relation and see if it holds. P = C + Xe–rt – V $2.35 = $3.04 + $35e-(0.04)(6/12) - $35

Since the put-call parity relation holds, there is no arbitrage opportunity. LO: 1 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.31 Two call options have been written on the same underlying stock. Call #1 has a strike price of $42, and call #2 has a strike price of $52. Call #1 is selling for $5.00, and call #2 is selling for $6.00. What arbitrage opportunity do these prices present investors? Show the potential payoffs from this opportunity.

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Option Value at Expiration

Solution: The payoff diagrams for the buyers of the two call options are as follows:

$20 $18 $16 $14 $12 $10 $8 $6 $4 $2 $0

$42 Call $52 Call

$28

$32

$36

$40

$44

$48

$52

$56

$60

Stock Price

Notice that call #1 has a lower strike price and costs less. In a situation like this you can earn an arbitrage opportunity by purchasing the less expensive option (#1) and selling the more expensive (#2). The payoffs for this strategy are:

Buy $42 Call $0 $0 $0 $0 $0 $0 $0 $0 $2 $4 $6 $8 $10 $12 $14 $16 $18

Sell $52 Total Call Proceeds $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $6 $8 $6 $10 $6 $12 $6 $14 $6 $16 $4 $16 $2 $16 $0 $16 -$2 $16

$20

Option Value at Expiration

Stock Price $28 $30 $32 $34 $36 $38 $40 $42 $44 $46 $48 $50 $52 $54 $56 $58 $60

$42 Call

$15

$52 Call Total Proceeds

$10

$28

$32

$36

$40

$44

$48

-$5 Stock Price

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AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.32 Husky Motors has two debt issues outstanding, both of which mature in five years. The senior debt issue, which has a face value of $10 million, must be paid in full before any of the principal for the junior debt issue is paid. The junior debt issue also has a face value of $10 million. Draw the payoff diagrams for Husky’s equity and both debt issues as the value of the firm changes. Under what circumstances would you expect to see conflicts between the senior and junior debt holders?

Solution: The payoff functions are as follows:

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VD Senior

VF VD Junior

VF VE VF $10

$20

From these payoff functions you can see that there are likely to be conflicts between the senior and junior debt holders when the value of the firm is near or below $20 million. Below $20 million, the payoff function for the junior debt holder looks like that for the stockholders. This means that the junior debt holders will prefer riskier investments and strategies than the senior debt holders. These types of conflicts between lenders are quite common when a firm gets into financial distress. LO: 4 Bloomcode: Analysis AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.33 The payoff function for the holder of straight debt looks like that for the seller of a put option. Convertible debt is straight debt plus a call option on a firm’s stock. How does the

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addition of a call option to straight debt affect the concern that lenders have about the asset substitution problem, and why?

Solution: It mitigates this concern because the lenders will benefit through the call option from increased volatility in the value of the firm. How much a conversion option mitigates this concern depends on the specific characteristics of the option. LO: 2 Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Sample Test Problems

20.1

You own a call option on Pepsico stock with a strike price of $60 per share that expires in 60 days. The current market price of Pepsico stock is $63.50 per share. What are the limits on the value of the call option you own?

Solution: The value of a call option must be equal to or greater than zero. The option also cannot be worth less than the value that you would receive if you exercised it immediately, where the exercise price is computed using the present value of the $60 exercise price, discounted for 60 days at the risk free rate. Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.2

Assume that the current market price of Montrose Industrials stock is $28 per share and will either rise to $38 per share or fall to $21 per share in one month. The risk-free rate for one month is 1 percent. What is the value of a one-month call option with a strike price of $24 per share?

Solution: If the stock rises to $38, the option will be exercised and the payoff will be the $38 – $24 = $14. If the stock falls to $21, then the option will not be exercised and its payoff will be

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$0.

Today

Expiration

Stock (x)

Risk-Free (y)

Option

$28

???

$21

$38

$1.01

$14

The two equations define the replicating portfolio are: $14 = ($38 × x) + ($1.01 × y) $0 = ($21 × x) + ($1.01 × y) Solving for x and y yields x = 0.8235 and y = –$17.12. That is, we borrow $17.12 and buy 0.8235 of a share of Montrose Industrial stock at a cost of $28 per share. The total cost of this portfolio is ($28.00 × 0.8235) – $17.12 = $5.94, which is the value of the call option. Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.3

The market value of Whole Foods stock is currently $53.73 per share, and the annual risk-free rate is 3 percent. A three-month call option on the stock with a strike price of $55 sells for $2.15. What is the value of a put option on Whole Foods stock that has the same strike price and expiration date if there are no arbitrage opportunities?

Solution: P = C + Xe–rt – V = $2.15 + $55e–(0.03)(3/12) – $53.73

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= $3.01 Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.4

Why is it hard to account for real options in an NPV analysis

Solution: The riskiness of a project with real options varies with time and the appropriate discount rate varies with risk. To account for real options in an NPV analysis, you must not only project future cash flows, but also the probability that the options will be exercised and the impact of these exercise decisions on the rate used to discount the cash flows. Bloomcode: Comprehension AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

20.5

Fuel costs are a significant fraction of total costs in the airline industry. How might airline managers use options to manage fuel costs? What is the downside of doing this?

Solution: Airline managers can use options to reduce volatility in operating expenses (fuel costs) and therefore profitability. By purchasing call options on fuel, they can lock in fuel prices for at least some of their fuel purchases. This can reduce the impact of increases in fuel prices on profits. The downside of doing this is that if fuel prices go down, the options

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will expire worthless and yet the airlines will still incur the costs (the call premiums) of buying the options. Bloomcode: Application AASCP: Analytic IMA: Corporate Finance AICPA: Industry/Sector Perspective

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Chapter 21 International Financial Management Before You Go On Questions and Answers Section 21.1 1. What is globalization? Globalization refers to the removal of barriers to free trade and the closer integration of national economies. Consumers in many countries buy goods that are purchased from a number of countries, other than just their own. The production of goods and services has also become highly globalized. Like product markets, the financial system has also become highly integrated. 2.

What are multinational corporations? Multinational corporations are business firms that have their operations in at least one other country than their home country where they are headquartered. These firms are headquartered all over the world and are owned by a mixture of domestic and foreign stockholders.

Explain the difference between American and European business executives’ views on wealth maximization. American business executives embrace shareholder wealth maximization as their number one goal, whereas in most parts of Europe, the main goal of business executives is to maximize corporate wealth. This means that shareholders are treated on par with other stakeholders, such as management, employees, creditors, or the government.

Section 21.2 1. What is foreign exchange rate risk? Foreign exchange risk is the risk of a change in investment’s value due to changes in currency exchange rates. This risk usually affects firms that import/export goods as well as investors that make international investments. 2.

How is the equilibrium exchange rate determined?

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The equilibrium exchange rate is the point of intersection between the currencies’ supply and demand curves. It is the point at which the quantity of the currency demanded equals the quantity of currency supplied. 3.

What does it mean to hedge a financial transaction? To hedge a financial transaction with foreign exchange means to reduce the potential gains or losses caused by fluctuations in the price of foreign exchange. Many instruments can be used to hedge this risk, such as foreign currency options.

Section 21.3 17. What difficulties do firms face in estimating cash flows from an overseas project? Estimating cash flows from an overseas project is difficult because of the various ways a firm is likely to get cash flows from a subsidiary – dividends, royalty or license payments, debt repayment, management or consulting fees. It is also difficult to precisely time the cash flows or estimate the magnitude because of restrictions and controls a country is likely to put on the transfer of funds from the overseas project back to the home country. 2.

Why is the repatriation of cash flows from an overseas project considered critical? From a parent firm’s point of view, the cash flows expected from the subsidiary are the basis for undertaking a project or rejecting it. Any delays in receiving the cash flows will affect the NPV of the project. Parent companies often rely on the cash flows from foreign operations to be repatriated and to fund projects in other countries. 17.

When do companies have to consider country or political risk? Any company doing business in a foreign country has to consider political or country risks. Especially if the target country has a relatively unstable political environment, financial managers must incorporate the potential risk into the cost of the project.

Section 21.4 17. Which currency is the preferred currency of exchange in global financial markets? Why? The U.S. dollar is the preferred currency of exchange on the global financial markets, as it is perceived to be the most stable currency. This is mainly due to the size and strength of the U.S. economy, the long history of political stability, and the strength of military forces.

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What is the difference between foreign bonds and Eurobonds? Both foreign bonds and Eurobonds are types of international bonds. However, foreign bonds are long-term debt instruments sold by a foreign firm to investors in another country, and they are denominated in that country’s currency. On the other hand, Eurobonds are longterm debt instruments sold by a firm in one country but are denominated in the currency of another country.

Section 21.5 17. Why is credit risk higher in international markets? In international markets, the credit risk of borrowers is higher, as it is more difficult to obtain credit information abroad. It is mainly the issue of familiarity with foreign economic conditions and business practices. Thus, the cost of gathering all this necessary information is higher, which is then being passed onto the customer in terms of higher premium. 2.

List the inputs that are used in calculating a Eurocredit price. The loan pricing for Eurocredits is similar to the loan pricing that U.S. money center banks use for their largest domestic customers. The loan rate (k) is equal to a base rate, such as LIBOR, which represents the bank’s cost of funds, plus a markup, which is the bank’s lending margin: k = Base rate + X where X is the lending margin. The lending margin depends on the borrower’s credit risk; international risk factors, such as foreign exchange risk and country risk; and the bank’s gross profit margin. Equation 21.3 represents the Eurocredit pricing. K = BR + DRP + FXR + CR + GPMAR where k = individual firm’s loan rate BR = Eurocurrency base rate, such as LIBOR DRP = default risk premium FXR = foreign exchange or currency risk premium CR = country risk premium GPMAR = bank’s gross profit margin

Self-Study Problems

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21.1

If a Volkswagen Passat costs $26,350 in Baltimore and €21,675 in Frankfurt, what is the exchange rate between the U.S. dollar and the euro?

Solution: Cost of the car in Baltimore = Cost of the car in Frankfurt = Dollar to euro exchange rate = =

21.2

$26,350 €21,675 $26,350 / €21,675 $1.2157/€

Calculate the following exchange rates given the following information. Given Compute a. ¥86.3500/$ $/¥ b. $1.8694/£ £/$ c. $0.9981/C$ C$/$

Solution: a. b. c.

21.3

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1 / ¥86.3500/$ 1 / $1.8694/£ 1 / $0.9981/C$

= = =

$0.01581/¥ £0.5349/$ C$1.00190/$

Digital, Inc., an electronic games manufacturer, is planning to purchase flash memory from one of two sources. Kyoto, Inc., quotes a price of ¥6,800 per gigabyte. The current exchange rate is ¥84.30/$. Another Japanese manufacture offers to supply the same flash memory at a price of €58.46 per gigabyte. The spot rate available is ¥121.57/€. Which is the cheaper source of flash memory for Digital?

Solution: Cost from Vendor 1: Flash memory price quote Spot rate for U.S. dollar Cost to Digital in dollars

Cost from Vendor 2: Flash memory price quote Spot rate for U.S. dollar

= = = =

¥6,800 per gigabyte ¥84.30/$ ¥6,800 / ¥84.30/$ $80.66 per gigabyte

= =

€58.46 per gigabyte ¥121.57/€

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To compute the dollar cost, we need to compute the cross rate between the euro and the dollar. ¥121.57 / € = $1.4421 / € ¥84.30 / $ Cost to Digital in dollars = €58.46 × $1.4421/€ = $84.31 per gigabyte The first vendor has the cheaper quote for Digital.

21.4

Columbia Corp. has just made a sale to a British customer. The sale was for a total value of £135,000 and is to be paid 60 days from now. Columbia is concerned that the British pound will depreciate against the U.S. dollar, and management plans to hedge. The company’s bank informs management that the spot rate is $1.8133/£ and the 60-day forward rate is $1.7864/£. If Columbia sells its pounds receivable at the forward rate, what is the dollar value of its receivables? If it did not enter into a forward contract and the spot rate 60 days later was $1.7635/£, how much did the company lose by not hedging?

Solution: Amount received by Columbia by selling at the forward rate: = £135,000 × $1.7864/£ = $241,164 Amount received by Columbia by selling at the spot rate 60 days later: = £135,000 × $1.7635/£ = $238,072.50 Loss incurred by not hedging = $241,164 - $238,072.50 = $3,091.50

21.5

American Bancorp is planning to make a $3.5 million loan to a French firm. Currently, LIBOR is at 4.5 percent. American considers a default risk premium of 1.15 percent, a foreign exchange risk premium of 0.35 percent, and a country risk premium of 0.13 percent. What is the loan rate charged by American Bancorp?

Solution: The loan rate charged by American Bancorp is calculated as follows: k = BR + DRP + FXR + CR = 4.5% + 1.15% + 0.35% + 0.13% = 6.13%

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Discussion Questions 21.1 Royal Dutch Shell, an oil company, has headquarters in both the Netherlands and the United Kingdom. What type of firm is it?

This company is both a multinational corporation and a transnational company. Since it produces, refines, and sells oil in a variety of different locations around the world, it is an MNC. Since it is owned by investors in more than one country and is managed from a global perspective, it is a transnational firm. LO: 1 Level: Basic Bloomcode: Knowledge AASCB: Diversity IMA: Global Business AICPA: Industry/Global Perspective

21.2

International economic integration and technological changes in the last couple of decades have dramatically increased globalization across many industries. Explain how a biotech firm or a medical firm (for example, a hospital) can take advantage of these changes.

Technological changes have come in a variety of forms—computers, telecommunication, data digitalization, and such. A biotech firm may be able to conduct research and development on new drugs in India, clinical trials in other countries before submitting it for FDA approval. A hospital in the United States may be able to cost efficiently digitalize medical records by transmitting the records overseas. Hospitals and doctors can use these digital records to consult physicians halfway across the world to get a more precise diagnosis. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Diversity IMA: Global Business AICPA: Industry/Global Perspective

21.3

In the United States, managers are asked to focus on maximizing stockholder value. Is this consistent with the goals of managers in Germany and Japan?

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In countries such as France and Germany, stockholders are treated no differently from other stakeholders of the firm. Thus, they are on a par with employees, suppliers, creditors, customers, and even the government. The firm’s management focus is on maximizing the wealth of the firm such that everyone benefits, not just the shareholders. In Japan, a group of businesses have ownerships in each other. This is known as keiretsu. Japanese managers focus on growing the market share of their firm such that the wealth of their keiretsu, and not the wealth of the shareholders, is maximized. Maximizing shareholder wealth is consistent with these other goals. Management taking this approach will, in the long run, help all the stakeholders of the firms, including the community in which they operate, to benefit. LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Diversity IMA: Global Business AICPA: Industry/Global Perspective

21.4

A Canadian cooperative of wheat farmers sold wheat to a grain company in Russia. Under what circumstances will the Canadian farmers be exposed to foreign exchange risk? When will the Russian importer be facing foreign exchange risk? If the payment to the Canadian exporter is in any currency other than the Canadian dollar, the Canadian exporter faces foreign exchange risk. If the Russian importer is forced to pay the Canadian exporter in Canadian dollars, then the entire foreign exchange risk is borne by the Russian importer.

LO: 1 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.5

Stardust, Inc., is an exporter of plumbing fixtures. About 30 percent of its sales are made in Canada. The sales department just found out that the Canadian dollar is at a premium against the U.S. dollar based on the 90-day forward rate, while the 180-day forward rate indicates that the Canadian dollar is at a forward discount. What is the likely impact of these rates on the company’s sales to Canada?

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The fact that the Canadian dollar is at a forward premium indicates that the Canadian dollar will be able to buy more U.S. dollars. In the short run, this can lead to increased sales for Stardust since Canadians will be able to buy more with their money. Six months from now, this Canadian dollar is at a forward discount. Imports from the United States will be more expensive for Canadians, and this could lead to Stardust seeing a decrease in their exports to Canada at that time. LO: 2 Level: Basic Bloomcode: Analysis AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.6

Mello Wines, a California winery, grows its grapes locally, uses local labor, and sells its wines only in the United States. Can this firm be exposed to foreign exchange risk?

Even though Mello is merely a domestic company, it does have foreign exchange risk. Suppose the U.S. dollar appreciates against the euro. This will make imported wine from the euro zone more affordable to Americans and increase import competition to Mello. LO: 2 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.7

A U.S. firm owns a subsidiary in Belgium. What kind of foreign exchange risk does the U.S. firm face?

Since it owns assets and has liabilities in Belgium denominated in euros, the firm faces foreign exchange risk. Converting the euro-denominated assets and liabilities to U.S. dollars for reporting purposes will make the dollar value of the Belgian subsidiary’s assets and liabilities fluctuate. LO: 5 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Global Business Copyright © 2015 John Wiley & Sons, Inc.

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21.8

Ray Corp is a U.S. electronics manufacturer with a production plant in Turkey. This morning, the Turkish government introduced a new law prohibiting the repatriation of any funds from the country for two years. What type of risk does Ray Corp. face?

Ray Corp. is facing a form of country or political risk. Country risk can be of many forms, including changes in tax or labor laws, currency or trade controls, remittance controls, or even expropriation of the firm’s assets. LO: 5 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.9

Suppose GE issues bearer bonds in France denominated in British pounds. What type of bonds are these?

This is an example of a Eurobond. GE, a foreign issuer in France is issuing a bearer bond in a currency (British pounds) to investors in a country whose currency is different from that of the bond issue. LO: 4 Level: Basic Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.10 Give examples of U.S. banks facing different risks in international lending.

The first risk that a bank will face in any market is credit risk—the risk that the interest and/or principal will not be paid. Suppose Citicorp made a loan to a firm in Honduras. Unlike lending in the domestic market, the bank is likely to be less familiar with the new market, economic conditions, and business practices. That makes it more difficult to Copyright © 2015 John Wiley & Sons, Inc.

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judge the credit worthiness of a loan customer. The second risk to consider is currency risk. The loan is made in the Honduran currency, and repayment of principal and interest payments are also going to be in it. So, Citicorp needs to protect itself against currency risk. The third risk is potentially the worst. This is political or country risk, which relates the ability of Citicorp making a profitable loan and being able to remit the funds back to the United States due to the political climate in Honduras. The more unstable a government is, the higher the country risk that Citicorp will face. LO: 5 Level: Basic Bloomcode: Comprehension AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

Questions and Problems BASIC 21.1

Spot rate: Ryan wants to buy a pair of leather shoes at Harrods in London that cost £113.60. If the exchange rate is $1.6177/£, what is Ryan’s cost in U.S. dollars?

Solution: Cost of shoes in London = £113.60 Spot rate = $1.6177/£ Dollar cost of shoes = £113.60 × $1.6177/£ = $183.77 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.2

Spot rate: Crescent Corporation’s recent sale to a firm in Mexico produced revenues of 13,144,800 Mexican pesos (MPs). If the firm sold the pesos to its bank and was credited with $1,077,873.60, what was the spot rate at which the pesos were converted? Solution: Revenue from sale to Mexican firm = MP 13,144,800 Dollar revenue received from sale = $1,077,873.60 Spot rate at which the foreign currency revenue was converted:

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$ 1,077,873.60 MP 13,144,800

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$0.082 /MP

This is the same as MP12.195/$ LO:2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.3

Spot rate: Given the following direct quotes, calculate the equivalent indirect quotes. a. $0.0844/Mexican pesos b. £0.8513/€ c. Rs 54.64/ C$

Solution: a. b. c.

1 = MP11.8483/$ $0.0844 / MP 1 / £0.8513/€ = €1.1747£ 1 / Rs 54.64/ C$ = C$0.0183/Rs.

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective 21.4

Spot rate: Convert the following indirect quotes to the appropriate American quotes. a. £0.6917/$ b. ¥104.28/$ c. SF 1.0769/$

Solution: a. 1 / £0.6917/$ = $1.4457/£ b. 1 / ¥104.28/$ = $0.0096 / ¥ c. 1 / SF 1.0769/$ = $0.9286 / SF LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business Copyright © 2015 John Wiley & Sons, Inc.

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21.5

Spot rate: Suppose a BMW 528i is priced at $68,750 in New York and € 50,267 in Berlin. In which place is the car more expensive if the spot rate is $1.3677/€?

Solution: Cost of car in New York = $68,750 Cost of car in Berlin = € 50,267 Spot rate = $1.3677/€? Dollar cost in Berlin = € 50,267 × $1.3677/€? = $68,750 The cost of the car is almost the same in both cities based on the spot rate! LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.6

Forward rate: Explain the relation between each pair of currencies. Spot Rate Forward Rate a. $1.655/ £ $1.6001/£ b. ¥104.45/$ ¥102.33/$ c. C$1.1121/$ C$1.0940/$

Solution: a.

b. c.

Since the forward rate indicates that fewer dollars will be required to buy a pound in the future, we say that the dollar is at a forward premium against the British pound. The yen is at a forward premium against the dollar as the forward quote indicates that the dollar can be purchased with fewer yen. The U.S. dollar is at a forward discount against the Canadian dollar as a dollar is expected to purchase fewer Canadian dollars in the future.

LO: 2 Bloomcode: Analysis AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

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Forward rate: If the spot rate was $1.0413/C$ and the 90-day forward rate was $1.0507/C$, how much more (in U.S. dollars) would you receive by selling C$ 1,000,000 at the forward rate than at the spot rate?

Solution: If C$1,000,000 was sold at the spot rate, dollar revenue received: C$1,000,000 × $1.0413/C$ = $1,041,300 If C$1,000,000 was sold at the 90 day forward rate, dollar revenue received: C$1,000,000 × $1.0507/C$ = $1,050,700 Additional revenue received by selling forward = $1,050,700 - $1,041,300 = $9,400 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective 21.8

Forward rate: Crane, Inc., sold equipment to an Irish firm and will receive €1,319,405 in 30 days. If the company entered a forward contract to sell at the 30-day forward rate of $1.3012/€, what is the dollar revenue received?

Solution: Expected euro revenue = €1,319,405 30-day forward rate = $1.3012/€ Dollar revenue received = €1,319,405 × $1.3012/€ = $1,716,809.79 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective 21.9

Forward rate: Brilliant Equipment purchased machinery from a Japanese firm and must make a payment of ¥313.25 million in 45 days. The bank quotes a forward rate of ¥103.01/$ to buy the required yen. What is the cost to Brilliant in U.S. dollars?

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Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.10 Forward rate: Triumph Autos has contracted with an Indian software firm for design software. The payment of 22,779,750 rupees (₹) is due in 30 days. What is the cost in dollars if the 30-day forward rate is ₹64.39/$. Solution: Cost of software = ₹22,779,750 Forward rate= ₹64.39/$ Cost of software in dollars = ₹22,779,750 / ₹64.39/$= $353,777.76 LO :2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.11 Forward rate: Use the data in Exhibit 21.5 to answer these questions: a. What is the six-month forward rate (in U.S. dollars) for Swiss francs? Is the Swiss franc selling for a premium or a discount? b. What is the six-month forward rate (in U.S. dollars) for the Japanese yen? Is the Japanese yen selling for a premium or a discount? c. Given the information above, what do you think will happen to the value of the U.S. dollar relative to the Swiss franc and the Japanese yen? Solution: a. The six month forward rate on the Swiss Francs is $1.1201/SF relative to the spot rate of $1.1182/SF. The forward premium (discount) = (1.1201 – 1.1182)/1.1182 = 0.17%. So there is a forward premium on the Swiss franc. b. The six month forward rate on the Japanese yen is $0.00979/¥, while the spot rate is $0.00977/¥. The forward premium (discount) = (0.00979 – 0.00977)/0.00977= 0.20%. The yen is a forward premium against the U. S. dollar. c. Given the data on forward rates in a.) and b.) above, we can expect the Swiss franc and the Japanese yen to appreciate relative to the U.S. dollar. LO: 2 Bloomcode: Analysis Copyright © 2015 John Wiley & Sons, Inc.

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AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.12 Bid-ask spread: Nova Scotia Bank offers quotes on the Canadian dollar as shown below. What is the bid-ask spread based on these quotes? Bid Ask C$ 0.9973/$ C$ 0.9978/$ Solution:

Ask rate - Bid rate 0.9978 - 0.9973 = Ask rate 0.9978 = 0.0005 = 0.05%

Bid - ask spread =

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.13 Bid-ask spread: A local community bank has requested foreign exchange quotes for the Swiss Franc from Citibank. Citibank quotes a bid rate of $1.0934/SF and an ask rate of $1.0997/SF. What is the bid-ask spread? Solution:

Ask rate - Bid rate 1.0997 -1.0934 = Ask rate 1.0997 = 0.000573 = 0.573%

Bid - ask spread =

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective 21.14 Bid-ask spread: A foreign exchange dealer is willing to buy the Danish krone (DKr) at $0.1556/DKr and will sell it at a rate of $0.1563/DKr. What is the bid-ask spread on the Danish krone?

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Solution:

Ask rate - Bid rate 0.1563 - 0.1556 = Ask rate 0.1563 = 0.00448 = 0.45%

Bid - ask spread =

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.15 Cross rate: Given the following quotes, calculate the €/£ cross rate. Bank of America $1.663/£ JP Morgan Chase $1.3914/€ Solution: To find the €/£ cross rate, divide the Bank of America quote by the JP Morgan Chase quote. Cross rate = $1.663/£ / $1.3914/€ = €1.1952/£ LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.16 Cross rate: Barclays Bank of London has offered the following exchange rate quotes: ¥134.64/£ and Korean won 13.8374/¥. What is the cross rate between the Korean won and the British pound? Solution: To find the won/£ cross rate, multiply the Korean won quote by the yen quote. Cross rate = Won 13.8374/¥ × ¥ 134.64/£ = Won 1,863.07 /£ LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

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21.17 Cross rate: Bremer Corporation observes that the Swiss franc (SF) is being quoted at €0.7660/SF, while the Swedish krona (SK) is quoted at €0.1114/SK. What is the SK/SF cross rate? Solution: To find the SK/SF cross rate, divide the Swiss franc quote by the Swedish krona quote. Cross rate = €0.7660/SF / €0.1114/SK = SK6.8761/SF LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective 21.18 Country risk: Ford Motor Company maintains production facilities in many different countries including Brazil, Taiwan, and the United States. Given the data in Exhibit 21.6, which production plant is likely to face the greatest country risk? How does country risk affect a firm’s capital budgeting decisions? Solution: Exhibit 21.6 contains composite country risk ratings as per 2014 survey. Using these ratings, Brazil has the greatest country risk while Taiwan has the least. Country risk factors are associated with additional systematic risk for projects located in that country and therefore are associated with a relatively higher discount rate. LO: 3 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.19 Foreign exchange risk: How is transaction exposure different from operating exposure? Solution: Transaction exposure is related to foreign exchange risk faced by firms that are expecting revenues in foreign currency or have expenses in foreign currency that relate to transactions they have already entered into. As the exchange rate changes, the home currency value of these revenues or expenses change, leading to transaction exposure. If exchange rate changes are more permanent in nature and modify the way a firm does its business, then we say that a firm is facing operating exposure.

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LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective 21.20 International debt: What are Yankee bonds?

Solution: When corporate bonds are issued by a foreign firm in the United States and denominated in U.S. dollars, they are considered to be foreign bonds and referred to as “Yankee” bonds. LO :4 Bloomcode: Knowledge AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective INTERMEDIATE 21.21 Forward premium: The spot rate on the London market was £0.5514/$, while the 90day forward rate is £0.5589/$. What is the annualized forward premium or discount on the British pound? Solution:

Forward rate - Spot rate 360   100 Spot rate n 0.5589 − 0.5514 360 =  = 5.44% 0.5514 90 The British pound is at a forward discount against the U.S. dollar as it takes more pounds to buy a dollar at the forward rate. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective Forward discount (premium) =

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21.22 Forward premium: Bank of America quoted the 180-day forward rate on the Swiss franc at $1.0407/SF. The spot rate was quoted at $1.0268/SF. What is the forward premium or discount on the Swiss franc? Solution:

Forward rate - Spot rate 360   100 Spot rate n $1.0407 − $1.0268 360 =  = 2.71% $1.0268 180 The Swiss franc is at a 2.71 percent forward premium against the dollar. Forward premium (discount) =

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.23 Forward premium: The foreign exchange department at Tokyo’s Daiwa Bank quoted the spot rate on the euro at €0.007269/¥. The 90-day forward rate is quoted at a premium of 5.42 percent on the euro. What is the 90-day forward rate? Solution: Spot rate = €0.007269/¥ 90-day forward premium on the euro = 5.42% It’s mean that 90-day forward discount on the Yen= –5.42% F - 0.00727 360 x 0.007269 90 0.007269 = -0.0542 X 0.007269 X 90 360 = €0.007171/¥

-0.054 = F

The 90-day forward rate is €0.007171/¥.

LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

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21.24 Forward premium: The spot rate of the Australian dollar (A$) is A$1.1667/$. The Australian dollar is quoted at a 30-day forward premium of 4.90 percent against the U.S. dollar. What is the 30-day forward quote? Solution: Spot rate = A$1.1667/$ 30-day forward premium on the Australian dollar = 4.90%Its mean that 90-day forward discount on the dollar= –4.90%

Forward rate - Spot rate 360  100 Spot rate n F − 1.1667 360 − 0.049 = 0  1.1667 30 − 0.049 1.1667  30 F0 − 1.1667 = 360 F0 = −0.004764 + 1.1667

Forward premium (discount) =

= A$ 1.1619/$ The 30-day forward rate is A$1.1619/$. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.25 Bid-ask spread: The foreign exchange department of Bank of America has a bid quote on Canadian dollars (C$) of C$1.0800/$. If the bank typically tries to make a bid-ask spread of 0.5 percent on these foreign exchange transactions, what will the ask rate have to be? Solution: Bid-ask spread = Ask rate - Bid rate Ask rate 0.005 = Ask rate -1.08 Ask rate Ask rate - 0.005 x Ask rate = 1.08 Ask rate = 1.08 1.08 = 1.09 1.09 0.995

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Ask rate - Bid rate Ask rate Ask Rs. 43.21 / $ 0..005 = Ask Ask 43.21 = 0.005× Ask Ask - 0.005 Ask = 43.21 43.21 Ask rate = = Rs.43.43 / $ 0.995 The ask rate will have to be C$1.09/$ to provide a 0.5 percent bid-ask spread. LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective Bid - ask spread =

21.26 Bid-ask spread: Banco Santiago wants to make a bid-ask spread of 0.65 percent on its foreign exchange transactions. If the ask rate on the Mexican peso (MP) is MP10.3092/$, what does the bid rate have to be? Solution: Bid -ask spread = Ask rate - Bid rate Ask rate 0.0065 = MP10.3092 - Bid rate MP10.3092 MP10.3092 - Bid rate = 0.0065 × MP10.3092 = 0.067 Bid rate = MP10.3092 -0.067 = MP10.2422/$

Ask rate - Bid rate Ask rate 10.3092 - Bid rate 0..0065 = 10.3092 10.3092 - Bid rate = 0.0065×10.3092 = 0.0067 Bid rate = 10.3092 - 0.0067 = MP10.2422 / $ The ask rate will have to be MP10.2422/$ to provide a 0.65 percent bid-ask spread. LO: 2 Bloomcode: Application AASCB: Analytic Bid - ask spread =

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IMA: Global Business AICPA: Industry/Global Perspective

21.27 Cross rate: Alcor Pharma just received revenues of $3,165,300 in Australian dollars (A$). Management has the following exchange rates:A$1.08010/£ and $1.5906/£. What is the U.S. dollar value of the company’s revenues? Solution: Revenues received by Alcor Pharma = A$3,165,300 To determine the A$ /$ cross rate, you divide the A$ to £ quote by the $/£ quote. Cross rate = A$1.08010/£ / $1.5906/£ = A$0.6796/$ U.S. dollar value of their revenue = A$3,165,300 / A$0.6796/$ = $4,657,593 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.28 Cross rate: Flint Corp. recently purchased auto parts worth 17.5 million Mexican pesos (MP) on credit. Management needs to find out the U.S. dollar cost of the purchase. It has access to two quotes for Canadian dollars (C$): C$1.0174/$ and C$0.0820/MP. What did it cost Flint to purchase the auto parts? Solution: Foreign currency payables = MP 17.5 million To find the MP/$ quote, divide the C$/MP quote by the C$/$ quote. Cross rate = C$0.0820/MP / C$1.0174/$ = $0.08060/MP Dollar cost of payables = MP 17,500,000 × $0.08060/MP = $1,410,458 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

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21.29 Hedging: Tricolor Industries has purchased equipment from a Brazilian firm for a total cost of 272,500 Brazilian reals. The firm has to pay in 30 days. Citibank has given the firm a 30-day forward quote of $0.4723/real. Assume that on the day the payment is due, the spot rate is at $0.4917/real. How much would Tricolor save by hedging with a forward contract? Solution: Foreign currency payables = BR 272,500 Spot rate on payment date = $0.4917/real Dollar cost of payables = BR 272,500 × $0.4917/real = $133,988.25 30-day forward rate = $0.4723/real Cost if hedged at forward rate = BR 272,500 × $0.4723/real = $128,701.75 Cost savings = $133,988.25 − $128,701.75 = $5,286.50 LO :2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.30 Eurocredit Loan: A Swiss sporting goods company borrows in yen in the Eurocredit market at a rate of 4.35 percent from Bank of America using a three-month rollover loan. Bank of America assigns a default risk premium of 2 percent on the loan, and the country risk is an additional 0.75 percent. The Bank can borrow funds in the Euromarket at the three-month LIBOR rate of 0.40 percent. What is Bank of America’s gross profit margin on this loan? Solution: GPMAR = k - BR – DRP – CR = 4.35% - 0.40% - 2.0% - 0.75% = 1.2% LO: 5 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

ADVANCED 21.31 Covington Industries just sold equipment to a Mexican firm. Payment of 11,315,000 pesos will be due to Covington in 30 days. Covington has the option of selling the pesos today at a 30-day forward rate of $0.09139/peso. If it waits 30 days to sell the pesos, the Copyright © 2015 John Wiley & Sons, Inc.

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expected spot rate is $0.0907/peso. In dollars, how much better off is Covington by selling the pesos in the forward market? Solution: Foreign currency receivables = MP 11,315,000 Spot rate on payment date = $0.0907/peso Dollar revenues from receivables = MP 11,315,000 × $0.0907/peso= $1,026,270.50 30-day forward rate = $0.09139/peso Revenues if hedged at forward rate = MP 11,315,000 × $0.09139/peso= $1,034,077.85 Additional revenues received = $1,034,077.85 − $1,026,270.50 = $7,807.35 LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.32 Barrington Fertilizers, Inc., exports its specialized lawn care products to Canada. It made a sale worth C$1,150,000, with the payment due in 90 days. Barrington’s banker gave it a forward quote of $0.9021/C$. By using the forward rate, the firm gained an additional $8,433.25 over what it would have gotten if it had sold the Canadian dollars in the spot market 90 days later. What was the spot rate at the time the payment was received? Solution: Foreign currency receivables = C$1,150,000 90-day forward rate = $0.9021/C$ Revenues if hedged at forward rate = C$1,150,000 × $0.9021/C$= $1,037,415 Additional dollar revenues received = $8,433.25 Revenues at spot rate = $1,037,415− $8,433.25 = $1,028,981.75 Spot rate on payment date = $1,028,981.75/ C$1,150,000 = $0.8948/C$ LO: 2 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.33 Moon Rhee Auto Supply, a Korean supplier of parts to Kia Motors, is evaluating an opportunity to set up a plant in Alabama, where Kia Motors has an auto assembly plant for its SUVs. The cost of this plant will be $13.5 million. The current spot rate is

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1,120.318 Korean won per U.S. dollar. The firm is expected to use this plant for the next five years and is expecting to generate the following cash flows. Years Cash flows ($ millions) Expected exchange rate (Korean won/$)

$2.3

$4.2

$3.6

$5.8

$7.6

1,105.231

1,115.632

1,146.155

1,120.221

1,110.670

The firm uses a discount rate of 9 percent for projects like this in the United States. What is the NPV of this project? Should Moon Rhee Auto Supply take on this project? Solution: Moon Rhee Auto Supply knows what the expected cash flows in U. S. dollars and the expected cash flows to the parent firm in Korean won can be calculated by dividing the dollar cash flows by the appropriate exchange rate. Year Cash flows ($ millions)

4___________5__

2.3

4.2

3.6

5.8

7.6

Given in the following table are the cash flows that the Korean firm expects to receive from its American subsidiary in U.S. dollars.

Year 0 1 2 3 4 5

Cash Flows (in millions of U.S. $) (13.5) 2.3 4.2 3.6 5.8 7.6

Exchange Rate (won/$) 1,120.318 1,105.231 1,115.632 1,146.155 1,120.221 1,110.670

Cash Flows (in millions of won) (15,124.293) 2,542.031 4,685.654 4,126.158 6,497.282 8,441.092

The firm has determined that the appropriate discount rate is 9 percent for capital budgeting projects in the United States. By discounting the cash flow at the risk-adjusted discount rate of 9 percent, we can compute the NPV for this project. NPV = −15,124.293 + 2,542.031/(1.09)1 + 4,685.654/(1.09)2 + 4,126.158/(1.09)3 +6,497.282/(1.09)4 + 8,441.092/(1.09)5 million won Copyright © 2015 John Wiley & Sons, Inc.

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=-15124.293 + 2,332.13881+ 3,943.82156 + 3,186.15104 + 4,602.83823 + 5,486.13063 million won= 4,426.787million won Since NPV is positive, the project should be accepted. LO: 3 Bloomcode: Analysis AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.34 The Boeing Company has two different debt issues, both maturing four years from now. The domestic bond issue pays semiannual coupons and has a coupon rate of 4.80 percent. The current price on the bond is $962.75. The Eurobond issue is priced at $964.33 and pays an annual coupon of 4.95 percent. What is the yield to maturity for each bond? Solution: For the Euro bond with annual compounding, the coupon payment is $49.50 per year, and the yield calculation is: $49.50 $49.50 $49.50 $1,049.50 $964.33 = + + + (1 + i )1 (1 + i )2 (1 + i )3 (1 + i )4 Using our financial calculator, the annual yield of the Eurodollar bond issue is 5.9789 percent. For the domestic bond issue the semiannual coupon payments are $24 ($48/2), and the semiannual bond yield calculation is: $24 $24 $1,024 $962.75 = + + + 1 2 (1 + i ) (1 + i ) (1 + i )8 Making the calculation, the bond issue’s semiannual yield is 2.9291 percent. As discussed in Chapter 8, to compare interest rates with different compounding periods, we need to compute the effective annual yield (EAY). Applying the equation EAY: EAY = (1 + quoted rate/m)m – 1 = (1 + 0.029291)2 – 1 = 1.05944 – 1 = 5.94% An investor in Boeing’s Eurobond will earn 5.98 percent, while the domestic bond would provide a yield of 5.94 percent. Thus, the Eurobond is the better investment. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective Copyright © 2015 John Wiley & Sons, Inc.

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21.35 Caterpillar, Inc. management is trying to decide between selling a new bond issue in the U.S. or the Eurodollar bond market. In either market the bonds will be denominated in dollars and will have a three-year maturity. The domestic bond will have a coupon rate of 4.1 percent, paid semiannually and would sell at a market price of $1,034.25. The Eurobonds will have a coupon rate of 4 percent, paid annually, and will sell at $1,029.76. Which bond issue will have the lowest cost to the firm? Solution: For the domestic bond issue the semiannual coupon payments are $20.50 ($41/2), and the semiannual bond yield calculation is: $20.50 $20.50 $1,020.50 $1,034.25 = + + + 1 2 (1 + i ) (1 + i ) (1 + i )6 Making the calculation, we see that the bond issue’s semiannual yield is 1.4499 percent. As discussed in Chapter 8, to compare interest rates with different compounding periods, we need to compute the effective annual yield (EAY). Applying the equation EAY: EAY = (1 + quoted rate/m)m – 1 = (1 + 0.014499)2 – 1 = 1.02921 – 1 = 2.92% For the Eurodollar bond with annual compounding, the coupon payment is $40 per year, and the yield calculation is: $40 $40 $1,040 $1,029.76 = + + 1 (1 + i ) (1 + i )2 (1 + i )3 Using our financial calculator, the annual yield of the Eurodollar bond issue yield is 2.9489 percent. From Caterpillar’s perspective, the domestic bond issue is the cheaper alternative. LO: 4 Bloomcode: Analysis AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

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loan in Euros? If the exchange rate on the payoff date is €0.8164/$, what is the dollar cost of the loan? Solution: Amount IBM plans to borrow = €7.5 million Term of loan = 90 days Interest cost = LIBOR + 0.25% = 3.875% + 0.25% = 4.125% Interest cost in euros = €7,500,000 x 0.04125 × (90/360) = €77,343.75 Spot rate on payoff date = €0.8164/$ Dollar interest cost = €77,343.75 / €0.8164/$ = $94,737.57 LO: 5 Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.37 Toyota is interested in borrowing $5 million for 90 days. Bank of America has quoted a rate that is 1.125 percent under the prime rate of 6.25 percent. Daiwa Bank is offering Toyota a rate that is 0.75 percent over the three-month LIBOR of 4.2 percent. Which is the better deal for Toyota, and what is the lower interest cost in dollars? Solution: Bank of America Loan Amount Toyota plans to borrow = $5 million Term of loan = 90 days Interest cost = Prime rate − 1.125% = 6.25% − 1.125% = 5.125% Interest cost = $5,000,000 × 0.05125 × (90/360) = $64,062.50 Daiwa Bank Loan Amount Toyota plans to borrow = $5 million Term of loan = 90 days Interest cost = LIBOR + 0.75% = 4.2% + 0.75% = 4.95% Interest cost = $5,000,000 × 0.0495 × (90/360) = $61,875 The Daiwa Bank offers Toyota the lower cost loan with a lower interest cost of $61,875 versus $64,062.50. LO: 5 Bloomcode: Analysis AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective Copyright © 2015 John Wiley & Sons, Inc.

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Sample Test Problems 21.1

What are six factors that cause international transactions to differ from domestic transactions? Solution: Six factors that cause international transactions to differ from domestic transactions are differences in: 1) Currencies 2) Legal systems and tax codes 3) Languages 4) Cultures 5) Economic systems 6) Country risks

Bloomcode: Knowledge AASCB: Diversity IMA: Global Business AICPA: Industry/Global Perspective

21.2

If a Dell Studio laptop sells for $999 in Austin, Texas and £689 in London, what is the implied exchange rate between the U.S. dollar and the euro? Solution: Cost of the computer in Austin

= $999

Cost of the computer in London = £689 Dollar to euro exchange rate

= $999 / £689 = $1.4499/£

Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

21.3

A bank in India has offered a spot rate quote on Indian rupees (Rs) of Rs62.2905/$. The Indian rupee is quoted at a 30-day forward premium of 5.22 percent against the dollar. What is the 30-day forward quote?

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Solution: Spot rate = Rs62.2905/$ 30-day forward premium on the dollar = 5.22%

Forward premium = 0.0522 = F0 − 62.2905 =

Forward rate − Spot rate 360 × × 100 Spot rate n F0 − Rs62.2905/$ 360 × Rs62.2905/$ 30 0.0522 × Rs62.2905/$ × 30 360

F0 = 0.2710 + Rs62.2905/$ = Rs62.5615/$ The 30-day forward rate is Rs62.5615/$. Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective 21.4

Technocorp has purchased industrial parts from a German company for a total cost of €1,225,000. The firm has 30 days to pay. A bank has given Technocorp a 30-day forward quote of $1.355/€. Assume that on the day the payment is due, the spot rate is $1.368/€. How much would Technocorp have saved by hedging with a forward contract? Solution: Foreign currency payable = €1,225,000 Spot exchange rate on payment date = $1.368/€. Dollar cost of payables = €1,225,000 × $1.368/€ = $1,675,800 30-day forward rate = $1.355/€ Cost if hedged at forward rate = €1,225,000 × $1.355/€ = $1,659,875 Cost savings = $1,675,800 − $1,659,875 = $15,925

Bloomcode: Application AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

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Tass Co., Ltd, a Japanese electrical parts producer, is considering building a plant in the U.S. The cost of this plant will be $20 million and the current spot exchange rate between the yen and the U.S. dollar is ¥101.8/$. Tass management expects to use this plant for the next five years and expects it to generate the following cash flows during this period. Year Cash flows ($ millions) Expected exchange rate (¥/$)

1 $2.0 ¥101.5/$

2 $3.6 ¥100.4/$

3 $5.0 ¥98.6/$

4 $6.8 ¥95.9/$

5 $8.0 ¥92.5/$

If Tass uses a discount rate of 8 percent for projects in the United States, what is the NPV of this project? Should Tass Company take on this project? Solution: Expected cash flows to Tass in yen can be calculated by multiplying the dollar cash flows by the appropriate exchange rate.

Year 0 1 2 3 4 5

Cash Flows (U.S. $ in millions) ($20) $2.0 $3.6 $5.0 $6.8 $8.0

Exchange Rate (¥/$) ¥101.8/$ ¥101.5/$ ¥100.4/$ ¥98.6/$ ¥95.9/$ ¥92.5/$

Cash Flows (in millions of ¥) (¥2,036) ¥203 ¥361.44 ¥493 ¥652.12 ¥740

By discounting the cash flow at the risk-adjusted discount rate of 8 percent, we can compute the NPV for this project. NPV = −2,036 + 203 / 1.08 + 361.44 / (1.08)2 + 493 / (1.08)3 +652.12 / (1.08)4 + 740 / (1.08)5 = −2,036 + 187.96 + 309.88 + 391.36 + 479.33 + 503.63 = −¥163.84 million The NPV is negative, so the project should be rejected. Bloomcode: Analysis AASCB: Analytic IMA: Global Business AICPA: Industry/Global Perspective

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Chapter 1 The Financial Manager and the Firm

Learning Objectives 1. Identify the key financial decisions facing the financial manager of any business firm. 2. Identify the basic forms of business organization in the United States and their respective strengths and weaknesses. 3. Describe the typical organization of the financial function in a large corporation. 4. Explain why maximizing the value of the firm’s stock is the appropriate goal for management. 5. Discuss how agency conflicts affect the goal of maximizing shareholder value. 6. Explain why ethics is an appropriate topic in the study of corporate finance.

Chapter Outline

1.1

The Role of the Financial Manager A.

Stakeholders

It’s All about Cash Flows •

The financial manager is responsible for making decisions that are in the best interest of the firm’s owners.

•

A firm generates cash flows by selling the goods and services produced by its productive assets and human capital. After meeting its obligations, the firm

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can pay the remaining cash, called residual cash flows, to the owners as a cash dividend, or it can keep the money and reinvest the cash in the business. C.

Three Fundamental Decisions in Financial Management •

The capital budgeting decision: Which productive assets should the firm buy? This is the most important decision because they drive the firm’s success or failure.

•

The financing decision: How should the firm finance its assets?

•

Working capital management decisions: How should day-to-day financial matters be managed so that the firm can pay its bills, and how should surplus cash be invested?

1.2

Forms of Business Organization A.

A sole proprietorship is a business owned by one person. •

Sole proprietors keep all the profits from the business and do not have to share decision making authority.

•

All business income is taxed as personal income.

•

The simplest and least regulated type of business to start.

•

A sole proprietor is responsible for paying all the firm’s bills and has unlimited liability for all business debts and other obligations of the firm.

A partnership consists of two or more owners joined together legally to manage a business.

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A general partnership has the same basic advantages and disadvantages as a sole proprietorship.

•

The problem of unlimited liability can be avoided in a limited partnership where there must still be a general partner with unlimited liability.

Corporations are legal entities authorized under a state charter. •

In a legal sense, it is a “person” distinct from its owners.

•

The owners of a corporation are its stockholders.

•

A major advantage of the corporate form of business is that stockholders have limited liability for debts and other obligations of the corporation.

•

A major disadvantage of the corporate form of organization is taxes. o The owners of corporations are subject to double taxation—first at the corporate level and then at the personal level when dividends are paid to them.

•

Some operate as a public corporation, which can sell their debt or equity in the public securities markets.

•

Others operate as a private corporation, where the common stock is often held by a small number of investors, typically the management and wealthy private backers.

Hybrid Forms of Business Organization •

Limited liability partnerships (LLPs) combine the limited liability of a corporation with the tax advantage of a partnership—there is no double taxation.

•

Limited liability companies (LLCs)

•

Professional corporations (PCs)

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Managing the Financial Function A.

Organizational Structure •

The Chief Executive Officer has the final decision-making authority in the firm. o Sets and executes the strategic plan for the firm. o Reports directly to the board of directors, which is accountable to the company’s owners.

•

The Chief Financial Officer (CFO) has the responsibility for seeing that the best possible financial analysis is presented to the CEO, along with an unbiased recommendation.

Positions Reporting to the CFO o The treasurer looks after the collection and disbursement of cash, investing excess cash so that it earns interest, raising new capital, handling foreign exchange transactions, and overseeing the firm’s pension fund managers. o The risk manager monitors and manages the firm’s financial risk exposure as well as the relationship with insurance providers. o The controller typically prepares the financial statements, oversees the firm’s financial and cost accounting systems, prepares the taxes, and works closely with the firm’s external auditors. The position is really the chief accounting officer.

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o The internal auditor is responsible for in-depth risk assessments and for performing audits of areas that have been identified as high-risk areas, where the firm has the potential to incur substantial losses. C.

External Auditors •

Provide an independent annual audit of the firm’s financial statements. o Ensure that the financial numbers are reasonably accurate and that accounting principles have been consistently applied year to year and not in a manner that significantly distorts the firm’s performance.

The Audit Committee •

Powerful subcommittee of the board of directors and has the responsibility of overseeing the accounting function and preparing the firm’s financial statements.

•

If necessary, it conducts investigations of significant fraud, theft, or malfeasance in the firm.

1.4

The Compliance and Ethics Director

The Goal of the Firm A.

What Should Management Maximize? •

Minimizing risk or maximizing profits without regard to the other is not a successful strategy.

Why Not Maximize Profits? •

To a skilled accountant, however, a decision that increases profits under one set of accounting rules can reduce it under another.

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•

Accounting profits are not necessarily the same as cash flows.

•

The problem with profit maximization as a goal is that it does not tell us when cash flows are to be received.

• C.

Profit maximization ignores the uncertainty or risk associated with cash flows.

Maximizing the Value of the Firm’s Stock •

When analysts and investors determine the value of a firm’s stock, they consider: o The size of the expected cash flows o The timing of the cash flows o The riskiness of the cash flows

•

Thus, the mechanism for determining stock prices overcomes all the cashflow objections we raised with regard to profit maximization as a goal.

Can Management Decisions Affect Stock Prices? •

Yes, management makes a series of decisions when executing the firm’s strategy that affect the firm’s cash flows and, hence, the price of the firm’s stock.

1.5

Agency Conflicts: Separation of Ownership and Control A.

Ownership and Control •

Once ownership and management are separated, managers may be tempted to pursue goals that are in their own self-interest rather than the interests of the owners.

Agency Relationships

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An agency relationship arises whenever one party, called the principal, hires another party, called the agent, to perform some service or represent the principal’s interest.

Do Managers Really Want to Maximize Stock Price? •

Shareholders own the corporation, but managers control the money and have the opportunity to use it for their own benefit.

•

Agency costs arise due to a conflict of interest between the firm’s owners and its management.

Aligning the Interests of Management and Stockholders •

Board of Directors: The board has the legal responsibility to represent stockholder’s interests. Its duties include hiring and firing the CEO, setting his or her compensation, and monitoring his or her performance. The board also approves major decisions concerning the firm.

•

Management Compensation: A significant portion of management compensation is tied to the performance of the firm, usually to the firm’s stock price.

•

Management Labor Market o Firms that have a history of poor performance or a reputation for “shady operations” or unethical behavior have difficulty hiring top managerial talent. o The penalty for extremely poor performance or a criminal conviction is a significant reduction in the manager’s lifetime

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earnings potential. Managers know this, and the fear of such consequences helps keep them working hard and honestly. •

Other Managers o Competition amongst managers helps provide incentives for managers to act in the interest of shareholders.

•

Large Stockholders: May have enough money and enough power for them to actively monitor managers and to try to influence their decisions.

•

The Takeover Market: If the interests of the manager and the firm are not aligned, then eventually the firm will underperform relative to its true potential, and the firm’s stock price will fall below its maximum potential price. With its stock underpriced, the firm will become a prime target for a takeover by so-called corporate raiders or by other corporate buyers.

•

The Legal and Regulatory Environment: Laws and regulations may limit the ability of managers to make decisions that harm the interests of shareholders.

1.6

Sarbanes-Oxley and Other Regulatory Reforms •

Greater board independence

•

Internal accounting controls

•

Compliance programs

•

Ethics program

•

Expansion of audit committee’s oversight powers

The Importance of Ethics in Business

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Business Ethics •

Business ethics are a society’s ideas about what actions are right and wrong. Are Business Ethics Different?

•

Studies suggest that traditions of morality are very relevant to business and to financial markets in particular.

•

Corruption in business creates inefficiencies in an economy, inhibits the growth of capital markets, and slows a country’s rate of economic growth.

Types of Ethical Conflicts in Business •

Agency Costs – Financial managers have an agency obligation to act honestly and to see that subordinates also act honestly. However, revelations of dishonesty, deception, and fraud in financial matters can have a large impact on the stock price.

•

Conflicts of Interest—occur when the agent’s interests are different from those of the principal.

•

Information Asymmetry—occurs when one party in a business transaction has information that is unavailable to the other parties in the transaction.

The Importance of an Ethical Business Culture •

An ethical business culture means that people have a set of principles that helps them identify moral issues and then make ethical judgments without being told what to do.

Serious Consequences •

In recent years, the “rules” have changed, and the legal cost of ethical mistakes can be extremely high.

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II.

Instructor’s Manual

Suggested and Alternative Approaches to the Material

This chapter presents a general survey of interesting topics in corporate finance. It begins with a brief discussion of the role of the financial manager and is followed by an examination of the different legal organizational forms of business. Although all of the most common organizational forms are discussed, the most common form for the purposes of the remainder of the text is the corporate form. The chapter then proceeds with the financial function of the manager and the goal of the firm, which is to maximize shareholder value. It is this goal that requires that we recognize its conflicts such as agency and ethical problems. This chapter is intended to help students begin to understand the long list of interesting problems that confront the financial manager and shareholders of the firm. While omitting this chapter from a course syllabus will not necessarily diminish the direct understanding of the material, such an omission could give the impression that the remaining material in the course is mechanical in nature. Therefore, it is recommended that the instructor devote a lecture, or a portion of a lecture, on the chapter in order to establish a proper basis for future chapter-related discussions.

III. Summary of Learning Objectives 1.

Identify the key financial decisions facing the financial manager of any business firm. The financial manager faces three basic decisions: (1) which productive assets the firm should buy (capital budgeting decisions), (2) how the firm should finance the productive

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assets purchased (financing decisions), and (3) how the firm should manage its day-today financial activities (working capital decisions). The financial manager should make these decisions in a way that maximizes the current value of the firm’s stock.

Identify the basic forms of business organization in the United States and their respective strengths and weaknesses. A business can organize in three basic ways: as a sole proprietorship, a partnership, or a corporation (public or private). The owners of a firm select the form of organization that they believe will best allow management to maximize the value of the firm. Most large firms elect to organize as public corporations because of the ease of raising money; the major disadvantage is double taxation. Smaller companies tend to organize as sole proprietorships or partnerships. The advantages of these forms of organization include ease of formation and taxation at the personal income tax rate. The major disadvantage is the owners’ unlimited personal liability.

Describe the typical organization of the financial function in a large corporation. In a large corporation, the financial manager generally has the rank of vice president and goes by the title of chief financial officer. The CFO reports directly to the firm’s CEO. Positions reporting directly to the CFO generally include the treasurer, the risk manager, the controller, and the internal auditor. The audit committee of the board of directors is also important in the financial function. The committee hires the external auditor for the firm, and the internal auditor, external auditor, and compliance officer all report to the audit committee.

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Explain why maximizing the current value of the firm’s stock is the appropriate goal for management. Maximizing stock value is an appropriate goal because it forces management to focus on decisions that will generate the greatest amount of wealth for stockholders. Since the value of a share of stock (or any asset) is determined by its cash flows, management’s decisions must consider the size of the cash flow (larger is better), the timing of the cash flow (sooner is better), and the riskiness of the cash flow (given equal returns, lower risk is better.)

Discuss how agency conflicts affect the goal of maximizing shareholder value. In most large corporations, there is a significant degree of separation between management and ownership. As a result, stockholders have little control over corporate managers, and management may thus be tempted to pursue its own self-interest rather than maximizing the value of the owners’ stock. The resulting conflicts give rise to agency costs. Ways of reducing agency costs include developing compensation agreements that link employee compensation to the firm’s performance and having independent boards of directors monitor management.

Explain why ethics is an appropriate topic in the study of corporate finance. If we lived in a world without ethical norms, we would soon discover that it would be difficult to do business. As a practical matter, the law and market forces provide important incentives that foster ethical behavior in the business community, but they are

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not enough to ensure ethical behavior. An ethical culture is also needed. In an ethical culture, people have a set of moral principles—a moral compass—that helps them identify ethical issues and make ethical judgments without being told what to do.

IV.

Summary of Key Equations

The chapter is primarily a qualitative chapter and does not have a relevant summary of key equations.

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Chapter 2 The Financial System and the Level of Interest Rates

Learning Objectives 1. Describe the role of the financial system in the economy and the two basic ways in which money flows through the system. 2. Discuss direct financing and the important role that investment banks play in this process. 3. Describe the primary, secondary, and money markets, explaining the special importance of secondary and money markets to business organizations. 4. Explain what an efficient market is and why market efficiency is important to financial managers. 5. Explain how financial institutions serve the needs of consumers and small businesses. 6. Compute the nominal and the real rates of interest, differentiating between them.

Chapter Outline 2.1

The Financial System A. The Financial System at Work • It is competitive. • Money is aggregated in small amounts and loaned in large amounts. • Directs money to the best investment opportunities in the economy. • Banks earn much of their profits from the spread which involves borrowing at a low rate from depositors and lending at a higher rate. B. How Funds Flow through the Financial System • The primary concern of the financial system is funneling money from lenderssavers to borrowers-spenders. ▪ Direct funds flow, or ▪ Indirect funds flow (intermediation)

2.2

Direct Financing Financial markets perform the important function of channeling funds from lenderssavers directly to borrowers-spenders. A. A Direct Market Transaction

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A Direct Market Transaction—wholesale market transaction in which the borrower raises capital from the market rather than borrowing from another institution. Investment Banks and Direct Financing—firms that specialize in helping companies sell new debt or equity issues directly in the public or private security markets. ▪ Money Center Banks—large commercial banks located in major U.S. financial centers that transact in both the national and international money markets. ▪ Origination is the process of preparing a security issue for sale. ▪ Underwriting—a basic investment banking service is to assist firms in the sale of debt or equity in the primary market. To underwrite a new security issue, the investment banker buys the entire issue at a guaranteed price from the issuing firm and resells the securities to institutional investors and the public. ▪ Distribution is the process of marketing and reselling the securities to investors.

2.3 Types of Financial Markets A. Primary and Secondary Markets - any financial market in which new security issues are sold for the first time is a primary market while a financial market in which the owners of outstanding securities can resell them to other investors is a secondary market. • Investors are willing to pay higher prices for securities in primary markets if the securities have active secondary markets. • The ease with which a security can be sold and converted into cash is called marketability. • The ability to convert an asset into cash quickly without loss of value is called liquidity. • Brokers—market specialists who bring buyers and sellers together in secondary markets. ▪ They execute transactions for their clients and are compensated for their services with a commission fee. ▪ They bear no risk of ownership of the securities in the transactions; their only service is that of a “matchmaker.” • Dealers—“make markets” for securities and do bear risk. They make a market for a security by buying and selling from an inventory of securities they own. The risk is that they will not be able to sell a security for more than they paid for it. B. Exchanges and Over-the-Counter Markets Copyright ©2015 John Wiley & Sons, Inc.

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•

2.4

Organized Exchanges—provide a physical meeting place and communication facilities for members to conduct business under a specific set of rules and regulations. Only members can use the exchange, and each exchange has a limited number of seats. • Over-the-Counter (OTC) Markets—have no central trading location, as the NYSE has. Instead, investors can execute OTC transactions by visiting or telephoning an OTC dealer or by using a computer-based electronic trading system linked to the OTC dealer. Money and Capital Markets— money markets where short-term debt instruments, which have maturities of less than one year, are traded. • Money markets are wholesale markets in which the minimum transactions $1 million. • Capital markets transact equity and debt instruments with maturities of greater than one year are traded. Public and Private Markets • Public markets are organized financial markets where the general public buys and sells securities through their stockbroker. • Private markets involve direct transactions between two parties. Transactions in private markets are called private placements. Futures and Options Markets—are often called derivative securities because they derive their value from some underlying asset. • Futures Contracts—contracts for future delivery of securities, foreign currencies, interest rates, or commodities. • Options Contracts—call for one party (the option writer) to perform a specific act if called upon to do so by the option buyer or owner.

Market Efficiency A. Overview • The supply and demand for securities are better reflected in organized markets. • Any price that balances the overall supply and demand for a security is a market equilibrium price. • A security’s true (intrinsic) value is the price that reflects investors’ estimates of the value of the cash flows they expect to receive in the future. • In an efficient capital market, security prices fully reflect the knowledge and expectations of all investors at a particular point in time. ▪ If markets are efficient, investors and financial managers have no reason to believe the securities are not priced at or near their true value. ▪ The more efficient a security market, the more likely securities are to be priced at or near their true value.

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The overall efficiency of a capital market depends on its operational efficiency and its informational efficiency. ▪ Market Operational efficiency focuses on bringing buyers and sellers together at the lowest possible cost. ▪ Markets exhibit informational efficiency if market prices reflect all relevant information about securities at a particular point in time. ▪ In an informationally-efficient market, market prices adjust quickly to new information about a security as it becomes available. ▪ Competition among investors is an important driver of informational efficiency. Efficient Market Hypotheses • Prices of securities adjust as the buying and selling from investors lead to the price that truly reflects the market’s consensus. This reflects the market’s efficiency. • Market efficiency can be explained at three levels—strong form, semistrong form, and weak form. • Strong-form market efficiency states that the price of a security in the market reflects all information—public as well as private or inside information. ▪ Strong-form efficiency implies that it would not be possible to earn abnormally high returns (returns greater than those justified by the risks) by trading on private information. • Semistrong-Form market efficiency implies that only public information that is available to all investors is reflected in a security’s market price. ▪ Investors who have access to inside or private information will be able to earn abnormal returns. ▪ Public stock markets in developed countries like the United States have a semistrong-form of market efficiency. ▪ New information is immediately reflected in a security’s market price. • In weak-form market efficiency, all information contained in past prices of a security is reflected in current prices. ▪ It would not be possible to earn abnormally high returns by looking for patterns in security prices, but it would be possible to do so by trading on public or private information.

Financial Institutions and Indirect Financing A. Indirect Market Transactions—when a financial intermediary such as a commercial bank or insurance company stands between the borrower and the lender. B. Financial Institutions and Their Services

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1. Commercial Banks—are the most prominent and largest financial intermediaries in the economy and offer the widest range of financial services to businesses. • The major services commercial banks offer consumers are checking accounts, and a variety of credit and loan arrangements. • They also do a significant amount of equipment lease financing. 2. Life and Casualty Insurance Companies—life insurance companies obtain funds by selling life insurance policies that protect individuals against the loss of income from a family member’s premature death while casualty insurance companies sell protection against loss of property from fire, theft, accidents, negligence, and other predictable causes. 3. Pension Funds—provide retirement programs for businesses as part of their employee benefit programs. They obtain money from employee and employer contributions during the employee’s working years, and they provide monthly payments upon retirement. 4. Investment Funds—sell shares to investors and use the funds to purchase securities. 5. Business Finance Companies—sell short-term debt, called commercial paper, to investors in the direct credit markets, where these funds are used to make a variety of short- and intermediate-term loans and leases to small and large businesses. 2.6

The Determinants of Interest Rate Levels A. The Real Rate of Interest—an interest rate determined in the absence of inflation. • The nominal rate of interest is the rate that we actually observe in the market place at a given time and is unadjusted for inflation. • The determinants of the real rate are a firm’s return on investment as well as the time preference for consumption. In equilibrium, the desired level of borrowing by borrower-spenders equals the desired level of lending by lendersavers. • Fluctuations in the Real Rate o Any economic factor that causes a shift in the desired lending or desired borrowing will cause a change in the equilibrium rate of interest. o The real rate of interest reflects a complex set of forces that control the desired level of lending and borrowing in the economy. B. Loan Contracts and Inflation—the real rate of interest ignores inflation. C. The Fisher Equation and Inflation • How do we write a loan contract that provides protection against loss of purchasing power due to inflation?

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To incorporate “inflation expectations” into a loan contract we need to adjust the real rate of interest by amount of inflation expected during the contract period. • The mathematical formula for this is called the Fisher Equation. • ( 1 + Nominal Rate) = (1 + Real Rate of interest) x (1 + Expected Price Level Change) • Simplified Fisher Equation: Nominal Rate = Real Rate of Interest + Expected Price Level Change. Cyclical and Long-Term Trends in Interest Rates • Inflationary expectations have a major impact on interest rates. • Interest rates tend to follow the business cycle—during periods of economic expansion, interest rates tend to rise; during a recession, the opposite tends to occur.

Suggested and Alternative Approaches to the Material This chapter provides useful background for the material presented later in the course. At some universities, this material has already been covered in a previous course, and therefore the chapter will serve as an optional review to ensure that the students are comfortable with the nomenclature and general workings of the financial markets. In that event, this chapter can be covered in a single lecture or a portion of a single lecture. If the students have not had a previous course in Money and Banking, then the text offers a proper introduction of the material. This might provide non-Finance majors with the only source of this important material, such as the relationship between real and nominal interest rates. In addition, the chapter introduces many definitions and concepts that will be used later in the text.

Summary of Learning Objectives 1.

Describe the primary role of the financial system in the economy and the two basic ways in which money flows through the system. The role of the financial system is to gather money from people and businesses with surplus funds to invest (lender-savers) and channel that money to businesses and consumers who need to borrow money (borrower-spenders). If the financial system works properly, only investment projects with high rates of return and good credit are financed and all other projects are rejected. Money flows through the financial system in two basic ways: (1) directly, through financial markets, or (2) indirectly, through financial institutions.

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Discuss direct financing and the important role that investment banks play in this process. Direct markets are wholesale markets where large public corporations transact. For example, corporations sell securities, such as stocks and bonds, directly to investors in exchange for money, which they use to invest in their businesses. Investment banks are important in the direct markets because they help firms sell their new security issues. The services provided by investment bankers include origination, underwriting, and distribution.

Describe the primary, secondary, and money markets, explaining the special importance of secondary and money markets to business organizations. Primary markets are markets in which new securities are sold for the first time. Secondary markets provide the aftermarket for securities that were previously issued. Not all securities have secondary markets. Secondary markets are important because they enable investors to convert securities easily to cash. Business firms whose securities are traded in secondary markets are able to issue securities at a lower cost than they otherwise could because investors are willing to pay a premium price for securities that have secondary markets. Large corporations use money markets to adjust their liquidity because cash inflows and outflows are rarely perfectly synchronized. Thus, on the one hand, if cash expenditures exceed cash receipts, a firm can borrow short-term in the money markets. If that firm holds a portfolio of money market instruments, it can sell some of these securities for cash. On the other hand, if cash receipts exceed expenditures, the firm can temporarily invest the funds in short-term money market instruments. Businesses are willing to invest large amounts of idle cash in money market instruments because of their high liquidity and their low default risk.

Explain what an efficient market is and why market efficiency is important to financial managers. An efficient market is a market where security prices reflect the knowledge and expectations of all investors. Public markets, for example, are more efficient than private markets because issuers of public securities are required to disclose a great deal of information about these securities to investors and investors are constantly evaluating the prospects for these securities and acting on the conclusions from their analyses by trading them. Market efficiency is important to investors because it assures them that the securities they buy are priced close to their true value.

Explain how financial institutions serve the needs of consumers, small businesses, and corporations.

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Parrino, Kidwell, Bates / Fundamentals of Corporate Finance, 3rd Edition

One problem with direct financing is that it takes place in a wholesale market. Most small businesses and consumers do not have the expert skills, financing requirements, or the money to transact in this market. In contrast, a large portion of the indirect market focuses on providing financial services to consumers and small businesses. For example, commercial banks collect money from consumers in small dollar amounts by selling them checking accounts, saving accounts, and consumer CDs. They then aggregate the funds and make loans in larger amounts to consumers and businesses. The financial services bought or sold by financial institutions are tailor-made to fit the needs of the markets they serve. Exhibit 2.3 illustrates how corporations use the financial system. 6.

Compute the nominal and the real rates of interest, differentiating between them. Equations 2.1 and 2.2 are used to compute the nominal (real) rate of interest when you have the real (nominal) rate and the inflation rate. The real rate of interest is the interest rate that would exist in the absence of inflation. It is determined by the interaction of (1) the rate of return that businesses can expect to earn on capital goods and (2) individuals’ time preference for consumption. The interest rate we observe in the marketplace is called the nominal rate of interest. The nominal rate of interest is composed of two parts: (1) the real rate of interest and (2) the expected rate of inflation.

Summary of Key Equations Equation

Description

Formula

2.1

Fisher equation

i = r + ∆Pe+ r∆Pe

2.2

Fisher equation simplified

i = r + ∆Pe

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Chapter 3 Financial Statements, Cash Flows, and Taxes Learning Objectives 1. Discuss generally accepted accounting principles (GAAP) and their importance to the economy. 2. Explain the balance sheet identity and why a balance sheet must balance. 3. Describe how market-value balance sheets differ from book-value balance sheets. 4. Identify the basic equation for the income statement and the information it provides. 5. Understand the calculation of cash flows from operating, investing, and financing activities required in the statement of cash flows. 6. Explain how the four major financial statements discussed in this chapter are related. 7. Identify the cash flow to a firm’s investors using its financial statements. 8. Discuss the difference between average and marginal tax rates.

Chapter Outline 3.1

Financial Statements and Accounting Principles A. The Annual Report • The annual report is the most important report that firm’s issue to their shareholders and the general public. • The annual report has three sections—the financial tables and accompanying summary explaining the firm’s performance over the past year; a corporate public relations piece discussing the firm’s product lines; and audited financial statements. B. Generally Accepted Accounting Principles (GAAP) • The GAAP is accounting rules and standards that companies need to adhere to when they prepare financial statements and reports. • GAAP is prepared by the Financial Accounting Standards Board (FASB) and is authorized by the SEC. C. Fundamental Accounting Principles • The Assumption of Arm’s-Length Transaction—Two parties involved in an economic transaction arrive at a decision independently and rationally. • The Cost Principle—The value of an asset that is recorded on a company’s books reflects its historical cost.

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3.2

The Realization Principle—Revenue is recognized when transaction is completed, while cash may not be collected until a later time. • The Matching Principle—Expenses related to generating any revenue are matched. • The Going Concern Assumption—It is assumed that a company will continue to operate for the foreseeable future. International GAAP • The SEC is reviewing proposals for U.S. corporations to adopt IASB for financial reporting by as early as 2015.

The Balance Sheet A. The balance sheet identifies all the assets and liabilities and stockholder’s equity of a firm at a point in time. • The left-hand side of the balance sheet shows all the assets that the firm owns and uses to generate revenues. • The right-hand side represents the liabilities and stockholder’s equity of the firm. • While assets are listed in their order of their liquidity, the liabilities are listed in the order in which they must be paid. • Stockholders of the firm’s common equity are listed last. B. Current Assets and Liabilities • All assets that are likely to be converted to cash within a year are considered to be current assets. These include cash and marketable securities, accounts receivables, and inventory. • All liabilities that have to be paid within a year are listed as part of the current liabilities. • Net Working Capital is a measure of the liquidity of a firm, which is the ability of the firm to meet its obligations as they come due. • As expressed in Equation 3.2, net working capital is the difference between total current assets and total current liabilities. • Accounting for Inventory • Inventory, the least liquid of current assets, is reported in one of two different ways on the balance sheet. • First in, first out, or FIFO, refers to the practice of recognizing a sale as being made up of inventory that was purchased earlier and having the lowest cost (if prices have been rising). • Last in, last out, or LIFO, calls for the firm to attribute any sale made to the most recently acquired and most expensive inventory (if prices have been rising). • FIFO reporting leads to higher current asset value and higher net income.

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3.3

Firms may switch from one to another only under extraordinary circumstances and not frequently. Long-Term Assets and Liabilities • Long-term assets are the real assets that the firm acquires to generate most of its income. These include land, buildings, plant, and equipment. o Intangible assets, such as goodwill, patents, and copyrights, are also listed here. o Long-term real assets are usually depreciated, while intangible assets are amortized. Depreciating assets allows a firm to lower taxable income and reduce taxes. o Firms are allowed to depreciate assets using the straight-line method or an accelerated depreciation method that is allowed by the IRS. • Long-term liabilities consist of the long-term debt of the company. o They include bank loans, mortgages, bonds, and other types of liabilities, such as pension obligations, that have a maturity of one year or longer. Equity • There are two sources of equity funds—common equity and preferred equity. • Common equity represents the true ownership of the firm. • Multiple accounts identify the various sources of equity funds—par value, additional paid-in capital, retained earnings, and treasury stock. • Par value and paid-in capital represent the outside equity capital raised by the firm by issuing shares. • Retained earnings result from the funds that the firm has reinvested in the firm from its earnings. These funds are not cash since they already have been put to work. • The treasury stock account reflects the value of the shares that the firm repurchased from investors. • The other source of equity capital is preferred stock. It has features that make it a combination of a fixed income security and an equity security. o In the event of bankruptcy, it has a higher claim that common stock but a lower claim than debt.

Market Value versus Book Value Traditionally, all assets are reported at their historical cost. A. A More Informative Balance Sheet • The balance sheet does not reflect the current market value of the assets, only their acquired cost. • Adopting a marking to market approach—that is, reporting assets at their current market value—provides better information to management and investors.

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3.4

Instructor’s Manual

A Market-Value Balance Sheet • The difficulty of a market value balance sheet lies in estimating market values of assets. • When both the liabilities and assets of a firm are reported at their current market value, their difference represents the true market value of shareholders’ equity.

The Income Statement and the Statement of Retained Earnings A. The Income Statement • The profitability of a firm for any reporting period is measured in this financial statement. The basic identity is shown in Equation 3.3. • Revenues represent the value of the products and services sold by the firm, and they include both cash and credit sales. • Expenses range from the cost of producing goods for sale and asset utilization costs such as depreciation or amortization. • Net income is the difference between the firm’s revenues and expenses. B. A Closer Look at Some Expense Categories • Depreciation expense reduces a firm’s taxable income as well as the firm’s taxes, while increasing the cash flow available to shareholders. • Firms can use one of two methods of depreciating an asset: the straight-line method and the accelerated depreciation method. Firms are allowed to use one approach for internal purposes and another for tax purposes. • Firms prefer the accelerated depreciation method for tax purposes because it allows the firm to write off larger amounts of the cost of an asset over a shorter period. • Amortization expenses are related to the writing off of the value of intangible assets like goodwill, patents, and licenses. It is also a noncash expense like depreciation. • Extraordinary items refer to income or expenses associated with nonoperating events that are not expected to happen on a regular basis. C. Step by Step to the Bottom Line • The first bottom-line income figure that would be of interest to shareholders and creditors is earnings before interest, taxes, depreciation, and amortization (EBITDA), which is the earnings generated from operations prior to the recognition of expenses not directly connected to the production of the products. • After netting out the expenses related to depreciation and amortization, we arrive at earnings before interest and taxes (EBIT). • The next important income line is earnings before taxes (EBT) and represents the taxable income for the period.

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Finally, subtracting taxes from EBT yields net income, or net income after taxes. This amount tells us the amount available to management to pay dividends, pay off debt, or reinvest in the firm. The Statement of Retained Earnings • This financial statement shows the changes in this account from one period to the next. • This account will show changes whenever a firm reports a loss or profit and when a cash dividend is declared.

3.5

The Statement of Cash Flows A. Sources and Used of Cash • The statement of cash flows shows the company’s cash inflows and cash outflows for a period of time. o Derived by looking at the firm’s net income during the period and at changes in balance sheet accounts from the beginning of the period to the end of the period. o Increases (decreases) in assets or decreases (increases) in liabilities and equity are uses (sources) of cash. B. Organization of the Statement of Cash Flows • The statement is broken down into three parts to identify the cash flows resulting from operating activities, investing activities, and financing activities. • Operating activities: Cash inflows that are related to a firm’s principal business activities. • Long-Term Investing activities: Cash inflows and outflows arise out of the acquisition and sale of long-term assets. • Financing Activities: When a firm issues debt or equity securities and borrows money from banks or other lenders, it produces cash inflows. If the firm pays interest or dividends on the investor’s funds, or pays off debt or purchases treasury stock, the firm has cash outflows. • Cash Reconciliation: This last part reconciles the cash account from the beginning of the period to the end of the period. • The sum of the cash flows from these activities measures the net cash flows of the firm during a given period and is the bottom line of this financial statement.

3.6

Tying the Financial Statements Together The role of the balance sheet includes the following: • The balance sheet brings all the financial statements together, summarizing the financing and investment activities of the firm at a point in time.

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It recognizes the changes in the company’s financial position since the last reporting period that resulted from new activities or discontinued activities. Those changes are more descriptively measured in the income statement, the statement of cash flows, and the statement of retained earnings.

3.7

Cash Flows to Investors A. Net Income versus the Cash Flow to Investors • The cash flow that a firm generates for its investors in a given period, excluding the cash inflows from the sale of securities to investors. o Cash flow to investors from operating activity equal to (CFOA): EBIT – Current taxes + Noncash Expense (Equation 3.4). o Cash Flow Invested in Working Capital is (CFNWC): NWC current period – NWC previous period (Equation 3.5). o Cash Flow Invested in Long-Term Assets is (CFLTA): Long-term assets current period – Long-term assets previous period (Equation 3.6). o Cash Flow to Investors is (CFI): CFOA – CFNWC – CFLTA (Equation 3.7).

3.8

Federal Income Tax A. Corporate Income Tax Rates • The federal income tax schedule for the year 2013 is shown in Exhibit 3.6. • It is a progressive tax schedule with rates ranging from 15 to 39 percent. This means the higher a firm’s taxable income, the higher the tax liability. B. Average versus Marginal Tax Rates • The average tax rate is the total taxes paid divided by taxable income for the period. • The marginal tax rate is the tax rate that is paid on the last dollar earned or the next dollar earned. C. Unequal Treatment of Dividends and Interest Payments • The current tax code in the United States allows interest payments on debt issued by firms to be tax deductible. • Dividends paid on the firm’s preferred stock or common stock is not deductible for tax purposes and is paid from after-tax income. • The result is a lower cost of debt financing relative to the cost of equity financing.

Suggested and Alternative Approaches to the Material

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This chapter focuses on the four important financial statements that every firm uses to provide information about the financial condition of the company to both management and investors. In addition, there are discussions on the generally accepted accounting principles (GAAP) and International GAAP. The chapter also overviews market value accounting. Many instructors may choose to cover this chapter in detail. This allows the students to better understand the reporting of accounting information before moving on to the analysis of financial statements in Chapter 4. This material becomes even more critical when the majority of students taking the required first course in Finance are not Finance or Accounting majors. Other instructors may choose to skim through the topics in this chapter if they feel that their students are adequately prepared to tackle the topics in the next couple of chapters. Or they can choose to skip this chapter altogether if their students have a strong enough accounting background. This alternative will be especially helpful if this is a second Finance course, and it will allow the instructor to cover other material.

Summary of Learning Objectives 1.

Discuss generally accepted accounting principles (GAAP) and their importance to the economy. GAAP are a set of authoritative guidelines that define accounting practices at a particular point in time. The principles determine the rules for how a company maintains its accounting system and how it prepares financial statements. Accounting standards are important because without them, each firm could develop its own unique accounting practices, which would make it difficult for anyone to monitor the firm’s true performance or compare the performance of different firms. The result would be a loss of confidence in the accounting system and the financial reports it produces. Fundamental accounting principles include that transactions are arms-length, the cost principle, the realization principle, the matching principle, and the going concern assumption.

Explain the balance sheet identity and why a balance sheet must balance. A balance sheet provides a summary of a firm’s financial position at a particular point in time. It identifies the productive resources (assets) that a firm uses to generate income, as well as the sources of funding from creditors (liabilities) and owners (stockholders’ equity) that were used to buy the assets. The balance sheet identity is: Total assets = Total liabilities + Total stockholders’ equity. Stockholders’ equity represents ownership in the firm and is the residual claim of the owners after all other obligations to creditors, employees, and vendors have been paid. The balance sheet must always balance because the owners get what is left after all creditors have been paid—that is Total stockholders’ equity = Total assets – Total liabilities.

Describe how market-value balance sheets differ from book-value balance sheets.

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Book value is the amount a firm paid for its assets at the time of purchase. The current market value of an asset is the amount that a firm would receive for the asset if it were sold on the open market (not in a forced liquidation). Most managers and investors are more concerned about what a firm’s assets can earn in the future than about what the assets cost in the past. Thus, marked-to-market balance sheets are more helpful in showing a company’s true financial condition than balance sheets based on historical costs. The reason that marked-to-market balance sheets are not commonly used is that it is difficult to estimate market values for some assets and liabilities. 4.

Identify the basic equation for the income statement and the information it provides. An income statement presents a firm’s profit or loss for a period of time, usually a month, quarter, or year. The income statement identifies the major sources of revenues generated by the firm and the corresponding expenses needed to generate those revenues. The equation for the income statement is Net income = Revenues – Expenses. If revenues exceed expenses, the firm generates a net profit for the period. If expenses exceed revenues, the firm generates a net loss. Net profit or income is the most comprehensive accounting measure of a firm’s performance.

Understand the calculation of cash flows from operating, investing, and financing activities required in the statement of cash flows. Cash flows from operating activities in the statement of cash flows are the net cash flows that are related to a firm’s principal business activities. The most important items are the firm’s net income, depreciation and amortization expense, and working capital accounts (other than cash and short-term debt obligations, which are classified elsewhere). Cash flows from long-term investing activities relate to the buying and selling of long-term assets. Cash flows from financing occur when cash is obtained from or repaid to creditors or owners (stockholders). Typical financing activities involve cash received from the issuance of common or preferred stock, as well as cash from bank loans, notes payable, and long-term debt. Cash payments of dividends to stockholders and cash purchases of treasury stock reduce a company’s cash position.

Explain how the four major financial statements discussed in this chapter are related. The four financial statements discussed in the chapter are the balance sheet, the income statement, the statement of retained earnings, and the statement of cash flows. The key financial statement that ties the other three statements together is the statement of cash flows, which summarizes changes in the balance sheet from the beginning of the year to the end. These changes reflect the information in the income statement and the statement of retained earnings.

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Identify the cash flow to a firm’s investors using its financial statements. Cash flow to investors is the cash flow that a firm generates in a given period (cash receipts less cash payments and investments), excluding cash inflows from new equity sales or long-term debt issues. Cash flow to investors is the cash flow in a given period that is used to meet the firm’s obligations to its debt holders and that is distributed to its equity investors, which in turn defines the value of their investments in the firm over time. The cash flow to investors is calculated as the cash flow to investors from operating activity, minus the cash flow invested in net working capital, minus the cash flow invested in long-term assets.

Discuss the difference between average and marginal tax rates. The average tax rate is computed by dividing the total taxes by taxable income. It takes into account the taxes paid at all levels of income and will normally be lower than the marginal tax rate, which is the rate that is paid on the last dollar of income earned. However, for very high income earners, these two rates can be equal. When companies are making financial investment decisions, they use the marginal tax rate because new projects are expected to generate additional cash flows, which will be taxed at the firm’s marginal tax rate.

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Parrino, Kidwell, Bates / Fundamentals of Corporate Finance, 3rd Edition

Summary of Key Equations

Equation

Description

Formula

3.1

Balance sheet identity

Total assets = Total liabilities + Total stockholders’ equity

3.2

Net working capital

Net working capital = Total current assets – Total current liabilities

3.3

Income Statement identity

Net income = Revenues – Expenses

3.4

Cash flow from operating activity

CFOA = EBIT – Current Taxes + Noncash expenses

3.5

Cash flow invested in net working capital

CFNWC = NWC current period – NWC previous period

3.6

Cash flow invested in long-term assets

CFLTA = Long-term assets current period – Long-term assets previous period

3.7

Cash flow to investors

CFI = CFOA – CFNWC – CFLTA

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Chapter 4 Analyzing Financial Statements Learning Objectives 1. Explain the three perspectives from which financial statements can be viewed. 2. Describe common-size financial statements, explain why they are used, and be able to prepare and use them to analyze the historical performance of a firm. 3. Discuss how financial ratios facilitate financial analysis, and be able to compute and use them to analyze a firm’s performance. 4. Describe the DuPont system of analysis and be able to use it to evaluate a firm’s performance and identify corrective actions that may be necessary. 5. Explain what benchmarks are, describe how they are prepared, and discuss why they are important in financial statement analysis. 6. Identify the major limitations in using financial statement analysis.

Chapter Outline 4.1

Background for Financial Statement Analysis A. Stockholders’ Perspective • Shareholders’ focus centers on the value of the stock they hold. • Their interest in the financial statement is to gauge the cash flows that the firm will generate from operations. • This allows them to determine the firm’s profitability, their return for that period, and the dividend they are likely to receive. B. Managers’ Perspective • Management’s interest in the firm’s financial statement is similar to that of stockholders. • Managers are responsible for running the business on a daily basis and must make decisions that will maximize stockholder wealth in the long run. • In addition, management gets feedback on their investing, financing, and working capital decisions by identifying trends in the various accounts that are reported in the financial statements. C. Creditors’ Perspective • Creditors or lenders are primarily concerned about getting their loans repaid and receiving interest payments on time.

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4.2

Common-Size Financial Statements A common-sized balance is created by dividing each asset or liability by a base number like total assets or sales. Such common-size or standardized financial statements allow one to compare firms that are different in size. A.

4.3

Their focus is on the ability to generate sufficient cash flows to meet all legal obligations first and still have sufficient cash flows to meet debt repayment and interest payments. Guidelines for Financial Statement Analysis • Identify whose perspective you are using to analyze a firm—management, shareholder, or creditor. • Use only audited financial statements if possible. • Perform analysis over a three- to five-year period—trend analysis. • Compare the firm’s performance to its direct competitors—that is, firms that are similar in size and offer similar products. • Perform a benchmark analysis. This involves comparing it to one or more of the most relevant competitors—Boeing with Piper Aircraft.

Common-Size Balance Sheets • Each asset and liability item on the balance sheet is standardized by dividing it by total assets. • This results in these accounts being represented as percentages of total assets. Common-Size Income Statements • Each income statement item is standardized by dividing it by the dollar amount of sales. • Each income statement item is now indicated as a percentage of sales.

Financial Ratios and Firm Performance A. Why Ratios Are Better Measures • A ratio is computed by dividing one balance sheet or income statement item by another. • A variety of ratios can be computed to focus on specialized aspects of the firm’s performance. • Different ratios can be calculated based on the type of firm being analyzed or the kind of analysis being performed. B. Short-Term Liquidity Ratios • Liquidity ratios measure the ability of the firm to meet short-term obligations with short-term assets without putting the firm in financial trouble. • There are two commonly used ratios to measure liquidity—current ratio and quick ratio.

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Current ratio is calculated by dividing the current assets by current liabilities. ▪ It tells how many dollars of current assets the firm has per dollar of current liabilities. ▪ The higher the number, the more liquid the firm and the better its ability to pay its short-term bills. • Quick ratio or acid-test ratio is calculated by dividing the most liquid of current assets by current liabilities. Inventory that is not very liquid is subtracted from total current assets to determine the most liquid assets. ▪ It tells us how many dollars of liquid assets the firm has per dollar of current liabilities. ▪ The higher the number, the more liquid the firm and the better its ability to pay its short-term bills. Efficiency Ratios • This set of ratios, sometimes called asset turnover ratios, measures the efficiency with which a firm’s management uses the assets to generate sales. • While management can use these ratios to identify areas of inefficiency that require improvement, creditors can use some of these ratios to determine the speed with which inventory can be converted to receivables, which can then be converted to cash and help the firm to meet its debt obligations. • These efficiency ratios focus on inventory, receivables, and the use of fixed and total assets. • Inventory turnover ratio is calculated by dividing the cost of goods sold by inventory. ▪ Year-end inventory can be used or, if a firm experiences significant changes in the inventory level during the year, the average inventory level can be used. ▪ It measures how many times the inventory is turned over into saleable products. ▪ The more times a firm can turn over the inventory, the better. ▪ Too high a turnover or too low a turnover could be a warning sign. • Another ratio that builds on the inventory turnover ratio is the days’ sales in inventory. ▪ It is defined as (365 days / Inventory turnover). ▪ It measures the number of days the firm takes to turn over the inventory. ▪ The smaller the number, the faster the firm is turning over its inventory and the more efficient it is. • Accounts receivables turnover ratio measures how quickly the firm collects on its credit sales. ▪ It is defined as (Net sales / Accounts receivable).

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▪

The higher the frequency of turnover, the quicker it is converting its credit sales into cash flows. • Another measure of the firm’s efficiency in this regard is Days Sales Outstanding. ▪ It is defined as (365 days / Account receivable turnover). ▪ It measures in days the time the firm takes to convert its receivables into cash. ▪ The fewer days it takes the firm to collect on its receivables, the more efficient the firm is. ▪ Recognize, however, that an overzealous credit department may turn off the firm’s customers. • Total asset turnover ratio measures the level of sales a firm is able to generate per dollar of total assets. ▪ It is defined as (Net sales / Total assets). ▪ The higher the total asset turnover, the more efficiently management is using total assets. • Fixed asset turnover ratio measures the level of sales a firm is able to generate per dollar of fixed assets. ▪ It is defined as (Net sales / Net fixed assets). ▪ The higher the fixed asset turnover, the more efficiently management is using its plant and equipment. ▪ This ratio is more significant for equipment-intensive manufacturing industry firms, while the total assets turnover ratio is more relevant for service industry firms. Leverage Ratios • The ability of a firm and its owners to use their equity to generate borrowed funds is reflected in the leverage ratios. • Financial leverage refers to the use of long-term debt in a firm’s capital structure. • The use of debt increases shareholders’ returns thanks to the tax benefits provided by the interest payments on debt. • Two sets of ratios can be used to analyze leverage—debt ratios that quantify the use of debt in the capital structure and coverage ratios that measure the ability of the firm to meet its debt obligations. • The first ratio, total debt ratio, is calculated by dividing total debt by total assets. ▪ Total debt includes short-term and long-term debt. ▪ The higher the amount of debt, the higher the firm’s leverage, and the more risky it is. • The second leverage ratio is debt-to-equity ratio (Total debt / Total equity).

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▪ It measures the amount of debt per dollar of equity. • The third leverage ratio is called the equity multiplier or leverage multiplier (Total assets / Total equity). ▪ It tells us the amount of assets that the firm has for every dollar of equity. • Of the coverage ratios, the first one is times interest earned. ▪ It is defined as (EBIT / Interest expense). ▪ It measures the number of dollars in operating earnings the firm generates per dollar of interest expense. ▪ The higher the number, the greater the ability of the firm to meet its interest obligations. • The second ratio is the cash coverage ratio. ▪ It is defined as (EBITDA / Interest expense). ▪ It measures the amount of cash a firm has to meet its interest payments. Profitability Ratios • These ratios measure the financial performance of the firm. • Gross profit margin ( {Net sales – Cost of goods sold} / Net sales) measures the amount of gross profit generated per dollar of net sales, while operating profit margin (EBIT / Net sales) measures the amount of operating profit generated by the firm for each dollar of net sales. Net profit margin (Net income / Net sales) measures the amount of net income after taxes generated by the firm for each dollar of net sales. • In each case, the higher the ratio, the more profitable the firm. • While management and creditors are likely to focus on these profitability measures, shareholders are likely to concentrate on two others. • The return on assets (ROA) (Net income / Total assets) ratio measures the amount of net income per dollar of total assets. • A variation of this ratio, called the EBIT return on assets (EBIT / Total assets), is a powerful measure of return because it tells us how efficiently management utilized the assets under their command, independent of financing decisions and taxes. This measures the amount of EBIT per dollar of total assets. • The return on equity (ROE) (Net income / Total assets) ratio measures the dollar amount of net income per dollar of shareholder s’ equity. • For a firm with no debt ROA = ROE; for firms with leverage ROE > ROA (assuming that ROA is positive). Market-Value Indicators • The ratios that follow tell us how the market views the company’s liquidity, efficiency, leverage, and profitability.

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The earnings per share (EPS) (Net income / Shares outstanding) ratio measures the income after taxes generated by the firm for each share outstanding. The price-earnings (P/E) (Price per share / Earnings per share) ratio ties the firm’s earnings per share to price per share. ▪ The P/E ratio reflects investors’ expectations that the firm’s earnings will grow in the future. The market-to-book ratio (Market value of equity per share / Book value of equity per share) compares the market value of a firm’s investments to its book value per share.

The DuPont System: A Diagnostic Tool A. An Overview of the DuPont System • The DuPont system is a set of related ratios that links the balance sheet and the income statement. • It is used as a diagnostic tool to evaluate a firm’s financial health. • Both management and shareholders can use this tool to understand the factors that drive a firm’s ROE. • It is based on two equations that relate a firm’s ROA and ROE. B. The ROA Equation • Return on assets, which is Net income / Total assets, can be broken down into two components—net profit margin and total assets turnover ratio. See Equation 4.23. • The net profit margin measures management’s ability to generate sales and efficiently manage the firm’s operating expenses; overall, this is a measure of operating efficiency. • Total asset turnover looks at how efficiently management uses the assets under its command—that is, how much output can be generated with a given asset base. Thus, asset turnover is a measure of asset use efficiency. • The ROA equation says that if management wants to increase the firm’s ROA, it can increase the net profit margin, asset turnover, or both. • By the same token, management can examine a poor ROA and determine whether operating efficiency is the problem or asset use efficiency problem. C. The ROE Equation • This equation is simply a restatement of Equation 41.9. Reorganization of the terms allows ROE to be restated as a product of the ROA and the equity multiplier. • ROE is determined by the firm’s ROA and its use of leverage. • A firm with a small ROA can magnify it by using a higher leverage to get a higher ROE.

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The DuPont Equation • Substituting the ROA into the ROE equations gives us the DuPont (equation 4.26) equation as shown in Equations 4.23 and 4.24. • The DuPont equation shows that a firm’s ROE is determined by three factors: (1) net profit margin, which measures the firm’s operating efficiency; (2) total asset turnover, which measures the firm’s asset use efficiency; and (3) the equity multiplier, which measures the firm’s financial leverage. • Analyzing a firm’s financial performance will allow one to identify where the inefficiencies are and where the strengths are. • If operational efficiency is the area of weakness, then it calls for a closer look at the firm’s income statement items. • If asset turnover or leverage is the problem area, then the focus shifts to the balance sheet. Applying the DuPont System Is Maximizing ROE an a appropriate Goal? • The issue of whether maximizing ROE is equivalent to maximizing shareholders’ wealth is something to be discussed. • Those who do not agree that they are the same identify three key weaknesses. ▪ The first weakness with ROE is that it is based on after-tax earnings, not cash flows. ▪ Next, ROE does not consider risk. ▪ Third, ROE ignores the size of the initial investment as well as future cash flows.

Selecting a Benchmark • A ratio analysis becomes relevant only if it can be compared against a benchmark. • Financial managers can create a benchmark for comparison in three ways: through trend analysis, industry analysis, and peer group analysis. A.

Trend Analysis • This benchmark is based on a firm’s historical performance. • It allows management to examine each ratio over time and determine whether the trend is good or bad for the firm. Industry Analysis • Industry analysis is another way of developing a benchmark. • Firms in the same industry are grouped by size, sales, and product lines to establish benchmark ratios. • One way of identifying industry groups is the Standard Industrial Classification (SIC) System.

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• C.

4.6.

Another method is by using the North American Industry Classification System (NAICS). Peer Group Analysis • Instead of selecting an entire industry, management may choose to identify a set of firms that are similar in size or sales, or who compete in the same market. • The average ratios of this peer group would then be used as the benchmark.

Using Financial Ratios A. Performance Analysis of Diaz Manufacturing B. Limitations of ratio analysis include the following: • It depends on accounting data based on historical costs. • There is no theoretical backing in making judgments based on financial statement and ratio analysis.

Suggested and Alternative Approaches to the Material Financial statement analysis is the focus in this chapter. The chapter begins with an overview of how different stakeholders—management, shareholders, and creditors—will view the financial statements of a firm and what their focus will be. This is followed by a discussion of the idea of the common-size balance sheet and income statement. Then, a comprehensive coverage of various financial ratios is provided. The DuPont system of equations is developed in detail, thus allowing students to understand how this tool can be used to diagnose the strengths and weaknesses of the firm being analyzed. The chapter concludes with a review of the shortcomings of ratio analysis. As with the previous chapter on financial statements, instructors might choose either to cover the chapter in depth or to call for the students to complete a self-study review of the material. This, of course, depends on the students’ background and knowledge acquired from prerequisite courses such as introductory accounting courses. Both Finance majors and non-Finance majors will benefit by a review of the ratios regardless of their background. Instructors at the various schools will be able to determine the extent of their coverage based on the time available in a semester or quarter and the backgrounds of their students.

Summary of Learning Objectives 1.

Explain the three perspectives from which financial statements can be viewed. Financial statements can be viewed from the owners’, managers’, or creditors’ perspective. All three groups are ultimately interested in a firm’s profitability, but each

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group takes a different view. Stockholders want to know how much cash they can expect to receive for their stock, what their return on investment will be, and how much their stock is worth in the market. Managers are concerned with maximizing the firm’s longterm value through a series of day-to-day management decisions; thus, they need to see the impact of their decisions on the financial statements to confirm that things are going as planned. Creditors monitor the firm’s use of debt and are concerned with how much debt the firm is using and whether the firm will have enough cash to meet its obligations. 2.

Describe common-size financial statements, explain why they are used, and be able to prepare and use them to analyze the historical performance of a firm. Common-size financial statements are financial statements in which each number has been scaled by a common measure of firm size: balance sheets are expressed as a percentage of total assets, and income statements are expressed as a percentage of net sales. Common-size financial statements are necessary when comparing firms that are significantly different in size. The preparation of common-size financial statements and their use are illustrated for Diaz Manufacturing in Section 4.2.

Discuss how financial ratios facilitate financial analysis, and be able to compute and use them to analyze a firm’s performance. Financial ratios are used in financial analysis because they eliminate problems caused by comparing two or more companies of different size, or when looking at the same company over time as the size changes. Financial ratios can be divided into five categories: (1) Liquidity ratios measure the ability of a company to cover its current bills. (2) Efficiency ratios tell how efficiently the firm uses its assets. (3) Leverage ratios tell how much debt a firm has in its capital structure and whether the firm can meet its longterm financial obligations. (4) Profitability ratios focus on the firm’s earnings. Finally, (5) market value indicators look at a company based on market data as opposed to historical data used in financial statements. The computation and analysis of major financial ratios are presented in Section 4.3 (also see the Summary of Key Equations that follows the Summary of Learning Objectives).

Describe the DuPont system of analysis and be able to use it to evaluate a firm’s performance and identify corrective actions that may be necessary. The DuPont system of analysis is a diagnostic tool that uses financial ratios to assess a firm’s financial condition. Once the financial ratios are calculated and the assessment is complete, management can focus on correcting the problems within the context of maximizing the firm’s ROE. For analysis, the DuPont system breaks ROE into three components: net profit margin, which measures operating efficiency; total asset turnover, which measures how efficiently the firm deploys its assets; and the equity multiplier,

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which measures financial leverage. A diagnostic analysis of a firm’s performance using the DuPont system is illustrated in Section 4.4. 5.

Explain what benchmarks are, describe how they are prepared, and discuss why they are important in financial statement analysis. Benchmarks are used to provide a standard for evaluating the financial performance of a firm. In financial statement analysis, a number of benchmarks are used. Most often, benchmark comparisons involve competitors that are roughly the same size and that offer a similar range of products. Another form of benchmarking is time-trend analysis, which compares a firm’s current financial ratios against the same ratios from past years. Timetrend analysis tells us whether a ratio has increased, decreased, or remained the same over time. The preparation and use of peer group benchmark data are illustrated in Section 4.6.

Identify the major limitations in using financial statement analysis. The major limitations to financial statement and ratio analysis are the use of historical accounting data and the lack of theory to guide the decision maker. The lack of theory explains, in part, why there are so many rules of thumb. Rules of thumb are useful, and they may work under certain conditions. However, they may lead to poor decisions if circumstances change.

Summary of Key Equations

Equation

4.1

Description

Formula

Current Ratio

Current Assets Current Liabilities

Quick Ratio

Current Assets − Inventory Current Liabilities

4.2

4.3 Inventory Turnover

Cost of goods sold Inventory

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Day’s sales in inventory

365 days Inventoryturnover

4.5

Accounts receivable turnover

Net sales Accounts receivable

4.6

Day’s sales outstanding

4.7

Total asset turnover

Net sales Total assets

4.8

Fixed asset turnover

Net sales Net fixed assets

4.9

Total debt ratio

Total debt Total assets

4.10

Debt-to-equity ratio

Total debt Total equity

4.11

Equity multiplier

Total assets Total equity

4.12

Times interest earned

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365 days Accounts receivable turnover

EBIT Interest exp ense

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EBITDA Interest exp ense

4.13

Cash coverage

4.14

Gross profit margin

4.15

Operating profit margin

EBIT Net sales

4.16

Net profit margin

Net income Net sales

4.17

EBIT return on assets (EROA)

EBIT Total assets

4.18

Return on assets (ROA)

Net income Total assets

4.19

Return on equity (ROE)

Net income Total equity

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Net sales − Cost of goods sold Net sales

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4.20

Earnings per share

Net income Shares outstanding

4.21

Price-earnings ratio

Pr ice per share Earnings per share

4.22

Market-to-book ratio

Market value of equity per share Book value of equity per share

4.23

ROA

Net profit m arg in  Total asset turnover

4.24

ROE

ROA Equitymultiplier

4.25

ROE

Net profit m arg in  Total asset turnover  Equitymultiplier

4.26

ROE

Net income Net sales Total assets   Net sales Total assets Total equity

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Chapter 5 The Time Value of Money Learning Objectives 1. Explain what the time value of money is and why it is so important in the field of finance. 2. Explain the concept of future value, including the meaning of the terms principal, simple interest, and compound interest, and use the future value formula to make business decisions. 3. Explain the concept of present value and how it relates to future value, and use the present value formula to make business decisions. 4. Discuss why the concept of compounding is not restricted to money, and use the future value formula to calculate growth rates.

Chapter Outline

5.1

The Time Value of Money •

A basic problem faced by managers in financial decision making is to determine the value of future cash flows, whether paying for an asset or evaluating a project.

•

The question that is being raised is: What is the value of the stream of future cash flows today?

•

We refer to this value as the time value of money.

Consuming Today or Tomorrow •

People prefer to consume goods today rather than wait to consume similar goods in the future—that is, a positive time preference.

•

The time value of money is based on the belief that people have a positive time preference for consumption.

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Money has a time value because a dollar in hand today is worth more than a dollar to be received in the future. The dollar in hand could be either invested to earn interest or spent today. ▪

The value of a dollar invested at a positive interest rate grows over time, and the further in the future you receive a dollar, the less it is worth today.

▪

The trade-off between spending the money today versus spending the money at some future date depends on the rate of interest you can earn by investing. The higher the interest rate, the more the likelihood of consumption being deferred.

Time Lines as Aids to Problem Solving •

Timelines are an easy way to visualize the cash flows associated with investment decisions.

•

A timeline is a horizontal line that starts at time zero (today) and shows cash flows as they occur over time. See Exhibit 5.1.

•

It is conventional to show that all cash outflows are given a negative value; then all cash inflows must have a positive value.

Financial Calculator •

A financial calculator is just an ordinary calculator that has preprogrammed future value and present value algorithms.

5.2

Future Value and Compounding A.

Single-Period Investment •

We can determine the value of an investment at the end of one period (whether it is a month, quarter or year) if we know the interest rate to be earned by the investment.

•

If you invest for one period at an interest rate of i, your investment, or principal, will grow by (1 + i) per dollar invested.

•

The term (1+ i) is the future value interest factor—often called simply the future value factor.

Two-Period Investment

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A two-period investment is simply two single-period investments back-toback.

•

When more than one period is considered, we need to recognize that after the first period, interest accrues on both the original investment (principal) and the interest earned in the preceding periods.

•

The principal is the amount of money on which interest is paid.

•

Simple interest is the amount of interest paid on the original principal amount only.

•

With compounding, you are able to earn compound interest, which consists of both simple interest and interest-on-interest.

The Future Value Equation •

Equation 5.1 gives us the general equation to find the future value after any number of periods.

The Future Value Factor •

The term (1 + i)n is the future value factor.

•

We can use future value tables to find the future value factor at different interest rates and maturity periods. Or we can use any calculator that has a power key (the yx key) to make this computation.

•

The total simple interest earned is equal to the number of periods, times the principal, times the interest rate (number of periods x (P0 x i)).

Future Value Factor Tables •

A future value factor table is provided in Appendix A.

The Power of Compounding

Compounding More Frequently Than Once a Year •

The more frequently the interest payments are compounded, the larger the future value of $1 for a given time period. See Equation 5.2.

Continuous Compounding •

5.3

When interest is compounded on a continuous basis, we can use Equation 5.3.

Present Value and Discounting •

Present value calculations involve bringing a future amount back to the present.

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This process is called discounting, and the interest rate i is known as the discount rate.

•

The present value (PV) is often called the discounted value of future cash payments.

•

The present value factor is more commonly called the discount factor.

•

Equation 5.4 gives us the general equation to find the present value after any number of periods.

•

The further in the future a dollar will be received, the less it is worth today.

•

The higher the discount rate, the lower the present value of a dollar.

•

Financial problems can either be evaluated in terms of future cash flows or cash flows evaluated in the present. However, in most instances we prefer to evaluate problems using the present value of cash flows.

5.4

Additional Concepts and Applications A.

Finding the Interest Rate •

In finance, a number of situations will require you to determine the interest rate (or discount rate) for a given stream of future cash flows.

•

For an individual investor or a firm, it may be necessary to determine: ▪

the return on an investment.

▪

the interest rate on a loan

▪

a growth rate.

When solving for the interest rate in a problem it may be useful to be familiar with the algebraic properties of the logarithm.

Finding How Many Periods It Takes an Investment to Grow a Certain Amount

The Rule of 72 •

People use rules of thumb to approximate difficult present value calculations.

•

One such rule is the Rule of 72, which can be used to determine the amount of time it takes to double an investment.

•

The Rule of 72 says that the time to double your money (TDM) approximately equals 72/i, where i is expressed as a percentage.

• D.

The rule is fairly accurate for interest rates between 5 and 20 percent.

Compound Growth Rates

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Compound growth occurs when the initial value of a number increases or decreases each period by the factor (1 + growth rate).

•

Such changes over time include the population growth rate of a city, or the sales or earnings growth rate of a firm.

II.

Suggested and Alternative Approaches to the Material

This chapter is really the first chapter that exposes students to real finance concepts. The chapter begins with a review of the time value of money concepts and introduces the use of timelines and calculators as problem-solving aids. This is followed by a discussion of the ideas of present value versus future value. The chapter continues with a discussion of compounding and determining the future value of an investment over a single period and over multiple periods. The next section discusses the idea of present value and discounting along similar lines. The discussion is completed by an overview of some basic principles of finding growth rates, interest rates, and the rule of 72. Instructors may start this chapter after reviewing the basic financial statements, ratio analysis, and other topics covered in the first five chapters. For a better prepared audience, instructors may choose to start this chapter right after the introductory chapter. In any case, it may make sense to get into the material covered in Chapters 5 and 6 prior to discussing risk and return (Chapter 7) or bonds and stocks (Chapters 8 and 9). Regardless of the route taken, students have to be impressed with the fact that the material covered in this chapter and the next form the foundation for the material following and may be viewed as the most fundamental concepts of finance along with risk and return.

III. Summary of Learning Objectives 1.

Explain what the time value of money is and why it is so important in the field of finance. The idea that money has a time value is one of the most fundamental concepts in the field of finance. The concept is based on the idea that most people prefer to consume goods today rather than wait to have similar goods in the future. Since money buys goods, they would rather have money today than in the future. Thus a dollar today is worth more than

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a dollar received in the future. Another way of viewing the time value of money is that your money is worth more today than at some point in the future because, if you had the money now, you could invest it and earn interest. Thus, the time value of money is the opportunity cost of forgoing consumption today. Applications of the time value of money focus on the trade-off between current dollars and dollars received at some future date. This is an important element in financial decisions because most investment decisions require the comparison of cash invested today with the value of expected future cash inflows. Time value of money calculations facilitate such comparisons by accounting for both the magnitude and timing of cash flows. Investment opportunities are undertaken only when the value of future cash inflows exceeds the cost of the investment (the initial cash outflow).

Discuss the concept of future value, including the meaning of the terms principal, simple interest, and compound interest, and use the future value formula to make business decisions. The future value is the sum to which an investment will grow after earning interest. The principal is the amount of the investment. Simple interest is the interest paid on the original investment; the amount of simple interest remains constant from period to period. Compound interest includes not only simple interest, but also interest earned on the reinvestment of previously earned interest, the so-called interest earned on interest. For future value calculations, the higher the interest rate, the faster the investment will grow. The application of the future value formula in business decisions is presented in Section 5.2.

Explain the concept of present value and how it relates to future value, and use the present value formula to make business decisions. The present value is the value today of a future cash flow. Computing the present value involves discounting future cash flows back to the present at an appropriate discount rate. The process of discounting cash flows adjusts the cash flows for the time value of money. Computationally, the present value factor is the reciprocal of the future value factor, or

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1/(1 + i). The calculation and application of the present value formula in business decisions is presented in Section 5.3.

Discuss why the concept of compounding is not restricted to money, and use the future value formula to calculate growth rates. Any number of changes that are observed over time in the physical and social sciences follow a compound growth rate pattern. The future value formula can be used in calculating these growth rates as illustrated in Section 5.4.

IV. Summary of Key Equations Equation

5.1

5.2

Description

Formula

Future value of an n-period investment with

FVn = PV  (1 + i)n

annual compounding Future value with more frequent than annual

FVn = PV  (1 + i/m)m  n

compounding

5.3

Future value with continuous compounding

FV∞ = PV  ei  n

5.4

Present value of an n-period investment

PV =

5.5

Rule of 72

TDM =

5.6

Future value with general growth rate



FVn (1+ i) n

72 i

FVn = PV  (1 + g)n



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Chapter 6 The Time Value of Money, Discounted Cash Flows, and Valuation

Learning Objectives 1

2 3 4

Explain why cash flows occurring at different times must be adjusted to reflect their value as of a common date before they can be compared, and compute the present value and future value for multiple cash flows. Explain what a perpetuity is and where we see them in business, and calculate the value of a perpetuity. Discuss growing annuities and perpetuities, as well as their application in business, and calculate their values. Discuss why the effective annual interest rate (EAR) is the appropriate way to annualize interest rates, and calculate the EAR.

Chapter Outline 6.1

Multiple Cash Flows A. Future Value of Multiple Cash Flows • Solving future value problems with multiple cash flows involves a simple process. ▪ First, draw a timeline to make sure that each cash flow is placed in the correct time period. ▪ Second, calculate the future value of each cash flow for its time period. ▪ Third, add up the future values. B. Present Value of Multiple Cash Flows • Many situations in business call for computing the present value of a series of expected future cash flows. • The process is similar, but the reversal to determining the future value of multiple cash flows. ▪ First, prepare a timeline to identify the magnitude and timing of the cash flows. ▪ Next, calculate the present value of each cash flow using Equation 5.4 from the previous chapter. ▪ Finally, add up all the present values.

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The sum of the present values of a stream of future cash flows is the current market price, or value.

Level Cash Flows: Annuities and Perpetuities • When someone faces a stream of constant payments on a bank loan for a period of time, we call that stream of cash flows an annuity. ▪ Individual investors may make constant payments on their home or car loans, or invest a fixed amount year after year to save for their retirement. ▪ Any financial contract that calls for equally spaced and level cash flows over a finite number of periods is called an annuity. • If the cash flow payments continue forever, the contract is called a perpetuity. • Constant cash flows that occur for a finite number of periods at the end of each period are called ordinary annuities. A. •

•

Present Value of an Annuity We can calculate the present value of an annuity the same way as we calculated the present value of multiple cash flows. However, if the number of payments were very large, then this process will be tedious. Instead we can use Equation 6.1, which can be used to calculate the present value of an annuity. PVAn = CF  Present value factor for an annuity

 (1 − Present value factor)  = CF    i  1   1 − (1 + i ) n   = CF   i     • • •

One problem that is widely solved using a financial calculator is finding the monthly payment on a car loan or home loan. Monthly payments, instead of yearly payments, can be found using Equation 6.1 and adjusting the interest rate, i, to match the number of monthly time periods, n. Preparing a Loan Amortization Schedule ▪ Amortization refers to the way the borrowed amount (principal) is paid down over the life of the loan. ▪ The monthly loan payment is structured so that each month a portion of the principal is paid off and at the time the loan matures, the loan is entirely paid off. ▪ With an amortized loan, each loan payment contains some payment of principal and an interest payment.

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▪

• • • • B. • •

A loan amortization schedule is a table that shows the loan balance at the beginning and end of each period, the payment made during that period, and how much of that payment represents interest and how much represents repayment of principal. ▪ With an amortized loan, a bigger proportion of each month’s payment goes toward interest in the early periods. As the loan gets paid down, a greater proportion of each payment is used to pay down the principal. Finding the Interest Rate The annuity equation can also be used to the find the interest rate or discount rate for an annuity. To determine the rate of return for the annuity, we need to solve the equation for the unknown value i. Other than using a trial-and-error approach, it is easier to solve using this with a financial calculator. Future Value of an Annuity Future value annuity calculations usually involve finding what a savings or an investment activity is worth at some point in the future. The future value annuity equation, Equation 6.2, as follows.

FVA n = CF  Future value factor for an annuity Future value factor - 1 i n  (1 + i ) − 1 = CF    i  

= CF 

C. • • •

Perpetuities A perpetuity is a constant stream of cash flows that goes on for an infinite period. In the stock markets, preferred stock issues are considered to be perpetuities, with the issuer paying a constant dividend to holders. The equation for the present value of a perpetuity can be derived from the present value of an annuity equation with n tending to infinity. PVA  = CF  Present value factor for anannuity

1   1 − (1 + i )   (1 − 0) = CF    = CF  i i     CF = i Annuities Due

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• • •

6.3

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When you have an annuity with the payment being incurred at the beginning of each period rather than at the end, the annuity is called an annuity due. Rent or lease payments are typically made at the beginning of each period rather than at the end of each period. The annuity transformation method (Equation 6.4) shows the relationship between the ordinary annuity and the annuity due. ▪ Each period’s cash flow thus earns an extra period of interest compared to an ordinary annuity. Thus, the present value or future value of an annuity due is always higher than that of ordinary annuity. ▪ Equation 6.4: Annuity due = Ordinary annuity value  (1 + i)

Cash Flows That Grow at a Constant Rate • In addition to constant cash flow streams, one may have to deal with cash flows that grow at a constant rate over time. • These cash flow streams are called growing annuities or growing perpetuities. A. Growing Annuity • Businesses may need to compute the value of multiyear product or service contracts with cash flows that increase each year at a constant rate. These are called growing annuities. • Equation 6.5 can be used when the growth rate is less than the discount rate. n CF1   1+g   PVA n = × 1-    (i - g )   1+i  

B. • •

Growing Perpetuity When the cash flow stream features a constant growing annuity forever, it is called a growing perpetuity. Equation 6.6. CF1 PVA  = (i - g )

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The Effective Annual Interest Rate A. Why the Confusion? • Interest rates can be quoted in the financial markets in a variety of ways. • The most common quote, especially for a loan, is the annual percentage rate (APR). ▪ The APR is a rate that represents the simple interest accrued on a loan or an investment in a single period. This is annualized over a year by multiplying it by the appropriate number of periods in a year. B. Calculating the Effective Annual Interest Rate (EAR) • The correct way to compute an annualized rate is to reflect the compounding that occurs. This involves calculating the effective annual rate (EAR). • The effective annual interest rate (EAR) is defined as the annual interest rate that takes compounding into account. • Equation 6.7 shows how the EAR is computed. EAR = (1 + Quoted rate/m)m – 1, where, m is the number of compounding periods during a year. • The EAR conversion formula accounts for the number of compounding periods and, thus, effectively adjusts the annualized interest rate for the time value of money. • The EAR is the true cost of borrowing and lending. C. Comparing Interest Rates • The easiest way to make interest rates comparable for making finance decisions is to convert them to effective annual interest rates. D. Consumer Protection Acts and Interest Rate Disclosure • Congress passed the Truth-in-Lending Act in 1968 to ensure that the true cost of credit was disclosed to consumers so that they could make sound financial decisions. • Similarly, another piece of legislation called the Truth-in-Savings Act was passed to provide consumers with an accurate estimate of the return they would earn on an investment. • These two pieces of legislation require by law that the APR be disclosed on all consumer loans and savings plans and that it is prominently displayed on advertising and contractual documents. • It is important to note that the EAR, not the APR, is the appropriate rate to use in present and future value calculations. E. The Appropriate Interest Rate Factor • It is important to note that the EAR, not the APR, is the appropriate rate to use in present and future value calculations.

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Suggested and Alternative Approaches to the Material This chapter is really the first chapter that exposes students to real finance concepts. The chapter begins with a review of the time value of money concepts and introduces the use of timelines and calculators as problem-solving aids. This is followed by a discussion of the ideas of present value versus future value. The chapter continues with a discussion of compounding and determining the future value of an investment over a single period and over multiple periods. The next section discusses the idea of present value and discounting along similar lines. The discussion is completed by an overview of some basic principles of finding growth rates, and interest rates. The chapter continues with a discussion of present value and future value computations when a stream of cash flows, not all being equal, is involved. This is followed by an analysis of situations when the recurring cash flows over time are constant—namely, annuities. Both present value and future value of an annuity are developed in detail. In addition, the cases of a perpetuity, growing annuity, and growing perpetuity are also covered. Finally, the discussion evolves to the merits of annual percentage rates and effective annual rates. Instructors may start this chapter after reviewing the basic financial statements, ratio analysis, and other topics covered in the first four chapters. For a better prepared audience, instructors may choose to start this chapter right after the introductory chapter. In any case, it may make sense to get into the material covered in Chapter 5 prior to discussing risk and return (Chapter 6) or bonds and stocks (Chapters 7 and 8). Regardless of the route taken, students have to be impressed with the fact that the material covered in this chapter form the foundation for the material following and may be viewed as the most fundamental concepts of finance along with risk and return. The instructor has the flexibility to cover all or some of the concepts. Some may choose to cover the chapter in full, whereas others may focus their discussion on the computation of the present value and future value of uneven and level cash flow streams only. The end of the chapter presents a large number of exercises that can be utilized to help students learn the basic concepts in this chapter before moving on to other topics.

Summary of Learning Objectives

1. Explain why cash flows occurring at different times must be adjusted to reflect their value as of a common date before they can be compared, and compute the present value and future value for multiple cash flows. When making decisions involving cash flows over time, we should first identify the magnitude and timing of the cash flows and then adjust each individual cash flow to reflect its value as of a common date. For example, the process of discounting (compounding) cash flows adjusts them for the time value of money because today’s dollars are not equal in value Copyright ©2015 John Wiley & Sons, Inc.

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to dollars in the future. Once all of the cash flows are in present (future) value terms, they can be compared to make decisions. Section 6.1 discusses the computation of present values and future values of multiple cash flows. 2. Explain what a perpetuity is and where we see them in business, and calculate the value of a perpetuity. A perpetuity is like an annuity except that the cash flows are perpetual—they never end. British Treasury Department bonds, called consols, were the first widely used securities of this kind. The most common example of a perpetuity today is preferred stock. The issuer of preferred stock promises to pay fixed-rate dividends forever. The cash flows from corporations can also look like perpetuities. To calculate the present value of a perpetuity, we simply divide the constant cash flow (CF) by the interest rate (i). 3. Discuss growing annuities and perpetuities, as well as their application in business, and calculate their values. Financial managers oft en need to value cash flow streams that increase at a constant rate over time. These cash flow streams are called growing annuities or growing perpetuities. An example of a growing annuity is a 10-year lease with an annual adjustment for the expected rate of inflation over the life of the contract. If the cash flows continue to grow at a constant rate indefinitely, this cash flow stream is called a growing perpetuity. Application and calculation of cash flows that grow at a constant rate are discussed in Section 6.3. 4. Discuss why the effective annual interest rate (EAR) is the appropriate way to annualize interest rates, and calculate the EAR. The EAR is the annual growth rate that takes compounding into account. Thus, the EAR is the true cost of borrowing or lending money. When we need to compare interest rates, we must make sure that the rates to be compared have the same time and compounding periods. If interest rates are not comparable, they must be converted into common terms. The easiest way to convert rates to common terms is to calculate the EAR for each interest rate. The use and calculation of EAR are discussed in Section 5.7.

Summary of Key Equations Equation

Description

Formula

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PVA n =

6.1

Present value of an ordinary annuity

CF  1   1 − i  (1 + i ) n 

1 − 1/ (1 + i) n = CF  i 1 − P resent value factor = CF  i = CF×PV annuity factor

6.2

Future value of an ordinary annuity

CF  [(1 + i) n − 1] i (1 + i ) n − 1 = CF  i Future value factor − 1 = CF  i = CF  FV annuity factor

6.3

Present value of a perpetuity

PVP =

6.4

Value of an annuity due

Annuity due value = Ordinary annuity value  (1 + i)

6.5

Present value of a growing annuity

PVA n =

6.6

Present value of a growing perpetuity

PVP =

6.7

Effective annual interest rate

EAR = (1 + Quoted interest rate/m)m – 1

FVA n =

CF i

n CF1   1+g   1    (i - g )   1+i  

CF1 i−g

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Chapter 7 Risk and Return Learning Objectives 1. Explain the relation between risk and return. 2. Describe the two components of a total holding period return, and calculate this return for an asset. 3. Explain what an expected return is and calculate the expected return for an asset. 4. Explain what the standard deviation of returns is and why it is very useful in finance, and calculate it for an asset. 5. Explain the concept of diversification. 6. Discuss which type of risk matters to investors and why. 7. Describe what the Capital Asset Pricing Model (CAPM) tells us and how to use it to evaluate whether the expected return of an asset is sufficient to compensate an investor for the risks associated with that asset.

Chapter Outline 7.1

Risk and Return • The greater the risk, the larger the return investors require as compensation for bearing that risk. • Higher risk means you are less certain about the expected level of compensation.

7.2

Quantitative Measures of Return A. Holding Period Returns • The total holding period return consists of two components: (1) capital appreciation and (2) income. • The capital appreciation component of a return, RCA: Capital Appreciation P1 - P0 P R CA = = = Initial Price P0 P0 •

The income component of a return RI: R I =

•

The total holding period return is simply P + CF1 P CF1 R T = R CA + R I = + = . P0 P0 P0

Cash Flow CF1 = Initial Price P0

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Expected Returns • Expected value represents the sum of the products of the possible outcomes and the probabilities that those outcomes will be realized. • The expected return, E(RAsset), is an average of the possible returns from an investment, where each of these returns is weighted by the probability that it n

will occur: E ( R Asset ) =  ( pi  R i ) = ( p1  R1 ) + ( p2  R 2 ) + .... + ( pn  R n ) i =1

•

If each of the possible outcomes is equally likely (that is, p1 = p2 = p3 = … = n

 ( R ) R + R +...+ R

pn = p = 1/n), this formula reduces to: E ( R Asset ) = i =1 7.3

The Variance and Standard Deviation as Measures of Risk A. Calculating the Variance and Standard Deviation • The variance (2) squares the difference between each possible occurrence and the mean (squaring the differences makes all the numbers positive) and multiplies each difference by its associated probability before summing them n

(

up: Var (R) =  R2 =  pi  R i − E ( R ) i =1

•

)

If all of the possible outcomes are equally likely, then the formula becomes: n

  R − E(R)

 R2 = i =1

n • Take the square root of the variance to get the standard deviation (). Interpreting the Variance and Standard Deviation • The normal distribution is a symmetric frequency distribution that is completely described by its mean (average) and standard deviation. • The normal distribution is symmetric in that the left and right sides are mirror images of each other. The mean falls directly in the center of the distribution, and the probability that an outcome is a particular distance from the mean is the same whether the outcome is on the left or the right side of the distribution. ▪ The standard deviation tells us the probability that an outcome will fall a particular distance from the mean or within a particular range: Number of Standard Fraction of Total Deviations from the Mean Observations 1.000 68.26% 1.645 90% 1.960 95%

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C. •

7.4

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2.575 99% Historical Market Performance The key point is that, on average, annual returns have been higher for riskier securities. For instance, Exhibit 7.3 shows that small stocks, which have the largest standard deviation of total returns, also have the largest average return. On the other end of the spectrum, Treasury bills have the smallest standard deviation and the smallest average annual return.

Risk and Diversification • By investing in two or more assets whose values do not always move in the same direction at the same time, an investor can reduce the risk of his or her investments or portfolio. This is the idea behind the concept of diversification. A. Single-Asset Portfolios • Returns for individual stocks from one day to the next have been found to be largely independent of each other and approximately normally distributed. • A first pass at comparing risk and return for individual stocks is the coefficient of variation, CV,

CVi = • •

R

E (R i )

A lower value for the CV is what we are looking for. If investors can earn a positive risk-free rate without bearing any risk, then it really only makes sense to compare the risk of the investment with the return that investors expect to earn over and above the risk-free rate. This is called the modified coefficient of variation,

CVi

R

E (Ri ) − Rrf

• The Sharpe Ratio is simply the inverse of the modified coefficient of variation, E (Ri ) − Rrf i S=

R

Portfolios with More Than One Asset • The coefficient of variation and the Sharpe Ratio have a critical shortcoming that is not quite evident when we are only considering a single asset. • The expected return of a portfolio that is made up of two assets: E (R Portfolio ) = x1E (R1 ) + x2 E (R 2 )

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The expected return of a portfolio that is made up of multiple assets: n

E ( R Portfolio ) =  ( xi  E(R i ) ) i =1

= ( x1  E(R1 ) ) + ( x2  E(R 2 ) ) + .... + ( xn  E(R n ) ) . •

• • •

The expected return of each asset must be found before applying either of the two above formulas. The fraction of the portfolio invested in each asset must also be known. The prices of two stocks in a portfolio will rarely, if ever, change by the same amount and in the same direction at the same time. When the stock prices move in opposite directions, the change in the price of one stock offsets at least some of the change in the price of the other stock. As a result, the level of risk for a portfolio of the two stocks is less than the average of the risks associated with the individual shares.

•

 R2

•

R1,2 is the covariance between stocks 1 and 2. The covariance is a measure of how the returns on two assets covary, or move together:

= x12 R21 + x22 R2 2 + 2 x1 x2 R12

2 Asset Portfolio

(

Cov(R1 , R 2 ) =  R12 =  pi  (R1,i − E(R1 )   (R 2,i − E(R 2 )  i =1

•

The covariance calculation is very similar to the variance calculation. The difference is that, instead of squaring the difference between the value from each outcome and the expected value for an individual asset, we calculate the product of this difference for two different assets. In order to ease the interpretation of the covariance, we divide the covariance by the product of the standard deviations of the returns for the two assets. This gives us the correlation coefficient between the returns on the two assets,

 R1,2 =

R . RR 12

•

)

The value of the correlation between the returns on two assets will always have a value between –1 and +1. ▪ A negative correlation means that the returns tend to have opposite signs. ▪ A positive correlation means that when the return on one asset is positive, the return on the other asset also tends to be positive. ▪ A correlation of 0 means that the returns on the assets are not correlated. If we have imperfect correlation between assets, or a correlation coefficient less than +1, then we have a benefit from diversification by holding more than one asset with different risk characteristics.

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•

7.5

As we add more and more stocks to a portfolio, calculating the variance becomes increasingly complex because we have to account for the covariance between each pair of assets. The Limits of Diversification • If the returns on the individual stocks added to our portfolio do not all change in the same way, then increasing the number of stocks in the portfolio will reduce the standard deviation of the portfolio returns even further. • However, the decrease in the standard deviation for the portfolio gets smaller and smaller as more assets are added. • As the number of assets becomes very large, the portfolio standard deviation does not approach zero. It only decreases up to a point. • That is because investors can diversify away risk that is unique to the individual assets, but they cannot diversify away risk that is common to all assets. • The risk that can be diversified away is called diversifiable or unsystematic risk, and the risk that cannot be diversified away is called nondiversifiable or systematic risk. • Most of the risk-reduction benefits from diversification can be achieved in a portfolio with 15 to 20 assets.

Systematic Risk • With complete diversification, all of the unique risk is eliminated from the portfolio, but the investor still faces systematic risk. A. Why Systematic Risk Is All That Matters • Diversified investors face only systematic risk, whereas investors whose portfolios are not well diversified face systematic risk plus unsystematic risk. • Because diversified investors face less risk, they will be willing to pay higher prices for individual assets than other investors. • Therefore, expected returns on individual assets will be lower than the total risk (systematic plus unsystematic risk) of those assets suggests they should be. • The bottom line is that only systematic risk is rewarded in asset markets, and this is why we are only concerned about systematic risk when we think about the relation between risk and return in finance. B. Measuring Systematic Risk • If systematic risk is all that matters when we think about expected returns, then we cannot use the standard deviation as a measure of risk since the standard deviation is a measure of total risk. • Since systematic risk is, by definition, risk that cannot be diversified away, the systematic risk (or market risk) of an individual asset is really just a measure

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•

• •

7.6

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of the relation between the returns on the individual asset and the returns on the market. We quantify the relation between the returns on a stock and the general market by finding the slope of the line of best fit between the returns of the stock and the general market. We call the slope of the line of best fit beta (β). If the beta of an asset is: ▪ Equal to one, then the asset has the same systematic risk as the market. ▪ Greater than one, then the asset has more systematic risk than the market. ▪ Less than one, then the asset has less systematic risk than the market. ▪ Equal to zero, then the asset has no systematic risk.

Compensation for Bearing Systematic Risk • The difference between required returns on government securities and required returns for risky investments represents the compensation investors require for taking risk: E(Ri) = Rrf + Compensation for taking riski. • If we recognize that the compensation for taking risk varies with asset risk, and that systematic risk is what matters, we find: E(Ri) = Rrf + (Units of systematic riski  Compensation per unit of systemic risk)

•

If beta, β, is the appropriate measure for the number of units of systematic risk, we find: Compensation for taking risk = β  Compensation per unit of systemic risk

•

7.7

The required rate of return on the market, over and above that of the risk-free return, represents compensation required by investors for bearing a market (systematic) risk: Compensation per unit of systemic risk = E(Rm) – Rrf Which brings us to the equation for expected return: E(Ri) = Rrf + βi[E(Rm) – Rrf]

The Capital Asset Pricing Model • The Capital Asset Pricing Model (CAPM) is a model that describes the relation between risk and expected return: E(Ri) = Rrf + βi[E(Rm) – Rrf]. A. The Security Market Line • Security Market Line (SML) is the line described by: E(Ri) = Rrf + βi[E(Rm) – Rrf] • The SML illustrates what the CAPM predicts the expected total return should be for various values of beta. The actual expected total return depends on the P + CF1 price of the asset: R T = . If an asset’s price implies that the P0

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expected return is greater than that predicted by the CAPM, that asset will plot above the SML. The Capital Asset Pricing Model and Portfolio Returns • The expected return for a portfolio: E(Rn Asset portfolio) = Rrf + βn Asset portfolio[E(Rm) – Rrf] • The above can be found by applying the expected return and the beta of a portfolio: ▪ The expected return of a portfolio: n

E ( R Portfolio ) =  ( xi  E(R i ) ) i =1

= ( x1  E(R1 ) ) + ( x2  E(R 2 ) ) + .... + ( xn  E(R n ) ) . ▪

n Asset Portfolio =  xi i = x11 + x2  2 + x3 3 + ... + xn  n . i =1

Suggested and Alternative Approaches to the Material This is a key chapter in that it addresses the measurable aspect of the risk and return relationship for assets. The chapter begins with simple statistical concepts of expected return and variance/standard deviation. The chapter quickly points out that these simple statistical tools do not properly capture the correct measure of risk for an asset. Covariance and correlation coefficients are then introduced for their impact on the variance of a multi-asset portfolio where the benefits of diversification can be easily seen. The difference between systematic and nonsystematic risk is then discussed as well as the need for a new measure of the systematic risk component, separate from the nonsystematic risk component. Beta is then introduced as well as the intuitional arguments for the CAPM and the SML and the SML equation. Applications for all of the concepts are spread throughout the chapter. The basis for how an instructor should approach this chapter depends on the student’s statistical background. For advanced students, a review of the concepts will suffice before proceeding. For less-prepared students, the instructor may need to take a day of lecture to reinforce concepts that should have been learned in other courses. Regardless of the level of student preparedness, this chapter holds important intuitional arguments that will escape the students if they are unable to focus at a level beyond the simple statistical concepts. Those arguments will then be required for material such as the cost of capital, capital budgeting, and dividends. Therefore, it is imperative that the instructor adequately cover the material in this chapter.

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Summary of Learning Objectives 1.

Explain the relation between risk and return. Investors require greater returns for taking greater risk. They prefer the investment with the highest possible return for a given level of risk or the investment with the lowest risk for a given level of return.

Describe the two components of a total holding period return, and calculate this return for an asset. The total holding period return on an investment consists of a capital appreciation component and an income component. This return is calculated using Equation 7.1. It is important to recognize that investors do not care whether they receive a dollar of return through capital appreciation or as a cash dividend. Investors value both sources of return equally.

Explain what an expected return is and calculate the expected return for an asset. The expected return is a weighted average of the possible returns from an investment, where each of these returns is weighted by the probability that it will occur. It is calculated using Equation 7.2.

Explain what the standard deviation of returns is and why it is especially useful in finance, and calculate it for an asset. The standard deviation of returns is a measure of the total risk associated with the returns from an asset. It is useful in evaluating returns in finance because the returns on many assets tend to be normally distributed. The standard deviation of returns provides a convenient measure of the dispersion of returns. In other words, it tells us about the probability that a return will fall within a particular distance from the expected value or within a particular range. To calculate the standard deviation, the variance is first calculated using Equation 7.3. The standard deviation of returns is then calculated by taking the square root of the variance.

Explain the concept of diversification. Diversification is reducing risk by investing in two or more assets whose values do not always move in the same direction at the same time. Investing in a portfolio containing assets whose prices do not always move together reduces risk because some of the changes in the prices of individual assets offset each other. This can cause the overall volatility in the value of an investor’s portfolio to be lower than if it consisted of only a single asset.

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Discuss which type of risk matters to investors and why. Investors care about only systematic risk. This is because they can eliminate unsystematic risk by holding a diversified portfolio. Diversified investors will bid up prices for assets to the point at which they are just being compensated for the systematic risks they must bear.

Describe what the Capital Asset Pricing Model (CAPM) tells us and how to use it to evaluate whether the expected return of an asset is sufficient to compensate an investor for the risks associated with that asset. The CAPM tells us that the relation between systematic risk and return is linear and that the risk-free rate of return is the appropriate return for an asset with no systematic risk. From the CAPM we know what rate of return investors will require for an investment with a particular amount of systematic risk (beta). This means that we can use the expected return predicted by the CAPM as a benchmark for evaluating whether expected returns for individual assets are sufficient. If the expected return for an asset is less than that predicted by the CAPM, then the asset is an unattractive investment because its return is lower than the CAPM indicates it should be. By the same token, if the expected return for an asset is greater than that predicted by the CAPM, then the asset is an attractive investment because its return is higher than it should be.

Summary of Key Equations

Equation

Description

Formula

7.1

Total holding period return

R T = R CA + R I =

7.2

Expected return on an asset

E ( R Asset ) =  ( pi  R i )

P1 - P0 CF1 + P0 P0

i =1

(

Variance of return on an asset

Var (R) =  R2 =  pi  R i − E ( R )

7.4

Coefficient of variation

CVi =

7.5

Sharpe Ratio

7.3

i =1

)

R

E (R i )

E (Ri ) − Rrf

R

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Expected return for a portfolio

E ( R Portfolio ) =  ( xi  E(R i ) )

7.7

Variance for a two-asset portfolio

 R2

7.8

Covariance between two assets

 R =  p  (R1,i − E(R1 )  x (R 2,i − E(R 2 ) 

Correlation between two assets

=

Expected return and systematic risk

E(Ri) = Rrf + βi(E(Rm) – Rrf)

Portfolio beta

 n Asset Portfolio =  xi i

7.6

7.9 7.10

i =1

2 Asset Portfolio

i =1

(

= x12 R21 + x22 R2 2 + 2 x1 x2 R12

)

R RR 12

7.11

i =1

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CHAPTER 8 Bond Valuation and the Structure of Interest Rates Learning Objectives 1. Describe the market for corporate bonds and three types of corporate bonds. 2. Explain how to calculate the value of a bond and why bond prices vary negatively with interest rate movements. 3. Distinguish between a bond’s coupon rate, yield to maturity, and effective annual yield. 4. Explain why investors in bonds are subject to interest rate risk and why it is important to understand the bond theorems. 5. Discuss the concept of default risk and know how to compute a default risk premium. 6. Describe the factors that determine the level and shape of the yield curve.

Chapter Outline 8.1

Corporate Bonds A. Market for Corporate Bonds • In October 2013, for example, the amount of corporate and foreign bonds outstanding was $11.1 trillion. • The next largest bond market is the market for U.S. government long-term Treasury securities valued at $10.4 trillion, followed by state and local government debt markets valued at $3.6 trillion. • The largest investors in corporate bonds are life insurance companies and pension funds, with trades in this market tending to be in very large blocks of securities. • Most secondary market transactions for corporate bonds take place through dealers in the over-the-counter (OTC) market. • Only a small number of the total bonds that exist actually trade on a single day. As a result, the market for corporate bonds is thin compared to the market for money market securities or corporate stocks. • Corporate bonds are less marketable than the securities that have higher daily trading volumes. • Prices in the corporate bond market also tend to be more volatile than securities sold in markets with greater trading volumes. • The market for corporate bonds is not as efficient as that for stocks sold on the major stock exchanges or highly marketable money market instruments such as U.S. Treasury securities.

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Bond Price Information • The corporate bond market is not considered to be very transparent because it trades predominantly over the counter and investors do not find it easy to view prices and trading volume. • In addition, many corporate bond transactions are negotiated between the buyer and the seller, and there is little centralized reporting of these deals. Types of Corporate Bonds • Corporate bonds are long-term IOUs that represent claims against a firm’s assets. • Debt instruments, where the interest income paid to investors is fixed for the life of the contract, are called fixed-income securities. • There are three types of corporate bonds: vanilla bonds, zero coupon bonds, and convertible bonds. 1. Vanilla Bonds • These bonds have coupon payments that are fixed for the life of the bond, and at maturity, the principal is paid and the bonds are retired. • Vanilla bonds have no unusual features. • Payments are usually made annually or semiannually. • The face value, or par value, for most corporate bonds is $1,000. • The bond’s coupon rate is calculated as the annual coupon payment (C) divided by the bond’s face value (F). 2. Zero Coupon Bonds • Corporations sometimes issue bonds that have no coupon payments over their lives and only offer a single payment at maturity. • Zero coupon bonds sell well below their face value (at a deep discount) because they offer no coupons. • The most frequent and regular issuer of zero coupon securities is the U.S. Treasury Department. 3. Convertible Bonds • These are bonds that can be converted into shares of common stock at some predetermined ratio at the discretion of the bondholder. • The convertible feature allows the bondholders to share in the good fortunes of the firm if the firm’s stock rises above a certain level. • The conversion ratio is set so that the firm’s stock price must appreciate 15 to 20 percent before it is profitable to convert bonds into equity. • To secure this advantage, bondholders would be willing to pay a premium.

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8.2

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Bond Valuation • The value, or price, of any asset is the present value of its future cash flows. • To calculate the price of the bond, we follow the same process as we would to value any financial asset. ▪ Estimate the expected future cash flows—these are the coupons that the bond will pay. ▪ Determine the required rate of return, or discount rate. The required rate of return, or discount rate, for a bond is the market interest rate called the bond’s yield to maturity (or more commonly, yield). This is the return one would earn from bonds that are similar in maturity and default risk. ▪ Compute the present value of the future cash flows. A. The Bond Valuation Formula • Compute the current value, or price, of a bond (PB) by calculating the present value of the bond’s expected cash flows: PB = PV (Coupon payments) + PV (Principal payments) • The general equation for the price of a bond can be written as follows in Equation 8.1: C3 C1 C2 C +F PB = + + +  + n n 1 2 3 (1 + i ) (1 + i ) (1 + i ) (1 + i )

1   1 − (1 + i ) n  F = C + n i   (1 + i )   B.

Par, Premium, and Discount Bonds • If a bond’s coupon rate is equal to the market rate, then the bond will sell at a price equal to its face value. Such bonds are called par bonds. • If a bond’s coupon rate is less than the market rate, then the bond will sell at a price that is less than its face value. Such bonds are called discount bonds. • If a bond’s coupon rate is greater than the market rate, then the bond will sell at a price that is more than its face value. Such bonds are called premium bonds. Semiannual Compounding • While bonds in Europe pay annual coupons, bonds in the United States pay coupons semiannually. • In calculating the current price of a bond paying semiannual coupons, one needs to modify Equation 8.1. ▪ Each coupon payment is half of an annual coupon. ▪ The number of payments is twice the number of years to maturity.

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The discount rate used is then half of the annual rate. ( C m ) + Fmn C m C m C m PB = 1 + + + + 2 3 (1 + i m) (1 + i m) (1 + i m) (1 + i m) mn

Instructor’s Manual

(8.2)

Zero Coupon Bonds • Zero coupon bonds have no coupon payments but promise a single payment at maturity. • The price (or yield) of a zero coupon bond is simply a special case of Equation 7.2, in that all the coupon payments are equal to zero. • Hence, the pricing equation is: PB = Fmn/(1 + i/m)mn (8.3) • Zero coupon bonds, for which all the cash payments are made at maturity, must sell for less than similar bonds that make periodic coupon payments.

8.3

Bond Yields A. Yield to Maturity • The yield to maturity of a bond is the discount rate that makes the present value of the coupon and principal payments equal to the price of the bond. • It is the yield that the investor earns if the bond is held to maturity and all the coupon and principal payments are made as promised. • A bond’s yield to maturity changes daily as interest rates increase or decrease. • We can compute a bond’s yield to maturity using a trial-and-error approach. B. Effective Annual Yield • As pointed out in Chapter 6, the correct way to annualize an interest rate (yields) is to compute the effective annual interest rate (EAR). • On Wall Street, the EAR is called the effective annual yield (EAY) and EAR = EAY. • The correct way to annualize the yield on a bond is as follows: EAY = (1 + Quoted rate/m)m – 1 • The simple annual yield is the yield per period multiplied by the number of compounding periods. For bonds with annual compounding, the simple annual yield = semiannual yield  2. C. Realized Yield • The realized yield is the return earned on a bond given the cash flows actually received by the investor. • The interest rate at which the present value of the actual cash flows generated by the investment equals the bond’s price is the realized yield on an investment. • The realized yield is an important bond calculation because it allows investors to see the return they actually earned on their investment.

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8.4

Interest Rate Risk • The prices of bonds fluctuate with changes in interest rates, giving rise to interest rate risk. A. Bond Theorems 1. Bond prices are negatively related to interest rate movements. • As interest rates decline, the prices of bonds rise; and as interest rates rise, the prices of bonds decline. 2. For a given change in interest rates, the prices of long-term bonds will change more than the prices of short-term bonds. • Long-term bonds have greater price volatility than short-term bonds. • All other things being equal, long-term bonds are more risky than short-term bonds. 3. For a given change in interest rates, the prices of lower-coupon bonds change more than the prices of higher-coupon bonds. • The lower a bond’s coupon rate, the greater its price volatility, and hence, lower coupon bonds have greater interest rate risk. • The lower the bond’s coupon rate, the greater the proportion of the bond’s cash flow investors will receive at maturity. • All other things being equal, a given change in the interest rates will have a greater impact on the price of a low-coupon bond than a higher-coupon bond with the same maturity. B. Bond Theorem Applications • If rates are expected to increase, a portfolio manager should avoid investing in long-term securities. The portfolio could see a significant decline in value. • If you are an investor and you expect interest rates to decline, you may well want to invest in long-term zero coupon bonds. As interest rates decline, the price of long-term zero coupon bonds will increase more than that of any other type of bond.

8.5

The Structure of Interest Rates • Market analysts have identified four risk characteristics of debt instruments that are responsible for most of the differences in corporate borrowing costs: the security’s marketability, call provision, default risk, and term to maturity. A. Marketability • Marketability refers to the ability of an investor to sell a security quickly, at a low transaction cost, and at its fair market value. • The lower these costs are, the greater a security’s marketability. • The interest rate, or yield, on a security varies inversely with its degree of marketability.

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The difference in interest rates or yields between a marketable security (imarkt) and a less marketable security (iless) is known as the marketability risk premium (MRP). MRP = ilow mkt – ihigh mkt > 0 • U.S. Treasury bills have the largest and most active secondary market and are considered to be the most marketable of all securities. Call Provision • A call provision gives the firm issuing the bonds the option to purchase the bond from an investor at a predetermined price (the call price); the investor must sell the bond at that price. • When bonds are called, investors suffer a financial loss because they are forced to surrender their high-yielding bonds and reinvest their funds at the lower prevailing market rate of interest. • Bonds with a call provision sell at higher market yields than comparable noncallable bonds. • The difference in interest rates between a callable bond and a comparable noncallable bond is called the call interest premium (CIP) and can be defined as follows: CIP = icall – incall > 0 • Bonds issued during periods when interest is high are likely to be called when interest rates decline, and as a result, these bonds have a high CIP. Default Risk • The risk that the lender may not receive payments as promised is called default risk. • Investors must be paid a premium to purchase a security that exposes them to default risk. • The default risk premium (DRP) can thus be defined as follows: DRP = idr – irf > 0 • U.S. Treasury securities do not have any default risk and are the best proxy measure for the risk-free rate. • Individuals and small business have to rely on outside agencies to provide them information on the default potential of bonds. • The three most prominent credit rating agencies are Moody’s Investors Service (Moody’s), Standard and Poor’s (S&P) and Fitch. All rank bonds in order of their expected probability of default and publish the ratings as letter grades. • The rating schemes used are shown in Exhibit 8.4. • The highest-grade bonds, those with the lowest default risk, are rated Aaa (or AAA). • Bonds in the top four rating categories are called investment-grade bonds— AAA to Baa.

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State and federal laws typically require commercial banks, insurance companies, pension funds, other financial institutions, and government agencies to purchase securities rated only as investment grade. The Term Structure of Interest Rates • The relationship between yield and term to maturity is known as the term structure of interest rates. • Yield curves show graphically how market yields vary as term to maturity changes. • The shape of the yield curve is not constant over time. • As the general level of interest rises and falls over time, the yield curve shifts up and down and has different slopes. • There are three basic shapes (slopes) of yield curves in the marketplace. ▪ Ascending upward-sloping yield curves that occur when an economy is growing. ▪ Descending or downward-sloping yield curves that occur when an economy is declining or heading into a recession. ▪ Flat yield curves imply that interest rates are unlikely to change in the near future. ▪ The Shape of the Yield Curve • Three economic factors determine the shape of the yield curve: (1) the real rate of interest, (2) the expected rate of inflation, and (3) interest rate risk. 1. The Real Rate of Interest • The real rate of interest varies with the business cycle, with the highest rates seen at the end of a period of business expansion and the lowest at the bottom of a recession. • Changes in the expected future real rate of interest can affect the slope of the yield curve. 2. The Expected Rate of Inflation • If investors believe that inflation will be increasing in the future, the yield curve will be upward sloping because long-term interest rates will contain a larger inflation premium than short-term interest rates. • If investors believe inflation will be subsiding in the future, the prevailing yield curve will be downward sloping. 3. Interest Rate Risk • The longer the maturity of a security, the greater its interest rate risk, and the higher the interest rate. • The interest risk premium always adds an upward bias to the slope of the yield curve. • The Cumulative Effect

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Exhibit 8.6 shows the cumulative effect of the three economic factors that influence the shape of the yield curve: the real rate of interest, the inflation premium, and the interest rate risk premium. In a period of economic expansion, both the real rate of interest and the inflation premium tend to increase monotonically over time. In a period of contraction, both the real rate of interest and the inflation premium decrease monotonically over time.

Suggested and Alternative Approaches to the Material This chapter is all about bonds and how they are valued or priced in the marketplace. The bond valuation models presented in this chapter are derived from the present value materials discussed in Chapter 6. In the first part of the chapter, the authors discuss the concept of efficient capital markets. Next, the discussion centers on the corporate bond market, bond price information that is available, and the types of bonds found in the market. The development of the basic equation used to calculate bond prices follows and leads to the steps required to compute a bond’s: (1) yield to maturity, (2) realized yield, and (3) effective annual yield. This is followed by a discussion on interest rate risk, and the three bond theorems that describe how bond prices respond to changes in interest rates are identified. The chapter concludes with a discussion on the term structure of interest rates and yield curves. Instructors have the flexibility of covering the chapter in its entirety or of focusing on bonds alone. In a first course in finance, the discussion on term structure of interest rates may be ignored so as to place a heavier emphasis on bonds and their valuation.

Summary of Learning Objectives 1.

Describe the market for corporate bonds and three types of corporate bonds. The market for corporate bonds is a very large market in which the most important investors are large institutions. Most trades in this market take place through dealers in the OTC market, making the corporate bond market relatively thin. Prices of corporate bonds tend to be more volatile than prices of securities that trade more frequently, such as stock and money markets, and the corporate bond market tends to be less efficient than markets for these other securities. A vanilla bond pays fixed regular coupon payments over the life of the bond, and the entire principal is repaid at maturity. A zero coupon bond pays all interest and all principal at maturity. Since there are no payments before maturity, zero coupon bonds are issued at prices below their face value. Convertible bonds can be exchanged for common stock at a predetermined ratio.

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Explain how to calculate the value of a bond and why bond prices vary negatively with interest rate movements. The value of a bond is equal to the present value of the future cash flows (coupon payments and principal repayment) discounted at the market rate of interest for bonds with similar risk. Bond prices vary negatively with interest rates because the coupon rate on most bonds is fixed at the time the bond is issued. As market interest rates go up, the prices of bonds with fixed coupon payments will bid down by investors, driving the yields of those bonds up to market levels. When interest rates decline, the yield on fixedincome securities will be higher relative to yield on similar securities price to market; the favorable yield will increase investor demand for these securities, increasing their price and lowering their yield to the market yield.

Distinguish between a bond’s coupon rate, yield to maturity, realized yield, and effective annual yield. A bond’s coupon rate is the stated interest rate on the bond when it is issued. U.S. bonds typically pay interest semiannually, whereas European bonds pay once a year. The yield to maturity is the expected return on a bond if it is held to maturity date, whereas the realized yield is the return earned on a bond given the cash flows actually received by the investor. If the bond is held to maturity and the issuer does not default, these two rates are the same. Effective annual interest rate is the yield an investor actually earns in one year, adjusting for the effects of compounding. If the bond pays coupon payments more often than annually, the effective annual yield will be higher than the simple annual yield because of compounding. Work through Learn by Doing Applications 8.2, 8.3, and 8.4 to master these calculations.

Explain why investors in bonds are subject to interest rate risk and why it is important to understand the bond theorems. Because interest rates are always changing in the market, all investors who hold bonds are subject to interest rate risk. Interest rate risk is the change in bond prices caused by fluctuations in interest rates. Three of the most important bond theorems can be summarized as follows: 1. Bond prices are negatively related to interest rate movements. 2. For a given change in interest rates, the prices of long-term bonds will change more than the prices of short-term bonds. 3. For a given change in interest rates, the prices of lower-coupon bonds will change more than the prices of higher-coupon bonds. Understanding these theorems is important because it helps investors better understand why bond prices change and thus make better decisions regarding the purchase or sale of bonds and other fixed-income securities.

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Parrino, Kidwell, Bates / Fundamentals of Corporate Finance, 3rd Edition

Discuss the concept of default risk and know how to compute a default risk premium. Default risk is the risk that the issuer will be unable to pay its debt obligation. Since investors are risk averse, they must be paid a premium to purchase a security that exposes them to default risk. The default risk premium has two components: (1) compensation for the expected loss if a default occurs and (2) compensation for bearing the risk that a default could occur. All factors held constant, the degree of default risk a security possesses can be measured as the difference between the interest rate on a risky security and the interest rate on a default-free security. The default risk is also reflected in a company’s bond rating. The highest-grade bonds, those with the lowest default risk, are rated Aaa (or AAA). The default risk premium on corporate bonds increases as the bond rating becomes lower.

Describe the factors that determine the level and shape of the yield curve. The level and shape of the yield curve are determined by three economic factors: (1) the real rate of interest, (2) the expected rate of inflation, and (3) interest rate risk. The real rate of interest is the base interest rate in the economy and varies with the business cycle. The real rate of interest affects only the level of the yield curve and not its shape. The expected rate of inflation does affect the shape of the yield curve. If investors believe inflation will be increasing in the future, for example, the curve will e upward sloping, as long-term rates will contain a larger inflation premium than short-term rates. Finally, interest rate risk, which increases with a security’s maturity, adds an upward bias to the slope of the yield curve.

Summary of Key Equations

Equation

Description

Formula

Cn + Fn

8.1

Price of a bond

PB=

C1 C2 + + 1+ i (1+ i ) 2

8.2

Price of a bond semiannual compounding

PB=

Cm Cm Cm + + + 2 1+ i m (1+ i m) (1+ i m)3

8.3

Price of zero coupon bond

PB=

Fmn (1+ i m) mn

(1+ i ) n

C m +Fmn (1+ i m) mn

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Chapter 9 Stock Valuation Learning Objectives 1. List and describe the four types of secondary markets. 2. Explain why many financial analysts treat preferred stock as a special type of bond rather than as an equity security. 3. Describe how the general dividend-valuation model values a share of stock. 4. Discuss the assumptions that are necessary to make the general dividend-valuation model easier to use, and use the model to compute the value of a firm’s stock. 5. Explain why g must be less than R in the constant-growth dividend model. 6. Explain how valuing preferred stock with a stated maturity differs from valuing preferred stock with no maturity, and calculate the price of a share of preferred stock under both conditions.

Chapter Outline 9.1

The Market for Stocks • Equity securities are certificates of ownership of a corporation. • Households dominate the holdings of equity securities, owning about 35 percent of outstanding corporate equities. A. Secondary Markets • In secondary markets, outstanding shares of stock are bought and sold among investors. • An active secondary market enables firms to sell their new debt or equity issues at a lower funding cost than firms selling similar securities that have no secondary market. B. Secondary Markets and Their Efficiency • In the United States, most secondary market transactions are conducted on one of the many stock exchanges. ▪ In terms of total volume of activity and total capitalization of the firms listed, the NYSE and the NASDAQ are the most important. • The NASDAQ is one of the world’s largest electronic stock markets, listing over three thousand companies.

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NASDAQ is an acronym for National Association of Securities Dealers Automated Quotation System. ▪ Firms listed on the NYSE tend to be, on average, larger in size and their shares trade more frequently than firms whose securities trade on NASDAQ. ▪ The largest markets outside of the United States include the Tokyo Stock Exchange, NYSE Euronext, the London Stock Exchange, the Shanghai Stock Exchange, the Hong Kong Stock Exchange, and the Toronto Stock Exchange. • There are four types of secondary markets, and each type differs according to the amount of price information available to investors, which in turn affects the efficiency of the market. 1. Direct Search ▪ The secondary markets farthest from our ideal of complete price information are those in which buyer and seller must seek each other out directly. ▪ It is too costly to perform a thorough search among all possible partners to locate the best price. ▪ Securities that sell in direct search markets are usually bought and sold so infrequently that no third party, such as a broker or dealer, finds it profitable to serve the market. ▪ The sales of common stock of small private companies and private placement transactions are good examples of direct search markets. 2. Broker ▪ Brokers bring buyers and sellers together to earn a fee, called a commission. ▪ By charging a commission fee less than the cost of direct search, brokers give investors an incentive to make use of the information by hiring them as brokers. 3. Dealer ▪ Market efficiency is improved if there is someone in the marketplace to provide continuous bidding (selling or buying) for the security. ▪ Dealers provide this service by holding inventories of securities, which they own, then buying and selling from the inventory to earn a profit. ▪ Dealers earn their profits from the spread on the securities they trade—the difference between their bid price (the price at which they buy) and their offer price (the price at which they sell). ▪ The advantage of a dealer over a brokered market is that brokers cannot guarantee that an order will be executed promptly, while dealers can because they have an inventory of securities.

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A dealer market eliminates the need for a time-consuming search for a fair deal by buying and selling immediately from the dealers’ inventory of securities. ▪ NASDAQ is the best-known example of a dealer market. ▪ Electronic communications network (ECN) systems provide additional price information to investors and increase marketability and competition, which should improve NASDAQ efficiency. 4. Auction ▪ In an auction market, buyers and sellers confront each other directly and bargain over price. ▪ The New York Stock Exchange is the best-known example of an auction market. ▪ In the NYSE, the auction for a security takes place at a specific location on the floor of the exchange called a post. ▪ The auctioneer in this case is the specialist who is designated by the exchange to represent orders placed by public customers. C. Stock Market Indexes • Stock market indexes are used to measure the performance of the stock market. o Dow Jones Industrial Average: Consists of 30 companies that represent about 20 percent of the market value of all U.S. stocks. o New York Stock Exchange Index: Includes all common and preferred stocks listed on the NYSE. o Standard and Poor’s 500 Index: Consists of 500 stocks and represents more than 70% of the total market capitalization of all stocks traded in the United States. o NASDAQ Composite Index: Consist of all the common stocks listed on the NASDAQ stock exchange. D. Reading the Stock Market Listings • The Wall Street Journal, the New York Times, and other newspapers in large metropolitan areas provide stock listings for the major stock exchanges, such as the NYSE and the relevant regional exchanges. • Exhibit 9.1 shows a section of the listing in the Wall Street Journal for the NYSE. E. Common and Preferred Stock • The two types of equity securities are common stock and preferred stock. • Common stock represents the basic ownership claim in a corporation. ▪ One of the rights of the owners is to vote on all important matters that affect the life of the company, such as electing the board of directors or voting on a proposed merger or acquisition. Copyright ©2015 John Wiley & Sons, Inc.

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Owners of common stock are not guaranteed any dividend payments and have the lowest-priority claim on the firm’s assets in the event of bankruptcy. ▪ Legally, common stockholders enjoy limited liability. ▪ Common stocks are perpetuities in the sense that they have no maturity. • Preferred stock also represents ownership interest in the corporation, but preferred stock receives preferential treatment over common stock in certain matters. ▪ If a preferred dividend payment is not paid due to the firm’s financial condition, the firm is not in default technically. ▪ Preferred stock owners are given priority treatment over common stock with respect to dividends payments and the claims against the firm’s assets in the event of bankruptcy or liquidation. ▪ Dividends payments are paid with after-tax dollars subject to taxation. ▪ Even though preferred stock is equity, the owners have no voting privileges. ▪ Preferred stocks are legally classified as perpetuities because they have no maturity. However, most preferred stocks are not true perpetuities because the shares contain a call provision and the share contract often requires management to retire a certain percent of the stock annually until the entire issue is retired. F. Preferred Stock: Debt or Equity? • Legally, preferred stock is equity. • Like the dividends on common stock, preferred stock dividends are taxable. • A strong case can be made that preferred stock is really a special type of bond. ▪ First, regular preferred stock confers no voting powers. ▪ Second, preferred stockholders receive a fixed dividend, regardless of the firm’s earnings, and if the firm is liquidated, they receive a stated value (usually par) and not the residual value. ▪ Third, preferred stocks often have “credit” ratings that are similar to those issued to bonds. ▪ Fourth, preferred stock is sometimes convertible into common stock. ▪ Finally, most preferred stock issues today are not true perpetuities. Increasingly, preferred stock issues have the sinking fund feature, which require mandatory annual retirement schedules. 9.2

Common Stock Valuation • Valuation of common and preferred stock is done by using the same basic methodology that was discussed for bond valuations in Chapter 8.

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Applying the valuation procedure to common stocks is more difficult than applying it to bonds for various reasons. ▪ First, in contrast to coupon payments on bonds, the size and timing of the dividend cash flows are less certain. ▪ Second, common stocks are true perpetuities in that they have no final maturity date. ▪ Finally, unlike the rate of return, or yield, on bonds, the rate of return on common stock is not directly observable. A. A One-Period Model • A one-period model provides an estimate of the market price. • The value of an asset is the present value of its future cash flows—the future dividend and the end-of-period stock price. B. A Perpetuity Model • A series of one-period stock pricing models is strung together to arrive at a stock perpetuity model. • Though theoretically sound, this model is not practical to apply because the number of dividends could be infinite. C. The General Dividend Valuation Model • Equation 9.1 is a general expression for the value of a share of stock. It says that the price of a share of stock is the present value of all expected future dividends. ▪ The formula does not assume any specific pattern for future cash dividends, such as a constant growth rate. ▪ It does not make any assumption about when the share of stock is going to be sold in the future. ▪ Finally, the model says that to compute a stock’s current value, we need to forecast an infinite number of dividends. • Equation 9.1 implies that the underlying value of a share of stock is determined by the market’s expectations of future cash flows that the firm can generate. • In efficient markets, stock prices change constantly as new information becomes available and is discounted into the firm’s market price. • For publicly traded companies, there is a constant stream of information about the firm that reaches the market, with some having an impact on the stock price while other information has no effect. D. The Growth Stock Pricing Paradox • Growth stocks are typically defined as the stocks of companies whose earnings are growing at above-average rates and are expected to continue to do so for some time.

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Fast-growing companies typically pay no dividends on their stock during their growth phase because management believes that the company has a number of high-return investment opportunities and that both the company and its investors will be better off if earnings are reinvested. Equation 9.1 predicts and common sense says that if you own stock in a company that will never pay you any cash, the market value of those shares of stock are worth absolutely nothing. In reality, these firms will eventually pay out dividends in the distant future. If the internal investments succeed, the stock’s price should go up significantly, and investors can sell their stock at a price much higher than what they paid.

Stock Valuation: Some Simplifying Assumptions • To make Equation 9.1 more applicable, some simplifying assumptions about the pattern of dividends are necessary. • Three different assumptions can cover most growth patterns. ▪ Dividend payments remain constant over time; that is, they have a growth rate of zero. ▪ Dividends have a constant-growth rate. ▪ Dividends have a mixed growth rate pattern; that is, dividends have one payment pattern then switch to another. A. Zero-Growth Dividend Model • The dividend payment pattern remains constant over time: D1 = D2 = D3 = . . . = D∞ • In this case the dividend-discount model (Equation 9.1) becomes: D D D D P0 = + + + + ........... 2 2 (1 + R ) (1 + R ) (1 + R ) (1 + R )3 •

This cash flow pattern essentially describes a perpetuity with a constant cash flow. In Chapter 6 we developed the present value of a perpetuity with a constant cash flow as CF/i, where CF is the constant cash flow and i is the interest rate. Similarly, Equation 9.2 gives the valuation model for a zerogrowth stock. D P0 = R Constant-Growth Dividend Model • Cash dividends do not remain constant but instead grow at some average rate g from one period to the next forever. • Constant dividend growth is an appropriate assumption for mature companies with a history of stable growth.

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While an infinite horizon is still hard to comprehend, far-distant dividends have a small present value and contribute very little to the price of the stock. • Deriving the constant-growth dividend model is fairly straightforward. First, we need to build a model to compute the value of dividend payments for any time period. • The constant-growth dividend model is easy to do because it is just an application of Equation 5.10 from Chapter 5. • Recall that the equation for a growing perpetuity in Chapter 5 is given by Equation 5.10: • PVA∞ = CF1/(i − g) • In other words, the constant-growth dividend model tells us that the current price of a share of stock is the next period dividend divided by the difference between the discount rate and the dividend growth rate. • Equation 9.4 shows how to value a constant-growth stock: D1 P0 = (R − g ) C.

Computing Future Stock Prices • The constant-growth dividend model (Equation 9.4) can be modified to determine the value, or price, of a share of stock at any point in time. • This results in Equation 9.5, which shows that the price of a share of stock at time t is as follows: D Pt = t +1 (R-g )

The Relationship between R and g • The constant-growth dividend model yields solutions that are invalid anytime the dividend growth rate equals or exceeds the discount rate (g ≥ R). • If g = R, the value of the denominator is zero and the value of the stock is infinite, which makes no sense. • If g > R, the present value of the dividend gets bigger and bigger rather than smaller and smaller, as it should. This implies that a firm that is growing at a very fast rate and does so forever. Mixed (Supernormal) Growth Dividend Model • During the early part of their lives, very successful firms experience a supernormal rate of growth in earnings. • To value a share of stock for a firm with supernormal dividend growth patterns, we can apply Equation 9.1, our general dividend model, and Equation 9.5, which gives us the price of a share of stock with constant dividend growth at any point in time. • Thus, our valuation model is (Equation 9.6):

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P0 = PV (Mixed dividend growth) + PV (Constant dividend growth) Dt Pt D1 D2 P0 = + +  + + 2 t (1 + R ) (1 + R ) (1 + R ) (1 + R ) t 9.4

Valuing Preferred Stock • In computing the value of preferred stock, one needs to know whether the preferred stock has an effective “maturity” because of a sinking fund option or call option. • The most significant difference between preferred stock with a fixed maturity and a bond is the risk of default. • Since preferred stock dividends are declared by the board of directors, failure to pay dividends does not result in default. • The failure to pay a preferred stock dividend as promised is a serious financial breach and signals to the market that the firm is in serious financial difficulty. A. Preferred Stock with a Fixed Maturity • We can use the bond valuation model developed in Chapter 8 to determine its price, or value. • Equation 8.2 can be restated as the price of a share of preferred stock (PS0): Preferred stock price = PV (Dividend payments) + PV (Par value) (D m ) + Pmn $ D1 m Dm Dm (9.7) PS 0 = + + ++ 1 2 3 (1 + i m) (1 + i m) (1 + i m) (1 + i m)mn B.

• Since most preferred stock make quarterly dividend payments, m equals 4. Preferred Stock with No Maturity • Some preferred stock issues have no maturity. ▪ Dividends are constant over time (g = 0). ▪ Fixed dividend payments go on forever. • We can use Equation 9.2 to value such preferred stock issues. D P0 = R

Suggested and Alternative Approaches to the Material This chapter focuses on equity securities and how they are valued. First, the fundamental factors that determine a stock’s price or value are examined; then the authors construct several valuation models that estimate this price. These models tell us what the stock’s price should be, and can then be used to compare our estimate against the actual market price. This chapter begins with a discussion of the secondary markets for equity securities and their market efficiency. Next, the authors explain how to read stock market price listings in the newspaper, and introduce the types of equity securities that firms typically issue. Then they develop a general valuation model and conclude that the value of a share of stock is the present Copyright ©2015 John Wiley & Sons, Inc.

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value of all expected future cash dividends. Some simplifying assumptions about dividend payments are used to implement this valuation model. These assumptions correspond to actual practice and allow for the development of several valuation models that are theoretically sound and easy to apply. Since market efficiency was discussed in Chapter 7, instructors can begin with a overview of the market structure before proceeding to a discussion of stock valuation.

Summary of Learning Objectives 1. List and describe the four types of secondary markets. The four types of secondary markets are: (1) direct search, (2) broker, (3) dealer, and (4) auction. In direct search markets, buyers and sellers seek each other out directly. In broker markets, brokers bring buyers and sellers together for a fee. Trades in dealer markets go through dealers who buy securities at one price and sell at a higher price. The dealers face the risk that prices could decline while they own the securities. Auction markets have a fixed location where buyers and sellers confront each other directly and bargain over the transaction price. 2. Explain why many financial analysts treat preferred stock as a special type of bond rather than as an equity security. Preferred stock represents ownership in a corporation and entitles the owner to a dividend, which must be paid before dividends are paid to common stockholders. Similar to bonds, preferred stock issues have credit ratings, are sometimes convertible to common stock, and are often callable. Unlike owners of common stock, owners of nonconvertible preferred stock do not have voting rights and do not participate in the firm’s profits beyond the fixed dividends they receive. It is because of their strong similarity to bonds that many financial analysts treat preferred stocks that are not true perpetuities as a form of debt rather than equity. 3. Describe how the general dividend-valuation model values a share of stock. The general dividend-valuation model values a share of stock as the present value of all future cash dividend payments, where the dividend payments are discounted using the rate of return required by investors for investments with a similar level of risk. 4. Discuss the assumptions that are necessary to make the general dividend-valuation model easier to use, and use the model to compute the value of a firm’s stock. The problems with the general dividend-valuation model are that future dividends are uncertain and some companies do not pay dividends at all. To make the model easier to apply, we make assumptions about the dividend payment patterns of more manageable models, and they also conform with the actual dividend policies of many firms. Dividend Copyright ©2015 John Wiley & Sons, Inc.

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patterns include the following: (1) dividends are constant (zero growth), as computed in Learning by Doing Application 9.1; (2) dividends have a constant-growth pattern (they grow forever at a constant rate g), as computed in Learning by Doing Application 9.2; and (3) dividends grow first at a non-constant rate, then at a constant rate, as computed in the Redteck example at the end of Section 9.3. 5. Explain why g must be less than R in the constant-growth dividend model. The constant-growth dividend model assumes that dividends will grow at a constant rate forever. With the constant-growth model, if g = R, the value of the denominator is zero and the value of the stock is infinite, which of course is impossible. If g > R, the value of the denominator is negative, as is the value of the stock, which also does not make economic sense. Thus, g must always be less than R (g < R). 6. Explain how valuing a preferred stock with a stated maturity differs from valuing a preferred stock with no maturity, and calculate the price of a share of preferred stock under both conditions. When preferred stock has a stated maturity, financial analysts value it as they value any other fixed obligation—that is, like a bond. To value such preferred stock, we can use the bond valuation model from Chapter 8. Before using the model, we need to recognize that we will be using dividends in the place of coupon payments and that the stated (par) value of the preferred stock will replace the par value of the bond. In addition, while bond coupons are paid semiannually in the United States, preferred dividends are paid quarterly. When a preferred stock has no stated maturity, it becomes a perpetuity, with the dividend becoming a constant payment that goes on forever. We use the perpetuity valuation model represented by Equation 9.2 to price such stocks. The calculations appear in Learning by Doing Applications 9.5 and the Delta Airlines example at the end of Section 9.4.

Summary of Key Equations Equation

Description

9.1

General dividendvaluation model

9.2

Zero-growth dividend model

Formula

P0 =

D3 D5 D1 D4 D2 + + + + + 2 4 5 (1 + R) (1 + R) (1 + R) (1 + R) (1 + R)5

D (1 + R) 



Dt t t =1 (1 + R)

=

P0 = D/R

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9.3

Value of a dividend at time t in a constantgrowth scenario.

Dt = D0 x (1 + g)t

9.4

Constantgrowth dividend model

P0 =

D1 (R − g )

9.5

Value of a stock at time t when dividends grow at a constant rate.

Pt =

Dt +1 (R − g )

9.6

Supernormal growth stockvaluation model

P0 =

Dt Pt D1 D2 + +  + + 2 t (1 + R ) (1 + R ) (1 + R ) (1 + R ) t

9.7

Value of preferred stock with a fixed maturity

PS0 =

Dm Dm Dm + + + 2 1 + i m (1 + i m) (1 + i m)3

( D m ) + Pmn (1 + i m)mn

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CHAPTER 10 The Fundamentals of Capital Budgeting

Learning Objectives 1. Discuss why capital budgeting decisions are the most important investment decisions made by a firm’s management. 2. Explain the benefits of using the net present value (NPV) method to analyze capital expenditure decisions, and calculate the NPV for a capital project. 3. Describe the strengths and weaknesses of the payback period as a capital expenditure decision-making tool and compute the payback period for a capital project. 4. Explain why the accounting rate of return (ARR) is not recommended for use as a capital expenditure decision-making tool. 5. Compute the internal rate of return (IRR) for a capital project and discuss the conditions under which the IRR technique and the NPV technique produce different results. 6. Explain how the profitability index can be used to rank projects when a firm faces capital rationing and describe the limitations that apply to the profitability index. 7. Explain the benefits of postaudit and ongoing reviews of capital projects.

Chapter Outline 10.1

An Introduction to Capital Budgeting A. The Importance of Capital Budgeting • Capital budgeting decisions are the most important investment decisions made by management. • The goal of these decisions is to select capital projects that will increase the value of the firm. • Capital investments are important because they involve substantial cash outlays and, once made, are not easily reversed. • Capital budgeting techniques help management to systematically analyze potential business opportunities in order to decide which are worth undertaking. B. The Capital Budgeting Process • The capital budgeting process starts with a firm’s strategic plan, which spells out its strategy for the next three to five years.

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The process then continues with the division managers who convert the firm’s strategic objectives into business plans. • The capital budget is generally prepared by the CFO’s staff and financial staffs at the divisional and lower levels. Sources of Information • Most of the information needed to make capital budgeting decisions is generated internally, likely beginning with the sales force. • The production team is then involved, followed by the accountants. • All this information is then reviewed by the financial managers, who evaluate the feasibility of the project. Classification of Investment Projects • Capital budgeting projects can be broadly classified into three types: (1) independent projects; (2) mutually exclusive projects; and (3) contingent projects. 1. Independent Projects • Projects are independent when their cash flows are unrelated. • If two projects are independent, accepting or rejecting one project has no bearing on the decision on the other. 2. Mutually Exclusive Projects • When two projects are mutually exclusive, accepting one automatically precludes the other. • Mutually exclusive projects typically perform the same function. 3. Contingent Projects • Contingent projects are those in which the acceptance of one project is dependent on another project. • There are two types of contingency situations: ▪ Projects that are mandatory. ▪ Projects that are optional. Basic Capital Budgeting Terms • The cost of capital is the minimum return that a capital budgeting project must earn for it to be accepted. • It is an opportunity cost since it reflects the rate of return investors can earn on financial assets of similar risk. • Capital rationing implies that a firm does not have the resources necessary to fund all of the available projects. • It implies that funding needs exceed funding resources. • Thus, the available capital will be allocated to the set of projects that will benefit the firm and its shareholders the most.

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Net Present Value • Net present value is a capital budgeting technique that is consistent with the goal of maximizing shareholder wealth. • The method estimates the amount by which the benefits or cash flows from a project exceeds the cost of the project in present value terms. A. Valuation of Real Assets • Valuing real assets calls for the same steps as valuing financial assets. ▪ Estimate future cash flows. ▪ Determine the investor’s cost of capital or required rate of return. ▪ Calculate the present value of the future cash flows. • However, there are some practical difficulties in following the process for real assets. ▪ First, cash flow estimates have to be prepared in-house and are not readily available as they are for financial assets in legal contracts. ▪ Second, estimates of required rates of return are more difficult to determine than it is for financial assets because no market data is available for real assets. B. NPV—The Basic Concept • The present value of a project is the difference between the present value of the expected future cash flows and the initial cost of the project. • Accepting a positive NPV project leads to an increase in shareholder wealth, while accepting a negative NPV project leads to a decline in shareholder wealth. C. NPV and Value Creation D. Framework for Calculating NPV • The NPV technique uses the discounted cash flow technique. • Our goal is to compute the net cash flow (NCF) for each time period t, where NCFt = (Cash inflows – Cash outflows) for the period t. • A five-step approach can be utilized to compute the NPV. 1. Determine the cost of the project. ▪ Identify and add up all expenses related to the cost of the project. ▪ While we are mostly looking at projects whose entire cost occurs at the start of the project, we need to recognize that some projects may have costs occurring beyond the first year also. ▪ The cash flow in year 0 (NCF0) is negative, indicating a cost. 2. Estimate the project’s future cash flows over its expected life. ▪ Both cash inflows (CIF) and cash outflows are likely in each year of the project. Estimate the net cash flow (NCFt) = CIFt – COFt for each year of the project.

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▪

Remember to recognize any salvage value from the project in its terminal year (NCFt) = CIFt – COFt + SV. 3. Determine the riskiness of the project and the appropriate cost of capital. ▪ The cost of capital is the discount rate used in determining the present value of the future expected cash flows. ▪ The riskier the project, the higher the cost of capital for the project. 4. Compute the project’s NPV. ▪ Determine the difference between the present value of the expected cash flows from the project and the cost of the project. 5. Make a decision. ▪ Accept the project if it produces a positive NPV or reject the project if NPV is negative. E. Net Present Value Techniques F. Concluding Comments on NPV • Beware of optimistic estimates of future cash flows. • Recognize that the estimates going into calculating NPV are estimates and not market data. Estimates based on informed judgments are considered acceptable. • The NPV method of determining project viability is the recommended approach for making capital investment decisions. • The NPV decision criteria can be summed up as follows: Summary of Net Present Value (NPV) Method Decision Rule: NPV > 0: Accept the project. NPV < 0: Reject the project. Key Advantages Key Disadvantages 1. Uses the discounted cash flow 1. Difficult to understand without an valuation technique. accounting and finance background. 2. Provides a direct measure of how much a capital project will increase the value of the firm. 3. Consistent with the goal of maximizing shareholder wealth. 10.3

The Payback Period • The payback period is one of the most widely used tools for evaluating capital projects. • The payback period represents the number of years it takes for the cash flows from a project to recover the project’s initial investment. • A project is accepted if its payback period is below some pre-specified threshold.

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This technique can serve as a risk indicator—the more quickly you recover the cash, the less risky the project. A. Computing the Payback Period • To compute the payback period, we need to know the project’s cost and to estimate its future net cash flows. • Equation 10.2 shows how to compute the payback period. Remaining cost to recover PB = Years before cost recovery + Cash flow during the year • •

B. • • C. • • • • D. • • • • • • •

There is no economic rationale that links the payback method to shareholder wealth maximization. If a firm has a number of projects that are mutually exclusive, the projects are selected in order of their payback rank: projects with the lowest payback period are selected first. How the Payback Period Performs The payback period analysis can lead to erroneous decisions because the rule does not consider cash flows after the payback period. A rapid payback does not necessarily mean a good investment. See Exhibit 10.6—Projects D and E. Discounted Payback Period One weakness of the ordinary payback period is that it does not take into account the time value of money. The discounted payback period calculation calls for the future cash flows to be discounted by the firm’s cost of capital. The major advantage of the discounted payback is that it tells management how long it takes a project to reach a positive NPV. However, this method still ignores all cash flows after the arbitrary cutoff period, which is a major flaw. Evaluating the Payback Rule The standard payback period is widely used in business. It provides a simple measure of an investment’s liquidity risk. The greatest advantage of the payback period is its simplicity. It ignores the time value of money. It does not adjust or account for differences in the overall, or total, risk for a project, which could include operating, financing, and foreign exchange risk. The biggest weakness of either the standard or discounted payback methods is their failure to consider cash flows after the payback. The following table summarizes this capital budgeting technique.

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Summary of Payback Method Decision Rule: Payback period ≤ Payback cutoff point  Accept the project. Payback period > Payback cutoff point  Reject the project. Key Advantages Key Disadvantages 1. Easy to calculate and understand for 1. Most common version does not account people without strong finance for time value of money. backgrounds. 2. Does not consider cash flows past the 2. A simple measure of a project’s payback period. liquidity. 3. Bias against long-term projects such as research and development and new product launches. 4. Arbitrary cutoff point. 10.4

The Accounting Rate of Return • It is sometimes called the book rate of return. • This method computes the return on a capital project using accounting numbers—the project’s net income (NI) and book value (BV) rather than cash flow data. • The most common definition is the one given in Equation 10.3: Average NI ARR = Average BV •

10.5

It has a number of major flaws as a tool for evaluating capital expenditure decisions. ▪ First, the ARR is not a true rate of return. ARR simply gives us a number based on average figures from the income statement and balance sheet. ▪ It ignores the time value of money. ▪ There is no economic rationale that links a particular acceptance criterion to the goal of maximizing shareholders’ wealth.

Internal Rate of Return • The IRR is an important and legitimate alternative to the NPV method. • The NPV and IRR techniques are similar in that both depend on discounting the cash flows from a project. • When we use the IRR, we are looking for the rate of return associated with a project so we can determine whether this rate is higher or lower than the firm’s cost of capital. • The IRR is the discount rate that makes the NPV to equal zero. A. Calculating the IRR • The IRR is an expected rate of return, much like the yield to maturity calculation that was made on bonds. • We will need to apply the same trial-and-error method to compute the IRR.

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B. • •

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When the IRR and NPV Methods Agree The two methods will always agree when the projects are independent and the projects’ cash flows are conventional. After the initial investment is made (cash outflow), all the cash flows in each future year are positive (inflows).

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When the NPV and IRR Methods Disagree • The IRR and NPV methods can produce different accept/reject decisions if a project either has unconventional cash flows or the projects are mutually exclusive. 1. Unconventional Cash Flows ▪ Unconventional cash flows could follow several different patterns.  A positive initial cash flow followed by negative future cash flows.  Future cash flows from a project could include both positive and negative cash flows.  A cash flow stream that looks similar to a conventional cash flow stream except for a final negative cash flow. ▪ In these circumstances, the IRR technique can provide more than one solution. This makes the result unreliable and should not be used in deciding about accepting or rejecting a project. 2. Mutually Exclusive Projects ▪ When you are comparing two mutually exclusive projects, the NPVs of the two projects will equal each other at a certain discount rate. This point at which the NPVs intersect is called the crossover point. Depending on whether the required rate of return is above or below this crossover point, the ranking of the projects will be different. While it is easy to identify the superior project based on the NPV, one cannot do so based on the IRR. Thus, ranking conflicts can arise. ▪ A second situation arises when you compare projects with different costs. While IRR gives you a return based on the dollar invested, it does not recognize the difference in the size of the investments. NPV does. D. Modified Internal Rate of Return (MIRR) • A major weakness of the IRR compared to the NPV method is the reinvestment rate assumption. ▪ IRR assumes that the cash flows from the project are reinvested at the IRR, while the NPV assumes that they are invested at the firm’s cost of capital. ▪ This optimistic assumption in the IRR method leads to some projects being accepted when they should not be. • An alternative technique is the modified internal rate of return (MIRR). Here, each operating cash flow is reinvested at the firm’s cost of capital. • The compounded values are summed up to get the project’s terminal value. • The MIRR is the interest rate that equates the project’s cost to the terminal value at the end of the project. • Equation 10.5 shows how to calculate the MIRR.

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E. • •

• •

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IRR versus NPV: A Final Comment While the IRR has an intuitive appeal to managers because the output is in the form of a return, the technique has some critical problems. On the other hand, decisions made based on the project’s NPV are consistent with the goal of shareholder wealth maximization. In addition, the result shows management the dollar amount by which each project is expected to increase the value of the firm. For these reasons, the NPV method should be used to make capital budgeting decisions. The following table summarizes the IRR decision-making criteria.

Review of Internal Rate of Return (IRR) Decision Rule: IRR > Cost of capital  Accept the project. IRR < Cost of capital  Reject the project. Key Advantages Key Disadvantages 1. Intuitively easy to understand. 1. With nonconventional cash flows, IRR 2. Based on the discounted cash flow approach can yield no or multiple answers. technique. 2. A lower IRR can be better if a cash inflow is followed by cash outflows. 3. With mutually exclusive projects, IRR can lead to incorrect investment decisions. 4. IRR calculation assumes cash flows are reinvested at the IRR. 10.6

Investment Decisions with Capital Rationing If managers and investors agreed on which projects had positive NPVs, investors would provide capital to those projects because returns from them would be greater than the returns the investors could earn elsewhere in the capital markets; however the world is not ideal and firms often cannot invest in all of the available projects with positive NPVs.

A. Capital Rationing in a Single Period • Choosing the set of projects that creates the greatest value in a given period is to select the projects that yield the largest value per dollar invested. We can do this by computing the profitability index (equation 10.6) NPV + Initial Investment PI = Initial Investment B. Capital Rationing across Multiple Periods

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10.7

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You cannot rely solely on the PI if you are faced with capital rationing over several years since you must maximize the total NPV across all of the years in which you will be investing.

Capital Budgeting in Practice A. Practitioners’ Methods of Choice • Exhibit 10.14 summarizes surveys of practitioners on the capital budgeting methods of choice. • By 1981, over 65 percent of financial managers surveyed used the IRR, but only 16.5 percent of managers used the NPV. • In a recent study of Fortune 1000 managers, 74.9 percent of managers used the NPV while 75.7 percent used the IRR. Surprisingly, over 50 percent of managers used the payback method. B. Postaudit and Ongoing Reviews • Management should systematically review the status of all ongoing capital projects and perform postaudits on all completed capital projects. • In a postaudit review, management compares the actual results of a project with what was projected in the capital budgeting proposal. ▪ A postaudit examination would determine why the project failed to achieve its expected financial goals. • Managers should also conduct ongoing reviews of capital projects in progress. ▪ The review should challenge the business plan, including the cash flow projections and the operating cost assumptions. • Management must also evaluate people responsible for implementing a capital project.

Suggested and Alternative Approaches to the Material This chapter is about capital budgeting, a topic we first visited in Chapter 1. We open the chapter with a discussion of the types of capital projects that firms undertake and how the capital budgeting process is managed within the firm. Next we examine some of the techniques financial managers use to evaluate capital budgeting decisions. We first discuss the net present value (NPV) method, which is the capital budgeting approach recommended in this book. We then examine two other capital budgeting techniques that have some serious deficiencies with regard to selecting capital projects—the payback period and the accounting rate of return. These techniques do not consider the time value of money and can lead to decisions that decrease stockholders’ wealth.

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The fourth and last capital budgeting technique discussed in this chapter is the internal rate of return (IRR), which is the expected rate of return for a capital project. We close the chapter by looking at survey data that provide information on what capital budgeting techniques financial managers actually use when making capital decisions. The instructor can decide to take up the capital budgeting techniques in any order, although the authors’ intent is to emphasize the net present value as the best possible approach to capital budgeting decision making.

Summary of Learning Objectives 1.

Discuss why capital budgeting decisions are the most important investment decisions made by a firm’s management. Capital budgeting is the process by which management decides which productive assets the firm should invest in. Because capital expenditures involve large amounts of money, are critical to achieving the firm’s strategic plan, define the firm’s line of business over the long term, and determine the firm’s profitability for years to come, they are the most important investment decisions made by management.

Explain the benefits of using the net present value (NPV) method to analyze capital expenditure decisions, and calculate the NPV for a capital project. The net present value (NPV) method leads to better investment decisions than other techniques because it: (1) uses the discounted cash flow valuation approach, which accounts for the time value of money, and (2) provides a direct measure of how much a capital project is expected to increase the dollar value of the firm. Thus, NPV is consistent with the top management goal of maximizing stockholders value. NPV calculations are described in Section 10.2 and Learning by Doing Application 10.1.

Describe the strengths and weaknesses of the payback period as a capital expenditure decision-making tool and compute the payback period for a capital project. The payback period is the length of time it will take for the cash flows from a project to recover the cost of the project. The payback period is widely used, mainly because it is simple to apply and easy to understand. It also provides a simple measure of liquidity risk because it tells management how quickly the firm will get its money back. The payback period has a number of shortcomings, however. For one thing, the payback period, as most commonly computed, ignores the time value of money. We can overcome this objection by using discounted cash flows to calculate the payback period. Regardless of how the payback period is calculated, however, it fails to take account of cash flows recovered after the payback period. Thus, the payback period is biased in favor of short-

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lived projects. Also, the hurdle rate used to identify what payback period is acceptable is arbitrarily determined. Payback period calculations are described in Section 10.3 and Learning by Doing Application 10.2. 4.

Explain why the accounting rate of return (ARR) is not recommended as a capital expenditure decision-making tool. The ARR is based on accounting numbers, such as book value and net income, rather than cash flow data. As such, it is not a true rate of return. Instead of discounting a project’s cash flows over time, it simply gives us a number based on average figures from the income statement and balance sheet. Furthermore, as with the payback method, there is no economic rationale for establishing the hurdle rate. Finally, the ARR does not account for the size of the projects when a choice between two projects of different sizes must be made.

Compute the internal rate of return (IRR) for a capital project and discuss the conditions under which the IRR technique and the NPV technique produce different results. The IRR is the expected rate of return for an investment project; it is calculated as the discount rate that equates the present value of a project’s expected cash inflows to the present value of the project’s outflows—in other words, as the discount rate at which the NPV is equal to zero. Calculations are shown in Section 10.5 and Learning by Doing Application 10.3. If a project’s IRR is greater than the required rate of return, the cost of capital, the project is accepted. The IRR rule often gives the same investment decision for a project as the NPV rule. However, the IRR method does have operational pitfalls that can lead to incorrect decisions. Specifically, when a project’s cash flows are unconventional, the IRR calculation may yield no solution or more than one IRR. In addition, the IRR technique cannot be used to rank projects that are mutually exclusive because the project with the highest IRR may not be the project that would add the greatest value to the firm if accepted—that is, the project with the highest NPV.

Explain how the profitability index can be used to rank projects when a firm faces capital rationing and describe the limitations that apply to the profitability index. The profitability index (PI) aids in the process of choosing the most valuable bundle of projects that the firm can afford. It is a measure of value received per dollar invested, which can be used to rank projects in a given period. The major limitation of the PI is that, although it can be used to rank projects in a given period, it can lead to misleading project choices in a multiperiod context.

Explain the benefits of postaudit and ongoing reviews of capital projects.

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A postaudit review enables managers to determine whether a project’s goals were met and to quantify the actual benefits or costs of the project. By conducting these reviews, managers can avoid making similar mistakes in future projects, learn to better recognize opportunities, and keep people involved in the budgeting process honest. An ongoing review enables managers to assess the impact of changing information and market conditions on the value of a project that is already underway. Unexpected changes in conditions can affect the viability of continuing such a project as originally conceived.

Summary of Key Equations Equation

Description

Formula

NPV = NCF0 + 10.1

NCF1 NCF2 NCFn + +  + 1 2 (1 + k ) (1 + k ) (1 + k ) n

Net present value

NCFt t t =0 (1 + k ) n

= 10.2

Payback period

PB = Years before cost recovery +

10.3

Average rate of return

ARR =

10.4

Internal rate of return

NPV = 

Remaining cost to recover Cash flow during the year

Average Net Income Average Book Value n

t =0

NCFt =0 (1+IRR) t

10.5

Modified internal rate of return

PVCost = TV/ (1 + MIRR)n

10.6

Profitability Index

PI = (NPV + Initial Investment) / Initial Investment

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Chapter 11 Cash Flows and Capital Budgeting Learning Objectives 1. Explain why incremental after-tax free cash flows are relevant in evaluating a project and calculate them for a project. 2. Discuss the five general rules for incremental after-tax free cash flow calculations and explain why cash flows stated in nominal (real) dollars should be discounted using a nominal (real) discount rate. 3. Describe how distinguishing between variable and fixed costs can be useful in forecasting operating expenses. 4. Explain the concept of equivalent annual cost and use it to compare projects with unequal lives. 5. Determine the appropriate time to harvest an asset.

Chapter Outline 11.1

Calculating Project Cash Flows • All of the cash flow estimates are forward-looking. • In this chapter we are interested in the expected cash flows of a project rather than that of the entire firm, as in Chapter 3. A. Incremental After-Tax Free Cash Flows • The cash flows we discount in an NPV analysis are the incremental after-tax free cash flows, which refers to the fact that these cash flows reflect the amount by which the firm’s total after-tax free cash flows will change if the project is adopted. See Equation 11.1: o FCFProject = FCFFirm with project – FCFFirm without project • The term free cash flows (FCF) refers to the fact that the firm is free to distribute these cash flows to creditors and stockholders because these are the cash flows that are left over after a firm has made necessary investments in working capital and long-term assets. B. The FCF Calculation • Referring to 10.2, which is a more detailed version of 11.1: FCF = [(Revenue – Op Exp – D&A) x (1 – t)] + D&A – Cap Exp – Add WC

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•

E. F.

We first compute the incremental cash flow from operations (CF Opns), which is the cash flow that the project is expected to generate after all operating expenses and taxes have been paid. • We then subtract the incremental capital expenditures (Cap Ex) and incremental additions to working capital (Add WC) required for the project to obtain FCF. • The FCF is therefore a measure of the after-tax cash flows from operations over and above what is necessary to make any required investments. • The idea that we can evaluate the cash flows from a project independently of the cash flows for the firm is known as the stand-alone principle. It is another way of saying that we can treat the project as if it is a stand-alone firm that has its own revenue, expenses, and investment requirements. Cash Flows from Operations • Note that the incremental cash flow from operations, CF Opns, equals the incremental net operating profits after tax (NOPAT) plus the incremental depreciation and amortization (D&A) associated with the project. • We exclude interest expenses when calculating NOPAT because the cost of financing a project is reflected in the discount rate that is used in the NPV calculation. • We use the firm’s marginal tax rate (t) to calculate NOPAT because the profits from a project are assumed to be incremental to the firm. • We add incremental depreciation and amortization (D&A) to NOPAT when calculating CF Opns because, as in the accounting statement of cash flows, D&A represents a noncash charge that reduces the firm’s tax obligation. • However, since D&A is a noncash charge, we have to add it back to NOPAT in order to get the cash flow from operations right. Cash Flows Associated with Capital Expenditures and Net Working Capital • Once we have estimated CF Opns, we simply subtract cash flows associated with required investment to obtain FCF for a project in a particular period. • Investments can be required to purchase long-term tangible assets and intangible assets, or to fund current assets. The FCF Calculation: An Example FCF versus Accounting Earnings • The impact of a project on a firm’s overall value or on its stock price does not depend on how the project affects the company’s accounting earnings. It depends only on how the project affects the company’s free cash flows. • Accounting earnings can differ from cash flows for a number of reasons, making accounting earnings an unreliable measure of the costs and benefits of a project.

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Accounting earnings also reflect noncash charges, such as depreciation and amortization, which are intended to account for the costs associated with deterioration of the assets in a business as those assets are used.

Estimating Cash Flows in Practice A. Five General Rules for Incremental After-Tax Free Cash Flow Calculations • Rule 1: Include cash flows and only cash flows in your calculations. Do not include allocated costs or overhead unless they reflect cash flows. • Rule 2: Include the impact of the project on cash flows from other product lines. If the product associated with a project is expected to affect sales of another product, you must include the expected impact of the new project on the cash flows from the other product in the analysis. • Rule 3: Include all opportunity costs. By opportunity costs, we mean the cost of giving up another opportunity. • Rule 4: Forget sunk costs. Sunk costs are costs that have already been incurred, but all that matters when you evaluate a project at a particular point in time is how much you have to invest in the future and what you could expect to receive in return for that investment; this means that past investments are irrelevant. • Rule 5: Include only after-tax cash flows in the cash flow calculations. The incremental pretax earnings of a project only matter to the extent that they affect the after-tax cash flows that the firm’s investors receive. B. Nominal versus Real Cash Flows • Nominal dollars are the dollars that we typically think of. They represent the actual dollar amounts that we expect a project to generate in the future, without any adjustments. • When prices are going up, a given nominal dollar amount will buy less and less over time. o Real dollars represent dollars stated in terms of constant purchasing power. • We can write the cost of capital , k, as o 1 + k = (1 + ∆Pe) x (1 + r) ▪ r is the real cost of capital ▪ (∆Pe) is the expected rate of inflation ▪ (r) is the real rate of return • It is important to make sure that all cash flows are stated in either nominal dollars or real dollars. C. Tax Rates and Depreciation

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•

A progressive tax system, which we have in the United States, is one in which the marginal tax rate at low levels of income is lower than the marginal tax rate at high levels of income. • One especially important difference from a capital budgeting perspective is that the depreciation methods allowed by GAAP differ from those allowed by the IRS. o The straight-line depreciation method illustrated earlier in this chapter in the example is allowed by GAAP and is often used for financial reporting. o An “accelerated” method of depreciation, called the Modified Accelerated Cost Recovery System (MACRS), has been in use for U.S. federal tax calculations since the Tax Reform Act of 1986 went into effect. ▪ MACRS thus enables a firm to deduct depreciation charges sooner, thereby realizing the tax savings sooner and increasing the present value of the tax savings. Computing the Terminal-Year FCF • The FCF in the last, or terminal, year of a project often includes cash flows that are not typically included in the calculations for other years. o For instance, in the final year of a project, the assets acquired during the life of the project may be sold and the working capital that has been invested may be recovered. ▪ Add WC = Change in cash and cash equivalents + Change in accounts receivable + Change in inventories – Change in accounts payable. o When an asset is expected to have a salvage value, we must include the salvage value realized from the sale (net of any tax consequences) of the asset and the impact of the sale on the firm’s taxes in the terminal-year FCF calculations. Expected Cash Flows • We are estimating when we forecast FCF in an NPV analysis. o The expected FCF for a particular year equals the sum of the products of the possible outcomes (FCFs) and the probabilities that those outcomes will be realized.

11.3 Forecasting Free Cash Flows A. Cash Flows from Operations • To forecast incremental cash flows from operations we must forecast the incremental net revenue, operating expenses, and depreciation and Copyright ©2015 John Wiley & Sons, Inc.

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amortization associated with the project, as well as the firm’s marginal tax rate. • When forecasting operating expenses, analysts often distinguish between variable costs and fixed costs. Cash Flows Associated with Capital Expenditures and Net Working Capital • We must consider two general classes of investments when calculating FCF: incremental capital expenditures and incremental additions to working capital. 1. Capital Expenditures o Capital expenditure forecasts in an NPV analysis reflect the expected level of investment during each year of the project’s life. o Capital expenditures are typically required at the beginning of a project. 2. Working Capital o Cash flow forecasts in an NPV analysis include four working capital items: 1) cash and cash equivalents, 2) accounts receivable, 3) inventories, and 4) accounts payable.

Special Cases A. Projects with Different Lives • A problem that arises quite often in capital budgeting involves choosing between two mutually exclusive investments where the investments have different lives. o In a situation like this, we can effectively make the lives of projects the same by assuming repeated investments over some identical period and then comparing the NPVs of their costs. o A less cumbersome and more powerful method to handle the problem is to compute the equivalent annual cost (EAC). The EAC can be calculated as follows: EACi = kNPVi [(1 + k)t / (1 + k)t – 1]

(11.5)

 (1 + k )  EACi = k NPVi   t  (1 + k ) −1 t

▪ ▪ ▪ ▪ ▪

k is the opportunity cost of capital NPVi is the normal NPV of the investment i t is the life of the investment EAC simply reflects the annuity that has the same present value as the ∆FCFs of an investment over the investment period we are considering.

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When to Harvest an Asset • A problem that arises from time to time involves deciding when to harvest an investment. o Harvesting is put off as long as the asset is earning a return that is greater than or equal to the opportunity cost of capital.

When to Replace an Existing Asset • Managers may be asked to determine the appropriate time to replace an existing piece of equipment that tis still operating.. o The proper question is whether the benefits of replacing the existing machine exceed the costs, and if they do not now, when twill they. o The Equivalent Annual Cost, similar to the Equivalent Annual Annuity, method is used to make that analysis.

Suggested and Alternative Approaches to the Material This is a very important chapter for all students. Finance majors will need the basic capital budgeting concepts introduced here for their more advanced course work, whereas non-majors will require a basic foundation for the material in their professional lives as they will undoubtedly be involved in project analysis at some point in their careers. The chapter begins with a general framework for capital budgeting, so that the overall approach to capital budgeting can be seen before proceeding to the detailed aspects of the subject matter. Free cash flow (FCF) is then formally introduced, along with individual subcalculations that make it up. The chapter includes a number of examples to accompany the individual aspects of the material and finishes by introducing cases where the net present value of the projects FCFs will require further adjustments. Thorough coverage of the material is recommended before proceeding to the next chapter where the tools are then applied further. As such, it may be necessary to allocate additional time for this chapter as the material is central to finance while it also incorporates a number of tools that were learned in earlier chapters.

Summary of Learning Objectives 1. Explain why incremental after-tax cash flows are relevant in evaluating a project and calculate them for a project.

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The incremental after-tax free cash flows, FCFs, for a project equal the expected change in the total after-tax cash flows of the firm if the project is adopted. The impact of a project on the firm’s total cash flows is the appropriate measure of cash flows because these are the cash flows that reflect all of the costs and benefits from the project and only the costs and benefits from the project. The incremental after-tax free cash flows are calculated using Equation 11.2. This calculation is also illustrated in Exhibit 11.1. 2. Discuss the five general rules for incremental after-tax free cash flow calculations and why cash flows stated in nominal (real) dollars should be discounted using a nominal (real) discount rate. The five general rules are: Rule 1: Include cash flows and only cash flows in your calculations. Stockholders only care about the impact of a project on the firm’s cash flows. Rule 2: Include the impact of the project on cash flows from other product lines. If a project affects the cash flows from other projects, we must take this fact into account in NPV analysis in order to fully capture the impact of the project on the firm’s total cash flows. Rule 3: Include all opportunity costs. If an asset is used for a project, the relevant cost for that asset is the value that could be realized from its most valuable alternative use. By including this cost in the NPV analysis, we capture the change in the firm’s cash flows that is attributable to the use of this asset for the project. Rule 4: Forget sunk costs. The only costs that matter are those to be incurred from this point on. Rule 5: Include only after-tax cash flows in the cash flow calculations. Since stockholders receive cash flows after taxes have been paid, they are only concerned about aftertax cash flows. Since a nominal discount rate reflects both the expected rate of inflation and the real return, we would be overadjusting for inflation if we discounted a real cash flow with a nominal rate. Similarly, if we discounted a nominal cash flow using a real discount rate, we would be undercompensating for expected inflation in the discounting process. This is why we discount nominal cash flows using only a nominal discount rate and we discount real cash flows using only a real discount rate. 3. Describe how distinguishing between variable and fixed costs can be useful in forecasting operating expenses. Variable costs vary directly with the number of units sold, while fixed costs do not. When forecasting operating expenses, it is often useful to treat variable and fixed costs separately. We can forecast variable costs by multiplying unit variable costs by the number of units sold. Fixed costs are more accurately based on the specific characteristics of those costs, rather

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than as a function of sales. Separating fixed costs from the variable also makes it easier to identify the factors that will cause them to change over time and therefore easier to forecast them. 4. Explain the concept of equivalent annual cost and use it to compare projects with unequal lives. The equivalent annual cost (EAC) is the annualized cost of an investment that is stated in nominal dollars. In other words, it is the annual payment from an annuity that has the same NPV and the same life as the project. Since it is a measure of the annual cost or cash inflow from a project, the EAC for one project can be compared directly with the EAC from another project, regardless of the lives of those two projects. Application of the EAC concept is illustrated in Section 11.4. 5. Determine the appropriate time to harvest an asset.. The appropriate time to harvest an asset is that point in time where harvesting the asset yields the largest present value, in today’s dollars, of the project NPV.

Summary of Key Equations Equation

Description

Formula

11.1

Incremental free cash flow definition

FCFProject = FCFFirm with project – FCFFirm without project

11.2

Incremental free cash flow calculation

FCF = [(Revenue – Op Exp – D&A) x (1 – t)] + D&A – Cap Exp – Add WC

11.3

11.4

Inflation and real components of cost of capital

Incremental additions to working capital Equivalent annual cost

11.5

1 + k = (1 + ∆Pe) x (1 + r)

Add WC = Change in cash and cash equivalents + Change in accounts receivable + Change in inventories – Change in accounts payable.

 (1 + k ) t  EACi = k NPVi   t  (1 + k ) −1

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Chapter 12 Evaluating Project Economics

Learning Objectives 1. Explain and demonstrate how variable costs and fixed costs affect the volatility of pretax operating cash flows and accounting operating profits. 2. Calculate and distinguish between the degree of pretax cash flow operating leverage and the degree of accounting operating leverage. 3. Define and calculate the pretax operating cash flow and accounting operating profit break-even points and the crossover levels of unit sales for a project. 4. Define the economic break-even point and be able to calculate it for a project. 5. Define sensitivity analysis, scenario analysis, and simulation analysis and describe how they are used to evaluate the risks associated with a project.

Chapter Outline

12.1

Variable Costs, Fixed Costs, and Project Risk •

Variable costs (VC) are costs that vary directly with the number of units sold.

•

Fixed costs (FC), in contrast, do not vary with unit sales in the short run.

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The cash flows and accounting profits for a project are sensitive to the proportion of its costs that are variable and the proportion that are fixed.  A project with a higher proportion of fixed costs will have cash flows and accounting profits that are more sensitive to changes in revenues than an otherwise identical project with a lower proportion of fixed costs.

•

EBITDA is often called pretax operating cash flow because it equals the incremental pretax cash operating profits from a project.  EBITDA = Revenue – VC – FC  Op Ex = VC + FC

Cost Structure and Sensitivity of EBITDA and EBIT to Revenue Changes

•

By comparing the sensitivity of EBITDA to changes in revenue between two project alternatives, it may help to better understand the risks and returns for each of the alternatives.  Distinguishing between fixed and variable costs will then enable us to calculate the sensitivity of EBITDA to changes in revenue. ▪

The greater the proportion that total costs are fixed will make it more difficult to adjust costs when revenue changes.

 EBIT is more sensitive to changes in revenue than EBITDA because the EBITDA does not include depreciation and amortization. ▪

Depreciation and amortization acts just like a fixed cost because it is based on the amount that was invested in the project.

12.2

Calculating Operating Leverage

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Operating leverage is a measure of the sensitivity of EBITDA or EBIT to changes in revenue.

•

Two measures of operating leverage are often used by analysts: the degree of pretax cash flow operating leverage and the degree of accounting operating leverage.

Degree of Pretax Cash Flow Operating Leverage •

The degree of pretax cash flow operating leverage (Cash Flow DOL) provides us with a measure of how sensitive pretax operating cash flows are to changes in revenue.

Fixed Costs FC = 1+ . Pretax Operating Cash Flows EBITDA

▪

Cash Flow DOL = 1 +

▪

Cash Flow DOL changes with the level of revenue; the sensitivity of operating cash flows is not the same for all levels of revenue.

Degree of Accounting Operating Leverage •

The degree of accounting operating leverage (Accounting DOL) is a measure of how sensitive accounting operating profits, EBIT, are to changes in revenue.

Accounting DOL = 1 +

Fixed Charges Accounting Operating Profits

=1+

FC + D&A EBITDA - D&A

=1+

FC + D&A . EBIT

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o D&A is treated as a fixed cost and is added to FC to obtain the total of the cash and noncash fixed costs that would be reflected in the income statement if the project were adopted.

12.3 •

Break-Even Analysis Break-even analysis tells us how many units must be sold in order for a project to break even on a cash flow or accounting profit basis.

Pretax Operating Cash Flow Break-Even The pretax operating cash flow (EBITDA) break-even point is calculated as follows: o

EBITDA Break-Even =

▪

FC Price - Unit VC

Simply divide the fixed costs, FC, by the per-unit contribution (Price – Unit VC).

o The cross-over level of unit sales (CO) is calculated as follows:

COEBITDA =

FCAlternative1 - FC Alternative2 Unit Contribution Alternative1 - Unit Contribution Alternative2

where Unit contribution stands for the per-unit contribution. ▪

When using the above formula, make sure that the smaller value of FC is in the second term in the numerator since putting the smaller number first will usually give you a negative answer.

Accounting Break-Even •

The accounting operating profit (EBIT) break-even point is calculated as:

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EBIT Break-Even =

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FC + D&A . Price - Unit VC

o When we calculate the accounting operating profit break-even point, we are calculating how many units must be sold to avoid an accounting operating loss. 12.4

The Economic Break-Even Point A.

The Economic break-even point is a more comprehensive break-even measure that can help a financial manager assess the overall economic viability of a project. ▪

The measure tells how low unit sales can get before a project destroys stockholder value.

▪

It considers the entire life of a project, rather than a single year while it focuses on the after-tax free cash flows associated with the project.

▪

The steps to calculate the economic break-even point are: •

Step 1: Identify the present value of the net non-recurring investments in real assets and working capital that are required for the project and use that value to calculate the annual incremental after-tax free cash flow (FCF) that would make the project NPV = $0, then

•

Step 2: Use the FCF formula to solve for the EBIT that corresponds to the step 1 value, then

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Step 3: Add the EBIT in step 2 to the annual Depreciation and Amortization and Fixed Costs. This will give you the annual total contribution, then

•

Step 4: Divide the annual total contribution margin, in step 3, by the unit contribution to obtain the number of units that would have to be sold annually for the project to have an NPV = $0.

12.5

Risk Analysis A.

Sensitivity analysis involves examining the sensitivity of the output from an analysis, such as the NPV estimate, to changes in individual assumptions. ▪

In a sensitivity analysis, an analyst might examine how a project’s NPV changes if there is a decrease in the value of individual cash inflow assumptions or an increase in the value of individual cash outflow assumptions.

Scenario analysis will be performed if one wants to examine how the results from a financial analysis will change under alternative scenarios. ▪

A scenario might describe how a set of project inputs might be different under different economic conditions.

▪

By comparing the range of NPVs provided by the different scenarios, it is possible to understand how much uncertainty is associated with an NPV estimate.

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Simulation analysis is like scenario analysis except that in simulation analysis, an analyst typically uses a computer to examine a large number of scenarios in a short period of time. ▪

Rather than selecting individual values for each of the assumptions—such as unit sales, unit price, and unit variable costs—the analyst assumes that those assumptions can be represented by statistical distributions.

▪

A computer program then calculates the cash flows associated with a large number of scenarios by repeatedly drawing numbers for the distributions for various assumptions, plugging them into the cash flow model, and computing the annual cash flows and then the NPV.

▪

In addition to providing an estimate of the expected cash flows, simulation analysis gives information on the distribution of the cash flows that the project is likely to produce in each year.

II. Suggested and Alternative Approaches to the Material The focus of Chapter 12 is on the nonfinancially related or operational risks to the firm—that is, the risks that arise primarily due to the cost structure of the firm rather than the level of debt that the firm relies on to finance its assets. A large portion of the chapter is allocated to understanding the effects of operating leverage on a firm’s break-even as well as the concept of variability within the estimated revenues, costs, and consequently the net cash flows produced by a project or the firm. The chapter begins with a descriptive understanding of variable and fixed costs. A more formal understanding of a firm’s cost structure is then discussed within an operating Copyright ©2015 John Wiley & Sons, Inc.

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leverage framework where the impact of revenue changes can be evaluated for EBIT or EBITDA. That understanding is then used to calculate a firm’s unit break-even from cash, as well as from an accounting perspective. Those ideas are then used to forecast the impact of input changes on cash flow by using sensitivity, scenario, and simulation analysis. The chapter then concludes with a discussion on capital rationing within capital budgeting decisions. A good portion of the chapter contains material that should be familiar to students who have completed a managerial accounting course. Therefore the chapter may provide the students some comfortable ground before they proceed with later chapters, which tend to have a theoretical basis.

III. Summary of Learning Objectives 1. Explain and demonstrate how variable costs and fixed costs affect the volatility of pretax operating cash flows and accounting operating profits. Because the fixed costs associated with a project do not change as revenue changes, fluctuations in revenue are magnified so that pretax operating cash flows and accounting operating profits fluctuate more than revenue in percentage terms. The greater the proportion of total costs that are fixed, the more the fluctuations in revenue will be magnified. To demonstrate this, you can perform calculations like those in the hammock-manufacturing example and in Learning by Doing Applications 12.1 and 12.2.

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2. Calculate and distinguish between the degree of pretax cash flow operating leverage and the degree of accounting operating leverage. The degree of pretax cash flow operating leverage is a measure of how much pretax operating cash flow will change in relation to a change in revenue. Similarly, the accounting degree of operating leverage is a measure of how much accounting operating profits will change in relation to a change in revenue. The only difference between cash flow operating leverage and accounting operating leverage is that the accounting measure treats incremental depreciation and amortization charges as a fixed cost in the calculation. These charges are excluded from the cash flow operating leverage measure because they do not reflect actual cash expenses and, therefore, do not affect pretax cash flows. Equations 12.2 and 12.3 are used to calculate these two measures.

3. Define and calculate the pretax operating cash flow and accounting operating profit break-even points and the crossover levels of unit sales for a project. The pretax operating cash flow break-even point is the number of units that must be sold in a particular year to break even on a pretax operating cash flow basis. It is calculated using Equation 12.4. The accounting operating profit break-even point is the number of units that must be sold in a particular year to break even on an accounting operating profit basis. A project breaks even on an accounting operating profit basis when it produces exactly $0 in incremental operating profits, EBIT. It is calculated using Equation 12.6.

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The crossover level of unit sales is the level of unit sales at which the pretax operating cash flows or accounting operating profits for one project alternative switches from being lower than that of another alternative to being higher. The EBITDA and EBIT crossover levels of unit sales are calculated using Equations 12.5 and 12.7, respectively.

4. Define the economic break-even point and be able to calculate it for a project. The economic break-even point is the number of units that must be sold each year during the life of a project so that the NPV of the project equals $0. Section 12.4 illustrates how the economic break-even point is calculated.

5. Define sensitivity analysis, scenario analysis, and simulation analysis and describe how they are used to evaluate the risks associated with a project. Sensitivity analysis is concerned with how sensitive the output from a financial analysis, such as the NPV, is to changes in an individual assumption. It helps identify which assumptions have the greatest impact on the output and therefore on the value of a project. Knowing this helps an analyst identify which assumptions are especially important to that analysis. Scenario analysis is used to examine how the output from a financial analysis changes under alternative scenarios. This type of analysis recognizes that changing economic and market conditions affect more than one variable at a time and tries to account for how each of the different variables will change under alternative scenarios. Simulation analysis is like scenario analysis except that in simulation analysis a computer is used to examine a large number of scenarios in a short period of time. Copyright ©2015 John Wiley & Sons, Inc.

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IV. Summary of Key Equations Equation

12.1

12.2

12.3

12.4

12.5

12.6

12.7

Description

Formula

Op Ex in terms of incremental variable and fixed costs

Op Ex = VC + FC

Degree of pretax cash flow operating leverage Degree of accounting operating leverage

Cash Flow DOL = 1 +

FC EBITDA

Accounting DOL = 1 +

FC + D&A EBIT

Pretax operating cash flow (EBITA) break-even point

EBITDA Break-Even =

FC Price - Unit VC

Crossover level of unit sales for EBITDA

COEBITDA =

Accounting operating profit (EBIT) break-even point Crossover level of unit sales for EBIT

FCAlternative1 - FC Alternative2 Unit Contribution Alternative1 - Unit Contribution Alternative2

EBIT Break-Even =

COEBIT =

FC + D&A Price - Unit VC

(FC+ D&A)Alternative1 -(FC + D&A)Alternative 2 (Unit Contribution Alternative1 - Unit Contribution Alternative 2 )

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Chapter 13 The Cost of Capital

Learning Objectives 1.

Explain what the weighted average cost of capital for a firm is and why it is often used as a discount rate to evaluate projects.

Calculate the cost of debt for a firm.

Calculate the cost of common stock and the cost of preferred stock for a firm.

Calculate the weighted average cost of capital for a firm, explain the limitations of using a firm’s weighted average cost of capital as the discount rate when evaluating a project, and discuss the alternatives to the firm’s weighted average cost of capital.

Chapter Outline

13.1

The Firm’s Overall Cost of Capital •

Since unsystematic risk can be eliminated by holding a diversified portfolio, systematic risk is the only risk that investors require compensation for bearing.

•

We concluded in Chapter 7 that we could rely on the CAPM to arrive at the expected rate of return for a particular investment. •

In this chapter, we address the practical concerns that can make that concept difficult to implement. ▪

Firms do not issue publicly traded shares for individual projects.

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As a result, firms have no way to directly estimate the discount rate that reflects the risk of the incremental cash flows from a particular project.

▪

Financial managers deal with this problem by estimating the cost of capital for the firm as a whole and then requiring analysts within the firm to use this cost of capital to discount the cash flows for all projects. o

A problem with this approach is that it ignores the fact that a firm is really a collection of projects with varying levels of risk.

The Finance Balance Sheet •

The finance balance sheet is based on market values rather than book values. ▪

The total book value of the assets reported on an accounting balance sheet does not necessarily reflect the total market value of those assets since the book value is largely based on historical costs, while the total market value of the assets equals the present value of the total cash flows that those assets are expected to generate in the future.

•

The left-hand side of the accounting balance sheet reports the book values of a firm’s assets, while the right-hand side reports how those assets were financed.

•

The value of the claims that investors hold must equal the value of the cash flows that they have a right to receive. ▪

This is because the total market value of the debt and the equity at a firm equals the present value of the cash flows that the debt holders and the stockholders have the right to receive. o

The people who have lent money to a firm and the people who have purchased the firm’s stock have the right to receive all of

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the cash flows that the firm is expected to generate in the future. • B.

MV of assets = MV of liabilities + MV of equity How Firms Estimate Their Cost of Capital ▪

If analysts at a firm could estimate the betas for each of the firm’s individual projects, they could estimate the beta for the entire firm as a weighted average of the betas for the individual projects. o

Unfortunately, because analysts are not typically able to estimate betas for individual projects, they generally cannot use this approach.

Instead, analysts must use their knowledge of the finance balance sheet, along with the concept of market efficiency, to estimate the cost of capital for the firm.

▪

Rather than perform the calculations for the individual projects represented on the left-hand side of the finance balance sheet, analysts perform a similar set of calculations for the different types of financing (debt and equity) on the right-hand side of the finance balance sheet. o

As long as they can estimate the cost of each type of financing by observing that cost in the capital markets, they can compute the cost of capital for the firm by using the following equation: n

kFirm =  xi ki = x1k1 + x2k2 + x3k3 + i =1

+ xn kn

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If we divide the costs of capital into debt and equity portions of the firm, then we can use the above to arrive at the weighted average cost of capital (WACC) for the firm:

kFirm = xDebtkDebt + xEquitykEquity

13.2

The Cost of Debt •

Analysts often cannot directly observe the rate of return that investors require for a particular type of financing and instead must rely on the security prices they can observe in the financial markets to estimate that required rate. o It makes sense to rely on security prices only if you believe that the financial markets are reasonably efficient at incorporating new information into these prices. o If the markets were not efficient, estimates of expected returns that were based on market security prices would be unreliable.

Key Concepts for Estimating the Cost of Debt ▪

With regard to the cost associated with each type of debt that a firm uses when we estimate the cost of capital for a firm, we are particularly interested in the cost of the firm’s long-term debt. •

When we refer to debt we usually mean the debt that, when it was borrowed, was set to mature in more than one year.

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Debt with a maturity of more than one year can typically be viewed as permanent debt because firms often borrow the money to pay off this debt when it matures.

▪

The cost of a firm’s long-term debt is estimated on the date on which the analysis is done. •

This is important because the interest rate (or historical interest rate determined at the time of original debt issuance) that the firm is paying on its outstanding debt does not necessarily reflect its current cost of debt.

▪

The current cost of long-term debt is the appropriate cost of debt for WACC calculations. •

This is the relevant cost because the WACC is the opportunity cost of capital for the firm’s investors as of today.

Estimating the Current Cost of a Bond or an Outstanding Loan •

The current cost of debt for a publicly traded bond is the yield-to-maturity calculation. o To estimate this cost, we first convert the bond data to reflect semiannual compounding as well as account for the effective annual interest rate (EAR) to account for the actual current annual cost of the debt. ▪

We must also account for the cost of issuing the bond— issuance costs using the net proceeds that the company receives for the bond rather than the price that is paid by the investor.

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For the current cost of long-term bank or other private debt, the firm may simply call its banker and ask what rate the bank would charge if it decided to refinance the debt today.

Taxes and the Cost of Debt •

Firms can deduct interest payments for tax purposes.

•

The after-tax cost of interest payments equals the pretax cost times 1 minus the tax rate: kDebt after-tax = kDebt pretax  (1 – t)

Estimating the Cost of Debt for a Firm •

To estimate the firm’s overall cost of debt when it has several debt issues outstanding, we must first estimate the costs of the individual debt issues and then calculate a weighted average of these costs.

13.3

The Cost of Equity •

The cost of equity for a firm is a weighted average of the costs of the different types of stock that the firm has outstanding at a particular point in time.

Common Stock o Just as information about market rates of return is used to estimate the cost of debt, market information is also used to estimate the cost of equity. ▪

There are several ways to do this, and the most appropriate approach will depend on what information is available and how reliable the analyst believes it is.

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o The text discusses three alternative methods for estimating the cost of common stock. o Method 1: Using the Capital Asset Pricing Model (CAPM) ▪

Using the CAPM equation, E(Ri) = Rrf + βi[E(Rm) – Rrf], we find that the cost of common stock equals the risk-free rate of return plus compensation for the systematic risk associated with the common stock.

▪

Some practical considerations must be considered when choosing the appropriate risk-free rate, beta, and market risk premium for the above calculation. •

The recommended risk-free rate to use is the risk-free rate on a long-term Treasury security because the equity claim is a longterm claim on the firm’s cash flows. o A long-term risk-free rate better reflects long-term inflation expectations and the cost of getting investors to part with their money for a long period of time than a short-term rate.

•

You can estimate the beta for that stock using a regression analysis. o Identifying the appropriate beta is much more complicated if the common stock is not publicly traded.

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o This problem may be overcome by identifying a “comparable” company with publicly traded stock that is in the same business and that has a similar amount of debt. o When a good comparable company cannot be identified, it is sometimes possible to use an average of the betas for the public firms in the same industry. •

It is not possible to directly observe the market risk premium since we don’t know what rate of return investors expect for the market portfolio. o For this reason, financial analysts generally use a measure of the average risk premium investors have actually earned in the past as an indication of the risk premium they might require today. o From 1926 through the end of 2012, actual returns on the U.S. stock market exceeded actual returns on long-term U.S. government bonds by an average of 5.71 percent per year. ▪

If a financial analyst believes that the market risk premium in the past is a reasonable estimate of the risk premium today, then he or she might use 5.71 percent (or a value close to it) as the market risk premium for the future.

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o Method 2: Using the Constant-Growth Dividend Model ▪

Using Equation 9.4, P0 =

D1 , we can rearrange to solve for R—or kcs as R-g

we now prefer to call it: kcs =

▪

D1 +g P0

In order to solve for the cost of common stock, we must estimate the dividend that stockholders will receive next period, D1, as well as the rate at which the market expects dividends to grow over the long run, g.

▪

This approach is useful for a firm that pays dividends that will grow at a constant rate. •

This approach might be consistent for an electric utility but not for a fast growing high-tech firm.

o Method 3: Using a Multistage-Growth Dividend Model ▪

The multistage-growth dividend model allows for faster dividend growth rates in the near term, followed by a constant long-term growth rate. •

The approach is based on the mixed (supernormal) growth dividend model discussed in Chapter 9. o The complexity of this approach lies in choosing the correct number of stages of forecasted growth as well as how long each stage will last.

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Because of the algebraic complexity in solving for the required rate of return, the value is generally solved for using a trial-and-error method, after forecasting the different stages of dividend growth.

o Which Method Should We Use? ▪

In practice, most people use the CAPM (Method 1) to estimate the cost of equity if the result is going to be used in the discount rate for evaluating a project.

Preferred Stock • The characteristics of preferred stock allow us to use the perpetuity model to estimate the cost of preferred equity. o Just as with common stock, we can find the cost of preferred equity by rearranging the pricing equation for preferred shares: kps =

D ps Pps

o Note that the CAPM can be used to estimate the cost of preferred equity, just as it can be used to estimate the cost of common equity.

13.4

Using the WACC in Practice •

The after-tax version of the formula for the weighted-average cost of capital is: WACC = xDebt kDebt pretax (1 − t ) + xps kps + xcs kcs .

•

The financial analyst should use market values rather than book values to calculate WACC.

Calculating WACC: An Example

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Limitations of WACC as a Discount Rate for Evaluating Projects •

Financial theory tells us that the rate that should be used to discount these incremental cash flows is the rate that reflects their systematic risk.

•

This means that the WACC is going to be the appropriate discount rate for evaluating a project only when the project has cash flows with systematic risks that are exactly the same as those for the firm as a whole. o When a single rate, such as the WACC, is used to discount cash flows for projects with varying levels of risk, the discount rate will be too low in some cases and too high in others. o When the discount rate is too low, the firm runs the risk of accepting a negative-NPV project. ▪

The estimated NPV will be positive even though the true NPV is negative.

o When the discount rate is too high, the firm runs the risk of rejecting a positive-NPV project. ▪

The estimated NPV will be negative even though the true NPV is positive.

•

The key point is that it is correct to use a firm’s WACC to discount the cash flows for a project only if the following conditions hold. o Condition 1: A firm’s WACC should be used to evaluate the cash flows for a new project only if the level of systematic risk for that project is the same as that for the portfolio of projects that currently comprise the firm.

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o Condition 2: A firm’s WACC should be used to evaluate a project only if that project uses the same financing mix—the same proportions of debt, preferred shares, and common shares—used to finance the firm as a whole. C.

Alternatives to Using WACC for Evaluating Projects •

If the discount rate for a project cannot be estimated directly, a financial analyst might try to find a public firm that is in a business that is similar to the project. o This public company would be what financial analysts call a pure-play comparable because it is exactly like the project. o This approach is generally not feasible due to the difficulty of finding a public firm that is only in the business represented by the project.

•

Financial managers sometimes classify projects into categories based on their systematic risks. o They then specify a discount rate that is to be used to discount the cash flows for all projects within each category.

II. Suggested and Alternative Approaches to the Material Chapter 13 concentrates on the tools needed to understand the firm’s cost of capital as well as the complications and corresponding limitations associated with this value. On first glance, it appears to be a relatively simple concept that is described by a static equation. Instead, the chapter describes the weighted average cost of capital (WACC) as a snapshot that is based on the firmwide systematic risk, which is affected by the current portfolio of projects as well as the

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financial leverage that the firm is employing. After introducing the concept of WACC, the text then provides an understanding of the subcomponents of WACC: the cost of debt, the cost of common equity, and the cost of preferred equity for the firm. While the cost of debt and cost of preferred equity for the firm are relatively easy calculations, the cost of common equity is somewhat tricky due to the many assumptions required to estimate the future cash flows associated with common shareholder ownership. This material is required in order for the student to be able to proceed to the later capital budgeting chapters in the text. The current chapter also includes material that is commonly misunderstood by finance practitioners. As such, careful attention to the conditions required for using WACC for a firm’s new projects should be discussed and understood.

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III. Summary of Learning Objectives 1. Explain what the weighted average cost of capital for a firm is and why it is often used as a discount rate to evaluate projects. The weighted average cost of capital (WACC) for a firm is a weighted average of the current costs of the different types of financing that a firm has used to finance the purchase of its assets. When the WACC is calculated, the cost of each type of financing is weighted according to the fraction of the total firm value represented by that type of financing. The WACC is often used as a discount rate in evaluating projects because it is not possible to directly estimate the appropriate discount rate for many projects. As we also discuss in Section 13.4, having a single discount rate reduces inconsistencies that can arise when different analysts in the firm use different methods to estimate the discount rate and can also limit the ability of analysts to manipulate discount rates to favor pet projects.

2. Calculate the cost of debt for a firm. The cost of debt can be calculated by solving for the yield to maturity of the debt using the bond pricing model (Equation 8.1), computing the effective annual yield, and adjusting for taxes using Equation 13.3.

3. Calculate the cost of common stock and the cost of preferred stock for a firm.

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The cost of common stock can be estimated using the CAPM, the constant-growth dividend formula, and a multistage-growth dividend formula. The cost of preferred stock can be calculated using the perpetuity model for the present value of cash flows.

4. Calculate the weighted average cost of capital for a firm, explain the limitations of using a firm’s weighted average cost of capital as the discount rate when evaluating a project, and discuss the alternatives to the firm’s weighted average cost of capital that are available. The weighted average cost of capital is estimated using either Equation 13.2 or Equation 13.7, with the cost of each individual type of financing estimated using the appropriate method. When a firm uses a single rate to discount the cash flows for all of its projects, some project cash flows will be discounted using a rate that is too high and other project cash flows will be discounted using a rate that is too low. This can result in the firm’s rejecting some positive-NPV projects and accepting some negative-NPV projects. It will bias the firm toward accepting more risky projects and can cause the firm to create less value for stockholders than it would have if the appropriate discount rates had been used. One approach to using the WACC is to identify a firm that engages in business activities that are similar to those associated with the project under consideration and that has publicly traded stock. The returns from this pure-play firm’s stock can then be used to estimate the common stock’s beta for the project. In instances where pure-play firms are not available, financial managers can classify projects according to their systematic risks and can use a Copyright ©2015 John Wiley & Sons, Inc.

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different discount rate for each classification. This is the type of classification scheme illustrated in Exhibit 13.4.

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IV. Summary of Key Equations Equation

Description

Formula

13.1

Finance balance sheet identity

MV of assets = MV of liabilities + MV of equity

13.2

General formula for weighted average cost of capital (WACC) for a firm

kFirm =  xi ki = x1k1 + x2 k2 + x3k3 + . . . + xn kn

13.3

After-tax cost of debt

kDebt after-tax = kDebt pretax × (1 – t)

13.4

CAPM formula for the cost of common stock

kcs = Rrf + (βcs × Market risk premium)

13.5

Constant-growth dividend formula for the cost of common stock

kcs =

13.6

Perpetuity formula for the cost of preferred stock

kps =

13.7

Traditional WACC formula

i =1

D1 +g P0

D ps Pps

WACC = xDebt kDebt pretax (1− t ) + xps kps + xcs kcs

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CHAPTER 14 Working Capital Management Learning Objectives 1.

Define net working capital, discuss the importance of working capital management, and compute a firm’s net working capital.

Define the operating and cash conversion cycles, explain how they are used, and compute their values for a firm.

Discuss the relative advantages and disadvantages of pursuing (1) flexible and (2) restrictive current asset investment strategies.

Explain how accounts receivable are created and managed, and compute the cost of trade credit.

Explain the trade-off between carrying costs and reorder costs, and compute the economic order quantity for a firm’s inventory orders.

Define cash collection time, discuss how a firm can minimize this time, and compute the economic costs and benefits of a lockbox.

Describe three current asset financing strategies and discuss the main sources of short-term financing.

Chapter Outline

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Working Capital Basics •

Working capital management involves two key issues. ▪

What is the appropriate amount and mix of current assets for the firm to hold?

▪

How should these current assets be financed?

Working Capital Terms and Concepts

•

Let us review some basic definitions related to working capital. ▪

Current assets are cash and other assets that the firm expects to convert into cash in a year or less.

▪

Current liabilities (or short-term liabilities) are obligations that the firm expects to pay off in a year or less.

▪

Working capital, also called gross working capital, is the funds invested in a company’s cash account, account receivables, inventory, and other current assets.

▪

Net working capital (NWC) refers to the difference between current assets and current liabilities. o

NWC is important because it is a measure of liquidity and represents the net short-term investment the firm keeps in the business.

▪

Working capital management involves making decisions regarding the use and sources of current assets.

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Working capital efficiency refers to the length of time between when a working capital asset is acquired and when it is converted into cash.

▪

Liquidity is the ability of a company to convert assets—real or financial—into cash quickly without suffering a financial loss.

Working Capital Accounts and Trade-Offs •

The various working capital accounts are: ▪

Cash: This account includes cash and marketable securities like Treasury securities. o

The higher the cash balance, the better the ability of the firm to meet its short-term financial obligations.

▪

Receivables: These represent the amount owed by customers who have taken advantage of the firm’s trade credit policy.

▪

Inventory: Firms maintain inventory of raw materials and work in process and finished goods.

▪

Payables: The payables balance represents the amount owed to the firm’s vendors and suppliers on materials purchased on credit.

14.2

The Operating and Cash Conversion Cycles

•

The cash conversion cycle begins when the firm invests cash to purchase the raw materials that would be used to produce the goods that the firm manufactures; the cycle ends not with the finished goods being sold to customers and the cash collected on the sales, but when you take into account the time taken by the firm to pay for its purchases.

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See Exhibit 14.2 for a graphical representation of the cash conversion cycle.

When managing working capital accounts, financial managers want to do the following: ▪

Delay paying accounts payable as long as possible without suffering any penalties.

▪

Maintain minimal raw material inventories without causing manufacturing delays.

▪

Use as little labor as possible to manufacture the product while producing a quality product.

▪

Maintain minimal finished goods inventories without losing sales.

▪

Offer customers the most attractive credit terms possible on trade credit to maximize sales while minimizing the risk of nonpayment.

▪ •

Collect cash payments on accounts receivable as fast as possible to close the loop.

With the financial manager’s goal being to maximize the value of the firm, each of the decisions above is intended to shorten the cash conversion cycle and improve the firm’s liquidity.

•

Two tools to measure the working capital management efficiency are the operating cycle and the cash conversion cycle. A.

Operating Cycle

•

The operating cycle begins when the firm receives the raw materials it purchased and ends when the firm collects cash payments on its credit sales.

•

Two measures—days’ sales outstanding and days’ sales in inventory—help determine the operating cycle.

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Days’ sales in inventory (DSI) shows how long the firm keeps its inventory before selling it. o

It is the ratio of the inventory balance to the daily cost of goods sold.

The quicker a firm can move out its raw materials as finished goods, the shorter the duration when the firm holds it inventory, and the more efficient it is in managing its inventory.

▪

Days’ sales outstanding (DSO) estimates how long it takes on average for the firm to collect its outstanding accounts receivable balance. o

This ratio is also called the average collection period (ACP).

An efficient firm with good working capital management should have a low average collection period compared to its industry.

•

The operating cycle is calculated by summing the days’ sales outstanding and the days’ sales in inventory.

Operating Cycle = DSO + DSI

(14.1)

Cash Conversion Cycle

•

The cash conversion cycle is related to the operating cycle, but it does not start until the firm actually pays for its inventory. ▪

The cash conversion cycle is the length of time between the cash outflow for materials and the cash inflow from sales.

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To measure the cash conversion cycle, we need another measure called the days’ payables outstanding.

•

Days’ payable outstanding (DPO) shows how long a firm takes to pay off its suppliers for the cost of inventory.

•

The cash conversion cycle is then calculated by summing the days’ sales outstanding and the days’ sales in inventory and subtracting the days’ payables outstanding. ▪

The formula is shown in Equation 14.2:

CashConversionCycle = DSO + DSI − DPO

14.3

Working Capital Management Strategies

•

Financial managers use two types of strategies for current assets investments: flexible and restrictive. A.

Flexible Current Asset Investment Strategy

•

The flexible strategy has a high percent of current assets to sales, whereas a restrictive policy has a low percent of current assets to sales.

•

The flexible strategy calls for management to invest large amounts in cash, marketable securities, and inventory.

•

The strategy also promotes a liberal trade credit policy for customers, which results in high levels of accounts receivable.

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The flexible strategy is perceived be a low risk and low return course of action for management to follow.

•

The advantage of this policy is the large working capital balances the firm holds.

•

The strategy’s downside is the high inventory-carrying cost associated with owning a high level of inventory and providing liberal credit terms for its customers.

•

The higher carrying costs result for two reasons: ▪

The investment in the low return current assets deprives the higher returns that management could earn on longer term assets like plant and equipment.

▪

Higher amounts of inventory results in higher warehousing and storage costs.

Restrictive Current Asset Investment Strategy

•

Current assets are kept to a minimum in the restrictive strategy.

•

The firm barely invests in cash and inventory, and has tight terms of sale intended to curb credit sales and accounts receivable.

•

The restrictive strategy is a high-risk, high-return alternative to the flexible strategy. ▪

The high risk comes in the form of shortage costs that can be either financial or operating.

▪

Financial shortage costs arise mainly from the illiquidity shortage of cash and a lack of marketable securities to sell for cash.

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If unpaid bills are due, the firm will be forced to use expensive external emergency borrowing.

If funding cannot be secured, default occurs on some current liability and the firm runs the risk of being forced into bankruptcy by creditors.

▪

Operating shortage costs result from lost production and sales. o

If the firm does not hold enough raw materials in inventory, time may be wasted by a halt in production.

If the firm runs out of finished goods, sales may also be lost, and customer dissatisfaction may arise.

Restrictive sale policies such as allowing no credit sales will also result in lost sales.

Overall, operating shortage costs can be substantial, especially if the product markets are competitive.

The Working Capital Trade-off

•

The optimal current asset investment strategy will depend on the relative magnitudes of carrying costs versus shortage costs. This conflict is often referred to as the working capital trade-off. ▪

Financial managers need to balance shortage costs against carrying costs to find an optimal strategy.

▪

If carrying costs are larger than shortage costs, then the firm will maximize value by adopting a more restrictive strategy.

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On the other hand, if shortage costs dominate carrying costs, the firm will need to move toward a more flexible policy.

▪

Overall, management will try to find the level of current assets that minimizes the sum of the carrying costs and shortage costs.

14.4

Accounts Receivables A.

Terms of Sale

•

Whenever a firm sells a product, the seller spells out the terms and conditions of the sale in a document called the terms of sale.

•

The agreement specifies when the cash payment is due and the amount of any discount if early payment is made.

•

Trade credit, which is short-term financing, is typically made with a discount for early payment rather an explicit interest charge. ▪

An offer of “3/10, net 40” means that the selling firm offers a 3 percent discount if the buyer pays the full amount of the purchase in cash within 10 days of the invoice date. o

Otherwise, the buyer has 40 days to pay the balance in full from the date of delivery.

•

To calculate the cost, we need to determine the interest rate the buyer is paying and convert it to an equivalent annual rate.

•

The formula for calculating the EAR for a problem like this is shown below, in Equation 14.4,

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  Discount Effective annual rate = 1+   Discounted price 

365/dayscredit

−1

•

Trade credit is a loan from the supplier and it can be a very costly form of credit.

Aging Accounts Receivables

•

A common tool that credit managers use is called an aging schedule.

•

The aging schedule shows the breakdown of the firm’s accounts receivable by their date of sale—how long has the account not been paid in days.

•

Its purpose is to identify and then track delinquent accounts and to see that they are paid.

•

Aging schedules are also an important financial tool for analyzing the quality of a company’s receivables. ▪

The aging schedule reveals patterns of delinquency and shows where collection efforts should be concentrated.

▪

Exhibit 14.6 shows aging schedules for three different firms.

14.5

Inventory Management

•

Inventory management is largely a function of operations management, not financial management.

•

Manufacturing companies generally carry three types of inventory: raw materials, work in process, and finished goods. A.

Economic Order Quantity

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The economic order quantity (EOQ) mathematically determines the minimum total inventory cost, taking into account reorder costs and inventory-carrying costs.

•

The optimal order size strikes the balance between these two costs.

•

Equation 14.5 shows how to calculate EOQ.

Just-in-Time Inventory Management

•

In this system the exact day-by-day, or even hour-by-hour, raw material needs are delivered by the suppliers, who deliver the goods “just in time” for them to be used on the production line.

•

A big advantage of this system is that there are essentially no raw inventory costs and no chance of obsolescence or loss to theft.

•

On the other hand, if the supplier fails to make the needed deliveries, then production shuts down.

•

If the system works for a firm, it cuts down their investment in working capital dramatically.

14.6

Cash Management and Budgeting A.

Reasons for Holding Cash

•

Three reasons exist for holding a cash balance. First, it facilitates transactions with suppliers, customers and employees.

•

The second reason is simply that most banks require firms to hold minimum cash balances, or compensating balances, in exchange for the services they provide.

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The third reason is that banks often require firms to hold minimum cash balances a partial compensation for the loans and other services the banks provide.

Cash Collection

•

Collection time, or float, is the time between when a customer makes a payment and when the cash becomes available to the firm.

•

Collection time can be broken down into three components. ▪

First is delivery time, or mailing time. o

When a customer mails payment, it may take several days before that payment arrives.

▪

Second is processing delay. o

Once the payment is received, it must be opened, examined, accounted for, and deposited at the firm’s bank.

▪

Finally, there is a delay between the time of the deposit and the time when the cash is available for withdrawal.

▪

Payments in cash at the point of sale reduce the collection time to zero. o

Payment by check or credit card at the point of sale eliminates the mail time but not the processing time.

•

A lockbox system allows geographically dispersed customers to send their payments to a post office box close to them.

•

With a concentration account, a post office box is replaced by a local branch, which receives the mailings, processes the payments, and makes the deposits.

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Either approach will reduce the collection time to an extent, but there is a cost associated with it.

•

Another increasingly popular means of reducing cash collection time is through the use of electronic funds transfers, which reduces cash collection times in every phase. ▪

First, mailing time is eliminated.

▪

Second, processing time is reduced or eliminated since no data entry is necessary.

▪

Finally, electronic funds transfers typically have little or no delay in funds availability.

14.7

Financing Working Capital A.

Strategies for Financing Working Capital

•

Exhibit 14.7 shows the three basic strategies that a firm can follow to finance its working capital and fixed assets. ▪

Each of the three panels show: (1) the total long-term financing needed, which consists of long-term debt and equity; and (2) the seasonal needs for working capital that fluctuates with the level of sales.

•

The maturity matching strategy is shown in Figure A of Exhibit 14.7.

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All working capital is funded with short-term borrowing, and, as the level of sales varies seasonally, short-term borrowing fluctuates between some minimum and maximum level.

▪

All fixed assets are funded with long-term financing.

▪

The “matching of maturities” is one of the most basic techniques used by financial managers to reduce risk when financing assets.

▪

The long-term funding strategy is shown in Figure B in Exhibit 14.7.

▪

This strategy relies on long-term debt to finance both capital assets and working capital.

▪

This strategy reduces the risk of funding current assets because there is no need to worry about refinancing assets since all funding is long term.

▪

Figure C in Exhibit 14.7 shows the short-term funding strategy whereby all working capital and a portion of fixed assets are funded with short-term debt.

▪

While this lowers the cost under some interest rate scenarios, it forces the firm to continually refinance the funding of the long-term assets in a changing interest rate environment.

Financing Working Capital in Practice

•

Many financial managers try to match the maturities of assets and liabilities when funding the firm. ▪

That is, short-term assets are funded with short-term financing, and longterm assets are funded with long-term financing.

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Most financial managers like to fund some of their currents assets with long-term debt as shown in Figure A of Exhibit 14.7, so-called permanent working capital.

Sources of Short-Term Financing

•

Accounts payable (trade credit), bank loans, and commercial paper are common sources of short-term financing.

•

Accounts payable constituted about 35 percent of total current liabilities for all publicly traded manufacturing firms. ▪

The buyer needs to figure out whether it makes financial sense to pay early and take advantage of the discount or to wait and pay in full when the account is due.

•

Short-term bank loans accounted for about 20 percent of total current liabilities for all publicly traded manufacturing firms. ▪

An informal line of credit is a verbal agreement between the firm and the bank, allowing the firm to borrow up to an agreed-upon upper limit.

▪

In exchange for providing the line of credit, a bank may require that the firm holds a compensating balance with them.

▪

A formal line of credit is also known as “revolving credit,” whereby the bank has a legal obligation to lend to the firm an amount of money up to a preset limit.

▪

The firm pays a yearly fee, in addition to the interest expense on the amount they borrow.

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If the firm backs the loan with an asset, the loan is defined as secured; otherwise, the loan is unsecured.

▪

Secured loans allow the borrower to borrow at a lower interest rate, all else being equal.

•

Commercial paper is a promissory note issued by large financially secure firms, which have high credit ratings. ▪

Commercial paper is not “secured,” which means that the issuer is not pledging any assets to the lender in the event of default.

▪

However, most commercial paper is backed by a credit line from a commercial bank.

▪

Therefore, the default rate on commercial paper is very low, resulting in an interest rate that is usually lower than what a bank would charge on a direct loan.

•

For medium-size and small businesses, accounts receivable financing is an important source of funds. ▪

A company can secure a bank loan by pledging the firm’s accounts receivable as security.

▪

A second way for a business to finance itself with accounts receivables is to sell the receivables to a factor at a discount.

▪

The firm that sold the receivables without recourse has no further legal obligation to the factor.

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Suggested and Alternative Approaches to the Material

This chapter focuses on short-term financial decisions that involve cash inflows and outflows that will occur within a year or less. Examples include the purchase of raw materials, payment for the purchases of raw materials, sale of finished inventory, and the collection of cash for sales made on credit. This chapter focuses on these types of decisions, which are called working capital management. The chapter begins by reviewing some basic definitions and concepts that are necessary to further our study of working capital management. Next, the authors examine the individual working capital accounts and then learn how to construct and analyze the operating and cash conversion cycles. Then they examine how the different working capital accounts are managed: the cash account, accounts receivables, and inventory. Finally, the different financing options that financial managers consider, and the risks involved, are discussed. Instructors may choose to cover this chapter at any point in the semester. The material is sufficiently independent of previous material to allow that. It is important to recognize that many undergraduates are more likely to deal with working capital management issues on their first job than with issues like capital budgeting decisions or capital structure decisions. None of the quantitative material is likely to be overwhelming, and as in previous chapters, the end-of-chapter problems emphasize repetition to allow instructors to work some problems in class and assign others for the students to work on their own.

III. Summary of Learning Objectives

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1. Define net working capital, discuss the importance of working capital management, and compute a firm’s net working capital. Net working capital is the difference between current assets and total current liabilities. Working capital management refers to the decisions made regarding the use of current assets and how they are financed. The goal of working capital management is to ensure that the firm can continue its day-to-day operations and pay its short-term debt obligations. The computation of net working capital is illustrated in Section 14.1.

2. Discuss the operating and conversion cash cycles, explain how are they used, and compute their values for a firm. The operating cycle is the period starting with the receipt of raw materials and ending with the receipt of cash for finished goods made from those raw materials. It can be divided into two components: (1) days’ sales in inventory, which shows how long a firm keeps its inventory before selling it, and (2) days’ sales outstanding, which indicates how long it takes on average for the firm to collect its outstanding accounts receivable. Related to the operating cycle is the cash conversion cycle, which is the length of time between the cash outflow for materials and the cash inflow from sales. An additional measure, days’ payables outstanding, is required to calculate the cash conversion cycle. Financial managers compute these cycles to help them monitor the efficiency with which working capital is being managed. The computations are illustrated in Section 14.2.

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3. Discuss the relative advantages and disadvantages of pursuing (1) flexible and (2) restrictive current asset investment strategies. A flexible strategy involves maintaining relatively high levels of cash, marketable securities, and inventory, while a restrictive strategy keeps the levels of current assets relatively low. In general, a flexible strategy is thought to be low risk and low return; its downsides include low returns on current assets, potentially high inventory-carrying costs, and the cost of the money necessary to provide liberal credit terms. The restrictive strategy involves higher risk and return, with higher potential financial and operating shortage costs as its major drawbacks.

4. Explain how accounts receivable are created and managed, and compute the cost of trade credit. Accounts receivable are promises of future payment from customers that buy goods or services on credit. The details of trade credit agreements are defined in the terms of sale, which include the due date, the interest rate charged, and any discounts for early payment. The terms of sale are affected by the practice in the industry and the creditworthiness of the customer. To manage accounts receivable, a financial manager keeps close track of both days’ sales outstanding and the aging schedule and takes necessary actions to ensure that neither goes outside the range that is acceptable to senior management.

5. Explain the trade-off between carrying costs and reorder costs, and compute the economic order quantity for a firm’s inventory orders.

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The trade-off between carrying costs and reorder costs exists because as the size of a firm’s orders for materials increases, the number of orders and total reorder costs decline. At the same time, larger order sizes increase the average inventory size and, therefore, average inventory carrying costs. The economic order quantity (EOQ) calculation enables us to mathematically find the combination of the two costs that minimizes the firm’s total inventory cost. Learning by Doing Application 14.3 offers practice in computing a firm’s EOQ.

6. Define cash collection time, discuss how a firm can minimize this time, and compute the economic costs or benefits of a lockbox. The cash collection time is the time between when a customer makes a payment and when the cash becomes available to the firm. It has three components: (1) delivery or mailing time, (2) processing delay, and (3) delay between deposit time and availability. A firm can minimize this time through lockboxes, concentration accounts, electronic funds transfers, and other methods. Learning by Doing Application 14.4 illustrates the computations necessary to decide whether a lockbox is worth keeping.

7. Describe three current asset financing strategies and discuss the main sources of shortterm financing. Three current asset financing strategies are: (1) the maturity matching strategy, which matches the maturities of assets with the maturities of liabilities; (2) the long-term funding strategy, which finances both seasonal working capital needs and long-term assets with long-

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term funds; and (3) the short-term funding strategy, which uses short-term funds; and (3) the short-term funding strategy, which uses short-term debt for both seasonal working capital needs and some permanent working capital and long-term assets. Sources of short-term financing include accounts payable, short-term financing include accounts payable, shortterm bank loans, lines of credit, and commercial paper.

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IV. Summary of Key Equations

Equation

Description

Formula

14.1

Operating cycle

Operating cycle = DSO + DSI

14.2

Cash conversion cycle

Cash conversion cycle =DSO + DSI − DPO

14.3

Cash conversion cycle

Cash conversion cycle = Operating cycle − DPO

14.4

14.5

Effective annual rate (EAR)

Economic order quantity (EOQ)

  Discount 1+  Discounted price  EAR = 

EOQ =

365/dayscredit

−1

2 × Reorder costs × Sales per period Carrying costs

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CHAPTER 15 How Firms Raise Capital

Learning Objectives 1.

Explain what is meant by bootstrapping when raising seed financing and why bootstrapping is important.

Describe the role of venture capitalists in the economy and discuss how they reduce their risk when investing in start-up businesses.

Discuss the advantages and disadvantages of going public and compute the net proceeds from an IPO.

Explain why, when underwriting new security offerings, investment bankers prefer that the securities be underpriced. Compute the total cost of an IPO.

Discuss the costs of bringing a general cash offer to market.

Explain why a firm that has access to the public markets might elect to raise money through a private placement.

Review some advantages of borrowing from a commercial bank rather than selling securities in financial markets, and discuss bank term loans.

Chapter Outline

15.1 Bootstrapping A.

How New Businesses Get Started

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Most businesses are started by an entrepreneur who has a vision for a new business or product and a passionate belief in the concept’s viability.

•

The entrepreneur often fleshes out his or her ideas and makes them operational through informal discussions with people whom the entrepreneur respects and trusts, such as friends and early investors.

Initial Funding of the Firm

•

The process by which many entrepreneurs raise “seed” money and obtain other resources necessary to start their businesses is often called bootstrapping.

•

The initial “seed” money usually comes from the entrepreneur or other founders.

•

Other cash may come from personal savings, the sale of assets such as cars and boats, loans from family members and friends, and loans secured from credit cards.

•

The seed money, in most cases, is spent on developing a prototype of the product or service and a business plan.

15.2

Venture Capital

•

The bootstrapping period usually lasts no more than one or two years.

•

At some point, the founders will have developed a prototype of the product and a business plan, which they can “take on the road” to seek venture capital funding to grow the business.

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Venture capitalists are individuals or firms that help new businesses get started and provide much of their early-stage financing. ▪

Individual venture capitalists, angels (or angel investors), are typically wealthy individuals who invest their own money in emerging businesses at the very early stages in small deals.

The Venture Capital Industry

•

The venture capital industry as we know it today emerged in the late 1960s with the formation of the first venture capital limited partnerships.

•

Today, the venture industry consists of several thousand professionals at about one thousand venture capital firms, with the biggest concentration of firms in California and Massachusetts.

•

Modern venture capital firms tend to specialize in a specific line of business, such as clean energy, business software, hospitality, or medical devices.

•

A significant number of venture capital firms focus on high-technology investments.

Why Venture Capital Funding Is Different

•

Venture capital is important because entrepreneurs have only limited access to traditional sources of funding.

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Three reasons exist as to why traditional sources of funding do not work for new or emerging businesses: ▪

The high degree of risk involved in starting a new business.

▪

Types of productive assets. New firms whose primary assets are often intangibles, such as patents or trade secrets, find it difficult to secure financing from traditional lending sources.

▪

Informational asymmetry problems. An entrepreneur knows more about his or her company’s prospects than a lender does.

The Venture Capital Funding Cycle

•

The venture capital funding cycle is summarized in Exhibit 15.2.

•

How Venture Capitalists Reduce Their Risk ▪

Venture capitalists know that only a handful of new companies will survive to become successful firms.

▪

They use a number of tactics when they invest in new ventures, including funding the ventures in stages, requiring entrepreneurs to make personal investments, syndicating investments, and maintaining in-depth knowledge about the industry in which they specialize. o

Staged Funding. The key idea behind staged funding is that each funding stage gives the venture capitalist an opportunity to reassess the management team and the firm’s financial performance.

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✓ The venture capitalists’ investments give them an equity interest in the company, which is typically in the form of preferred stock that is convertible into common stock at the discretion of the venture capitalist. o

Personal Investment. Venture capitalists often require an entrepreneur to make a substantial personal investment in the business.

Syndication. It is a common practice to syndicate seed- and earlystage venture capital investments. ✓ Syndication occurs when the originating venture capitalist sells a percentage of a deal to other venture capitalists. ✓ Syndication reduces risk in two ways: ✓ First, it increases the diversification of the originating venture capitalist’s investment portfolio. ✓ Second, the willingness of other venture capitalists to share in the investment provides independent corroboration that the investment is a reasonable decision.

In-depth Knowledge. Another factor that reduces risk is the venture capitalist’s in-depth knowledge of the industry and technology.

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The Exit Strategy •

Venture capitalists are not long-term investors in the companies, but usually exit over a period of three to seven years.

•

Every venture capital agreement includes provisions identifying who has the authority to make critical decisions concerning the exit process. ▪

•

Those provisions usually include the following: o

Timing (when to exit)

The method of exit

What price is acceptable

Venture capital firms exit venture-backed companies in three principal ways: selling to a strategic buyer, selling to a financial buyer, and offering stock to the public. ▪

Strategic Buyer. A common way for venture capitalists to exit is to sell part of the firm’s equity to a strategic buyer in the private market.

▪

Financial Buyer. In recent years, sales to financial buyers have become a common way for venture capitalists to exit a firm.

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Occurs when a financial group buys the new firm with the intention of holding it for a period of time, usually three to five years, and then selling it for a higher price.

▪

Initial Public Offering. A venture capitalist may also exit an investment by selling common stock in an initial public offering (IPO).

Venture Capitalists Provide More Than Financing

•

The extent of the venture capitalists’ involvement in management of the firm depends on the experience and depth of the management team.

•

One of their most important roles is to provide advice to entrepreneurs. ▪

Because of their industry knowledge and their general knowledge about what it takes for a business to succeed, venture capitalists are able to provide counsel to entrepreneurs when a business is being started and during the early period of the business’s operation.

The Cost of Venture Capital Funding

•

The cost of venture capital funding is very high, but the high rates of return earned by venture capitalists are not unreasonable.

•

A typical venture capital fund may generate annual returns of 15 to 25 percent on the money that it invests, compared with an average annual return for the S&P 500 of about 12 percent.

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15.3 Initial Public Offering •

One way to raise larger sums of cash or to facilitate the exit of a venture capitalist is through an initial public offering, or IPO, of the company’s common stock.

•

First-time stock issues are given a special name (IPO) because the marketing and pricing of these issues are distinctly different from those of seasoned offerings. A.

Advantages and Disadvantages of Going Public

•

A firm’s decision to go public depends on an assessment of whether the advantages outweigh the disadvantages.

•

Going public has a number of potential advantages. ▪

The amount of equity capital that can be raised in the public equity markets is typically larger than the amount that can be raised through private sources.

▪

Once an IPO has been completed, additional equity capital can usually be raised through follow-on seasoned public offerings at a low cost.

▪

Going public can enable an entrepreneur to fund a growing business without giving up control.

▪

After the IPO, there is an active secondary market in which stockholders can buy and sell its shares.

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Publicly traded firms find it easier to attract top management talent and to better motivate current managers if a firm’s stock is publicly traded.

•

There are several disadvantages to going public. ▪

One disadvantage of going public is the high cost of the IPO itself.

▪

The costs of complying with ongoing SEC disclosure requirements also represent a disadvantage of going public.

▪

The transparency that results from this compliance can be costly for some firms.

▪

Finally, some investors argue that the SEC’s requirement of quarterly earnings forecasts and quarterly financial statements encourages managers to focus on short-term profits rather than long-term wealth maximization.

Investment Banking Services

•

To complete an IPO, a firm will need the services of investment bankers, who are experts in bringing new securities to market.

•

Investment bankers provide three basic services when bringing securities to market—origination, underwriting, and distribution.

•

Identifying the investment banking firm that will manage the IPO process is an important task for the management of a firm because not all investment banks are equal.

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Securing the services of an investment banking firm with a reputation for quality and honesty will improve the market’s receptivity and help ensure a successful IPO.

•

Origination includes giving the firm financial advice and getting the issue ready to sell. ▪

During the origination phase, the investment banker helps the firm determine whether it is ready for an IPO.

▪

Once the decision to sell stock is made, the firm’s management must obtain a number of approvals.

▪

Since securities sold to the public must be registered in advance with the SEC, the first step in this process is to file a registration statement with the SEC.

•

Underwriting is the risk-bearing part of investment banking. ▪

The securities can be underwritten in two ways: (1) on a firm-commitment basis or (2) on a best-effort basis. o

In the firm-commitment underwriting, which is more typical, the investment banker guarantees the issuer a fixed amount of money from the stock sale. ✓ The investment banker actually buys the stock from the firm at a fixed price and then resells it to the public.

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o The underwriter bears the risk that the resale price might be lower than the price the underwriter pays—this is called price risk. ✓ The investment banker’s compensation is called the underwriter’s spread. o In a firm-commitment offering, the spread is the difference between the investment banker’s purchase price and the offer price. ✓ The underwriter’s spread in the vast majority of initial public stock offerings in the United States is 7 percent. o

With a best-effort underwriting, the investment banking firm makes no guarantee to sell the securities at a particular price. ✓ In best-effort offerings, the investment banker does not bear the price risk associated with underwriting the issue, and compensation is based on the number of shares sold. ✓ To share the underwriting risk and to sell a new security issue more efficiently, underwriters may combine to form a group called an underwriting syndicate.

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✓ Participating in the syndicate entitles each underwriter to receive a portion of the underwriting fee as well as an allocation of the securities to sell to its own customers. ▪

One of the investment banker’s most difficult tasks is to determine the highest price at which the bankers will be able to quickly sell all of the shares being offered and that will result in a stable secondary market for the shares.

▪

Before the shares are sold, representatives from the underwriting syndicate hold a due diligence meeting with representatives of the issuer.

▪

Investment bankers hold due diligence meetings to protect their reputations and to reduce the risk of investors’ lawsuits in the event the investment goes sour later on.

•

Distribution involves reselling the securities to the public. ▪

Once the due diligence process is complete, the underwriters and the issuer determine the final offer price in a pricing call.

▪

If management finds the price acceptable, the issuer files an amendment to the registration statement with the SEC, which contains the terms of the offering and the final prospectus. o

Once the securities are registered with the SEC, they can be sold to investors.

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The syndicate’s primary concern is to sell the securities as quickly as possible at the offer price.

▪

At the closing of a firm-commitment offering, the issuing firm delivers the security certificates to the underwriter and the underwriter delivers the payment for the securities, net of the underwriting fee, to the issuer. o

The closing usually takes place on the third business day after trading has started.

15.4

IPO Pricing and Cost A.

The Underpricing Debate

•

The issuer prefers the stock price to be as high as realistically possible while the underwriters prefer some degree of underpricing.

•

Underpricing is defined as offering new securities for sale at a price below their true value.

•

In a firm-commitment offering, the underwriters will suffer a financial loss if the offer price is set too high; under a best-effort agreement, the issuing firm will lose.

•

If the underpricing is significant, the investment banking firm will suffer a loss of reputation for failing to price the new issue correctly and raising less money for its client than it could have.

IPOs Are Consistently Underpriced

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Data from the marketplace show that the shares sold in an IPO are typically priced between 10 and 15 percent below the price at which they close at the end of the first day of trading.

•

Exhibit 15.4 shows recent information on the number of IPOs per year and the average first-day return to investors for the years 1997–2013. ▪

The average first-day return is a measure of the amount of underpricing.

The Cost of an IPO

•

Three basic costs are associated with issuing stock in an IPO—underwriting spread, out-of-pocket expenses, and underpricing.

•

Exhibit 15.5 presents some market data on the cost of issuing an IPO.

15.5

General Cash Offer by a Public Company

•

If a public firm has a high credit rating, the lowest-cost source of external funds is often a general cash offer, also referred to as a registered public offering.

•

A general cash offer is a sale of debt or equity, open to all investors, by a registered public company that has previously sold stock to the public. A.

Competitive versus Negotiated Sale

•

In a general cash offer, management must decide whether to sell the securities on a competitive or a negotiated basis.

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In a competitive sale, the firm specifies the type and amount of securities it wants to sell and hires an investment banking firm to do the origination work.

▪

Once the origination is completed, the firm invites underwriters to bid competitively to buy the issue.

▪

In a negotiated sale, the issuer selects the underwriter at the beginning of the origination process.

▪

At that time, the scope of the work is defined, and the issuer negotiates the origination and underwriter’s fees to be charged.

•

For debt issues, most experts believe that competitive sales are the least costly method of selling so-called vanilla bonds when market conditions are stable.

•

For equity securities, negotiated sales provide the lowest-cost method of sale.

Shelf Registration

•

Since November 1983, the SEC has allowed some two thousand large corporations the option of using shelf registration.

•

Shelf registration allows a firm to register an inventory of securities for a twoyear period. ▪

During that time, the firm can take the securities “off the shelf” and sell them as needed.

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Costs associated with selling the securities are reduced because only a single registration statement is required.

▪

A shelf registration statement can cover multiple securities, and there is no penalty if authorized securities are not issued.

•

Corporations gain two important benefits from shelf registration. ▪

First is the greater flexibility in bringing securities to market in that securities can be taken off the shelf and sold within minutes.

▪

Second, shelf registration allows firms to periodically sell small amounts of securities, raising money as it is actually needed, rather than banking a large amount of money from a single security sale and spending it over time.

The Cost of a General Cash Offer

•

Exhibit 15.6 shows the average underwriting spread, out-of-pocket expenses, and total cost for common stock, preferred stock, and corporate bond issues of various sizes.

•

Comparing Exhibits 15.5 and 15.6 reflects the greater risk involved in underwriting an IPO and the higher cost of distributing the IPO.

15.6

Private Markets and Bank Loans

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Private versus Public Markets

•

For many smaller firms and firms of lower credit standing that have limited access, or no access, to the public markets, the cheapest source of external funding is often the private markets.

•

When market conditions are unstable, some smaller firms that were previously able to sell securities in the public markets no longer can do so.

•

Bootstrapping and venture capital financing are part of the private market as well.

•

Many private companies that are owned by entrepreneurs, families, or family foundations and are sizable companies of high credit quality prefer to sell their securities in the private markets even though they can access public markets.

•

Their choice of markets is a function of: ▪

their desire to avoid the regulatory costs and transparency requirements; and

▪

their preference for a small group of sophisticated investors rather than the public at large.

Private Placements

•

Private placement occurs when a firm sells unregistered securities directly to investors such as insurance companies, commercial banks, or wealthy individuals.

•

About half of all corporate debt is sold through the private placement market.

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Investment banks and money center banks often assist firms with private placements.

•

They help the issuer locate potential buyers for their securities, put the deal together, and do the necessary origination work, but they do not underwrite the issue.

•

In a traditional private placement, the issuer sells the securities directly to investors.

•

Private placements have a number of advantages, relative to public offerings, for certain issuers. ▪

Net of transaction costs, lower cost of funds.

▪

Private lenders are more willing to negotiate changes to a bond contract.

▪

If a firm suffers financial distress, the problems are more likely to be resolved without going to a bankruptcy court.

▪

Other advantages include the speed of private placement deals and flexibility in issue size.

•

The biggest drawback of private placements involves restrictions on the resale of the securities.

•

The SEC limits the sale of private placements to several dozen “knowledgeable” investors who have the capacity to evaluate the securities’ investment potential and risk.

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To compensate for the lack of marketability, investors in private placements require a higher yield relative to a comparable public offering.

•

In April 1990, the SEC adopted Rule 144A, which allows large financial institutions to trade unregistered securities among themselves. ▪

Since 1995, about half of all private placement deals have been conducted under Rule 144A.

Private Equity Firms

•

Like venture capitalists, private equity firms pool money from wealthy investors, pension funds, insurance companies, and other sources to make investments.

•

Private equity firms invest in more mature companies, and they often purchase 100 percent of a business.

•

Private equity firm managers look to increase the value of the firms they acquire by closely monitoring their performance and providing better management.

•

Once value is increased, they sell the firms for a profit after holding investments typically for three to five years.

•

Large public firms often sell businesses when they no longer fit the firms’ strategies or when they are offered a price they cannot refuse.

•

Private equity firms establish private equity funds to make investments. These funds are usually organized as limited partnerships or limited liability companies.

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Private equity investors focus on firms that have stable cash flows because they use a lot of debt to finance their acquisitions. ▪

When a large amount of leverage is used to take over a company, the transaction is called a leveraged buyout.

•

Private equity firms improve the performance of firms in which they invest by: ▪

making sure that the firms have the best possible management teams.

▪

closely monitoring each firm’s performance and providing advice and counsel to the firm’s management team.

▪

facilitating mergers and acquisitions that help improve the competitive positions of the companies in which they invest.

•

Private equity firms carry a much smaller regulatory burden and fewer financial reporting requirements than do public firms. ▪

They are able to avoid most of the SEC’s registration and compliance costs and other regulatory burdens, such as compliance with the SarbanesOxley Act.

Private Investments in Public Equity

•

Private investment in public equity (PIPE) transactions are transactions in which a public company sells unregistered stock to an investor—often a hedge fund or some other institutional investor.

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PIPE transactions have been around for a long time, but the number of these transactions has increased greatly since the late 1990s.

•

In a PIPE transaction, investors purchase securities (equity or debt) directly from a publicly traded company in a private placement.

•

The securities are virtually always sold to the investors at a discount to the price at which they would sell in the public markets to compensate the buyer for limits on the liquidity associated with these securities and, often, for being able to provide capital quickly.

•

Because the securities sold in a PIPE transaction are not registered with the SEC, they are “restricted securities.” ▪

Under federal securities law, they cannot be resold to investors in the public markets for a year or two unless the company registers them.

▪

As part of the PIPE contract, the company often agrees to register the restricted securities with the SEC, usually within 90 days of the PIPE closing.

▪

If the registration is delayed past a deadline date, the issuer might be required to pay the investor liquidity damages, usually 1 or 1.5 percent per month, as compensation for the loss of liquidity.

•

The major advantage of a PIPE transaction to issuers is that it gives them faster access to capital and a lower funding cost than a registered public offering.

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PIPE transactions involving a healthy firm can also be executed without the use of an investment bank, resulting in a cost saving of 7 to 8 percent of the proceeds.

•

A PIPE transaction can be the only way for a small financially distressed company to raise equity capital.

Commercial Bank Lending

•

Almost every company has a working relationship with at least one bank, and smaller companies depend on them for funding and for financial advice.

•

Prime-rate loans are loans in which the borrowing rate is based on the prime rate of interest, which is historically the loan rate that banks charge their most creditworthy customers. ▪

Some customers are able to borrow below the prime rate.

▪

Prime-rate loans are often used to finance working capital needs such as inventory purchases.

▪

Banks often require that the loan balance be brought to zero for a short time each year.

▪

The prime rate charged by a bank might be higher than other market borrowing rates.

▪

The cost of a prime-rate loan can includes the cost of the advisory services as well as the cost of the financing.

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Bank Term Loans are defined as business loans with maturities greater than one year. ▪

Term loans are the most common form of intermediate-term financing provided by commercial banks.

▪

Bank term loans may be secured or unsecured, and the funds can be used to buy inventory or to finance plant and equipment.

•

In determining the interest rate to charge on a loan, the bank takes the prime rate plus two other factors into account.

•

Before making a loan, the bank conducts a credit analysis of the customer.

▪

To determine the customer’s credit category (DRP), banks usually look at five to seven credit risk categories, which look very much like bond ratings.

▪

Those with the highest credit rating borrow at the prime rate or below, while others have to pay a default risk premium over and the prime rate.

•

The second step, if the customer wants a term loan, is to adjust for the term to maturity (MAT).

II.

Suggested and Alternative Approaches to the Material

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This chapter is about how firms raise capital so that they can acquire the productive assets needed to grow and remain profitable. The chapter begins by examining how many new businesses acquire their first equity funding through “bootstrapping” and the role venture capitalists play in providing equity to help firms get started. Once a firm is successfully launched, the venture capitalists’ job is done and they exit the scene. At this juncture, management has a number of other funding options; we discuss those options in the remainder of the chapter. The chapter next explains how firms sell their first issue of common stock in the public markets and the role of investment banks in completing these sales. First-time equity sales are known as initial public offerings, or IPOs. The role that private markets play in funding business firms and the factors that managers consider when deciding between a public and a private market sale are then discussed. The chapter closes with a discussion of the importance of commercial banks in providing short-term and intermediate-term financing. This chapter may be introduced right after the fundamental finance concepts have been covered. It allows students to get a firm grasp of how firms can raise long-term capital in both public and private markets. While finance majors will receive more in-depth coverage in upper level courses, nonfinance, business students will benefit from the coverage of these topics in the basic finance courses. Material at the end of the chapter is structured to give students a good conceptual and quantitative understanding of the chapter.

III. Summary of Learning Objectives 1.

Explain what is meant by bootstrapping when raising seed financing and why bootstrapping is important.

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Bootstrapping is the process by which many entrepreneurs raise “seed” money and obtain other resources necessary to start new businesses. Seed money often comes from the entrepreneur’s savings and credit cards and from family and friends. Bootstrapping is important because business start-ups are a significant factor in determining and sustaining long-term economic growth in an economy. Indeed, some state and local governments have invested heavily in business incubators, hoping to foster new business formation.

Describe the role of venture capitalists in the economy and discuss how they reduce their risk when investing in start-up businesses. Venture capitalists specialize in helping business firms get started by advising management and providing early-stage financing. Because of the high risk of investing in start-up businesses, venture capitalists finance projects in stages and often require the owners to make a significant personal investment in the firm. The owners’ equity stake signals their belief in the viability of the project and ensures that management actions are focused on building a successful business. Risk is also reduced through syndication and because of the venture capitalist’s in-depth knowledge of the industry and technology.

Discuss the advantages and disadvantages of going public and compute the net proceeds from an IPO. The major advantages of entering public markets are that they provide firms with access to large quantities of money at relatively low cost, enable firms to attract and motivate good managers, and provide liquidity for existing stockholders, such as entrepreneurs, other managers, and venture capitalists. Disadvantages include the high cost of the IPO,

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the cost of ongoing SEC disclosure requirements, the need to disclose sensitive information, and a possible incentives focus on short-term profits rather than on longterm value maximization. Section 15.3 and Learning by Doing Applications 15.1 and 15.2 provide practice in computing IPO proceeds.

Explain why, when underwriting new security offerings, investment bankers prefer that the securities be underpriced. Compute the total cost of an IPO. When underwriting new securities, investment bankers prefer that the issue be underpriced because it increases the likelihood of a successful offering. The lower the offering price, the more likely that the securities will sell out quickly—and the less likely that the underwriters will end up with unsold inventory. Furthermore, many investment bankers will argue that some underpricing helps attract long-term institutional investors who help provide stability for the stock price. The total cost of issuing an IPO includes three elements: (1) the underwriter’s spread; (2) out-of-pocket expenses, which include legal fees, SEC filing fees, and other expenses; and (3) the cost of underpricing. For calculations of these costs, see Section 15.4, including Learning by Doing Application 15.3. Exhibit 15.5 gives average costs for IPOs in recent years.

Discuss the costs of bringing a general cash offer to market. The total cost of bringing a general cash offer to market is lower than the cost of issuing an IPO because these seasoned offerings do not include a large underpricing cost and

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underwriting spreads are smaller. Section 15.5 explains how to compute the total cost of a general cash offer, and some average costs are listed in Exhibit 15.6.

Explain why a firm that has access to the public markets might elect to raise money through a private placement. There are a number of advantages to private placement, even for companies with access to the public markets. A private placement may be more cost effective and can be accomplished much more quickly. In addition, some larger companies, especially those owned by entrepreneurs or families, may not wish to be exposed to the public scrutiny that comes with public sales of securities.

Review some of the advantages of borrowing from a commercial bank rather than selling securities in financial markets, and discuss bank term loans. Most small- and medium-size firms borrow from commercial banks on a regular basis. Small- and medium-sized firms may have limited access to the financial markets. For these firms, banks provide not only funds but a full range of services, including financial advice. Furthermore, if a firm’s financial circumstances change over time, it is much easier for the firm to borrow or renegotiate the debt contract with a bank than with other lenders. For many companies, bank borrowing may be the lowest-cost source of funds. Bank term loans are business loans with maturities greater than one year. Most bank term loans have maturities from one to five years, though the maturity may be as long as fifteen years. The cost of the loans depends on three factors: the prime rate, an adjustment for default risk, and an adjustment for the term to maturity.

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IV. Summary of Key Equations Equation

15.1

Description

Formula

Bank loan pricing model

kl = PR + DRP + MAT

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Chapter 16 Capital Structure Policy

Learning Objectives 1.

Describe the two Modigliani and Miller propositions, the key assumptions underlying them, and their relevance to capital structure decisions. Use Proposition 2 to calculate the return on equity.

Discuss the benefits and costs of using debt financing and calculate the value of the income tax benefit associated with debt.

Describe the trade-off and pecking order theories of capital structure choice and explain what the empirical evidence tells us about these theories.

Discuss some of the practical considerations that managers are concerned with when they choose a firm’s capital structure.

Chapter Outline

16.1

Capital Structure and Firm Value •

A firm’s capital structure is the mix of financial securities used to finance its activities. •

The mix will always include common stock and will often include debt and preferred stock.

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The firm may have several classes of common stock, for example, with different voting rights and, possibly, different claims on the cash flows available to stockholders.

▪

The debt at a firm can be long term or short term, secured or unsecured, convertible or not convertible into common stock, and so on.

▪

Preferred stock can be cumulative or noncumulative and convertible or not convertible into common stock.

•

The fraction of the total financing that is represented by debt is a measure of the financial leverage in the firm’s capital structure. ▪

A higher fraction of debt indicates a higher degree of financial leverage. o

The amount of financial leverage in a firm’s capital structure is important because it affects the value of the firm.

The Optimal Capital Structure ▪

Managers at a firm choose a capital structure so that the mix of securities making up the capital structure minimizes the cost of financing the firm’s activities. o

This mix is the optimal capital structure because the capital structure that minimizes the cost of financing the firm’s projects is also the capital structure that maximizes the total value of those projects and, therefore, the overall value of the firm.

B. The Modigliani and Miller Propositions •

M&M Proposition 1

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States that a firm’s capital structure decisions will have no effect on the value of the firm if •

(1) there are no taxes,

•

(2) there are no information or transaction costs, and

•

(3) the firm’s real investment policy is not affected by its capital structure decisions. ▪

The real investment policy of the firm includes the criteria that the firm uses in deciding which real assets (projects) to invest in.

The market value of the debt plus the market value of the equity must equal the value of the cash flows produced by the firm’s assets.

▪

M&M Proposition 1 states that the combined value of the equity and debt claims (represented by the present value of free cash flows the firm’s assets are expected to produce in the future) does not change when changes are made in the capital structure of the firm if no one other than the stockholders and the debt holders is receiving cash flows. o

Such a change is called a financial restructuring, in which a combination of financial transactions occurs that changes the capital structure of the firm without affecting its real assets.

▪

M&M Proposition 2

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M&M’s Proposition 2 states that the cost of (required return on) a firm’s common stock is directly related to the debt-toequity ratio. •

This can be seen by looking at Equation 16.3: ▪

V  kcs = kAssets +  Debt  ( kAssets − kDebt )  Vcs 

▪

The first source of risk is the underlying risk of the assets, which is reflected in the expected return on the firm’s asset and is known as the business risk of the firm. •

It is the risk associated with the characteristics of the firm’s business activities.

▪

The second source of risk is the capital structure of the firm, which reflects the effect of the firm’s financing decisions on the riskiness of the cash flows that the stockholders will receive. •

Financial risk is associated with required payments to a firm’s lenders.

▪

What the M&M Propositions Tell Us o

M&M analysis tells us exactly where we should look if we want to understand how capital structure affects firm value and the cost of equity.

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If financial policy matters, it must be because ▪

(1) taxes matter,

▪

(2) information or transaction costs matter, or

▪

(3) capital structure choices affect a firm’s real investment policy.

16.2

The Benefits and Costs of Using Debt A.

The Benefits of Debt ▪

The most important benefit from including debt in a firm’s capital structure stems from the fact that firms can deduct interest payments for tax purposes but cannot deduct dividend payments. •

This makes it less costly to distribute cash to security holders through interest payments than through dividends.

▪

The total dollar amount of interest paid each year and, therefore, the amount that will be deducted from the firm’s taxable income is: D × kDebt •

This will result in a reduction in taxes paid (the interest tax shield) of D × kDebt × t where t is the firm’s marginal tax rate that applies to the interest expense deduction.

▪

If this reduction will continue in perpetuity, the perpetuity model, to calculate the present value of the tax savings from debt, is:

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•

▪

VTax savings debt = PVA =

Instructor’s Manual

CF D  kDebt  t = i i

Since the firm will benefit from the interest tax shield only if it is able to make the required interest payments, the cash savings associated with the tax shield are about as risky as the cash flow stream associated with the interest payments:

D  k Debt  t = Dt k Debt

•

VTax savings debt =

•

The perpetuity model assumes that (1) the firm will continue to be in business forever, (2) the firm will be able to realize the tax savings in the years in which the interest payments are made (the firm’s EBIT will always be at least as great as the interest expense), and (3) the firm’s tax rate will remain constant.

Other Benefits •

Underwriting spreads and out-of-pocket costs are more than three times as large for stock sales as they are for bond sales.

•

Debt provides managers with incentives to focus on maximizing the cash flows that the firm produces since interest and principal payments must be made when they are due.

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o Because managers must make these interest and principal payments or face the prospect of bankruptcy, this can destroy a manager’s career. •

Debt can be used to limit the ability of bad managers to waste the stockholders’ money on things such as fancy jet aircraft, plush offices, and other negative-NPV projects that benefit the managers personally.

The Costs of Debt •

Financial managers limit the amount of debt in their firms’ capital structures in part because there are costs that can become quite substantial at high levels of debt. o At low levels of debt, the benefits are greater than the costs, and adding more debt increases the overall value of the firm. o At some point, the costs begin to exceed the benefits, and adding more debt financing destroys firm value. o Financial managers want to add debt just to the point at which the value of the firm is maximized.

•

Bankruptcy costs, also referred to as costs of financial distress, are costs associated with the financial difficulties that a firm might get into because it uses too much debt financing. o The term bankruptcy cost is used rather loosely in capital structure discussions to refer to costs incurred when a firm gets into financial distress.

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o Firms can incur bankruptcy costs even if they never actually file for bankruptcy. o Direct bankruptcy costs are out-of-pocket costs that a firm incurs as a result of financial distress. ▪

They include things such as fees paid to lawyers, accountants, and consultants.

o Indirect bankruptcy costs are costs associated with changes in the behavior of people who deal with a firm in financial distress. ▪

Some of this firm’s potential customers will decide to purchase a competitor’s products because •

of concerns that the firm will not be able to honor its warranties.

• ▪

parts or service will not be available in the future.

Some investors will demand a lower price to compensate them for these risks.

▪

When suppliers learn that a firm is in financial distress, they will worry about not being paid; to protect against losses for future shipments, they often begin to require cash on delivery.

▪

Employees at a distressed firm will worry that their jobs or benefits are in danger, and some will start looking for new jobs.

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If the firm enters into the formal bankruptcy process, it incurs another indirect bankruptcy cost because a bankruptcy judge must approve all investments made by the firm.

o Agency costs result from conflicts of interest between principals and agents where one party, known as the principal, delegates its decisionmaking authority to another party, known as the agent. ▪

The agent is expected to act in the interest of the principal, but agents sometimes have interests that conflict with those of the principal.

▪

Stockholder-manager agency costs occur to the extent that the incentives of the managers are not perfectly identical to those of the stockholders, managers will make some decisions that benefit themselves at the expense of the stockholders. •

Using debt financing provides managers with incentives to focus on maximizing the cash flows that the firm produces and limits the ability of bad managers to waste the stockholders’ money on negative-NPV projects. o These benefits amount to reductions in the agency costs associated with the principal-agent relationship between stockholders and managers.

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While the use of debt financing can reduce agency costs, it can also increase these costs by altering the behavior of managers who have a high proportion of their wealth riding on the success of the firm, through their stockholdings, future income, and reputations. o The use of debt increases the volatility of a firm’s earnings and the probability that the firm will get into financial difficulty. o Increased risk causes managers to make more conservative decisions.

•

Stockholder-lender agency costs can occur when investors lend money to a firm and delegate authority to the stockholders to decide how that money will be used. o Lenders expect that the stockholders, through the managers they appoint, will invest the money in a way that enables the firm to make all of the interest and principal payments that have been promised. o However, stockholders may have incentives to use the money in ways that are not in the best interests of the lenders. o Lenders know that stockholders have incentives to distribute some or all of the funds that they

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borrow as dividends, and so they protect themselves against this sort of behavior by including provisions in the lending agreements that limit the ability of stockholders to pay dividends and other behavior. ▪

These protections are not foolproof.

o One type of this behavior is known as the asset substitution problem in which once a loan has been made to a firm, the stockholders have an incentive to substitute less risky assets for more risky assets such as negative-NPV projects. •

Another type of behavior is known as the underinvestment problem, and it occurs in a financially distressed firm when the value that is created by investing in a positive-NPV project is likely to go to the lenders instead of the stockholders; therefore the firm forgoes financing and undertaking the project.

16.3 A.

Two Theories of Capital Structure The Trade-Off Theory

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o The trade-off theory of capital structure states that managers choose a specific target capital structure based on the trade-offs between the benefits and the costs of debt. ▪

The theory says that managers will increase debt to the point at which the costs and benefits of adding an additional dollar of debt are exactly equal because this is the capital structure that maximizes firm value.

The Pecking Order Theory o The pecking order theory recognizes that different types of capital have different costs. This leads to a pecking order in the financing choices that managers make to choose the least expensive capital first and then move to increasingly costly capital when the lower-cost sources of capital are no longer available. •

Managers view internally generated funds, or cash on hand, as the cheapest source of capital.

•

Debt is more costly to obtain than internally generated funds but is still relatively inexpensive.

• C.

Raising money by selling stock is the most expensive.

The Empirical Evidence o When researchers compare the capital structures in different industries, they find evidence that supports the trade-off theory. o Some researchers argue that, on average, debt levels appear to be lower than the trade-off theory suggests they should be.

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o More general evidence also indicates that the more profitable a firm is, the less debt it tends to have, which is exactly opposite what the trade-off theory suggests we should see. •

This evidence is consistent with the pecking order theory.

o The pecking order theory is also supported by the fact that, in an average year, public firms actually repurchase more shares than they sell. o Both the trade-off theory and the pecking order theory offer some insights into how managers choose the capital structures for their firms, but neither is able to explain all of the capital structure choices that we observe. 16.4

Practical Considerations in Choosing a Capital Structure •

Managers don’t think only in terms of a trade-off or a pecking order but are concerned with how their financing decisions will influence the practical issues that they must deal with when managing a business.

•

Financial flexibility is an important consideration in many capital structure decisions. o Managers must ensure that they retain sufficient financial resources in the firm to take advantage of unexpected opportunities as well as unforeseen problems. ▪

They try to manage their firms’ capital structures in a way that limits the risk to a reasonable level.

o Managers think about leverage and the effect that interest expense has on the reported dollar value of net income. o Managers consider control implications when choosing between equity and debt financing of the firm. Copyright ©2015 John Wiley & Sons, Inc.

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II.

Instructor’s Manual

Suggested and Alternative Approaches to the Material

Chapter 16 discusses capital structure and how it affects firm value. It introduces the Modigliani and Miller (M&M) theory of capital structure as well as the three major assumption required for the theorem to hold. These assumptions are that (1) neither the firm nor the investor is subject to taxes, (2) there are no information or transactions costs, and (3) the way in which the firm is financed does not affect its real investment policy. The theorem shows that the firm value is unaffected by the firm’s choice of capital structure. The chapter then proceeds to relax the no-tax assumption to discuss the value of the tax shield to the firm. At that point, the theory predicts that firms should have greater leverage than what we see in practice. The chapter then discusses the benefits and costs of leverage, which further relax the assumptions of M&M in order to discuss a more realistic understanding of capital structure. The chapter proceeds with two theories of capital structure. Trade-off theory suggests that firms will adjust their capital structure to maximize the value of the firm. Pecking order theory suggests that firms will always select the cheapest form of capital to finance a project. The empirical evidence does not completely support either theory. The chapter concludes with a practical discussion of capital structure. This material constitutes a bit of a theoretical discussion with a number of examples to help the student understand the arguments involved. Although the instructor might view the material as optional, it does address a financial issue that future business executives will have to deal with in their careers. As such, the material is recommended for an introductory course where the students may not be required to take another corporate finance course.

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III. Summary of Learning Objectives 1.

Describe the two Modigliani and Miller propositions, the key assumptions underlying them, and their relevance to capital structure decisions. Use Proposition 2 to calculate the return on equity. M&M Proposition 1 states that the value of a firm is unaffected by its capital structure if the following three conditions hold: (1) there are no taxes, (2) there are no information or transaction costs, and (3) capital structure decisions do affect the real investment policies of the firm. This proposition tells us the three reasons that capital structure choices affect firm value. M&M Proposition 2 states that the expected return on a firm’s equity increases with the amount of debt in its capital structure. This proposition also shows that the expected return on equity can be separated into two parts—a part that reflects the risk of the underlying assets of the firm and a part that reflects the risk associated with the financial leverage used by the firm. This proposition helps managers understand the implications of financial leverage for the cost of the equity used to finance the firm’s investments. Equation 16.3 can be used to calculate the cost of equity for common stock.

Discuss the benefits and costs of using debt financing and calculate the value of the income tax benefit associated with debt. Using debt financing provides several benefits. A major benefit arises from the deductibility of interest payments. Since interest payments are tax deductible and dividend payments are not, distributing cash to investors through interest payments are

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not, distributing cash to investors through interest payments can increase the value of a firm. Debt is also less expensive to issue than equity. Finally, debt can benefit stockholders in certain situations by providing managers with incentives to maximize the cash flows produced by the firm and by reducing their ability to invest in negative NPV projects. The costs of debt include bankruptcy and agency costs. Bankruptcy costs arise because financial leverage increases the probability that a firm will get into financial distress. Direct bankruptcy costs are the out-of-pocket costs that a firm incurs when it gets into financial distress, while indirect bankruptcy costs are associated with actions the people who deal with the firm take to protect their own interests when the firm is in financial distress. Agency costs are costs associated with actions taken by managers and stockholders who are acting in their own interests rather than in the best interests of the firm. When a firm uses financial leverage, managers have incentives to take actions that benefit themselves at the expense of stockholders, and stockholders have incentives to take actions that benefit themselves at the expense of lenders. To the extent that these actions reduced the value of lenders’ claims, the expected losses will be reflected in the interest rates that lenders require. Equation 16.4 can be used to calculate the value of the income tax benefit associated with debt.

Describe the trade-off and pecking order theories of capital structure choice and explain what the empirical evidence tells us about these theories.

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The trade-off theory says that managers balance, or trade off, the benefits of debt against the costs of debt when choosing a firm’s capital structure in an effort to maximize the value of the firm. The pecking order theory says that managers raise capital as they need it in the least expensive way available, starting with internally generated funds, then moving to debt, then to the sale of equity. In contrast to the trade-off theory, the pecking order theory does not imply that managers have a particular target capital structure. There is empirical evidence that supports both theories, suggesting that each helps explain the capital structure choices made by managers.

Discuss some of the practical considerations that managers are concerned with when they choose a firm’s capital structure. Practical considerations that concern managers when they choose a firm’s capital structure include the impact of the capital structure on financial flexibility, risk, net income, and the control of the firm. Financial flexibility involves having the necessary financial resources to take advantage of unforeseen opportunities and to overcome unforeseen problems. Risk refers to the possibility that normal fluctuations in operating profits will lead to financial distress. Managers are also concerned with the impact of financial leverage on their reported net income, especially on a per-share basis. Finally, the impact of capital structure decisions on who controls the firm also affects capital structure decisions.

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IV.

Summary of Key Equations

Equation

Description

Formula

16.1

Value of the firm as the sum of the debt and equity values

VFirm = VAssets = VDebt + VEquity

16.2

16.3

16.4

Instructor’s Manual

Formula for weighted average cost of capital (WACC) for a firm with only common stock and no taxes

WACC = xDebt kDebt + xcs kcs

Cost of common stock in terms of the required return on assets and the required return on debt

V  kcs = kAssets +  Debt  ( kAssets − kDebt )  Vcs 

Value of the tax savings of debt (upper bound)

VTax-savings debt = D × t

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Chapter 17 Dividends and Dividend Policy Learning Objectives 1. Explain what a dividend is, and describe the different types of dividends and the dividend payment process. Calculate the expected change in a stock’s price around an exdividend date. 2. Explain what a stock repurchase is and how companies repurchase their stock. Calculate how taxes affect the after-tax proceeds that a stockholder receives from a dividend and from a stock repurchase. 3. Discuss the benefits and costs associated with dividend payments and compare the relative advantages and disadvantages of dividends and stock repurchases. 4. Define stock dividends and stock splits and explain how they differ from other types of dividends and from stock repurchases. 5. Describe factors that managers consider when setting the dividend payouts for their firms.

Chapter Outline

17.1

Dividends

•

The term payout policy is generally used to refer to a firm’s overall policy regarding distributions of value to stockholders.

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A dividend is something of value that is distributed to a firm’s stockholders on a pro-rata basis—that is, in proportion to the percentage of the firm’s shares that they own. •

A dividend can involve the distribution of cash, assets, or something else, such as discounts on the firm’s products that are available only to stockholders.

•

When a firm distributes value through a dividend, it reduces the value of the stockholders’ claims against the firm. ▪

A dividend reduces the stockholders’ investment in a firm by returning some of that investment to them.

Types of Dividends •

The most common form of dividend is the regular cash dividend, which is a cash dividend paid on a regular basis. ▪

These dividends are generally paid quarterly and are a common means by which firms return some of their profits to stockholders.

•

The size of a firm’s regular cash dividend is typically set at a level that management expects the company to be able to maintain in the long run, barring some major change in the fortunes of the company. ▪

•

Management does not want to have to reduce the dividend.

Management can afford to err on the side of setting the regular cash dividend too low because it always has the option of paying an extra dividend if earnings are higher than expected.

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Extra dividends are often paid at the same time as regular cash dividends and are used by some companies to ensure that a minimum portion of earnings is distributed to stockholders each year.

•

A special dividend, like an extra dividend, is a one-time payment to stockholders. ▪

Special dividends tend to be considerably larger than extra dividends and to occur less frequently.

▪ •

They are used to distribute unusually large amounts of cash.

A liquidating dividend is a dividend that is paid to stockholders when a firm is liquidated.

•

Distributions of value to stockholders can also take the form of discounts on the company’s products, free samples, and the like. ▪

These noncash distributions are not thought of as dividends, in part because the value received by stockholders is not in the form of cash and in part because the value received by individual stockholders does not often reflect their proportional ownership in the firm.

The Dividend Payment Process •

The Board Vote: The process begins with a vote by a company’s board of directors to pay a dividend. ▪

As stockholder representatives, the board must approve any distribution of value to stockholders.

•

The Public Announcement: The date on which this announcement is made is known as the declaration date, or announcement date, of the dividend.

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The announcement typically includes the amount of value that stockholders will receive for each share of stock that they own, as well as the other dates associated with the dividend payment process.

▪

The price of a firm’s stock often changes when a dividend is announced because the public announcement sends a signal to the market about what management thinks the future performance of the firm will be. o

If the signal differs from what investors expected, they will adjust the prices at which they are willing to buy or sell the company’s stock accordingly.

This means that a dividend decision sends information to investors and that information is incorporated into stock prices at the time of the public announcement.

•

The Ex-Dividend Date: The ex-dividend date is the first date on which the stock will trade without rights to the dividend. ▪

An investor who buys shares before the ex-dividend date will receive the dividend, while an investor who buys the stock on or after the ex-dividend date will not.

▪

Before the ex-dividend date, a stock is said to be trading cum dividend, or with dividend.

▪

On or after the ex-dividend date, the stock is said to trade ex dividend.

▪

The price of the firm’s shares changes on the ex-dividend date even if there is no new information about the firm.

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This drop simply reflects the difference in the value of the cash flows that the stockholders are entitled to receive before and after the ex-dividend date.

•

The Record Date: The record date typically follows the ex-dividend date by two days. ▪

The record date is the date on which an investor must be a stockholder of record (that is, officially listed as a stockholder) in order to receive the dividend.

▪

The ex-dividend day precedes the record date because it takes time to update the stockholder list when someone purchases shares.

•

The Payable Date: The final date in the dividend payment process is the payable date, when the stockholders of record actually receive the dividend. ▪

The divided payment process is not as well defined for private companies as it is for public companies, because in private companies shares are bought and sold less frequently, there are fewer stockholders, and no stock exchange is involved in the dividend payment process.

17.2

Stock Repurchases

•

With a stock repurchase, a company buys some of its shares from stockholders. A.

How Stock Repurchases Differ from Dividends

•

Stock repurchases differ from dividends in four ways. ▪

First, they do not represent a pro-rata distribution of value to the stockholders because not all stockholders participate.

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Individual stockholders decide whether they want to participate in a share repurchase.

▪

Second, when a company repurchases its own shares, it removes them from circulation. o

This reduces the number of shares of stock that are held by investors, thereby removing a large number of shares from circulation. This can change the ownership of the firm.

▪

Third, stock repurchases are taxed differently than dividends. o

The total value of dividends is normally taxed.

Conversely, when a stockholder sells shares back to the company, the stockholder is taxed only on the profit from the sale.

▪

Fourth, the way in which we account for dividends and stock repurchases on a company’s balance sheet is also different. o

When the company pays a cash dividend, the cash account on the assets side of the balance sheet and the retained earnings account on the liabilities and stockholders’ equity side of the balance sheet are reduced.

In contrast, when a company uses cash to repurchase stock, the cash account on the assets side of the balance sheet is reduced, while the treasury stock account on the liabilities and stockholders’ equity side of the balance sheet is increased.

How Stock Is Repurchased

•

Companies repurchase stock in three general ways.

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First, they can simply purchase shares in the market, much as you would. These kinds of purchases are known as open-market repurchases, which are a very convenient way of repurchasing shares on an ongoing basis. o

Open-market repurchases can be cumbersome because the government limits the number of shares that a company can repurchase on a given day. ▪

These limits, which are intended to restrict the ability of firms to influence their stock price through trading activity, mean that it could take months for a company to distribute a large amount of cash using open-market repurchases.

When the management of a company wants to distribute a large amount of cash at one time and does not want to use a special dividend, it can repurchase shares using a tender offer, which is an open offer by a company to purchase shares. ▪

There are two types of tender offers: fixed price and Dutch auction. •

With a fixed-price tender offer, management announces the price that will be paid for the shares and the maximum number of shares that will be repurchased. o Interested stockholders then tender their shares by letting management

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know how many shares they are willing to sell. •

With a Dutch auction tender offer, the firm announces the number of shares that it would like to repurchase and asks the stockholders how many shares they would sell at a series of prices, ranging from just above the price at which the shares are currently trading to some higher number. o Stockholders then tell the company how many of their shares they would sell at the various offered prices.

The third general way in which shares are repurchased is through direct negotiation with a specific stockholder, where targeted stock repurchases are typically used to buy blocks of shares from large stockholders.

These repurchases can benefit stockholders because managers may be able to negotiate a per-share price that is below the current market price because the stockholder who owns a large block of shares might have to offer the shares for a below-market price in order to sell them all in the open market.

17.3

Dividends and Firm Value

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Dividend policy can affect the value of a firm.

•

The general conditions under which capital structure policy does not affect firm value:

•

There are no taxes.

There are no information or transaction costs.

The real investment policy of the firm is fixed.

Dividend policy does not matter under the above conditions because a stockholder can “manufacture” any dividends he or she wants at no cost when these conditions hold.

•

A stockholder could also undo a company’s dividend policy by simply reinvesting the dividends that the company pays in new shares.

•

If investors could replicate a company’s dividend policy on their own at no cost, they would not care whether or not the company paid a dividend. A.

Benefits and Costs of Dividends

•

One benefit of paying dividends is that it attracts investors who prefer to invest in stocks that pay dividend yields.

•

Although it is true that the investor could simply sell some stock each month to cover expenses, in the real world it may be less costly—and it is certainly less trouble—to simply receive regular cash dividend payments instead. ▪

Recall that under the M&M conditions, there are no transaction costs.

▪

In the real world, however, the retiree or institutional investor will have to pay brokerage commissions each time he or she sells stock.

▪

The dividend check, in contrast, simply arrives each quarter.

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Of course, the retiree will have to consider the impact of taxes on the value of dividends versus the value of proceeds from the sale of stock; but it is quite possible that receiving dividends might, on balance, be more appealing.

▪

Other investors have no current need for income from their investment portfolios and prefer not to receive dividends.

▪

Some argue that a large regular dividend indicates that a company is financially strong because the “signal” of strength can result in a higher stock price. o

This argument is based on the assumption that a company that is able to pay a large dividend, rather than holding on to cash for future investments, is a company that is doing so well that it has more money than it needs to fund its available investments.

The problem with this line of reasoning is that it ignores the possibility that a company might have more than enough money for all its future investment opportunities because it does not have many future investment opportunities.

▪

If the board of directors of a company votes to pay the stockholders dividends that amount to more than the excess cash that the company is producing from its operations, then the money to pay the dividends will have to come from selling equity periodically in the public markets.

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The need to raise equity in the capital markets will help align the incentives of managers with those of stockholders because it increases the cost to mangers of operating the business inefficiently.

•

There are costs to the firm associated with dividends. ▪

Taxes are among the most important costs.

▪

Owners of stocks that pay dividends often have to pay brokerage fees if they want to reinvest the proceeds. o

To eliminate this cost, some companies offer dividend reinvestment programs (DRIPs). Through a DRIP, a company sells new shares, commission free, to dividend recipients who elect to automatically reinvest their dividends in the company’s stock.

▪

To the extent that a company uses a lot of debt financing, paying dividends can increase the cost of debt.

•

Using the cash flow identity of sources and uses of cash, we can see that an expected increase in the cash flow from operations is a good signal, and investors will interpret it as suggesting that cash flows to stockholders will increase in the future.

Stock Price Reactions to Dividend Announcements

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The cash flow identity suggests that managers change dividend polices when something fundamental has changed in the business; it is this fundamental change that causes the stock price to change. ▪

The dividend announcement is really just the means by which investors find out about the fundamental change.

Dividends versus Stock Repurchases

•

Stock repurchases are an alternative to dividends as a way of distributing, and they have some distinct advantages over dividends. ▪

They give stockholders the ability to choose when they receive the distribution, which affects the timing of the taxes they must pay as well as the cost of reinvesting funds that are not immediately needed.

▪

Stockholders who sell shares back to a company pay taxes only on the gains they realize. Historically, these capital gains have been taxed at a lower rate than dividends.

▪

From management’s perspective, stock repurchases provide greater flexibility in distributing value. o

Even when a company publicly announces an ongoing openmarket stock repurchase program, as opposed to a regular cash dividend, investors know that management can always quietly cut back or end the repurchases at any time.

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This means that if future cash flows are not certain, managers are likely to prefer to distribute extra cash today by repurchasing shares through open-market purchases because this enables them to preserve some flexibility.

Since most ongoing stock repurchase programs are not as visible as dividend programs, they cannot be used as effectively to send a positive signal about the company’s prospects to investors.

A more subtle issue concerns the fact that managers can choose when to repurchase shares in a stock repurchase program. ▪

Just like other investors, managers prefer purchasing shares when they believe that the shares are undervalued in the market.

▪

The problem is that since managers have better information about the prospects of the company than do other investors, they can take advantage of this information to the detriment of other investors. o

Management is supposed to act in the best interest of all its stockholders.

17.4

Stock Dividends and Stock Splits A.

Stock Dividends

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One type of “dividend” that does not involve the distribution of value is known as a stock dividend. ▪

When a company pays a stock dividend, it distributes new shares of stock on a pro-rata basis to existing stockholders.

▪

The only thing that happens when the stock dividend is paid is that the number of shares each stockholder owns increases and their value goes down proportionately. o

The stockholder is left with exactly the same value as before.

Stock Splits

•

A stock split is quite similar to a stock dividend, but it involves the distribution of a larger multiple of the outstanding shares. ▪

We can often think of a stock split as an actual division of each share into more than one share.

•

Besides their size, a key distinction between stock dividends and stock splits is that typically stock dividends are regularly scheduled events, like regular cash dividends, while stock splits tend to occur infrequently during the life of a company.

Reasons for Stock Dividends and Splits

•

The most often cited reason for stock dividends or splits is known as the trading range argument, which proposes that successful companies use stock dividends or stock splits to make their shares more attractive to investors. ▪

It has historically been more expensive for investors to purchase odd lots of less than 100 shares than round lots of 100 shares.

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Odd lots are less liquid than round lots because more investors want to buy round and it is relatively expensive for companies to service odd-lot owners.

▪

Researchers have found little support for this explanation.

▪

The transaction costs argument no longer carries much weight, as there is now little difference in the costs of purchasing round lots and odd lots.

•

One real benefit of stock splits is that they can send a positive signal to investors about management’s outlook for the future, and this, in turn, can lead to a higher stock price. ▪

Management is unlikely to want to split the stock of a company 2-for-1 or 3-for-1 if it expects the stock price to decline. It is likely to split the stock only when it is confident that the stock’s current market price is not too high.

•

Reverse stock splits may be undertaken to satisfy exchange requirements. ▪

The New York Stock Exchange generally requires listed shares to trade for more than $5, and the NASDAQ requires shares to trade for at least $1.

17.5

Setting a Dividend Payout

What Managers Tell Us

•

The best-known survey of dividend policy was published in 1956, more than 55 years ago, by John Lintner. The survey asked managers at 28 industrial firms how they set their firms’ dividend policies. ▪

The key conclusions from the Lintner study are as follows:

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Firms tend to have long-term target payout ratios.

Dividend changes follow shifts in long-term sustainable earnings.

Managers focus more on dividend changes than on the absolute level (dollar amount) of the dividend.

Managers are reluctant to make dividend changes that might have to be reversed.

•

A more recent study, by Brav, Graham, Harvey, and Michaely published in 2005, updates Lintner’s findings. ▪

The link between earnings and dividends is weaker today than when Lintner conducted his survey.

▪

They found that rather than setting a target level for repurchases, managers tend to repurchase shares using cash that is left over after investment spending.

▪

In addition, many managers prefer repurchases because repurchase programs are more flexible than dividend programs and because they can be used to time the market by repurchasing shares when management considers a company’s stock price too low.

▪

Finally, the managers who were interviewed appeared to believe that institutional investors do not prefer dividends to repurchases or vice versa. o

In other words, the choice between these two methods of distributing value does not have much of an effect on who owns the company’s stock.

Practical Considerations in Setting a Dividend Policy

•

A company’s dividend policy is largely a policy about how the excess value in a company is distributed to its stockholders.

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It is extremely important that managers choose their firms’ dividend polices in a way that enables them to continue to make the investments necessary for the firm to compete in its product markets.

•

Managers should consider several practical questions when selecting a dividend policy: 1.

Over the long term, how much does the company’s level of earnings (cash flows from operations) exceed its investment requirements? How certain is this level?

Does the firm have enough financial reserves to maintain the dividend payout in periods when earnings are down or investment requirements are up?

Does the firm have sufficient financial flexibility to maintain dividends if unforeseen circumstances wipe out its financial reserves when earnings are down?

Can the firm raise equity capital quickly if necessary?

If the company chooses to finance dividends by selling equity, will the increased number of stockholders have implications for control of the company?

II.

Suggested and Alternative Approaches to the Material

Chapter 17 discusses dividends and other methods of distributing value to stockholders. The discussion begins with a definition of a dividend as well as some practical details that are needed

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to study the topic. The chapter then turns to stock repurchases as an alternative to delivering value to stockholders. The chapter next discusses how a firm’s dividend policy might affect firm value. A brief discussion of dividend splits and stock dividends is then discussed, and finally the chapter ends by discussing the practical matters associated with setting a dividend policy. Although the material in the chapter is introduced formally, for the first time, the discussion of whether dividend policy matters will look familiar to the student due to the irrelevance arguments used by the Modigliani and Miller discussion just as with the capital structure chapter. As such, the student should understand the line of reasoning needed to comprehend the material. It may be tempting to leave the practical discussion of dividends for students to pick up from the text, but they need that material to reconcile how dividends actually affect firm value, versus the theoretical discussion. This material is generally considered advanced, but the chapter is highly recommended to anyone who has the time to cover the material during a quarter or semester. Many students will not be exposed to this topic again, and others will find this discussion useful for their later work in this area.

III. Summary of Learning Objectives 1.

Explain what a dividend is, and describe the different types of dividends and the dividend payment process. Calculate the expected change in a stock’s price around an ex-dividend date. A dividend is something of value that is distributed to a firm’s stockholders on a pro-rata basis—that is, in proportion to the percentage of the firm’s shares that they own. There

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are four types of dividends: (1) regular cash dividends, (2) extra dividends, (3) special dividends, and (4) liquidating dividends. Regular cash dividends are the cash dividends that firms pay on a regular basis (typically quarterly). Extra dividends are paid, often at the same time as a regular cash dividend, when a firm wants to distribute additional cash to its stockholders. Special dividends are one-time payments that are used to distribute a large amount of cash. A liquidating dividend is the dividend that is paid when a company goes out of business and is liquidated. The dividend payment process begins with a vote by the board of directors to pay a dividend. This vote is followed by the public announcement of the dividend on the declaration date. On the ex-dividend date, the shares begin trading without the right to receive the dividend. The record date, which follows the ex-dividend date by two days, is the date on which an investor must be a stockholder of record in order to receive the dividend. Finally, the payable date is the date on which the dividend is paid. Learning by Doing Application 17.1 shows how to calculate the expected change in a stock’s price around the ex-dividend date.

Explain what a stock repurchase is and how companies repurchase their stock. Calculate how taxes affect the after-tax proceeds that a stockholder receives from a dividend and from a stock repurchase. A stock repurchase is a transaction in which a company purchases some of its own shares from stockholders. Like dividends, stock repurchases are used to distribute value to stockholders. The three ways in which stock is repurchased are (1) open-market repurchases, (2) tender offers, and (3) targeted stock repurchases. With open-market

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repurchases, the company purchases stock on the open market, just like any investor does. A tender offer is an open offer by a company to purchase shares. Finally, targeted stock repurchases are used to purchase shares from specific stockholders. The calculation of the after-tax proceeds that a stockholder receives is illustrated in the text and in Learning by Doing Application 17.2.

Discuss the benefits and costs associated with dividend payments and compare the relative advantages and disadvantages of dividends and stock repurchases. The potential benefits from paying dividends include (1) attracting certain investors who prefer dividends, (2) sending a positive signal to the market concerning the company’s prospects, (3) helping to provide managers with incentives to manage the company more efficiently, and (4) helping to manage the company’s capital structure. One cost of dividends is the fact that a stockholder must take a dividend, and pay taxes on the dividend, whether or not he or she wants the dividend. Stockholders who want to reinvest the dividend in the company must, unless there is a dividend reinvestment program (DRIP), pay brokerage fees to reinvest the money. Finally, paying a dividend can increase a company’s leverage and thereby increase its cost of debt. With a stock repurchase program, investors can choose whether they want to sell their shares back to the company. Stock repurchases also receive more favorable tax treatment. From management’s point of view, stock repurchase programs offer more flexibility than dividends and can have less of an effect on the company’s stock price. One disadvantage of stock repurchases involves an ethical issue: Managers have better information than others about the prospects of their companies, and a stock repurchase

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can enable them to take advantage of this information in a way that benefits the remaining stockholders at the expense of the selling stockholders.

Define stock dividends and stock splits and explain how they differ from other types of dividends and from stock repurchases. Stock dividends involve the pro-rata distribution of additional shares in a company to its stockholders. Stock splits are much like stock dividends but involve larger distributions of shares than stock dividends. Stock dividends and stock splits differ from other types of dividends because they do not involve the distribution of value to stockholders. The total value of each stockholder’s shares is the same after a stock dividend or stock split as it was before the distribution. Since they do not involve the distribution of value, stock dividends are not really dividends at all.

5. Describe factors that managers consider when setting the dividend payouts for their firms. A company’s dividend payout decision is largely about how excess value in the company is distributed to its stockholders. Setting the payout depends on several factors: the expected level and certainty of the firm’s future profitability, the firm’s future investment requirements, the firm’s financial reserves and financial flexibility, the firm’s ability to raise capital quickly if necessary, and the control implications of financing dividends by selling equity.

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Summary of Key Equations

The chapter is primarily a qualitative chapter and does not have a relevant summary of key equations.

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CHAPTER 18 Business Formation, Growth, and Valuation

Learning Objectives 1.

Explain why the choice of organizational form is important, and describe two financial considerations that are especially important in starting a business.

Describe the key components of a business plan and explain what a business plan is used for.

Explain the three general approaches to valuation and value a business using common business valuation approaches.

Explain how valuations can differ between public and private companies and between young and mature companies, and discuss the importance of control and key person considerations in valuation.

Chapter Outline

18.1

Starting a Business •

Individuals go into business for a variety of reasons.

•

Regardless of their motivation, the first decision they must make is whether they want to found a business or acquire an existing business.

•

Starting a business is inherently more risky than buying and growing a business that someone else has already established.

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The founder of a company must start from scratch and make several critical decisions, including:

•

▪

Choosing the product(s) to sell

▪

Choosing the markets to sell them in

▪

Choosing the best strategy for selling them

▪

Raising the money necessary to develop the product(s)

▪

Acquiring the necessary assets

▪

Hiring the right people

As the business is being built, the founder must also manage the day-to-day operations to ensure that his or her overall plan is being implemented.

Making the Decision to Proceed •

According to the SBA, 533,945 businesses were started in 2010 in the United States, but less than 45 percent of them will still be in business by 2014.

•

Businesses fail for a number of different reasons including: ▪

Lack of acceptance of the products by customers.

▪

Poorly thought-out strategy

▪

Poor management skills to properly execute a good strategy.

▪

Underestimating how much money it will take to get their businesses up and running.

•

Chances of succeeding in a business can improve if you ▪

Do not jump into a business without careful thought.

▪

Don’t overanalyze opportunities to the point where you are just convincing yourself not to proceed.

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Take on calculated risks.

▪

Don’t think that failure will ruin your chances of ultimately achieving business success.

Choosing the Right Organizational Form •

In addition to the organizational forms discussed in Chapter 1—sole proprietorship, partnerships, and corporations—two other forms of organizations are discussed here. They are the limited liability companies (LLC) and the S-corporation.

•

An LLC is a hybrid of a limited partnership and a corporation. ▪

Like a corporation, an LLC provides limited liability for the people who make the business decisions in the firm while enabling all investors to retain the tax advantages of a limited partnership.

▪

Limited partnerships are more costly to form than sole proprietorships because the partners must hire an attorney to draw up and maintain the partnership agreement.

▪

The lives of partnerships and LLCs are flexible.

▪

Limited partners and LLCs are less constrained than general partnerships because they can raise money from limited partners or “members,” General partnerships can turn to all of the partners for additional capital.

•

An S-corporation is a variation of the C-corporation form that is used by public corporations.

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This change allows the stockholders to avoid double taxation but places limits on the ownership of the firm’s stock.

▪

All profits of an S-corporation pass directly to the stockholders as they would pass to the partners in a partnership.

▪

Corporations, which are “legal persons” under state law, automatically have an indefinite life.

•

Exhibit 18.1 provides a comparison of these common forms of business organization on a number of different dimensions.

Financial Considerations •

Two tools are particularly useful in understanding the cash requirements of a business and in estimating how much financing a new business will require— cash flow break-even analysis and the cash budget.

•

It is important for an entrepreneur to understand the concept of cash flow breakeven and how to calculate this point for each product a business produces. ▪

This calculation focuses the entrepreneur’s attention on the importance of maximizing a product’s per unit contribution and minimizing its associated overhead costs.

▪

It also provides a means of estimating how long it will take for a product to reach the break-even point and, therefore, how much money will be needed to launch a new product or business.

•

The cash budget is also a very useful planning tool for entrepreneurs. It summarizes the cash flows into and out of a firm over a period of time.

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Cash budgets often present the inflows and outflows on a monthly basis but can be prepared for any period, including daily or weekly.

▪

Preparing a cash budget helps an entrepreneur better understand where money is coming from, where it is going, and how much external financing is likely to be needed and when.

▪

Knowing how much external financing is likely to be needed and when helps the entrepreneur plan fund-raising efforts before it is too late.

18.2

The Role of the Business Plan A.

Why Business Plans Are Important •

The entrepreneur must convince potential investors that purchasing debt or equity in the firm will yield attractive returns.

•

To overcome the skepticism of outside investors, many entrepreneurs prepare a business plan.

•

A business plan is like a road map for a business in that it presents results from a strategic planning process that focuses on how the business will be developed over time.

•

A business plan is a tool that can

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▪

help raise capital;

▪

help an entrepreneur set the goals and objectives for the company;

▪

serve as a benchmark for evaluating and controlling the company’s performance; and

▪

communicate the entrepreneur’s ideas to managers, outside directors, customers, suppliers, and others.

The Key Elements of a Business Plan •

A well-developed business plan includes the following: ▪

An executive summary, which summarizes the key issues presented in the report.

▪

A company overview, which describes what the company does and what its comparative advantages are.

▪

A detailed description or the product(s) and services the company will sell, its current state of development or market penetration, competitive advantages, product life cycle, and any patents or legal protections that might provide a competitive advantage.

▪

A market analysis, which discusses the industry and highlights the important characteristics of the industry as they relate to the company.

▪

A discussion of the marketing and sales activities that will enable the business to achieve the sales and margin levels reflected in the financial forecasts.

▪

A discussion of the operations of the business.

▪

Detailed information on the management team and ownership of the

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business. ▪

A detailed discussion of capital requirements and uses.

▪

A business plan also presents historical financial results when they are available and financial forecasts.

▪

The end of a business plan often includes appendixes, which contain information providing detailed support for the analyses that are presented earlier in the report.

18.3

Valuing a Business •

The value of a business is determined by the magnitude of the cash flows that it is expected to produce, the timing of those cash flows, and the likelihood that the cash flows will be realized.

Fundamental Business Valuation Principles •

There are two important valuation principles. ▪

The first principle is that the value of a business changes over time.

▪

The second valuation principle is that there is no such thing as the value for a business.

•

The value of a business changes over time. ▪

Changes in general economic conditions, industry conditions, and decisions that are made by the managers all affect the value of the cash flows that a business is expected to generate in the future.

▪

Actions by competitors also affect the value of a business.

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The investment, operating, and financing decisions made by managers also affect the value of a business.

•

The value of a business can be different to different investors. ▪

A strategic investor is one who has an interest in acquiring the business. o The investment value of the firm to a strategic investor will take into consideration the benefits that can accrue from the acquisition and hence is likely to carry a higher value.

▪

A financial investor, on the other hand, is only interested in financial performance of the firm and not in acquiring the business. o Their valuation, known as the fair market value, will be lower than that of the strategic investor.

Business Valuation Approaches •

Business valuation methods can be classified into one of three general categories: (1) cost approaches, (2) market approaches, and (3) income approaches.

Cost Approaches •

Two cost approaches that are commonly used are replacement cost and adjusted book value.

•

The replacement cost of a business is the cost of duplicating the assets of the business in their present form as of the valuation date. ▪

The replacement cost valuation approach is generally used to value individual assets within a business when they are being insured.

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When using the replacement cost approach in a buy-versus-build analysis, you must include the cost of all tangible assets and all intangible assets.

▪

You must also include the cost of hiring the people necessary to run the business and the time that it would take to build the business.

▪

The timing of the cash flows is very important and must be taken into consideration because, generally, acquired businesses lead to quicker cash flows.

•

The adjusted book value approach involves restating the value of the individual assets in a business to reflect their fair market values. ▪

The fair market value of each individual asset is estimated separately, and the total value of the business is then obtained by summing the fair market values of the individual assets.

▪

An adjusted book value analysis should include all tangible and intangible assets.

▪

The adjusted book value approach is useful in valuing holding companies whose main assets are publicly traded or other investment securities but is generally less applicable for operating businesses.

▪

The value of an operating business is usually greater than the sum of its individual assets, and the excess value is called the “going concern” value.  The going-concern value of an asset reflects the value associated with additional future cash flows the business

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produces because of the way in which the individual assets are managed together. ▪

The adjusted book value approach is useful in estimating a floor value for a business under certain circumstances: (1) it is especially difficult to forecast the cash flows that a business is likely to produce, (2) you suspect that the going-concern value of the business is negative, and (3) liquidation is being explicitly considered.

Market Approaches

Two market approaches that are commonly used are multiples analysis and transactions analysis. •

Multiples analysis uses stock price or other value multiples that are observed for public companies to estimate the value of a company’s stock or an entire business.

•

The process calls for: ▪

identifying publicly traded companies engaged in business activities that are similar to those of the company being analyzed, and

▪

using the prices at which shares of those comparables are trading, along with accounting data, to estimate the value of the company of interest.

•

This approach is often used to help price a company’s shares for an IPO, or when all of its shares are being sold privately to investors.

•

Price/earnings (P/E) and price/revenue multiples (ratios) are commonly used to directly estimate the value of the stock in a company.

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Analysts either use the average multiple from other publicly held peers, or a multiple from a single comparable company to estimate the value of the company of interest.

•

While doing a multiples analysis, you need to be aware of certain issues. ▪

When using multiples of publicly held firms to value one that is not, you should be aware of the presence of a marketability discount that can be sizable.

▪

Identifying one or more comparable firms is not an easy task.

▪

When using the multiple of a comparable firm, you need to be aware of differences in the capital structures of the firms being compared.

▪

You are estimating a fair market value, not the investment value.

▪

It is important to make sure that the numerator and the denominator of the ratio you are using are consistent with each other.

▪

The data used to compute the multiple for the comparable company should include the stock price as of the valuation date and accounting data from the same period for which you have accounting data for the company of interest.

•

In the transaction approach, analysts use the information on what someone has paid for a comparable company in a merger or an acquisition to estimate a value for the firm.

•

This transaction information is used to compute the same types of multiples that are used in a multiples analysis, and these multiples are used in the same way to value the company of interest.

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Since transaction data reflects the price that a particular investor paid for an entire company, it provides an estimate of the investment value to that investor.

•

Transaction information is obtained from the financial statements of public companies that have acquired other companies or from services that collect and sell this type of information.

•

It is difficult to use this approach in practice for several reasons. ▪

Transactions data are not typically as reliable as the data available for multiples analysis, especially when they are associated with a private firm.

▪

Transactions involving the purchase or sale of an entire business in an industry tend to occur relatively infrequently and hence the data is not very timely.

▪ E.

The terms of the transactions can be difficult to assess.

Income Approaches •

The most direct approaches for estimating the value of the cash flows a business is expected to produce are the income approaches, which, like NPV analysis, directly estimate the value of those cash flows.

•

These approaches provide the intrinsic value for the firm, which can be different from the market value. ▪

While market value reflects what people are willing to pay for the firm, the intrinsic value reflects what the firm is truly worth.

•

There are a couple of things to consider when using the income approach

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First, unlike the case with projects, it is difficult to estimate the life of a business.

▪

Second, businesses often have cash or other assets that are not necessary for operations that can complicate the valuation. ▪

These assets will be identified as nonoperating assets; Equation 18.2 shows how these factors are taken into consideration when valuing the firm using an income approach.

•

In the free cash flow from the firm (FCFF) approach, an analyst values the free cash flows that the assets of the firm are expected to produce in the future. ▪

The present value of these cash flows equals the total value of the firm, or its enterprise value.

▪

We do not include the cash necessary to pay short-term liabilities that do not have interest charges associated with them, such as accounts payable and accrued expenses. ▪

The costs associated with these non-interest-bearing current liabilities, which are included in the firm’s cost of sales and other operating expenses, are subtracted in the calculation of FCFF.

▪

Exhibit 18.3 shows how to determine the value of FCFF.

▪

In this approach the total value of the firm, VF, is computed as the present value of the FCFF, discounted by the firm’s WACC.

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When analysts use the WACC approach to value a business, they must make an assumption about how the firm’s operations will be financed in the future.

•

The free cash flow to equity (FCFE) approach uses only the portion of the cash flows that are available for distribution to stockholders. ▪

Stripping out the cash flows to or from the lenders leaves the cash flows available to stockholders.

▪

Three specific cash flows associated with lenders are not included: the interest expense on existing debt, the repayment of debt principal, and the proceeds from new debt issues.

▪

Exhibit 18.6 shows how FCFE is calculated.

▪

In using the FCFE valuation approach, the cost of equity, kE, is used to discount the residual cash flows as shown in Equation 18.4.

•

The dividend discount model (DDM) approach estimates the value of equity directly by discounting cash flows to stockholders. ▪

In contrast to the FCFE approach, which values cash flows that are available for distribution to stockholders, the DDM approach values the stream of cash flows that stockholders expect to receive through dividend payments. ▪

Recognize that the firm may or may not be expected to distribute all available cash flows in any particular year.

▪

The constant-growth dividend model, Equation 9.4, is an example of a DDM.

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However, only some firms have a constant growth. ▪

More often, use of the DDM approach involves discounting dividends that either do not begin until some point in the future or that are currently growing at a high rate that is not sustainable in the long run.

18.4

Important Issues in Valuation A.

Financial Statements •

Incomplete and unreliable financial statements can complicate the process of valuing a private business, making it more difficult to accurately assess its value.

•

Some private companies have complete, audited financial statements, while others have incomplete financial statements that are not prepared in accordance with the GAAP. ▪

All public companies are required to file audited financial statements with the SEC.

•

In contrast to the financial statements of publicly held firms, private company financials often include personal expenses of the owner and excess compensation expenses.

Marketability •

The shareholder of a private firm may have to spend considerable resources (both money and time) to sell his or her shares.

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The shareholders of publicly held firms find it much easier to liquidate their holdings.

•

The higher transaction costs associated with the stock at the private firm will result in a lower price for that investment.

•

This must be taken into account in the form of a marketability discount when estimating the value of any claim to the cash flows of a firm.

Young (Rapidly Growing) versus Mature Companies •

Young, rapidly growing companies tend to be more difficult to value than mature, stable companies.

•

One factor that makes it more difficult to value a young company is that less reliable historical information is available.

•

Another factor is that the future of a young, rapidly growing company is often less certain than that of a mature company because much of the young company’s future growth depends on investment, operating, and financing decisions that have not yet been made.

•

Without profits, it is difficult to use earnings multiples to value the business, leaving price/revenue or enterprise value/revenue multiples as the only viable alternatives for a multiples analysis.

•

In order to grow, many young companies have to invest a considerable amount of money.

•

The cash flows will be negative until the business becomes profitable and its investment expenditures are less than those profits.

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This means that the positive cash flows, which represent the value of the business, are further into the future and are, therefore, less certain.

Controlling Interest versus Minority Interest •

Another important issue that must be considered when valuing a business is whether a controlling ownership interest or a minority interest is being valued.

•

The amount of stock that is required for an investor to exercise control can vary depending on the ownership structure of the company. ▪

Whether a controlling ownership interest is being sold has important implications for a valuation analysis.

•

An adjustment must be made to reflect the benefits of control if one used multiples based on public stock market prices to estimate the value of a controlling interest.

•

Similarly, when you use an income approach to value a business, the cash flow forecasts and discount rate assumptions will differ depending on whether you are valuing a minority or a controlling ownership interest.

•

A discount rate based on CAPM might be too high for a valuation that involves a controlling position. ▪

To adjust for the effects of an incorrect discount rate and for any possible cash flows that are not reflected in a valuation based on an income approach, analysts add a control premium.

Key People

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Analysts must also consider whether it is appropriate to adjust the estimated value of the business for the likelihood that these “key people” may not remain with the firm as long as expected.

•

If an analyst believes that those customers may go to another firm if the CEO departs, then a key person discount may be appropriate.

II.

Suggested and Alternative Approaches to the Material

The earlier chapters discussed how businesses are organized and how financial managers make long-term investment decisions, manage working capital requirements, and finance the investments and activities of their businesses. In this chapter these concepts are reexamined in the context of a discussion of business formation, growth, and valuation. This chapter provides an integrated perspective on how financial managers’ decisions affect firm value. The authors begin by considering the decision by an entrepreneur to start a business and how the business should be organized. They then discuss financial considerations that must be of concern to managers of young, rapidly growing firms. Next, they focus on the role that a carefully prepared business plan plays in raising capital for a young, rapidly growing business and in providing a road map of where the business is going for use in managerial decision making. The last two sections of this chapter address business valuation concepts. The discussions in these sections provide a broad overview of the business valuation approaches that financial managers use and how differences in the characteristics of public and private companies and of young, rapidly growing, and mature companies affect valuation analyses. The impact of control considerations and key people on business valuations is also considered. Copyright ©2015 John Wiley & Sons, Inc.

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This chapter is an ideal way to complete a semester’s discussion on the principles of finance and how they apply in a corporate context. The instructor is encouraged to use the end– of-chapter material to help convey the information to the students because the material is consistent with the approach in previous chapters in providing a variety of questions, yet allowing for repetition to benefit the students.

III. Summary of Learning Objectives 1.

Explain why the choice of organizational form is important, and describe two financial considerations that are especially important in starting a business. The choice of organizational form is important because it affects the returns from a business in a number of ways. For example, it affects the cost of getting started, the life of the business, management’s ability to raise capital and grow the business, the control of the business, the ability to attract and retain good managers, the exposure of the investors to liabilities, and the taxes that are paid on the earnings of the business. Two especially important financial considerations are the cash flow break-even point for the business and its overall cash inflows and outflows. The cash flow breakeven point represents the level of unit sales that must be achieved in order for the business to break even on a cash flow basis. Entrepreneurs must also understand where money is coming from, where it is going, and how much external financing is likely to be needed and when. The cash budget helps with this understanding.

Describe the key components of a business plan and explain what a business plan is used for.

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The key components of a business plan include the executive summary, a company overview, a description of the company’s products and services, a market analysis, a discussion of marketing and sales activities, a discussion of the businesses operations, a discussion of the management team, the ownership structure of the firm, capital requirements and uses, and financial forecasts. A business plan helps an entrepreneur set the goals and objectives for a company, serves as a benchmark for evaluating and controlling the company’s performance, and helps communicate the entrepreneur’s ideas to managers and others (including investors) outside the firm.

Explain the three general approaches to valuation and value a business using common business valuation approaches. The three general valuation approaches are (1) cost approaches, (2) market approaches, and (3) income approaches. Cost approaches commonly used in business valuation are the replacement cost and adjusted book value approaches. The market approaches are multiples analysis and transactions analysis. Three key income approaches are the free cash flow from the firm, free cash flow to equity, and dividend discount approaches. The application of these approaches is discussed in Section 18.3.

Explain how valuations can differ between public and private companies and between young and mature companies, and discuss the importance of control and key person considerations in valuation.

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Valuations differ between public and private companies for a number of reasons, including (1) the quality of the financial statements and (2) the marketability of the securities being valued. Marketability is important because it affects the price that investors are willing to pay for a security. The less marketable a security, the lower the price investors are willing to pay. Young, rapidly growing companies are more difficult to value than mature companies because there is less reliable historical information on young companies and their futures tend to be less certain. Control is an important consideration in business valuation because having control of a business provides an investor with more flexibility in managing the business. Investors value this flexibility and will, therefore, pay more for a controlling interest in a company. If the cash flows that a business is expected to generate depend heavily on certain employees, those employees are key people. When valuing a business, an analyst must account for the possibility that the key people will unexpectedly leave the company and must consider the associated impact on the company’s cash flows.

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IV. Summary of Key Equations

Equation

Description

18.1

Price/earnings multiple based on constant-growth model

18.2

Implementing the income approach to business valuation

18.3

FCFF approach

Formula

P0 b = E1 kcs − g

VF = PV(FCFT) + PV(TVT) + NOA

 FCFFt VF =  t t = 0 (1+ WACC) 

18.4

FCFE approach

VE =  t =0

FCFEt

(1 + kE )

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Chapter 19 Financial Planning and Managing Growth

Learning Objectives 1.

Explain what a financial plan is and why financial planning is so important.

Discuss how management uses financial planning models in the planning process, and explain the importance of sales forecasts in the construction of financial planning models.

Discuss how the relation between projected sales and balance sheet accounts can be determined, and analyze a strategic investment decision using a percent of sales model.

Describe the conditions under which fixed assets vary directly with sales, and discuss the impact of so-called lumpy assets on this relation.

Explain what factors determine a firm’s sustainable growth rate, discuss why it is of interest to management, and compute the sustainable growth rate for a firm.

Chapter Outline

19.1

Financial Planning A.

The Planning Documents

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Financial planning relates to the identification of the kinds of projects that a firm needs to undertake and the ways of financing those projects. This results in a financial plan.

•

In putting together a financial plan, four main issues are addressed by management through detailed planning. ▪

Strategic plan—Where is the company headed?

▪

Investment plan—What capital resources does the management need to get there?

▪

Financing plan—How is the firm going to pay for the resources needed?

▪

Divisional business plan – What will each division do to achieve the firm’s strategic goals?

▪ •

Cash budget—How is the firm going to pay its day-to-day bills?

The financial plan integrates the firm’s basic plans into a single planning document with a detailed budget.

•

Typically, the plan extends over a three- to five-year period called the planning horizon. 1. The Strategic Plan

•

The strategic plan describes the vision of the firm.

•

It provides high-level direction to management for making business decisions and guidance about what the firm will and will not do.

•

The planning is done by the firm’s top management, with the financial manager providing key input, and it has to be approved by the board of directors.

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The strategic plan identifies: ▪

The line of business that the firm will compete in.

▪

Major areas of investment in real assets.

▪

Capital expenditures

▪

Acquisitions and new lines of business.

▪

Mergers, alliances, and divestitures that may happen in the near future.

2. Investment Plan (Capital Budget) •

The investment plan is the part of the financial plan that describes the firm’s outlay for plant and equipment.

•

A firm’s business strategy determines the capital expenditures it will make.

•

Capital expenditures can be one-time investments or routine investments that allow the firm to continue its operations. 3. The Financing Plan

•

Based on the list prepared in the capital budget, management now needs to decide how to fund the projects.

•

The firm will try to use a blend of internally generated funds and externally raised funds to finance the capital expenditures.

•

Depending on the level of internally generated funds available to the firm, the firm will seek to raise funds in the form of either debt or equity.

•

There are three elements to a financing plan: ▪

First, a financing plan identifies the dollar amount of funds that has to be raised externally and the sources of funds available to the firm.

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Second, the plan states management’s desired capital structure for the firm.

▪

Finally, the financing plan states the firm’s payout policy, which is relevant because it dictates the amount of funds that have to be raised in the capital markets.

4. Operating Unit (Divisional) Business Plans •

The business plans prepared by the firm’s various business divisions are also part of the firm’s financial plans.

•

They identify how the various divisions will strive to achieve the corporate goals.

•

They also identify the resources needed by each of the divisions to implement their strategies. 5. Cash Budget

•

An overall cash budget for the firm is generated based on all the operating unit cash budgets and that of the corporate offices.

19.2

•

It focuses on the cash inflows and outflows of the firm.

•

It allows the firm to determine if any borrowing is necessary.

•

A poorly developed cash budget could lead to serious cash shortages.

Financial Planning Models •

Financial planning models help management analyze investment and financing alternatives.

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Most sophisticated planning models are now created as software and make the process speedy and accurate.

The Sales Forecast •

Sales forecast techniques come in quite an array—from best estimates by the sales staff to complex statistical models.

•

They are usually generated from within the company.

•

Since sales are often correlated to the regional or national economy, macroeconomic forecast are incorporated into the model.

Building a Financial Planning Model •

Inputs are necessary to build the financial models that are designed to provide specific outputs.

•

Financial statements serve as the first major input and become the baseline to compare the projected financial statements.

•

Next comes the sales forecast in the form of the projected growth in sales.

•

Changes in the firm’s balance sheet and income statement items as a result of the growth in sales are also used in these models.

•

Last, investment and financing decisions are incorporated as inputs.

•

The outputs of the financial planning model are a series of pro forma financial statements and financial ratios based on these statements.

A Simple Planning Model •

A very basic planning model is called the percent of sales model.

•

The driving factor of this model is the expected sales growth rate.

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All or most of the input variables (i.e., the income statement and balance sheet elements) vary directly with sales.

19.3

A Better Financial Planning Model •

Unlike the previously described model, this model takes a more realistic approach in its assumptions.

•

Not all balance sheet and income statement items vary directly with sales. ▪

All working capital accounts, current assets and current liabilities, vary directly with sales.

The Income Statement •

The pro forma income statement is generated by recognizing all variable costs change directly with sales.

•

Two key ratios are calculated—dividend payout ratio and retention ratio. ▪

The first measures the percentage of net income paid out as dividends to shareholders, while the second measures the percentage of net income reinvested by the firm as retained earnings.

The Balance Sheet •

Some balance sheet items vary directly with sales, while others do not.

•

To determine which accounts vary directly with sales, a trend analysis may be conducted on historic balance sheets of the firm.

•

Typically, working capital accounts like inventory, accounts receivables, and accounts payables vary directly with sales.

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Fixed assets do not always vary directly with sales. They will do so only if the firm is operating at 100 percent capacity and fixed assets can be incrementally changed.

•

The ratio of total assets to net sales is called the capital intensity ratio. This ratio tells us the amount of assets needed by the firm to generate $1 sales. ▪

The higher the ratio, the more capital the firm needs to generate sales—the more capital intensive the firm.

▪

Firms that are highly capital intensive are more risky than those that are not because a downturn can reduce sales sharply, but fixed costs do not change rapidly.

•

Only current liabilities are likely to vary directly with sales. The exception here is notes payables (short-term borrowings) that changes as the firm pays it down or makes an additional borrowing.

•

Long-term liabilities and equity accounts change as a direct result of managerial decisions like debt repayment, stock repurchase, and issuing new debt or equity.

•

Retained earnings will vary as sales change but not directly. It is affected by the firm’s dividend payout policy.

The Preliminary Pro Forma Balance Sheet •

First, calculate the projected values for all the accounts that vary with sales.

•

Second, calculate the projected value of any other balance sheet account for which an end-of-period value can be forecast or otherwise determined.

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Third, enter the current year’s number for all the accounts for which the next year’s figure cannot be calculated or forecast.

•

At this point, the balance sheet will be unbalanced. A plug value is necessary to get the balance sheet to balance. ▪

First, determine the retained earnings based on the firm’s dividend policy.

▪

Next, the plug figure will represent the external financing necessary to make the total assets equal total liabilities and equity. This calls for management to choose a financing option—choosing debt, equity or a combination—to raise the additional funds needed.

•

The first decision relates to the firm’s dividend policy. Should the firm

alter its dividend policy to increase the amount of retained earning? •

If external funding is still needed, should the firm issue new debt, or issue

equity? Or should it be a mix of both? •

It is important to recognize that while financial planning models can

identify the amount of external financing needed, the financing option is a managerial decision. D.

19.4

The Final Pro Forma Balance Sheet

Beyond the Basic Planning Models A.

Improving Financial Planning Models •

There are several weaknesses in the previously described models.

•

First, interest expense was not accounted for. This is difficult to do until all the financing options are finalized.

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Second, all working capital accounts do not necessarily vary directly with sales, especially cash and inventory.

•

Third, how fixed assets are adjusted plays a significant role. ▪

When a firm is not operating at full capacity, sales may be increased without adding any new fixed assets.

▪

Fixed assets are added in large discrete amounts called lumpy assets. Since it requires time to get new assets operational, they are added as the firm nears full capacity.

19.5

Managing and Financing Growth •

Managers prefer rapid growth as a goal to capture market share and establish a competitive position.

•

Most firms experiencing rapid growth fund the growth with debt, increasing the firm’s leverage and putting it at risk.

External Funding Needed •

External funding needed (EFN) is defined as the additional debt or equity a firm needs to issue so it can purchase additional assets to support an increase in sales.

•

EFN is tied to new investments the management has deemed necessary to support the sales growth.

•

The new investments are the projected capital expenditure plus the increase in working capital necessary to sustain increases in sales.

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Companies first resort to internally generated funds in the form of addition to retained earnings.

•

Once internally generated funds are exhausted, the firm looks to raise funds externally. See Equations 19.5 and 19.6.

•

In analyzing Equation 19.6, two things are apparent. ▪

First, holding dividend policy constant, the amount of EFN depends on the firm’s projected growth rate. Higher growth rate implies that the firm needs more new investments and therefore, more funds to have to be raised externally.

▪

Second, the firm’s dividend policy also affects EFN. Holding the growth rate constant, the higher the firm’s payout ratio, the larger the amount of debt or equity financing needed.

•

The internal growth rate (IGR) is defined as the maximum growth rate

that a firm can achieve without external financing. See Equation 19.7. •

The higher the retained earnings generated by a firm and the lower the

total assets a firm has, the higher the growth possible without using external funding. •

Equation 19.8 relates IGR to the plowback ratio, return on equity, and

leverage. Firms that achieve higher growth rates without seeking external financing have the following characteristics: ▪

They have a high plowback ratio.

▪

They employ less equity and/or are able to generate high net

income leading to a high ROE.

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They are not highly leveraged.

The Sustainable Growth Rate •

The sustainable growth rate (SGR) is the rate of growth that the firm can sustain without selling additional shares of equity.

•

This measure is important to management because it helps them determine whether they can avoid issuing new equity. New equity issues are expensive and cause dilution of earnings to existing shareholders.

•

As Equation 19.9 shows, the SGR is a function of the plowback ratio and the ROE.

II.

Growth Rates and Profits

Growth as a Planning Goal

Suggested and Alternative Approaches to the Material

The chapter begins with a discussion of what financial planning is all about. This is followed by an overview of some simple financial planning models. Then the weaknesses in the simple models are identified, and some better planning models are discussed. The chapter concepts of internal growth rates and sustainable growth rates are introduced, and this is followed by coverage of determination of external funding needed to facilitate growth in sales. Instructors may choose to cover this chapter in a couple of different ways. Some may choose to take up this chapter in the order it has been placed in the text. Others may elect to cover it toward the end of the course. This chapter’s material also lends itself to being placed anywhere the instructor chooses.

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III. Summary of Learning Objectives 1.

Explain what a financial plan is and why financial planning is so important. A financial plan is a set of actionable goals derived from the firm’s strategic plan and other planning documents, such as the investment and financing plans. The financial plan focuses on selecting the best investment opportunities and determining how they will be financed. The financial plan is a blueprint for the firm’s future. Financial planning is important to management because the plan communicates the firm’s strategic goals throughout the organization, builds support for the firm’s strategies, and helps align operating units with the firm’s strategic goals.

Discuss how management uses financial planning models in the planning process, and explain the importance of sales forecasts in the construction of financial planning models. Financial models are the analytical part of the financial planning process. A planning model is simply a series of equations that model a firm’s financial statements, such as the income statement and balance sheet. Once the model is constructed, management can generate projected (pro forma) financial statements to determine the financial impact of proposed strategic initiatives on the firm. For most financial planning models, a forecast of the firm’s sales is the most important input variable. The sales forecast is the key driver in financial planning models because many items on the income statement and balance sheet vary directly with sales. Thus, once sales are forecast, it is easy to generate projected financial statements using the historical relationship between a particular account and sales.

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Discuss how the relation between projected sales and balance sheet accounts can be determined, and analyze a strategic investment decision using a percent of sales model. Historical financial data can be examined to determine whether and how a variable changes with sales. One way to do this is to prepare a table that shows four or five years of historical financial statement accounts data as a percent of sales. Then fit trend lines to the data to see what type of relation exists between that variable and sales. Many income statement and balance sheet items vary directly with sales, but others may vary in a nonlinear manner. The analysis in the Blackwell Sales Company example illustrates how to analyze a strategic investment decision.

Describe the conditions under which fixed assets vary with sales, and discuss the impact of so-called lumpy sales on this relation. Fixed assets vary directly with sales only when assets can be added in small increments and production facilities are operating near full capacity. This is typically not the case. In most situations, fixed assets are added in large, discrete units, and, as a result, much of the new capacity may go unused for a period of time. These types of assets are often called lumpy assets. After lumpy assets are added, sales can increase for a period of time with no corresponding change in the level of fixed assets.

Explain what factors determine a firm’s sustainable growth rate, discuss why it is of interest to management, and compute the sustainable growth rate for a firm.

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A firm’s sustainable growth rate (SGR) is the maximum rate at which a firm can grow without external equity financing and with leverage held constant. The determinants of SGR are: (1) profit margins (the greater a firm’s profit margins, the greater the firm’s SGR); (2) asset utilization (the more efficiently a firm uses its assets, the higher its SGR); (3) financial leverage (as a firm increases its use of leverage, its SGR increases); (4) payout policy (as a firm decreases its payout ratio, its SGR increases; and (5) economic conditions (the more favorable the economic environment, the higher the firm’s SGR). Management may be interested in knowing the SGR for two reasons. First the SGR is the rate of growth at which a firm’s capital structure (debt to equity) will remain constant without the firm selling or repurchasing stock. Second, if a firm’s actual growth rate exceeds its SGR, the firm could face cash shortage problems in the future unless it can sell new equity. Learning by Doing Application 19.3 uses the SGR formula.

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IV. Summary of Key Equations

Equation

Description

Formula

Percent change in

%ΔS =

19.1 sales

(St +1 - St ) St

Percent of net income 19.2

Dividend payout ratio = paid out as dividends

Cash dividends Net income

Percent of net income 19.3

retained (plowed

Retention (plowback) ratio =

Addition to retained earnings Net income

back into the firm) Level of assets 19.4

needed to generate $1

Capital intensity ratio =

Total assets Net sales

of sales

19.5

External funding

EFN = New investments – Addition to retained earnings

needed to support 19.6

growth in sales

= (Growth rate × Initial assets) – Addition to retained earnings

19.7

Internal growth rate (level of growth that

IGR = 19.8

can be supported

Addition to retained earnings Initial assets

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without raising external funds)

= Plowback ratio × Return on equity × Measure of leverage

Sustainable growth rate (level of growth that can be supported 19.9

without raising

SGR = Plowback ratio × ROE

external equity or increasing current leverage)

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Chapter 20 Options and Corporate Finance Learning Objectives 1. Define a call option and a put option, and describe the payoff function for each of these options. 2. List and describe the variables that affect the value of an option. Calculate the value of a call option and of a put option. 3. Name some of the real options that occur in business and explain why traditional NPV analysis does not accurately incorporate their values. 4. Describe how the agency costs of debt and equity are related to options. 5. Explain how options can be used to manage a firm’s exposure to risk.

Chapter Outline

20.1

Financial Options

•

A financial option is a derivative security in that its value is derived from the value of another asset.

•

The owner of a financial option has the right, but not the obligation, to buy or sell an asset on or before a specified date for a specified price.

•

The asset that the owner has a right to buy or sell is known as the underlying asset.

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The last date on which an option can be exercised is called the exercise date or expiration date, and the price at which the option holder can buy or sell the asset is called the exercise price or strike price. A.

Call Options •

A call option gives the owner the right to buy, or “call,” the underlying asset.

•

Once the asset price goes above the exercise price, the value of the call option at exercise increases dollar for dollar with the price of the underlying asset.

•

The buyer pays the seller a fee to purchase the option.

•

This fee, which is known as the call premium, makes the total return to the seller positive when the price of the underlying asset is near or below the exercise price.

Put Options •

The owner of a put option has the right to sell the underlying asset at a prespecified price.

•

The payoff function for the owner of a put option is similar to that for a call option, but it is the reverse in the sense that the owner of a put option profits if the price of the underlying asset is below the exercise price. ▪

The owner of a put option will not want to exercise that option if the price of the underlying asset is above the exercise price.

▪

When the value of the underlying asset is below the exercise price, however, the owner of the put option will find it profitable to exercise the option.

•

The payoff for the seller of the put option is negative when the price of the underlying asset is below the exercise price.

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The seller of a put option hopes to profit from the fee, or put premium, that he or she receives from the buyer of the put option.

American, European, and Bermudan Options •

Options that can only be exercised on the expiration date are known as European options.

•

American options can be exercised at any point in time on or before the expiration date.

•

Bermudan options can be exercised only on specific dates during the life of the option.

More on the Shapes of Option Payoff Functions •

The payoff functions for options are not straight lines for all possible values of the underlying asset. ▪

Each payoff function has a “kink” at the exercise price, which exists because the owner of the option has a right, but not the obligation, to buy or sell the underlying asset. If it is not in the owner’s interest to exercise the option, he or she can simply let it expire.

20.2

Option Valuation

•

It is more complicated to determine the value of an option at a point in time before the expiration date because we don’t know exactly how the value of the underlying asset will change over time, and therefore we don’t know if it will make sense to exercise the option. A.

Limits on Option Values

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We know that the value of a call option can never be less than zero, since the owner of the option can always decide not to exercise it if doing so is not beneficial.

•

The value of a call option can never be greater than the value of the underlying asset because it would not make sense to pay more for the right to buy an asset than you would pay for the asset itself.

•

The value of a call option prior to expiration will never be less than the value of that option at expiration because there is always a possibility that the value of the underlying asset will be greater than it is today at some time before the option expires.

•

When we consider the value of a call option at some time prior to expiration, we must compare the current value of the underlying asset with the present value of the exercise price, discounted at the risk-free rate. ▪

The present value of the exercise price is the amount that an investor would have to invest in risk-free securities at any point prior to the expiration date to ensure that he or she would have enough money to exercise the option when it expired.

Variables That Affect Option Values •

The higher the current value of the underlying asset, the more likely it is that the value of the asset will be above the exercise price when the call option expires.

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The higher the current value of the asset, the greater the likely difference between the value of the asset and the exercise price when the option expires.

▪

This means that, holding the exercise price constant, investors will pay more for a call option if the underlying asset value is higher, because the expected value of the option at expiration is higher.

•

The opposite relation applies to the exercise price in that the lower the exercise price, the more likely that the value of the underlying asset will be higher than the exercise price when the option expires.

•

The greater the volatility of the underlying asset value, the higher the value of a call option on the asset prior to valuation. ▪

The intuition here is that the value of an option will increase more when the value of the underlying asset goes up than it will decrease when the value of the underlying asset goes down. This means that a greater potential change in the underlying price will be more beneficial to the value of the option.

•

The greater the time to expiration, the more the value of the underlying asset is likely to change by the time the option expires; this increases the value of an option. ▪

The time until the expiration affects the value of a call option through its effect on the volatility of the value of the underlying asset.

•

The value of a call option increases with the risk-free rate.

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Exercising a call option involves paying cash in the future for the underlying asset.

▪

The higher the interest rate, the lower the present value of the amount that the owner of a call option will have to pay to exercise it, which translates into value for the owner of the option.

The Binomial Option Pricing Model •

This simple model assumes that the underlying asset will have one of only two possible values when the option expires. ▪

The value of the underlying asset will either increase to some value above the exercise price or decrease to some value below the exercise price.

•

To solve for the value of the call option using this model, we must assume that investors have no arbitrage opportunities with regard to this option. ▪

Arbitrage is the act of buying and selling assets in a way that yields a return above that suggested by the Security Market Line (SML).

•

To value the call option in our simple model, we will first create a portfolio that consists of the asset underlying the call option and a risk-free loan. ▪

The relative investments in these two assets will be selected so that the combination of the asset and the loan has the same cash flows as the call option when it expires, regardless of whether the value of the underlying asset goes up or down.

▪

This is called a replicating portfolio, since it replicates the cash flows of the option.

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The replicating portfolio will consist of: ▪

x shares of the underlying stock, and

▪

a risk-free loan with a face value of y.

The value of the call option can be calculated. ▪

Solve for the values of x and y.

▪

Multiply the current cost of the underlying stock by x.

▪

Subtract y from the above amount to yield the value of the call option.

D. •

Put-Call Parity

Although there are other methods, the value of a put option can be calculated by the relationship of a put to a call option with the same maturity and exercise price. ▪

This relation is called put-call parity.

▪

The formula for put-call parity is: P = C + Xe–rt – V, where P is the value of the put option, C is the value of the call option, X is the exercise price, V is the current value of the underlying asset, and e is the exponential function.

E. Valuing Option Associated with the Financial Securities That Firms Issue •

A key principle that we use in valuing securities is that the value of a financial security with an option equals the value of the same security without the option, plus the value of the option.

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When the managers of young, rapidly growing companies issue debt, they may be able to reduce the amount of interest they pay by making the bonds convertible into the company’s common stock. o Investors will be willing to accept a lower interest rate due to the convertibility of the bonds into common stock.

•

Managers may also issue preferred stock that is convertible into common stock.

20.3

Real Options

•

Real options are options on real assets.

•

NPV analysis does not adequately reflect the value of real options, and while it might not always be possible to directly estimate the value of the real options associated with a project, it is important to recognize that they exist when we perform a project analysis. A.

Options to Defer Investment •

An example is as stated in the text concerning a mining project.

•

Another example of deferring investment is the investment to develop oil wells. ▪

The underlying asset in this option is the stream of cash flows that the developed oil field would produce, while the exercise price is the amount of money that the company would have to spend to develop it (drill the well and build any necessary infrastructure).

•

The value of an option to defer investment is not reflected in an NPV analysis, for NPV analysis does not allow for the possibility of deferring an investment decision.

Options to Make Follow-On Investments

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Some projects open the door to future business opportunities that would not otherwise be available. This type of real option is an option to make follow-on investments.

•

Options to make follow-on investments are inherently difficult to value because, at the time we are evaluating the original project, it may not be obvious what the follow-on projects will be. ▪

Even if we know what the projects will be, we are unlikely to have enough information to estimate what they are worth.

▪

Projects that lead to investment opportunities that are consistent with a company’s overall strategy are more valuable than otherwise similar projects that do not.

Options to Change Operations •

Options to change operations are related to the flexibility that managers have once an investment decision has been made. These include the option to change operations and to abandon a project. These options affect the NPV of a project and must be taken into account at the time the investment decision is made. ▪

The changes that managers might make can involve something as simple as reducing output if prices decline or increasing output if prices increase.

Options to Abandon Projects •

An option to abandon a project is the ability to choose to terminate a project by shutting it down.

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Management will save money that would otherwise be lost if the project kept going. The amount saved represents the gain from exercising this option.

Concluding Comments on NPV Analysis and Real Options •

In order to use NPV analysis to value such an option, we would not only have to estimate all the cash flows associated with the expansion but would also have to estimate the probability that we would actually undertake the expansion and determine the appropriate rate at which to discount the value of the expansion back to the present.

20.4

Agency Costs

•

Agency conflicts between stockholders and debt holders and between stockholders and managers arise because the interests of stockholders, lenders (creditors), and managers are not perfectly aligned.

•

One reason is that the claims that they have against the cash flows produced by the firm have payoff functions that look like different types of options. A.

Agency Costs of Debt

•

The payoff functions for stockholders and lenders (creditors) differ, as do the payoff functions for different options.

•

The payoff function for the stockholders looks exactly like that for the owner of a call option, where the exercise price is the amount owed on the loan and the underlying asset is the firm itself.

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If the value of the firm exceeds the exercise price, the stockholders will choose to exercise their option; if it does not exceed the exercise price, they will let their option expire unexercised.

•

One way to think about the payoff function for the lenders is that when they lend money to the firm, they are essentially selling a put option to the stockholders. ▪

This option gives the stockholders the right to “put” the assets to the lenders for an exercise price that equals the amount they owe.

▪

When the value of the firm is less than the exercise price, the stockholders will exercise their option by defaulting.

•

The Dividend Payout Problem: The incentives that stockholders of a leveraged firm have to pay themselves dividends arise because of their option to default. ▪

If a company faces some realistic risk of going bankrupt, the stockholders might decide that they are better off taking money out of the firm by paying themselves dividends.

▪

This situation can arise because the stockholders know that the bankruptcy laws limit their possible losses.

•

The Asset Substitution Problem: When bankruptcy is possible, stockholders have an incentive to invest in very risky projects, some of which might even have negative NPVs. ▪

Stockholders have this incentive because they receive all of the benefits if things turn out well but do not bear all of the costs if things turn out poorly.

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The Underinvestment Problem: Stockholders have incentives to turn down positive-NPV projects when all of the benefits are likely to go to the lenders. The problem arises from the differences in the payoff functions.

Agency Costs of Equity

•

Managers are hired to manage the firm on behalf of the stockholders, but managers do not always act in the stockholders’ best interest.

•

The payoff function for a manager can be quite different from that for stockholders. In fact, it can look a lot like that for a lender. ▪

If a company gets into financial difficulty and a manager is viewed as responsible, that manager could lose his or her job and find it difficult to obtain a similar job at another company. o

The most obvious way for a company to get into financial difficulty is to default on its debt.

Thus, as long as a company is able to avoid defaulting on its debt, a manager has a reasonable chance of retaining his or her job.

•

The fact that the payoff function for a manager resembles that for a lender means that managers, like lenders, have incentives to invest in less risky assets and to distribute less value through dividends and stock repurchases than the stockholders would like.

20.5

Options and Risk Management

•

Risk management typically involves hedging or reducing the financial risks faced by a firm.

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Options, along with other derivative instruments, such as forwards, futures, and swaps, are commonly used to reduce risks associated with commodity prices, interest rates, foreign exchange rates, and equity prices.

•

One interesting benefit of using options in this way is that they provide downside protection but do not limit the upside. ▪

This is just like buying insurance. o

•

Many insurance contracts are little more than specialized put options.

Options and other derivative instruments can be used to manage commodity price risks, large swings in interest rates, risks associated with foreign exchange rates, as well as to manage risks associated with equity prices as occurs within defined benefit pension plans.

II.

Suggested and Alternative Approaches to the Material

Chapter 20 considers the description, valuation, and use of options. The discussion begins with financial options and how they are valued in a simple model. The chapter then turns to options on real assets, known as real options. Real options often arise in corporate investment decisions, such as the right to delay investing in a project, expanding a project, abandoning a project, or making a change in the technology employed in a project. This framework provides a valuation tool that is not properly reflected in an NPV analysis. The chapter then revisits the agency costs of debt discussed earlier in Chapter 16. The option-like payoffs that are embedded in the payoff to equity investors contribute to the problems of asset substitution, underinvestment, dividend payout, and claim dilution. The discussion then

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follows with how option-like payoffs contribute to conflicts between stockholders and the managers. The chapter concludes with a discussion of the ways in which managers use financial options to alter their companies’ exposures to various types of risks. This material is generally considered advanced for a first course in finance, but the subject matter is presented through a simple real-world discussion and the concepts are easy for students to grasp. It is a chapter that students generally find interesting, given the frequent appearance of derivatives in the popular press.

III. Summary of Learning Objectives 1.

Define a call option and a put option, and describe the payoff function for each of these options. An option is the right, but not the obligation, to buy or sell an asset for a given price on or before a specific date. The price is called the exercise or strike price, and the date is called the exercise date or expiration date of the option. The right to buy the asset is known as a call option. The payoff from a call option equals $0 if the value of the underlying asset is less than or equal to the exercise price at expiration. If the value of the underlying asset is greater than the exercise price at expiration, then the payoff from a call option is equal to the value of the asset value minus the exercise price. The right to sell the asset is called a put option. The payoff from a put option is $0 if the value of the underlying asset is greater than or equal to the exercise price at expiration. If the value of the underlying asset is less than the exercise price, then the payoff from a put option equals the exercise price minus the value of the underlying asset.

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List and describe the variables that affect the value of an option. Calculate the value of a call option and of a put option. The value of an option is affected by five variables: the current price of the underlying asset, the exercise price of the option, the volatility of the value of the underlying asset, the time left until the expiration of the option, and the risk-free rate. Section 20.2 describes how to calculate the values of call and put options, both at expiration and at some point before the expiration date.

Name some of the real options that occur in business and explain why traditional NPV analysis does not accurately incorporate their values. Real options that are associated with investments include options to defer investments, make follow-on investments, change operations, and abandon projects. Traditional NPV analysis is designed to make a decision to accept or reject a project at a particular point in time. It is not intended to incorporate potential value associated with deferring the investment decision. Incorporating the value of the other real options into an NPV framework is technically possible but would be very difficult to do because the rate used to discount the cash flows would change over time with their riskiness. In addition, the information necessary to value real options using the NPV approach is not always available.

Describe how the agency costs of debt and equity are related to options.

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The chapter discusses two principal classes of agency conflicts. The first is between stockholders (owners) and lenders. When there is a risk of bankruptcy, stockholders may have incentives to increase the volatility of the firm’s assets, turn down positive NPV projects, or pay out assets in the form of dividends. Stockholders have these incentives because their payoff functions look like those for the owner of a call option. The other principal class of agency conflicts is between managers and stockholders. Managers tend to prefer less risk than stockholders. They also prefer to distribute fewer assets in the form of dividends because their payoff functions are more like those of lenders than those of stockholders. These preferences are magnified by the fact that managers are risk-averse individuals whose portfolios are not well diversified.

Explain how options can be used to manage a firm’s exposure to risk. A company can adjust its exposure to risks associated with commodity prices, interest rates, foreign exchange rates, and equity prices by buying or selling options. For example, a company that is concerned about the prices it will receive for products that will be delivered in the future can purchase put options to partially or totally eliminate that risk.

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IV. Summary of Key Equations Equation

Description

Formula

20.1

Put-call parity

P = C + Xe-rt – V

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Chapter 21 International Financial Management

Learning Objectives 1.

Discuss how the basic principles of finance apply to international financial transactions.

Discuss the importance of the Euromarkets to large U.S. multinational firms, and calculate the cost of borrowing in the Eurobond market.

Explain how large U.S. money center banks make and price Eurocredit loans to their customers and compute the cost of a Eurocredit bank loan.

Chapter Outline

21.1 Introduction to International Financial Management

Globalization of the World Economy

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Globalization refers to the removal of barriers to free trade and the closer integration of national economies.

•

Consumers in many countries buy goods that are purchased from a number of countries, other than just their own.

•

The production of goods and services has also become highly globalized.

•

Like product markets, the financial system has also become highly integrated.

The Rise of Multinational Corporations

•

A multinational corporation is a business firm that operates in more than one country.

•

Multinational corporations may purchase raw materials from one country, obtain financing from a capital market in another country, produce finished goods with labor and capital equipment from a third country, and sell finished goods in a number of other countries.

•

Multinationals are owned by a mixture of domestic and foreign stockholders.

•

Transnational corporations, regardless of the location of their headquarters, are managed from a global perspective rather than the perspective of a firm residing in a particular country.

•

Exhibit 21.1 lists the top 15 multinational business firms ranked by total revenues.

Factors Affecting International Financial Management

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Six factors can cause international business transactions to differ from domestic deals. ▪

The uncertainty of future exchange rate movements is called foreign exchange rate risk, or just exchange rate risk.

▪

Differences in legal systems and tax codes can also impact the way firms operate in foreign countries.

▪

There are two important levels of communication in international business deals: business communication and social communication. o

Although English is the official business language, it is not the world’s social language.

▪

The cultures of different countries, and even different regions within the same country, can vary considerably. o

Cultural views also shape business practices and people’s attitudes toward business.

▪

An economic system determines how a country mobilizes its resources to produce goods and services needed by society, as well as how the production is distributed.

▪

Country risk refers to political uncertainty associated with a particular country.

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At the extreme, a country’s government may even expropriate— that is, take over—a business’s assets within the country.

These types of actions clearly can affect a firm’s cash flows and, thus, the value of the firm.

Goals of International Financial Management

•

Stockholder wealth maximization is the accepted goal for firms in the United States, as well as in some other countries that share a similar heritage, such as the United Kingdom, Australia, India, and Canada.

•

In Continental Europe, for example, countries such as France and Germany focus on maximizing corporate wealth. ▪

The European manager’s goal is to earn as much wealth as possible for the firm while considering the overall welfare of all stakeholders.

•

In Japan, companies form tightly knit, interlocking business groups called keiretsu, such as Mitsubishi, Mitsui, and Sumitomo, and the goal of the Japanese business manager is to increase the wealth and growth of the keiretsu. ▪

As a result, they might focus on maximizing market share rather than stockholder wealth.

•

In China, which is making a transition from a command economy to a marketbased economy, there are sharp differences between state-owned companies and emerging private-sector firms.

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The large state-owned companies have an overall goal that can best be described as maintaining full employment in the economy while the new private-sector firms fully embrace the Western standard of stockholder wealth maximization.

Basic Principles Remain the Same

•

The basic principles of managerial finance remain the same whether a transaction is domestic or international. ▪

The time value of money is not affected by whether a business transaction is domestic or international. Likewise, the same models are used for valuing capital assets, bonds, stocks, and entire firms.

•

Exhibit 21.2 lists some of the important finance concepts and procedures and indicates where there are differences between domestic and international operations.

21.2

Foreign Exchange Markets

•

The foreign exchange market is a group of international markets connected electronically where currencies are bought and sold in wholesale amounts.

•

Foreign exchange markets provide three basic economic benefits: ▪

A mechanism to transfer purchasing power from individuals who deal in one currency to people who deal in a different currency.

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A way for corporations to pass the risk associated with foreign exchange price fluctuations to professional risk-takers.

▪

A channel for importers and exporters to acquire credit for international business transactions.

•

The market for foreign exchange is very large, and the daily volume was more than $5 trillion in 2013. ▪

London is by far the largest foreign exchange trading center, with 41% of average daily volume, while New York City is second with 19%, and Singapore is third with 5.7%.

Market Structure and Major Participants

•

Participants are linked by telephone and electronic networks.

•

The major participants in the foreign exchange markets are multinational commercial banks, large investment banking firms, and small currency boutiques that specialize in foreign exchange transactions.

•

In addition, the central banks, which intervene in the markets primarily to smooth out fluctuations in their exchange rates, also play a significant role.

Foreign Exchange Rates

•

A foreign exchange rate is the price of one monetary unit.

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One of two parties in an international transaction will be forced to deal in a foreign currency and incur foreign exchange rate risk.

•

Exhibit 21.4 shows the equilibrium exchange rate, which is at the point where the supply and demand curves intersect. ▪

Equilibrium occurs at the price at which the quantity of the currency demanded exactly equals the quantity supplied.

▪

In general, whatever causes U.S. residents to buy more or fewer foreign goods shifts the demand curve for the foreign currency.

▪

Similarly, whatever causes foreigners to buy more or fewer U.S. goods shifts the supply curve for the foreign currency.

Foreign Currency Quotations

•

Exhibit 21.5 shows selected exchange rate quotations from the Wall Street Journal.

•

The spot rate is the cost of buying a foreign currency today, “on the spot.” ▪

If the exchange rate is the price in dollars for a foreign currency, it is often called the American or direct quote.

▪

If the exchange rate is the price in foreign currency for a dollar, the quote is called a European or an indirect quote.

•

Foreign exchange dealers quote two prices: bid and ask quotes.

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The bid quote represents the rate at which the dealer will buy foreign currency.

▪ •

The ask quote is the rate at which the dealer will sell foreign currency.

When one is given two quotes of foreign exchange rates involving three currencies, it is possible to find the exchange rate between the third pair of currencies, and this is known as the cross rate.

•

The forward rate is the rate at which one agrees to buy or sell a currency at some future date. ▪

Note that the forward rate is established at the date on which the agreement is made and defines the exchange rate to be used when the transaction is completed in the future.

▪

By contracting now to buy or sell foreign currencies at some future date, businesses can lock in the cost of foreign exchange at the beginning of the transaction and do not have to worry about the risk of an unfavorable movement in the exchange rate in the future.

•

The difference between the forward rate and the spot rate is called the forward premium or forward discount.

•

A hedge is used to engage in a financial transaction to reduce risk such as entering into a forward rate contract to lock in the cost of foreign exchange.

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21.3

International Capital Budgeting

•

When a multinational firm wants to consider overseas capital projects, the financial manager faces the decision of which capital projects should be accepted on a companywide basis.

•

The decision to accept international projects with a positive NPV increases the value of the firm and is consistent with the fundamental goal of financial management, which is to maximize stockholder wealth.

•

Although the same basic principles apply to both international and domestic capital budgeting, firms must deal with some differences. A.

Determining Cash Flows

•

A number of issues complicate the determination of cash flows from overseas capital projects.

•

First, most companies find it more difficult to estimate the incremental cash flows for foreign projects.

•

Second, problems with cash flows can arise when foreign governments restrict the amount of cash that can be repatriated, or returned, to the parent company.

Exchange Rate Risk

•

Financial managers have to deal with foreign exchange rate risk on international capital investments.

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To convert the project’s future cash flows into another currency, we need to come up with projected or forecast exchange rates.

•

One of the problems with obtaining currency rate forecasts for use in analysis of capital projects is that many projects have lives of 20 years or more.

Country Risk

•

Financial managers must also incorporate a country risk premium when evaluating foreign business activities.

•

If a firm is located in a country with a relatively unstable political environment, management will require a higher rate of return on capital projects as compensation for the additional risk.

•

At the extreme, a local government could take over the plant and equipment of the overseas operation without giving the company any compensation. This expropriation of assets is called nationalization.

•

Some other ways that a foreign government can affect the risk of a foreign project include: ▪

Changing tax laws in a way that adversely impacts the firm.

▪

Imposing laws related to labor, wages, and prices that are more restrictive than those applicable for domestic firms.

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Disallowing any remittance of funds from the subsidiary to the parent firm for either a limited period of time or the duration of the project.

▪

Requiring that the subsidiary be headed by a local citizen or have a local firm as a major equity partner.

▪ •

Imposing tariffs and quotas on any imports.

Once management has gauged a capital project’s country risk, that risk must be incorporated into the capital budgeting analysis by, for example, adjusting the firm’s discount rate for the additional risk.

21.4

Global Money and Capital Markets

The Emergence of the Euromarkets

•

A Eurodollar is defined as a U.S. dollar deposited in a bank outside the United States, primarily in Europe.

•

The banks accepting these deposits are called Eurobanks.

•

The Euromarkets are vast, largely unregulated money and capital markets with major financial centers in Tokyo, Hong Kong, and Singapore.

The Eurocurrency Market

•

The Eurocurrency market is the short-term portion of the Euromarket.

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A Eurocurrency is a time deposit of money held by corporations and governments in a bank located in a country different from the country that issued the currency.

•

The most widely quoted Eurocurrency interest rate is the London Interbank Offer Rate, or LIBOR, which is the short-term interest rate that major banks in London charge one another.

The Eurocredit Market

•

The international banking system gathers funds from businesses and governments in the Eurocurrency market and then allocates funds to banks that have the most profitable lending opportunities.

•

These loans, which are short- to medium-term loans of a Eurocurrency to multinational corporations and governments of medium to high credit quality, are called Eurocredits.

•

Eurocredits are denominated in all major Eurocurrencies, although the dollar is the overwhelming favorite.

International Bond Markets

•

International bonds fall into two generic categories: foreign bonds and Eurobonds.

•

Foreign bonds are long-term debt sold by a foreign firm to investors in another country and denominated in that country’s currency.

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Foreign bonds may have colorful nicknames: foreign bonds sold in the United States are called Yankee bonds, and yen-denominated bonds sold in Japanese financial markets by non-Japanese firms are called Samurai bonds.

▪

Firms sell foreign bonds when they need to finance projects in a particular foreign country.

•

Eurobonds are long-term debt instruments sold by firms to investors in countries other than the country in whose currency the bonds are denominated. ▪

Multinational firms can use Eurobonds to finance international or domestic projects.

▪

Eurodollar and other Eurocurrency bonds have a number of characteristics that differ from similar U.S corporate bonds.

▪

Eurobonds are bearer bonds and do not have to be registered.

▪

Eurobonds also pay interest annually.

▪

While historically almost all Eurocurrency bonds were sold without credit ratings, today, more than half of the Eurodollar bonds sold in Europe have credit ratings.

21.5

International Banking

•

European governments fostered the growth of large international banks in their countries and viewed them as engines of territorial and economic expansion.

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To accommodate their customers’ needs, large U.S. banks established networks of foreign branches and affiliates.

•

Exhibit 21.7 shows the 15 largest banks in the world in 2013. A.

Risks Involved in International Bank Lending

•

The principles of loan administration and credit analysis are similar for domestic and overseas loans.

•

There are differences, however, including some additional risk exposures for overseas lending. ▪

Credit risk is the same whether a loan is domestic or international. However, it may be more difficult to obtain or assess credit information abroad.

▪

Bank loans that have foreign exchange risk will carry an additional risk premium.

▪

If an international loan or investment is expected to suffer some loss in value, the loan will carry an additional risk premium.

Eurocredit Bank Loans

•

Eurocredits are short- to medium-term loans of a Eurocurrency to multinational corporations or governments.

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They can have a high degree of credit risk and may be too large for a single bank to handle.

•

The lending banks often form a syndicate to spread the risk.

•

The loan rate (k) is equal to a base rate, such as LIBOR, which represents the bank’s cost of funds, plus a markup.

II.

•

The general equation for Eurocredit pricing is expressed in Equation 21.3.

•

Eurocredits typically are floating-rate loans structured as “rollovers.”

Suggested and Alternative Approaches to the Material

The chapter begins with some background information about the globalization of the world economy, the rise of multinational corporations, and the key factors that distinguish domestic from international business transactions. Emphasis is placed on the fact that the basic principles of finance remain valid for international business transactions, even though some of the variables used to calculate financial models change. Two risks are introduced that are not present in domestic business transactions: foreign exchange risk and country risk. The markets for foreign exchange are discussed next, and the authors explain how firms protect themselves from fluctuations in exchange rates. The discussion moves to how multinational firms manage their overseas capital investments and compute the NPV for these projects.

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Finally, the discussion turns to global money and capital markets. Particular attention is paid to the Euromarket, where large multinational companies adjust their liquidity, borrow short term from banks in the Eurocredit market, and borrow long term in the international bond markets. Finally, bank pricing and the structure of Eurocredits are discussed.

III. Summary of Learning Objectives 1.

Discuss how the basic principles of finance apply to international financial transactions. The basic principles of finance remain the same whether a transaction is domestic or international. For example, the time value of money calculations remain the same, as do the models used to calculate asset values. What does change, however, are some of the input variables. These variables may be affected by cultural or procedural differences between countries or differences in tax and accounting standards. Exhibit 21.2 lists some of these changes.

Differentiate among the spot rate, the forward rate, and the cross rate in the foreign exchange markets, perform foreign exchange and cross rate calculations, and hedge an asset purchase where payment is made in a foreign currency. The spot rate is the exchange rate at which one currency can be converted to another immediately, whereas the forward rate is a rate agreed on today for an exchange to take place at a specified point in the future. Forward rates are usually different from spot rates and are the market’s best estimate of what a future spot rate will be. The cross rate is

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simply the exchange rate between two currencies. Learning by Doing Applications 21.1 through 21.3 illustrate foreign exchange rate problems that you should be able to solve.

Identify the major factors that distinguish international from domestic capital budgeting, explain how the capital budgeting process can be adjusted to account for these factors, and compute the NPV for a typical international capital project. One issue that distinguishes international from domestic capital budgeting is the difficulty in estimating the incremental cash flows from an international project. These difficulties can stem from differences in operating, accounting, and legal practices, as well as from the variety of ways in which a multinational firm can transfer profits and funds from the subsidiary to the parent corporation. Furthermore, firms engaged in international capital budgeting face two risks that domestic firms do not have to deal with: foreign exchange rate risk and country risk. The Barcelona example in Section 21.3 and Learning by Doing Application 21.4 illustrate capital budgeting calculations.

Discuss the importance of the Euromarkets to large U.S. multinational firms, and calculate the cost of borrowing in the Eurobond market. The Eurocurrency markets are important to large multinational corporations around the world. These corporations hold Eurocurrency time deposits as investments and finance much of their business activity by borrowing in the Eurocredit market and selling debt in the Eurobond market. The Euromarkets are popular with large multinational firms because they are largely unregulated; thus, they offer more attractive borrowing and lending rates and greater flexibility in conducting transactions. Learning by Doing

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Application 21.5 illustrates how to calculate the cost of issuing bonds in the domestic and Eurobond markets.

Explain how large U.S. money center banks make and price Eurocredit loans to their customers and compute the cost of a Eurocredit bank loan. Eurocredit loans are made by large multinational banks. Eurocredits typically have fixed maturities and variable, or floating, rates of interest. The loan rate is tied to a base interest rate (BR), such as LIBOR. The total rate charged on a Eurocredit is BR + X, where X is the lending margin, which consists of risk premiums (credit, country, and currency risks) and the lender’s profit margin. The Citibank example in Section 21.5 and Learning by Doing Application 21.6 illustrate how loan costs are computed.

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IV. Summary of Key Equations

Equation

Description

21.1

Bid-ask spread

Bid-Ask spread =

21.2

Forward premium or discount

Forward premium (discount) =

Eurocredit bank loan pricing

k = BR + DRP + FXR + CR + GPMAR

21.3

Formula

Ask rate − Bid rate Ask rate Forward rate − Spot rate 360 × ×100 Spot rate n

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2.11.

a. b. c.

Investment Banking: Cranjet Inc. is issuing 10,000 bonds and its investment banker has guaranteed a price of $985 per bond. The investment banker sells the entire issue to investors for $10,150,000. What is the underwriting spread for this issue? What is the percentage underwriting cost? How much did Cranjet raise?

Price per bond guaranteed by investment banker Number of bonds issued Sales proceeds received by investment banker

Underwriting spread

Amount of money raised by Cranjet

Percentage underwriting cost

$985 10,000 $10,150,000

$300,000 $9,850,000 3.05%

2.28

Interest Rates: Imagine you borrow $500 from your roommate, agreeing to pay her back $500 plus 7 percent nominal interest in one year. Assume inflation over the life of the contract is expected to be 4.25 percent. What is the total dollar amount you will have to pay her back in a year? What percentage of the interest payment is the result of the real rate of interest?

Amount borrowed Term of loan Interest rate Expected rate of inflation

$500 1 year 7% 4.25%

Amount to be paid after 1 year $ 535 Real rate of interest 2.64% % of interest payment due to real rate of interest = 37.68%

2.29 Interest Rates: Your parents have given you $1,000 a year before your graduation so that you can take a trip when you graduate. You wisely decide to invest the money in a bank CD that pays 6.75 percent interest. You know the trip costs $1,025 right now and that inflation for the year is predicted to be 4 percent. Will you have enough money in a year to purchase the trip? Amount of gift Rate of interest on CD Cost of trip currently Expected rate of inflation Value of CD investment after 1 year Cost of trip after 1 year Will there be enough money?

$1,000 6.75% $1,025 4% $1,067.50 $1,066.00 Yes

before your You wisely decide erest. You know is predicted to be ase the trip?

STP 2.5 If the nominal rate of interest is 4.25 percent and the expected rate of inflation is 1.75 percent, what is the real rate of interest? Nominal Interest rate 7.50% Real interest rate 4.00% Expected Inflation Premium

3.37%

This document was exported from Numbers. Each table was converted to an Excel worksheet. All other objects on each Numbers sheet were placed on separate worksheets. Please be aware that formula calculations may differ in Excel.

Numbers Sheet Name

Numbers Table Name

#3.1 Table 1 #3.5 Table 1 3.32 Table 1 3.31 Table 1 3.30 Table 1 "All Drawings from the Sheet" 3.29 Table 1 STP #3.5 Table 1 STP #3.4 Table 1 STP #3.3 Table 1 STP #3.2 Table 1 STP #3.1 Table 1

3.28 Table 1 3.27 Table 1 "All Drawings from the Sheet" 3.26 Table 1 3.25 Table 1 3.24 Table 1 3.23 Table 1 3.22 Table 1 3.21 Table 1 3.20 Table 1 3.19 Table 1 #3.16 Table 1 3.18 Table 1 3.17 Table 1 "All Drawings from the Sheet" #3.10 Table 1 #3.9 Table 1

#3.7 Table 1 #3.6 Table 1

e was converted to an Excel worksheet. All eparate worksheets. Please be aware that

Excel Worksheet Name

#3.1 - Table 1 #3.5 - Table 1 3.32 - Table 1 3.31 - Table 1 3.30 - Table 1 3.30 3.29 - Table 1 STP #3.5 - Table 1 STP #3.4 - Table 1 STP #3.3 - Table 1 STP #3.2 - Table 1 STP #3.1 - Table 1

3.28 - Table 1 3.27 - Table 1 3.27 3.26 - Table 1 3.25 - Table 1 3.24 - Table 1 3.23 - Table 1 3.22 - Table 1 3.21 - Table 1 3.20 - Table 1 3.19 - Table 1 #3.16 - Table 1 3.18 - Table 1 3.17 - Table 1 3.17 #3.10 - Table 1 #3.9 - Table 1

#3.7 - Table 1 #3.6 - Table 1

3.1.

Balance sheet: Given the following information about Elkridge Sporting Goods, Inc., construct a balance sheet for June 30, 2014. On that date the firm had ca and marketable securities of $25,135, accounts receivable of $43,758, inventor of $167,112, net fixed assets of $325,422, and other assets of $13,125. It had accounts payables of $67,855, notes payables of $36,454, long-term debt of $223,125, and common stock of $150,000. How much retained earnings did th

Cash and Marketable securities Accounts Receivable Inventory Net fixed assets Other assets Accounts payables Notes payables Long-term debt Common stock

$ 25,135 $ 43,758 $ 167,112 $ 325,422 $ 13,125 $ 67,855 $ 36,454 $ 223,125 $ 150,000

Elkridge Sporting Goods, Inc. Balance Sheet for the period ending June 30, 2014 Cash and Marketable Securities Accounts Receivable Inventory Current Assets

$ $ $ $

25,135 Accounts payables 43,758 Notes payables 167,112 236,005 Current Liabilities

Net fixed assets Other assets

$ $

325,422 Long-term debt 13,125 Common stock

Retained Earnings Shareholder's Equity 574,552 Total Liabilities and Owner's equity

Total Assets

idge Sporting Goods, at date the firm had cash e of $43,758, inventory ets of $13,125. It had 4, long-term debt of tained earnings did the

4 $ $

67,855 36,454

104,309

$ $

223,125 150,000

$ $ $

97,118 247,118 574,552

3.5. Working capital: Laurel Electronics reported the following information at its annual meeting: The company had cash and marketable securities worth $1,235,455, accounts payables worth $4,159,357, inventory of $7,121,599, accounts receivables of $3,488,121, short-term notes payable worth $1,151,663, and other current assets of $121,455. What is the company’s net working capital? Cash and marketable securities (M/S) Accounts payables Inventory Accounts receivables Notes payable Other current assets

$ $ $ $ $ $

1,235,455 4,159,357 7,121,599 3,488,121 1,151,663 121,455

Net working capital = Current assets - Current liabilities Current assets Cash and M/S Accounts receivables Inventory Other current assets

$ $ $ $

1,235,455 3,488,121 7,121,599 121,455

Total Current assets

11,966,630

6,655,610

Net working capital

Current Liabilities Accounts payables Notes payable

$ 4,159,357 $ 1,151,663

Total Current liabilities

$ 5,311,020

3.6. Working capital: The financial information for Laurel Electronics referred to in problem 3.5 is all book value. Suppose marking-to-market reveals that the market value of the firm’s inventory is 20 percent below its book value and its receivables are 25 percent below its book value. The market value of its current liabilities is identical to the book value. What is the firm’s net working capital using market values? What is the percentage change in net working capital? Cash and marketable securities (M/S) Accounts payables Inventory Accounts receivables Notes payable Other current assets

$ 1,235,455 $ 4,159,357 $ 7,121,599 $ 3,488,121 $ 1,151,663 $ 121,455

Comment regarding market value of the balance sheet items same as book value 20% below book value 25% below book value same as book value

Market values of Laurel Electronics' current assets and current liabilities Current assets Current Liabilities Cash and M/S $ 1,235,455 Accounts payables $ Accounts receivables $ 2,616,091 Notes payable $ Inventory $ 5,697,279 Other current assets $ 121,455

4,159,357 1,151,663

Total Current assets

$ 9,670,280

5,311,020

Net working capital Percent change in Net Working Capital

$ 4,359,260 -34.50%

Total Current liabilities $

3.7. Income statement: The Oakland Mills Company has disclosed the following financial information in its annual reports for the period ending March 31, 2014: sales of $1.45 million, cost of goods sold of $812,500, depreciation expenses of $175,000, and interest expenses of $89,575. Assume that the firm has an average tax rate of 35 percent. What is the company’s net income? Set up an income statement to answer the Sales $ Cost of goods sold $ Depreciation expenses $ Interest expenses $ Tax rate

1,450,000 812,500 175,000 89,575 35%

Net income statement for the period ending March 31, 2014 Revenues Costs EBITDA Depreciation EBIT Interest expenses EBT Taxes (35%) Net Income

$ $ $ $ $ $ $ $ $

1,450,000.00 812,500.00 637,500.00 175,000.00 462,500.00 89,575.00 372,925.00 130,523.75 242,401.25

3.9. Cash flows: During 2014 Towson Recording Company increased its investment in marketable securities by $36,845, funded fixed-assets acquisition by $109,455, and had marketable securities of $14,215 mature. What is the net cash used in investing activities? Investment in marketable securities $ 36,845 Investment in fixed assets $ 109,455 Maturing of marketable securities $ 14,215 Net cash used in investment activities Investment in fixed assets

$ 109,455

3.10. Cash flows: Caustic Chemicals identified the following cash flows as significant in their year end meeting with analysts: During the year Caustic repaid existing debt of $312,080, and raised additional debt capital of $650,000. It also repurchased stock in the open markets for a total of $45,250. What is the net cash provided by Repayment of existing debt Additional debt raised Repurchase of stock

$ $ $

312,080 650,000 45,250

Net cash provided by financing activities Repayment of existing debt Additional debt raised Repurchase of stock

$ (312,080) $ 650,000 $ (45,250)

Net cash provided by financing activities$

292,670

3.12 Cash flows: Given the data for Oakland Mills Company in Problem 3.7, compute the cash flows to investors from CFOA = EBIT - CURRENT TAXES + NONCASH EXPENSES EBIT $462,500.00 CURRENT TAXES $130,523.75 NONCASH EXPENSES$175,000.00 CFOA $ 506,976.25

3.13 Cash flows: Hillman Corporation reported current assets of $3,495,055 for the year endin $3,103,839 for the year ending December 31, 2013. Current liabiliites for the firm were $2 and 2013, respectively. Compute the cash flow invested in net working capital at Hillman

CFNWC = (CURRENT ASSETS 2014 - CURRENT LIABILITIES 2014) -(CURRENT ASS CURRENT ASSETS 2014 CURRENT LIABILITIES 2014

$3,495,055.00 $2,867,225.00 $627,830.00

CURRENT ASSETS 2013 CURRENT LIABILITIES 2013

$3,103,839.00 $2,760,124.00 $343,715.00

CFNWC

$ 284,115.00

s of $3,495,055 for the year ending December 31, 2014 and current assets of rent liabiliites for the firm were $2,867,225 and $2,760,124 at the end of 2014 in net working capital at Hillman Corporation during 2014.

BILITIES 2014) -(CURRENT ASSETS 2013 - CURRENT LIABILITIES 2013)

3.14 Cash flows: Del Bridger Construction had long-term assets before depreciation of $990,560 on December 31, 2013 and $1,211,105 on December 31, 2014. How much cash flow was invested in long-term assets by Del Bridge during 2014? CFLTA = LTA 2014 - LTA 2013 LTA 2014 LTA 2013 CFLTA

$1,211,105.00 $990,560.00 $ 220,545.00

epreciation of 014. How much cash

3.17. Tax: Manz Property Management Company announced that in the year ended June 30, 2014, its earnings before taxes amounted to $1,478,936. Calculate its taxes using Exhibit 3.6 in the text. Earnings before interest and taxes

$1,478,936

U.S. Federal Corporate Income Tax Rates for 2013 Taxable Income from Upto Rate 0 50,000 15% 50,001 75000 25% 75001 100,000 34% 100,001 335,000 39% 335,001 10,000,000 34% 10,000,001 15,000,000 35% 15,000,001 18,333,333 38% 18,333,334 0% 35% Income Level Taxes $50,000 $7,500 $75,000 $6,250 $100,000 $8,500 $335,000 $91,650 $1,478,936 $388,938 Total tax $502,838.24

3.18 Balance sheet: Tim Dye, the CFO of Blackwell Automotive, Inc., is putting together this year’ statements. He has gathered the following information: The firm had a cash balance of $23,0 accounts payable of $163,257, common stock of $313,299, retained earnings of $512,159, in of $212,444, goodwill and other assets equal to $78,656, net plant and equipment of $711,25 notes payable of $21,115. It also has accounts receivable of $141,258 and other current ass $11,223. How much long-term debt does Blackwell Automotive have? Cash Accounts payable Common stock Retained earnings Inventory

$ $ $ $ $

23,015 163,257 313,299 512,159 212,444

Goodwill and other assets Net Plant and Equipment Notes payable Accounts receivable Other current assets

$ $ $ $ $

23,015 141,258 11,223 212,444 387,940

Accounts payable Notes payable

Net Plant and Equipment$ Goodwill and other assets $

711,256 78,656

Long-tern debt Common stock Retained earnings Shareholder's equity Total Debt and Shareholder's equity

Blackwell Automotive Inc. Balance Sheet Cash Accounts receivable Other current assets Inventory Total Current Assets

Total Assets

$ 1,177,852

Total Current Liabilities

putting together this year’s financial ad a cash balance of $23,015, ed earnings of $512,159, inventory and equipment of $711,256, and 258 and other current assets of ve? $ 78,656 $ 711,256 $ 21,115 $ 141,258 $ 11,223

$ $

163,257 21,115

184,372

$ 168,022 $ 313,299 $ 512,159 $ 825,458 $ 1,177,852

3.19 Working capital: Mukhopadhya Network Associates has a current ratio of 1.60, where the current ratio is defined as follows: Current ratio = Current assets/Current liabilities. The firm's current assets are equal to $1,233,265, its accounts payables are $419,357, and its notes payables are $351,663. Its inventory is currently at $721,599. The company plans to raise funds in the short-term debt market and invest the entire amount in additional inventory. How much can notes payable increase without the current ratio falling below 1.50? Current ratio Current assets Accounts payables Notes payables Inventory

$ $ $ $

1.6 1,233,265 419,357 351,663 721,599

Company wants to: Increase inventory by raising funds via notes payables Keep their current ratio at or above 1.5 Current ratio (right now) Total current liabilities Total current assets Desired minimum current ratio

$ $

1.6 770,791 1,233,265 1.5

Note: Total Current assets + (increase in inventory)/ Total current liabilities + (increase in notes payables) = 1.5 Let "increase in inventory" = "increase in notes payables" = X (TCA + X)/(TCL+X)=1.5 TCA + X = 1.5*TCL + 1.5X TCA - 1.5* TCL = 1.5X - X = 0.5X X = (TCA - 1.5*TCL)/0.5 X or increase in inventory

154,158.13

=increase in notes payables

New Total Current Assets New Total Current Liabilities

$ 1,387,423.13 $ 924,948.75

New Current Ratio

1.50

3.20 Market value: Reservoir Bottling Co. reported the following information at the end of the year. Total current assets are worth $237,513 at book value and $219,344 at market value. In addition, plant and equipment with a market of $343,222, and a book value of $362,145. The company’s total current liabilities are valued at market for $134,889 and has a book value of $129,175. Both the book value and the market value of its long-term debt is $144,000. If the company’s total assets are equal to a market value of $562,566 and a book value of $599,658, what is the difference in Current assets

Book value Market Value $ 237,513 $ 219,344 Current liabilities

Plant and equipment$ 362,145

Total assets

$ 599,658

Current assets

Book value Market Value $ 237,513 $ 219,344 Current liabilities

Plant and equipment$ 362,145

Total assets

$ 599,658

Book value Market Value $ 129,175 $ 134,889

343,222 Long-term debt $ Shareholder's equity 562,566

144,000 ????

$ 144,000 ?????

Book value Market ValueDifference $ 129,175 $ 134,889

343,222 Long-term debt $ 144,000 $ 144,000 Shareholder's equity$ 326,483 $ 283,677 Total Liabilities & 562,566 Shareholder's $ 599,658 $ 562,566

$ 42,806

3.21 Income statement: Nimitz Rental Company provided the following information to its auditors. For the year ended March 31, 2014, the company had revenues of $878,412, general and administrative expenses of $352,666, depreciation expenses of $131,455, leasing expenses of $108,195, and interest expenses equal to $78,122. If the company’s average tax rate is 34 percent, what is its net income after taxes? Revenues General and administrative expenses Depreciation expenses leasing expenses Interest espenses Tax rate

$ $ $ $ $

878,412 352,666 131,455 108,195 78,122 0.34

Nimitz Rental Company Income statement for year ending March 31, 2009 Revenues less Gen. and adm expenses less leasing expenses EBITDA less depreciation expenses EBIT Less Interest expenses EBT less Taxes (34%) Net income after taxes

$ $ $ $ $ $ $ $ $ $

878,412.00 352,666.00 108,195.00 417,551.00 131,455.00 286,096.00 78,122.00 207,974.00 70,711.16 137,263

3.22

Income statement: Sosa Corporation recently reported an EBITDA of $31.3 million and net income of $9.7 million. The company had $6.8 million in interest expense, and its average corporate tax rate was 35 percent. What was its EBITDA Net income Interest expense Corporate tax rate

$ $ $

31,300,000 9,700,000 6,800,000 35%

EBITDA

31,300,000

Less Depreciation

$ 9,576,923.08

Equals: EBIT

21,723,077

Less Interest expense

6,800,000

Equals: EBT

14,923,077

Less Taxes (35%)

$ 5,223,076.92

Equals: Net Income

9,700,000

3.23. Income statement: Fraser Corporation has announced that its net income for the year ended June 30, 2014, was $1,353,412. The company had EBITDA of $4,967,855, and its depreciation and amortization expense was equal to $1,112,685. The company’s average tax rate is 34 percent. EBITDA $ Net income $ Dep. & Amort. expense Corporate tax rate

4,967,855 1,353,412 1,112,685 34%

EBITDA

4,967,855

Less Depreciation

1,112,685

Equals: EBIT

3,855,170

Less Interest expense

1,804,545.76

Equals: EBT

2,050,624

Less Taxes (34%)

697,212.24

Equals: Net Income

1,353,412

3.24 Income statement: For its most recent fiscal year, Carmichael Hobby Shop recorded EBITDA of $512,725.20, EBIT of $362,450.20, zero interest expense, and cash flow to investors from operating activitiy of $348,461.25. Assuming there are no non-cash revenues recorded on the income statement, what is the firm's net income after taxes? EBITDA EBIT Cash flow

$ $ $

512,725.20 362,450.20 348,461.25

Depreciation & Amortization $

150,275.00

Net Income after taxes

198,186.25

hop recorded EBITDA of $512,725.20, EBIT perating activitiy of $348,461.25. Assuming t is the firm's net income after taxes?

3.25 Retained earnings: Columbia Construction Company earned $451,888 during the year ended June 30, 2014. After paying out $225,794 in dividends, the balance went into retained earnings. If the firm’s total retained earnings were $846,972, what was the retained earnings on its Net income after taxes Dividends paid Ending retained earnings

$ $ $

451,888 225,794 846,972

Increase in Retained earnings at June 30, 2014 $ 226,094 Retained earnings as at July 1, 2013 $ 620,878

3.26 Cash flows: Refer to the information given in problem 3.21. What is the cash flow for Revenues $ General and administrative expenses $ Depreciation expenses $ leasing expenses $ Interest espenses $ Tax rate

878,412 352,666 131,455 108,195 78,122 0.34

$ $ $ $ $ $ $ $ $ $ $

878,412.00 352,666.00 108,195.00 417,551.00 131,455.00 286,096.00 78,122.00 207,974.00 70,711.16 137,262.84 268,718

3.27 Tax: Mount Hebron Electrical Company’s financial statements indicated that the company had earnings before interest and taxes of $718,323. The interest rate on its $850,000 debt was 8.95 percent. Calculate the taxes the company is likely to owe. What are the marginal and average Earnings before interest and taxes Debt outstanding Interest rate on debt Earnings before interest and taxes Interest expense Taxable income Tax schedule 2007 Corporate Income Tax rates Taxable Income from Upto 0 $ 50,000 50,001 $ 75,000 75001 $ 100,000 100,001 $ 335,000 335,001 $ 10,000,000 10,000,001 $ 15,000,000 15,000,001 $ 18,333,333 18,333,334 $ -

Taxes owed Tax Breakdown: 0 to 50,000 50001 to 75000 75001 to 100000 100001 to 335,000 335001 to 642,248

218,364.32

$ $

$7500 $6250 8,500 91,650 104,464.32 218,364.32

Rate 15% 25% 34% 39% 34% 35% 38% 35%

Marginal tax rate Average tax rate

al statements indicated nd taxes of $718,323. percent. Calculate the marginal and average $ 718,323 $ 850,000 8.95% $ 718,323 76,075 $ 642,248

34% 34%

3.28 The Centennial Chemical Corp. announced that, for the period ending March 31, 2014, it had earned income after taxes worth $5,330,275 on revenues of $13,144,680. The company’s costs (excluding depreciation and amortization) amounted to 61 percent of sales and it had interest expenses of $392,168. What is the firm’s depreciation and amortization expense if its Income after taxes Revenues Cost of sales (excluding depreciation) Interest expenses Tax rate

$ $

Net income EBT Add interest EBIT EBITDA Depreciation and amortization

$ $ $

5,330,275 13,144,680 61% of sales 392,168 34% 5,330,275 8,076,174 392,168 8,468,342.24 8,018,254.80 (450,087)

Note there was a decline in depreciation and amortization perhaps from a sale of assets.

3.29 Eau Claire Paper Mill, Inc., had, at the beginning of the fiscal year, April 1, 2013, retained earnings of $323,325. During the year ended March 31, 2014, the company produced net income after taxes of $713,445 and paid out 45 percent of its net income as dividends. Construct a statement of retained earnings and compute the year-end balance of retained earnings. Retained earnings at at April 1, 2008

323,325

Net income after taxes Dividend payout ratio

713,445 45%

Eau Claire Paper Mill, Inc Statement of Retained Earnings for the period ended March 31,2009 Retained earnings as at April 1, 2008

$ 323,325.00

Add Net income after taxes

$ 713,445.00

Less dividends paid

$ 321,050.25

Ending Retained earnings on March3 1, 2009

$ 715,719.75

3.30

Menomonie Casino Company earned $23,458,933 before interest and taxes for the fiscal year ending March 31, 2014. If the casino had interest expenses of $1,645,123, calculate its tax burden using Exhibit 3.6. What are the marginal and the average tax rates for this company? EBIT Interest expenses

23,458,933 1,645,123

Tax schedule U.S. Federal Corporate Income Tax Rates for 2013 Taxable Income from Upto Rate 0 $ 50,000 15% 50,001 $ 75,000 25% 75001 $ 100,000 34% 100,001 $ 335,000 39% 335,001 $ 10,000,000 34% 10,000,001 $ 15,000,000 35% 15,000,001 $ 18,333,333 38% 18,333,334 $ 35% Taxable income

21,813,810

Tax breakdown: First 50,000 $ next 25,000 $ next 25,000 $ next 235,000 $ next 9,665,000 $

7,500 6,250 8,500 91,650 3,286,100

next 5,000,000 $ 1,750,000 next 3,333,333 $ 1,266,666.54 Last 3,480,477 1,218,166.95 Tax Burden $ 7,634,833

Average tax rate Marginal tax rate 35% 35%

3.31 Vanderheiden Hog Products Corp. provided the following financial information for the quarter ending Net income: $189,425 Depreciation and amortization: $63,114 Increase in receivables: $ 62,154 Increase in inventory: $57,338 Increase in accounts payable: $37,655 Decrease in marketable securities: $27,450 What is this firm's cash flow from operating activities during this quarter?

Depreciation and amortization: Net income: Increase in receivables: Increase in inventory: Increase in accounts payable: Decrease in marketable securities:

$63,114 $189,425 $62,154 $57,338 $37,655 $27,450

CASH FLOW FROM OPERATING ACTIVITIES Net income: Add Depreciation and Amortization

$189,425 $63,114

Add increase in accounts payables Less increase in receivables Less increase in inventory

$37,655 ($62,154) ($57,338)

Net Cash Flow from operating activities $170,702

Note: Marketable securities are assumed to be part of Cash and cash equivalents and therefore, not included as part of cash flow from operating activities.

3.32 Cash flows: Analysts following the Tomkovick Golf Company were given the following information for the year ended June 30, 2014 and June 30, 2013. Assets Cash and marketable securities Accounts receivable Inventory Other current assets Total current assets Plant and equipment Less: Accumulated depreciation Net plant and equipment Goodwill and other assets

2014

2013

$ $ $

33,411 260,205 423,819

$ $ $

16,566 318,768 352,740

41,251

29,912

758,686

717,986

1,931,719

1,609,898

$ $

($419,044) 1,512,675 382,145

$ $

($206,678) 1,403,220 412,565

$ 2,653,506 $ 2,533,771 Total assets In addition, it was reported that the company had a net income of $3,155,848 and that depreciation expenses were equal to $212,366 during 2014. a.Construct a 2014 cash flow statement for this firm. b.Calculate the net cash provided by operating activities. c.What is the net cash used in investing activities? d.Compute the net cash provided by financing activities.

Assets Cash and marketable securities Accounts receivable Inventory

2014 $ $ $

33,411 260,205 423,819

2013 $ $ $

16,566 318,768 352,740

Change $ $ $

16,845 (58,563) 71,079

Other current assets

41,251

Total current assets Plant and equipment Less: Accumulated depreciation Net plant and equipment Goodwill and other assets

Total assets Net Income Depreciation

29,912

11,339

758,686

717,986

1,931,719

1,609,898

321,821 (212,366)

$ $

$ ($206,678) $ 1,403,220 412,565 $

$ $

($419,044) 1,512,675 382,145

2,653,506

2,533,771

3,155,848 212,366

Tomkovic Golf Company Statement of Cash Flows for theyear ended June 30th, 2014 Cash Flow From Operating Activities Net Income Add Depreciation

3,155,848 212,366

Add decrease in A/R $ 58,563 Add increase in A/P $ 46,232 Add increase in Accrued Taxes $ 4,310 Less increase in inventory $ (71,079) Less increase in Other Current Assets $ (11,339) Net Cash Flow provided by operating activities Cash Flow From Investment Activities Increase in Gross Plant and Equipment $

(321,821)

3,394,901

(30,420)

Decrease in Goodwill and Other Assets $ Net Cash Flow used in investment activities

30,420

(291,401)

(3,086,655)

16,845

$ $

16,566 33,411

Cash Flow From Financing Activities Dividends paid $ (2,966,412) Treasury stock purchased $ (13,334) Increase in Notes Payables $ 6,625 Repayment of Long-term debt $ (113,534) Net Cash Flow provided by financing activities Change in Cash and Marketable Securities Balance plus Cash and Marketable Securities on July 1st, 2013 = Cash and Marketable Securities as at June 30, 2014

ng information

Liabilities and Equity

2014

2013

Accounts payable and accruals $ Notes payable $ Accrued income taxes $

378,236 14,487

$ $

332,004 7,862

$ $

16,815 356,681

793,515

Total current liabilities

21,125 413,848

Long-term debt

679,981

Total liabilities Preferred stock

1,093,829

$ 1,150,196

Common stock (10,000 shares) $ Additional paid-in capital $ Retained earnings $ Less: Treasury stock $ Total common equity $ Total liabilities and equity $

— 10,000 975,465 587,546 (13,334) 1,559,677 2,653,506

— 10,000 975,465 398,110

Liabilities and Equity

2014

Accounts payable and accruals $ Notes payable $ Accrued income taxes $

378,236 14,487

$ $

332,004 7,862

Change $ 46,232 $ 6,625

21,125

16,815

$ $ $

— $ 1,383,575 $ 2,533,771

2013

4,310

Total current liabilities

413,848

356,681

Long-term debt Total liabilities Preferred stock

679,981

793,515

1,093,829

Common stock (10,000 shares) $ Additional paid-in capital $ Retained earnings $ Less: Treasury stock $ Total common equity $ Total liabilities and equity $

— 10,000 975,465 587,546 (13,334) 1,559,677 2,653,506

$ (113,534)

$ 1,150,196 $ $ $

— 10,000 975,465 398,110

$ 1,383,575 $ 2,533,771

$ $ $ $ $

189,436 (13,334) 176,102

3.33 Cash flows: Based on the financial statements for Tomkovick Golf Company, problem 3.32 ab compute the cash flow invested in net working capital and the cash flow invested in long-term assets that you would use in a calculation of the cash flows to investors for 2014. CFNWC =(CA2011 - CL2010) - (CA2010 - CL2010)

CFLTA = (GROSS PP&E 2011 - GROSS PP&E 2010) + (GOODILL 2011 - GOODWILL 2010) CA2011 CL2011

$758,686.00 $413,848.00 $344,838.00

GROSS P&E 2011 GROSS P&E 2010

CA2010 CL2010

$717,986.00 $356,581.00 $361,405.00

GW2011 GW2010

CFNWC

($16,567.00)

CFLTA

ck Golf Company, problem 3.32 above, e cash flow invested in long-term o investors for 2014.

OODILL 2011 - GOODWILL 2010) $1,931,719.00 $1,609,898.00 $321,821.00 $382,145.00 $412,565.00 ($30,420.00) $291,401.00

STP #3.2 Wolf Pack Enterprises has total current assets of $346,002 and fixed assets of $476,306. The company also has long-term debt of $276,400, $100,000 in its common stock account, and retained earnings of $187,567. What is the value of its total Assets Liabilities and Equity Total current assets $346,002 Total current liabilities$??????? Fixed assets $476,306 Long-term debt $276,400 Common stock $100,000 Retained earnings $187,567 Liabilities and Total assets $??????? stockholders' equity $??????? Total assets = Total current liabilities (eq. 3.1) =

$822,308.00 $258,341.00

STP #3.4 ACME Corporation had revenues of $867,030 in 2014. It also had expenses (excluding depreciation) of $356,240, depreciation of $103,456, and interest expense of $52,423. What was the company's net income after taxes if its average tax rate was 40 percent? Revenues Expenses EBITDA Depreciation EBIT Interest EBT Taxes (40%) Net income

$867,030.00 $356,240.00 $510,790.00 $103,456.00 $407,334.00 $52,423.00 $354,911.00 $141,964.40 $212,946.60

STP #3.5 The Blue Company increased its investments in marketable securities by $323,370 and paid $1,220,231 for new fixed asset during 2014. The company also repaid $779,200 of existing long-term debt while raising $913,455 of new debt capital. In addition, True Blue had a net cash inflow of $345,002 from the sale of fixed assets, and repurchased stock in the open markets for a total of $56,001. What is the net cash used in investing activities by True Blue? What is the net cash provided Investing Activities Net property, equipment, and other assets(1,220,231) $ Net acquisitions and dispositions $ 345,002 Investments in marketable securities $ (323,370) Net cash used in investing activities $ (1,198,599)

4.2.

Liquidity ratios: Flying Penguins Corp. has total current assets of $11,845,175, current liabilities of $5,311,020, and a quick ratio of 0.89. What is its level of inventory?

Total current assets

$ 11,845,175.00

Total current liabilities

$ 5,311,020.00

Quick ratio

0.89

Quick ratio = (Total Current assets - Inventory) Current Liabilities Inventory = Total Current assets -(Quick ratio * Current Liabilities) Inventory =

$ 7,118,367.20

Check: Quick ratio=

0.89

s of $11,845,175, current level of inventory?

4.3.

Efficiency ratio: If Newton Manufacturers have an accounts receivable turnover of 4.8 times and net sales of $7,812,379, what is its level of receivables?

Accounts receivable turnover Net sales A/R Turnover =

A/R =

$ Net sales A/R

Net sales A/R Turnover 1,627,578.96

4.8 times 7,812,379

4.4.

Efficiency ratio: Bummel and Strand Corp. has a gross profit margin of 33.7 percent, sales of $47,112,365, and inventories of $14,595,435. What is its inventory turnover ratio?

Gross profit margin Sales Inventories

$ $

33.70% 47,112,365 14,595,435

Inventory turnover ratio = Cost of Goods Sold Average Inventory Cost of Goods Sold Inventory turnover ratio

31,235,498 2.14 times

4.5. Efficiency ratio: Sorenson Inc. has sales of $3,112,489, a gross profit margin of 23.1 percent, and inventory of $833,145. What are the company’s inventory turnover ratio and days’ sales in inventory? Sales Gross profit margin Inventory

$ 3,112,489 23.10% $ 833,145

Inventory turnover ratio = Cost of Goods Sold/Inventory Day's sales in inventory = 365 days/Inventory turnover ratio Cost of goods sold = $ 2,393,504 Inventory turnover ratio 2.87 Day's sales in inventory 127.05 days

4.6.

Leverage ratios: Breckenridge Ski Company has total assets of $422,235,811 and a debt ratio of 29.5 percent. Calculate the company’s debt-to-equity ratio and the equity multiplier.

Total assets Debt ratio

422,235,811 29.50%

Debt ratio = Total Debt / Total Assets --> Total Debt = Debt ratio * Total assets Debt-to-equity ratio = Total debt/Shareholder's equity Equity Multiplier = Total Assets/Shareholder's equity Shareholder's equity = Total Assets - Total Debt Total Debt = Shareholders' equity =

124,559,564.25 297,676,246.76

Debt-to-equity ratio =

41.84%

Equity Multiplier

1.42

4.7.

Leverage ratios: Norton Company has a debt-to-equity ratio of 1.65, ROA of 11.3 percent, and total equity of $1,322,796. What are the company’s equity multiplier, debt ratio, and ROE?

Debt-to-equity ratio ROA Total equity

1.65 11.30% $ 1,322,796

Equity multiplier = Total Assets/Total Equity Debt ratio=Total Debt/Total Assets ROE = ROA * Equity multiplier Debt-to-equity ratio = Total Debt/Total equity -->Total Debt = Debt-to-equity ratio*Total equity Total Debt= 2,182,613.40 Total Assets = Total Debt + Total Equity = 3,505,409.40 Equity multiplier= $ 2.65 Debt ratio = 62.26% ROE 29.95%

to-equity ratio of 1.65, ROA of 11.3 are the company’s equity multiplier,

bt = Debt-to-equity ratio*Total equity

4.8.

DuPont equation: The Rangoon Timber Company has the following relationships: Sales/Total assets = 2.23; ROA = 9.69%; ROE = 16.4% What are Rangoon’s profit margin and debt ratio? Sales/Total Assets= ROA= ROE=

2.23 9.69% 16.40%

Profit margin = Net Income/Sales Debt ratio = Total Debt/Total Assets ROA = Net Income/Total Assets ROE = Net Income/ Total equity Based on the Du Pont Breakdown: ROA = (Net Income/Sales)*(Sales/Total Assets) and ROE = (Net Income/Sales)*(Sales/Total Assets)*(Total Assets/Equity) ROA Breakdown: 9.69% =(Net Income/Sales)* ==>(Net Income/Sales) = 4.35% Profit Margin = 4.35% ROE=

2.23

9.69% *TA/Equity 16.40% =(TA/Equity) X 9.69% ==>(TA/Equity)= 1.692 ==>Equity/Total Assets= 1/(TA/Equity) ==>Equity/Total Assets= 59.09%

Debt/Total Assets = 1-(Equity/Total Assets)= Alternative way: TA/Equity = (ROE/ROA)= Equity/TA=1/(TA/EQ) Debt /TA= 1- (E/TA)

1.692 59.09% 40.91%

40.91%

4.9 DuPont Equation: Lemmon Enterprises has a total asset turnover of 2.1 and a net profi of 7.5%. If its equity multiplier is 1.90, what is the ROE for Lemmon Enterprises? ROE = ROA x EQUITY MULTIPLIER ROA = NET PROFIT MARGIN x TOTAL ASSET TURNOVER ROA =

7.50%

2.1

15.75%

ROE =

15.75%

1.9

29.93%

4.11

Benchmark analysis: Trademark Corp.’s financial manager collected the following information for its peer group so it can compare its own performance against the peers. Ratios DSO Total assets turnover Inventory turnover Quick ratio

Trademark Peer Group 33.5 days 27.9 days 2.3 X 1.8 X 0.6 X

3.7 X 2.8 X 1.3 X

a. Explain how Trademark is performing relative to its peers. b. How do the industry ratios help Trademark’s management?

Trademark is lagging behind its peer group in all four areas. It takes, on average, about 6 more days to collect its receivables, has a slower inventory and total assets turnover, and lower liquidity than its peers.

The industry ratios help Trademark's management by giving them a benchmark representing the average performance in the industry, against which they can compare the firm's performance. Accordingly, corrective action can be taken by determining how much the firm's assets and liabilities need to be changed to match the peer group.

4.12 Market value ratios: Rockwell Jewelers announced net earnings of $6,481,778 for this year. The company has 2,543,800 shares outstanding, and the year-end stock price is $54.21. What are the company’s earnings per share and P/E ratio? Net earnings # of shares outstanding Year-end stock price Earnings per share P/E ratio

6,481,778 2,543,800 $54.21 2.55 $21.27

4.13 Market-value ratios: Chisel Corporation has 3 million shares outstanding at a price per share of $3.25. If the debt-to-equity ratio is 1.7 and total book value of debt equals $12,400,000, what is the market-to-book ratio for Chisel Corporation?

Market value of equity = shares outstanding x price per share Book value of equity = Book value of debt / debt-to-equity ratio Market-to-book ratio = Market value of equity / Book value of equity Market value of equity =

3,000,000

3.25

Book value of equity =

$12,400,000.00

1.7

Market-to-book ratio =

$9,750,000.00

$7,294,117.65

on shares outstanding at a price per d total book value of debt equals hisel Corporation?

e per share

o-equity ratio

ok value of equity $9,750,000.00 $7,294,117.65 1.34

4.14 Liquidity ratios: Laurel Electronics has a quick ratio of 1.15, current liabilities of $5,311,020, and inventories of $7,121,599. What is the firm’s current ratio? Quick ratio

1.15

Current liabilities $

5,311,020

Inventories

7,121,599

Current ratio = Current assets/Current Liabilities Quick ratio =( Total Current Assets - Inventories)/ Current Liabilities ==>

Total Current Assets = (Quick ratio * Current Liabilities)+Inventories

==>

Total Current Assets = Current ratio=

$ 13,229,272 2.49

4.15 Efficiency Ratio: Lamda Corporation has current liabilities of $450,000, a quick ratio of 1.8, inventorey turnover of 5.0, and a current ratio of 3.5. What is the cost of goods sold for Lamda Corporation? CURRENT ASSETS = CURRENT RATIO * CURRENT LIABILITIES CURRENT ASSETS =

3.5 $450,000.00

QUICK RATIO = (CURRENT ASSETS - INVENTORY) / CURRENT LIABILITIES 1.8 $1,575,000.00 INVENTORY $450,000.00 INVENTORY =

$765,000.00

INVENTORY TURNOVER = COST OF GOOD SOLD / INVENTORY 5 CGS $765,000.00 COST OF GOODS SOLD $3,825,000.00 =

quick ratio of 1.8,

$1,575,000.00

RRENT LIABILITIES

4.16 Efficiency ratio: Norwood Corp. currently has accounts receivable of $1,223,675 on net sales of $6,216,900. What are its accounts receivable turnover ratio and days’ sales outstanding? Accounts receivable Net sales

$ 1,223,675 $ 6,216,900

Days' sales outstanding = 365/Accounts receivable turnover Accounts receivable turnover = Net sales/Accounts receivable Accounts receivable turnover= 5.081 Days' sales outstanding= 72 days

vable of s receivable

4.17 Efficiency ratio: If Norwood Corp.’s management wants to reduce the DSO from that calculated in the above problem to an industry average of 56.3 days and its net sales are expected to decline by about 12 percent, what would be Accounts receivable $ 1,223,675 Net sales (currently) $ 6,216,900 Days' sales outstanding (DSO) 72 days Expected decline in sales 12% Desired DSO 56.3 days Expected sales = $ 5,470,872 Days' sales outstanding = 365/Accounts receivable turnover Accounts receivable turnover = Net sales/Accounts receivable To reduce the DSO to 56.3 days at the new level of sales: Accounts receivable turnover= 6.48 Accounts receivable= $ 843,863

4.18 Coverage ratios: Nimitz Rental Company had depreciation expenses of $108,905, interest expenses of $78,112, and an EBIT of $1,254,338 for the year ended June 30, 2014. What are the times-interest-earned and cash coverage ratios for this company? Dpreciation expenses Interest expenses EBIT

$ 108,905 $ 78,112 $ 1,254,338

Times interest earned = EBIT / Interest expenses Cash coverage ratio = (EBIT + Depreciation) / Interest expense Times interest earned = Cash coverage =

16.06 times 17.45 times

4.19 Leverage ratios: Conseco, Inc., has a debt ratio of 0.56. What are the company’s debt-to-equity ratio and equity multiplier? Debt ratio

0.56

Debt ratio = Total Debt/Total Assets Debt-to-equity ratio = Total Debt/Total Equity Equity multiplier = Total assets/Total Equity Note: since Total Assets = Total Debt + Total Equity Total Debt/Total Assets + Total Equity/Total Assets = 1.0 ==> Total Equity/Total Assets = 1.0 - Debt ratio ==> Equity multiplier = 1/(1-debt ratio) So, Equity multiplier= 2.27 Debt-to-equity ratio = (Debt/Total Assets)/(Equity/Total Assets)=Debt ratio/(1-debt ratio) Debt-to-equity ratio = 1.273

4.20 Profitability ratios: Cisco Systems has total assets of $35.594 billion, total debt of $9.678 billion, and net sales of $22.045 billion. Their net profit margin for the year is 20 percent, while the operating profit margin was 30 percent. What are Cisco’s net income, EBIT ROA, ROA, and ROE? Total assets Total debt Net sales Net profit margin Operating profit margin Net income EBIT EBIT ROA ROA Equity ROE

$ 35.594 billion $ 9.678 billion $ 22.045 billion 20% 30% 4.41 billion 6.61 18.58% 12.39% 25.92 billion 17.01%

4.21 Profitability ratios: Procter & Gamble reported the following information for its fiscal year end: On net sales of $51.407 billion, the company earned a net income after taxes of $6.481 billion. It had cost of goods sold of $25.076 billion and an EBIT of $9.827 billion. What is the company’s (a) gross profit margin, (b) operating profit margin, and (c) net profit margin? Net sales Net income Cost of goods sold EBIT

$ 51.407 billion 6.481 billion 25.076 billion 9.827 billion

(a) Gross profit margin 51.22% (b) Operating profit margin19.12% (c) Net profit margin 12.61%

4.22 Profitability ratios: Wal-Mart, Inc., has net income of $9,054,000 on net sales of $256,329,812. The company has total assets of $104,912,112 and shareholders’ equity of $43,623,445. Use the extended DuPont identity to find the return on assets and return on equity for the firm. Net Income $ Net sales $ Total assets $ Shareholders' equity $

9,054,000 256,329,812 104,912,112 43,623,445

Return on assets = (Net Income/Sales)*(Sales/Total Assets) ROA = Net profit margin * Total asset turnover Net profit margin = Net income/Net sales= 3.53% Total asset turnover = Sales/Total Assets = $ 2.44 ROA =

8.63%

Return on equity = Net profit margin * Total Asset turnover * (Total assets/Shareholders' equity) Return on equity = 20.75%

4.23 Profitability ratios: Xtreme Sports Innovations has disclosed the following information: EBIT = $25,664,300 Net income = $13,054,000 Net sales = $83,125,336 Total debt = $20,885,753Total assets = $71,244,863 Compute the following ratios for this firm using the DuPont Identity: debt-to-equity ratio, EBIT ROA, ROA, and ROE. EBIT Net income Net sales Total debt Total assets

$ $ $ $ $

25,664,300 13,054,000 83,125,336 20,885,753 71,244,863

Debt-equity ratio EBIT ROA Net Profit Margin Total Asset Turnover Equity Multiplier

41.47% 36.02% 15.70% 1.167 1.41

ROA ROE

18.32% 25.92%

4.24 Market value ratios: Cisco Systems had net income of $4.401 billion and, at year end, 6.735 billion shares outstanding. Calculate the earnings per share for the Net income $ 4.401 billion # of shares outstanding 6.735 billion Earnings per share

0.65

4.25 Market value ratios: Use the information for Cisco Systems in the last problem. In addition, the company’s EBITDA was $6.834 billion and its share price was $22.36. Compute the firm’s price-earnings ratio and the price-EBITDA ratio. Net income # of shares outstanding EBITDA Share price

4.401 billion 6.735 billion 6.834 billion $22.36

Price-earnings ratio = Price/EPS EPS= $ 0.65 P/E ratio 34.22 Price-EBITDA ratio = Price/(EBITDA per share) EBITDA per share= $ 1.01 Price-EBITDA ratio= 22.04

4.26

DuPont equation: Carter, Inc., a manufacturer of electrical supplies, has an ROE of 23.1 percent, a profit margin of 4.9 percent, and a total assets turnover ratio of 2.6 times. Its peer group also has an ROE of 23.1 percent but has outperformed Carter with a profit margin of 5.3 percent and a total assets turnover ratio of 3.0 times. Explain how Carter managed to achieve the same level of profitability as reflected by the ROE.

Carter Inc. ROE 23.10% Profit margin 4.90% Total assets turnover 2.6 times

Peer Group 23.10% 5.30% 3 times

ROE = Profit margin * Total Asset Turnover * Equity Multiplier ==>

Equity Multiplier = ROE/(Profit Margin * Total Asset Turnover)

Equity Multiplier Debt ratio

Carter Inc.

Peer Group

181.319% 44.85%

145.283% 31.17%

Answer: Carter managed to achieve the same level of profitability (ROE) as its peer group, despite having a lower net profit margin and total assets turnover ratio, by having a higher debt ratio, i.e. 44.85% versus 31.17%

ercent, a profit margin of 4.9 .1 percent but has .0 times. Explain how

4.27 DuPont equation: Grossman Enterprises has an equity multiplier of 2.6 times, total assets of $2,312,000, an ROE of 14.8 percent, and a total assets turnover of 2.8 times. Calculate the firm’s sales and ROA. Equity multiplier Total assets ROE Total assets turnover

2.6 times $ 2,312,000 14.80% 2.8 times

==>

Total assets turnover = Sales / Total assets Sales = Total assets turnover × Total assets Sales = = 2.8 × 2,312,000 = $ 6,473,600

==>

ROE = Profit margin × Total assets turnover × Equity multiplier ROE = (Net income/Sales) × (Sales/Total assets) × (Total assets/Shareholders' equity) Net Income / Sales = 2.03% = ROE / (Total assets turnover) × (Equity multiplier) ROA = (Net income / Sales) × Total assets turnover ROA = 5.69%

4.28 Complete the balance sheet of Flying Roos Corp., given all of the following information: Flying Roos Corporation Balance Sheet as of December 31, 2014 Assets: Cash and marketable securities Accounts receivable Inventory Total current assets

Liabilities and Equity:

$ $

$1,059,589 240,411 500,000 $1,800,000

Net plant and equipment

$6,200,000

Total assets

$8,000,000

Accounts payable and accruals Notes payable Total current liabilities Long-term debt Common stock Retained earnings Total liabilities and equity

You have the following information: Debt ratio = 40% Current ratio = 1.5 X Sales = $2.25 million DSO = 39 days Inventory turnover ratio = 3.375 X Cost of goods sold = $1.6875 million

Debt ratio = Total debt / Total assets = Total equity / Total assets = Total equity = Common stock = Sales =

40% 40% 0.6 $4,800,000 $3,550,000 2,250,000

Current ratio = Current Liabilities = Current assets = Inventory turnover ratio = Cost of goods sold / Inventory = Inventory = Cost of goods sold / Inventory turnover ratio Inventory =

DSO (days) = 365 / A/R Turnover Cost of goods sold =

39 $1,687,500

A/R Turnover = A/R = Sales / A/R Turnover =

information:

$900,000 $300,000 $1,200,000 $2,000,000 $3,550,000 $1,250,000 $8,000,000

1.5 $1,200,000 $1,800,000 er ratio = Cost of goods sold / Inventory =3.375 of goods sold / Inventory turnover ratio $ 500,000

9.359 = Sales / Accounts Receivables 240,411

4.29 For the year ended June 30, 2014, Northern Clothing Company has total assets of $87,631,181, ROA of 11.67 percent, ROE of 21.19 percent, and a profit margin of 11.59 percent. What are the company’s net income and net sales? Calculate the firm’s debt-to-equity Total assets ROA ROE Net profit margin

87,631,181 11.67% 21.19% 11.59%

ROA = Net Profit Margin * Total asset turnover ==> Total asset turnover = ROA/Net profit margin Total asset turnover = 1.01 Total asset turnover = Net sales/Total assets ==> Net sales = Total asset turnover * Total assets Net sales = $ 88,236,055 Net income = Sales × Net profit margin= $ Equity multiplier = Total Assets / Equity = ROE / ROA = Equity ratio = 1 / Equity multiplier = Debt ratio = 1 − Equity ratio = Debt-to-equity ratio = Debt ratio / Equity ratio =

10,226,559 1.82 0.55 0.45 0.816

4.30

Blackwell Automotive’s balance sheet at the end of its most recent fiscal year shows the fo

Assets: Cash and marketable sec. Accounts receivable Inventories Total current assets Net plant and equipment Goodwill and other assets Total assets

Flying Roos Corporation Balance Sheet as of December 31, 2014 Liabilities and Equity: $23,015 Accounts payable and accruals $141,258 Notes payable $212,444 Total current liabilities $387,940 Long-term debt $711,256

Total liabilities Common stock

$78,656 $1,177,852

Retained earnings Total liabilities and equity

In addition on, it was reported that the firm had a net income of $156,042 on sales of $4,063,589. a. What are the firm’s current ratio and quick ratio? b. Calculate the firm’s days’ sales outstanding (DSO), total asset turnover ratio, and fixed asset turnover ratio. Current ratio = Total current assets/Total current liabilities Quick ratio = (Total current assets − Inventory) / Total current liabilities Sales = 4,063,589 Net income = Days' sales outstanding = 365 / Accounts receivables turnover Accounts receivables turnover = Sales / Accounts receivables Total asset turnover =Sales / Total assets Fixed asset turnover S = ales / Fixed assets

ecent fiscal year shows the following information:

$163,257 $21,115 $184,372 $168,022 $352,394 $313,299 $512,159 $1,177,852

of $156,042

2.10 times 0.95 times 156,042 12.69 times 28.77 3.45 times 5.71 times

4.31 The following are the financial statements of Nederland Consumer Products Company reported for the fiscal year ended September 30, 2014.

Nederland Consumer Products Company Income Statement for the Fiscal Year Ended September 30, 2014 Net sales Cost of products sold

$51,407 $25,076

Gross margin Marketing, research, administrative exp. Depreciation

$26,331 $15,746 $758

Operating income (loss) Interest expense Other nonoperating income (expense), net Earnings (loss) before income taxes

$9,827 $629

Income taxes

$2,869

Net earnings (loss)

$6,481

$152 $9,350

Nederland Consumer Product Company Balance Sheet as of September 30, 2014 Assets: Cash and cash equivalents Investment securities Accounts receivable Inventory Deferredexpenses income taxes Prepaid and other receivables

$5,469 423 4,062 4,400 958 1,803

Liabilities and Equity: Accounts payable Accrued and other liabilities Taxes payable Debt due within one year Total current liabilities Long-term debt

Total current assets

$17,115

Deferred income taxes

Property, plant, and equipment, at cost Less: Accumulated depreciation Net plant, andintangible equipment Net property, goodwill and other

25,304 11,196 $14,108

Other noncurrent liabilities Total liabilities Convertible class A preferred stock

assets

23,900

Common stock

Other noncurrent assets

1,925

Retained earnings shareholders' equity (deficit) Total liabilites and shareholders' equity

Total assets

$57,048

Calculate all the ratios (for which industry figures are available) for Nederland and compare the firm’s ratios with the industry ratios.

Industry Ratios Current ratio Quick ratio Gross margin Profit margin Debt ratio Long-term debt to equity Interest coverage ROA ROE

2.05 0.78 23.90% 12.30% 0.23 0.98 5.62 5.30% 18.80%

Nederland Consumer Products Co. 0.77 0.57 51.22% 12.61% 0.70 0.73 14.86 11.36% 37.51%

mer Products 14.

$3,617 7,689 2,554 8,287 $22,147 12,554 2,261 2,808 $39,770 1,526 2,141 13,611 $17,278 $57,048

rland and compare

mer Products Co.

Comment Weak Weak Much stronger Slightly better Highly leveraged with more short term debt Relatively less LTD Much higher Much higher Much higher

4.32 Ratio analysis: Refer to the information above for Nederland Consumer Products Company. Compute the firm’s ratios for the following categories and briefly evaluate the company’s performance from these numbers. a. b. c. d.

Efficiency ratios Asset turnover ratios Leverage ratios Coverage ratios Nederland Consumer Products Company Income Statement for the Fiscal Year Ended September 30, 2014 Net sales Cost of products sold

$51,407 $25,076

Gross margin Marketing, research, administrative exp. Depreciation

$26,331

Operating income (loss) Interest expense income Other nonoperating

$9,827 $629

(expense), net before income Earnings (loss) taxes

$152 $9,350

Income taxes

$2,869

Net earnings (loss)

$6,481

$15,746 $758

Nederland Consumer Product Company Balance Sheet as of September 30, 2014 Assets: Cash and cash equivalents

$5,469

Liabilities and Equity: Accounts payable

$3,617

Investment securities

423

Accounts receivable Inventory Deferredexpenses income taxes Prepaid and other receivables

Accrued and other liabilities

7,689

4,062

Taxes payable

2,554

4,400

Debt due within one year

8,287

958

Total current liabilities

$22,147

Long-term debt

12,554

Total current assets Property, plant, and equipment, at cost

$17,115

Deferred income taxes

2,261

25,304

Other noncurrent liabilities

2,808

Less: Accumulated depreciation Net property, plant, and equipment Net goodwill and other intangible

11,196

$39,770

$14,108

Total liabilities Convertible class A preferred stock

assets

23,900

Common stock

Other noncurrent assets

1,925

Retained earnings equity Total shareholders' (deficit) Total liabilites and shareholders' equity

Total assets

1,803

$57,048

Efficiency ratios Inventory Turnover = Cost of goods sold/Inventory = Day's Sales in Inventory = 365 days / Inventory turnover = Accounts Receivable Turnover = Net sales / Account receivable = Days' Sales Outstanding = 365 Days / Account receivable turnover

2008 5.70 times 64.05 days 12.66 times 28.84 days

Asset turnover ratios Total Asset Turnover = Net sales / Total assets Fixed Asset Turnover = Net sales / Net fixed assets

0.90 times 3.64 times

Leverage ratios Total Debt Ratio = Total debt / Total assets Debt-Equity Ratio = Total debt / Total equity

0.70 2.30

1,526 2,141 13,611 $17,278 $57,048

Equity Multiplier = Total assets / Total equity

3.30 times

Coverage ratios Interest Coverage = Times Interest Earned = EBIT / Interest expense Cash Coverage = (EBIT + Depreciation) / Interest expense

15.62 times 16.83 times

4.33 Refer to the information above for Nederland Consumer Products Company. Using the DuPont Identity, calculate the return on equity for Nederland, after calculating the ratios that make up the DuPont Identity. Nederland Consumer Products Company Income Statement for the Fiscal Year Ended September 30, 2014 Net sales Cost of products sold

$51,407 $25,076

Gross margin Marketing, research, administrative exp. Depreciation

$26,331

Operating income (loss) Interest expense Other nonoperating income (expense), net Earnings (loss) before income taxes

$9,827 $629

Income taxes

$2,869

Net earnings (loss)

$6,481

$15,746 $758

$152 $9,350

Nederland Consumer Product Company Balance Sheet as of September 30, 2014 Assets: Cash and cash equivalents

$5,469

Investment securities

423

Accounts receivable

4,062

Inventory

4,400

Deferred income taxes Prepaid expenses and other receivables

958 1,803

Total current assets Property, plant, and equipment, at cost

$17,115

Less: Accumulated depreciation

11,196

Net property, plant, and equipment Net goodwill and other intangible assets

$14,108

Other noncurrent assets Total assets

25,304

23,900 1,925 $57,048

Return on equity = Net Profit Margin * Total asset turnover * Equity Multiplier

Return on equity = Net income/Net sales * Sales/Total assets * Total assets/Shareholders' equit Net Profit Margin =

12.61%

Total asset turnover =

0.90

Equity multiplier =

3.30

ROE =

37.51%

Nederland Consumer Products Company. Using the n on equity for Nederland, after calculating the ratios

ederland Consumer Product Company

alance Sheet as of September 30, 2014 Liabilities and Equity: Accounts payable

$3,617

Accrued and other liabilities

7,689

Taxes payable

2,554

Debt due within one year

8,287

Total current liabilities

$22,147

Long-term debt

12,554

Deferred income taxes

2,261

Other noncurrent liabilities Total liabilities Convertible class A preferred stock

2,808 $39,770 1,526

Common stock

2,141

Retained earnings

13,611

Total shareholders' equity (deficit) Total liabilites and shareholders' equity

$17,278 $57,048

4.34 Nugent, Inc., has a gross profit margin of 31.7 percent on sales of $9,865,214 and total assets of $7,125,852. The company has a current ratio of 2.7 times, accounts receivable of $1,715,363, cash and marketable securities of $315,488, and current liabilities of $870,938. a. What is Nugent’s level of current assets? b. How much inventory does the firm have? What is the inventory turnover ratio? c. What is Nugent’s days’ sales outstanding? d. If management wants to set a target DSO of 30 days, what should Nugent’s accounts receivable be?

Sales Total assets Accounts receivable Cash and marketable securities Current liabilities Target DSO Gross profit margin Current ratio

$ $ $ $ $

9,865,214 7,125,852 1,715,363 315,488 870,938 30 days 31.70% 2.7 times

Current ratio = Current assets/Current liabilities ==> Current assets = Current ratio * Current liabilities ==> Current assets = $ 2,351,532.60

Total current assets = Cash and marketable securities + A/R + Inventory ==> Inventory = Total current assets -Cash and M/S - A/R Inventory = $ 320,681.60

Days' sales outstanding = 365/Accounts receivable turnover Accounts receivable turnover = Sales/Accounts receivable

Accounts receivable turnover = DSO = d)

5.75 63.47 days

Target DSO = 30 days Since, Days' sales outstanding = 365/Accounts receivable turnover ==> Accounts receivable turnover = 365/DSO Accounts receivable turnover would have to be and since, Accounts receivable = Sales/Accounts receivabel turnover Accounts receivable would have to be 810,839.51 i.e. A/R would have to decline by $ 904,523.49

12.167

4.35 Recreational Supplies Co. has net sales of $11,655,000, an ROE of 17.64 percent, and a total asset turnover of 2.89 times. If the firm has a debt-to-equity ratio of 1.43, what is the company’s net income? Net sales $ ROE Total asset turnover Debt-equity ratio

11,655,000 17.64% 2.89 times 1.43

What is the company's net income? Equity multiplier = 1 + Debt-to-equity ratio 2.43 Return on equity = Net profit margin * Total Asset turnover * Equity multiplier ==> Net profit margin = Return on equity/(Total asset turnover * Equity multiplier) ==> Net profit margin = 2.51% Net income = Net sales * Net profit margin =

292,756.63

4.4 Nutmeg Houseware Inc. has an operating profit margin of 10.3 percent on revenues of $24,547,125 and total assets of $8,652,352. a. Find the company’s total asset turnover ratio and its operating profit (EBIT). b. If the company’s management has set a target for the total asset turnover ratio to be 3.25 next year without any change in the total assets of the company, what will have to be the new sales level for the next year? Calculate change in sales necessary and the percentage sales necessary. c. If the operating profit margin now shrinks to 10 percent, what will be the EBIT at the new level of sales? Operating profit margin = Revenues = $ Total assets $ Target Total asset turnover ratio New operating profit margin a.

10.30% 24,547,125 8,652,352 3.25 10%

Find the company’s total asset turnover ratio and its operating profit (EBIT). Total asset turnover = Revenues/Total assets Operating profit = Operating profit margin*Revenues

If the company’s management has set a target for the total asset turnover ratio to be 3.25 next year without any change in the total assets of the company, what will have to be the new sales level for the next year? Calculate change in sales necessary and the percentage sales necessary.

==> c.

2.84 2,528,354

Target total asset turnover ratio = New sales level = Target Total asset turnover * Total assets

3.25 28,120,144

If the operating profit margin now shrinks to 10 percent, what will be the EBIT at the new level of sales?

New revenues = New EBIT =

28,120,144 2,812,014

4.37 Modern Appliances Corporation has reported its financial results for the year ended December 31, 2014. Modern Appliances Corporation Income Statement for the Fiscal Year Ended December 31, 2014 Sales Cost of goods sold

$5,398,412,000 $3,432,925,255

Gross profit margin $1,965,486,745 Selling, general, and administrative expenses$1,036,311,231 Depreciation $299,928,155 Operating income Interest expense EBT Income taxes Net earnings

$629,247,359 $35,826,000 $593,421,359 $163,104,554 $430,316,805 Modern Appliances Corporation Balance Sheet as of December 31, 2014

Assets: Cash and cash equivalents Accounts receivables

$514,412,159 1,046,612,233

Inventory Other current assets Total current assets Net fixed assets

981,870,990 313,621,610 $2,856,516,992 754,660,275

Liabilities and Equity Short-term borrowings Trade accounts payable Other current liabilities Total current liabilities Long-term debt

Goodwill Other assets

Total asssets

118,407,710 665,058,761

Common stock Retained earnings

$4,394,643,738

Total liabilities and equity

Using the information from the financial statements, complete a comprehensive ratio analysis for Modern Appliances Corporation. a. Calculate these liquidity ratios: current and quick ratios. b. Calculate these efficiency ratios: inventory turnover, accounts receivable turnover, DSO. c. Calculate these asset turnover ratios: total asset turnover, fixed asset turnover. d. Calculate these leverage ratios: total debt ratio, debt-to-equity ratio, equity multiplier. e. Calculate these coverage ratios: times interest earned, cash coverage. f. Calculate these profitability ratios: gross profit margin, net profit margin, ROA, ROE. g. Use the DuPont Identity, and after calculating the component ratios, compute the ROE for this firm. a.

Calculate these liquidity ratios: current and quick ratios. Current ratio = Current assets/ Current liabilities = Quick ratio = (Current assets − Inventories) / Current liabilities =

Calculate these efficiency ratios: inventory turnover, accounts receivable turnover, DSO. Inventory Turnover = Cost of goods sold/Inventory = Accounts Receivable Turnover = Net sales / Account receivable = Days' Sales Outstanding = 365 Days / Account receivable turnover =

1.81 1.19

Calculate these asset turnover ratios: total asset turnover, fixed asset turnover.

3.50 5.16 70.76

Total Asset Turnover = Net sales/Total assets = Fixed Asset Turnover = Net sales/Net fixed assets = d.

Calculate these leverage ratios: total debt ratio, debt-to-equity ratio, equity multiplier. Total Debt Ratio = Total debt / Total assets = Debt-Equity Ratio = Total debt / Total equity = Equity Multiplier = Total assets / Total equity =

1.23 7.15

0.63 1.72 2.72

Calculate these coverage ratios: times interest earned, cash coverage. Interest Coverage =Times Interest Earned = EBIT/Interest expense = Cash Coverage = (EBIT + Depreciation)/Interest expense =

Calculate these profitability ratios: gross profit margin, net profit margin, ROA, ROE. Gross profit margin = Gross profit/Sales Net profit margin = Net income/Sales ROA = Net income/Total assets ROE = Net income/Shareholders' equity

16.56 24.94

36.41% 7.97% 9.79% 26.63%

Use the DuPont Identity, and after calculating the component ratios, compute the ROE for this firm. Return on equity = Net Profit Margin * Total asset turnover * Equity Multiplier ROE = 26.63%

$117,109,865 466,937,985 994,289,383 $1,578,337,233 1,200,691,565

397,407,352 1,218,207,588

$4,394,643,738

or this firm.

times times days

times times

or this firm.

4.4 The TBI Company has a number of days of inventory of 50. Therefore, the TBI Compan inventory turnover is closest to

The days of inventory is equal to 365 days of the year divided by the inventorty turnove days in year Days of inventory

365 50

Invenmtory Turnover

7.3

[b]

#4.41

If a company's net profit margin is −5 percent, its total asset trunover is 1.5 times an its financial leverage ratio is 1.2 times, its return on equity is closest to

Dupont ROE = Profit margin x Total asset turnover x Equity multiplier profit margin total asset turnover financial leverage

-5.00% 1.5 1.2

ROE

-9.00%

[a]

nt, its total asset trunover is 1.5 times and eturn on equity is closest to

urnover x Equity multiplier

Greenfern Corporation recently filed the following financial statements with the SEC. Greenfern Corporation Income Statement for the Fiscal Year Ended July 31, 2014 Net sales Cost of products sold Gross profit Selling, general, and administrative expenses Depreciation Operating income (loss) Interest expense Earnings (loss) before income taxes Income taxes Net earnings (loss)

$ 73,236 52,092 $ 21,144 9,333 1,060 $ 10,751 649 $ 10,102 3,536 $ 6,566

Greenfern Corporation Balance Sheet as of July 31, 2014 Assets Cash and marketable securities $ 9,118 Accounts receivable 7,844 Inventory 8,900 Deferred income taxes 878 Prepaid expenses & other receivables 2,803 Total current assets $ 29,543 Property, plant, and equipment 62,467 Less: Accumulated depreciation 22,196

Liabilities and Stockholders' Equity Accounts payable Accrued and other liabilities Taxes payable Debt due within one year Total current liabilities Long-term debt Deferred income taxes

Net property plant and equip.

Goodwill and other assets

Total assets

40,271 16,270

Other non-current liabilities Total liabilities Common stock Retained earnings Total stockholders' equity (deficit)

86,084

Total liabilities and stockholders' equity

STP #4.1. Refer to the above balance sheet and income statement for Greenfern Corporation for the fiscal year ended July 31, 2014. What are the company's current ratio and quick ratio? What do these ratios tell us about Current ratio =

Quick ratio =

Current assets Current liabilities

$29,543 $27,641

1.07

Current assets − Inventory = Current liabilities = Current ratio =

1.07

Quick ratio =

0.75

$29,543 − $8,900 $27,641 0.75

The current ratio of just over one tells us that Greenfern's cash and marketable securities, and other current assets, such as accounts receivable and inventory, if liquidated, will just provide enough proceeds to cover short-term liabilities. The quick ratio of Greenfer indicates that if we exclude inventory, which might be considerably less liquid than other current assets, the remaining current assets can cover just 75 percent of the short-term liabilities.

ders' Equity $

6,379 5,663 4,821 10,778 $ 27,641 24,280 6,903

5,608 $ 64,432 3,667 17,985 $ 21,652 $ 86,084

e fiscal year ended s tell us about

$ 73,236 52,092 $ 21,144 9,333 1,060 $ 10,751 649 $ 10,102 3,536 $ 6,566

Greenfern Corporation Balance Sheet as of July 31, 2014 Assets Cash and marketable securities $ Accounts receivable Inventory Deferred income taxes Prepaid expenses & other receivables Total current assets $ Property, plant, and equipment Less: Accumulated depreciation

9,118 7,844 8,900 878 2,803 29,543 62,467 22,196

Liabilities and Stockholders' Equity Accounts payable $ 6,379 Accrued and other liabilities 5,663 Taxes payable 4,821 Debt due within one year 10,778 Total current liabilities $ 27,641 Long-term debt Deferred income taxes

24,280 6,903

Net property plant and equip.

Goodwill and other assets

Total assets

40,271 16,270

Other non-current liabilities 5,608 Total liabilities $ 64,432 Common stock 3,667 Retained earnings 17,985 Total stockholders' equity $ (deficit) 21,652

86,084

Total liabilities and stockholders' $ 86,084 equity

STP #4.2. Refer to the above balance sheet and income statement for Greenfern Corporation for the fiscal year ended July 31, 2014. Calculate the following ratios: a. b. c. d. e. f. g. h. a. b. c. d. e. f. g. h.

Inventory turnover Day's sales outstanding Total asset turnover Fixed asset turnover Total debt ratio Debt-to-equity ratio Times interest earned ratio Cash coverage ratio Inventory turnover Day's sales outstanding Total asset turnover Fixed asset turnover Total debt ratio Debt-to-equity ratio Times interest earned ratio Cash coverage ratio

$52,092 / $7,844 / $73,236 / $73,236 / $64,432 / $64,432 / $10,751 / ($10,751 + $1,060) /

$8,900 ($73,236 / 365) $86,084 $40,271 $86,084 $21,652 $649 $649

= = = = = = = =

e fiscal year ended

5.85 ####### 0.85 1.82 0.75 2.98 16.57 18.20

$ 73,236 52,092 $ 21,144 9,333 1,060 $ 10,751 649 $ 10,102 3,536 $ 6,566

9,118 7,844 8,900 878 2,803 29,543 62,467 22,196

Net property plant and equip.

Goodwill and other assets

Total assets

40,271 16,270

Other non-current liabilities 5,608 Total liabilities ###### Common stock 3,667 Retained earnings 17,985 Total stockholders' equity ###### (deficit)

86,084

Total liabilities and stockholders' ###### equity

STP #4.3. Refer to the above balance sheet and income statement for Greenfern Corporation for the fiscal year ended July 31, 2014. Use DuPont identity to calculate the return on equity (ROE). In the process, calculate the following ratios: net profit margin, total asset turnover, equity multiplier, EBIT return on assets (EROA), Net profit margin = Net income / Net sales =

$6,566 / $73,236

8.97%

Total asset turnover = Net sales / Total assets =

$73,236 / $86,084

0.85

Equity multiplier = Total assets / Total equity =

$86,084 / $21,652

3.98

EROA = EBIT / Total assets =

$10,751 / $86,084

12.49%

Return on assets = Net income / Total assets =

$6,566 / $86,084

7.63%

DuPont identity: ROE = ROA × Equity multiplier = Net profit margin × Total asset turnover × Equity multiplier = 0.0897 × 0.85 × 3.98 = 30.33%

4.4.

Last year Pontiff Enterprises reported net sales of $13,144,680, a gross profit of $4,127,429, EBIT of $2,586,150, and net income of $867,555. Compute Pontiff's cost of goods sold, gross profit margin, operating profit margin, and net profit

Cost of goods sold = Net sales −Gross=profit $13,144,680 − $4,127,429 = $ 9,017,251 Gross profit margin = Gross profit / Net=sales $4,127,429 / $13,144,680 = 31.40% Operating profit margin - EBIT / Net sales = $2,586,150 / $13,144,680 = 19.67% Net profit margin = Net income / Net sales = $867,555 / $13,144,680 = 6.60%

STP #4.5. National City Bank has 646,749,650 shares of common stock outstandingb that are currently selling for $37.55 per share on the New York Stock Exchange. If National City's net income is $2,780,955,000 in the year that just ended, what was its earnings per share and what is its current priceearnings ratio? If the typical price-earnings ratio for a bank is currently 15, Earnings per share (EPS) =

Price-earnings ratio =

Net income = Shares outstanding Share price EPS

$2,780,955,000 = $4.30 $646,749,650 $37.55 = 8.73 $4.30

stock outstandingb w York Stock 00 in the year that its current pricenk is currently 15,

Numbers Sheet Name

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Intermediate

Advanced

Sample Test Problems

STP #5.5 You just bought a corporate bond at $863.75 today. In five years thebond will mature and you will receive $1,000. What is the rate of returnon this Price of bond today Number of years till bond matures Future value of bond

$ 863.75 5 $1,000

PV $863.75

FVIF 1.1576

i% 2.970%

FV $999.87

The equation relating PV, FV, r, and n is: FV = PV(1 + r)n. Solving for r yie r = (FV/PV)1/n - 1 = (1000/863.75)1/5 - 1 = 0.029728 = 2.973%

Also, the same result can be obtained using Excel's Goal Seek (under "T Rate of return on bond investment

2.97% Alternatively, the Trial & Error Method to solve for i% that results in a FV $1,000 yields the same result.

STP #5.4.Twenty-five years ago, Amanda Carter investec $10,000 in an account paying an annual interest rate of 5.75 percent. What is the value of the investment today? What is the interest on interest earned on this investment? Amount invested 25 years ago Number of years invested Annual interest rate

$10,000 25 5.75%

Value of investment today Simple interest on investment

$40,458.46 $14,375.00

PV n i% FV

$10,000.00 25 0.0575 $40,458.46 Value of investment today $575.00 simple interest per year $14,375.00 Sinple interest over 25 years

Interest on interest

$16,083.46

$26,083.46 Interest on Interest + PV $16,083.46 Interest on Interest

STP #5.3. a. b. c.

What is the future value of an investment of $3,000 after three years with compounding at the following rates and 8.75 percent compounded monthly 8.625 percent compounded daily 8.5 percent compounded continuously

Investment Number of years a. Interest rate Compounding frequency Future value b Interest rate Compounding frequency Future value

c Interest rate Compounding frequency Future value

$3,000 3 8.75% 12 $3,896.82 8.625% 365 $3,885.81

8.500% 100000 $3,871.38

PV i% n m FV

3000 8.75% 3 12

PV i% n m FV

3000 8.625% 3 365

PV i% n m

3000 8.50% 3 100000

3000 0.007291667 36 $3,896.82 3000 0.0236301% 1095 $3,885.81

FV Also, FV = PV ´ e

3000 0.0000850% 300000 $3,871.38

i´n

$3,871.38

STP #5.2. Michael Carter is expecting an inheritance of $1.25 million in four years. If he had the money today, he could earn interest at an annual rate of 7.35 percent. What is the present value of this Future value of inheritance expected Number of years until inheritance Annual interest rate

$1,250,000 4 7.35%

Present value of inheritance

$941,243.13

FV n i%

$1,250,000.00 4 7.35% PV = FV × PVIF $941,243.13

STP #5.1. Santiago Hernandez is planning to invest $25,000 in a money market account for two years. The account pays interest of 5.75 percent compounded on a monthly basis. How much money will Santiago Amount of investment Term (years) Interest rate per year Frequency of compounding per year

25,000 2 5.75% 12

Amount Santiago will have after 2 years $28,039.13

PV n i% m

$25,000.00 2 5.75% 12 FV

$25,000.00 24 0.4792% FV = PV × FVIF $28,039.13

5.37

You will be graduating in two years, and are thinking about your future. You know that you will want to buy a house five years after you graduate and that you will want to put down $60,000. As of right now, you have $8,000 in your savings account. You are also fairly certain that once you graduate, you can go work in the family business and earn $32,000 a year, with a 5 percent raise every year. You plan to live with your parents for the first two years after graduation, which will enable you to minimize your expenses and put away $10,000 each year. The next three years, you will have to live out on your own as your younger sister will be graduating from college and has already announced her plan to move back into the family house. Thus, you will be able to save only 13 percent of your annual salary. Assume that you will be able to invest savings from your salary at 7.2 Hint: Draw a time line that shows all the cash flows for years 0 through 7. Remember, you want to buy a house seven years from now and your first salary will be in year 3.

Number of years until graduation Number of years until you buy a house Down payment required on house Current savings Annual income in family business Annual raise in salary Annual savings after graduation while living at home Number of years after graduation that you will live at home Annual saving (as a percent of salary)after moving out Rate of return on invested savings from salary

Cash flow 0 1 Down payment required on house Current saving $8,000 Salary

2 7 $60,000 $8,000 $32,000 5% $10,000 2 13% 7.20%

Year 4

$32,000

$33600

$35280

Annual Saving $10,000 $10,000 PVIF @ 7.20% 0.932835821 0.870182669 PV $9328.36 $8701.83 NPV $28,971.40 FV = PV × FVIF Amount that current savings account balance must amount to to reach down payment goal

Rate of return that current savings will have to earn to reach goal

$4586.40 0.811737564 $3722.95

FV = PV (1+ i%)^n 18984.93 = 8,000(1+i%)^7 FV/PV 2.3731 = (1+i%)^7 Raise 2.3731 to 1/7th power i%

$37044

7 Future value $60,000.00 $38896.20

$4815.72 0.757217877 $3646.55

$5056.51 0.70635996 $3571.71 $41,015.07 $18,984.93

PV = FV = n=

$8,000 $18,984.93 7

00(1+i%)^7 2.3731 1/7th power

1.131404979 13.14%

5.35 Eric Fisher, a number 1 draft pick of the Kansas City Chiefs, and his agent are evaluating three contract options. Each option offers a signing bonus and a series of payments over the life of the contract. Fisher uses a 10.25 percent rate of return to evaluate the contracts. Given the cash flows for each option, which one should he

Year Cash Option A Option B Option C Flow Type 0 Signing $3,100,000 $4,000,000 $4,250,000 Bonus 1 Annual $650,000 $825,000 $550,000 Salary 2 Annual $715,000 $850,000 $625,000 Salary 3 Annual $822,250 $925,000 $800,000 Salary 4 Annual $975,000 $1,250,000 $900,000 Salary 5 Annual $1,100,000 $1,000,000 Salary 6 Annual $1,250,000 Salary Interest rate

10.25%

Present Value $6,922,646.77 Decision: Option C is the best

$6,983,894.87

$7,083,096.26

0 1 2 3 4 5 6

d his agent are onus and a series of ent rate of return to ich one should he 10.25%

PVIF $3,100,000

10.25%

1 $3,100,000.00

$4,000,000

PVIF

PV 1 $4,000,000.00

$650,000

0.9070

$589,569.16

$825,000

0.9070

$748,299.32

$715,000

0.82270

$588,232.27

$850,000

0.8227

$699,297.10

$822,250

0.74622

$613,575.61

$925,000

0.7462

$690,249.24

$975,000

0.67684

$659,918.38

$1,250,000

0.6768

$846,049.20

$1,100,000

0.61391

$675,304.58

$1,250,000

0.55684

$696,046.77 $6,922,646.77 DECISION: OPTION C IS THE BEST

$6,983,894.87

10.25%

PVIF

$4,250,000

$4,250,000.00

$550,000

0.9070

$498,866.21

$625,000

0.82270

$514,189.05

$800,000

0.74622

$596,972.32

$900,000

0.67684

$609,155.43

$1,000,000

0.61391

$613,913.25

$7,083,096.26

5.36 Surmec, Inc., has reported sales of $2.1 million last year. The company’s primary business line is manufacturing of nuts and bolts. Since this is a mature industry, the analysts are certain that the sales will grow at a steady rate of 7 percent a year. The company reports net income that represents 23 percent of sales. The management would like to buy a new fleet of trucks but can only do so once the profit reaches $620,000 a year. At the end of what year will they be Last year's sales Annual growth rate of sales expected Net income as a percent of sales Target net income needed before fleet of trucks can be purchased Last year’s net income = Last Year’s sales * Net Income as % of sales

Number of years after which the fleet of truck can be purchased =

$2,100,000 7% 23% $620,000 $483,000.00 620000 7.00% FV = PV(1+i%)^n 620,000 = 483,000(1.07)^n FV/PV 1.2836 = (1.07)^n Trial & Error Method (1.07) ^ 3.69 = n=

Sales of the year after which trucks can be purchased =

$2,752,671.62 2100000 7.00% 4

Net income of the year after which trucks can be purchased =

633114.4728

Last year's net income Number of years after which the fleet of trucks can be purchased = Sales of the year after which trucks can be purchased = Net income of the year after which trucks can be purchased =

$ $

$483,000 3.69 2,752,671.62 633,114.47

PV FV i%

1.2836

1.28359 3.69 FV = PV × FVIF PV i% n = round up to 4.0

Also, applying log (or ln): log(1.2836) = log(1.07n) = n log(1.07) => n = log(1.2836) / log(1.07) =3.69 The same result can be obtained using Excel "Goal Seek" (under Tools).

5.34 When you were born your parents set up a bank account in your namewith an initial investment of $5,000. You are turning 21 in a few days and will have access to all your funds. The account was earning 7.3 percent for the first seven years then the rates went down to 5.5 percent for six years. The economy was doing well at the end of the 1990s and your account was earning 8.2 percent for three years in a row. Unfortunately, the next two years you earned only 4.6 percent. Finally, as the economy recovered, your return jumped to 7.6 percent a. b. c.

How much money was in your account before the rates went down drastically at the end of year 16? How much money is in your account now, at the end of year 21? What would be the balance now if your parents made another deposit of $1,200 at the end of year 7?

Initial investment = $5,000 Age at time of investment = 0 years Current age = 21 years Interest rate (years 1-7)= 7.30% Interest rate (years 8-13)= 5.50% Interest rate (years 14-16)= 8.20% Interest rate (years 17-18)= 4.60% Interest rate (years 19-21)= 7.60% FV at the end of year 7 FV at the end of year 8 FV at the end of year 9 FV at the end of year 10 FV at the end of year 11 FV at the end of year 12 FV at the end of year 13 FV at the end of year 14 FV at the end of year 15 FV at the end of year 16 FV at the end of year 17 FV at the end of year 18 FV at the end of year 19 FV at the end of year 20 FV at the end of year 21

$8187.82 $8638.15 $9113.24 $9614.47 $10143.27 $10701.15 $11289.71 $12215.47 $13217.14 $14300.94 $14958.78 $15646.89 $16836.05 $18115.59 $19492.38

FV at the end of year 21

$19492.38 $2856.79 $22349.16

[a]

[b]

[c]

Amount of money accumulated at age 16 =

$ 14,300.94

Amount of money in the account at end of year 21

$ 19,492.38

Amount in the account now with an additional deposit of $1200 at end of year 7

n your namewith an ys and will have cent for the first seven . The economy was arning 8.2 percent for earned only 4.6 mped to 7.6 percent

nt down drastically at

her deposit of $1,200

$1,200.00 $1,266.00 $1,335.63 $1,409.09 $1,486.59 $1,568.35 $1,654.61 $1,790.29 $1,937.09 $2,095.93 $2,192.35 $2,293.20 $2,467.48 $2,655.01 $2856.79

$ 22,349.16

5.33 You have $12,000 in cash. You can deposit it today in a mutual fund earning 8.2 percent semiannually, or you can wait, enjoy some of it, and invest $11,000 in your brother’s business in two years. Your brother is promising you a return of at least 10 percent on your investment. Whichever alternative you choose, you will need to cash in at the end of ten years. Assume your brother is trustworthy and both investments carry the same risk. Alternative A Cash available for investment = Rate of return on mutual fund= Compounding frequency (per year)= Term of investment =

$12,000 8.20% 2 10 years

Alternative B Cash available for investment after 2 years = Rate of return promised by brother = Compounding frequency (per year)= Term of investment=

$11,000 10% 1 8 years

Which alternative will you choose? Future value of alternative A = Future value of alternative B = I will choose Alternative A

$26,803.77 $23,579.48

PV i% m n FV

12000 0.041 2 20 $26,803.77

PV i% m n FV

11000 10.00% 1 8 $23,579.48

Choose alternative A

5.32 Patrick Seeley has $2,400 that he is looking to invest. His brother approached him with an investment opportunity that could double his money in four years. What interest rate would the investment have to yield in order for Patrick’s Patrick's investment = Period of investment = Value at end of term=

$2,400 4 years $4,800

Rate of return earned =

18.92%

PV n FV FV = PV × FVIF FV/PV = (1+ i%)^n FV/PV 2.0000 2.000 = (1+i%)^4 Raise 2.0 to 1/4th power 1.1892071 1.1892 = (1 + i%) i% = 18.92%

5.31 You have $2,500 you want to invest in your classmate’s start-up business. You believe the business idea to be great and hope to get $3,700 back at the end of three years. If all goes according to plan, what will your return Investment needed= $ 2,500 Period of investment= 3 years Expected terminal value= $3,700

Calculate the rate of return on investment Rate of return on investment =

13.96%

PV n FV FV = PV × FVIF 3,700= 2,500(1+I%)^3 FV/PV 1.4800 1.48 = (1+I%)^3 Raise 1.48 to 1/3rd power i% = 13.96%

1.13960

5.22 Multiple compounding periods: Samantha is looking to invest some money, so she can collect $5,500 at the end of three years. How much should she invest today? a. 4.2 percent compounded daily b. 4.9 percent compounded monthly c. 5.2 percent compounded quarterly d. 5.4 percent compounded annually Amount of money she would like to have after 3 years= Term of investment = 3 years

$5,500 FV

Interest rate=

4.20% Compounding frequency (per year) = 365

Amount of investment required today =

Interest rate=

4.90% Compounding frequency (per year) = 12

Amount of investment required today =

Interest rate=

$4,848.92

$4,749.54

5.20% Compounding frequency (per year) = 4

Amount of investment required today =

$4,710.31

i% n m PV

5500 0.042 3 365

0.000115 1095 $4,848.92

FV i% n m PV

5500 0.049 3

FV i% n m PV

5500 0.052 3 4

0.004083 36

$4,749.54

0.013 12 $4,710.31

Interest rate=

5.40% Compounding frequency (per year) = 1

Amount of investment required today =

$4,697.22

She should invest at 5.4% compounded annually, i.e., option D.

5500

i% n m PV

0.054 3 1

0.054 3 $4,697.22

5.21 Multiple compounding periods: Find the present value of $3,500 under each of the following rates and periods: a. b. c. d.

8.9 percent compounded monthly for five years. 6.6 percent compounded quarterly for eight years. 4.3 percent compounded daily for four years. 5.7 percent compounded continuously for three years.

Future value = a.

$3,500

PV = FV × PVIF

Interest rate = 8.90% Term = 5 years Compounding frequency (per year)= 12 Present value = $2,246.57

i% n m

Interest rate = 6.60% Term = 8 years Compounding frequency (per year)= 4 Present value = $2,073.16

i% n m

Interest rate = 4.30% Term = 4 years Compounding frequency (per year)= 365 Present value = $2,946.96

i% n m

Interest rate = 5.70% Term = 3 years Compounding frequency (per year)= 100000 Present value = $2,949.88

i% n m

0.74% 60 PV 0.0165 32 PV 0.00011781 1460 PV 5.7000E-07 300000 PV

= FV × PVIF

$2246.57

$2073.16

$2946.96

$2949.88

5.29. Present value: Caroline Weslin needs to decide whether to accept a bonus of $1,820 today or wait two years and receive $2,100 then. She can invest at 6 percent. What should she do? Bonus offered today = PV = Bonus after 2 years = FV = Rate of return = I = Period = n=

$ 1,820 $ 2,100 6% 2 years

What should Caroline Weslin do?

PV FV i% n FV=PV(FVIF) FV = Since 2,044.95 < 2,10 Do not accept the bon

Calculate future value of $1820 after 2 years if invested at 6% She should not accept the $1820 bonus today.

Alternative solution:

PV = FV × PVIF PV= Accept the alternative

Calculate the present value of $2100 to be received after 2 years and compare Present value of $2100 to be received after 2 years = Accept the alternative since it has a higher PV

$1,868.99

$1,820.00 $2,100.00 6.00% 2 FV=PV(FVIF) $2,044.95 Since 2,044.95 < 2,100.00 Do not accept the bonus today

PV = FV × PVIF $1868.99 Accept the alternative since it has a higher PV

5.25. Time to grow: Neon Lights Company is a private company with sales of $1.3 million a year. Management wants to go public but has to wait until the sales reach $2 million. If sales are expected to grow at a steady 12 percent annually, when is Current annual sales = $1,300,000 Sales level at which they can go public= $2,000,000 Expected annual growth rate of sales = 12% How long will it take for them to reach their goal? Time (using Excels' Nper function) =3.8 years Alternative method: Since FV=PV*(1+r)n Dividing by PV and applying natural logarithm yields: ln(FV/PV) = ln(1 + r)n = n*ln(1 + r) and thus, solving for n gives: n = ln(FV/PV) / ln(1 + r) =

3.8 years

PV $1,300,000 FV $2,000,000 g 12.00% FV=PV(1+g)^n FV/PV 1.5385 1.5384 = (1.12)^n Trial & Error Method 1.12 raised to the 3.8 power = 1.5383 n=

3.8

5.24. Time to grow: You are able to deposit $850 in a bank CD today, and you will withdraw the money only once the balance is $1,000. If the bank pays 5 percent interest, how long will it take you to attain your goal? Present value of deposit today = Amount of withdrawal required = Interest rate paid by bank per year=

$850 $1,000 5%

Dividing by PV and applying natural logarithm yields:

PV FV i% FV=PV(1+i%)^n FV/PV 1.1764 = (1.05) ^ n Trial & Error Method (or Goal S 1.05 raised to 3.331 =

ln(FV/PV) = ln(1 + r)n = n*ln(1 + r)

How long will it take to reach your goal? Time (Using Excel's Nper function) =3.331 years Alternative method: Since FV=PV*(1+r)n

and thus, solving for n gives: n = ln(FV/PV) / ln(1 + r) =

3.331 years

D today, and you will the bank pays 5 percent

850 1000 5 FV=PV(1+i%)^n 1.176470588 1.1764 = (1.05) ^ n Trial & Error Method (or Goal Seek) 1.05 raised to 3.331 = 1.176414 3.331 years

5.23.

Time to grow: Zephyr Sales Company has currently reported sales of $1.125 million. If the company expects its sales to grow 6.5 percent annually, how long will it be before the company can double its

Year 0 Sales 1,125,000 Growth rate of sales 6.50% per year PV g FV

How long will it be before sales double Expected sales= Time to double=

2,250,000 11 years

$1,125,000 6.50% $2,250,000 FV=PV(1+i%)^n FV/PV 2.0000 2.0 =(1.065)^n Trial & Error Method (or Goal Seek) n= 11 years

5.28.

Growth rate: Infosys Technologies, Inc., an Indian technology company, reported a net income of $419 million this year. Analysts expect the company’s earnings to be $1.468 billion in

Year 0 Net Income =

419,000,000

Year 5 Net Income =

1,468,000,000

Number of years =

FV = PV(1+i%)^n FV/PV = (1+i%)^n FV/PV = 3.5036 RAISE TO THE 1/5th Power (FV/PV)^.2 = 1.285 EXPECTED g = 28.50% Expected growth rate of earnings =

28.50%

Albegraic method: Since: Year 5 Sales = Year 0 Sales*(1+g)^5 ==> g =[ (Year 5 Sales)/(Year 0 Sales)]^(1/5)-1 g=

28.50%

5.27. Growth rates: Xenix Corp had sales of $353,866 in 2014. If management expects its sales to be at $476,450 in three years, what is the rate at which the company’s sales are expected to grow? 2014 Sales = $353,866 2017 Sales= $476,450 Number of years= 3

Growth rate =

10.42%

PV FV n

$353,866.00 $576,450.00 3 FV=PV(FVIF) FV/PV= 1.3464 1.3464 = (1+i%)^3 cube root of 1.3464 = 1.1042 Growth rate = 10.42%

5.20. Multiple compounding periods: Find the future value of an investment of $2,500 made today for the following rates a. 6.25 percent compounded semiannually for 12 years b. 7.63 percent compounded quarterly for 6 years c. 8.9 percent compounded monthly for 10 years d. 10 percent compounded daily for 3 years e. 8 percent compounded continuously for 2 years Present value of investment = a. interest rate = frequency of compounding= term = Future value of investment = b. interest rate = frequency of compounding= term = Future value of investment = c. interest rate = frequency of compounding= term = Future value of investment = d. interest rate = frequency of compounding=

$2,500

6.25% 2 times per year 12 years

i% m n

$5,232.09 7.63% 4 times per year 6 years $3,934.48 8.90% 12 times per year 10 years $6,067.86 10.00% 365 times per year

FV i% m n FV i% m n FV i% m

3.13% 24 FV=PV(FVIF) $5,232.09 1.91% 24 FV=PV(FVIF) $3,934.48 0.74% 120 FV=PV(FVIF) $6,067.86 0.0274%

term = Future value of investment = e. interest rate = frequency of compounding= term = Future value of investment =

3 years $3,374.51 8.00% 1000000 times per year 2 years $2,933.78

n FV i% m n FV

1095 FV=PV(FVIF) $3,374.51 0.0000080% 2000000 FV=PV(FVIF) $2,933.78

5.19. Future Value: You decide to take advantage of the current online dating craze and start your own Web site. You know that you have 450 people who will sign up immediately and, through a careful marketing research and analysis, determine that membership can grow by 27 percent in the first two years, 22 percent in year 3, and 18 percent in year 4. How many members # of members in Year 0= Growth rate in Years 1-2 Growth rate in Year 3 Growth rate in Year 4 PV n g FV (# members) YEAR

450 27% 22% 18% 450 0

1 2 3 4 27.00% 27.00% 22.00% 18.00% 450 572 726 885 1045 0 1 2 3 4

# of members after 4 years =

1045

5.18. Future value: CelebNav, Inc., had sales last year of $700,000, and the analysts are predicting a good year for the start-up, with sales growing 20 percent a year for the next three years. After that, the sales should grow 11 percent per year for two years, at which time the owners are planning to sell the company. What are Sales in Year 0 Growth rate in years 1-3 Growth rate in years 4 and 5 PV n g FV YEAR Year Sales

700000 0 ###### 0 0

700,000 20% 11%

1 2 3 4 20.00% 20.00% 20.00% 11.00% 840,000 1,008,000 1,209,600 1,342,656 1 2 3 4 1

700,000 840,000

1,008,000

1,209,600

1,342,656

0,000, and the analysts wing 20 percent a year w 11 percent per year for he company. What are

5 11.00% 1,490,348 5 5 1,490,348.16

5.17. Future value: Your finance textbook sold 53,250 copies in its first year. The publishing company expects the sales to grow at a rate of 20 percent for the next three years, and by 10 percent in the fourth year. Calculate the total number of copies that the publisher expects to sell in years 3 and 4. Draw a time line to show the sales level for each of the next four years. Sales in Year 0 Growth rate in years 1-3 Growth rate in year 4

53,250 20% 10%

PV n g FV Year

$53,250

Year

Sales

53,250

63,900

76,680

92,016

101,218

$53,250 0

1 20.00% $63,900 1

2 20.00% $76,680 2

3 20.00% $92,016 3

4 10.00% $101,218 4

5.16. Number of periods: You invest $150 in a mutual fund today that pays 9 percent interest annually. How long will it take to double your money? Present value of investment = Rate of interest = Future value of investment =

$ 150 9% $ 300

PV i% FV n

Time taken to double the investment = 8 years Also, following the "rule of 72," a quick computation yields the same answer right away: 72/9 = 8

FV=PV × (1.09)^n 300 = 150(1.09)^n 2.00 = (1.09)^n 1.09^8 = 1.99 or 2.0 n=8

5.15. Interest rate: You are in a desperate need of cash and turn to your uncle, who has offered to lend you some money. You decide to borrow $1,300 and agree to pay back $1,500 in two years. Alternatively, you could borrow from your bank that is charging 6.5 percent interest annually. Should you go with your uncle or the bank? Amount borrowed from uncle= Period of loan = Amount paid back to uncle = Rate of interest of bank loan =

$ $

1,300 2 1,500 6.50%

Which loan would be cheaper? Rate of interest on uncle's loan = Decision: Borrow from the bank

7.42%

PV n FV i% FV=PV(1+i%)^n 1,500 = 1,300(1+i%)^2 FV/PV = 1.1538 1.15385 = (1+i%)^2 1.15385^0.5 = 1.0742 7.42% Decision to Borrow from Bank

5.14.

$12,000 12 7.00% PV= $5,328.14

FV n i%

$12,000 12 7.00%

PV = FV × PVIF = $12000 × 1/1.0712 PV = $5,328.14

5.13. Present value: You want to buy some bonds that have a value of $1,000 at the end of seven years. The bonds are said to pay 4.5 percent interest annually. How much should you pay for them today? Future value of bonds = Maturity of bonds = Rate of interest =

$ 1,000 7 4.50%

Amount to be invested today =PV= $734.83

FV n i%

$1,000 7 4.50%

PV = FV × PVIF = $1000 × 1/1.0457 PV = $734.83

5.12.

Number of years until home purchase= Rate of return on fund investment = Amount to be invested today =

$35,000

5 9.25% PV= $22,488.52

FV n i%

$35,000 5 9.25%

PV = FV × PVIF = $35000 × 1/1.09255 PV =

$22,488.52

5.11.

Expected rate of return =

Term of loan = Future payment to be received = The amount he should be willing to lend =

6.00%

3 years $7,750 PV = $6,507.05

i% n FV

6.00% 3 $7,750.00

PV = FV × PVIF = $7750 × 1/1.063 PV = $6,507.05

5.10.

Present value: Maria Addai has been offered a future payment of $750 two years from now. If she can earn 6.5 percent compounded annually on her investment, what should she pay for this investment

Opportunity cost

Term = Future payment to be received Price she should pay =

6.50%

2 years 750 PV=

$661.24

i% n FV

6.50% 2 $750.00

PV = FV × PVIF = $750 × 1/1.0652 PV = $661.24

5.9.

Present value: Roy Gross is considering an investment that pays 7.6 percent, compounded anually. How much will he have to invest today such that the investment will be worth $25,000 in six years?

Rate of return= Term = Terminal value = Required investment today =

7.60% 6 years 25,000 PV= $16,108.92

i% n FV

PV = FV × PVIF = $25000 × 1/1.076 PV =

7.60% 6 $25,000.00

V × PVIF = $25000 × 1/1.0766 $16,108.92

5.8.

Growth rates: Joe Maur, a catcher for the Minnesota Twins is expected to hit 15 home runs in 2014. If his home-run-hitting ability is expected to grow by 12 percent every year for the following five years, how many home runs is he expected to hit in 2019?

Number of home runs expected in 2014 = Growth rate in hitting home runs = Number of years of growth = Number of home runs expected to be hit in 2019FV = =

15 12% 5 26 home runs

PV g n FV = PV × FVIF = 15 × 1.125 FV =

15 12% 5

FV = PV × FVIF = 15 × 1.125 26 home runs

5.7. a. b. c. d.

Multiple compounding periods: Find the future value of a five year $100,000 investment that pays 8.75 percent and that has the Quarterly Monthly Daily Continuous

a $100,000 2.1875% 20 4

Investment = $ (100,000.00) Interest rate= 8.75% Term = 5 # compounding Periods per Year = m = Future Value of the Investment

FV=

b $100,000 0.7292% 60 12

c $100,000 0.0240% 1825 365

$154,154.24 $154,637.37 $154,874.91 FV = PV × FVIFFV = PV × FVIFFV = PV × FVIF

Frequency of compounding =

Future value of investment=

FV=

$154,154.24

Frequency of compounding =

Future value of investment=

FV=

$154,637.37

Frequency of compounding =

365

Future value of investment=

FV=

$154,874.91

Frequency of compounding =

1000000

Future value of investment= Or solve using EXP function as FV = PV*EXP(rate*term)=

$154,883.03 $154,883.03

d $100,000 0.0000% 5000000 1000000 $154,883.03 FV = PV × FVIF

5.6.

Future value: Your birthday is coming up and instead of any presents, your parents promised to give you $1,000 in cash. Since you have a part-time job and, thus, don’t need the cash immediately, you decide to invest the money in a bank CD that pays 5.2 percent annually, compounded quarterly for the next two years. How much

Amount received as a gift= Interest rate (per year)= Frequency of compounding per year = Term of investment (years)=

$ (1,000) 5.20% 4 2

Expected value of gift after 2 years = FV= $1,108.86

PV i% n m

1000 0.052 2 4 FV =

1000 0.013 8 FV = PV × FVIF $1,108.86

5.5.

Future value: Your bank pays 5 percent annual interest compounded semiannually on your savings account. You don’t expect to add to the current balance of $2,700 over the next four years. How much money can you expect

Rate of interest = Current balance= Term (years)= Frequency of compounding (per year)=

Future value of savings=

5% $ (2,700) 4 2

FV= $3,289.69

i% PV n m

FV =

5.00% 2700 4 2

2.50% 2700 8

FV = PV × FVIF $3,289.69

5.4.

Future value: Kate Eden received a graduation present of $2,000 that she is planning on investing in a mutual fund that earns 8.5 percent each year. How much money will

Graduation gift = Rate of return per year = Period of investment = Amount of money she can collect FV= =

(2,000) 8.50% 3 years $2,554.58

PV i% n FV =

$2,000 8.50% 3 FV = PV × FVIF $2,554.58

5.2.

Future value: Ted Rogers is investing $7,500 in a bank CD that pays a 6 percent annual interest. How much will the CD be worth at the end of

Present value of investment Rate of return per year Term (years) Compounding per year

$7,500 6.00% 5 1

PV i% n m

Future value of investment $10,036.69

FV =

$7,500 6.00% 5 1 FV = PV × FVIF $10,036.69

5.3.

Future value: Your aunt is planning to invest in a bank deposit that will pay 7.5 percent annual interest compounded semiannually. If she has $5,000 to invest, how much will she

Present value of investment $5,000 Interest rate per year 7.50% Term (years) = n = 4 Compounding frequency = m = 2

Future value of investment

$6,712.35

PV i% n m

$5,000 7.50% 4 2 FV =

Adjust for Compounding $5,000 3.75% 8 FV=PV × FVIF $6,712.35

#5.26 Time to Grow: You have just inherited $550,000. You plan to save this money and con live off the money that you are earning in your current job. If you can invest the money that pays 4.6 percent interest annually, how long will it be before your inheritance is wo million? PV $550,000 i% 4.60% FV $1,000,000 n = ? (Solve applying log, Goal Seek, or Trial & Error) 13.29 PV $550,000

FVIF 1.81792552

FV $999,859

It will take approximately a little over 13 years for your inheritance to be worth $1 Number of years (using the Nper function) =

13.29

o save this money and continue to you can invest the money in a bond fore your inheritance is worth $1

FV $1,000,000 Prove this FV

heritance to be worth $1 million.

#5.30

Refer to problem 5.29. Congress and the president have decided to increase th tax rate in an effort to reduce the budget deficit. Suppose that Caroline Weslin, problem 5.29, will pay 35 percent of her bonus to the federal government for tax accepts the bonus today and 40 percent if she receives her bonus in two years. increase in tax rates affect her decision? Refer to problem #5.29 Her bonus today is $1,820 today She will pay 35.00% in taxes if she accepts the bonus today She will pay $637.00 in taxes. Net cash flow today is $1,183.00 PV of left over amount. Assume she receives her bonus of Year Bonus CF PVIF 0 1 2 $2,100 0.89000

$2,100.00 two years from PV

$1,869 40.00% She will pay in taxes if she $747.60 She will pay this in taxes $1,121 PV of left over amount

Yes, it makes a difference if the tax rate increases. Note the differences in Accepting the bonus today and paying the current tax rate is the most adv

have decided to increase the federal pose that Caroline Weslin, from federal government for taxes if she es her bonus in two years. Will the

e bonus today

today and a discount rate of

6.00%

he will pay in taxes if she accepts bonus 2 years from now. he will pay this in taxes V of left over amount

s. Note the differences in the two present values. t tax rate is the most advantangeous decision.

5.1.

Future value: Chuck Tomkovick is planning to invest $25,000 today in a mutual fund that will provide a return of 8 percent each year. What will be the value of the investment in ten years?

Present value of investment Rate of return per year Term (years) Compounding per year

$25,000 8.00% 10 1

PV i% n m

Future value of investment

$53,973.12

FV =

$25,000.00 8.00% 10 1 FV = PV × FVIF $53,973.12

6.1. Future value with multiple cash flows: Konerko, Inc., expects to earn cash flows of $13 the next four years. If the company uses an 8 percent discount rate, what is the future valu Year Cash Flow Discount rate Net Present Value at t = 0 Future Value at end of year 4

1 $

13,227 8%

$54,739.50 $74,472.48

$ 15,611

$ 18,970

pects to earn cash flows of $13,227, $15,611, $18,970, and $19,114 over unt rate, what is the future value of these cash flows at the end of year 4? 4 $ 19,114

Tabular solutions: 8.00% Year CFs FVIF FV 0 1 13,227 1.25971 16,662 2 15,611 1.1664 18,209 3 18,970 1.08 20,488 4 19,114 1 19,114 $74,472.48

6.3.

Future value with multiple cash flows: You are a freshman in college and are planning when you graduate from college at the end of four years. You plan to save the following a starting today: $625, $700, $700, and $750. If the account pays 5.75 percent annually, ho have at the end of four years? Year 0 1 2 3 Annual savings Discount rate Net Present Value at t = 0 Future Value at end of year 4

625 5.75%

$2,547.08 $2,547.08

$ 700

$ 750

an in college and are planning a trip to Europe ou plan to save the following amounts annually, pays 5.75 percent annually, how much will you Tabular Solution: 0.0575 Year CFs FVIF FV 0 625 1.25061 782 1 700 1.18261 828 2 700 1.11831 783 3 750 1.0575 793 4 1 0 $3,185.40

6.4. Present value with multiple cash flows: Saul Cervantes has just purchased some equip landscaping business. For this equipment he must pay the following amounts at the end of the next five years: $10,450, $8,500, $9,675, $12,500, and $11,635. If the approriate disco 10.875 percent, what is the cost in today's dollars of the equipment Saul purchased today? Year

Annual Payments

10,450

8,500

9,675

12,500

11,635

Discount rate

10.875%

Cost of equipment

$38,652.76

s just purchased some equipment for his lowing amounts at the end of each of 11,635. If the approriate discount rate is pment Saul purchased today? Tabular Solution: 10.875% Year CFs PVIF NPV 0 1 10450 0.901916573 9,425 2 8500 0.813453504 6,914 3 9675 0.733667197 7,098 4 12500 0.661706603 8,271 5 11635 0.596804152 6,944 $38,652.76

6.5. Present value with multiple cash flows: Jeremy Fenloch borrowed some money from his repay him the amounts of $1,225, $1,350, $1,500, $1,600, and $1,600 over the next five ye discounts investment cash flows at 8 percent annually, how much did Jeremy borrow? Year Annual Payments Discount rate

Amount Borrowed =

1,225

1,350

1,500

1,600

$5,747.40

some money from his friend and promised to 0 over the next five years. If the friend normally Jeremy borrow? Tabular Solution: Year

CFs

8.00% PVIF

NPV

0 1 2 3 4

1,225 1,350 1,500 1,600

0.925926 0.857339 0.793832 0.73503

1,134 1,157 1,191 1,176

1,600

0.680583

1,089

$5,747.40

6.6

Present value with multiple cash flows: Biogenesis Inc. management expect following cash flow stream over the next five years. They discount all cash flows percent discount rate. What is the present value of this cash flow stream?

Year Cash flow Discount rate=

1 2 $ (1,133,676) $ (978,452) $ 23%

Present value

$384,711.72

Tabular Solution: Year CFs 0 1 (1,133,676) 2 (978,452) 3 275,455 4 878,326 5 1,835,444

23.00% PVIF 0.81300813 0.66098222 0.53738392 0.43689749 0.35520122

3 275,455

NPV (921,688) (646,739) 148,025 383,738 651,952 ($384,711.72)

4 878,326

sis Inc. management expects the They discount all cash flows at a 23 this cash flow stream?

5 1,835,444

6.7. Present value of an ordinary annuity: An investment opportunity requires a payment of $ years, starting a year from today. If your required rate of return is 8 percent, what is the valu investment to you today? Annual Payment # of payments Required rate of return

750 12 8%

Present value of investment ($5,652.06)

Tabular Solution: 8.00% Year CFs PVIF 0 1 750 0.9259 2 750 0.8573 3 750 0.7938 4 750 0.735 5 750 0.6806 6 750 0.6302 7 750 0.5835 8 750 0.5403 9 750 0.5002 10 750 0.4632 11 750 0.4289 12 750 0.3971

Note: The present value of the investment ca a negative number. Here, It has been decided negative yet it is an outlay for an investment.

equires a payment of $750 for 12 ercent, what is the value of the

PVA 694 643 595 551 510 473 438 405 375 347 322 298 $5,652.06

of the investment can be considered a cash outlay, hence , It has been decided not to preresent the present value as ay for an investment. In a NPV situation, the present value

6.8.

Present value of an ordinary annuity: Dynamics Telecommunications Corp. has mad in another company that will guarantee it a cash flow of $22,500 each year for the next company uses a discount rate of 15 percent on its investments, what is the present val investment?

Annual cash flow # of years Discount rate Present value of investment

22,500 5 15%

($75,423.49)

Horizontal Solution:

PMT 22,500

PVIF PVIFA 0.4972 3.3522

nications Corp. has made an investment 0 each year for the next five years. If the what is the present value of this

n i% PVA $75,423.49

5 15.00%

6.9.

Future value of an ordinary annuity: Robert Hobbes plans to invest $25,000 a year at t for the next seven years in an investment that will pay him a rate of return of 11.4 percent will Robert have at the end of seven years?

Annual investment planned # of years Rate of return

25,000 7 11.40%

Future value after 7 years

$247,609.95

Horizontl Solution:

PMT FVIF FVIFA 25000 2.1291 9.9044

nvest $25,000 a year at the end of each year of return of 11.4 percent. How much money

n i%

FVA $247,609.95

7 11.40%

6.10.

Future value of an ordinary annuity: Cecelia Thomas is a sales executive at a Baltim years old and plans to invest $3,000 every year in an IRA account, beginning at the en turns 65 years old. If the IRA investment will earn 9.75 percent annually, how much wil when she turns 65?

Annual investment planned $ Current age Retirement age Rate of return

3,000 25 65 9.75%

Number of deposits 40 Future value after 40 years $1,240,676.41

Horozontal Solution:

PMT 3000

FVIF FVIFA 41.322 413.56

ales executive at a Baltimore firm. She is 25 ount, beginning at the end of this year until she t annually, how much will she have in 40 years,

n i% FVA $1,240,676.41

40 9.75%

6.1 Future value of an annuity due: Refer to Problem 6.10. if Cecelia invests at the beginning of each year, how much will she have at age 65? n i% PMT $3,000.00

FVIV FVIFA 41.321983 413.5588

40 9.75% FVIF 1.0975

FVA $1,361,642.36

0. if Cecelia invests at the 65?

6.12 Computing annuity payment: Kevin Winthrop is saving for an Australian vacation in thre estimates that he will need $5,000 to cover his airfare and all other expenses for a weekAustralia. If he can invest his money in an S&P 500 equity index fund that is expected to return of 10.3 percent over the next three years, how much will he have to save every yea the end of this year? Amount of Money needed $ 5,000 Number of years until trip 3 Rate of return expected on investment 10.30% Annual saving needed at end of each year

($1,506.20)

g for an Australian vacation in three years. He nd all other expenses for a week-long holiday in ity index fund that is expected to earn an average uch will he have to save every year if he starts saving HOROZONTAL SOLUTION:

N PVA I%

FVA FVIF PVIFA PMT $5,000.00 1.34192 3.31961 $1,506.20

3 $5,000.00 10.30%

6.13 Computing annuity payment: The Elkridge Bar & Grill has a seven-year loan of $23, with Bank of America. It plans to repay the loan in seven equal installments starting to If the rate of interest is 8.4 percent, how much will each payment be? Loan amount # of payments Interest rate Annual payment

23500 7 8.40% ($4,221.07)

Horizontal Solution

PVA PVIF PVIFA $23,500.00 0.56858 5.1359

THE KEY TO THIS PROBLEM IS THAT THE FIRST HAPPENS IN TIME PERIOD ZERO.

l has a seven-year loan of $23,500 n equal installments starting today. h payment be? n PVA i%

7 $23,500.00 8.40%

FVIF ADJ. PVIFA 108.40% 5.56731417

ROBLEM IS THAT THE FIRST PAYMENT ERIOD ZERO.

PMT $4,221.07

6.14 Perpetuity: Your grandfather is retiring at the end of next year. He would like to ensure payments of $10,000 a year forever, starting when he retires. If he can earn 6.5 percent, grandfather need to invest to produce the desired cash flow? Desired annual cash flow Rate of return # of years of cash flows

= PMT= =i=

10,000 6.50% Forever

Amount of money needed to be invested=

153,846.15

Horizontal Solution:

n i% PMT

500 6.50% $10,000.00

PMT $10,000.00

PVA $153,846.15

PVIF PVIFA 2.11444E-14 15.3846

ear. He would like to ensure that his heirs receive s. If he can earn 6.5 percent, how much does your ?

6.15 Perpetuity: Calculate the annual cash flows for each of the following investments: a. $250,000 invested at 6 percent. b. $50,000 invested at 12 percent. c. $100,000 invested at 10 percent. a.

PV = i =

$ 250,000 6%

PMT =

$ 15,000

PV = i =

50,000 12%

PMT =

PV = i =

$ 100,000 10%

PMT =

$ 10,000

6,000

TABULAR SOLUTION: PVA $250,000.00

I% 6.00%

N 500

PVIF 2.22365E-13

PVIFA 16.66667

$50,000.00

12.00%

500

2.4603E-25

8.333333

$100,000.00

10.00%

500

2.01214E-21

he following investments:

PMT $15,000.00 $6,000.00 $10,000.00

6.16.

Effective annual rate: Raj Krishnan bought a Honda Civic for $17,345. He put down $6,000 and financed the rest through the dealer at an APR of 4.9 percent for four years. What is the effective annual rate (EAR) if the loan payments are made monthly?

Purchase price of car Down payment = PV= Number of payments= Annual rate (APR) = Effective annual rate (EAR)=

$ 17,345 $ 6,000 12 4.90% 5.01%

Effective Annual Rate (EAR) nominal rate 4.90% compound rate 12 (1 + nom/m)^m 1.0501 ((1+ nom/m)^m -1) 5.01%

for $17,345. He at an APR of 4.9 AR) if the loan

Rate (EAR) monthly EAR

6.17.

Effective annual rate: Cyclone Rentals borrowed $15,550 from a bank for three year quoted rate (APR) is 6.75 percent, and the compounding is daily, what is the effective interest rate (EAR)? Term of loan 3 years nominal rate Interest rate (APR) 6.75% compound period Compounding frequency per year 365 (1+(nom/m))^m ((1+(nom/m))^m - 1) Effective annual rate =

6.98%

5,550 from a bank for three years. If the ing is daily, what is the effective annual nominal rate compound period (1+(nom/m))^m ((1+(nom/m))^m - 1)

6.75% 365 daily 1.0698 6.98% Effective

6.18.

Growing perpetuity: You are evaluating a growing perpetuity investment from a large initial payment of $20,000 at the end of this year and subsequent payments that will gr percent discount rate for investments like this, what is the present value of this growing Perpetuity value at end of year Growth rate= g= Discount rate = k =

20000 3.40% 9%

Present value of growing perpetuity = Initial year value/(k-g)

g perpetuity investment from a large financial services firm. The investment promises an nd subsequent payments that will grow at a rate of 3.4 percent annually. If you use a 9 at is the present value of this growing perpetuity?

$ 357,142.86

FUTURE CASH FLOW G K

$20,000.00 3.40% 9.00%

(K-G) PV OF GROWING PERPETUITY

5.60% $357,142.86

6.19. Future value with multiple cash flows: Trigen Corp. management will invest cash flow of $331,000, $616,450, $212,775, $818,400, $1,239,644, and $1,617,848 in research an development over the next six years. If the appropriate interest rate is 6.75 percent, wha the future value of these investment cash flows six years from today? Year Cash Flow Interest rate

1 331,000

2 616,450

3 212,775

4 $ 818,400

6.75%

Present Value

$3,643,684.79

Future Value at end of Year 6

$5,391,977.89

TABULAR SOLUTION YEAR 0 1 2 3 4 5 6

nt will invest cash flows 617,848 in research and e is 6.75 percent, what is y? 5 $ 1,239,644

6 $ 1,617,848

ABULAR SOLUTION CFs 331,000 616,450 212,775 818,400 1,239,644 1,617,848

6.75% FVIF 1.386243167 1.298588447 1.216476297 1.13955625 1.0675 1

FVA 458,846.49 800,514.85 258,835.74 932,612.84 1,323,319.97 1,617,848.00 $5,391,977.89

6.20.

Future value with multiple cash flows: Stephanie Watson plans to make the following investments beginning next year. She will invest $3,125 in each of the n three years and will then make investments of $3,650, $3,725, $3,875, and $4,00 over the following four years. If the investments are expected to earn 11.5 percen annually, how much will Stephanie have at the end of the seven years?

Year

Investment

3125

3650

3725

3875

Rate of return

11.50%

Present Value

$15,977.28

Future Value at end of Year 7

$34,231.57

TABULAR SOLUTION: 11.50% YEAR CFs FVIF 0 1 3,125 1.9215 2 3,125 1.7234 3 3,125 1.5456 4 3,650 1.3862 5 3,725 1.2432 6 3,875 1.115 7 4,000 1

on plans to make the $3,125 in each of the next 725, $3,875, and $4,000 ed to earn 11.5 percent seven years? 7 4000

FV 6,004.81 5,385.48 4,830.03 5,059.61 4,631.01 4,320.63 4,000.00 $34,231.57

6.21.

Present value with multiple cash flows: Carol Jenkins, a lottery winner, will r following payments over the next seven years. If she can invest her cash flows earn 10.5 percent annually, what is the present value of her winnings?

Cash Receipts

1 $200,000

Rate of return

10.50%

Present value of lottery winnings

2 $250,000

3 $275,000

4 $300,000

CFs

10.50% PVIF

200,000 250,000 275,000 300,000 350,000 400,000 550,000

0.904977 0.818984 0.741162 0.670735 0.607 0.549321 0.497123

$1,496,377.71

TABULAR SOLUTION: YEAR 0 1 2 3 4 5 6 7

180,995.48 204,746.01 203,819.56 201,220.46 212,449.96 219,728.47 273,417.77 $1,496,378

Jenkins, a lottery winner, will receive the she can invest her cash flows in a fund that will alue of her winnings? 5 $350,000

6 $400,000

7 $550,000

6.22.

Computing annuity payment: Gary Whitmore is a high school sophomore. He cur $7,500 in a savings account that pays 5.65 percent annually. Gary plans to use his savings plus what he can save over the next four years to buy a car. He estimates will cost $12,000 in four years. How much money should Gary save each year if he the car?

Money currently in money market account= Rate of return Amount needed to buy car = Number of years until car purchase =

PV = i= FV = n=

Annual savings required over next four years=

PMT =

($610.27)

N i%

7,500 5.65% $ 12,000 4

4 5.65%

STEP ONE: DETERMINE THE FUTURE VALUE OF THE $7,500 MONEY MAKRET AMOUNT. PV FVIF FV $7,500.00 1.24589 $9,344.14 STEP TWO: BALANCE DETERMINE OFTHE MONEY ANNUAL NEEDED SAVINGS TO BUYOVER CAR NEXT 4 YEARS $12,000.00 NEEDED $9,344.14 ACCUMULATED $2,655.86 FUTURE BALANCE NEEDED STEP THREE: ANNUAL SAVINGS REQUIRED OVER NEXT 4 YEARS FVA FVIF FVIFA PMT $2,655.86 1.24589 4.3519494 $610.27

high school sophomore. He currently has annually. Gary plans to use his current ars to buy a car. He estimates that the car hould Gary save each year if he wants to buy

0 MONEY MAKRET AMOUNT.

BALANCE NEEDED

6.23. Growing annuity: Modern Energy Company owns several gas stations. Management is looking to open a new station in the western suburbs of Baltimore. One possibility that managers at the company are evaluating is to take over a station located at a site that has been leased from the county. The lease, originally for 99 years, currently has 73 years before expiration. The gas station generated a net cash flow of $92,500 last year, and the current owners expect an annual growth rate of 6.3 percent. If Modern Energy uses a discount rate of 14.5 percent to evaluate such businesses, what is the present value of this growing annuity? CF0 = Net cash flow (last year) Number of years left on lease n= Expected annual growth rate of cash flow g = Discount rate i=

92,500 73 6.30% 14.50%

nù é æ ö CF1 ê 1+ g ú PVAn = ´ 1- ç ÷ (i - g) êë è 1+ i ø úû

Present value of growing annuity =

PVAn =

$ 1,193,831.54

ons. Management One possibility n located at a site ars, currently has w of $92,500 last rcent. If Modern sses, what is the

6.24.

Future value of an annuity due: Jeremy Denham plans to save $5,000 every year fo today. At the end of eight years, Jeremy will turn 30 years old and plans to use his sa payment on a house. If his investment in a mutual fund will earn him 10.3 percent ann saved in eight years when he buys his house?

Annual saving $ 5,000 Number of years of savings 8 Type of annuity Annuity due Rate of return on investment 10.30% Future value of annuity due

$63,760.19

n i% pmt PMT $5,000.00

ns to save $5,000 every year for the next eight years, starting ars old and plans to use his savings toward the down will earn him 10.3 percent annually, how much will he have

8 10.30% $5,000.00 FVIF FVIFA FVIF 2.1908069 11.5612 110.30%

FVA $63,760.19

6.25.

Present value of an annuity due: Grant Productions has borrowed a huge sum from 17.5 percent for a seven-year period. The loan calls for a payment of $1,540,862.19 e Grant borrow? Interest rate per year 17.50% i% Loan term (years) 7 n Annual Payment due $ 1,540,862 PMT Type of annuity Annuity due PMT Amount of loan borrowed $7,000,000 $1,540,862.00

has borrowed a huge sum from the California Finance Company at a rate of a payment of $1,540,862.19 each year beginning today. How much did 17.50% 7 $1,540,862.00 PVIF 0.323396216

PVIFA 3.86630734

FVIF 1.1750

PVA $6,999,999.12

6.26.

Present value of an annuity due: Sharon Kabana has won a state lottery and will rec every year, starting today, for the next 20 years. If she normally invests at a rate of 7.2 value of the cash flows that she will receive? Round to the nearest dollar.

Rate of return on investment 7.25% # of years of annuity 20 Annual Payment received $ 89,725.45 Type of annuity Annuity due Amount of loan borrowed

$999,955

I% n PMT PMT $89,725.45

has won a state lottery and will receive a payment of $89,729.45 he normally invests at a rate of 7.25 percent, what is the present to the nearest dollar. 7.25% 20 $89,725.45 PVIF PVIFA 0.246634589 10.3912

FVIF 1.0725

PVA $999,955.37

6.3 Present value of an annuity due: You wrote a piece of software that does a better job of allowing computers to network than any other program designed for this purpose. A large networking company wants to incorporate your software into its systems and is offering to pay you $500,000 today, plus $500,000 at the end of each of the following six years, for permission to do this. If the appropriate interest rate is 6 percent, what is the present value of the cash flow stream that the company is offering

Year 0 1 2 3 4 5 6

CFs 500,000 500,000 500,000 500,000 500,000 500,000 500,000

6.00% PVIF 1 0.943396 0.889996 0.839619 0.792094 0.747258 0.704961

PV 500,000.00 471,698.11 444,998.22 419,809.64 396,046.83 373,629.09 352,480.27 $2,958,662

e that does a better igned for this software into its 0 at the end of each riate interest rate is 6 e company is offering

6.3 Present Vlaue of an annuity: Suppose that the networking company in Problem 6.27 will not start paying you until the first of the new systems that use your software are sold in two years. What is the present value of that annuity? Assume the appropriate interest rate is still 6 percent. 6.00% Year CFs PVIF PV 0 0 1 0.00 1 0 0.943396 0.00 2 500,000 0.889996 444,998.22 3 500,000 0.839619 419,809.64 4 500,000 0.792094 396,046.83 5 500,000 0.747258 373,629.09 6 500,000 0.704961 352,480.27 $1,986,964

6.29 Perpetuity: Calculate the present value of the following perpetuities: a. $1,250 discounted back to the present at 7 percent. b. $7,250 discounted back to the present at 6.33 percent. c. $850 discounted back to the present at 20 percent. a. Cash flow = Discount rate =

$ 1,250 7%

Present value of perpetuity =

b. Cash flow = Discount rate =

$ 7,250 6.33%

Present value of perpetuity =

c. Cash flow = Discount rate =

Present value of perpetuity =

850 20%

17,857.14

$ 114,533.97

4,250.00

6.30. Effective annual interest rate: Find the effective annual interest rate (EAR) for each of t a. 6 percent compounded quarterly. b. 4.99 percent compounded monthly. c. 7.25 percent compounded semiannually. d. 5.6 percent compounded daily. a.

Nominal rate = Compounding frequency

6% 4

EAR = EAR =

6.14% 6.14%

Nominal rate = Compounding frequency

5% 12

EAR = EAR =

5.11% 5.11%

Nominal rate = Compounding frequency

7% 2

EAR = EAR =

7.38% 7.38%

Nominal rate = Compounding frequency

5.60% 365

EAR = EAR =

5.76% 5.76%

st rate (EAR) for each of the following:

6.31.

Effective annual interest rate: Which of the following investments has the highest effective annual interest rate (EAR)?

a. b. c. d. e.

A bank CD that pays 8.25 percent interest quarterly. A bank CD that pays 8.25 percent monthly. A bank CD that pays 8.45 percent annually. A bank CD that pays 8.25 percent semiannually. A bank CD that pays 8 percent daily (on a 365-day basis).

Nominal rate = Compounding frequency

8.25% 4

EAR = EAR =

8.51% 8.51%

Nominal rate = Compounding frequency

8.25% 12

EAR = EAR =

8.57% 8.57%

Nominal rate = Compounding frequency

8.45% 1

EAR = EAR =

8.45% 8.45%

Nominal rate = Compounding frequency

8.25% 2

EAR = EAR =

8.42% 8.42%

Nominal rate = Compounding frequency

8.00% 365

EAR = EAR =

8.33% 8.33%

Answer: The highest effective annual rate (EAR) is the CD that pays 8.25% monthly

g investments has

that pays 8.25% monthly

6.32. Effective annual interest rate: You are considering three alternative investments: (1) a three-year bank CD paying 7.5 percent compounded quarterly; (2) a three-year bank CD paying 7.3 percent compounded monthly; and (3) a three-year bank CD paying 7.75 percent compounded annually. Which investment has the highest effective annual interest rate (EAR)? 1 Nominal rate = Compounding frequency

7.50% 4

EAR = EAR =

7.71% 7.71%

2 Nominal rate = Compounding frequency

7.30% 12

EAR = EAR =

7.55% 7.55%

3 Nominal rate = Compounding frequency

7.75% 1

EAR = EAR =

7.75% 7.75%

Answer: The 3-year bank CD paying 7.75% compounded annually has the highest

rnative investments:

rterly; nthly; and nually. e (EAR)?

nnually has the highest EAR

6.3 You have been offered the opportunity to invest in a project which is exected to provide the following cash flows: $4,000 in 1 year, $12,000 in 2 years, and $8,000 in 3 years. If th appropriate interest rates are 6 percent for the first year, 8 percent for the second year, percent for the third year, what is the present value of these cash flows? i% year 1 i% year 2 i% year 3

6.00% 8.00% 12.00%

Year 1 2 3

CFs $4,000 $12,000 $8,000

6.00% PVIF 0.943396

8.00% PVIF 0.925926

12.00% PVIF

PV $3,773.58 $10,482.18 0.892857 $6,239.39 $20,495.16

t which is exected to provide you with s, and $8,000 in 3 years. If the percent for the second year, and 12 e cash flows?

Present Value of cash flows

6.34.

Tirade Owens, a professional athlete, currently has a contract that will pay him a large year of his contract and smaller amounts thereafter. He and his agent have asked the the contract. The team, though reluctant, obliged. Tirade and his agent came up with a are the present values of each of the contracts using a 14 percent discount rate? Whi contacts has the highest present value?

Current Contract 1 $8,125,000 2 $3,650,000 3 $2,715,000 4 $1,822,250 Discount rate=

Team’s Offer Counteroffer $4,000,000 $3,825,000 $3,850,000 $3,925,000 14%

$5,250,000 $7,550,000 $3,625,000 $2,800,000

NPV

$12,847,215

$11,374,541

$14,519,340

Contract A 8,125,000 3,650,000 2,715,000 1,822,250

Contract B 4,000,000 3,825,000 3,850,000 3,925,000

Contract C 5,250,000 7,550,000 3,625,000 2,800,000

Year

Year 1 2 3 4

14.00% PVIF 0.87719 0.76947 0.67497 0.59208

PV A 7,127,193 2,808,556 1,832,548 1,078,918 12,847,215

that will pay him a large amount in the first s agent have asked the team to restructure his agent came up with a counteroffer. What cent discount rate? Which of the three

PV B 3,508,772 2,943,213 2,598,640 2,323,915 11,374,541

PV C 4,605,263 5,809,480 2,446,772 1,657,825 $14,519,339.52

6.35.

Gary Kornig will be 30 years old next year and wants to retire when he is 65. So far he in which his money is earning 8.3 percent annually and (2) $5,000 in a money market percent annually.. Gary wants to have $1 million when he retires. Starting next year, h money, every year until he reitres, in a mutual fund in which he expects to earn 9 perc to invest every year to achieve his savings goal?

Gary's current age = Retirement age = IRA saving = Rate of return on IRA = Inheritance in money market account = Rate of return on money market account = Retirement Savings Target Expected rate of return on annuity in mutual fund = Future value of IRA = Future value of inheritance = Additional amount needed to accumulate $1,000,000 = Amount needed to be saved each year for 36 years = Gary's current age Retirement age n= IRA saving Rate of return on IRA Inheritance in money market account Rate of return on money market account Retirement Savings Target Expected rate of return on annuity in mutual fund

Additional amount needed to accumulate $1,000,000 Amount needed to be saved each year for 36 years

to retire when he is 65. So far he has saved (1) $6,950 in an IRA account nd (2) $5,000 in a money market account in which he is earning 5.25 en he retires. Starting next year, he plans to invest the same amount of n which he expects to earn 9 percent annually. How much will Gary have

29 65 6950 8.30% 5000 5.25% 1,000,000 9% $122,633.53 $31,547.56 $845,818.91 ($3,582.09) 29 65 36 $6,950 8.30% $5,000 5.25% $1,000,000 9.00% PV $6,950

FVIF FV 17.64511278 $122,633.53

$5,000

6.309511878

e $1,000,000 FVA $845,818.91

FV =

$31,548 $845,818.91

FVIF FVIFA 22.25122503 236.1247226

PMT $3,582.09

6.4 The top prize for the state lottery is $100,000,000. You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annual payment option. If you choose the annual payment option and win, you will receive $100,000,000 in 25 equal payments of $4,000,000 - one payment today and one payment at the end of each of the next 24 year If you choose the cash payment, you will receive a one-time lump sum payment of $59,194,567.18. If you can invest the proceeds and earn 6 percent, which option should you choose? Option One State Lottery $100,000,000.00 PV $59,194,567.18 Option Two Year CFs 0 $4,000,000 1 $4,000,000 2 $4,000,000 3 $4,000,000 4 $4,000,000 5 $4,000,000 6 $4,000,000 7 $4,000,000 8 $4,000,000 9 $4,000,000 10 $4,000,000 11 $4,000,000 12 $4,000,000 13 $4,000,000 14 $4,000,000 15 $4,000,000 16 $4,000,000 17 $4,000,000 18 $4,000,000 19 $4,000,000 20 $4,000,000 21 $4,000,000 22 $4,000,000 23 $4,000,000 24 $4,000,000

6.00% PVIF 1 0.943396226 0.88999644 0.839619283 0.792093663 0.747258173 0.70496054 0.665057114 0.627412371 0.591898464 0.558394777 0.526787525 0.496969364 0.468839022 0.442300964 0.417265061 0.393646284 0.371364419 0.350343791 0.33051301 0.311804727 0.294155403 0.277505097 0.261797261 0.246978548

PV $4,000,000 $3,773,585 $3,559,986 $3,358,477 $3,168,375 $2,989,033 $2,819,842 $2,660,228 $2,509,649 $2,367,594 $2,233,579 $2,107,150 $1,987,877 $1,875,356 $1,769,204 $1,669,060 $1,574,585 $1,485,458 $1,401,375 $1,322,052 $1,247,219 $1,176,622 $1,110,020 $1,047,189 $987,914

$54,201,430

CHOOSE OPTION ONE AS ITS PV OF $59,194,567 IS GREATER THAN THE PV OF $54,201,4

e decided it is time for you to the ticket, you must decide option. If you choose the 000 in 25 equal payments of d of each of the next 24 years. e lump sum payment of percent, which option should

THAN THE PV OF $54,201,430.

6.37 At what interest rate would you be indifferent between the cash and annual payment options in Problem 6

6.36 The top prize for the state lottery is $100,000,000. You have decided it is time for you to take a chance and a ticket. Before you purchase the ticket, you must decide whether to choose the cash option or the annua option. If you choose the annual payment option and win, you will receive $100,000,000 in 25 equal payme $4,000,000 - one payment today and one payment at the end of each of the next 24 years. If you choose th payment, you will receive a one-time lump sum payment of $59,194,567.18. If you can invest the proceeds percent, which option should you choose? Option One State Lottery PV Option Two Year 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

$100,000,000.00 $59,194,567.18 6.00% CFs $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000

PVIF 1 0.943396226 0.88999644 0.839619283 0.792093663 0.747258173 0.70496054 0.665057114 0.627412371 0.591898464 0.558394777 0.526787525 0.496969364 0.468839022 0.442300964 0.417265061 0.393646284 0.371364419 0.350343791 0.33051301 0.311804727 0.294155403 0.277505097 0.261797261 0.246978548

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

CFs ($59,194,567.18) $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000 $4,000,000

$54,201,430

Find the rate that equates the present value of Option 2. The rate of 4.519402% was found

ment options in Problem 6.36?

you to take a chance and purchase cash option or the annual payment 000,000 in 25 equal payments of 4 years. If you choose the cash u can invest the proceeds and earn 6

RATE OF INDIFFERENCE 4.519402% PVIF 1 0.956760165 0.915390013 0.8758087 0.837938876 0.801706537 0.767040878 0.733874157 0.702141559 0.671781074 0.642733371 0.614941686 0.588351709 0.562911478 0.538571278 0.515283545 0.49300277 0.471685411 0.451289812 0.431776114 0.413106186 0.395243543 0.378153277 0.361801992 0.346157733 0.33118993

PV ($59,194,567.18) $3,827,040.66 $3,661,560.05 $3,503,234.80 $3,351,755.50 $3,206,826.15 $3,068,163.51 $2,935,496.63 $2,808,566.24 $2,687,124.30 $2,570,933.48 $2,459,766.74 $2,353,406.84 $2,251,645.91 $2,154,285.11 $2,061,134.18 $1,972,011.08 $1,886,741.64 $1,805,159.25 $1,727,104.46 $1,652,424.75 $1,580,974.17 $1,512,613.11 $1,447,207.97 $1,384,630.93 $1,324,759.72 $0.00

quates the present value of Option 1 to the present value e of 4.519402% was found using Tools/Goal Seek.

6.38. Babu Baradwaj is saving for his son's college tuition. His son is currently 11 years old and investment of $7,500 that is earning 9.5 percent annually. Total expenses at the University total $15,000 per year, but are expected to grow at roughly 6 percent each year. Babu plan annually to make up the difference between the college expenses and his current savings first starting today and with the last being made a year before his son begins college. a. What will be the present value of the four years of college expenses just when the son starts college? Assume a discount rate of 5.5 percent. b. What will be the value of the index mutual fund when the son just starts college? c. What is the amount that the father has to have saved when his son turns 18? d. How much will the father have to invest every year in order for him to have enough funds to cover all tuition expenses? Son's current age 11 Son begin's college at age = 18 Index fund investment $ 7,500 Annual rate of return on index fund= 9.50% Current college cost per year = 15000 Annual growth rate in college expenses = 6% Rate of return on mutual fund investment= 11% Number of deposits into mutual fund = 7 a.

What will be the present value of the four years of college expenses just when the son sta Assume a discount rate of 5.5 percent.

Year 1 college expense Year 2 college expense Year 3 college expense Year 4 college expense Discount rate =

Years from now 7 8 9 10 5.50%

Present Value of 4 years of college expenses= b.

What will be the value of the index mutual fund when the son just starts college?

Future value of index mutual fund after 7 years = c.

$14,156.64

What is the amount that the father has to have saved when his son turns 18?

The amount of money that the father has to have saved when the son turns 18 =

How much will the father have to invest every year in order for him to have enough funds t cover all tuition expenses?

Amount needed to be invested per year for 7 years =

tion. His son is currently 11 years old and will begin college in seven years. Babu has an index fund annually. Total expenses at the University in Maryland, where his son says he plans to go, currently at roughly 6 percent each year. Babu plans to invest in a mutual fund that will earn 11 percent college expenses and his current savings. In total, Babu will make seven equal investments with the a year before his son begins college.

of college expenses just rate of 5.5 percent. when the son just starts college? aved when his son turns 18? ar in order for him to have

n 7 Index fund $7,500 Return on Index Fund 9.50% College cost per year $15,000 Growth rate in college costs 6.00% Return on Mutual Fund 11.00% Number of deposits in mutual fund 7 Discount Rate 5.50%

of college expenses just when the son starts college?

Future value $ $ $ $

22,554.45 23,907.72 25,342.18 26,862.72

1 2 3 4

YEARS FROM NOW 7 8 9 10

CFs $15,000 $22,554 $23,908 $25,342 Present value of 4 years of c

$86,124.36

when the son just starts college? YEAR 7

CF $7,500

aved when his son turns 18?

ed when the son turns 18 =

PV of college expensesFV of Index fund $71,967.73 $86,124.36 $14,156.64

ar in order for him to have enough funds to

($6,627.21)

FVA $71,967.73

FVIF 2.076160153

FVIF

FV 1.5036 $22,554.45 1.0600 $23,907.72 1.0600 $25,342.18 1.0600 $26,862.72 nt value of 4 years of college expenses

FVIF 1.887551606

Needed Savings $71,967.73

FV $14,156.64

PVIF 0.947867299 0.898452416 0.851613664 0.807216743

PV $21,378.63 $21,479.95 $21,581.75 $21,684.03 $86,124.36

FVIFA 9.783274117

FVIF 1.1100

PMT per year for 7 years $6,627.21

6.39. You are now 50 years old and plan to retire at age 65. You currently have a stock portfoli $150,000, a 401(k) retirement plan worth $250,000, and a money market account worth $50,000. Your stock portfolio is expected to provide you annual returns of 12 percent, yo 401(k) investment will earn you 9.5 percent annually, and the money market account earn percent, compounded monthly. Current age 50 Retirement age 65 Portfolio value $150,000 401(k) plan value $250,000 a.

If you do not save another penny for the next 15 years, how much will you have from your current savings when you retire at age 65?

Future value of Stock Portfolio after 15 years = Future value of 401(k) plan after 15 years = Future value of Money market account after 15 years =

$821,034.86 $975,330.48 $109,706.14

Total value of savings after 15 years = b.

Assume you plan to invest $12,000 every year in your 401(k) plan for the next 15 years s next year. How much will you have in total at retirement?

Annual 401(k) investment = Number of deposits = Retirement value = c.

12,000 15 $2,272,554.25

Assume that you expect to live 25 years after you retire (until age 90). Today, at age 50, take all of your investments and place them in an account that pays 8 percent (use the sc from part b in which you continue saving). If you start withdrawing funds starting at age 6 much can you withdraw every year (e.g., an ordianry annuity) and leave nothing in your y account after a 25th and final withdrawal at age 90?

Amount available at retirement Number of years expected during retirement phase Rate of return on investment Annual withdrawal possible during retirement phase d.

$1,906,071.49

PV = n= i= PMT =

You want your current investments, which are described in the problem statement, to sup perpetuity that starts a year from now. How much can you withdraw each year without to your principal?

Amount that can be withdrawn each year as a perpetuity =

$181,804.34

ntly have a stock portfolio worth y market account worth eturns of 12 percent, your ney market account earns 5.25 Money market account value Expected annual rate of return on stock portfolio Annual rate of return on 401(k) plan Money market account rate of return (compounded monthly)

FVIF $150,000 $250,000 50,000

50,000 12% 9.50% 5.25%

FV 5.473565759 $821,034.86 3.901321918 $975,330.48 2.194122845 $ 109,706.14 $1,906,071.49

n for the next 15 years starting

PMT $12,000

FVIFA 30.54023072

FV $366,482.77 $1,906,071.49 $2,272,554.25

n= i%=

25 8.00%

PV $2,272,554.25

PVIFA 10.67477619

PMT $212,890.11

Retirement Value

i% after Retirement

Withdrawal

90). Today, at age 50, you ys 8 percent (use the scenario g funds starting at age 66, how d leave nothing in your your

$2,272,554.25 25 8% $212,890.11

oblem statement, to support a aw each year without touching

$2,272,554.25

8.00%

$181,804.34

n m

15 12

6.40.

Trevor Diaz is looking to purchase a Mercedes Benz SL600 Roadster, which has an invoice price of $121,737 and a total cost of $129,482. Trevor plans to put down $20,000 and will pay the rest by taking on a 5.75 percent fiveyear loan. What is the monthly payment on this auto loan? Prepare an amortization table using Excel. Total cost price of car $ 129,482 Down payment $ 20,000 Interest rate on loan (APR) 5.75% Term of loan (years) 5 Loan amount Monthly payment

$ 109,482 ($2,103.89)

Amortization Table Month Balance Payment Interest 1 $ 109,482 $2,103.89 524.60 2 $ 107,903 $2,103.89 517.03 3 $ 106,316 $2,103.89 509.43 4 $ 104,721 $2,103.89 501.79 5 $ 103,119 $2,103.89 494.11 6 $ 101,510 $2,103.89 486.40 7 $ 99,892 $2,103.89 478.65 8 $ 98,267 $2,103.89 470.86 9 $ 96,634 $2,103.89 463.04 10 $ 94,993 $2,103.89 455.17 11 $ 93,344 $2,103.89 447.27 12 $ 91,688 $2,103.89 439.34 13 $ 90,023 $2,103.89 431.36 14 $ 88,350 $2,103.89 423.35 15 $ 86,670 $2,103.89 415.29 16 $ 84,981 $2,103.89 407.20 17 $ 83,285 $2,103.89 399.07 18 $ 81,580 $2,103.89 390.90 19 $ 79,867 $2,103.89 382.70 20 $ 78,146 $2,103.89 374.45 21 $ 76,416 $2,103.89 366.16 22 $ 74,678 $2,103.89 357.83 23 $ 72,932 $2,103.89 349.47 24 $ 71,178 $2,103.89 341.06 25 $ 69,415 $2,103.89 332.61

Principal Reduction $1,579.29 $1,586.86 $1,594.46 $1,602.10 $1,609.78 $1,617.49 $1,625.24 $1,633.03 $1,640.85 $1,648.72 $1,656.62 $1,664.55 $1,672.53 $1,680.54 $1,688.60 $1,696.69 $1,704.82 $1,712.99 $1,721.19 $1,729.44 $1,737.73 $1,746.06 $1,754.42 $1,762.83 $1,771.28

Ending Balance 107,902.71 106,315.85 104,721.39 103,119.29 101,509.52 99,892.03 98,266.79 96,633.76 94,992.90 93,344.19 91,687.57 90,023.02 88,350.49 86,669.94 84,981.35 83,284.66 81,579.84 79,866.85 78,145.66 76,416.22 74,678.49 72,932.43 71,178.01 69,415.18 67,643.91

26 $ 27 $ 28 $ 29 $ 30 $ 31 $ 32 $ 33 $ 34 $ 35 $ 36 $ 37 $ 38 $ 39 $ 40 $ 41 $ 42 $ 43 $ 44 $ 45 $ 46 $ 47 $ 48 $ 49 $ 50 $ 51 $ 52 $ 53 $ 54 $ 55 $ 56 $ 57 $ 58 $ 59 $ 60 $

67,644 65,864 64,076 62,279 60,474 58,659 56,837 55,005 53,165 51,316 49,458 47,591 45,715 43,830 41,936 40,033 38,121 36,200 34,269 32,330 30,381 28,422 26,455 24,478 22,491 20,495 18,489 16,474 14,449 12,414 10,370 8,316 6,252 4,178 2,094

$2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89 $2,103.89

324.13 315.60 307.03 298.42 289.77 281.08 272.34 263.57 254.75 245.89 236.98 228.04 219.05 210.02 200.94 191.83 182.66 173.46 164.21 154.91 145.57 136.19 126.76 117.29 107.77 98.20 88.59 78.94 69.23 59.49 49.69 39.85 29.96 20.02 10.03

$1,779.76 $1,788.29 $1,796.86 $1,805.47 $1,814.12 $1,822.81 $1,831.55 $1,840.32 $1,849.14 $1,858.00 $1,866.91 $1,875.85 $1,884.84 $1,893.87 $1,902.95 $1,912.06 $1,921.23 $1,930.43 $1,939.68 $1,948.98 $1,958.32 $1,967.70 $1,977.13 $1,986.60 $1,996.12 $2,005.69 $2,015.30 $2,024.95 $2,034.66 $2,044.40 $2,054.20 $2,064.04 $2,073.93 $2,083.87 $2,093.86

65,864.14 64,075.85 62,278.99 60,473.52 58,659.40 56,836.59 55,005.04 53,164.71 51,315.57 49,457.57 47,590.66 45,714.81 43,829.97 41,936.10 40,033.15 38,121.09 36,199.86 34,269.43 32,329.75 30,380.77 28,422.45 26,454.75 24,477.63 22,491.02 20,494.90 18,489.22 16,473.92 14,448.97 12,414.31 10,369.91 8,315.71 6,251.66 4,177.73 2,093.86 (0.00)

00 Roadster, which ,482. Trevor plans 5.75 percent five? Prepare an

6.41.

The Sundarams are buying a new 3,500-square-foot house in Muncie, Indiana, and will $237,000 from Bank One at a rate of 6.375 percent for 15 years. What is their monthly l payment? Prepare an amortization schedule using Excel.

Total cost of house Interest rate on loan (APR) Term of loan (years)

$ 237,000 6.375% 15

Loan amount Monthly payment

$ 237,000 ($2,048.27)

Amortization Table Month Balance 1 $ 237,000 2 $ 236,211 3 $ 235,417 4 $ 234,620 5 $ 233,818 6 $ 233,012 7 $ 232,201 8 $ 231,387 9 $ 230,568 10 $ 229,744 11 $ 228,917 12 $ 228,084 13 $ 227,248 14 $ 226,407 15 $ 225,561 16 $ 224,711 17 $ 223,857 18 $ 222,998 19 $ 222,134 20 $ 221,266 21 $ 220,393 22 $ 219,516 23 $ 218,634 24 $ 217,747 25 $ 216,855 26 $ 215,959

Payment $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27

Interest 1,259.06 1,254.87 1,250.65 1,246.42 1,242.16 1,237.88 1,233.57 1,229.24 1,224.89 1,220.52 1,216.12 1,211.70 1,207.25 1,202.79 1,198.29 1,193.78 1,189.24 1,184.68 1,180.09 1,175.48 1,170.84 1,166.18 1,161.49 1,156.78 1,152.04 1,147.28

Principal Reduction $789.21 $793.40 $797.62 $801.86 $806.12 $810.40 $814.70 $819.03 $823.38 $827.76 $832.15 $836.58 $841.02 $845.49 $849.98 $854.49 $859.03 $863.60 $868.19 $872.80 $877.43 $882.10 $886.78 $891.49 $896.23 $900.99

Ending Balance 236,210.79 235,417.39 234,619.77 233,817.91 233,011.80 232,201.40 231,386.69 230,567.66 229,744.28 228,916.52 228,084.37 227,247.79 226,406.77 225,561.29 224,711.31 223,856.81 222,997.78 222,134.18 221,266.00 220,393.20 219,515.76 218,633.67 217,746.89 216,855.39 215,959.16 215,058.17

27 $ 28 $ 29 $ 30 $ 31 $ 32 $ 33 $ 34 $ 35 $ 36 $ 37 $ 38 $ 39 $ 40 $ 41 $ 42 $ 43 $ 44 $ 45 $ 46 $ 47 $ 48 $ 49 $ 50 $ 51 $ 52 $ 53 $ 54 $ 55 $ 56 $ 57 $ 58 $ 59 $ 60 $ 61 $ 62 $ 63 $ 64 $ 65 $ 66 $ 67 $

215,058 214,152 213,242 212,326 211,406 210,481 209,551 208,616 207,676 206,731 205,781 204,826 203,866 202,900 201,930 200,954 199,974 198,988 197,997 197,000 195,999 194,992 193,979 192,961 191,938 190,910 189,876 188,836 187,791 186,740 185,684 184,622 183,555 182,482 181,403 180,318 179,228 178,132 177,030 175,922 174,808

$2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27 $2,048.27

1,142.50 1,137.68 1,132.85 1,127.98 1,123.09 1,118.18 1,113.24 1,108.27 1,103.28 1,098.26 1,093.21 1,088.14 1,083.04 1,077.91 1,072.75 1,067.57 1,062.36 1,057.12 1,051.86 1,046.56 1,041.24 1,035.89 1,030.51 1,025.11 1,019.67 1,014.21 1,008.71 1,003.19 997.64 992.06 986.45 980.81 975.13 969.43 963.70 957.94 952.15 946.32 940.47 934.59 928.67

$905.78 $910.59 $915.43 $920.29 $925.18 $930.09 $935.03 $940.00 $945.00 $950.02 $955.06 $960.14 $965.24 $970.37 $975.52 $980.70 $985.91 $991.15 $996.42 $1,001.71 $1,007.03 $1,012.38 $1,017.76 $1,023.17 $1,028.60 $1,034.07 $1,039.56 $1,045.08 $1,050.63 $1,056.22 $1,061.83 $1,067.47 $1,073.14 $1,078.84 $1,084.57 $1,090.33 $1,096.13 $1,101.95 $1,107.80 $1,113.69 $1,119.60

214,152.40 213,241.81 212,326.38 211,406.09 210,480.91 209,550.82 208,615.79 207,675.78 206,730.79 205,780.77 204,825.71 203,865.57 202,900.33 201,929.97 200,954.45 199,973.75 198,987.83 197,996.68 197,000.27 195,998.56 194,991.53 193,979.15 192,961.39 191,938.22 190,909.62 189,875.55 188,835.99 187,790.91 186,740.28 185,684.06 184,622.23 183,554.77 182,481.63 181,402.79 180,318.22 179,227.88 178,131.76 177,029.81 175,922.01 174,808.32 173,688.72

68 $ 69 $ 70 $ 71 $ 72 $ 73 $ 74 $ 75 $ 76 $ 77 $ 78 $ 79 $ 80 $ 81 $ 82 $ 83 $ 84 $ 85 $ 86 $ 87 $ 88 $ 89 $ 90 $ 91 $ 92 $ 93 $ 94 $ 95 $ 96 $ 97 $ 98 $ 99 $ 100 $ 101 $ 102 $ 103 $ 104 $ 105 $ 106 $ 107 $ 108 $

173,689 172,563 171,432 170,294 169,151 168,001 166,845 165,683 164,515 163,341 162,160 160,973 159,780 158,581 157,375 156,163 154,944 153,719 152,487 151,249 150,005 148,753 147,495 146,230 144,959 143,681 142,396 141,104 139,805 138,500 137,187 135,868 134,541 133,208 131,867 130,520 129,165 127,803 126,433 125,057 123,673

922.72 916.74 910.73 904.69 898.61 892.50 886.36 880.19 873.99 867.75 861.48 855.17 848.83 842.46 836.06 829.62 823.14 816.63 810.09 803.51 796.90 790.25 783.57 776.85 770.09 763.30 756.48 749.62 742.72 735.78 728.81 721.80 714.75 707.67 700.54 693.39 686.19 678.95 671.68 664.36 657.01

$1,125.55 $1,131.53 $1,137.54 $1,143.59 $1,149.66 $1,155.77 $1,161.91 $1,168.08 $1,174.29 $1,180.53 $1,186.80 $1,193.10 $1,199.44 $1,205.81 $1,212.22 $1,218.66 $1,225.13 $1,231.64 $1,238.18 $1,244.76 $1,251.37 $1,258.02 $1,264.71 $1,271.42 $1,278.18 $1,284.97 $1,291.80 $1,298.66 $1,305.56 $1,312.49 $1,319.47 $1,326.48 $1,333.52 $1,340.61 $1,347.73 $1,354.89 $1,362.09 $1,369.32 $1,376.60 $1,383.91 $1,391.26

172,563.16 171,431.63 170,294.09 169,150.50 168,000.84 166,845.07 165,683.16 164,515.08 163,340.80 162,160.27 160,973.47 159,780.37 158,580.93 157,375.12 156,162.90 154,944.24 153,719.11 152,487.47 151,249.29 150,004.53 148,753.15 147,495.13 146,230.42 144,959.00 143,680.82 142,395.85 141,104.06 139,805.40 138,499.84 137,187.35 135,867.88 134,541.41 133,207.89 131,867.28 130,519.55 129,164.66 127,802.58 126,433.25 125,056.66 123,672.75 122,281.49

109 $ 110 $ 111 $ 112 $ 113 $ 114 $ 115 $ 116 $ 117 $ 118 $ 119 $ 120 $ 121 $ 122 $ 123 $ 124 $ 125 $ 126 $ 127 $ 128 $ 129 $ 130 $ 131 $ 132 $ 133 $ 134 $ 135 $ 136 $ 137 $ 138 $ 139 $ 140 $ 141 $ 142 $ 143 $ 144 $ 145 $ 146 $ 147 $ 148 $ 149 $

122,281 120,883 119,477 118,063 116,642 115,214 113,777 112,333 110,882 109,423 107,956 106,481 104,998 103,508 102,010 100,503 98,989 97,467 95,936 94,397 92,851 91,296 89,732 88,161 86,581 84,993 83,396 81,791 80,177 78,554 76,924 75,284 73,636 71,978 70,313 68,638 66,954 65,262 63,560 61,849 60,130

649.62 642.19 634.72 627.21 619.66 612.07 604.44 596.77 589.06 581.31 573.52 565.68 557.80 549.89 541.93 533.92 525.88 517.79 509.66 501.49 493.27 485.01 476.70 468.35 459.96 451.52 443.04 434.51 425.94 417.32 408.66 399.95 391.19 382.39 373.54 364.64 355.69 346.70 337.66 328.58 319.44

$1,398.65 $1,406.08 $1,413.55 $1,421.06 $1,428.61 $1,436.20 $1,443.83 $1,451.50 $1,459.21 $1,466.96 $1,474.76 $1,482.59 $1,490.47 $1,498.39 $1,506.35 $1,514.35 $1,522.39 $1,530.48 $1,538.61 $1,546.79 $1,555.00 $1,563.27 $1,571.57 $1,579.92 $1,588.31 $1,596.75 $1,605.23 $1,613.76 $1,622.33 $1,630.95 $1,639.62 $1,648.33 $1,657.08 $1,665.89 $1,674.74 $1,683.63 $1,692.58 $1,701.57 $1,710.61 $1,719.70 $1,728.83

120,882.83 119,476.75 118,063.20 116,642.13 115,213.52 113,777.32 112,333.49 110,881.99 109,422.77 107,955.81 106,481.05 104,998.46 103,507.99 102,009.60 100,503.26 98,988.91 97,466.51 95,936.03 94,397.41 92,850.63 91,295.62 89,732.36 88,160.79 86,580.87 84,992.56 83,395.81 81,790.57 80,176.81 78,554.48 76,923.52 75,283.91 73,635.58 71,978.50 70,312.61 68,637.87 66,954.24 65,261.66 63,560.09 61,849.48 60,129.78 58,400.94

150 $ 151 $ 152 $ 153 $ 154 $ 155 $ 156 $ 157 $ 158 $ 159 $ 160 $ 161 $ 162 $ 163 $ 164 $ 165 $ 166 $ 167 $ 168 $ 169 $ 170 $ 171 $ 172 $ 173 $ 174 $ 175 $ 176 $ 177 $ 178 $ 179 $ 180 $

58,401 56,663 54,916 53,159 51,393 49,618 47,833 46,039 44,236 42,422 40,599 38,767 36,924 35,072 33,210 31,339 29,457 27,565 25,663 23,751 21,829 19,897 17,954 16,001 14,038 12,064 10,080 8,085 6,080 4,064 2,037

310.26 301.02 291.74 282.41 273.03 263.60 254.11 244.58 235.00 225.37 215.68 205.95 196.16 186.32 176.43 166.49 156.49 146.44 136.34 126.18 115.97 105.70 95.38 85.01 74.58 64.09 53.55 42.95 32.30 21.59 10.82

$1,738.02 $1,747.25 $1,756.53 $1,765.87 $1,775.25 $1,784.68 $1,794.16 $1,803.69 $1,813.27 $1,822.91 $1,832.59 $1,842.33 $1,852.11 $1,861.95 $1,871.84 $1,881.79 $1,891.78 $1,901.83 $1,911.94 $1,922.10 $1,932.31 $1,942.57 $1,952.89 $1,963.27 $1,973.70 $1,984.18 $1,994.72 $2,005.32 $2,015.97 $2,026.68 $2,037.45

56,662.93 54,915.67 53,159.14 51,393.27 49,618.03 47,833.35 46,039.19 44,235.50 42,422.23 40,599.32 38,766.73 36,924.41 35,072.30 33,210.35 31,338.50 29,456.71 27,564.93 25,663.10 23,751.16 21,829.06 19,896.76 17,954.18 16,001.29 14,038.02 12,064.33 10,080.15 8,085.42 6,080.10 4,064.13 2,037.45 (0.00)

se in Muncie, Indiana, and will borrow 5 years. What is their monthly loan

6.42.

Assume you will start working as soon as you graduate from college. You plan to start s retirement. on your 25th birthday and retire on your 65th birthday. After retirement, you least until you are 85. You wish to be able to withdraw $40,000 (in today’s dollars) ever time of your retirement until you are 85 years old (i.e., for 20 years). You can invest, sta turn 25 years old, in a portfolio fund. The average inflation rate is likely to be 5 percent.

Current age Graduation age Retirement age Life expectation Annual withdrawal during retirement (current dollars) Average inflation rate a.

Calculate the lump sum you need to have accumulated at age 65 to be able to draw the desired income. Assume that your return on the portfolio investment is likely to be 10 percent. Rate of return on the portfolio investment Annual withdrawal needed during retirement phase (inflation-adjusted) Lump sum needed at age 65 to achieve retirement income

What is the dollar amount you need to invest every year, starting at age 26 and ending at age 65 (i.e., for 40 years) to reach the target lump sum at age 65?

Annual saving necessary for 40 years to reach target lump sum

Now answer questions a and b assuming your rate of return to be 8 percent per year then again at 15 percent per year.

Rate of return on the portfolio investment Annual withdrawal needed during retirement phase (inflation-adjusted) Lump sum needed at age 65 to achieve retirement income Annual saving necessary for 40 years to reach target lump sum Rate of return on the portfolio investment

Annual withdrawal needed during retirement phase (inflation-adjusted) Lump sum needed at age 65 to achieve retirement income Annual saving necessary for 40 years to reach target lump sum d.

Now assume you start investing for your retirement when you turn 30 years old and analyze the situation under rate of return assumptions of (i) 8 percent, (ii) 10 percent, and (iii) 15 percent. Retirement Age Age when investing begins Rate of return Amount needed at retirement Annual saving necessary for 35 years to reach lump sum target

Repeat the analysis by assuming that you start investing when you are 35 years old. Age when investing begins Rate of return Amount needed at retirement Annual saving necessary for 35 years to reach lump sum target

from college. You plan to start saving for your birthday. After retirement, you expect to live at 40,000 (in today’s dollars) every year from the r 20 years). You can invest, starting when you on rate is likely to be 5 percent.

21 25 65 85 40,000 5%

at age 65 to be able to draw the o investment is likely to be 10

10% 342,286 $4,353,086.79

, starting at age 26 and ending m at age 65? ($9,835.43)

nù é CF1 ê æ 1+ g ö ú PVAn = ´ 1- ç ÷ ê (i - g) ë è 1+ i ø úû

n= i%= FV $4,353,086.79

40 10.00% FVIF 45.25925557

ANNUAL WITHDRAWAL $ 40,000

FVIF 8.55715028

FVA $5,160,266.49

FVIFA 259.0565187

turn to be 8 percent per year

8% 342,286 $5,160,266.49 ($19,919.46) 15%

342,286 $3,011,353.29 FVA $3,011,353.29

($1,692.64)

n you turn 30 years old and f (i) 8 percent, (ii) 10 percent,

30 30 8% 10% $5,160,266.49 $4,353,086.79 ($29,946.39) ($16,061.61)

30 15% $3,011,353.29 ($3,417.45)

g when you are 35 years old. 35 35 8% 10% $5,160,266.49 $4,353,086.79 ($45,551.91) ($26,463.50)

35 15% $3,011,353.29 ($6,926.71)

FVIFA 1779.090308

nù é æ ö 1+ g ú ´ ê1- ç ÷ ê ) ë è 1+ i ø úû

FVIFA PMT 442.5925557 $9,835.43

INFLATION ADJUSTED $ 342,286.01 PMT $19,919.46

[C]

[B]

PMT $1,692.64

[C]

FVA $5,160,266.49 $4,353,086.79 $3,011,353.29

FVIFA PMT 172.316804 $29,946.39 271.024368 $16,061.61 881.170156 $3,417.45

[D] [D] [D]

FVA $5,160,266.49 $4,353,086.79 $3,011,353.29

FVIFA PMT 113.283211 $45,551.91 164.494023 $26,463.50 434.745146 $6,926.71

[D] [D] [D]

STP #6.1.

Expected Cash Flow Rate of return

Freisinger, Inc., is expecting a new project to start paying off, beginning a next year. It expects cash flows to be as follows: Year 1 $433,676

Year 2 Year 3 $478,452 $475,455

7.80%

If Freisinger can reinvest these cash flows to earn a return of 7.8 percent what is the future value of this cash flow stream at the end of five years? What is its present value?

Future value

$2,788,620.68 YEAR

Present value

$1,915,559.47

1 2 3 4 5

CFs $433,676.00 $478,452.00 $475,455.00 $478,326.00 $535,444.00

7.80% PVIF 0.927644 0.860523 0.798259 0.7405 0.68692

start paying off, beginning at the end of ws: Year 4 $478,326

Year 5 $535,444

earn a return of 7.8 percent, m at the end of five years?

PV $402,296.85 $411,718.95 $379,536.14 $354,200.32 $367,807.22 $1,915,559.47

FVIF 1.3504 1.2527 1.1621 1.0780 1.0000

FV $585,653.08 $599,369.52 $552,518.65 $515,635.43 $535,444.00 $2,788,620.68

STP#6.2 Compare an annuity due with an ordinary annuity. The payments for both are made an are of the same dollar amounts. The two annuities also have the same duration in yea same discount rate. Which of the following statements is/are correct? a. The present value of the ordinary annuity is greater. b. The present value of the annuity due is greater. c. The future value of the ordinary annuity is greater. d. The future value of the annuity due is greater. The cash flows of the annuity due are received at the beginning of the period, resulting in less discounting and a higher PV and more compounding and a higher FV. Both b and d are correct.

nts for both are made annually and he same duration in years and the orrect?

STP#6.3 You plan to set up an endowment at your Alma Mater which will fund $200,000 of scholarships each year indefinitely. If the principal (the amount you donate) can be inv at 5.5 percent, compounded annually, how much do you need to donate to the univers today, so that the first scholarships can be awarded one year from now? Annual payment needed (PMT) Investment rate of return (i) Term of payment Present value of investment needed Amount you need to donate today = PV of Perpetuity = PV of Perpetuity = PMT / i = $200,000/0.055$3,636,363.64 =

which will fund $200,000 of e amount you donate) can be invested ou need to donate to the university ne year from now? $200,000 5.5% Perpetuity PV $3,636,363.64

STP#6.4 Annalise Genric wants to open a restaurant in a historic building. The property can be leased for 20 years, but not purchased. She believes her restaurant can generate a n cash flow of $76,000 the first year and expects an annual growth rate of 4 percent thereafter. If a discount rate of 15 percent is used to evaluate this business, what is th present value of the cash flows that it will generate? Length of lease (n), in years Next year's net cash flow (CF1), in $ Expected annual growth rate (g) Required rate of return (i) Present value of growing annuity (PVAn)

20 $76,000.00 4% 15% ?

nù 20 ù é é CF1 ê æ 1+ g ö ú $76,000 ê æ 1.04 ö ú PVAn = ´ 1- ç ´ 1- ç ÷ = ÷ = $690,909´ 0.86612 = $598,410.10 (i - g) êë è 1+ i ø úû (0.15- 0.04) êë è 1.15 ø úû

Present value of this annuity

$598,410.10

building. The property can be restaurant can generate a net al growth rate of 4 percent uate this business, what is the

STP#6.5 A credit card offers financing at an APR of 18 percent, with monthly compounding on o charges. What is the effective annual rate (EAR)? Interest rate (i) = Frequency of compounding (m) = EAR

18% 12 19.56%

8 percent, with monthly compounding on outstanding EAR)?

é iù é 0.18 ù EAR = ê1+ ú -1 = ê1+ ú -1 = 1.1956 -1 = 0.1956 = 19.56% 12 û ë mû ë 12

19.56%

7.2. Expected returns: John is watching an old game show rerun on television called Let’s Ma Deal in which the contestant chooses a prize behind one of two curtains. Behind one of th curtains is a gag prize worth $150, and behind the other is a round-the world trip worth $7, The game show has placed a subliminal message on the curtain containing the gag prize, which makes the probability of choosing the gag prize equal to 75 percent. What is the expected value of the selection, and what is the standard deviation of that selection?

Gag prize Main prize (Car)

Probability of choosing it Value $150 75% $7,200

25%

Expected value of selection

$1,912.50

Standard deviation of selection

$3,052.74

n television called Let’s Make a curtains. Behind one of the nd-the world trip worth $7,200. n containing the gag prize, 75 percent. What is the ion of that selection?

7.3. Expected returns: You have chosen biology as your college major because you would lik a medical doctor. However, you find that the probability of being accepted to medical scho about 10 percent. If you are accepted to medical school, then your starting salary when yo graduate will be $300,000 per year. However, if you are not accepted, then you would cho work in a zoo, where you will earn $40,000 per year. Without considering the additional educational years or the time value of money, what is your expected starting salary as wel standard deviation of that starting salary? Event

Probability

Salary

Accepted into Medical school

10%

$ 300,000

Work in a zoo

90%

Expected starting salary

$66,000.00

Standard deviation of starting salary

$78,000.00

40,000

because you would like to be epted to medical school is arting salary when you d, then you would choose to ering the additional starting salary as well as the

7.5. Single asset portfolios: Stocks A, B, and C have expected returns of 15 percent, 15 perc percent, respectively, while their standard deviations are 45 percent, 30 percent, and 30 pe respectively. If you were considering the purchase of each of these stocks as the only hold portfolio and the risk-free rate is 0 percent, which stock should you choose?

Stock

Expected Return

Standard Deviation

A B C

15% 15% 12%

45% 30% 30%

Stock B because it has the lowest risk per unit of return

ns of 15 percent, 15 percent, and 12 nt, 30 percent, and 30 percent e stocks as the only holding in your u choose?

Coefficient of Variation 3.00 2.00 2.50

7.12. The security market line: If the expected return on the market is 10 percent and the risk-free rate is 4 percent, what is the expected return for a stock with a beta equal to 1.5? What is the market risk premium for the set of circumstances described? E(Rm) Expected return on the market 10% Rf Risk-free rate 4% Beta β 1.5 Stock's expected return

(Rcs)

13%

Market risk premium

E(Rm) − Rf

7.13.

Expected returns: Jose is thinking about purchasing a soft drink machine and placing business office. He knows that there is a 5 percent probability that someone who profi each soft drink sold is $0.10. If Jose expects a thousand people per day to pass by the machine and requires a complete return of his investment in one year, then what is the maximum price that he should be willing to pay for the soft drink machine? Assume 25 working days in a year, and ignore taxes and the time value of money. Probability of purchase # of potential purchasers per day Profit per purchase # of working days in a year Expected period for return of investment

5% 1000 0.1 250 1 year

Maximum price that Jose should be willing to pay

$1,250.00

k machine and placing it in a at someone who profit on per day to pass by the e year, then what is the machine? Assume 250 money.

7.14. Interpreting the variance and standard deviation: The distribution of grades in an introductory finance class is normally distributed, with an expected grade of 75. If the standard deviation of grades is 7, in what range would you expect 95 percent of the grades to fall? Expected value of grade in the introductory finance class Standard deviation of grades 95% of the grades will fall within the range of ==>

Range for 95% of the grades =

75 7

(+ and -)1.96 standard deviations from th 61.28

88.72

stribution of grades in expected grade of ould you expect 95

6 standard deviations from the mean

7.15.

Calculating the variance and standard deviation: Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be −25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.4, 0.5, and 0.1, respectively, then what are the expected return and the standard deviation of the return on Kate’s investment? State of the Economy

Probability

Healthy Soft Recession

Rate of return

0.4 0.5 0.1

30% 10% -25%

Expected return on investment

14.50%

Expected Standard Deviation

16.19%

tly invested in real day. She has c scenarios. She will generate a 30 he return will be 10 s into a recession. If 0.4, 0.5, and 0.1, d deviation of the

7.16.

Calculating the variance and standard deviation: Barbara is considering investing i that the return on that investment is particularly sensitive to how the economy is perfor suggests that four states of the economy can affect the return on the investment. Usin and probabilities below, find the expected return and the standard deviation of the retu investment. Boom Good Level Slump

Prob 0.1 0.4 0.3 0.2

Return 25.00% 15.00% 10.00% -5.00%

Prob.*Return 2.50% 6.00% 3.00% -1.00% Expected Return=

10.50%

a is considering investing in a stock and is aware how the economy is performing. Her analysis rn on the investment. Using the table of returns andard deviation of the return on Barbara’s (Rs - ER)2*Prob 0.0021 0.0008 0.0000 0.0048

Prob.*Return

Variance =

0.0077

Standard deviation=

8.79%

7.17.

Calculating the variance and standard deviation: Ben would like to invest in gold an aware that the returns on such an investment can be quite volatile. Use the following ta of states, probabilities, and returns to determine the expected return and the standard deviation of the return on Ben’s gold investment.

Boom Good OK Level Slump

Prob 0.1 0.2 0.3 0.2 0.2

Return 40.00% 30.00% 15.00% 2.00% -12.00%

Prob*Rs 0.04 0.06 0.045 0.004 -0.024 Expected Return 12.50% Variance= Standard Deviation=

d like to invest in gold and is atile. Use the following table return and the standard

(Rs-ER)2*Prob 0.0075625 0.006125 0.0001875 0.002205 0.012005 0.028085 16.76%

7.18.

Single asset portfolios: Using the information from problems 7.15, 7.16, and 7.17, ca coefficient of variation.

Problem 7.15 State of the Economy

Probability

Healthy Soft Recession

0.4 0.5 0.1

Expected return on investment Expected Standard Deviation Expected Coefficient of Variation

Problem 7.16 Prob Boom 0.1 Good 0.4 Level 0.3 Slump 0.2

Return 25.00% 15.00% 10.00% -5.00% Expected Return=

Problem 7.17 Prob Boom 0.1 Good 0.2 OK 0.3 Level 0.2 Slump 0.2

Return 40.00% 30.00% 15.00% 2.00% -12.00%

Expected Return=

problems 7.15, 7.16, and 7.17, calculate each

Rate of return 30% 10% -25% 14.50% 16.19% 1.12

(Rs - ER)2*Prob 0.0021 0.0008 0.0000 0.0048

Prob.*Return 2.50% 6.00% 3.00% -1.00% 10.50%

Prob*Rs 0.04 0.06 0.045 0.004 -0.024

Variance =

0.0077

Standard deviation=

8.79%

Coefficient of Variation =

0.84

(Rs - ER)2*Prob 0.0075625 0.006125 0.0001875 0.002205 0.012005

12.50% Variance= Standard Deviation= Coefficient of Variation =

0.028085 16.76% 1.34

7.19.

Portfolios with more than one asset: Emmy is analyzing a two-stock portfolio that consists of a Utility stock and a Commodity stock. She knows that the return on the Utility stock has a standard deviation of 40 percent and the return on the Commodity stock has a standard deviation of 30 percent. However, she does no know the exact covariance in the returns of the two stocks. Emmy would like to p the variance of the portfolio for each of three cases—covariance of 0.12, 0, and −0.12—in order to understand how the variance of such a portfolio would react. D the calculation for each of the extreme cases (0.12 and −0.12), assuming an equ proportion of each stock in your portfolio.

Standard deviation

Utility Stock 40%

Commodity Stock 30%

Proportion invested

50%

Squared proportion Variance

0.25 0.16

0.25 0.09

Covariance 0.12 0 -0.12

Portfolio Variance 0.12 0.06 0.00

yzing a two-stock portfolio She knows that the return ent and the return on the ent. However, she does not ocks. Emmy would like to plot covariance of 0.12, 0, and ch a portfolio would react. Do d −0.12), assuming an equal

7.20.

Portfolios with more than one asset: Given the returns and probabilities for the three covariance between the returns of Stock A and Stock B. For convenience, assume tha 11.75 percent and 18 percent, respectively.

#REF! #REF! #REF! Expected Return

#REF! #REF! #REF! #REF!

Return(A) #REF! #REF! #REF! 0.1175

rns and probabilities for the three possible states listed here, calculate the B. For convenience, assume that the expected returns of Stock A and Stock B are

Return(B) #REF! #REF! #REF! 0.18

Rs,a − E(Ra ) #REF! #REF! #REF!

Rs,b − E(Rb) #REF! #REF! #REF! Covariance (Ra,Rb)

Ps × (Rs,a − E(Ra )) × (Rs,b − E(Rb)) #REF! #REF! #REF! #REF!

7.24. CAPM: Damien knows that the beta of his portfolio is equal to 1, but does not know the r return or the market risk premium. He also knows that the expected return on the market What is the expected return on Damien’s portfolio? Portfolio beta Expected Return on market

1 8%

Portfolio expected return = Risk-free rate + (Expected rate on Market - Risk-free rate)*Po Since Portfolio beta = 1; ====> Portfolio expected rate = Risk-free rate + Expected rate on market - Risk-free ra ====> Portfolio expected rate = Expected rate on market = 8%

but does not know the risk-free rate of ed return on the market is 8 percent.

ket - Risk-free rate)*Portfolio beta

on market - Risk-free rate

7.25 CAPM: In February 2014 the risk free rate was 4.75 percent, the market risk premium was 6 percent and the beta for Twitter stock was 1.31. What is the expected return that is consistent with the systematic risk associated with the

E(RTwitter stock) = Rrf + βTwitter srock × [E(Rm) - Rrf] Rrf β Market Risk Premium E(RTwitter stock)

4.75% 1.31 6.00% 12.61%

rket risk hat is the ted with the

7.26 CAPM: The market risk premium is 6 percent and the risk free rate is 5 percent. If the expected return on a bond is 6.5 percent, what is its beta?

E(Rbond) = Rrf + βbond × [E(Rm) - Rrf] E(Rbond) Risk Premium Rrf

6.50% 6.00% 5.00%

βbond

25.00%

7.27 David is going to purchase two stocks to form the initial holdings in his portfolio. Iron stock has an expected return of 15 percent, while Copper stock has an expected return of 20 percent. If David plans to invest 30 percent of his funds in Iron and the remainder in Copper, then what will be the expected return from his portfolio? What if David invests 70 percent of his funds in Iron stock? Iron stock Copper stock Expected return 15% 20% Proportion invested Portfolio expected return

Proportion invested Portfolio expected return

30%

70%

18.5% Iron stock 70% 16.5%

Copper stock 30%

holdings in his t, while Copper ns to invest 30 , then what will be ests 70 percent of

7.29 In order to fund her retirement, Glenda requires a portfolio with an expected return of percent per year over the next 30 years. She has decided to invest in Stocks 1, 2, and with 25 percent in Stock 1, 50 percent in Stock 2, and 25 percent in Stock 3. If Stocks 2 have expected returns of 9 percent and 10 percent per year, respectively, then what minimum expected annual return for Stock 3 that will enable Glenda to achieve her investment requirement? Stock Weight Expected return Weight * Expected return 1 25% 9% 2 50% 10% 3 25% ? Desired expected return 12% Minimum expected return for Stock 3 =

19.0%

olio with an expected return of 12 ed to invest in Stocks 1, 2, and 3, 5 percent in Stock 3. If Stocks 1 and er year, respectively, then what is the nable Glenda to achieve her Weight * Expected return 2.25% 5.00%

7.34 The expected return on the market portfolio is 15 percent, and the return on the risk-free security is 5 percent. What is the expected return on a portfolio with a beta equal to 0.5? Expected return on market

15%

Risk-free return

Portfolio beta

0.5

Expected return on portfolio

10%

7.35 You have been provided the following data on the securities of three firms and the market:

Security Stock A Stock B Stock C Market Portfolio Treasury-bills

E[Ri] 0.15 0.15 0.1 0.1 0.05

Standard Deviation 0.18 0.02 0.04 0

Co-Variance 1.0 0.5

Assume the CAPM and SML are true and fill in the missing values in the table. Would you invest in the stock of any of the three firms? If so, which one(s) and why?

Security Stock A Stock B Stock C Market Portfolio Treasury-bills

E[Ri] 0.15 0.15 0.1 0.1 0.05

Standard Deviation 1.00 0.18 0.02 0.04 0

Co-Variance 1.0 0.5 0.00 0.00 0.00

The missing values in the table are: Beta A = [(Covariance of stock A return and return on market portfolio) x (Standard Dev Beta of Stock A Covariance of stock A return and return on market portfolio Standard Deviation of Return on Market Portfolio Standard Deviation of Return on Stock A Expected Return on Stock B Standard Deviation of Stock B Standard Deviation of Market Portfolio Covariance between Stock B and Market Portfolio Beta of Stock B Expected Return on Stock C Standard Deviation of Stock C

Standard Deviation of Market Portfolio Beta of Stock C Covariance between Stock C and Market Portfolio

2) Using Equation for the CAPM, you can calculate the required returns for the differen Required Return on Stock A Required Return on Stock B Required Return on Stock c Compare the Required Returns with the Expected Returns given in the Table above: Required Return Required Return on Stock A Required Return on Stock B Required Return on Stock c

urities of three firms and the market:

Beta 1.5 0.5

sing values in the table. ? If so, which one(s) and why?

Beta 1.5 0.0 0.5 0.0 0.0

on market portfolio) x (Standard Deviation of Return on Stock A)] / (standard deviation of return on market p 1.5 1.0 Covariance of market return on the market return 0.04 Beta of the market portfolio 0.06 Covariance between treasury bill return and market return 0.15 Beta of treasury bill 0.18 0.04 0.5 2.25 0.10 0.02

0.04 0.5 1.00

the required returns for the different shares: 12.50% 5.00% 7.50%

Returns given in the Table above: Required Return Expected Return 12.50% 15.00% Buy Stock A 5.00% 15.00% Avoid Stock B 7.50% 10.00% Buy Stock C

E(Ri) = Rrf + (Rm - Rrf)β

viation of return on market portfolio) 1.0 1.0 0.0 0.0

STP7.1 Given the following information from Capstone Corporation, what price could CAPM predict that the company's stock will trade for 1 year from today. Assume that the risk free rate is 3 percent and that the market risk premium is 8 percent. Beta = Current stock price = Annual divident =

0.65 $64.61 $1.92

Using CAPM, we find:

E(RCapstone ) = Rrf + bCapstone ´(E(Rm )- Rrf ) = 0.03+0.65´0.08= 0.082 =8.2%

Uning the total holding period return formula (Equation 7.1), we can solve for the stock price in o

P1 - P0 +CF1 P1 -$64.61+$1.92 RT = Þ 0.082 = Þ P1 = $67.99 P0 $64.61

Predicted price of the stock =

$ 67.99

ation, what price could CAPM om today. Assume that the risk is 8 percent.

´0.08= 0.082 =8.2%

can solve for the stock price in one year:

P1 = $67.99

STP7.2 You are considering investing in a mutual fund. The fund is expected to earn a return o percent in the next year. If its annual return is normally distributed with a standard deviation of 6.5 percent, what return can you expect the fund to beat 95% of the time?

Since the annual returns earned by the mutual fund are normally distributed, a 90 perce confidence level corresponds to 1.645 standard deviations from the mean.

Therefore, 90 percent of the time you would expect the annual return for the next year t be in the range: = 0.15 ± (1.645 × 0.065) The lower end of this range is: = 0.15 − (1.645 × 0.065) = 0.04308 = 4.31% which is the return that you can expect the fund to beat 95 percent of the time Return that you can expect the fund to beat 95% of the time =

is expected to earn a return of 15 stributed with a standard und to beat 95% of the time?

normally distributed, a 90 percent s from the mean.

nnual return for the next year to

5 percent of the time 4.31%

STP7.3

You have just invested in a portfolio of three stocks. The amount of money that you in its beta are summarized below. Calculate the beta of the portfolio and used the capit (CAPM) to compute the expected rate of return for the portfolio. Assume that the exp market is 15 percent and that the risk-free rate is 7 percent. Stock

Investment

Beta

A B C

$200,000 300,000 500,000

1.50 0.65 1.25

Portfolio Beta =

b p = å wi bi i=1

A B C Total

200000 300000 500000 1000000

20% 30% 50% 100%

βp = (0.20 × 1.50) + (0.30 × 0.65) + (0.50 × 1.25) = E(Rportfolio) = Rrf + βPortfolio (E(RM) − Rrf) = 0.07 + [1.12 × (0.15 − 0.07)] = 0.1596 =

The amount of money that you invested in each stock and the portfolio and used the capital asset pricing model he portfolio. Assume that the expected rate of return on the ercent.

1.12

15.96%

8.1.

Bond price: BA Corp is issuing a ten-year bond with a coupon rate of 8 percent. The interest rate for similar bonds is currently 6 percent. Assuming annual payments, what is the value of the bond?

Maturity 10 years Coupon rate ## Expected yield ## Present value of bond = $1,147.20 Alternate solution: n coupon rate i% Par Value of Bond =

10 PMT PVIF PVIFA 8.00% $80.00 0.55839 7.360087 6.00% $1,000.00 (PMT)(PVIFA) + (Par)(PVIF)

n rate of 8 percent. ming annual

Par Value $1,000.00 $1,147.20

8.2.

Bond price: Pierre Dupont just received a cash gift from his grandfather. He plans to invest in a five-year bond issued by Venice Corp that pays an annual coupon of 5.5 percent. If the current market rate is 7.25 percent, what is the maximum amount Pierre should be willing to pay for this bond?

Maturity Coupon rate Current market rate

5 years 5.50% 7.25%

Maximum amount Pierre should pay Alternate solution: n 5 coupon rate 5.50% i% 7.25% Par $1,000.00

$928.72 PMT $55.00

PVIF PVIFA PAR 0.704715 4.0729 $1,000.00

m his grandfather. Corp that pays an e is 7.25 percent, o pay for this bond?

VALUE $928.72

8.3. Bond price: Knight, Inc., has issued a three-year bond that pays a coupon of 6.10 percent are made semiannually. Given the market rate of interest of 5.80 percent, what is the mark bond? Coupon rate 6.10% Number of years to maturity 3 Market rate of interest 5.80% # of coupon payments per year 2 Market value of bond Alternate solution: n 3 coupon rate 6.10% m 2 i% 5.80% PAR $1,000.00

$1,008.15

6 3.05% 2.90%

PMT 30.5

PVIF 0.84238

a coupon of 6.10 percent. Coupon payments percent, what is the market value of the

PVIFA PAR 5.43519 $1,000.00

VALUE $1,008.15

8.4. Bond price: Regatta Inc. has seven-year bonds outstanding that pay a 12 percent coupon rate. Investors buying these bonds today can expect to earn a yield to maturity of 8.875 percent. What is the current value of these bonds? Assume annual coupon payments.

Maturity Coupon rate Expected yield Present value of bond = Alternate solution: n 7 coupon rate 12.00% i% 8.875% Par $1,000.00

7 years 12% 8.875% $1,157.94 PMT PVIF PVIFA PAR $120.00 0.55145 5.05413 $1,000.00

a 12 percent coupon o maturity of 8.875 oupon payments.

VALUE $1,157.94

8.5.

Bond price: You are interested in investing in a five-year bond that pays 7.8 percen with interest to be received semiannually. Your required rate of return is 8.4 percent. most you would be willing to pay for this bond?

Coupon rate Number of years to maturity Market rate of interest # of coupon payments per year Market value of bond Alternate solution: n 5 coupon rate 7.80% i% 8.40% m 2 PAR $1,000.00

7.80% 5 8.40% 2 $975.91

10 3.90% 4.20%

PMT PVIF $39.00 0.66271

ear bond that pays 7.8 percent coupon d rate of return is 8.4 percent. What is the

PVIFA PAR VALUE 8.03074 $1,000.00 $975.91

8.6.

Zero coupon bonds: Diane Carter is interested in buying a five-year zero coupon bond whose face value is $1,000. She understands that the market interest rate for similar investments is 9 percent. Assume annual coupon payments. What is the current value of this bond?

Maturity Coupon rate Expected yield

5 0% 9%

years

Present value of bond =

($649.93)

Alternate solution: n 5 Par $1,000.00 i% 9.00% coupon rate 0.00%

PMT $0.00

PVIF PVIFA PAR 0.64993 3.88965 $1,000.00

ing a five-year zero ands that the . Assume annual nd?

VALUE $649.93

8.7.

Zero coupon bonds: Ten-year zero coupon bonds issued by the U.S. Treasury have of $1,000 and interested is compounded semiannually. If similar bonds in the market percent, what is the value for these bonds?

Maturity Coupon rate Face value Opportunity cost Coupon type

10 years 0% $ 1,000 10.50% 2

Market value

$359.38

Alternate solution: n 10 coupon rate 0.00% Par $1,000.00 m 2 i% 10.50%

5.25%

PMT $0.00

PVIF PVIFA 0.35938 12.2022

e U.S. Treasury have a face value bonds in the market yield 10.5

PAR $1,000.00

VALUE $359.38

8.8.

Zero coupon bonds: Northrop Real Estate Company is planning to fund a developme 10-year zero coupon bonds with a face value of $1,000. Assuming semiannual compo the price of these bonds if the appropriate discount rate is 14 percent? Maturity Coupon rate Face value Opportunity cost Coupon type

10 years 0% $ 1,000 14.00% 2

Market value

$258.42

Alternate solution: n 10 Par $1,000.00 m 2 i% 14.00% coupon rate 0.00%

7.00%

PMT 0

PVIF 0.25842

lanning to fund a development project by issuing ssuming semiannual compounding, what will be 14 percent?

PVIFA PAR 10.594 $1,000.00

VALUE $258.42

8.9.

Yield to maturity: Ruth Hornsby is looking to invest in a three-year bond that pays se coupon payments at a rate of 5.875 percent. If these bonds have a market price of $9 yield to maturity and effective annual yield can she expect to earn? Maturity Coupon rate Face value Market price Coupon type

3 years 6% $ 1,000 $ 981.13 2

Yield to maturity Effective annual yield

Alternate solution: n 3 m 2 coupon rate 5.875% Par 1000 Value

981.13

6.58% 6.69%

6 2.938%

YTM 6.58% PMT PVIF 29.375 0.82347 Annual Yield to Maturity Semi-annual Yield to Maturity Effective Annual Yield

This is a trial and error method to Since this is a discount bond, you

hree-year bond that pays semiannual s have a market price of $981.13, what to earn?

PVIFA PAR VALUE 5.36551 $1,000.00 981.087

Yield to Maturity nnual Yield to Maturity

6.58% 3.29%

e Annual Yield

6.69%

PROVE THIS VALUE 981.13

a trial and error method to determine the YTM. his is a discount bond, you know that the coupon rate < YTM.

8.10.

Yield to maturity: Rudy Sandberg wants to invest in four-year bonds that are These bonds have a coupon rate of 6 percent and pay semiannual coupon pa market yield on this bond?

Maturity Coupon rate Face value Market price Coupon type Market yield Alternate solution: n 4 value $868.43 coupon rate 6.00% m 2 Par $1,000.00

4 years 6% $ 1,000 $ 868.43 2 10.08%

8 3.00%

PMT $30.00

YTM 10.08% PVIF PVIFA 0.67478 6.45277

Annual YTM Semi-annual YTM Effective YTM

This is a trial and error method to determine Since this is a discount bond, you know tha

st in four-year bonds that are currently priced at $868.43. d pay semiannual coupon payments. What is the current

PAR $1,000.00

VALUE $868.36

PROVE THIS VALUE $868.43

10.0800% 5.0400% 10.3340%

d error method to determine the YTM. scount bond, you know that the coupon rate < YTM.

8.11. Realized yield: Josh Kavern bought ten-year, 12 percent coupon bonds issued by the U.S $913.44. If he sells these bonds, which have a face value of $1,000, at the current price o yield on the bonds? Assume similar coupon-paying bonds make annual coupon payments

Original maturity Remaining maturity Purchase price Selling price Face value Coupon rate Realized yield Alternate solution: coupon rate maturity Purchased Remaining maturity Par Purcahse Price Selling Price

10 years 7 years $ 913.44 $804.59 $1,000 12% 9.52%

12.00% 10 years 3 years ago 7 years $1,000.00 $913.44 $804.59

PMT $120.00 REALIZED RATE PMT $120.00

REALIZED RATE OF RETU NOTE THE FUTURE VALUE

upon bonds issued by the U.S. Treasury three years ago at $1,000, at the current price of $804.59, what is the realized ake annual coupon payments.

YTM 14.01% PVIF PVIFA 0.399392017 4.2870 REALIZED RATE 9.52% PVIF PVIFA 0.761236659 2.50802

PAR $1,000.00

PAR $804.59

VALUE $913.83

VALUE $913.45

PROVE VALUE $913.44

REALIZED RATE OF RETURN IS 9.52%. NOTE THE FUTURE VALUE OR PAR BECOMES THE SELLING PRICE OF $804.59.

8.12 Realized yield: Four years ago, Lisa Stills bought six-year, 5.5 percent coupon bonds for $947.68. If she sells these bonds at the current price of $894.52, what will be the r Assume similar coupon-paying bonds make annual coupon payments. Original maturity Remaining maturity Purchase price Selling price Face value Coupon rate Realized yield

6 years 2 years $ 947.68 $894.52 $1,000 5.50% REALIZED YIELD 4.49%

4.49%

Alternate solution: original maturity 6 Remaining maturity 2 Time period 4 Coupon rate 5.50% Par $1,000.00 Purchase price $947.68 Selling Price $894.52

PMT $55.00

PVIF PVIFA 0.838882 3.588365

REALIZED RATE OF RETURN IS 4.49%

NOTE THE FUTURE VALUE OR PAR BECOMES THE SELL

ar, 5.5 percent coupon bonds issued by the Fairways Corp. of $894.52, what will be the realized yield on the bonds? on payments.

PAR $894.52

VALUE $947.76

PROVE VALUE $947.68

RN IS 4.49%

E OR PAR BECOMES THE SELLING PRICE OF $894.52

8.13. Bond price: The International Publishing Group is raising $10 million by issuing fifteen-ye bonds with a coupon rate of 8.5 percent. Coupon payments will be be made annually. Investors buying the bonds today will earn a yield to maturity of 8.5 percent. At what price the bonds sell in the marketplace? Explain. Coupon rate Number of years to maturity Market rate of interest # of coupon payments per year Market value of bond Alternate solution: n coupon rate m i% Par

8.50% 15 8.50% 1 $1,000.00

15 8.50% 1 8.50% $1,000.00

PMT PVIF $85.00 0.29414

0 million by issuing fifteen-year will be be made annually. of 8.5 percent. At what price will

PVIFA PAR 8.30424 $1,000.00

VALUE $1,000.00

8.14. Bond price: Pullman Corp issued ten-year bonds four years ago with a coupon rate of 9. sold at par. Today bonds of similar risk and maturity must pay an annual coupon of 6.25 semiannual coupon payments, what will be the current market price of the firm’s bonds? Original maturity Remaining maturity Original selling price Current coupon rate Face value Original coupon rate Number of coupons per year

10 years 6 years $ 1,000 6.25% $1,000 9.375% 2

Current market price of the firms bonds Altrnate solution: original maturity Remaining maturity Coupon rate Par Original selling price New Coupon rate m

10 6 9.375% $1,000.00 $1,000.00 6.25% 2

$1,229.80

20 4.6875%

3.1250%

PMT $46.88

The Payment is based The PVIF and PVIFA a

with a coupon rate of 9.375 percent. At the time of issue, the bonds annual coupon of 6.25 percent to sell at par value. Assuming ce of the firm’s bonds?

PVIF PVIFA PAR 0.54041 14.707 $1,000.00

VALUE $1,229.80

The Payment is based on the original coupon rate of 9.375%. The PVIF and PVIFA are based on the new coupon rate of 6.25%.

8.15.

Bond price: Marshall Company is issuing eight-year bonds with a coupon rate of 6.5 If the current market rate for similar bonds is 8 percent, what will be the bond price? If how many bonds does the firm have to sell?

Coupon rate Number of years to maturity Market rate of interest # of coupon payments per year Amount of capital to be raised Market value of bond # of bonds that would have to be sold Alternate solution: n Coupon rate Par i% m Amount of capital to be raised

6.50% 8 8% 2 1,250,000 $912.61 (1,370)

8 6.50% $1,000.00 8.00% 2 $1,250,000.00

16 3.25% 4.00%

nds with a coupon rate of 6.5 percent and semiannual coupon payments. what will be the bond price? If the company wants to raise $1.25 million,

PMT PVIF PVIFA PAR $32.50 0.53391 11.6523 $1,000.00 NUMBER OF BONDS TO SELL

VALUE $912.61 1370

8.16. Bond price: Rockne, Inc., has outstanding bonds that will mature in six years and pay an 8 percent coupon semiannually. If you paid $1,036.65 today and your required rate of return was 6.6 percent, did you pay the right price for the bond? Remaining maturity (years) 6 Coupon rate 8% Purchase price paid $ 1,036.65 Required rate of return 6.60% Number of coupons per year 2 Appropriate price for the bond Did you pay the right price for the bond? Alternate solution: n Coupon rate Par i% m Purchase price

$1,068.45 No

6 8.00% $1,000.00 6.60% 2 $1,036.65

12 4.00% 3.30%

mature in six years 036.65 today and e right price for the

PMT 40

PVIF PVIFA 0.67732 9.77808

PAR 1000

VALUE 1068.447

INTRINSIC VALUE 1068.4465 PURCHASE PRICE $1,036.65 YOU PAID THE RIGHT PRICE AS IT IS WORTH MORE THAN $1,036.65.

8.17.

Bond price: Nanotech, Inc., has a bond issue maturing in seven years and paying a c (semiannual payments). The company wants to retire a portion of the issue by buying market. If it can refinance at 8 percent, how much will Nanotech pay to buy back its c

Coupon rate Number of years to maturity Market rate of interest # of coupon payments per year

9.50% 7 8% 2

Current purchase price of bond

$1,079.22

Alternate solution: n Coupon rate Par m i%

9.50% $1,000.00 2 8.00%

4.75%

4.00%

PMT $47.50

ven years and paying a coupon rate of 9.5 percent on of the issue by buying the securities in the open ech pay to buy back its current outstanding bonds?

PVIF PVIFA PAR 0.57748 10.5631 $1,000.00

VALUE $1,079.22

8.18.

Zero coupon bonds: Kintel, Inc., wants to raise $1 million by issuing six-year zero co $1,000. Its investment banker states that investors would use an 11.4 percent discoun price would these bonds sell in the marketplace? How many bonds would the firm hav Assume semiannual coupon payments.

Coupon rate Number of years to maturity Market rate of interest # of coupon payments per year Amount of capital to be raised Market value of bond # of bonds that would have to be issued Alternate solution: n coupon rate Par i% m Capital to be raised

0.00% 6 11% 2 1,000,000 $514.16 (1,945)

6 0.00% $1,000.00 11.40% 2 $1,000,000.00

12 0 5.70%

n by issuing six-year zero coupon bonds with a face value of use an 11.4 percent discount rate on such bonds. At what ny bonds would the firm have to issue to raise $1 million?

PMT PVIF PVIFA PAR $0.00 0.51416 8.52347 $1,000.00

Number of bonds to be issued

VALUE $514.16

1945

8.19. Zero coupon bonds: Rockinghouse Corp. plans to issue seven-year zero coupon bonds. It has learned that these bonds will sell today at a price of $439.76. Assuming annual interest payments, what is the yield to maturity on these bonds? Maturity Coupon rate Face value Market price Coupon type

7 years 0% $ 1,000 $ 439.76 1 per year

Yield to maturity

12.453% YTM 12.453%

Alternate solution: n 7 coupon rate 0.00% par $1,000.00 value $439.76 m 1

PV FVIF $439.76 2.274036

FV $1,000.03

Trial and error method to solve for 12.453% YTM

n-year zero coupon of $439.76. Assuming bonds?

PROVE FV $1,000.00

to solve for 12.453% YTM.

8.20. Yield to maturity: Electrolex, Inc., has four-year bonds outstanding that pay a coupon rat payments semiannually. If these bonds are currently selling at $914.89, what is the yield expect to earn on these bonds? What is the effective annual yield? Maturity Coupon rate Face value Market price Coupon type

4 years 6.6% $ 1,000 $ 914.89 2

Yield to maturity Effective annual yield

Alternate solution: n coupon rate par value m

9.19% 9.40%

4 6.60% $1,000.00 $914.89 2

8 3.30%

YTM 9.19% PMT PVIF $33.00 0.69809 EFFECTIVE ANNUAL RATE

g that pay a coupon rate of 6.6 and make coupon 4.89, what is the yield to maturity that an investor can

PROVE PVIFA PAR VALUE VALUE 6.57036 $1,000.00 $914.91 $914.89

TIVE ANNUAL RATE

9.40%

8.21. Yield to maturity: Serengeti Corp. has five-year bonds outstanding that pay a coupon of are priced at $1,064.86, what is the yield to maturity on these bonds? Assume semiannua the effective annual yield? Maturity Coupon rate Face value Market price Coupon type Yield to maturity Effective annual yield

5 years 8.8% $ 1,000 $ 1,064.86 2 7.23% 7.36% YTM 7.230%

Alternate solution: n 5 coupon rate 8.80% par $1,000.00 market value $1,064.86 m 2

10 4.40%

PMT PVIF $44.00 0.70109 ANNUAL YTM EFFECTIVE RATE

anding that pay a coupon of 8.8 percent. If these bonds bonds? Assume semiannual coupon payments. What is

TIVE RATE

PROVE PVIFA PAR 8.26861 $1,000.00 7.23% 7.3607%

VALUE $1,064.91

VALUE $1,064.86

8.22. Yield to maturity: Adrienne Dawson is planning to buy ten-year zero coupon bonds issu these bonds with a face value of $1,000 and are currently selling at $404.59, what is the Assume that interest compounds semiannually on similar coupon paying bonds. Maturity Coupon rate Face value Market price Coupon type Yield to maturity Effective rate of return

10 years 0% $ 1,000 $ 404.59 2 per year 9.26% 9.47% YTM 9.26%

Alternate solution: n 10 coupon 0.00% par $1,000.00 market value $404.59 m 2

20 0.00%

PMT $0.00

PVIF 0.40446

ANNUAL YTM EFFECTIVE RATE

-year zero coupon bonds issued by the U.S. Treasury. If elling at $404.59, what is the expected return on them? oupon paying bonds.

PROVE PVIFA PAR 12.8626 $1,000.00 9.26% 9.47%

VALUE $404.46

VALUE $404.59

8.23. Realized yield: Brown & Co. issued seven-year bonds two years ago that can be called payments at a coupon rate of 7.875 percent. Each bond has a market value of $1,053.40 by the firm today, what is the investor's realized return? Original maturity of bonds (years) Number of years since the bonds were issued Call protection period (years) Coupon rate Market value of bond Call price # of coupons per year Yield to call

8.20%

Alternate solution: call protection period (years) number of years since bond issued n coupon rate market value call price of bond m par

7 2 5 7.875% $ 1,053.40 $ 1,078.75 2

2 3 7.8750%

4 6 3.9375%

$1,053.40 $1,078.75 2 $1,000.00

years ago that can be called after five years. The bond makes semiannual coupon s a market value of $1,053.40, and the call price is $1,078.75. If the bonds are called

YTC 8.20%

PROVE

PMT PVIF PVIFA PAR $39.38 0.78577 5.22511 $1,078.75

YIELD TO CALL (YTC)

VALUE $1,053.39

VALUE $1,053.40

8.20%

YTC FOUND THROUGH TRIAL AND ERROR METHOD.

8.24.

Realized yield: Trevor Price bought ten-year bonds issued by Harvest Foods five yea semiannual coupon payments at a rate of 8.4 percent. If the current price of the bond that Trevor would earn by selling the bonds today?

Original maturity Remaining maturity Purchase price Selling price Face value Coupon rate Number of coupons per year Realized yield Effective yield

Alternate solution: original maturity

10 years 5 years $ 936.05 $1,048.77 $1,000 8.4% 2 10.85% 11.15%

PMT $42.00

remaining maturity 5 m 2 Purchase price $936.05 Selling price $1,048.77 Par value $1,000.00 Coupon rate 8.40%

10 ANNUAL REALIZED YIELD EFFECTIVE ANNUAL YIELD 4.20%

sued by Harvest Foods five years ago for $936.05. The bonds make If the current price of the bond is $1,048.77 each, what is the yield

REALIZED YIELD 10.85% PVIF PVIFA PAR 0.589608727 7.56482 $1,048.77

ANNUAL REALIZED YIELD

10.85%

EFFECTIVE ANNUAL YIELD

11.14%

VALUE $936.09

PROVE VALUE $936.05

8.25. Realized yield: You bought a six-year bond issued by Runaway Corp. four years ago. A pays a coupon rate of 7.375 percent, and interest is paid semiannually. Currently the bo earn on this bond if you sell it today? Original maturity 6 years Remaining maturity 2 years Purchase price $ 974.33 Selling price $1,023.56 Face value $1,000 Coupon rate 7.375% Number of coupons per year 2 Realized yield Effective yield

8.65% 8.84%

Alternate solution: original maturity remaining maturity n m Purchase price Selling price

6 2 4 2 $974.33 $1,023.56

Par value coupon rate

$1,000.00 7.375%

PMT $36.88 8

TREAT THE SELLING PRICE REALIZED YIELD = EFFECTIVE YIELD = 3.6875%

unaway Corp. four years ago. At that time, you paid $974.33 for the bond. The bond semiannually. Currently the bond is priced at $1,023.56. What yield can you expect to

REALIZED YIELD 8.65% PVIF PVIFA PAR 0.7126772 6.6433 $1,023.56

VALUE $974.44

PROVE VALUE $974.33

TREAT THE SELLING PRICE AS THE FUTURE VALUE OR PAR REPLACEMENT. REALIZED YIELD = 8.65% EFFECTIVE YIELD = 8.84%

8.26 Lopez Information Systems is planning to issue ten-year bonds. The going market rate fo made semiannually. The firm is trying to decide between issuing an 8 percent coupon bon a. b. c. d.

What will be the price of an 8 percent coupon bonds? How many coupon bonds would have to be issued? What will be the price of the zero coupon bonds? How many zero coupon bonds will have to be issued?

Number of years until maturity Market rate Coupon rate # of coupons per year Amount of capital to be raised Face value of bond a.

Price of 8% coupon bond

# of 8% bonds that will have to be issued

Price of zero coupon bond

# of zero coupon bonds that will have to be issued

$ $

10 8.125% 8% 2 1,000,000 1,000 ($991.55) 1,009 ($450.94) 2,218

Alternate solution: n 10 coupon rate 8.00% Zero coupon bond rate 0.00% m 2 market rate 8.125% par value $1,000.00 Amount of capital to be raised $1,000,000.00

onds. The going market rate for such bonds is 8.125 percent. Assume that coupon payments will be ssuing an 8 percent coupon bond or a zero coupon bond. The company needs to raise $1 million.

[a] 20 4.00% 0.00%

PMT $40.00

[b]

Number of 8% bonds needed to be issued

4.0625%

[c] [d]

$0.00

PVIF PVIFA 0.450936 13.5154

0.450936 13.5154

PAR $1,000.00

VALUE $991.55

$1,000.00

Number of Zero coupon bonds needed to be issued

1,009 $450.94 2,218

8.27.

a. b.

Showbiz, Inc., has issued eight-year bonds with a coupon of 6.375 percent and semiann return on such bonds is 7.65 percent. What is the market price of these bonds? Now assume that the above bond is callable after five years at an 8.5 percent premium on the face value. What is the expected return on this bond?

Years until maturity Coupon rate Market return Face value # of coupons per year a.

Market price of the bond

Years until first call Call premium Expected return

8 6.375% 7.65% $ 1,000 2

Alternate solution: n 8 coupon rate 6.375% market return 7.650% par value $1,000.00 m 2 years until first call 5 call premiem 8.50% call value $1,085.00

16 3.188% 3.825%

($924.75)

[a]

5 8.50% 9.67%

[b]

75 percent and semiannual coupon payments. The market’s required rate of

n 8.5 percent

PMT $31.88

PVIF PVIFA PAR 0.5484903 11.8042 $1,000.00

VALUE $924.75

EXPECTED RETURN PROVE PMT 8.400% PVIFA FV PV PV $31.875 0.6627089 8.81807 $1,085.00 $1,000.12 $1,000.00 EXPECTED RETURN EFFECTIVE RATE

8.40% 8.58%

8.28.

Peabody Corp. has seven-year bonds outstanding. The bonds pay a coupon of 8.375 $1,063.49. The bonds can be called in three years at a price of $1,075.

a. b. c. d.

What is the yield to maturity on the bond? What is the effective annual yield? What is the yield to call on the bond? If you plan to invest in one of these bonds today, what is the expected yield on the inv

Number of years until maturity Coupon rate Price of bond Number of years until first call Call Price Number of coupons per year

7 8.375% $1,063.49 3 1075 2

a. Yield to maturity on the bond

7.20%

b. Effective annual yield

7.334%

c. Yield to call on the bond

8.20%

d. Expected yield on this investment

8.37%

Alternate solution: n 7 14 couon rate 8.3750% 4.188% price of bond $1,063.49 number of years until first call 3 6 call price $1,075.00 m 2 par value $1,000.00 years to maturity 4 8

PMT $41.88

onds pay a coupon of 8.375 percent semiannually and are currently worth ice of $1,075.

he expected yield on the investment? Explain.

YTM 7.20%

PROVE

PMT PVIF PVIFA PAR VALUE VALUE $41.88 0.6094856 10.8476 $1,000.00 $1,063.73 $1,063.49 [a] YTM =

7.20%

[b] EFFECTIVE RATE =

7.33%

YTC 8.20%

PROVE

PMT PVIF PVIFA PAR VALUE VALUE $41.88 0.7857703 5.22511 $1,075.00 $1,063.50 $1,063.49 [c] YIELD TO CALL =

8.20%

EXPECTED YIELD 6.550% PMT $41.88

PROVE

PVIFA PVIFA PAR 0.7727489 6.93897 $1,000.00

[d] EXPECTED YIELD =

6.55%

VALUE $1,063.32

VALUE $1,063.49

8.29.

The Maryland Department of Transportation has issued 25-year bonds that pay sem of 9.875 percent. The current market rate for similar securities is 11 percent.

a. b. c. d.

What is the bond’s current market value? What will be the bond’s price if rates in the market (i) decrease to 9 percent or (ii) inc Refer to your answers in part b. How do the interest rate changes affect premium bo Suppose the bond were to mature in 12 years. How do the interest rate changes in p

Years to maturity Coupon rate Face value Yield # of coupons per year

25 9.875% $1,000 11% 2

a. Current market value of bond

($904.76)

b. If yield decreases to

9% ($1,086.46)

Bond price =

If yield increases to Bond price =

c. Bond prices, in general, change inversely with changes in interest rates. d. If maturity of bonds =

12 years

If yield decreases to Bond price =

9% ($1,063.42)

Note: Bonds with shorter maturities are less volatile

Alternate solution: years to maturity 25 m 2 n coupon rate 9.8750% par $1,000.00 market yield 11.00% market yield 9.00% market yield 12.00%

50 4.9375% 5.50% 4.50% 6.00%

If yield increases to Bond price =

maturity

ued 25-year bonds that pay semiannual coupon payments at a rate securities is 11 percent.

) decrease to 9 percent or (ii) increase to 12 percent? rate changes affect premium bonds and discount bonds? do the interest rate changes in part b affect the bond prices?

If yield increases to Bond price =

12% ($832.53)

in interest rates.

If yield increases to Bond price =

12% ($866.65)

PMT PVIF PVIFA $49.375 0.06876652 16.9315 $49.375 0.11070965 20.6941 $49.375 0.05428836 15.5206

VALUE $904.76 $1,132.48 $820.62

[a] [b] [b]

Bond prices, in general, change inversely with changes in interest rates

[c]

$49.375 0.34770347 14.4955 $49.38 0.24697855 12.5504

PAR $1,000.00 $1,000.00 $1,000.00

$1,000.00 $1,000.00

$1,063.42 $866.65

[d] [d]

Bonds with shorter maturities are less volatile.

CURRENT MARKET VALUE YIELD DECREASES TO 9% YIELD INCREASES TO 12%

8.30. Rachette Corp. has 18-year bonds outstanding. These bonds, which pay interest semian 9.735 percent and a yield to maturity of 7.95 percent. a. b. c.

Compute the current price of these bonds. If the bond can be called in five years at a premium of 13.5 percent over par value, what is the investor's realized yield? If you bought one of these bonds today, what is your expected rate of return? Explain.

Number of years until maturity Coupon rate Number of coupons per year Face value of bond Yield to maturity of bond a.

Bond's current price =

Number of years until bond can be called Call premium Call price Yield to call

Expected rate of return =

Alternate solution: n m coupon rate YTM Par call premium Call value call maturity

7.83%

18 2

9.735% 4.868% 7.950% 3.975% $1,000.00 13.50% $1,135.00 5 10

N=36

bonds, which pay interest semiannual, have a coupon rate of

13.5 percent over par

xpected rate of return? Explain. 18 9.735% 2 $1,000 7.95% ($1,169.34) 5 13.50% 1135 7.83%

PMT $48.675

over par value

PVIF PVIFA 0.2457868 18.974

PAR $1,000.00

VALUE $1,169.34

[a]

N=36 YTC 10.000% PROVE PMT PVIF PVIFA PAR VALUE VALUE $48.675 0.61391325 9.7129 $1,135.00 $1,169.57 $1,169.34 N=10 10.00% [b] YIELD TO CALL EXPECTED RATE 7.95% PROVE PMT PVIF PVIFA PAR VALUE VALUE $48.68 0.2457868 18.974 $1,000.00 $1,169.34 1169.34

N=36 7.95%

[c]

EXPECTED RATE OF RETURN

Bond's current price

1057.25

8.31 Zippy Corporation just sold $30 million of convertible bonds with a conversion ratio of 4 bond is convertible into 25 shares of Zippy's stock. a. b.

What is the conversion price of Zippy's stock? If the current price of Zippy's stock is $15 and the Company's annual return is normally a standard deviation of $5, what is the probability that investors will find it attractive to c into Zippy stock in the next year?

The conversion price is the par value of the bond divided by the conversion ratio One bond $1,000.00 conversion ratio 40 conversion price = $25.00

conversion price $25.00 current price $15.00 one standard deviation = $5.00 conversion price of $25 = current price of $15 + 2 $5 standard deviations $25.00 $15.00 $10.00

THE STOCK WOULD HAVE TO INCRESE BY 2 STANDARD DEVIATIONS FOR THE 95% OF POSSIBLE OUTCOMES FALL WITHIN 2 STANDARD DEVIATIONS OF THE DISTRIBUTION. THERE WILL BE A 5% PROBABILITY THAT THE STOCK WILL MO THERE WILL BE A 5% PROBABILITY THAT THE STOCK WILL MOVE UP OR DOW DISTRIBUTION IS SYMMETRIC, THERE IS A 2.5% (.05 X .5) CHANCE THAT ZIPPY IT TO BECOME ATTRACTIVE FOR INVESTORS TO EXERCISE THE CONVERSION Probability = 2.5%

ds with a conversion ratio of 40. each $1,000

ny's annual return is normally distributed with estors will find it attractive to convert the bond

ded by the conversion ratio.

tandard deviations

ARD DEVIATIONS FOR THE STOCK TO BECOME ATTRACTIVE. DARD DEVIATIONS OF THE MEAN VALUE OF THE NORMAL THAT THE STOCK WILL MOVE UP OR DOWN BY $10 OR MORE. CK WILL MOVE UP OR DOWN BY $10 OR MORE. SINCE THE NORMAL X .5) CHANCE THAT ZIPPY'S STOCK WILL INCREASE ENOUGH FOR ERCISE THE CONVERSION OPTION IN THE NEXT YEAR.

STP #8.1. Seven years ago, Eastern Corporation issued 20-year bonds that had a $1000 face v paid interest annually, and that had a coupon rate of interest of 7 percent. If the mark of interest is 5.5 percent today, what is the current price of an Eastern Corporation bo Are these bonds selling at a premium or discount? Years to maturity = n = Coupon rate = C = Annual coupon payment = $1,000 × 0.07 = Current market rate = i Present value of bond =

13 7% $70 5.50% PB

é é 1 ù 1 ù ê1ê1nú 13 ú F (1+ i) ú ê (1.055) ú + $1000 = $498.56+ $638. PB = C ´ ê + = $70 ´ ê ú (1+i)n ê 0.055 ú (1.055)13 i ê ú ê ú ë û ë û Current market price of bond These bonds are selling at a premium.

$1,136.76

at had a $1000 face value, 7 percent. If the market rate Eastern Corporation bond?

= $498.56+ $638.20 = $1,136.76

STP #8.2. You are considering investing in a 10-year zero coupon bond that compounds interes semiannually. If the current market rate is 5.65 percent, what is the maximum price y should have to pay for this bond? Years to maturity = n = Coupon rate = C = Current market rate = i Frequency of payments = m =

PB =

10 0% 5.65% 2

Fmn $1,000 = = $572.83 2´10 mn (1+ 0.0565 / 2) (1+ i ) m

Maximum price to pay

-$572.83

on bond that compounds interest nt, what is the maximum price you

STP #8.3. Bigbox, Inc. has bonds outstanding that will mature in eight years. These bonds pay semiannually and have a coupon rate of 4.6 percent. If the bonds are currently sellin what is the yield to maturity that an investor who buys them today can expect to earn effective annual yield? Years to maturity = n = Coupon rate = C = Current market rate = i Semiannual coupon payment = $1,000 × (0.046/2) = Present value of bond = PB

8 4.6% $70 $888.92

é ù 1 ê1ú (1+ i )n ú ê FV 2 ú+ PB = C ´ ê i ê ú (1+ i ) n 2 2 ê ú ë û Try = 6% Þ i / 2 = 3% é ù 1 ê1 16 ú (1.03) ú $1000 = $23 ´ ê + = $288.91+ $623.16 = $912.17 ¹ $888.92 ê ú (1.03)16 0.03 ê ú ë û Try a higher rate, i = 7% Þ i / 2 = 3.5% é ù 1 ê1 ú $1000 (1.035)16 ú ê = $23 ´ + = $278.17 + $576.71 = $854.57 ¹ $888.92 ê ú (1.035)16 0.035 ê ú ë û

Try a lower rate, i = 6.4% Þ i / 2 = 3.2% é ù 1 ê1 ú $1000 (1.032)16 ú ê = $23 ´ + = $284.54 + $604.12 = $888.66 » $888.92 ê ú (1.032)16 0.032 ê ú ë û

The YTM is approximately 6.40% Using a financial calculator, Excel's RATE function, or Excel's Goal Seek provides an exact YTM

If you use a financial calculator, enter:

16 N

Answer: The effective annual yield can be computed as: EAY = (1 + Quoted rate / m)m − 1 = (1 + 0.063955 / 2)2 − 1 = (1.03198 / 2)2 − 1 = 0.064977 =

6.4977%

The same answers using Excel's RATE and EFFECT functions: Yield to maturity 6.3955% Effective annual yield 6.4977%

$23 PMT 6.3955%

ars. These bonds pay interest nds are currently selling at $888.92, day can expect to earn? What is the

2.17 ¹ $888.92

854.57 ¹ $888.92

$888.66 » $888.92

provides an exact YTM =

6.3955%

-$888.92 $1,000 PV FV

9.5 Present value of dividends: Fresno Corp. is a fast-growing company that expec rate of 30 percent over the next two years and then slow down to a growth rate of the following three years. If the last dividend paid by the company was $2.15, est dividends for the next five years. Compute the present value of these dividends if rate of return was 14 percent. Growth rate in Phase 1 Number of years in phase 1 Growth rate in phase 2 Number of years in phase 2 Required rate of return Last paid dividend

30% 2 18% 3 14% $2.15

D1 D2 D3 D4 D5 Present value of the dividends

2.80 3.63 4.29 5.06 5.969957 $14.24

Year 1 2 3 4 5

CFs 2.8 3.63 4.29 5.06 5.97

14.00% PVIF 0.87719 0.76947 0.67497 0.59208 0.51937

PV 2.45614 2.793167 2.895628 2.995926 3.100631 14.24149 Present Value of the Dividends

st-growing company that expects to grow at a n slow down to a growth rate of 18 percent for by the company was $2.15, estimate the sent value of these dividends if the required

ue of the Dividends

9.6 Zero growth: Nynet, Inc., paid a dividend of $4.18 last year. The company does to increase its dividend for the next several years. If the required rate of return is percent, what is the current price of the stock? Dividend paid last year Growth rate of dividends Required rate of return

$4.18 0% 18.50%

Current stock price

$ 22.59

ar. The company does not expect quired rate of return is 18.5

9.7 Zero growth: Knight Supply Corp. has not grown for the past several years and e growth to continue. The firm last paid a dividend of $3.56. If you require a rate of what is the current stock price? Dividend paid last year Growth rate of dividends Required rate of return

$3.56 0% 13.00%

Current stock price

$ 27.38

ast several years and expects this lack of of f you require a rate of return of 13 percent,

9.8 Zero growth: Ron Santana is interested in buying the stock of First National Ban expects no growth in the near future, Ron is attracted by the dividend income. La a dividend of $5.65. If Ron requires a return of 14 percent on such stocks, what is he should be willing to pay for a share of the bank's stock? Dividend paid last year Growth rate of dividends Required rate of return

$5.65 0% 14.00%

Current stock price

$ 40.36

k of First National Bank. While the bank e dividend income. Last year the bank paid on such stocks, what is the maximum price

9.9 Zero growth: The current stock price of Largent, Inc., is $44.72. If the required ra percent, what is the dividend paid by this firm, if the dividend is not expected to gr

Current stock price Required rate of return Dividend growth rate

$44.72 19% 0%

Dividend paid by the firm

$ 8.497

44.72. If the required rate of return is 19 nd is not expected to grow in the near future?

9.10 Constant growth: Moriband Corp. paid a dividend of $2.15 yesterday. The compan expected to grow at a steady rate of 5 percent for the next several years. If stocks o Moriband require a rate of return of 15 percent, what should be the market price of

Dividend just paid Growth rate of dividends Required rate of return

$2.15 5% 15.00%

Current stock price

$ 22.58

5 yesterday. The company's dividend is several years. If stocks of companies like d be the market price of Moribund stock?

9.11 Constant growth: Nyeil, Inc., is a consumer products firm growing at a constan firm’s last dividend was $3.36. If the required rate of return is 18 percent, what stock? Dividend paid last year Growth rate of dividends Required rate of return

$3.36 6.5% 18.00%

Current stock price

$ 31.12

roducts firm growing at a constant rate of 6.5 percent. The ate of return is 18 percent, what is the market value of this

9.12 Constant growth: Reco Corp. is expected to pay a dividend of $2.25 next year. T stock price a year from now is $37.50. If the required rate of return is 14 percent, stock price? Assume constant growth. Dividend expected to be paid next year = D1 = Expected stock price after 1 year = P1 = Required rate of return = i = Current stock price = Price next year = ==> ==> ==> ==> ==> ==>

$2.25 $37.50 14%

P0 = D1/(i-g) P1 = D2/(i-g) P1 = D1(1+g)/(i-g) 37.5= 2.25(1+g)/(.14-g) 37.5 (.14-g) = 2.25+2.25g 5.25-37.5g = 2.25 +2.25g 39.75g=3 g= 7.55% P0 = $34.87

nd of $2.25 next year. The forecast for the of return is 14 percent, what is the current

9.13 Constant growth: Proxicam, Inc., is expected to grow at a constant rate of 7 per the company’s next dividend, which will be paid in a year, is $1.15 and its current price is $22.35, what is the required rate of return on this stock? Constant growth rate expected Next dividend to be paid Current stock price Current stock price =

7% $1.15 $22.35

Next Dividend/(Required rate - constant growth rate)

==>

$22.35 =

$1.15 /(Required rate - 0.07

==>

$22.35 * (Required rate -0.07)=

==>

22.35* r -

$1.56 =

==>

22.35* r

$2.71

==>

12.15%

)

$1.15 $1.15 Note: r = Required rate

w at a constant rate of 7 percent. If ear, is $1.15 and its current stock his stock?

growth rate)

Required rate

9.14 Preferred stock valuation: X-Centric Energy Company has issued perpetual pre stated (par) of $100 and a dividend of 4.5 percent. If the required rate of return is the stock’s current market price? Par value Dividend rate Required rate of return

$100 4.50% 8.25%

Current preferred stock price

$ 54.55

as issued perpetual preferred stock with a equired rate of return is 8.25 percent, what is

9.15 Preferred stock valuation: The First Bank of Ellicott City has issued perpetual p par value. The bank pays a quarterly dividend of $1.65 on this stock. What is the preferred stock given a required rate of return of 11.6 percent? Par value Quarterly dividend paid Required rate of return Current preferred stock price

$100 $1.65 11.60% $ 56.90

ott City has issued perpetual preferred stock with a $100 1.65 on this stock. What is the current price of this 1.6 percent?

9.16 Preferred stock: The preferred stock of Axim Corp. is selling currently at $47.13. of return is 12.2 percent, what is the dividend paid by this stock? Current preferred stock price Required rate of return

$47.13 12.20%

Dividend paid

$5.75

lling currently at $47.13. If the required rate stock?

9.17 Preferred stock: Each quarter, Sirkota, Inc., pays a dividend on its perpetual pre stock is selling at $63.37. If the required rate of return for such stocks is 15.5 perc quarterly dividend paid by this firm? Current preferred stock price Required rate of return

$63.37 15.50%

Annual dividend paid Quarterly dividend paid

$9.82 $2.46

d on its perpetual preferred stock. Today the ch stocks is 15.5 percent, what is the

9.18 Constant growth: Kay Williams is interested in purchasing the common stock of priced at $37.45. The company expects to pay a dividend of $2.58 next year and t constant rate of 7 percent. a. b.

What should the market value of the stock be if the required rate of return is14 pe Is this a good buy? Why or why not?

Current stock price Growth rate of dividends Required rate of return Next year's expected dividend

$37.45 7% 14% $2.58

Market value of the stock Is this a good buy?

$36.86 No, it is overvalued

g the common stock of Reckers, Inc., which is currently of $2.58 next year and to increase its dividend at a

d rate of return is14 percent?

9.19 Constant growth: Your required rate of return is 23 percent. Ninex Corp. has jus dividend of $3.12 and is expected to increase its dividend at a constant rate of 5 p What is the expected price of the stock three years from now? Required rate of return (r) Dividend just paid (Do) Constant growth rate (g)

23% $3.12 5%

Expected price in Year 3, i.e. (P3) = D4/(r-g) where ==>

D4 = D4 = P3 =

Do(1+g)4 $ 3.79 $ 21.07

rcent. Ninex Corp. has just paid a nd at a constant rate of 5 percent. m now?

9.20

Constant growth: Jenny Banks is interested in buying the stock of Fervan, Inc., constant rate of 6 percent. Last year the firm paid a dividend of $2.65. The requir percent. What is the current value of this stock? What should be the price of the s

Dividend paid last year Growth rate of dividends Required rate of return

$2.65 6.0% 16.00%

Current stock price Price in Year 5

$ 28.09 $ 37.59

stock of Fervan, Inc., which is growing at a nd of $2.65. The required rate of return is 16 uld be the price of the stock in year 5?

9.2 Constant Growth: You own shares of Old World DVD Company and are interestedin selling them. With so many people downloading music these days, sales, profits, and dividends at Old World have been declining 6 percent per year. The firm just paid a dividend of $1.15 per share. The required rate of return for a stock this risky is 15 percent. If dividends are expected to decline at 6 percent per year what is a share of the stock worth today? Do g D1 R Po

$1.15 -6.00% $1.08 15.00% $5.15

9.2 Nonconstant growth: You own a company that competes with Old World DVD Company (in the previous problem). Instead of selling DVDs, however, your company sells music downloads from a web site. Things are going well now, but you know that it is only a matter of time before someone comes up with a better way to distribute music. Your company just paid a $1.50 per share dividend and you expect to increase the dividend 10 percent next year. However, you then expect your dividend growth rate to begin going down to 5 percent the following year, 2 percent the next year, and to -3 percent per year thereafter. Based upon these estimates, what is the value of your company's stock? Assume the required Do g1 g2 g3 g4

$1.50 10.00% 5.00% 2.00% -3.00%

D1 D2 D3 D4

$1.6500 $1.7325 $1.7672 $1.7141

12.00%

$11.43

Year 1 2 3 3

12.00% Cash Flow PVIF $1.6500 0.892857 $1.7325 0.797194 $1.7672 0.71178 $11.4276 0.71178

NPV $1.47 $1.38 $1.26 $8.13 $12.25

with Old World DVD s, however, your e going well now, but mes up with a better share dividend and owever, you then ercent the following eafter. Based upon Assume the required

9.23

Nonconstant growth: Tre-Bien, Inc., is a fast-growing technology company. The rapid growth of 30 percent for the next two years, then a growth rate of 17 percen two years. After that, the firm expects a constant growth rate of 8 percent. The fir its first dividend of $2.45 a year from now. If the required rate of return on stocks 22 percent, what is the current price of the stock?

Growth rate in 1st phase Number of years in 1st phase Growth rate in 2nd phase Number of years in 2nd phase Constant growth rate Dividend in Year 1 Required rate of return

30% 2 17% 2 8% 2.45 22%

Calculation of current stock price (P0) Year

Cash flow 1 $ 2.45 =D1 2 3.19 =D2 3 3.73 =D3 4 4.36 =D4 4 33.63 =P4

P0 =

$23.35

Compute the NPV of the stock: 22.00% Year Cash Flow PVIF NPV 1 $ 2.45 0.81967213 $ 2.01 2 $ 3.19 0.6718624 $ 2.14 3 $ 3.73 0.55070689 $ 2.05 4 $ 4.36 0.45139909 $ 1.97 4 $ 33.63 0.45139909 $ 15.18 $23.35

ng technology company. The firm projects a n a growth rate of 17 percent for the following wth rate of 8 percent. The firm expects to pay ired rate of return on stocks with similar risk is

9.24

Nonconstant growth: ProCor, a biotech firm, has forecast the following growth r the next three years: 35 percent, 28 percent, and 22 percent. The company then grow at a constant rate of 9 percent forever. The company paid a dividend of $1.7 week. If the required rate of return is 20 percent, what is the value of this stock?

Growth rate in 1st phase Number of years in 1st phase Growth rate in 2nd phase Number of years in 2nd phase Growth rate in 3rd phase Number of years in 3rd phase Constant growth rate Dividend in Year 0 Required rate of return

35% 1 28% 1 22% 1 9% 1.75 20%

Calculation of current stock price (P0) Year

Cash flow 1 $ 2.36 =D1 2 $ 3.02 =D2 3 $ 3.69 =D3 3 $ 36.56 =P3

P0 =

$27.36

Determine the NPV of the Stock cash flows:

Year 1 2 3 3

Cash Flow $ 2.36 $ 3.02 $ 3.69 $ 36.56

20.00% PVIF 0.833333333 0.694444444 0.578703704 0.578703704

NPV $ $ $ $

1.97 2.10 2.14 21.16 $27.36

t the following growth rates for nt. The company then expects to paid a dividend of $1.75 last e value of this stock?

9.25

Nonconstant growth: Revarop, Inc., is a fast-growth company that is expected t percent for the next four years. It is then expected to grow at a constant rate of 6 first dividend of $4.25 will be paid in year 3. If the required rate of return is 17 pe current value of the stock if dividends are expected to grow at the same rate as th

Growth rate in Years 1- 4 Growth rate in Year 5 onwards Dividend in Year 3 Required rate of return

23% 6% 4.25 17%

Calculation of current stock price (P0) Year

Cash flow =D1 1 $ =D2 2 $ 3 $ 4.25 =D3 4 $ 5.228 4 $ 50.37 =P4

P0 =

$32.325

Determine the NPV of the cash flows:

Year 1 2 3 4 4

Cash Flow $ $ $ 4.25 $ 5.23 $ 50.37

17.00% PVIF NPV 0.854700855 $ 0.730513551 $ 0.624370556 $ 2.65 0.533650048 $ 2.79 0.533650048 $ 26.88 $32.33

pany that is expected to grow at a rate of 23 at a constant rate of 6 percent. Revarop's rate of return is 17 percent, what is the w at the same rate as the company?

9.26

Nonconstant growth: Quansi, Inc., expects to pay no dividends for the next six y projected a growth rate of 25 percent for the next seven years. After seven years, grow at a constant rate of 5 percent. Its first dividend, to be paid in year 7, will be If the required rate of return is 24 percent, what is the stock worth today?

Growth rate in Years 1- 7 Growth rate in Year 8 onwards First dividend paid in Year 7 Required rate of return

25% 5% 3.25 24%

Calculation of current stock price (P0) Year

Cash flow =D1 1 $ =D2 2 $ =D3 3 $ =D4 4 $ =D5 5 $ =D6 6 $ 7 $ 3.25 =D7 7 $ 17.961 =P7

P0 =

$4.71

Determine the current price of Quansi: 24.00% Year Cash Flow PVIF 1 $ 0.806451613 $ 2 $ 0.650364204 $ 3 $ 0.524487261 $ 4 $ 0.422973598 $ 5 $ 0.34110774 $ 6 $ 0.275086887 $ 7 $ 3.25 0.221844264 $ 7 $ 17.96 0.221844264 $

NPV 0.72 3.98 $4.71

ay no dividends for the next six years. It has seven years. After seven years, the firm will end, to be paid in year 7, will be worth $3.25. s the stock worth today?

9.27

Nonconstant growth: Staggert Corp. will pay dividends of $5, $6.25, $4.75, and next four years. Thereafter, the company expects its growth rate to be constant ra percent. If the required rate of return is 18.5 percent, what is the current value of

Growth rate in Year 5 onwards Dividend in Year 1 = Dividend in Year 2 = Dividend in Year 3 = Dividend in Year 4 = Required rate of return

6% $5 $6.25 $4.75 $3 18.5%

Calculation of current stock price (P0) Year

Cash flow 1 $5 =D1 2 $6.25 =D2 3 $4.75 =D3 4 $3 =D4 4 $ 25.440 =P4

P0 =

$25.95

Determine the current value of the stock: 18.50% Year Cash Flow PVIF 1 $5 0.843881857 2 $6 0.712136588 3 $5 0.600959146 4 $3 0.50713852 4 $25 0.50713852

NPV $4.22 $4.45 $2.85 $1.52 $12.90 $25.95

idends of $5, $6.25, $4.75, and $3 for the its growth rate to be constant rate at 6 ent, what is the current value of the stock?

9.28

Nonconstant growth: Diaz Corp. is expected to grow rapidly at a rate of 35 percent for the next seven years. The first dividend, to be paid three years from now, will be $5. After seven years, the company (and the dividends it pays) will grow at a rate of 8.5 percent. What is the value of this stock with a required rate o return of 14 percent?

Growth rate in Years 1- 7 Growth rate in Year 8 onwards First dividend paid in Year 3 Required rate of return

35% 8.5% 5.00 14%

Calculation of current stock price (P0) Year

Cash flow =D1 1 $ =D2 2 $ 3 $ 5.00 =D3 4 $ 6.75 =D4 5 $ 9.11 =D5 6 $ 12.30 =D6 7 $ 16.61 =D7 7 $ 327.62 =P7

P0 =

$155.28

Determine the market price of the stock: 14.00% Year Cash Flow PVIF 1 $ 0.877192982 2 $ 0.769467528 3 $ 5.00 0.674971516 4 $ 6.75 0.592080277 5 $ 9.11 0.519368664 6 $ 12.30 0.455586548 7 $ 16.61 0.399637323 7 $ 327.62 0.399637323

NPV $ $ $ $ $ $ $ $

3.37 4.00 4.73 5.60 6.64 130.93 $155.28

grow rapidly at a rate of 35 nd, to be paid three years from (and the dividends it pays) will of this stock with a required rate of

9.29

Nonconstant growth: Tin-Tin Waste Management, Inc., is growing rapidly. Dividend expected to grow at rates of 30 percent, 35 percent, 25 percent, and 18 percent over four years. Thereafter the company expects dividends to grow at a constant rate of 7 The stock is currently selling at $47.85, and the required rate of return is 16 percent. the dividend for the current year (D0).

Growth rate in Year 1 (g1)

30%

1.12069

Growth rate in Year 2

35%

1.304251

Growth rate in Year 3

25%

1.405443

Growth rate in Year 4

18%

1.429675

7% $ 47.85 16%

16.99724

Growth rate in Year 5 onwards Current stock price Required rate of return Calculation of D0 D0=

$2.15

22.2573

owing rapidly. Dividends are nt, and 18 percent over the next at a constant rate of 7 percent. of return is 16 percent. Compute

=(1+g1)/(1+r) =[(1+g1)(1+g2)]/(1+r)2 =[(1+g1)(1+g2)(1+g3)]/(1+r)3 4

=[(1+g1)(1+g2)(1+g3)(1+g4)]/(1+r)

=[((1+g1)(1+g2)(1+g3)(1+g4)(1+g5))/(r-g5)]*(1/(1+r)4) =Sum of all the above terms

9.30 Equation 9.4 shows the relation between a stock's value and the dividend that is expected ne dividends are also expected to grow at a constant rate forever. If a firm pays all of its earning dividends, show how Equation 9.4 can be rearranged to calculate that firm's P/E ratio. What us about the factors that determine a firm's P/E ratio? The P/E ratio can be written as follows: Po = D1/(R - g) = E1/(R-g)

E1 = the earnings per share next year

Rearranging the formula: Po/E1 = 1 / (R - g)

This formula tells us that the P/E ratio is determined b the risk of the dividend cash flows and the rate at whi they are expected to grow.

the dividend that is expected next year if the er. If a firm pays all of its earnings as ulate that firm's P/E ratio. What does this tell

hare next year

at the P/E ratio is determined by both cash flows and the rate at which

9.31

Riker Departmental Stores have forecasted a high growth rate of 40 percent for th two years, followed by growth rates of 25 percent and 20 percent for the following years. It then expects growth to stabilize at a constant rate of 7.5 percent forever firm paid a dividend of $3.50 recently. If the required rate of return is 18 percent, the current value of Riker's stock?

Growth rate in Years 1-2 Growth rate in Year 3 Growth rate in Year 4 Growth rate in Year 5 onwards Dividend paid recently (D0) Required rate of return

40% 25% 20.0% 7.5% $ 3.50 18%

Calculation of current stock price (P0) Year

Cash flow 1 $ 4.90 =D1 2 $ 6.86 =D2 3 $ 8.58 =D3 4 $ 10.29 =D4 4 $ 105.35 =P4

P0 =

$73.94

Determine the current value of Riker's stock: 18.00% Year Cash Flow PVIF NPV 1 $ 4.90 0.847457627 $ 4.15 2 $ 6.86 0.71818443 $ 4.93 3 $ 8.58 0.608630873 $ 5.22 4 $ 10.29 0.515788875 $ 5.31 4 $ 105.35 0.515788875 $ 54.34 $73.94

rate of 40 percent for the next percent for the following two e of 7.5 percent forever. The of return is 18 percent, what is

9.32 Courtesy Bancorp issued perpetual preferred stock a few years ago. The bank pays an dividend of $4.27 and your required rate of return is 12.2 percent. a. b.

What is the value of the stock given your required rate of return? Should you buy this stock if its current market price is $34.41? Explain.

Annual dividend paid on preferred stock Required rate of return

$4.27 12.2%

Current value of preferred stock

$35.00

If the current market price of this stock is Should this stock be bought?

$34.41 Yes, it is undervalued

ars ago. The bank pays an annual cent.

is undervalued

9.33 Rhea Kirby owns shares in Ryoko Corp. Currently the market price of the stock is $36. expects to grow at a constant rate of 6 percent for the foreseeable future. Its last divide $3.25. Rhea’s required rate of return for such stocks is 16 percent. She wants to find o should sell her shares or add to her holdings. a. b.

What is the value of this stock? Based on your answer above, should Rhea buy additional shares in Ryoko Corp? Why or why not?

Current market price of the stock Constant growth rate Last paid dividend (D0) Required rate of return

$36.34 6% $3.25 16%

Intrinsic value of this stock

$ 34.45

Should Rhea buy additional shares?

No, it is overvalued

price of the stock is $36.34. The company eable future. Its last dividend was worth rcent. She wants to find out whether she

ares in Ryoko Corp?

9.34 Perry, Inc., declared a dividend of $2.50 yesterday. You are interested in investin company, which has forecasted a constant growth rate of 7 percent for its dividen The required rate of return is 18 percent. a. b. c. d. e.

Compute the expected dividends D1, D2, D3, and D4. Compute the present value of these four dividends. What is the expected value of the stock four years from now (P4)? Calculate the present value of P4. Add the answer you got in part b. What is the v stock today? Use the equation for constant growth (Equation 9.4) to compute the price of the s Last paid dividend Constant growth rate Required rate of return

$2.50 7% 18% Present Value

b. c. d.

D1 = $2.68 D2 = $2.86 D3 = $3.06 D4 = $3.28 Sum of PV of D1-D4 P4 = $31.88 P0 =

Using the constant growth dividend discount model:

Po=

$24.32

$2.27 $2.06 $1.86 $1.69 $7.88 $16.44 $24.32

You are interested in investing in this ate of 7 percent for its dividends forever.

om now (P4)? ou got in part b. What is the value of the to compute the price of the stock today.

9.35 Zweite Pharma is a fast-growing drug company. The company forecasts that in the next three years, its dividend growth rates will be 30 percent, 28 percent, and 24 percent, respectively. Last week it paid a dividend of $1.67. After three years, the company expects dividend growth to stabilize at a rate of 8 percent. The required rate of return is 14 percent. a. Compute the dividends for the next three years, and find its present value. b. Calculate the price of the stock at the end of year 3, when the firm settles to a constant growth rate. c. What is the current price of the stock? Growth rate in Year 1 Growth rate in Year 2 Growth rate in Year 3 Growth rate in Year 4 onwards Dividend paid recently (D0) $ Required rate of return

30% 28% 24% 8.0% 1.67 14%

Calculation of current stock price (P0) a.

b. c

Year Cash flow 1 $ 2.17 =D1 2 $ 2.78 =D2 3 $ 3.45 =D3 3 $ 62.02 =P3 P0 = $48.23

Year 1 2 3 3

PV of D1-D3 =

$6.37

Cash Flow $ 2.17 $ 2.78 $ 3.45

14.00% PVIF NPV 0.877193 $ 1.90 0.769468 $ 2.14 0.674972 $ 2.33

0.674972 $

62.02

41.86 $48.23

company forecasts that in the percent, 28 percent, and 24 $1.67. After three years, the e of 8 percent. The required

ind its present value. when the firm settles to a

Dividends NPV $ 2.17 $ 1.90 $ 2.78 $ 2.14 $ 3.45 $ 2.33 $6.37

9.36 Triton Inc. expects to grow at a rate of 22 percent for the next five years then settle to a company recently paid a dividend of $2.35. The required rate of return is 15 percent. a. b. c.

Find the present value of the dividends during the rapid-growth period if dividends grow What is the value of the stock at the end of year 5? What is the value of the stock today? Last paid dividend Growth rate for Year 1-Year 5 Constant growth rate Required rate of return

$2.35 22% 6% 15% Present Value

b. c.

D1 = $2.87 D2 = $3.50 D3 = $4.27 D4 = $5.21 D5 = $6.35 Sum of PV of D1-D5 P5 = $74.80 P0 =

$2.49 $2.64 $2.81 $2.98 $3.16 $14.08 $37.19 $51.27

e next five years then settle to a constant growth rate of 6 percent. The d rate of return is 15 percent.

growth period if dividends grow at the same rate as the company.

9.37

Ceebros Builders is expanding very fast and expects to grow at a rate of 25 perce four years. The company recently paid a dividend of $3.60 but does not expect to dividends for the next three years. In year 4, it intends to pay a $5 dividend and th increase its divdidend at a constant rate of 6 percent. The required rate of return 20 percent.

a. b. c. d.

Calculate the present value of the dividends during the fast-growth period. What is the value of the stock at the end of the fast-growth period (P4)? What is the value of the stock today? Would today’s stock value be driven by the length of time you intend to hold the s Last paid dividend $3.60 Growth rate for Year 1-Year 4 25% Constant growth rate (Year 5 onwards)6% Required rate of return 20% Present Value

b. c.

D1 = $0.00 D2 = $0.00 D3 = $0.00 D4 = $5.00 Sum of PV of D1 − D4 P4 = $37.86 P0 =

No the length of the holding period has no bearing on the stock price.

$0.00 $0.00 $0.00 $2.41 $2.41 $18.26 $20.67

xpects to grow at a rate of 25 percent for the next end of $3.60 but does not expect to pay any intends to pay a $5 dividend and thereafter to ercent. The required rate of return on such stocks is

uring the fast-growth period. e fast-growth period (P4)?

ngth of time you intend to hold the stock?

bearing on the stock price.

STP #9.3 Burnes, Inc. is a mature firm that is growing at a constant rate of 5.5 percent per y last dividend that the firm paid was $1.50 per share. If dividends are expected to g same rate as the firm and the required rate of return of Burne's stock is 12 percen the market value of the company's stock? D0 = g= R= P0 =

$1.50 5.5% 12% D1 R−g

$1.50 × 1.055 = 0.12 − 0.055

$24.35

constant rate of 5.5 percent per year. The are. If dividends are expected to grow at the turn of Burne's stock is 12 percent, what is

STP #9.4 Abacus Corporation will pay dividends of $2.25, $2.95, and $3.15 in the next three years. After three years, the dividends are expected to grow at a constant rate of 4 percent per year. If the required rate of return is 14.5 percent, what is the current value of the Abacus common stock? g constant = D1 = D2 = D4 = R=

4% $2.25 $2.95 $3.15 14.5% Present Value

D1 = D2 = D3 = Sum of PV of D1-D3 P3 = P0 =

$2.25 $2.95 $3.15 $31.20

$1.97 $2.25 $2.10 $6.31 $20.78

$27.10

, and $3.15 in the next three o grow at a constant rate of 4 percent, what is the current

D4 $3.15´1.04 = = $31.20 R - g 0.145 - 0.04 $2.25 $2.95 $3.15 $31.20 P0 = + + + 2 3 1.145 1.145 1.145 1.1453 = $1.97 + $2.25+ $2.10 + $20.78 P3 =

= $27.10

STP #9.5 The preferred stock of Wellcare Inc. is currently trading at $137.50 per share. If the return is 8 percent and this stock has no maturity date, what is the quarterly divide stock? What is the quarterly dividend if the stock will mature in one year and it has $140? With no maturiry date: PS0 = $137.5; R = 8.0% PS0 = $137.5 =

D 0.08

D = $137.50 × 0.08 = $11.00

Annual dividend = $11.00 Quarterly dividend = $11.00 / 4 = $2.75

With a one year maturiry date: We can use Equation 9.7 to solve for the dividend with a one year maturity date:

+ Pmn m m m m PS0 = + + + Þ 2 3 4 i i i i (1+ ) (1+ ) (1+ ) (1+ ) m m m m D D D D + $140 m m m $137.50 = + + + m Þ 2 3 4 (1+ 0.08 ) (1+ 0.08 ) (1+ 0.08 ) (1+ 0.08 ) 4 4 4 4 D D D D + $140 m + m + m $137.50 = m + 2 1.02 (1.02) (1.02)3 (1.02) 4

Using a financial calculator to solve for PMT, we find that the quarterly dividend, D/m = $2.14

at $137.50 per share. If the required rate of what is the quarterly divident paid by this ture in one year and it has a par value of

maturity date:

+ Pmn

)

Þ D

+ $140 m + Þ 3 4 ) (1+ 0.08 ) 4 4

erly dividend, D/m = $2.14

10.1 Net present value: Riggs Corp. management is planning to spend $650,000 on a new marketing campaign. They believe that this action will result in additional cash flows of $325,000 over the next three years. If the discount rate is 17.5 percent, what is the NPV on this project? Year 0 1 2 3 Cost of Capital NPV

Cash flows $ (650,000) $ 325,000 $ 325,000 $ 325,000 17.50% $62,337.34

Year 0 1 2 3

17.50% Cash Flows PVIF NPV $ (650,000) 1.0000 $ (650,000.00) $ 325,000 0.8511 $ 276,595.74 $ 325,000 0.7243 $ 235,400.63 $ 325,000 0.6164 $ 200,340.96 $62,337.34

to spend $650,000 n will result in s. If the discount

10.2. Net present value: Kingston, Inc. management is considering purchasing a new machine at a cost of $4,133,250. They expect this equipment to produce cash flows of $814,322, $863,275, $937,250, $1,017,112, $1,212,960, and $1,225,000 over the next six years. If the appropriate discount rate is 15 percent, what is the NPV of this investment? Year 0 1 2 3 4 5 6 Discount rate NPV

Cash flow $ (4,133,250) $ 814,322 $ 863,275 $ 937,250 $ 1,017,112 $ 1,212,960 $ 1,225,000 15% ($441,933.01)

Year 0 1 2 3 4 5 6

Cash Flows $ (4,133,250) $ 814,322 $ 863,275 $ 937,250 $ 1,017,112 $ 1,212,960 $ 1,225,000

PVIF NPV 1.0000 $ (4,133,250.00) 0.8696 $ 708,106.09 0.7561 $ 652,759.92 0.6575 $ 616,257.09 0.5718 $ 581,537.09 0.4972 $ 603,055.49 0.4323 $ 529,601.30 ($441,933.01)

purchasing a new o produce cash 60, and $1,225,000 ercent, what is the

10.3.

Year 0 1 2 3 4 5 Discount rate

NPV Decision

$134,986.27 YES

Year 0 1 2 3 4 5

Cash Flows ($3,300,000) $875,123 $966,222 $1,145,000 $1,250,399 $1,504,445

PVIF 1 0.84746 0.71818 0.60863 0.51579 0.43711

NPV ($3,300,000) $741,630 $693,926 $696,882 $644,942 $657,607 $134,986.27

is planning to replace some uipment and the resulting e firm uses an 18 percent t go ahead with the project?

10.4.

Year 0 1 2 3 4 5 6 7

Net present value: Franklin Mints, a confectioner, is looking to purchase a new jellybe making machine at a cost of $312,500. The company management projects that the c flows from this investment will be $121,450 for the next seven years. If the appropriate discount rate is 14 percent, what is the NPV for the project?

$ $ $ $ $ $ $ $

Cash Flow (312,500) 121,450 121,450 121,450 121,450 121,450 121,450 121,450

14%

NPV

$208,314.62

Year 0 1 2 3 4 5 6 7

Cash Flows $ (312,500) $ 121,450 $ 121,450 $ 121,450 $ 121,450 $ 121,450 $ 121,450 $ 121,450

PVIF 1 0.8772 0.7695 0.675 0.5921 0.5194 0.4556 0.3996

$ $ $ $ $ $ $ $

NPV (312,500.00) 106,535.09 93,451.83 81,975.29 71,908.15 63,077.32 55,330.99 48,535.95 $208,314.62

purchase a new jellybeanent projects that the cash ears. If the appropriate

10.5 Net present Value: Blanda Incorporated mangement is considering investing in two al production systems. The systems are mutually exclusive, and the cost of the new equ resulting cash flows are shown in the accompanying table. If the firm uses a 9 percent for their production systems, in which system should the firm invest?

Year 0 1 2 3

System System 1 2 Cash Flows Cash Flows (15,000.00) (45,000.00) 15,000.00 32,000.00 15,000.00 32,000.00 15,000.00 32,000.00

Choose System 2

9.00% PVIF 1.0000 0.9174 0.8417 0.7722

NPV - 1 (15000.00) 13761.47 12625.20 11582.75 $22,969.42

is considering investing in two alternative ive, and the cost of the new equipment and the able. If the firm uses a 9 percent discount rate he firm invest?

NPV - 2 (45000.00) 29357.80 26933.76 24709.87 $36,001.43

10.6 Payback: Refer to Problem 10.5. What are the payback periods for production exclusive, and the the firm always chooses projects with the lowest payback perio

Year 0 1 2 3

System System 1 2 Cash Flows Cash Flows (15,000.00) (45,000.00) 15,000.00 32,000.00 15,000.00 32,000.00 15,000.00 32,000.00

Choose System 2 based on NPV

9.00% PVIF 1.0000 0.9174 0.8417 0.7722

NPV - 1 (15000.00) 13761.47 12625.20 11582.75 $22,969.42

ack periods for production systems 1 and 2? If the systems are mutually th the lowest payback period, in which system should the firm invest?

NPV - 2 Payback (45000.00) System 1 Payback 29357.80 0.00 1.00 26933.76 24709.87 $36,001.43

Payback System 2 Payback (13,000.00) 19,000.00 1.59

Choose System 1 based on Payback

10.7 Payback: Quebec, Inc., is purchasing machinery at a cost of $3,768,966. The company management expects the machinery to produce cash flows of $979,225, $1,158,886, an $1,881,497 over the next three years, respectively. What is the payback period?

Year 0 1 2 3

Cash Flow $ (3,768,966) $ 979,225 $ 1,158,886 $ 1,881,497

Payback Period

Cumulative Cash Flow $ (3,768,966) $ (2,789,741) $ (1,630,855)

2.87 years

of $3,768,966. The company's of $979,225, $1,158,886, and s the payback period?

10.8 Payback: Northern Specialties just purchased inventory-management computer softwa $1,645,276. Cost savings from the investment over the next six years will produc ethe fo flow stream: $212,455, $292,333, $387,479, $516,345, $645,766, and $618,325. What payback period on this investment?

Year 0 1 2 3 4 5 6

Cumulative Cash Flow Cash Flow $ (1,645,276) $ (1,645,276) $ 212,455 $ (1,432,821) $ 292,333 $ (1,140,488) $ 387,479 $ (753,009) $ 516,345 $ (236,664) $ 645,766 $ 409,102 $ 618,325 $ 1,027,427

Payback Period

4.37 years

anagement computer software at a cost of xt six years will produc ethe following cash 45,766, and $618,325. What is the

10.9 Payback: Nakamichi Bancorp has made an investment in banking software at a cost of $1,875,000. Management expects productivity gains and cost savings over the next several years. If the firm is expected to generate cash flows of $586,212, $713,277, $431,199, and $318,697 over the next four years, what is the investment’s payback period? Cumulative Cash Flow Year Cash Flow 0 $ 1 $ 2 $ 3 $ 4 $

(1,875,000) $ 586,212 $ 713,277 $ 431,199 $ 318,697 $

Payback Period

(1,875,000) (1,288,788) (575,511) (144,312) 174,385 3.45 years

nking software at a cost of savings over the next $586,212, $713,277, nvestment’s payback

10.10 Average accounting return (ARR): Capitol Corp. management is expecting to genera of $63,435 over each of the next three years. The average book value of the company that period will be $212,500. If the firm’s acceptance decision on any project is based o percent, should this project be accepted?

After-tax Income

1 63,435

Average Book Value ARR

Year 2 $ 63,435

3 3-year Average $ 63,435 $ 63,435 $

29.85%

212,500

is expecting to generate after-tax income value of the company's equipment over any project is based on an ARR of 37.5

10.11 Internal rate of return: Refer to problem 10.4. What is the IRR that Franklin Mints management can expect on this project?

10.4

Net present value: Franklin Mints, a confectioner, is looking to purchase a new jellybe making machine at a cost of $312,500. The company management projects that the c from this investment will be $121,450 for the next seven years. If the appropriate disco is 14 percent, what is the NPV for the project?

Year 0 1 2 3 4 5 6 7

Cash Flow $ (312,500) $ 121,450 $ 121,450 $ 121,450 $ 121,450 $ 121,450 $ 121,450 $ 121,450

14%

NPV

$208,314.62 33.80%

Year 0 1 2 3 4 5 6 7

Cash Flows $ (312,500) $ 121,450 $ 121,450 $ 121,450 $ 121,450 $ 121,450 $ 121,450 $ 121,450

PVIF 1 0.7474 0.5586 0.4175 0.312 0.2332 0.1743 0.1303

Trial and Error Method to find IRR $ $ $ $ $ $ $ $

NPV (312,500.00) 90,769.81 67,839.91 50,702.48 37,894.23 28,321.55 21,167.07 15,819.94 $14.98

The IRR equates the NPV to z Approximate IRR of 33.8%

R that Franklin Mints

purchase a new jellybeanment projects that the cash flows If the appropriate discount rate

Method to find IRR

R equates the NPV to zero.

imate IRR of 33.8%

10.12

Year 0 1 2 3 4 5 6

Internal rate of return: Hathaway, Inc., a resort management company, is refurbishing hotels at a cost of $7.8 million. The firm expects that this will lead to additional cash fl million for the next six years. What is the IRR of this project? If the appropriate cost o percent, should they go ahead with this project?

$ $ $ $ $ $ $

Cash Flow (7,800,000) 1,800,000 1,800,000 1,800,000 1,800,000 1,800,000 1,800,000 12%

NPV $ (399,466.82) IRR 10.17% Decision No

Year 0 1 2 3 4 5 6

$ $ $ $ $ $ $

Cash Flows (7,800,000) 1,800,000 1,800,000 1,800,000 1,800,000 1,800,000 1,800,000

IRR 10.169% PVIF NPV 1 $ (7,800,000) 0.907696 $ 1,633,853 0.823913 $ 1,483,043 0.747863 $ 1,346,153 0.678832 $ 1,221,898 0.616173 $ 1,109,112 0.559298 $ 1,006,737 $795.84

Trial and Error method to sol IRR is rate that equates NPV Approximate IRR of 10.17%

ompany, is refurbishing one of its ad to additional cash flows of $1.8 the appropriate cost of capital is 12

d Error method to solve for IRR. ate that equates NPV to zero. imate IRR of 10.17%

10.14 Net present value: Champlain Corp. is investigating two computer systems. The Alph will generate annual cost savings of $1,345,500 over the next five years. The Beta 210 will produce cost savings of $1,125,000 in the first three years and then $2 million for company’s discount rate for similar projects is 14 percent, what is the NPV for the two chosen based on the NPV?

Year 0 1 2 3 4 5

Cash Flows ALPHA BETA -3,122,300 -3,750,000 1,345,000 1,125,000 1,345,000 1,125,000 1,345,000 1,125,000 1,345,000 2,000,000 1,345,000 2,000,000

14%

NPV Decision

$1,495,193.90 Pick Alpha

$1,084,733.91

Year 0 1 2 3 4 5

ALPHA (3,122,300) 1,345,000 1,345,000 1,345,000 1,345,000 1,345,000

BETA (3,750,000) 1,125,000 1,125,000 1,125,000 2,000,000 2,000,000

PVIF 1.0000 0.8772 0.7695 0.6750 0.5921 0.5194

ating two computer systems. The Alpha 8300 costs $3,122,300 and over the next five years. The Beta 2100 system costs $3,750,000 and rst three years and then $2 million for the next two years. If the 4 percent, what is the NPV for the two systems? Which one should be

NPV Alpha (3,122,300) 1,179,825 1,034,934 907,837 796,348 698,551 $1,495,193.90

NPV Beta (3,750,000) 986,842 865,651 759,343 1,184,161 1,038,737 $1,084,733.91

Choose Alpha with higher NPV.

10.15 Net present value: Briarcrest Condiments is a spice-making firm. Recently, it developed a new process for producing spices. This calls for acquiring machinery that would cost $1,968,450. The machinery will have a life of five years and will produce the cash flows shown in the following table. What is the NPV if the discount rate is 15.9 percent? Year 0 1 2 3 4 5

Cashflows $ (1,968,450) $ 512,496 $ (242,637) $ 814,558 $ 887,225 $ 712,642

15.90%

NPV

($351,223.03)

Year 0 1 2 3 4 5

Cashflows (1,968,450) 512,496 (242,637) 814,558 887,225 712,642

PVIF 1 0.8628128 0.7444459 0.6423174 0.5541997 0.4781705

NPV (1,968,450.00) 442,188.09 (180,630.11) 523,204.78 491,699.79 340,764.41 ($351,223.03)

ing firm. Recently, alls for acquiring ill have a life of five wing table. What is

10.16 Net present value: Cranjet Industries is expanding its product line and its production the two independent projects are given in the following table. The firm uses a discoun a. b. c.

Are these projects independent or mutually exclusive? What are the NPVs of the two projects? Should both projects be accepted? Or either? Or neither? Explain your reasoning. Year 0 1 2 3 4 5 k

a. b. c.

Product Line Expansion $ (2,575,000) $ 600,000 $ 875,000 $ 875,000 $ 875,000 $ 875,000 16.4%

These projects are independent NPV $27,222.17 Accept both, since they are independent projects and both NPVs > 0

Year 0 1 2 3 4 5

Product Line Expansion (2,575,000) 600,000 875,000 875,000 875,000 875,000

Accept both, since they are independent projects and both NPVs > 0.

t Industries is expanding its product line and its production capacity. The costs and expected cash flows of cts are given in the following table. The firm uses a discount rate of 16.4 percent for such projects.

ndent or mutually exclusive? two projects? cepted? Or either? Or neither? Explain your reasoning. Production Capacity Expansion $ (8,137,250) $ 2,500,000 $ 2,500,000 $ 2,500,000 $ 3,250,000 $ 3,250,000 16.4%

$732,227.95 are independent projects and both NPVs > 0

Production Capacity Expansion (8,137,250) 2,500,000 2,500,000 2,500,000 3,250,000 3,250,000

ey are independent projects and both NPVs > 0.

PVIF 1.0000 0.8591 0.7381 0.6341 0.5447 0.4680

Product NPV (2,575,000.00) 515,463.92 645,806.02 554,816.17 476,646.20 409,489.86 $27,222.17

s and expected cash flows of ent for such projects.

Production NPV (8,137,250.00) 2,147,766.32 1,845,160.07 1,585,189.06 1,770,400.16 1,520,962.34 $732,227.95

10.17

Net present value: Emporia Mills is evaluating two heating systems. Costs and pr savings are given in the followin table. The firm uses 11.5 percent to discount such flows. Which system should be chosen?

Year 0 1 2 3 4

System 100 $ (1,750,000) $ 275,223 $ 512,445 $ 648,997 $ 875,000

11.5%

NPV

($56,667.41)

$75,758.21

Decision Year 0 1 2 3 4

$ $ $ $ $

System 200 (1,735,000) 750,000 612,500 550,112 384,226

System 200 should be chosen System 100 (1,750,000) 275,223 512,445 648,997 875,000

System 200 (1,735,000) 750,000 612,500 550,112 384,226

PVIF 1.0000 0.8969 0.8044 0.7214 0.6470

NPV 100 (1,750,000.00) 246,836.77 412,190.07 468,185.64 566,120.11 ($56,667.41)

Choose System 200 as the NPV > 0.

heating systems. Costs and projected energy 11.5 percent to discount such project cash

NPV 200 (1,735,000.00) 672,645.74 492,670.27 396,850.12 248,592.08 $75,758.21

10.18 Payback: Creative Solutions, Inc., has just invested $4,615,300 in new equipment. The firm uses payback period criteria of not accepting any project that takes more than four years to recover costs. The company anticipates cash flows of $644,386, $812,178, $943,279, $1,364,997, $2,616,300, and $2,225,375 over the next six years. Does this investment meet the firm's payback criteria?

Year

Cash Flow 0 $ (4,615,300) 1 $ 644,386 2 $ 812,178 3 $ 943,279 4 $ 1,364,997 5 $ 2,616,300 6 $ 2,225,375 Payback Period

Cumulative Cash Flow $ (4,615,300) $ (3,970,914) $ (3,158,736) $ (2,215,457) $ (850,460)

4.33 years

in new equipment. ct that takes more flows of $644,386, over the next six

10.19

Year 0 1 2 3 4 Discount rate

Discounted payback: Timeline Manufacturing Co. is evaluating two projects. Th payback criteria of three years or less. Project A has a cost of $912,855, and pro $1,175,000. Cash flows from both projects are given in the following table. Wha payback periods and which will be accepted with a discount rate of 8 percent? Project A -912,855 86,212 313,562 427,594 285,552 8%

Project B -1,175,000 586,212 413,277 231,199

$ $ $ $ $

DCF(A) (912,855) 79,826 268,829 339,438 209,889

Discounted Payback Period

Decision: Neither project will be accepted since they both have DPPs greater than

uring Co. is evaluating two projects. The company uses ect A has a cost of $912,855, and project B’s cost is are given in the following table. What are their discounted d with a discount rate of 8 percent?

$ $ $ $

DCF(B) (1,175,000) 542,789 354,318 183,533

$ $ $ $ $

CCF(A) (912,855) (833,029) (564,200) (224,762) (14,873)

Over 4 years

$ $ $ $

CCF(B) (1,175,000) (632,211) (277,893) (94,359)

Over 3 years

e they both have DPPs greater than the 3 year cutoff.

10.20

Year 0 1 2 3 4 5 6 Payback Period Decision:

Payback: Regent Corp. is evaluating three competing pieces of equipment projections for all three are given in the following table. Which would be the on payback period?

$ $ $ $ $ $

Cash Flows Type 1 Type2 (1,311,450) $ (1,415,888) 212,566 $ 586,212 269,825 $ 413,277 455,112 $ 331,199 285,552 $ 141,442 121,396

4.73

3.60

Type 3 $ (1,612,856) $ 786,212 $ 175,000 $ 175,000 $ 175,000 $ 175,000 $ 175,000 5.72

Type 2 would be the best choice

hree competing pieces of equipment. Costs and cash flow e following table. Which would be the best choice based

Cumulative Cash Flows CCF[Type 1] CCF[Type 2] CCF[Type 3] $ (1,311,450) $ (1,415,888) $ (1,612,856) $ (1,098,884) $ (829,676) $ (826,644) $ (829,059) $ (416,399) $ (651,644) $ (373,947) $ (85,200) $ (476,644) $ (88,395) $ 56,242 $ (301,644) $ 33,001 $ 56,242 $ (126,644) $ 33,001 $ 56,242 $ 48,356

10.21

Years Cash flows Discount rate

Discounted payback: Nugent Communication Corp. is investing $9,365,000 significant benefits in the first three years after installation (as can be seen by amount for four more years. What is the discounted payback period for the p percent? 1 2 3 4–7 $2,265,433 $4,558,721 $3,378,911 $1,250,000 10%

0 1 2 3 Cash Flows $ (9,365,000) $ 2,265,433 $ 4,558,721 $ 3,378,911 Disc. Cash Flows $ (9,365,000) $ 2,059,485 $ 3,767,538 $ 2,538,626 CCF $ (9,365,000) $ (7,305,515) $ (3,537,977) $ (999,352) DPP 4.19

p. is investing $9,365,000 in new technologies. The company expects llation (as can be seen by the following cash flows), and a constant payback period for the project assuming a discount rate of 10

4 5 $ 1,250,000 $ 1,250,000 $ 853,767 $ 776,152 $ (145,585) $ 630,567

6 $ 1,250,000 $ 705,592 $ 1,336,159

7 $ 1,250,000 $ 641,448 $ 1,977,607

10.22

Cash Flows Compound Cash Flows Cost of Capital MIRR

Modified internal rate of return (MIRR): Morningside Bakeries has r purchased equipment at a cost of $650,000. The firm expects to gene flows of $275,000 in each of the next four years. The company’s cost is 14 percent. What is the MIRR for this project?

0 1 2 3 (650,000) $ 275,000 $ 275,000 $ 275,000 ($650,000) 14% 20.12%

$407,425

$357,390

$313,500

orningside Bakeries has recently . The firm expects to generate cash ears. The company’s cost of capital ect? 4 $ 275,000 $275,000

$1,353,315

10.23

Cash Flows Cost of Capital MIRR

Modified internal rate of return (MIRR): Sycamore Home Furnishings is look machine that can create customized window treatments. The equipment will co generate cash flows of $85,000 over each of the next six years. If the company percent, what is the MIRR on this project? 0 1 $ (263,400) $ 85,000 12% 17.40%

2 $ 85,000

3 $ 85,000

4 $ 85,000

re Home Furnishings is looking to acquire a new ments. The equipment will cost $263,400 and will ext six years. If the company’s cost of capital is 12

5 $ 85,000

6 $ 85,000

Terminal Value $ 689,791

10.24

Internal rate of return: Great Flights, Inc., an aviation firm, is considering purcha million. The company would lease the aircraft to an airline. Cash flows from leasi following table. What is the IRR on this project? The firm’s required rate of return Years 0 1–4 5–7 8–10

Cash Flow -$161,000,000 $23,500,000 $72,000,000 $80,000,000

Discount rate 0 Cash Flows $ (161,000,000) $ Discount rate 15% IRR

15% 1 23,500,000

2 23,500,000

$ $ $ $ $ $ $ $ $ $ $

NPV (161,000,000.00) 19,160,524.43 15,622,370.06 12,737,566.09 10,385,465.80 25,943,594.24 21,152,888.13 17,246,826.80 15,624,503.37 12,739,305.46 10,386,883.98

(71.65)

22.65% 22.6480% Year 0 1 2 3 4 5 6 7 8 9 10

Cash Flows $ (161,000,000) $ 23,500,000 $ 23,500,000 $ 23,500,000 $ 23,500,000 $ 72,000,000 $ 72,000,000 $ 72,000,000 $ 80,000,000 $ 80,000,000 $ 80,000,000

PVIF 1.00000 0.81534 0.66478 0.54202 0.44193 0.36033 0.29379 0.23954 0.19531 0.15924 0.12984

ation firm, is considering purchasingthree aircraft for a total cost of $161 an airline. Cash flows from leasing the proposed leases are shown in the The firm’s required rate of return is 15 percent.

3 $ 23,500,000

4 $ 23,500,000

5 $ 72,000,000

Trial and Error method to find IRR IRR is rate that equates NPV to zero. Irr is approximately 22.648%

6 $ 72,000,000

7 $ 72,000,000

8 $ 80,000,000

9 $ 80,000,000

10 $ 80,000,000

10.25

Internal rate of return: Refer to problem 10.5. Compute the IRR for both productio system 2. Which hasa the higher IRR? Which production system has the higher NPV rankings of systems 1 and 2 are different.

10.5

Net present Value: Blanda Incorporated mangement is considering investing in t systems. The systems are mutually exclusive, and the cost of the new equipmen are shown in the accompanying table. If the firm uses a 9 percent discount rate f which system should the firm invest?

Year 0 1 2 3

System System 1 2 Cash Flows Cash Flows (15,000.00) (45,000.00) 15,000.00 32,000.00 15,000.00 32,000.00 15,000.00 32,000.00

9.00% PVIF 1.0000 0.9174 0.8417 0.7722

NPV - 1 (15,000.00) 13,761.47 12,625.20 11,582.75 22,969.42

Choose System 2 IRR for Production system 1 IRR for Production system 2 NPV for Production system 1 NPV for Production system 2

System 1 delivers a higher IRR because Thus, even with lower cash inflows in th System 2 has a higher initial investmen

e the IRR for both production system 1 and production ction system has the higher NPV? Explain why the IRR and

is considering investing in two alternative production e cost of the new equipment and the resulting cash flows a 9 percent discount rate for their production systems, in

NPV - 2 (45,000.00) 29,357.80 26,933.76 24,709.87 36,001.43

IRR 83.93% PVIF 1.00000 0.54369 0.29559 0.16071

NPV - 1 (15,000) 8,155 4,434 2,411 (0)

IRR 50.07% PVIF 1.00000 0.66636 0.44403 0.29588

NPV - 2 (45,000) 21,323 14,209 9,468 1

83.93% Choose Production system 1 50.07% 22,969.42 36,001.43 Choose Production system 2

ers a higher IRR because it requires a lower initial investment. h lower cash inflows in the years after startup, system 1 ia able to deliver a higher return on the initial inves a higher initial investment but delivers a higher net cash flow for the firm.

10.3 Internal rate of return: Ancala Corporation is considering investments in two new season: Gold hats and belts. Due to a funding constraint, these line are mutually each project's estimated cash flows over its three year life, as well as the IRRs an outlined below. The CFO of the firm has decided to manufacture the belts, howe questioning the decision given that the IRR is higher for manufacturing hats. Ex IRRs and NPVs of the belt and hat projects disagree? Is the Cfo's decision corre Year 0 1 2 3 NPV IRR

Golf Belts ($1,000) $1,000 $500 $500 $698 54%

Golf Hats ($500) $500 $300 $300 $428 61%

The IRRs and NPVs of the belt and hat lines disagree because of the differences the project. Hats deliver a higher IRR because they require a lower initial investm even with lower cash inflows in the years after the startup, the hat project is able return on the initial investment. While the golf belt project does not cost more, it net cash flow for Ancala investors. This NPV factors in the initial cost of the proj the total net cash flow for the firm's shareholders.

g investments in two new golf apparel lines for next t, these line are mutually excluisve. A summary of fe, as well as the IRRs and NPVs of each, are ufacture the belts, however, the CEO is manufacturing hats. Explain to the CEO why the the Cfo's decision correct?

cause of the differences in the scale of ire a lower initial investment. Thus, up, the hat project is able to deliver a higher ct does not cost more, it delivers a higher he initial cost of the project, and reflects

10.27

Internal rate of return: Compute the IRR on the following cash flow streams:

a. b. c.

An initial investment of $25,000 followed by a single cash flow of $37,450 in ye An initial investment of $1 million followed by a single cash flow of $1,650,000 An initial investment of $2 million followed by cash flows of $1,650,000 and $1,

Cash Flow [a] IRR(a)

Cash Flow [b] IRR(b)

Cash Flow [c] IRR [c]

0 (25,000)

1 0

2 0

Year 2

Year 3 0

6.97%

0 $ (1,000,000) $

3 -

13.34%

0 $ (2,000,000)

1 $

Year 2 1,650,000

30.42% IRR A 6.9675%

Year 0 1 2 3 4 5 6

Cash Flow A Cash Flow B Cash Flow C $ (25,000) $ (1,000,000) $ (2,000,000) 0 0 0 0 0 $ 1,650,000 0 0 0 0 $ 1,650,000 $ 1,250,000 0 $ 37,450

PVIF 1 0.93486 0.87397 0.81704 0.76382 0.71407 0.66756

ng cash flow streams:

h flow of $37,450 in year 6. ash flow of $1,650,000 in year 4. of $1,650,000 and $1,250,000 in years 2 and 4, respectively. Year 4 0

5 0

4 1,650,000

4 1,250,000

IRR B 13.3368%

IRR C 30.4215%

PVIF

PVIF 1

0.88233 0.77850 0.68689 0.60606

0.76674 0.58790 0.45077 0.34562

6 $

1 $ $ $ $ $ $ $ $

NPV function:

37,450

NPV A (25,000) $ $ $ $ $ 25,000 (0) $

NPV B (1,000,000) $ $ $ $ 1,000,000 $

($0.00)

$0.00

NPV C (2,000,000) 970,030 432,029

(597,941) $0.00

10.28

Internal rate of return: Compute the IRR for the following project cash flows.

a. b. c.

An initial outlay of $3,125,000 followed by annual cash flows of $565,325 for th An initial investment of $33,750 followed by annual cash flows of $9,430 for the An initial outlay of $10,000 followed by annual cash flows of $2,500 for the next

Cash Flow (a)

IRR(A)

Cash Flow (b)

IRR [c]

2 $ 565,325

3 565,325

3 9,430

3 2,500

9.03%

IRR(B)

Cash Flow[c]

0 1 (3,125,000) $ 565,325

0 (33,750) $

1 9,430

2 9,430

1 2,500

2 2,500

12.29%

0 (10,000) $ 16.33%

IRR A 9.0342% Year 0 1 2 3 4 5 6 7 8

Cash Flow A Cash Flow BCash Flow C $ (3,125,000) $ (33,750) $ (10,000) $ 565,325 $ 9,430 $ 2,500 $ 565,325 $ 9,430 $ 2,500 $ 565,325 $ 9,430 $ 2,500 $ 565,325 $ 9,430 $ 2,500 $ 565,325 $ 9,430 $ 2,500 $ 565,325 $ 2,500 $ 565,325 $ 2,500 $ 565,325

PVIF A 1 0.91714355 0.84115229 0.7714574 0.70753718 0.64891316 0.59514652 0.54583479 0.50060886

Trial and Error method to find the Alternatively, use Excel's Goal Se

The IRR equates the NPV to zero

he following project cash flows.

al cash flows of $565,325 for the next eight years nual cash flows of $9,430 for the next five years cash flows of $2,500 for the next seven years

4 565,325

4 9,430

4 2,500

5 565,325

6 565,325

7 $ 565,325

8 $ 565,325

5 9,430

6 2,500

IRR B 12.2903%

IRR C 16.3267%

PVIF B

PVIF C

1 0.89054899 0.7930775 0.70627437 0.62897192 0.56013031 0.49882348 0.44422675 0.39560568

2,500

7 2,500

1 0.859647804 0.738994346 0.635274867 0.546112644 0.469464535 0.403574156 0.346931637 0.29823902

NPV A (3,125,000) 518,484 475,524 436,124 399,988 366,847 336,451 308,574 283,007 (0)

NPV B (33,750) 8,398 7,479 6,660 5,931 5,282 0 0 0 (0)

NPV C (10,000) 2,149 1,847 1,588 1,365 1,174 1,009 867 0 (0)

NPV function:

($0.00)

al and Error method to find the IRR. ernatively, use Excel's Goal Seek.

10.31

Draconian Measures, Inc., is evaluating two independent projects. The company 13.8 percent discount rate for such projects. The cost and cash flows for the pro shown in the following table. What are the NPVs of the two projects?

Year 0 1 2 3 4 5 6 7

$ $ $ $ $ $ $

Project 1 Project 2 ($8,425,375) $ (11,368,000) 3,225,997 $2,112,589 1,775,882 $3,787,552 1,375,112 $3,125,650 1,176,558 $4,115,899 1,212,645 $4,556,424 1,582,156 1,365,882

Discount rate = 13.8% NPV

13.80% ($668,283)

Year 0 1 2 3 4 5 6 7

$375,375

Project 1 Project 2 ($8,425,375) $ (11,368,000) $3,225,997 $ 2,112,589 $1,775,882 $ 3,787,552 $1,375,112 $ 3,125,650 $1,176,558 $ 4,115,899 $1,212,645 $ 4,556,424 $1,582,156 $1,365,882

PVIF 1 0.87873462 0.77217454 0.6785365 0.59625351 0.52394861 0.46041178 0.40457977

wo independent projects. The company uses a cts. The cost and cash flows for the projects are e NPVs of the two projects?

NPV 1 NPV 2 ($8,425,375) $ (11,368,000) $2,834,795 $ 1,856,405 $1,371,291 $ 2,924,651 $933,064 $ 2,120,868 $701,527 $ 2,454,119 $635,364 $ 2,387,332 $728,443 $ $552,608 $ (668,283.21) $ 375,375.16

10.32

Refer to problem 10.31

a. b. c.

What are the IRRs for both Projects? Does the IRR decision criterion differ from the earlier decisions? Explain how you would expect the mangement of Draconian Measures to decide

10.31

Draconian Measures, Inc., is evaluating two independent projects. The company uses a 13.8 percent discount rate for such projects. The cost and cash flows for projects are shown in the following table. What are the NPVs of the two projects

Year 0 1 2 3 4 5 6 7

$ $ $ $ $ $ $

Project 1 Project 2 ($8,425,375) $ (11,368,000) 3,225,997 $2,112,589 1,775,882 $3,787,552 1,375,112 $3,125,650 1,176,558 $4,115,899 1,212,645 $4,556,424 1,582,156 1,365,882

Discount rate = 13.8% NPV

13.80% ($668,283)

$375,375

[a] Year 0 1 2 3 4 5 6 7

Project 1 Project 2 ($8,425,375) $ (11,368,000) $3,225,997 $ 2,112,589 $1,775,882 $ 3,787,552 $1,375,112 $ 3,125,650 $1,176,558 $ 4,115,899 $1,212,645 $ 4,556,424 $1,582,156 $1,365,882

IRR 1 10.6773%

IRR 2 15.0226%

PVIF

1 0.90352787 0.8163626 0.73760636 0.6664479 0.60215425 0.54406314 0.49157621

1 0.869394651 0.75584706 0.657129391 0.571304778 0.496689319 0.431819037 0.375421161 NPV function:

[b]

No, in the case of independent projects, the IRR criterion will give the same

[c]

I would expect the management of Draconian Measures, Inc. to accept only

an Measures to decide?

projects. The company cost and cash flows for the PVs of the two projects?

NPV 1 NPV 2 ($8,425,375) $ (11,368,000) $2,914,778 $ 1,836,674 $1,449,764 $ 2,862,810 $1,014,291 $ 2,053,956 $784,115 $ 2,351,433 $730,199 $ 2,263,127 $860,793 $ $671,435 $ ($0) $ (0) ($0) ($0)

10.33 Net present value: Dravid, Inc., is currently evaluating three projects that are indepen 14.8 percent depending upon their financing plan. All three projects cost the same at $ accepted at a discount rate of 14.8 percent? What if the discount rateshown in the foll discount rate of 14.8 percent? What if the discount rate was 13.6 percent? Year 0 1 2 3 4 Discount rate (1) Discount rate (2) NPV (at a discount rate =13.6%) NPV (at a discount rate =14.8%)

Project 1 Project 2 $ (500,000) $ (500,000) 0 0 $125,000 0 $150,000 $500,000 $375,000 $500,000 13.60% 14.80% ($75,645.18) $141,295.11 ($90,103.11) $118,353.37

At a discount rate of 14.8% At a discount rate of 13.6%

Accept Accept 13.60%

Year 0 1 2 3 4

Project 1 PVIF (500,000) 1 0 0.88028169 125,000 0.774895854 150,000 0.682126632 375,000 0.600463585

0 1 2 3 4

Project 2 (500,000) 1 0 0.88028169 0 0.774895854 500,000 0.682126632 500,000 0.600463585

Project 3 (500,000)

1 2 3 4

245,125 212,336 112,500 74,000

0.88028169 0.774895854 0.682126632 0.600463585

three projects that are independent. The cost of funds can be either 13.6 percent or ree projects cost the same at $500,000. Expected cash flow streams are would be e discount rateshown in the following table. Which projects would be accepted at a was 13.6 percent? Project 3 $ (500,000) $245,125 $212,336 $112,500 $74,000

$1,490.89 ($8,396.83)

Accept 14.80% NPV PVIF NPV (500,000) 1 (500,000) 0 0.8710801 0 96,862 0.7587806 94,848 102,319 0.6609587 99,144 225,174 0.575748 215,906 (75,645) (90,103)

(500,000) 1 0 0.8710801 0 0.7587806 341,063 0.6609587 300,232 0.575748 141,295

(500,000) 0 0 330,479 287,874 118,353

(500,000)

Reject

Accept Accept

215,779 164,538 76,739 44,434 1,491

0.8710801 0.7587806 0.6609587 0.575748

213,524 161,116 74,358 42,605 (8,397)

Accept Reject

10.34 Intrepid, Inc., is considering investing in two or three independent projects. The costs flows are given in the following table. Theappropriate cost of capital is 14.5 percent. C IRRs and identify the projects that should be accepted.

Year 0 1 2 3 4 IRR Cost of Capital Decision

Project 1 Project 2 $ (275,000) $ (312,500) $ $ 63,000 $153,250 $ 85,000 $167,500 $ 85,000 $112,000 $ 100,000

7.57% 19.22% 14.50% Reject Accept Accept

Year 0 1 2 3 4

7.57% Project 1 PVIF (275,000) 1 63,000 0.92962722 85,000 0.86420677 85,000 0.80339013 100,000 0.74685334

Year 0 1 2 3 4

Project 2 (312,500) 153,250 167,500 112,000 0

19.22% PVIF 1 0.83878544 0.70356101 0.59013673 0.4949981

Project 3 (500,000) 212,000 212,000 212,000

25.07% PVIF 1 0.79955225 0.6392838 0.5111408

Year 0 1 2 3

Project 3 (500,000) $212,000 $212,000 $212,000 $212,000 25.07%

Reject NPV (275,000) 58,567 73,458 68,288 74,685 (2) Accept NPV (312,500) 128,544 117,846 66,095 0 (14) Accept NPV (500,000.00) 169,505.08 135,528.17 108,361.85

212,000

0.40868378

86,640.96 36.05

Trial and Error Method (or Goal Seek) to find IRR. IRR is rate that equates NPV to zero.

dent projects. The costs and the cash capital is 14.5 percent. Compute the

10.35

Jekyll & Hyde Corp. is evaluating two mutually exclusive projects. The cost of capit is 15 percent. Costs and cash flows are given in the following table. Which project should be accepted? Year PROJECT 1 PROJECT 2 0 $ (1,250,000) $ (1,250,000) 1 $ 250,000 $350,000 2 $ 350,000 $350,000 3 $ 450,000 $350,000 4 $ 500,000 $350,000 5 $ 750,000 $350,000 Cost of Capital = 15%

NPV IRR

Decision

186,683 $ 20.13% Accept

Year 0 1 2 3 4 5

0 1 2 3 4 5

PROJECT 1 (1,250,000) 250,000 350,000 450,000 500,000 750,000

PROJECT 2 $ (1,250,000) $ 350,000 $ 350,000 $ 350,000 $ 350,000 $ 350,000

(76,746) 12.38% Reject

20.13% PVIF

NPV (1,250,000) 208,108 242,530 259,572 240,084 299,781 75

1 0.832431533 0.692942256 0.576826984 0.480168971 0.399707792 12.38% PVIF 1 $ 0.889838049 $ 0.791811754 $ 0.704584227 $ 0.626965854 $ 0.557898073 $

NPV (1,250,000) 311,443 277,134 246,604 219,438 195,264

(116)

e projects. The cost of capital owing table. Which project

Reject

10.36

Larsen Automotive, a manufacturer of auto parts, is planning to invest in two projects. The company typically compares project returns to a cost of funds of 17 percent. Compute the IRRs based on the given cash flows in the following table. Which project(s) will be accepted? Year 0 1 2 3 4

Cost of Capital

Project 1 $ (475,000) $ 300,000 $ 110,000 $ 125,000 $ 140,000

Project 2 $ (500,000) $ 117,500 $ 181,300 $ 244,112 $ 278,955

18.84% $14,524.07 ACCEPT

19.96% $34,150.15 ACCEPT

17%

IRR NPV Decision

Year 0 1 2 3 4

Project 1 ($475,000) $300,000 $110,000 $125,000 $140,000

18.84% PVIF

ACCEPT NPV ($475,000) $252,440 $77,887 $74,477 $70,190 ($5)

1 0.84146752 0.70806759 0.59581588 0.50135971

19.96% PVIF

0 1 2 3 4

Project 2 NPV $ (500,000) 1 $ (500,000) $ 117,500 0.8336112 $ 97,949 $ 181,300 0.69490764 $ 125,987 $ 244,112 0.57928279 $ 141,410 $ 278,955 0.48289663 $ 134,706 $

lanning to invest in returns to a cost of given cash flows in ?

10.37

Compute the IRR for each of the following projects. Year 0 1 2 3 4 5 IRR

Year 0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4

Project 1 Project 2 Project 3 $ (10,000) $ (10,000) $ (10,000) $ 4,750 $ 1,650 $ 800 $ 3,300 $ 3,890 $ 1,200 $ 3,600 $ 5,100 $ 2,875 $ 2,100 $ 2,750 $ 3,400 $ 800 $ 6,600 16.08%

13.68%

Project 1 (10,000) 4,750 3,300 3,600 2,100 0

16.08% PVIF 1.0000 0.8615 0.7421 0.6393 0.5508 0.4745

Project 2 (10,000) 1,650 3,890 5,100 2,750 800

13.68% PVIF 1.0000 0.8797 0.7738 0.6807 0.5988 0.5267

Project 3 (10,000) 800 1,200 2,875 3,400

10.86% PVIF 1.0000 0.9020 0.8137 0.7340 0.6621

10.86%

NPV (10,000) 4,092 2,449 2,302 1,157 0 (1)

NPV (10,000) 1,451 3,010 3,472 1,647 421 1

NPV (10,000) 722 976 2,110 2,251

6,600

0.5972

3,942 1

10.38

a. b. c.

Primus Corp. is planning to convert an existing warehouse into a new plant that increase its production capacity by 45 percent. The cost of this project will be $7,125,000. It will result in additional cash flows of $1,875,000 for the next eight years. The company uses a discount rate of 12 percent. What is the payback period? What is the NPV for this project? What is the IRR?

0 $ (7,125,000) $

1 2 1,875,000 $ 1,875,000 $

CCF $ (5,250,000) $ (3,375,000) $ PPB 3.8 years NPV $2,189,325 IRR 20.33% Cost of Capital 12.00%

Year 0 1 2 3 4 5 6 7 8

Cash Flows $ (7,125,000) 1,875,000 1,875,000 1,875,000 1,875,000 1,875,000 1,875,000 1,875,000 1,875,000

12.00% PVIF 1.0000 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039

Annual Cash Flows 3 4 1,875,000 $ 1,875,000 (1,500,000)

$ $ $ $ $ $ $ $ $

NPV (7,125,000) 1,674,107 1,494,739 1,334,588 1,191,596 1,063,925 949,933 848,155 757,281

2,189,325

20.33% PVIF 1.0000 0.8310 0.6906 0.5740 0.4770 0.3964 0.3294 0.2738 0.2275

use into a new plant that will st of this project will be 875,000 for the next eight t.

Cash Flows $

5 6 7 8 1,875,000 $ 1,875,000 $ 1,875,000 $ 1,875,000

Accept $ $ $ $ $ $ $ $ $

NPV (7,125,000) 1,558,215 1,294,951 1,076,167 894,346 743,244 617,672 513,315 426,589

(501)

10.39

a. b. c. d.

Quasar Tech Co. is investing $6 million in new machinery that will produce the routers. Sales to its customers will amount to $1,750,000 for the next three ye $2.4 million for three more years. The project is expected to last six years and $898,620 (excluding depreciation). The machinery will be depreciated to zero straight-line method. The company’s tax rate is 30 percent, and its cost of cap What is the payback period? What is the average accounting return (ARR)? Calculate the project NPV. What is the IRR for the project?

1 $ 1,750,000 $ $ 898,620 $

2 1,750,000 $ 898,620 $

3 1,750,000 898,620

1 $ 1,750,000 $ 898,620 $ 1,000,000 $ (148,620)

$ $ $ $

2 1,750,000 898,620 1,000,000 (148,620)

$ $ $ $

3 1,750,000 898,620 1,000,000 (148,620)

Taxes Net Income AT Cash Flow CCF Book Value

$ 44,586 $ (104,034) $ (6,000,000) $ 895,966 $ (6,000,000) $ (5,104,034) $ 6,000,000 $ 5,000,000

$ $ $ $ $

44,586 (104,034) 895,966 (4,208,068) 4,000,000

$ $ $ $ $

44,586 (104,034) 895,966 (3,312,102) 3,000,000

ARR NPV IRR PPB

4.94% ($2,043,927) 3.14% 5.45

Revenues Expenses Depreciation

$ 6,000,000 Straight line

Tax rate Cost of Capital

30% 16% 0

Revenues Expenses Depreciation Taxable Income Tax rate Cost of Capital

$ 6,000,000

30% 16%

[a]

Payback period $

5.45

[b]

ARR

4.94%

[c]

Year 0 1 2 3 4 5 6

Cash Flows $ (6,000,000) $ 895,966 $ 895,966 $ 895,966 $ 1,350,966 $ 1,350,966 $ 1,350,966

16.00% PVIF 1.00000 0.86207 0.74316 0.64066 0.55229 0.47611 0.41044

$ $ $ $ $ $ $

NPV (6,000,000) 772,384 665,849 574,007 746,126 643,212 554,494

(2,043,927)

ry that will produce the next-generation 0 for the next three years then increase to d to last six years and cost the firm annually be depreciated to zero by year 6 using the ent, and its cost of capital is 16 percent.

4 $ 2,400,000 $ $ 898,620 $

5 6 2,400,000 $ 2,400,000 898,620 $ 898,620

4 $ 2,400,000 $ 898,620 $ 1,000,000 $ 501,380

5 2,400,000 898,620 1,000,000 501,380

$ $ $ $

6 $ 2,400,000 $ 898,620 $ 1,000,000 $ 501,380

Average $ (150,414) $ 350,966 $ 1,350,966 $ (1,961,136) $ 2,000,000

$ $ $ $ $

(150,414) 350,966 1,350,966 (610,170) 1,000,000

$ (150,414) $ 350,966 $ $ 1,350,966 $ 740,796 $ $

123,466

2,500,000

[d] 3.1450% PVIF 1.00000 $ 0.96951 $ 0.93995 $ 0.91129 $ 0.88350 $ 0.85656 $ 0.83045 $

NPV (6,000,000) 868,647 842,161 816,483 1,193,580 1,157,187 1,121,903

(39)

REJECT

10.40

a. b. c. d.

Skywards, Inc., an airline caterer, is purchasing refrigerated trucks at a tota tax net income from this investment is expected to be $750,000 for the nex depreciation expense was $650,000. The company’s cost of capital is 17 p What is the discounted payback period? Compute the ARR. What is the NPV on this investment? Calculate the IRR.

0 After-tax Net Income Depreciation Total Cost of trucks $ Cost of Capital

(3,250,000) 17%

AT Cash Flow Disc. Cash Flows CCF Book Value

(3,250,000) $ $ (3,250,000) $ 3,250,000 $

ARR NPV IRR DPP

$ $ $

1 750,000 650,000

$ $

2 750,000 650,000

1,400,000 $ 1,400,000 1,196,581 $ 1,022,719 (2,053,419) $ (1,030,700) 2,600,000 $ 1,950,000

57.69% $1,229,085 32.55% 3.21 years [a]

3.21 years

[b]

57.69% ARR

[c]

year 0 1 2 3 4 5

Cash Flows $ (3,250,000) 1,400,000 1,400,000 1,400,000 1,400,000 1,400,000

17.00% PVIF 1.00000 0.85470 0.73051 0.62437 0.53365 0.45611

rchasing refrigerated trucks at a total cost of $3.25 million. Afterexpected to be $750,000 for the next five years. Annual The company’s cost of capital is 17 percent.

$ $

3 750,000 650,000

4 750,000 650,000

$ $

5 750,000 650,000

$ $ $ $

1,400,000 $ 1,400,000 874,119 $ 747,110 (156,581) $ 590,529 1,300,000 $ 650,000

$ $ $ $

1,400,000 638,556 1,229,085 -

$ $ $ $ $ $

NPV (3,250,000) 1,196,581 1,022,719 874,119 747,110 638,556

[d] IRR 32.55% PVIF 1.00000 $ 0.75443 $ 0.56917 $ 0.42940 $ 0.32395 $ 0.24440 $

NPV (3,250,000) 1,056,205 796,835 601,158 453,533 342,160

1,229,085

(108)

$ $

AVG Book Value $1,300,000

10.41 Trident Corp. is evaluating two independent projects. The costs and expected cash flo cost of capital is 10 percent. Year 0 $ 1 2 3 4 5 a. b. c. d.

A (312,000) $ $121,450 $121,450 $121,450 $121,450 $121,450

B (395,000) $153,552 $158,711 $166,220 $132,000 $122,000

Calculate the project’s NPV. Calculate the project’s IRR. What is the decision based on NPV? What is the decision based on IRR? Is there a c If you are the decision maker for the firm which project or projects will be accepted? E

Cost of capital = a) b)

Year 0 $ 1 2 3 4 5 10% NPV IRR

A (312,000) $ $121,450 $121,450 $121,450 $121,450 $121,450

$148,391.05 27.27%

B (395,000) $153,552 $158,711 $166,220 $132,000 $122,000

$166,552.57 26.09%

c) Based on NPV, accept Project B; Based on IRR, accept Project A d) Since the cost of capital is less than the crossover rate of 20.58%, we are in t decision is to pick the project with the higher NPV, which is project B. The addi generates an IRR of 20.58%, which is better than the company's hurdle rate of 10

Year 0 1

Cash Flow A $ (312,000) $ 121,450

10.00% PVIF 1 0.90909

2 3 4 5

$ $ $ $

121,450 121,450 121,450 121,450

0.82645 0.75131 0.68301 0.62092

0 1 2 3 4 5

Cash Flow B $ (395,000) $ 153,552 $ 158,711 $ 166,220 $ 132,000 $ 122,000

10.00% PVIF 1 0.90909 0.82645 0.75131 0.68301 0.62092

c) Based on NPV, accept Project B; Based on IRR, accept Project A

d) Since the cost of capital is less than the crossover rate of 20.58%, we are in t decision is to pick the project with the higher NPV, which is project B. The addi generates an IRR of 20.58%, which is better than the company's hurdle rate of 10

ects. The costs and expected cash flows are given in the following table. The

e decision based on IRR? Is there a conflict? project or projects will be accepted? Explain your reasoning.

B-A (83,000) 32102 37261 44770 10550 550

$16,510.47 20.58%

n IRR, accept Project A rossover rate of 20.58%, we are in the range of conflict, the correct NPV, which is project B. The additional investment of $83,000 in B han the company's hurdle rate of 10%

$ $

NPV (312,000) 110,409

IRR 27.27% [b] PVIF 1.00000 $ 0.78573 $

NPV (312,000) 95,427

$ $ $ $

100,372 91,247 82,952 75,411

148,391 [a]

$ $ $ $ $ $ $

NPV (395,000) 139,593 131,166 124,884 90,158 75,752 166,553 [a]

0.61737 0.48509 0.38115 0.29948

$ $ $ $

74,980 58,914 46,291 36,372

(16)

IRR 26.09% [b] PVIF 1.00000 $ 0.79308 $ 0.62898 $ 0.49884 $ 0.39562 $ 0.31376 $

NPV (395,000) 121,780 99,826 82,917 52,222 38,279

n IRR, accept Project A

rossover rate of 20.58%, we are in the range of conflict, the correct NPV, which is project B. The additional investment of $83,000 in B han the company's hurdle rate of 10%

10.42 Tyler, Inc., is looking to considering switching to a new technology. The cost of the req discount rate is 12 percent. The cash flows tht the firm expects to generate are as follo

a. b. c.

Year

1-2 3-5 6-9

0 845000 1450000

Compute the payback and discounted payback periods for the project. What is the NPV for the project? Should the firm go ahead with the project? What is the IRR, and what would be the decision based on the IRR?

0 Net Cash Flow -4,000,000 Disc. NCF CCF CDCF

b. c. a. a.

(4,000,000) $

$845,000

601,454

(4,000,000) $

(3,155,000)

(4,000,000) $

(3,398,546)

Cost of Capital 12% NPV $116,979.48 Accept IRR 12.54% Accept PP 6.0 years DPP 8.8 years [a]

6.01

years

[a]

8.78

years

Year 0 1 2 3 4

Cash Flows (4,000,000) 0 0 845,000 845,000

12.00% PVIF 1.00000 0.89286 0.79719 0.71178 0.63552

NPV (4,000,000) 0 0 601,454 537,013

5 6 7 8 9

845,000 1,450,000 1,450,000 1,450,000 1,450,000

0.56743 0.50663 0.45235 0.40388 0.36061

479,476 734,615 655,906 585,631 522,885 116,979 [b]

gy. The cost of the required equipment will be $4 million. The to generate are as follows:

project. the project? IRR?

$845,000

$1,450,000

537,013

(2,310,000) $

(2,861,533) $

479,476

655,906

585,631

522,885

(1,465,000) $

(15,000) $

1,435,000

2,885,000

4,335,000

(2,382,057) $

(1,647,442) $

(405,905) $

116,979

[c] IRR 12.54% PVIF 1 0.888572952 0.789561891 0.70158334 0.623407979

NPV (4,000,000) 0 0 592,838 526,780

734,615

(991,536) $

0.553943468 0.492219183 0.437372652 0.388637509 0.345332778

468,082 713,718 634,190 563,524 500,733 0

STP #10.1

Testco Corporation is considering adding a new product line. The cost of the fa equipment to produce this product is $1,780,000. Company management expe flows from the sale of this product to be $450,000 in each of the next eight yea uses a discount rate of 12 percent for projects like this, what is the net present project? What is the internal rate of return?

Investment = Annual net cash flow = NCF = Discount rate = k = Length of project = n =

$1,780,000 $450,000 12% 8 years

é 1 ù 1ê 8ú NCFt 1.12 ú NPV = å = -$1,780,000 + $450,000 ´ ê t 0.12 ê ú t=0 (1+ k) êë úû n

= -$1,780,000 + $2,235,438 = $455,437.90 Determine the IRR using trial and error. Since NPV > 0, try IRR > k. Try IRR = 20%

é 1 ù 1n ê 8ú NCFt 1.20 ú NPV = 0 = å = -$1,780,000 +$450,000 ´ ê t ê 0.20 ú t=0 (1+ IRR) êë úû = -$1,780,000 +$1,726,722 = -$53,278 ¹ 0 Try IRR = 19%

é 1 ù n ê1- 8 ú NCFt NPV = 0 = å = -$1,780,000 +$450,000 ´ ê 1.19 ú t ê 0.19 ú t=0 (1+ IRR) êë úû = -$1,780,000 +$1,779,465 = -$535 » 0

1 1ê 8ú NCFt 1.19 ú NPV = 0 = å = -$1,780,000 +$450,000 ´ ê t 0.19 (1+ IRR) ê ú t=0 êë úû n

= -$1,780,000 +$1,779,465 = -$535 » 0 The IRR is approximately 19 percent. Using a financial calculator, we find that the IRR is

NCF Cost of Capital NPV IRR

0 1 (1,780,000) $ 450,000 12% $455,437.90 18.99%

2 $ 450,000

3 $ 450,000

w product line. The cost of the factory and 00. Company management expects net cash 000 in each of the next eight years. If Testco like this, what is the net present value of this

ulator, we find that the IRR is 18.99 percent.

4 $ 450,000

5 $ 450,000

6 $ 450,000

7 $ 450,000

8 $ 450,000

STP #10.2

Discount rate = k = Year 0 1 2 3 4 5 6 7

Flowers Unlimited is considering purchasing an additional delivery truck w The new truck will cost $42,000. Cost savings with this truck are expected $8,900 for the following two years, and $5,000 for the last three years of th period for this project? What is the discounted payback period for this proj 10% NCF Cumulative NCF PV(NCF) $ (42,000) $ (42,000) $ (42,000) 12,800 (29,200) 11,636 12,800 (16,400) 10,579 8,900 (7,500) 6,687 8,900 1,400 6,079 5,000 6,400 3,105 5,000 11,400 2,822 5,000 16,400 2,566

PB = Years before cost recovery + (Remaining cost to recover / PV Cash flow during the year) = 3 + ($7,500 / $8,900) = 3.84 years Discounted PB = Years before cost recovery + (Remaining cost to recover / PV Cash flow during the year) = = 6 + ($1,092 / $2,566) = 6.43 years

g purchasing an additional delivery truck wchich will have a seven-year useful life. Cost savings with this truck are expected to be $12,800 for the first two years, rs, and $5,000 for the last three years of the truck's useful life. What is the payback he discounted payback period for this project with a discount rate of 10 percent?

Cumulative PV(NCF) $ (42,000) (30,364) (19,785) (13,098) (7,020) (3,915) (1,093) 1,473

o recover / PV Cash flow during the year) =

aining cost to recover / PV Cash flow

STP #10.3 What is the average accounting rate of return (ARR) on a piece of equipment that w million and that will result in pretax cost savings of $380,000 for the first three years $280,000 for the following three years? Assume that the machinery will be deprecia salvage value of 0 over 6 years using the straight-line method and the company's a rate is 32 percent. If the acceptance decision is based on the project exceeding an percent, should this machinery be purchased? Year 1 Year 2 Year 3 Year 4 $ 380,000 $ 380,000 $ 380,000 $ 280,000 Cost savings 200,000 200,000 200,000 200,000 Depreciation 180,000 180,000 180,000 80,000 EBIT 57,600 57,600 57,600 25,600 Taxed (32%) 122,400 122,400 122,400 54,400 Net income 1,200,000 Beg. book value 200,000 Less: Depreciation $1,000,000 End. book value

1,000,000 200,000 $800,000

800,000 200,000 $600,000

Average after-tax income (years 1 through 6) = Average book value of equipment (years 2 through 6) = Accounting rate of return

Average after-tax income Average book value

600,000 200,000 $400,000

88400 600000 =

RR) on a piece of equipment that will cost $1.2 of $380,000 for the first three years and then that the machinery will be depreciated to a t-line method and the company's average tax based on the project exceeding and ARR of 20 Year 5 Year 6 $ 280,000 $ 280,000 200,000 200,000 80,000 80,000 25,600 25,600 54,400 54,400 400,000 200,000 $200,000

$88,400 $600,000

200,000 200,000 $0

14.7%

STP #10.5 West Street Automotive is considering adding state safety inspections to their servi offerings. The equipment necessary to perform these inspections will cost $557,000 will generate cash flows of $195,000 over each of the next five years. If the cost of is 14 percent, what is the MIRR on this project? Investment (cost) = Annual net cash flow = NCFt = Length of project = n = Cost of capital = k =

$557,000 $195,000 5 years 14%

TV = NCF1(1 + k)n −1 + NCF2(1 + k)n −2 + … + NCFn(1 + k)n −n

= $195,000 ´ 1.14 4 + $195,000 ´1.143 + $195,000 ´ 1.142 + $195,000 ´ 1.14 + $195 = $329,347+ $288,901+ $253,422 + $222,300 + $195,000 = $1,288,970 Solve for the MIRR:

TV (1+ MIRR)n $1,288,970 %557,000 = (1+ MIRR)5 $1,288,970 Þ (1+ MIRR)5 = = 2.3141 $557,000 Þ (1+ MIRR)5 = 2.31411/5 = 1.1827 PVCost =

Þ MIRR = 0.1827 = 18.3% MIRR =

18.3%

ate safety inspections to their service hese inspections will cost $557,000 and of the next five years. If the cost of capital

Fn(1 + k)n −n

0 ´ 1.142 + $195,000 ´ 1.14 + $195,000

195,000

11.6

Computing terminal-year FCF: Healthy Potions, Inc., a pharmaceutical company, bo a machine at a cost of $2,000,000 five years ago that produces pain-reliever medicine The machine has been depreciated over the past five years, and the current book valu $800,000. The company decides to sell the machine now at its market price of $1 milli The marginal tax rate is 30 percent. What are the relevant cash flows? How do they change if the market price of the machine is $600,000 instead? The relevant cash flows would be as follows:

Salvage value of machine = Book Value of machine = Marginal tax rate =

$ 1,000,000 $ 800,000 30%

Taxable Gain from sale = Taxes on gain=

$ $

200,000 60,000

After tax Salvage value=

940,000 =cash inflow in terminal year

Salvage value of machine = Book Value of machine = Loss on sale Tax saving from write-off on loss=

$ $ $ $

600,000 800,000 (200,000) 60,000

After tax Salvage value=

660,000 =cash inflow in terminal year

If the machine is sold for $600,000

harmaceutical company, bought uces pain-reliever medicine. s, and the current book value is t its market price of $1 million. cash flows? How do they ad?

nflow in terminal year

11.9 Investment cash flows: Zippy Corporation just purchased computing equipment for $2 equipment will be depreciated using a five-year MACRS depreciation schedule. If the sold at the end of its fourth year for $12,000, what are the after-tax proceeds from the the marginal tax rate is 35 percent?

MACRS Year 1 2 3 4 5 6

% 20.00% 32.00% 19.20% 11.52%

Cost 20,000 4,000 6,400 3,840 2,304

16,544 Total Depreciation

Book Value

3,456

mputing equipment for $20,000. The preciation schedule. If the equipment is ter-tax proceeds from the sale, assuming

12,000 selling price 3,456 book value 8,544 Gain 35.00% Tax rate $2,990.40 Tax Expense 12,000 selling price $2,990.40 Tax Expense $9,009.60 After tax proceeds from the sale

11.10 Investment cash flows: Six Twelve Inc. is considering opening up a new convenience store in downtown New York City. The expected annual revenue is $800,000. To estimate the increase in working capital, analysts estimate the ratio of cash and cash equivalents to revenue to be 0.03 and the ratio of receivables, inventories, and payables to revenue to be 0.05, 0.10, and 0.04, respectively in the same industry. What is the incremental cash flows related to working capital when the store is opened? Expected annual revenue Ratio of cash and cash equivalents to revenue Ratio of receivables to revenue Ratio of inventories to revenue Ratio of payables to revenue

800,000 3% 5% 10% 4%

Investment in Working Capital = Change in Current Assets - Change in current liabilities Investment in Working Capital = $

144,000

minus

$ 32,000

ening up a new ed annual revenue is ysts estimate the ratio of atio of receivables, 0.04, respectively in the o working capital when

e in current liabilities $

112,000

11.11 Investment cash flows: Keswick Supply Company wants to set up a division that pro services to businesses. Customers will be given 20 days to pay for such services. The division is estimated to be $25,000. Assuming that the customers take the full 20 days incremental cash flow associated with accounts receivable? Annual Credit Sales Day sales outstanding Average daily credit sales Average Accounts receivables

$25,000 20

$68.49 $1,369.86 =Incremental cash flow associated w

ts to set up a division that provides copy and fax to pay for such services. The annual revenue of the ustomers take the full 20 days to pay, what is the le?

ental cash flow associated with accounts receivable

Nominal Cash flows $ (200) $ (300) $ (300) $ (300)

Real Cash Flows $ (200.00) $ (288.46) $ (277.37) $ (266.70)

4% 10%

Nominal Rate

14.40%

Price of Sofa

$891.84

14.40% YEAR CFS PVIF NPV 0 $ (200) 1.00000 1 $ (300) 0.87413 2 $ (300) 0.76410 3 $ (300) 0.66792

($891.84)

$ $ $ $

(200) (262) (229) (200) ($891.84)

fa. You will pay nts of $300 in the pected inflation rate

Real Cash Flows $ (200.00) $ (288.46) $ (277.37) $ (266.70)

11.17 Nominal versus real cash flows: You are graduating in two years. You want to inves in bonds and use the proceeds to purchase a new car when you graduate and start to in either bond A, a two-year bond with a 3 percent annual interest rate, or bond B, an paying 1 percent real interest above the inflation rate (assume this bond makes annua inflation rate over the next two years is expected to be 1.5 percent. Assume that both the same market price. Which bond should you invest in? Time until graduation 2 years Current savings 5,000 MaturityAnn. Interest rate Bond A 2 3% Bond B

1% above real interest rate

Expected inflation rate

1.50%

At 3% per year, $5000 invested in Bond A would provide you with a terminal value of

At an inflation-indexed rate of return equal to 1% + inflation rate….Bond B will provide Real Inflation rate Nominal rate Terminal value

1.00% 2.00% $ 5,202.00 1.50% 2.50% $ 5,253.13 2.00% 3.00% $ 5,304.50 2.50% 3.50% $ 5,356.13 3.00% 4.00% $ 5,408.00 3.50% 4.50% $ 5,460.13 4.00% 5.00% $ 5,512.50 Since the inflation rate expected over the next two years is 1.5%, Bond A would be the

o years. You want to invest your current savings of $5,000 you graduate and start to work. You can invest the money terest rate, or bond B, an inflation-indexed two-year bond me this bond makes annual interest payments). The ercent. Assume that both bonds are default free and have

erminal value of

5304.5

rate….Bond B will provide a terminal value of

1.5%, Bond A would be the better choice.

$ 5,253.13

11.18 Marginal and average tax rates: Given the U.S. Corporate Tax Rate Schedule in Exh is the marginal tax rate and average tax rate of a corporation that generates a taxable million in 2013? Exhibit 11.6 U.S. Corporate Tax Rate Schedule in 2007 Taxable Income More Than $0 $50,000 $75,000 $100,000 $335,000 $10,000,000 $15,000,000 $18,333,333

But Not More Than $50,000 $75,000 $100,000 $335,000 $10,000,000 $15,000,000 $18,333,333 ---------

Tax Owed $7,500 + $13,750 + $22,250 + $113,900 + $3,400,000 + $5,150,000 +

15% 25% 34% 39% 34% 35% 38% 35%

Taxable Income

12,000,000

Taxes=

4,100,000

Marginal Tax rate Average Tax rate

35% 34.17%

rate Tax Rate Schedule in Exhibit 11.6, what ation that generates a taxable income of $12

Tax Owed of amount beyond $0 of amount beyond $50,000 of amount beyond $75,000 of amount beyond $100,000 of amount beyond $335,000 of amount beyond $10,000,000 of amount beyond $15,000,000

11.19 Investment cash flows: Healthy Potions, Inc. is considering investing in a new production line of eye drops. Other than investing in the equipment, the company needs to increase its cash and cash equivalents by $10,000, increase the level of inventory by $30,000, increase accounts receivable by $25,000, and increase accounts payable by $5,000 at the beginning of the investment. Healthy Potions will recover these changes in working capital at the end of the project 10 years later. Assume the appropriate discount is 12 percent. What are the present values of the relevant cash flows? Increase in cash Increase in inventory Increase in AR Increase in AP Discount rate Number of years until end of project

$ $ $ $

10,000 30,000 25,000 5,000 12% 10

Change in NWC in Year 0 Recovery of NWC in Year 10 Present value of recovery of NWC

$ (60,000) $ 60,000 $ 19,318.39

11.20 Cash flows from operations: Given the soaring price of gasoline, Ford is considering introducing a new production line of gas-electric hybrid sedans. The expected annual sales number of such hybrid cars is 30,000; the price is $22,000 per car. Variable costs of production amount to $10,000 per car. The fixed overhead including salary of top executives is $80,000,000 per year. However, the introduction of the hybrid sedan will decrease Ford’s sales of regular sedans by 10,000 cars per year; the regular sedans have a unit price of $20,000 and unit variable cost of $12,000, and fixed costs of $250,000 per year. Depreciation costs of the production plant are $50,000 per year. The marginal tax rate is 40 percent. What is the incremental annual cash flow from operations? Expected annual unit sales Price Variable Prod Cost Exec salaries Annual Depreciation Marginal Tax rate

$ $ $

Hybrids 30,000 22,000 $ 10,000 $ 80,000,000 $ 50,000 40%

Sedans 10,000 Lost Sales (units) 20,000 Unit Price 12,000 250,000 Fixed Costs

Lost EBIT from Sedans $ 80,000,000 Calculation of Incremental Annual Cash Flow from Operations Revenue from hybrid sales Less Variable Costs Less Fixed Op Costs EBITDA Less Dep. EBIT from Hybrids Less Lost EBIT from sedans

$ 660,000,000 $ 300,000,000 $ 80,000,000 $ 280,000,000 $ (50,000) $ 279,950,000 $ 80,000,000

Net EBIT from new operat

$ 199,950,000

Less Taxes

NOPAT

$ 119,970,000

Add back Depreciation

Incremental Operating Cash Flow

$ 120,020,000

79,980,000

50,000

soline, Ford is hybrid sedans. The ; the price is ,000 per car. The 000 per year. Ford’s sales of have a unit price of $250,000 per per year. The ual cash flow from

Lost Sales (units) Unit Price Fixed Costs

11.21

FCF and NPV for a project: Archers Daniels Midland Company is considering buying million for land and $10 million for trucks and other equipment. The land, all trucks, and in expected to produce revenue of $2 million each year and annual cash flow from ope investment. 0 Investment cash flows Land $ (2,000,000) Trucks and Equipment $ (10,000,000)

Revenues Cash Flow from Operations Capital Exp NWC FCF NPV Depreciation BV at end of 10 years Annual Sline Dep Salvage Value Marginal Tax rate Disc. Rate

$ $

2,000,000 1,800,000

$ $

(12,000,000)

$718,056.93 3,000,000 5,000,000 35% 10%

Year 0 1 2 3 4 5 6 7 8 9 10

CFs $ (12,000,000) 1,800,000 1,800,000 1,800,000 1,800,000 1,800,000 1,800,000 1,800,000 1,800,000 1,800,000 6,100,000

mpany is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investme ment. The land, all trucks, and all other equipment are expected to be sold at the end of 10 years for a price of $5 mi nd annual cash flow from operations equal $1.8 million. The marginal tax rate is 35 percent, and the appropriate disc 1

$ 1,800,000

1,800,000

$ 1,800,000

1,800,000

$ 1,800,000

10.00% PVIF

NPV 1.00000 $ 0.90909 $ 0.82645 $ 0.75131 $ 0.68301 $ 0.62092 $ 0.56447 $ 0.51316 $ 0.46651 $ 0.42410 $ 0.38554 $

(12,000,000) 1,636,364 1,487,603 1,352,367 1,229,424 1,117,658 1,016,053 923,685 839,713 763,376 2,351,814 $718,056.93

e farm will require an initial investment of $12 million. This investment will consist of $2 end of 10 years for a price of $5 million, which is $2 million above book value. The farm 5 percent, and the appropriate discount rate is 10 percent. Calculate the NPV of this 6

$ 1,800,000

$ $

1,800,000 4,300,000

$ 1,800,000

6,100,000

11.22 Projects with different lives: You are trying to choose between purchasing one of two Machine A costs $15,000 to purchase and has a three-year life. Machine B costs $17, four-year life. Regardless of which machine you purchase, it will have to be replaced a life. Which machine would you choose? Assume a marginal tax rate of 35 percent and percent. Since the machines have different economic lives, choose the machine with the i% = 15.00% n of A 3 tax rate = 35.00% n of B 4

Model A

PVIF PVIFA (15,000) 0.6575162 2.2832251

EAC (6,570)

Model B

(17,700) 0.5717532 2.8549784

(6,200) Choose Machine B, be

n purchasing one of two machines for a factory. Machine B costs $17,700 to purchase but has a l have to be replaced at the end of its operating rate of 35 percent and a discount rate of 15

he machine with the lowest EAC.

hoose Machine B, because of lowest EAC.

11.23

Projects with different lives: You are starting a family pizza parlor and need to buy a two models in mind. Model A costs $9,000 and is expected to run for six years; model $14,000, and has an expected life of 10 years. The annual maintenance costs are $80 Assume that the opportunity cost of capital is 10 percent. Which one should you buy?

Costs $ Life (years) Maint. Costs $ Cost of Capital

Model A (9,000) $ 6 800 $ 10%

Model B (14,000) 10 600

NPV EAC Decision

($12,484.21) ($17,686.74) ($2,866.47) ($2,878.44) Choose A ; lower EAC

Model A

PMT $

(800)

PVIFA Cost 0.56447 4.35526 $ (9,000)

(600)

0.38554 6.14457 $ (14,000)

Model B

PVIF

zza parlor and need to buy a motorcycle for delivery orders. You have d to run for six years; model B is more expensive, with a price of l maintenance costs are $800 for model A and $700 for model B. Which one should you buy?

NPV EAC $ (12,484.21) $ (2,866.47) Choose A; Lower EAC $

(17,686.74) $ (2,878.44)

11.24 When to harvest an asset: Predator LLC, a leveraged-buyout specialist, recently bou a company and wants to determine the optimal time to sell it. The partner in charge of investment has estimated the after-tax cash flows at different times as follows: $700,0 sold one year later; $1,000,000 if sold two years later; $1,200,000 if sold three years la and $1,300,000 if sold four years later. The opportunity cost of capital is 12 percent. When should Predator sell the company? Why? End of Year After-tax CFs 1 $ 700,000 2 $ 1,000,000 3 $ 1,200,000 4 $ 1,300,000 Disc. Rate

PV at Year 0 $ 625,000 $ 797,194 $ 854,136 Optimal $ 826,174

12%

Predator should sell the company at the end of Year 3, since it will provide the highest

uyout specialist, recently bought l it. The partner in charge of this ent times as follows: $700,000 if 200,000 if sold three years later; ost of capital is 12 percent.

ce it will provide the highest NPV.

11.25 Replace an existing asset: Bell Mountain Vineyards is considering updating its current accounting system with a high-end electronic system. While the new accounting system save the company money, the cost of the system continues to decline. The Bell Mounta opportunity cost of capital is 10 percent and the costs and values of investments made a different times in the future are as follows: Year 0 1 2 3 4 5

Cost $5,000 $4,500 $4,000 $3,600 $3,300 $3,100

When should Bell Mountain buy the new accounting system?

Year 0 1 2 3 4 5

Cost $5,000 $4,500 $4,000 $3,600 $3,300 $3,100

Value of Future Savings (at time of purchase) $7,000 $7,000 $7,000 $7,000 $7,000 $7,000

Answer: Bell Mountain should buy the new accounting system at the end of Year

neyards is considering updating its current manual system. While the new accounting system would em continues to decline. The Bell Mountain’s e costs and values of investments made at Value of Future Savings (at time of purchase) $7,000 $7,000 $7,000 $7,000 $7,000 $7,000

unting system?

NPV (at purchase) $2,000 $2,500 $3,000 $3,400 $3,700 $3,900

NPV today $ 2,000.00 $ 2,272.73 $ 2,479.34 $ 2,554.47 $ 2,527.15 $ 2,421.59

new accounting system at the end of Year 3

11.26

Year 0 1 2 3 4-15 Opp. Cost EAC PV of Costs

Replace an existing asset: You have a 2000 Nissan that is expected to run for an three years, but you are considering buying a new Hyundai before the Nissan wear You will donate the Nissan to Goodwill when you buy the new car. The annual maintenance cost is $1,500 per year for the Nissan and $200 for the Hyundai. The of your favorite Hyundai model is $18,000 and it is expected to run for 15 years. Yo opportunity cost of capital is 3 percent. Ignore taxes. When should you buy the new Hyundai? Costs Nissan Hyundai $ $ (18,000) $ 1,500 $ 200 $ 1,500 $ 200 $ 1,500 $ 200 $ 200 3% ($1,500.00) ($1,707.80) ($4,242.92) ($20,387.59)

Answer: Since the annual cost of driving the Nissan is less than the EAC of the Hyundai, You should drive it for three more years and then buy the new Hyundai.

Nissan

PMT (1,500)

Hyundai

(200)

PVIF PVIFA 0.91514 2.82861 $

Cost -

NPV (4,243)

EAC (1,500)

0.64186 11.9379 $ (18,000) (20,388)

(1,708)

expected to run for another before the Nissan wears out. w car. The annual 0 for the Hyundai. The price to run for 15 years. Your should you buy the new

e EAC of the Hyundai, dai.

11.28 When to harvest an existing asset: Anaconda Manufacturing Company currently owns to contain a certain amount of gold. Since Anaconda does not have any gold-mining company plans to sell the entire mine and base the selling price on a fixed multiple of gold and have determined that the price will increase by 14 percent, 12 percent, 9 per during the next one, two, three, and four years, respectively. If Anaconda's opportunit percent, what is the optimal time for Anaconda to sell the mine?

The rate of gold price appreciation is greater than the opportunity cost of capita years and then it drops below the opportunity cost of capital. Therefore, Anacon gold at the beginning of the third year (or at the end of the second year).

ring Company currently owns amine that is known es not have any gold-mining expertise, the ng price on a fixed multiple of the spot price for 14 percent, 12 percent, 9 percent, and 6 percent ely. If Anaconda's opportunity cost of capital is 10 e mine?

e opportunity cost of capital for the next two f capital. Therefore, Anaconda should sell the of the second year).

$ (20,000) 5 7%

EAC

($4,878)

Replacing your car, will cost you on average $4,878 per year based on its EAC. So, that would be the opportunity cost of using your car to deliver pizzas in your spare tim COST OF NEW CARPVIF PVIFA EAC $ (20,000) 0.7129862 4.1002 ($4,878)

11.30 You are the CFO of SlimBody Inc., a retailer of the exercise machine Slimbody6 and re opening up a new store in Los Angeles. The store will have a life of 20 years. It will gen and the price of each machine is $2,500. The annual sales of accessories will be $600 store including labor and rent will amount to 50 percent of the revenues concerning the store will equal $30 million and will be fully depreciated on a straight-line basis over the invest $2,000,000 in additional working capital immediately, and recover it at the end o 30 percent. The opportunity cost of opening up the store is 10 percent. What are the in beginning of the project as well as in Years 1–19 and 20? Should you approve it? Units 5,000

Price 2,500

Annual Exp. Sales $ Accessories sales Op. expenses 50% of revenues concerning exercise machines Initial cost 30,000,000 Add. Working capital 2,000,000 Recovery of Working Capital 2,000,000 in year 20 Life 20 years Tax rate 30% Cost of Capital 10%

Initial Cost Add. W. Capital

Initial Year $ (30,000,000) $ (2,000,000)

Years 1-19

Exer. Mach Revenue Accessories Revenue

$ 12,500,000 $ 600,000

Op Exp

6,250,000

EBITDA

6,850,000

Less Dep

1,500,000

EBT Less Taxes

$ $

5,350,000 1,605,000

Net OP Inc…

3,745,000

Add Dep

1,500,000

$ (32,000,000) $

5,245,000

Net Cash Flow

NPV

$ 12,950,929

Decision

Approve it

PMT 5,245,000

PVIF 0.163507991 0.148643628

xercise machine Slimbody6 and related accessories. Your firm is considering ill have a life of 20 years. It will generate annual sales of 5,000 exercise machines l sales of accessories will be $600,000 and the operating expenses of running the ent of the revenues concerning the exercise machines. The initial investment in the ed on a straight-line basis over the 20-year life of the store. Your firm will need to diately, and recover it at the end of the investment. Your firm’s marginal tax rate is tore is 10 percent. What are the incremental cash flows from this project at the d 20? Should you approve it?

Revenues $ 12,500,000 $ 600,000 cerning exercise machines

Year 20 $

2,000,000

$ $

12,500,000 600,000

6,250,000

6,850,000

1,500,000

$ $

5,350,000 1,605,000

3,745,000

1,500,000

7,245,000

PVIFA 8.364920092

I/O

NPV

$ 7,245,000 $ (32,000,000)

$12,950,929 APPROVE IT

11.31

Merton Shovel Corporation has decided to bid for a contract to supply shovels to t Honduran Army intends to buy 1000 shovels per year for the next three years. To will have to acquire manufacturing equipment at a cost of $150,000. This equipm straight-line basis over its 5-year lifetime. At the end of the third year Merton can its book value ($60,000). Additional fixed costs will be $36,000 per year and varia shovel. An additional investment of $25,000 in net working capital will be required this investment will be recovered at the end of the third year. Merton Shovel has a and a 17 percent required rate of return on the project. What is the lowest possib Merton can offer for the contract and still create value for its stockholders?

Year 0 cash flow

Cap Exp Add WC CF

(150,000) (25,000) (175,000)

Year 3 CF

Cap Exp Add WC CF

60,000 25,000 85,000

17.00%

NPV of Shovel Contract CF 85,000 IO PV PVIFA PMT

PVIF PVIFA 0.624371 2.209585 (175,000) 53,071 2.209585

121,929 55,182

= =

CF Payment = [Revenue - Operating Expense - D&A) x (1 - t)] + D&A CF Payment $55,182 Revenue 100P OpExpense $3,000.00 $3.00 1000 Depreciation $30,000 $150,000 5 Fixed costs $36,000

Tax rate

35.00%

$55,181 = [(Px1000)-$3,000-$36,000-$30,000] x (.65) + $30,000 $25,181 = 650P - $44850 $70,031 = $70,031/650 = $107.74 =

650P P P

This is the minimum bid price for a shovel. If Merton Shovel charges less th the NPV of the contract will be less than zero.

contract to supply shovels to the Honduran Army. The r for the next three years. To supply these shovels, Merton st of $150,000. This equipment will be depreciated on a of the third year Merton can sell the equipment for exactly be $36,000 per year and variable costs will be $3.00 per working capital will be required when the project is initiated: rd year. Merton Shovel has a 35 percent marginal tax rate ct. What is the lowest possible per shovel price that e for its stockholders?

IO NPV (175,000) 12814.72

PMT PMT

&A) x (1 - t)] + D&A

2.209585

11.32

Rocky Mountain Lumber, Inc. is considering purchasing a new wood saw that costs $ generate revenues of $100,000 per year for five years. The cost of materials and lab these revenues will total $60,000 per year, and other cash expenses will be $10,000 expected to sell for $1,000 at the end of its five-year life, and will be depreciated on a five years to zero. Rocky Mountain’s tax rate is 34 percent and its opportunity cost of Should the company purchase the saw? Explain why or why not. Cost of Saw Revenues Expenses Other Cash expenses Salvage value Life Cost of Capital Tax Rate

$ $ $ $ $

50,000 100,000 60,000 10,000 1,000 5 10% 34% 0

Revenues Materials & Labor Other Cash Expenses Depreciation

1 $ 100,000 $ 60,000 $ 10,000 $ 10,000

2 $ 100,000 $ 60,000 $ 10,000 $ 10,000

$ 20,000 $ 6,800 $ 23,200

Capital Expenditures Salvage Value Tax on Gain AT Salvage Value

(50,000)

Before Tax Cash Flow Taxes ATCF

(50,000) $ 20,000 $ 6,800 (50,000) $ 23,200

NPV Decision

$ 38,356 BUY THE SAW

YEAR 0 1 2 3 4

CFs $ (50,000) $ 23,200 $ 23,200 $ 23,200 $ 23,200

PVIF 1 0.9090909 0.8264463 0.7513148 0.6830135

$ 23,860

0.6209213

a new wood saw that costs $50,000. The saw will he cost of materials and labor needed to generate h expenses will be $10,000 per year. The machine is and will be depreciated on a straight-line basis over nt and its opportunity cost of capital is 10 percent. why not.

3 $ 100,000 $ 60,000 $ 10,000 $ 10,000

$ 20,000 $ 6,800 $ 23,200

NPV $ (50,000) $ 21,091 $ 19,174 $ 17,431 $ 15,846

4 $ 100,000 $ 60,000 $ 10,000 $ 10,000

$ 20,000 $ 6,800 $ 23,200

$ $ $ $

5 100,000 60,000 10,000 10,000

$ $ $

1,000 340 660

$ $ $

20,660 6,800 23,860

$ 14,815 $ 38,356

11.33

A beauty product company is developing a new fragrance named Happy Forever. The probability of 0.5 that consumers will love Happy Forever, and in this case, annual sale 1,000,000 bottles; a probability of 0.4 that consumers will find the smell acceptable an sales will be 200,000 bottles; and a probability of 0.1 that consumers will find the smel unpleasant and annual sales will be only 50,000 bottles. The selling price is $38, and variable cost is $8 per bottle. There is a fixed production cost of $1 million per year, an depreciation costs are $1.2 million. Assume that the marginal tax rate is 40 percent. are the expected annual incremental cash flows from the new fragrance? Probability 0.5 0.4 0.1 $38 $8

Selling Price Variable Cost Fixed Prod. Cost Depreciation Tax rate

$ $

1,000,000 1,200,000 40%

Expected Sales (Units) Expected Revenues Variable Costs Fixed Prod Cost EBTDA Less Dep EBT Taxes Inc. After Taxes Add back Dep $ Incremental Cash Flow

585000 $22,230,000 $4,680,000 1,000,000 $16,550,000 1,200,000 $15,350,000 $6,140,000 $9,210,000 1,200,000 $10,410,000

Sales (units) 1,000,000 200,000 50,000

med Happy Forever. There is a n this case, annual sales will be he smell acceptable and annual umers will find the smell elling price is $38, and the f $1 million per year, and tax rate is 40 percent. What ragrance?

11.34 Great Fit, Inc., is a company that manufactures clothing. The company has a productio regular sizes. The same machine could be used to produce petite sizes as well. Howev reduced from four more years to two more years if the petite size production is added. life of eight years is $2 million. Assume the opportunity cost of capital is 8 percent. Wh petite sizes? Cost of new machine Life Opp. Cost

2,000,000 8 8%

EAC

($348,030)

If the current machine is used to produce petite size dresses, it's life will be only 2years. Thus, we would need to purchase the new machine, two years earlier, i.e i Since the EAC of the new machine is 348,030 per year. With payments occuring in Years 2 an the opportunity cost of using the machine to make petite sized dresses would be the present value of the two $348,030 payments which would be incurred in years 2 and 3 respectiv Opportunity Cost

($574,656.27)

Cost of new machine (2,000,000) Year 0 1 2 3

PVIF PVIFA 0.540268885 5.7466 CFs

PVIF

(348,030) (348,030)

1 0.9259 0.8573 0.7938

EAC (348,030) Opportunity Cost 0.00 0.00 (298,379.63) (276,277.43) (574,657.06)

e company has a production line that produces women’s tops of petite sizes as well. However, the life of the machines will be size production is added. The cost of identical machines with a t of capital is 8 percent. What is the opportunity cost of adding

hine, two years earlier, i.e in two years from now (year 2) ents occuring in Years 2 and 3 respectively es would be the d in years 2 and 3 respectively at the rate of 8%

11.35 Biotech Partners LLC has been farming a new strain of radioactive-material-eating bacte can use to help dispose of its nuclear waste. Two opposing effects are affecting Biotech bacteria. The bacteria are currently growing at a 22 percent annual rate, but due to know Biotech analysts estimate that the price for the bacteria will decline according to the sca capital is 10 percent, then when should Biotech harvest the entire bacteria colony at one

Year 1 2 3 4 5 6

Change in Price Due to Competition (%) 5% -2% -8% -10% -15% -25%

Year 0 1 2 3 4 5 6

Bacteria growth Cost of Capital Quantity Price 10% 1 $ 1.0000 22% 10% 1.22 $ 1.0500 22% 10% 1.4884 $ 1.0290 22% 10% 1.8158 $ 0.9467 22% 10% 2.2153 $ 0.8520 22% 10% 2.7027 $ 0.7242 22% 10% 3.2973 $ 0.5432

Value $ 1.00 $ 1.28 $ 1.53 $ 1.72 $ 1.89 $ 1.96 $ 1.79

Here the bacteria are growing at a rate of 22% per year, but the price for the bacteria is de When the % decline in price exceeds the % growth in the bacteria, is when it would be be Since the price would drop by 28% in year 5, end of year 4 would be the optimal year. Not maximized (1.29) at the end of year 4.

oactive-material-eating bacteria that the electrical utility industry effects are affecting Biotech’s decision of when to harvest the annual rate, but due to known competition from other top firms, decline according to the scale below. If the opportunity cost of entire bacteria colony at one time?

$ $ $ $ $ $ $

PV at 0 1.00 1.16 1.27 1.29 1.29 1.22 1.01

price for the bacteria is declining progressively as well. eria, is when it would be better to fully harvest the asset. uld be the optimal year. Note that the Present Value is

11.36

ACME Manufacturing is considering replacing an existing production line with a new capacity and operates with less labor than the existing line. The new line would cost life, and would be depreciated using MACRS over three years. At the end of five yea as scrap for $200,000 (in year 5 dollars). Because the new line is more automated, i operators, resulting in a savings of $40,000 per year before tax and unadjusted for in Additional sales with the new machine are expected to result in additional net cash in per year (in today’s dollars). If ACME invests in the new line, a one-time investment working capital will be required. The tax rate is 35 percent, the opportunity cost of ca annual rate of inflation is 3 percent. What is the NPV of the new production line? Cost Life Depreciation Salvage Value Cost Savings/year Add net cash inflows Add NWC Tax rate Cost of Capital

$ $ $

1,000,000 5 years 3-year MACRS 200,000 Year 5 dollars 40,000 Before-tax and in Year 0 dollars 60,000 Before-tax and in Year 0 dollars $10,000 35% 10%

Inflation rate

Year 1 2 3 4

MACRS rate 33.33% 44.45% 14.81% 7.41%

0 Add Rev Cost Savings Dep EBT Less Taxes AT OP Inc ATOPInc+Dep Cost Add WC BTSV BV

$ $ $ $ $ $ $

2 61,800 $ 63,654 41,200 $ 42,436 333,300 $ 444,500 (230,300) $ (338,410) 80,605 $ 118,444 (149,695) $ (219,967) 183,605 $ 224,534

666,700

$ 1,000,000 $ 10,000 $ 1,000,000

$ 222,200

Tax on Cap Gain ATSV NCF NPV

$ (1,010,000) $ $ (370,023)

Year 0 1 2 3 4 5

$ $ $ $ $ $

183,605 Reject

$ 224,534

CFs (1,010,000) 183,605 224,534 122,862 99,093 205,353

PVIF 1.00000 0.90909 0.82645 0.75131 0.68301 0.62092

production line with a new line that has a greater output . The new line would cost $1 million, have a five-year ars. At the end of five years, the new line could be sold line is more automated, it would require fewer e tax and unadjusted for inflation (in today’s dollars). ult in additional net cash inflows, before tax, of $60,000 e, a one-time investment of $10,000 in additional the opportunity cost of capital is 10 percent, and the e new production line?

ar 0 dollars ar 0 dollars

3 $ $ $ $ $ $ $

4 65,564 $ 67,531 43,709 $ 45,020 148,100 $ 74,100 (38,827) $ 38,451 13,590 $ (13,458) (25,238) $ 24,993 122,862 $ 99,093

5 $ 69,556 $ 46,371 $ $ 115,927 $ (40,575) $ 75,353 $ 75,353

74,100

$ 200,000 $ -

$ 70,000 $ 130,000 $

122,862

$ $ $ $ $ $

NPV (1,010,000) 166,914 185,565 92,308 67,682 127,508

$ 99,093

(370,023) Reject

$ 205,353

11.37 The alternative to investing in the new production line in Problem 11.36 is to overhaul th which currently has both a book value and a salvage value of $0. It would cost $300,000 existing line, but this expenditure would extend its useful life to five years. The line woul salvage value at the end of five years. The overhaul outlay would be capitalized and de MACRS over three years. Should ACME replace or renovate the existing line? Cost $ Life Depreciation Salvage Value Cost Savings/year $ Add net cash inflows $ Add NWC Tax rate Cost of Capital

300,000 5 years 3 MACRS 0 Year 5 dollars Before-tax and in Year 0 dollars Before-tax and in Year 0 dollars $0 35% 10%

Inflation rate

Year 1 2 3 4

MACRS rate 33.33% 44.45% 14.81% 7.41%

0 Add Rev Cost Savings Dep EBT Less Taxes AT OP Inc ATOPInc+Dep Cost Add WC BTSV BV Tax on Cap Gain ATSV

$ $

300,000 -

300,000

$ $ 0 $ 99,990 $ (99,990) $ 34,996 $ (64,993) $ 34,997

$ $ 0 $ 133,350 $ (133,350) $ 46,672 $ (86,677) $ 46,673

$ 200,010

66,660

NCF NPV

$ (300,000) $ 34,997 $ (212,615) Reject

Year 0 1 2 3 4 5

CFs $(300,000) $ 34,997 $ 46,673 $ 15,551 $ 7,781 $ 0

46,673

PVIF 1.00000 0.90909 0.82645 0.75131 0.68301 0.62092

ine in Problem 11.36 is to overhaul the existing line, ge value of $0. It would cost $300,000 to overhaul the useful life to five years. The line would have a $0 ul outlay would be capitalized and depreciated using r renovate the existing line?

in Year 0 dollars in Year 0 dollars

3 $ $ $ $ $ $ $

$ 0 $ 0 44,430 $ 22,230 (44,430) $ (22,230) 15,550 $ 7,780 (28,879) $ (14,449) 15,551 $ 7,781

22,230

$ $ $ $ $ $ $

$ $ $ $

0 0 (0) 0 0

15,551

7,781

$ $ $ $ $ $

NPV (300,000) 31,815 38,572 11,683 5,314 0

(212,615) Reject

11.38 FITCO is considering the purchase of new equipment. The equipment costs $350,000 needed to install it. The equipment will be depreciated straight-line to zero over a fiveadditional annual revenues of $265,000, and it will have annual cash operating expen be sold for $85,000 after five years. An inventory investment of $73,000 is required du is in the 40 percent tax bracket, and its cost of capital is 10 percent.What is the projec

a. $47,818 b. $63,658 c. $80,189 d. $97,449

Cost of equipment $350,000 Installation cost $110,000 Life (years) 5 Depreciation method Straight line Additional annual revenues due to equipment $265,000 Annual cash operating expenses $83,000 Salvage value after 5 years $85,000 Investment in inventory $73,000 Corporate tax rate 40% Cost of capital 10% 0 Initial cost Equipment Installation Increase in net working capital

($350,000) ($110,000) ($73,000)

Total initial outlay

($533,000)

Increase in revenues Operating expenses Depreciation

$265,000 $83,000 92000

EBIT Taxes Net income

$90,000 $36,000 $54,000

After-tax salvage value Net after-tax cash flow

$146,000

Net Present Value of the project =

$97,449.11

Year 0 1 2 3 4 5

CFs ($533,000) $146,000 $146,000 $146,000 $146,000 $270,000

t. The equipment costs $350,000, and an additional $110,000 is d straight-line to zero over a five-year life.The equipment will generate ave annual cash operating expenses of $83,000. The equipment will estment of $73,000 is required during the life of the investment. FITCO l is 10 percent.What is the project NPV?

$73,000

$265,000 $83,000 92000

$265,000 $265,000 $83,000 $83,000 92000 92000

$265,000 $83,000 92000

$90,000 $36,000 $54,000

51000 $146,000

$146,000

$270,000

PVIF 1 0.909091 0.826446 0.751315 0.683013 0.620921

NPV (533,000.00) 132,727.27 120,661.16 109,691.96 99,719.96 167,648.76 97,449.11

11.39 After estimating a project’s NPV, the analyst is advised that the fixed capital outlay will fixed capital outlay is depreciated straight-line over an eight-year life.The tax rate is 40 is 10 percent. No changes in cash operating revenues, cash operating expenses, or sa a. $100,000 decrease b. $73,325 decrease c. $59,988 decrease d. No change Increase in fixed capital outlay Depreciation method Project's life (years) Tax rate Required rate of return

0 Increased outlay $ (100,000) Depreciation Depreciation tax shield Effect on NPV

$100,000 Straight line 8 40% 10%

Annual cash flow effects 3

$12,500 $5,000

CFs $ (100,000) 5,000 5,000 5,000 5,000 5,000 5,000 5,000 5,000

PVIF 1.00000 0.90909 0.82645 0.75131 0.68301 0.62092 0.56447 0.51316 0.46651

$ $ $ $ $ $ $ $ $

NPV (100,000) 4,545 4,132 3,757 3,415 3,105 2,822 2,566 2,333

(73,325)

Year 0 1 2 3 4 5 6 7 8

ixed capital outlay will be revised upward by $100,000.The r life.The tax rate is 40 percent, and the required rate of return erating expenses, or salvage value are expected. What is the

nual cash flow effects 4

$12,500 $5,000

11.40 When assembling the cash flows to calculate an NPV or IRR, the project’s after-tax interest expenses should be subtracted from the cash flows for a. the NPV calculation, but not the IRR calculation b. the IRR calculation, but not the NPV calculation c. both the NPV calculation and the IRR calculation d. neither the NPV calculation nor the IRR calculation Answer : D

V or IRR, the project’s after-tax h flows for

STP #11.1 You purchased 100 shares of stock in an oil company, Texas Energy, Inc., at $50 pe company has 1 million shares outstanding. Ten days later, Texas Energy announce investment in an oil field in east Texas. The probability that the investment will be su generate an NPV of $10 million is 0.2; the probability that the investment will be a fa generate an NPV of negative $1 million is 0.8. How would you expect the stock price upon the company’s announcement of the investment? Probability 20% 80%

Outcome Successful Failure

Expected NPV Number of shares NPV per share

$ $

1,200,000 1,000,000 1.20

Increase in Price

1.20

NPV $ 10,000,000 $ (1,000,000)

oil company, Texas Energy, Inc., at $50 per share. The . Ten days later, Texas Energy announced an e probability that the investment will be successful and probability that the investment will be a failure and 0.8. How would you expect the stock price to change investment?

STP #11.2 A division of Virginia City Highlands Manufacturing is considering purchasing for $1, automates the process of inserting electronic components onto computer motherboa operating the machine will be $50,000, but it will save the company $370,000 in labo machine will have a useful life of 10 years and its salvage value in 10 years is estim Straight-line depreciation will be used in calculating taxes for this project and the ma percent. If the appropriate discount rate is 12 percent, what is the NPV of this projec

The incremental after-tax free cash flow (FCF) in year 0 is: FCF0 = ($1,500,000)

The FCF in Years 1 through 9 is: Annual Depreciation =($1,500,000 − $300,000)/10 = $120,000 per year FCFt = [($370,000 − $50,000) × (1 − 0.32)] + [0.32 × $120,000] = $2

The FCF in Year 10 is: FCF10 = $256,000 + $300,000 − [(Salvage Value − Book Value) × 0.3 Therefore the NVP of the project is:

é æ 1 öù 1ê ç ÷ú é 9 1.12 ê ç ÷ú + ê$556,000 ´ 1 NPV = -$1,500,000 + $256,000 ´ ê ç 0.12 ÷ú ë 1.12 ç ÷ êë è øúû = -$1,500,000 + $1,364,032 + $179,017 = $43,049

Virginia City Highlands Manufacturing should approve the project since it has a posi Net present value

$43,049

considering purchasing for $1,500,000 a machine that nents onto computer motherboards. The annual cost of the company $370,000 in labor costs each year. The vage value in 10 years is estimated to be $300,000. axes for this project and the marginal corporate tax is 32 , what is the NPV of this project?

= $120,000 per year 0.32)] + [0.32 × $120,000] = $256,000

vage Value − Book Value) × 0.32 = $556,000

æ 1 öù 1ç ÷ú é ù 9 ç 1.12 ÷ú + ê$556,000 ´ 1 ú ç 0.12 ÷ú ë 1.1210 û ç ÷ú è øû

e the project since it has a positive NVP.

STP #11.3 After examining the NPV analysis for a potential project that would increase the firm analyst's manager thells the analyst to increase the initial fixed capital outlay in the a fixed capital outlay would be fully depreciated on a straight-line basis over a 23 year increased. If the firm's average tax rate is 28 percent, its marginal tax rate is 35 perc return is 10 percent, what is the effect of the adjustment on the project NPV?

The additional annual depreciation is: $480,000/12 = $40,000.

For a project such as this, we would use the marginal tax rate. Therefore, the annua 0.35 × $40,000 = $14,000 The change in the overall NPV of the project is:

é æ 1 öù ê ç 1÷ú 12 1.10 ÷ú Change in NPV = - $480,000 + ê$14,000 ´ ç 0.10 ê ç ÷ú ç ÷ú êë è øû = −$480,000 + $95,392 = ($384,608) The NPV will be reduced by $384,608

would increase the firm's output by 5 percent, the ed capital outlay in the analysis by $480,000. The initial ine basis over a 23 year life, regardless of whether it is rginal tax rate is 35 percent, and the required rate of the project NPV?

te. Therefore, the annual depreciation tax savings is:

æ 1 öù ç 1÷ú 12 1.10 ç ÷ú 0.10 ç ÷ú ç ÷ú è øû

STP #11.4 Which of the following are relevant cash flows in the evaluation of a proposal to prod

a. Decrease in the cash flows of a substitute product. b. Alternative of leasing an existing building that will be used for manufacturing this p c. The cost of a new machine required to produce this product. d. Salvage value of the new machine at the end of its useful life. e. Increase in net working capital at the beginning of the project's life. f. Cost to develop a product prototype last year.

a, b, c, d, and e are all relevant cash flows. f is a sunk cost and is therefore not relev

uation of a proposal to produce a new product?

sed for manufacturing this product.

project's life.

ost and is therefore not relevant.

STP #11.5 Managers of Central Embroidery have decided to purchase a new monogram mach machines. The first machine costs $100,000 and is expected to last 5 years. The se expected to lasts 8 years. Assume that the opportunity cost of capital is 8 percent. W Embroidery purchase? The equivalent annual cost for each system is:

é 1.085 ù EAC Machine 1 =0.08´$100,000 ´ ê ú = $25,045.65 5 ë1.08 -1û

é 1.088 ù ú = $27,842.37 8 ë1.08 -1û

EAC Machine 2 =0.08´$160,000 ´ ê

Central Embroidery should purchase the first machine beca

a new monogram machine and are considering two alternative d to last 5 years. The second machine costs $160,000 and is of capital is 8 percent. Which machine should Central

the first machine because it has a lower EAC.

STP #11.6 You have inherited an apple orchard and want to sell it in the next four years. An ex estimated the after-tax cash flow you would receive if you sold at the end of each of if you sell in one year; $1,300,000 if you sell in two years; $1,500,000 if you sell in th four years. Your opportunity cost of capital is 10 percent. When should you sell the o The NPV in today's dollars for each alternative is: NPV1 = $1,000,000

/ 1.01

NPV2 = $1,300,000

/ 1.01

NPV3 = $1,500,000

/ 1.01

NPV4 = $1,600,000

/ 1.01

1 2 3 4

$990,099

= $1,274,385 = $1,455,885 = $1,537,569

You should sell the orchard in 3 years because the present value of the NPV is highest in year three. After year three, the value of the orchard is expected to increase at a rate that is less than your opportunity cost of capital. Therefore, is is better for you to sell the orchard after three years and invest the proceeds elsewhere.

n the next four years. An expert in apple orchard valuation has u sold at the end of each of the next four years as follows: $1,000,000 s; $1,500,000 if you sell in three years; and $1,600,000 if you sell in . When should you sell the orchard?

present value of the ue of the orchard is opportunity cost of ard after three years

Op Ex = VC + FC EBITDA = Revenue – Op Ex EBITDA = Revenue – VC – FC EBIT = Revenue – VC – FC – D&A

Cash Flow DOL = 1 +

Fixed costs FC = 1+ Pretax operating cash flows EBITDA

Accounting DOL = 1 +

FC+ D&A $3,000 + $1,000 =1+ = 3.00 EBIT $2,000

EBITDA Break-even =

FC Price - Unit VC

COEBIT =

(FC+ D&A)Alternative1 − (FC + D&A)Alternative2 Unit contribution Alternative1 − Unit contribution Alternative2

Profitability index

PI =

NPV + Initial investment Initial investment

NPV+Initia PI = Initial Inv

= 1+

000

FC EBITDA

= 3.00

NPV+Initial Investment PI = Initial Investment

12.3

Price Unit Variable Cost FC(incl. dep) Expected Sales

Current New $100 $100 $50 $25.0 2,000,000 $ 3,000,000 45,000

45,000

Revenues $4,500,000 Less VC $2,250,000 Less FC $ 2,000,000 EBITDA $250,000 Contribution Margin $50

$4,500,000 $1,125,000 3,000,000 $375,000 $75

DOL EBITDA Break Even

9 40000

$125,000

9 40000

Answer: Yes, the firm should switch technologies since both production technologies have the same EBITDA break even point, i.e. 40,000 books,and with sales expected to be at 45,000 books, the new technology would add $25 more to its EBITDA per additional book sold, i.e., 5000*$25 = $125,000.

its books for $100 each text. The fixed are currently $2 technology, which ase the variable ooks next year,

oth production 40,000 books,and ogy would add $25 = $125,000.

12.4 EBIT: WalkAbout Kangaroo Shoe Stores forecasts that it will sell 9,500 pairs of shoes next year. The firm buys its shoes for $50 per pair from the wholesaler and sells them for $75 per pair. If the firm will incur fixed costs plus depreciation and amortization of $100,000, then what is the percent increase in EBIT if the actual sales next year equal 11,500 pairs of shoes?

Selling Price Variable Cost Fixed Cost (incl. depreciation) Forecasted Sales EBIT Percent Increase in EBIT=

$75 $50 $100,000 9500 pairs $137,500 36.36%

11500 $187,500

9,500 pairs of shoes aler and sells them nd amortization of ales next year equal

12.5

Cash Flow DOL

$100,000 $5,000 $250,000

1.39

has monthly fixed costs its office furniture and m.

12.6 Cash Flow DOL: The degree of pretax cash flow operating leverage at Rackit Corporat units of its new tennis racket and its EBITDA is $95,000. Ignoring the effects of taxes, w Corporation? Cash Flow DOL = 1 + FC/EBITDA, where: cash flow DOL = EBITDA = Fixed Costs =

2.7 95,000 $161,500.00

ng leverage at Rackit Corporation is 2.7 when it sells 100,000 Ignoring the effects of taxes, what are the fixed costs for Rackit

12.10 Break-even: Calculate the accounting operating profit break-even point and pretax ope break-even point for each of the production choices outlined below. Choice A B C

Price $250.00 $55.00 $10.00

Unit VC $160.00 $10.00 $1.50

FC $15,000.00 $1,100.00 $100.00

D&A $3,000.00 $200.00 $100.00

Choice A B C

Unit Price $250.00 $55.00 $10.00

Unit VC $160.00 $10.00 $1.50

Fixed Costs Depreciation $15,000.00 $3,000.00 $1,100.00 $200.00 $100.00 $100.00

fit break-even point and pretax operating cash flow outlined below.

EBIT Break-even $166.67 $24.44 $11.76

Pretax Operating Cash Flow Break-even $200.00 $28.89 $23.53

12.14 EBIT: Duplicate Footballs, Inc., expects to sell 15,000 balls this year. The balls sell for $110 each and have a variable cost per unit of $80. Fixed costs, including depreciation and amortization, are currently $220,000 per year. How much can either the fixed costs or the variable cost per unit increase in order to keep the company from having a negative EBIT? Expected Sales Unit price Unit Variable Cost Fixed Costs (incl. dep)

15,000 balls $110 $80 $220,000

EBIT

$230,000

Maximum Increase in VC per unit=$15.33 which will result in EBIT = 0 Max. Increase in Fixed Costs= $230,000 which will result in EBIT = 0 EBIT

EBIT

ls this year. The of $80. Fixed costs, 0,000 per year. per unit increase in

12.15 EBIT: Specialty Light Bulbs anticipates selling 3,000 light bulbs this year at a price of $15 Specialty $10 in variable costs to produce each light bulb, and the fixed costs for the firm Specialty has an opportunity to sell an additional 1,000 bulbs next year at the same price but by doing so the firm will incur an additional fixed cost of $4,000 if it chooses to sell th Should Specialty produce and sell the additional bulbs?

Expected Sales Unit price Unit variable cost Fixed Cost

Current 3,000 $15 $10 $10,000

With Added sales Opportunity 4,000 $15 $10 $14,000

EBITDA

$5,000

$6,000

Answer: Yes, they should produce and sell the additional 1000 bulbs, since their E increase from $5000 to $6000

bs this year at a price of $15 per bulb. It costs d the fixed costs for the firm are $10,000. next year at the same price and variable cost, 4,000 if it chooses to sell the additional bulbs.

al 1000 bulbs, since their EBITDA would

12.17 Cash Flow DOL: For the Vinyl CD Co. in self-study problem 12.3, what percentage inc pretax operating cash flow will be driven by the additional revenue? Self-Study Problem 12.3

The Vinyl CD Co. is going to take a project that will increase its EBIT by $90,000 next y The firm’s fixed cost cash expenditure is expected to increase by $100,000, and depre and amortization will increase by $80,000 next year. If the project just happens to yield additional 10 percent in revenue, then what percentage increase in the project’s EBIT w driven by that additional revenue?

Increase in Fixed Costs Increase in EBIT Increase in Dep.& Amort. Increase in Revenue

Cash Flow DOL = 1 +

Cash Flow DOL =

$ 100,000 $ 90,000 $80,000 10%

Fixedcosts FC = 1+ Pretax operatingcash flows EBITDA

1.588

Percentage Increase in Pre-tax operating Cash Flow as a result of the 10% increase in expected revenues= 15.88%

oblem 12.3, what percentage increase in al revenue?

ease its EBIT by $90,000 next year. crease by $100,000, and depreciation he project just happens to yield an increase in the project’s EBIT will be

s a result of the 10%

Information for Problems 12.18-12.20 Dandle’s Candles will be producing a new line of drip-less candles in the coming years and has choice of producing the candles in a large factory with a small number of workers or a small fact a large number of workers. Each candle will be sold for $10. If the large factory is chosen, the co unit to produce each candle will be $2.50, while the cost per unit will be $7.50 for the small facto large factory would have fixed cash costs of $2 million and a depreciation expense of $300,000 while those expenses would be $500,000 and $100,000 in the small factory.

Problem 12.18 Accounting operating profit break-even: Calculate the accounting operating profit break-even both factory choices for Dandle’s Candles.

Data given

Large Factory Small Factory

Unit Cost Selling Price Fixed Cash Costs Depreciation Accounting Op. Profit Break-even (EBIT BE)

$2.50 $10 $2,000,000 $300,000

$7.50 $10 $500,000 $100,000

306,667

240,000

Problem 12.19 Crossover level of unit sales: Calculate the number of candles for Dandle’s Candles for which accounting operating profit is the same regardless of the factory choice.

Crossover EBIT =

Difference in Fixed Costs plus D&A Difference in Contribution Margin

Crossover EBIT Check Crossover EBIT

340,000 $250,000

$250,000

Problem 12.20 Pretax operating cash flow break-even: Calculate the pretax operating cash flow break-even both factory choices for Dandle’s Candles. Pre-tax Operating Cash Flow Break-even = Fixed Cost/(Contribution Margin) where: Contribution Margin = Unit Price-Unit Variable Cost

Pre-tax Operating Cash Flow Break-even

Large Factory Small Factory 266,667 200,000

n the coming years and has the ber of workers or a small factory with arge factory is chosen, the cost per l be $7.50 for the small factory. The ciation expense of $300,000 per year, l factory.

g operating profit break-even point for

r Dandle’s Candles for which the oice.

rating cash flow break-even point for

n Margin)

12.22 Economic break-even point: Management of March and Dine Inc. has estimate that t must generate $10,200 in FCF during each of the next six years to have an NPV of $0. depreciation and amortization charges will equal $3,000, captial expenditures will equa working capital will equal $500 during each of those years. What level of EBIT correspo $10,200 if the firm is subject to the 30 percent marginal tax rate?

From step 2 of the economic break-even point calculations described in the text, we can calcula EBIT = (FCF − D&A + Cap Exp + Add WC) / (1 − t ) EBIT = ($10,200 − $3,000 + $2,000 + $500) / (1 − 0.3) =

$13,857.14

nc. has estimate that the firml's new IV dinner project o have an NPV of $0. Management anticipates that expenditures will equal $2,000, and additions to level of EBIT corresponds to an annual FCF of

e text, we can calculate the EBIT as follows:

12.23 Economic break-even point: RoseWeiser Company management is considering a pr require an initial investment of $50,000 and will last for 10 years. No other capital expe increaseses in working capital are anticipated during the life of the project. What is the that will make the project economically viable if the cost of capital for the project is 9 pe the firm will depreciate the investment using straight-line depreciation and a salvage va Assume that the marginal tax rate is 40 percent.

If the FCF are expected to be equal in each of the ten years, we can solve for FCF using the p of an ordinary annuity formula:

æ 1 ö $50,000 = FCF ´ ç1÷ Þ FCF = $7.791.00 10 è 1.09 ø EBIT = (FCF - D&A + Cap Exp + Add WC) / (1- t) EBIT = ($7,791- $5,000 + $0 + $0) / (1- 0.4) = $4,651.67

gement is considering a project that will ars. No other capital expenditures or of the project. What is the annual EBIT pital for the project is 9 percent and reciation and a salvage value of $0?

solve for FCF using the present value

12.24 Economic break-even point: The BowGus Archery Company management estimates Galactically Flexible Bow project will have to generate EBIT of $20,000 each year to be project's fixed cash expenses are expected to equal $8,000 and its depreciation and am expenses are expected to be $5,000 each year. If the Galactically Flexible bows are ex $100, then how many of these bows must the firm produce and sell each year to gener EBIT of $20,000?

Using step 3 of the economic break-even point calculations described in the text, we can comp total contribution for the project must be:

Revenue - VC = EBIT + D&A + FC = $20,000 + $5,000 + $8,000 = $33,000. From step 4, we know that we can divide this value by the contribution margin per unit to obtain number of units: $33,000 / ($150 − $100) = 660 units

ny management estimates that its new of $20,000 each year to be viable. The and its depreciation and amortization ically Flexible bows are expected to be nd sell each year to generate annual

d in the text, we can compute what the

margin per unit to obtain the required

12.27

Scenario analysis: Chip’s Home Brew Whiskey forecasts that if it sells each bottle o then the demand for the product will be 15,000 bottles per year, whereas sales will be the price is raised 10 percent. Chip’s variable cost per bottle is $10, and the total fixed is $100,000. Depreciation and amortization charges are $20,000, and the firm is in th tax rate. The firm anticipates an increased working capital need of $3,000 for the yea effect of the price increase on the firm’s FCF for the year?

FCF = [(Revenue − Op Ex − D&A) × (1 − t )] + D&A − Cap Exp − Add WC

Scenario 1:Selling Price = $20 per bottle Selling Price $20 per bottle Demand 15,000 bottles Variable Cost $10 per bottle Total Fixed Cash Cost $100,000 per year Dep. And Amort. $20,000 per year Marginal Tax Rate 30% Additional Working Capital $3,000 per year

Answer:

Selling Price = $22 per bottle Selling Price Demand Variable Cost Total Fixed Cash Cost Dep. And Amort. Marginal Tax Rate Additional Working Capital

Revenues Operating Expenses

$300,000 $150,000

Revenues Operating Expenses

Free Cash Flow

$108,000

Free Cash Flow

The Free Cash Flow will increase by

$8,400

f it sells each bottle of Snake-Bite for $20, whereas sales will be 90 percent as high if $10, and the total fixed cash cost for the year 0, and the firm is in the 30 percent marginal of $3,000 for the year. What will be the

e = $22 per bottle

Cash Cost

Working Capital

$22 13500 bottles $10 per bottle $100,000 per year $20,000 per year 30% $3,000 per year

$297,000 $135,000 $116,400

Increase in FCF $8,400

12.29 Mick’s Soft Lemonade is starting to develop a new product for which the fixed cash expenditures are expected to be $80,000. The projected EBIT is $100,000, and the Accounting DOL will be 2.0. What is the Cash Flow DOL for the firm? Fixed Cash Expenses Projected EBIT Accounting DOL

$80,000 $100,000 2

Accounting DOL = 1 +

FC+ D&A $3,000+$1,000 =1+ = 3.00 EBIT $2,000

Cash Flow DOL = 1 +

Fixed costs FC = 1+ Pretax operating cash flows EBITDA

Note: Fixed Cash expenses + D&A = EBIT * (Accounting DOL -=1)

$ 100,000

D&A

EBITDA

$120,000

Cash Flow DOL

1.67

20,000

for which the fixed ed EBIT is Cash Flow DOL

FC EBITDA

12.31 Silver Polygon, Inc., has determined that if its revenues were to increase by 10 percent EBIT would increase by 25 percent to $100,000. The fixed costs (cash only) for the firm $100,000. Given the same 10 percent increase in revenues, what would be the corresp change in EBITDA?

Accounting DOL = 1 +

FC + D&A $3,000 + $1,000 =1+ = 3.00 EBIT $2,000

Cash Flow DOL = 1 +

Cash Fixed Costs Accounting DOL EBIT after 25% increase

$100,000 2.5 100,000

Original EBIT FC + D&A D&A Original EBITDA Cash Flow DOL

80000 $ 120,000 $ 20,000 $ 100,000 2.00

Fixed costs FC = 1+ Pretax operating cash flows EBIT

Answer: Based on the Cash Flow DOL, a 10% increase in revenues would increase the fi EBITDA by 20%, i.e., it would increase from $100,000 to $120,000.

were to increase by 10 percent, then d costs (cash only) for the firm are es, what would be the corresponding

000 + $1,000 = 3.00 $2,000

sts FC = 1+ cash flows EBITDA

enues would increase the firm's 000.

12.34 Using the same logic as with the accounting break-even calculation in problem 12.19, ad cross over level of unit sales to find the number of units sold where the pretax operating c same whether the firm chooses the large or small factory. Data given

Large FactorySmall Factory

Unit Cost Selling Price Fixed Cash Costs Depreciation

Crossover EBITDA = Check EBITDA =

$2.50 $10 $2,000,000 $300,000

$7.50 $10 $500,000 $100,000

300,000 candles $250,000 $250,000

The formula for the cross-over level of unit sales, based on accounting EBIT, ia as follows: CO = (FC + D&A)Alternative 1 − (FC + D&A)Alternative 2 / (Unit ContributionAlter Eliminating D&A, since D&A are non-cash charges, gives us CO = (FC)Alternative1 − (FC)Alternative 2 / (Unit ContributionAlternative 1 − Unit ContributionAlternative CO =

300,000

ulation in problem 12.19, adapt the formula for where the pretax operating cash flow is the

counting EBIT,

tive 2 / (Unit ContributionAlternative1 − Unit ContributionAlternative 2)

− Unit ContributionAlternative 2)

12.35

You are the project manager for eagle Golf Corporation. The company is conside design. The company has estimated the information in the following table about t manufacturing price. Eagle Golf expects to sell the club for five years. The equip depreciated using straight line depreciation over five years and will have a zero sa capital expenditures are required. No new working capital is needed for the projec percent and the company has a 35 percent marginal tax rate. You estimate that th expected sales and a 25 percent chance of achieving either the weak or strong sa

Units sold Selling price per unit Variable cost per unit Fixed Costs Initial Investment Chance of happening Expected unit sales Expected unit price Expected unit variable cost

Strong Sales Expected Sales 15,000 10,000 130 120 70 65 1,290,000 1,290,000 1,400,000 1,400,000 25.00% 50.00% 10,500 120 65 0 Revenue less VC less FC EBITDA less D&A EBIT less Taxes NOPAT add D&A CF Opns less Cap Exp (1,400,000) add WC 0 FCF (1,400,000) PVIF 1 PV (1,400,000) NPV (279,365) Do not recommend the project as the NPV < 0.

oration. The company is considering manufacturing a new golf wedge with a unique groove tion in the following table about the market for the new club, and the associated selling and he club for five years. The equipment required for the manufacturing process can be five years and will have a zero salvage value at the end of the projext's life. No additional ng capital is needed for the project. The required return for projects of this type is 12 inal tax rate. You estimate that there is a 50 percent chance the company will achieve the eving either the weak or strong sales outcomes. Should you recommend the project?

Weak Sales 7,000 110 60 1,290,000 1,400,000 25.00%

Opportunity cost of capital Expected unit sales Expected unit price Expected unit variable cost Initial Investment D&A Fixed Costs Marginal Tax Rate

2 3 1,260,000 1,260,000 1,260,000 682,500 682,500 682,500 250,000 250,000 250,000 327,500 327,500 327,500 280,000 280,000 280,000 47,500 47,500 47,500 16,625 16,625 16,625 30,875 30,875 30,875 280,000 280,000 280,000 310,875 310,875 310,875 0 0 0 0 0 0 310,875 310,875 310,875 0.892857143 0.7971939 0.7117802 277,567 247,828 221,275

d the project as the NPV < 0.

12.00% 10,500 120 65 1,400,000 280,000 250,000 35.00%

4 5 1,260,000 1,260,000 682,500 682,500 250,000 250,000 327,500 327,500 280,000 280,000 47,500 47,500 16,625 16,625 30,875 30,875 280,000 280,000 310,875 310,875 0 0 0 0 310,875 310,875 0.635518078 0.5674269 197,567 176,399

12.36

Economic break-even point: Commodore Motors management is considering a pro produce toy cars. The project would require an initial outlay of $100,000 and have an life of 10 years. Management estimates that each year during the life of the project, depreciation and amortization would be $8,000, capital expenditures would be $4,000 additions to working capital would be $2,000, and fixed costs would be $3,000. Also, car would sell for $15 and cost $7 to produce. Finally, the cost of capital for the porjec be 12 percent, cash flows from the project would be taxed at a 25 percent rate, and th would be depreciated to a salvage value of $0. How many units must be sold each ye for this project to break-even from an economic standpoint?

Step one: The required annual FCF is:

$10,000 = FCF ´

1 æ 1 ö ´ ç1÷ Þ FCF = $17,698.42 0.12 è 1.1210 ø

Step two: The required EBIT is: EBIT = (FCF − D&A + Cap Exp + Add WC) / (1 − t ) EBIT = ($17,698.42 − $8,000 + $4,000 + $2,000) / (1 − 0.25 ) = $20,931.23 Step three: The required total contribution is: Revenue − VC = EBIT + D&A + FC = $200,931.22 + $8,000 + $3,000 = $31,931.23 Step three: The required total contribution is: = $31,931.22 / ($15 − $7) = 3,991.4 or 3,992 cars.

gement is considering a project to y of $100,000 and have an expected ring the life of the project, penditures would be $4,000, sts would be $3,000. Also, each toy cost of capital for the porject would at a 25 percent rate, and the assets units must be sold each year in order t?

25 ) = $20,931.23

12.39

The Fulcrum Company produces decorative swivel platforms for home televisions. If F each. The variable production costs are $65 per unit, whereas the fixed production cos

a. b. c. d.

The Fulcrum Company produces a positive operating income if it produces and sells m The Fulcrum Company’s degree of operating leverage is 1.333. If the Fulcrum Company increases production and sales by 5 percent, its operating ea Increasing the fixed production costs by 10 percent will result in a lower sensitivity of o

Expected Production Unit price

$100

Unit Variable Cost

$65

Fixed Production Costs EBITDA Break-Even Output Full Production EBITDA Degree of Operating Leverage a. b. c. d.

40,000,000

1,050,000,000 30,000,000 swivel platforms $350,000,000 4

for home televisions. If Fulcrum produces 40 million units, it estimates that it can sell them for $100 as the fixed production costs are $1.05 billion. Which of the following statements is true?

e if it produces and sells more than 25 million swivel platforms.

5 percent, its operating earnings are expected to increase by 20 percent. t in a lower sensitivity of operating earnings to changes in units produced and sold.

swivel platforms

e if it produces and sells more than 25 million swivel platforms.

5 percent, its operating earnings are expected to increase by 20 percent. t in a lower sensitivity of operating earnings to changes in units produced FALSE and sold.

FALSE FALSE TRUE FALSE

them for $100 e?

STP#12.1

Retro Inc. sells vintage football jerseys for $72 each. Variable costs and amortization expense) are $84,000 per year. If sales for next ye variable costs per unit increase without EBIT becoming negative?

The values in the problem statement indicate that the expectetd EBIT for Retro Inc. ne Revenue VC FC + D&A EBIT

$72 × 8,000 = $58 × 8,000 =

$576,000 464,000 84,000 $28,000

Therefore, total variable cost could increase by $28,000

If the firm sells 8,000 jerseys, then the variable cost per unit could increase by as muc

2 each. Variable costs are $58 per unit and total fixed costs (including depreciation ear. If sales for next year are expected to equal 8,000 jerseys, how much can becoming negative?

EBIT for Retro Inc. next year is:

d increase by $28,000 without EBIT becoming negative.

ld increase by as much as $3,50 ($28,000/8000 units = $3,50 per unit).

STP #12.2 How would a capital intensive company fare during good and poor economic times as compared with other companies? Explain. A capital intensive company has a higher proportion of fixed costos and therefore higher operating leverage than less capital intensive companies. High operating leverage causes the pretax operating cash flows and accounting profits to be more sensitive to changes in revenues. As a result, during good economic times these cash flows and profits will increase more and during poor economic times they will fall more than the corresponding measures at companies that have less operating levarage.

d and poor plain.

nd therefore h operating its to be more times these cash they will fall more ting levarage.

STP #12.3 The manager of Roy's Restaurant has determined that if revenues were to increase percent, then EBIT would increase by 45 percent to $87,000. What would be the corresponding change in EBITDA if revenues increased 20 percent and cash fixed c are $35,000?

If a 20 percent increase in revenue causes a 45 percent increase in EBIT, Accounti must equal 2.25. Also, since EBIT would be $87,000 after the 45 percent increase, original EBIT was $87,000/(1 + 0.45) = $60,000. Therefore: Accounting DOL = =

2.25 2.25

= 1 + (FC + D&A)/EBIT = 1 + ($35,000 + D&A)/$60,000 => D&A = $40,000

Cash Flow DOL = = 1 + FC/(EBIT + D&A) = 1 + $35,000/($60,000 + $40,000) = 1.35

Which tells us that a 20 percent increase in revenues will result in a 27 percen percent × 1.35 = 27 percent) increase in EBITDA.

at if revenues were to increase by 20 $87,000. What would be the sed 20 percent and cash fixed costs

ent increase in EBIT, Accounting DOL after the 45 percent increase, the refore:

$60,000 => D&A = $40,000

ues will result in a 27 percent (20

STP #12.4 Luminosity Inc. produces modern light fixtures that sell for $150 per unit. The firm's considering purchasing a high-capacity manufacturing machine. If the high-capacit then the firm's annual cash fixed costs will be $60,000 per year, variable costs will annual depreciation and amortization expenses will equal $30,000. If the machine cash fixed costs will be $25,000, variable costs will be $105 per unit, and annual d amortization expenses will equal $10,000. What is the minimum level of unit sales EBIT with the high-capacity machine will be higher than EBIT without that machine

This question is asking for the crossover level of unit sales for EBIT, CO EBIT. Using we find that: COEBIT =

COEBIT =

(FC + D&A)High capacity − (FC + D&A)No high capacity Unit contributionHigh capacity − Unit contributionNo high capacity $90,000 − $35,000 ($150 − $55) − ($150 − $105)

= 1,100 units

r $150 per unit. The firm's management is achine. If the high-capacity machine is purchased, r year, variable costs will be $55 per unit, and $30,000. If the machine is not purchased, annual 05 per unit, and annual depreciation and nimum level of unit sales necessary in order for BIT without that machine?

s for EBIT, CO EBIT. Using Equation 12.7

o high capacity

tionNo high capacity

, and so

STP #12.5 Paper Christmas Trees Inc. is considering introducing a new line of inexpensive for the project is $175,000, and the company will have to invest $5,000 in work assets each year during the six year life of the project. The initial outlay will be value of $0. Annual depreciation and amortization charges for the project will b costs will be $6,000 per year. The firm will sell each tree for $75, and the variab $40. Calculate the number of trees that the firm must produce and sell in order that the appropriate cost of capital for the project is 15 percent and that the ma percent.

Step one: The required annual FCF is:

$175,000 = FCF ´

1 æ 1 ö ´ ç1÷ Þ FCF = $46,241.46 0.15 è 1.156 ø

Step two: The corrresponding EBIT is: EBIT = (FCF − D&A + Cap Exp + Add WC) / (1 − t ) EBIT = ($43,241.46 − $15,000 + $10,000 + $5,000) / (1 − 0.4) = $77,069.10 Step three: Therefore, the total contribution is: Revenue − VC = EBIT + D&A + FC = $77,069.10 + $5,000 + $6,000 = $88,069.10 Step four: Finally, the economic break-even level of sales is: $88,069.10 / ($75 − $40) = 2,516.26 or 2,516 trees.

a new line of inexpensive Christmas trees. The initial outlay to invest $5,000 in working capital and $10,000 in fixed The initial outlay will be depreciated assuming a salvage rges for the project will be $15,000 and cash-related fixed ee for $75, and the variable cost to produce each tree will be produce and sell in order to break even economically. Assume percent and that the marginal tax rate for the firm is 40

) / (1 − 0.4) = $77,069.10

= $88,069.10

6 or 2,516 trees.

13.1

Finance balance sheet: KneeMan Markup Company has total debt obligations with a value equal to $30 million and $28 million, respectively. It also has total equity with a b equal to $20 million and $70 million, respectively. If you were going to buy all of the as Markup today, how much should you be willing to pay? Capital component Book value Market value Debt

$30 m

$28 m

Equity

$20 m

$70 m

Total

$50 m

$98 m

otal debt obligations with a book and market so has total equity with a book and market value e going to buy all of the assets of KneeMan

13.5

Cost of common stock: Whitewall Tire Co. just paid a $1.60 dividend on its common Whitewall is expected to increase its annual dividend by 2 percent per year into the fo future and the current price of Whitewall’s common shares is $11.66, what is the cost equity for Whitewall? Dividend just paid (Do) Dividend growth rate (perpetual) Current stock price

$1.60 2% $11.66

Cost of common equity

16.00%

dividend on its common shares. If rcent per year into the foreseeable $11.66, what is the cost of common

13.6

Cost of common stock: Seerex Wok Co. is expected to pay a dividend of $1.10 one y from today on its common shares. That dividend is expected to increase by 5 percent every year thereafter. If the price of Seerex is $13.75, what is Seerex’s cost of common equity? Expected dividend (D1) Growth rate Current stock price

$1.10 5% $13.75

Cost of common equity

13.00%

dividend of $1.10 one year increase by 5 percent Seerex’s cost of common

13.7

Cost of common stock: Two-Stage Rocket’s common stock is expected to pay an an dividend equal of $1.25, and it is commonly known that the firm expects dividends pai by 8 percent for the next two years and by 2 percent thereafter. If the current price of T common shares is $17.80, what is the cost of common equity capital for the firm? Expected dividend (D1) $1.25 Growth rate (first phase) 8% Number of years in first phase 2 nd Growth rate (2 phase) 2% Current stock price $17.80

Cost of common equity capital

==> ==>

Po = [D1/(1+k)] +[D1(1+g1)/(1+k)2]+ [D1(1+g1)2/(1+k)3]+[(D1(1+g1)2(1+g2)/k-g2)*(1/(1+k)3 17.8 = 1.25/(1+k) + (1.25(1.08))/(1+k)2+(1.25(1.08)(1.08))/(1+k)3 + (1.25(1.08)(1.08)(1 17.8 = 1.25/(1+k) + 1.35/(1+k)2+1.458/(1+k)3+1.487/(k-.02)*(1/(1+k)3

k cs =

9.8260% g2= 2% g1= 8% P0 = $17.800

Year 1 2 3

$1.250 = $1.354 = $20.584 =

Comment Change this number until the calculated price equals $ Growth rate for perpetuity Growth rate during the first phase of 2 years Formula: =NPV(d22,d29:d32) - This formula calculates the present value of the future dividends in cells d29 to with the discount rate in d22.

D1 D2 =d29 (1 + g 1) Formula: = [d30 * (1 + g 1)] + ([d30* (1 + g 1 )* (1 + g 2)]/ This formula calculates the value of D3 and the presen of all cash flows after Year 2 in Year 3 dollars.

ock is expected to pay an annual e firm expects dividends paid to increase after. If the current price of Two-Stage’s uity capital for the firm?

1+g1)2(1+g2)/k-g2)*(1/(1+k)3] (1+k)3 + (1.25(1.08)(1.08)(1.02)/(k-.02))/(1+k)3

he calculated price equals $17.8

phase of 2 years 32) - This formula calculates ure dividends in cells d29 to d31

+ ([d30* (1 + g 1 )* (1 + g 2)]/(d22-d23)) value of D3 and the present value 2 in Year 3 dollars.

13.8

Cost of preferred stock: Fjord Luxury Liners has preferred shares outstanding that p dividend equal to $15 per year. If the current price of Fjord preferred shares is $107.1 after-tax cost of preferred shares for Fjord? Annual preferred dividend Current preferred stock price

$15 $107.14

After-tax cost of preferred stock

14.00%

rred shares outstanding that pay an annual ord preferred shares is $107.14, what is the

13.9

Cost of preferred stock: Kresler Autos has preferred shares outstanding that pay an of $12, and the current price of the shares is $80.What is the after-tax cost of new pre for Kresler if the flotation (issuance) costs for a new issue of preferred are 5 percent?

Annual preferred dividend Current preferred stock price Issuance costs

$12 $80 5%

After-tax cost of preferred stock

15.79%

outstanding that pay annual dividends after-tax cost of new preferred shares preferred are 5 percent?

13.11 WACC for a firm: Capital Co. has a capital structure that is financed, based on curren values, with 50 percent debt, 10 percent preferred shares, and 40 percent common sh returns required by investors are 8 percent, 10 percent, and 15 percent for debt, prefe and common equity, respectively, what is Capital’s after-tax WACC? Assume that the marginal tax rate is 40 percent. Capital component

Weight Return offered to investors

Debt Preferred stock Common stock

50% 10% 40%

Marginal tax rate

40%

After-tax WACC

9.40%

8% 10% 15%

nanced, based on current market d 40 percent common shares. If the 15 percent for debt, preferred shares, WACC? Assume that the firm’s

13.15 Current cost of a bond: You know that the after-tax cost of debt capital for Bubbles C percent. If the firm has only one issue of five-year maturity bonds outstanding, what is of the bonds if the coupon rate on those bonds is 10 percent? Assume the bonds mak coupon payments and the marginal tax rate is 30 percent. After-tax cost of debt Maturity of bonds (years) Coupon rate Face value Tax rate Coupon frequency per year

7% 5 10% $1,000 30% 2

Before-tax cost of debt

9.10%

Bond Price PMT $50.00

PVIF 0.6409

10 5.00%

4.550%

$1,035.52 PVIFA 7.8933

PAR $1,000

VALUE $1,035.52

st of debt capital for Bubbles Champagne is 7 ty bonds outstanding, what is the current price cent? Assume the bonds make semiannual t.

13.16 Current cost of a bond: Perpetual Ltd. has issued bonds that never require the princ amount to be repaid to investors. Correspondingly, Perpetual must make interest paym the infinite future. If the bondholders receive annual payments of $75 and the current the bonds is $882.35, what is the after-tax cost of this borrowing for Perpetual if the fir the 40 percent marginal tax rate? Annual interest payments Current bond price Firm's tax rate After-tax cost of debt

$75 $882.35 40% 5.10%

s that never require the principal etual must make interest payments into ments of $75 and the current price of rrowing for Perpetual if the firm is in

13.17

Current cost of a bond: You are analyzing the cost of debt for a firm.You know tha maturity, 8.5 percent coupon bonds are selling at a price of $823.48. The bonds pay these bonds are the only debt outstanding for the firm, what is the after-tax cost of d has a 30 percent marginal and average tax rate? Maturity Coupon rate Current bond price Tax rate Par value Coupon frequency

12 8.50% $823.48 30% $1,000 2

After-tax cost of debt (at current price)

8.07%

After-tax cost of debt (if selling at par)

6.08%

r a firm.You know that the firm’s 12-year 23.48. The bonds pay interest semiannually. If the after-tax cost of debt for this firm if the firm

13.19

Cost of debt for a firm: You are analyzing the after-tax cost of debt for a firm. You k 12-year maturity, 9.5 percent coupon bonds are selling at a price of $1,200. If these debt outstanding for the firm, what is the after-tax cost of debt for this firm if the marg firm is 34 percent? What if the bonds are selling at par? Maturity Coupon rate Current bond price Tax rate Par value Coupon frequency

12 9.50% $1,200 34% $1,000 2

After-tax cost of debt (at current price)

4.71%

After-tax cost of debt (if selling at par)

6.42%

cost of debt for a firm. You know that the firm’s t a price of $1,200. If these bonds are the only debt for this firm if the marginal tax rate for the

13.20 Cost of common stock: Underestimated Inc.’s common shares currently sell for $36 that its shares should really sell for $54 per share. If the firm just paid an annual divide firm expects those dividends to increase by 8 percent per year forever (and this is com market), what is the current cost of common equity for the firm and what does the firm cost of common equity for the firm? Current stock price Firm's expected stock price Dividend just paid (D0) Constant growth rate Current cost of common equity Appropriate cost of equity (as per firm's belief)

$36 $54 $2 8% 14.00% 12.00%

hares currently sell for $36 per share.The firm believes m just paid an annual dividend of $2 per share and the ear forever (and this is common knowledge to the irm and what does the firm believe is a more appropriate

13.24 WACC for a firm: The Imaginary Products Co. currently has debt with a market value outstanding. The debt consists of 9 percent coupon bonds (semiannual coupon paym maturity of 15 years and are currently priced at $1,440.03 per bond. The firm also has preferred shares outstanding with a market price of $12.00. The preferred shares pay of $1.20. Imaginary also has 14 million shares of common stock outstanding with a pri share. The firm is expected to pay a $2.20 common dividend one year from today, and expected to increase by 5 percent per year forever. If Imaginary is subject to a 40 perc rate, then what is the firm’s weighted average cost of capital?

Capital component Bonds Preffered stock Common stock

Number outstanding 300,000 2,000,000 14,000,000

Coupon rate on debt Coupon frequency (per year) Bond maturity (years) Preferred dividend (annual) Expected dividend on common (D1) Constant annual dividend growth rate (forever) Marginal tax rate

9% 2 15 $1.20 $2.20 5% 40%

Capital component Bonds Preferred stock Common stock Total capital (market value)

Weight 0.587 0.033 0.380 1.000

Market Value $ 432,009,000.00 $ 24,000,000.00 $ 280,000,000.00 $ 736,009,000.00

has debt with a market value of $300 million ds (semiannual coupon payments) which have a 3 per bond. The firm also has an issue of 2 million 00. The preferred shares pay an annual dividend n stock outstanding with a price of $20.00 per dend one year from today, and that dividend is aginary is subject to a 40 percent marginal tax pital?

Current price $ 1,440.03 $ 12.00 $ 20.00

Weighted After-tax cost Cost (%) 2.94% 10.00% 16.00% WACC

1.73% 0.33% 6.09% 8.14%

13.25 Choosing a discount rate: For the Imaginary Products firm in Problem 13.4, calculat appropriate cost of capital for a new project that is financed with the same proportion o preferred shares, and common shares as the firm’s current capital structure. Also assu the project has the same degree of systematic risk as the average project that the firm currently undertaking (the project is also in the same general industry as the firm’s cur business).

Since Imaginary will be financing the project with the same mix of capital that the firm is utilizing for its projects, we will have met the first restriction concerning financing mix. In the new project will have the same degree of systematic risk (in addition to being in the s general line of business). Therefore, Imaginary can use the 8.14 percent cost of capital to its project.

rm in Problem 13.4, calculate the d with the same proportion of debt, nt capital structure. Also assume that average project that the firm is ral industry as the firm’s current line of

x of capital that the firm is currently oncerning financing mix. In addition, n addition to being in the same 4 percent cost of capital to evaluate

13.29 You know that the return of Momentum Cyclicals common shares is 1.6 times as sens as the return of the market. If the risk-free rate of return is 3.72 percent and market ris Momentum Cyclicals’s cost of common equity capital?

Risk-free rate Market risk premium Beta Cost of common equity

4% 6% 1.6 12.86%

We know that the beta for Momentum Cyclicals is 1.6, and we can use the remaining inform

E(RCS ) = Rrf + b (E(Rm ) - Rrf ) = 0.0372 +1.6´ 0.0571= 0.1286 =12.86%

on shares is 1.6 times as sensitive to macroeconomic information is 3.72 percent and market risk premium is 5.71 percent, what is

e can use the remaining information in the CAPM as follows:

13.31 RetRyder Hand Trucks has a preferred share issue outstanding that pays an annual d $1.30 per year. The current cost of preferred equity for RetRyder is 9 percent. If RetRy additional preferred shares that pay exactly the same dividend and the investment ban percent of the sale price, what is the cost of new preferred shares for RetRyder?

Current cost of preferred equity Annual preferred dividend Cost of issuance

9% $1.30 8%

Preferred stock price Cost of new preferred stock

$14.44 9.78%

ng that pays an annual dividend of yder is 9 percent. If RetRyder issues d and the investment banker retains 8 hares for RetRyder?

13.34

Hurricane Corporation is financed with debt, preferred equity, and common equity million, $10 million, and $30 million, respectively. The betas for the debt, preferred are 0.2, 0.5, and 1.1, respectively. If the risk free rate is 3.95 percent, the market r percent, and Hurricane’s average and marginal tax rates are both 30 percent, wha average cost of capital?

Solution: The fractions of the total financing represented by debt, common equity, and prefer Debt 20 Risk free Preferred equity 10 Mkt premium Common equity 30 beta Total capital 60 Xdebt 33.33% Tax rate Xps 16.67% Xcs 50.00% The costs of debt, common equity, and preferred equity are: E(RDebt) = Returnrf + βDebt (E(ReturnM) – Returnrf) = E(Rps) = Returnrf + βps (E(ReturnM) – Returnrf) = E(Rcs) = Returnrf + β (E(ReturnM) – Returnrf) = WACC

WACC =(0.3333´0.0515´(1-0.3))+(0.1667´0.0696)+(0.5´0.1

red equity, and common equity with market values of $20 he betas for the debt, preferred stock, and common stock ate is 3.95 percent, the market risk premium is 6.01 rates are both 30 percent, what is the company’s weighted

bt, common equity, and preferred equity are: 3.95% 6.01% 0.2 0.5 1.1 debt ps cs 30.00%

5.15% 6.96% 10.56% 7.64%

667´0.0696)+(0.5´0.106) = 0.0766 = 7.66%

13.35

You are working as an intern at Coral Gables Products, a privately owned manufac company. Shortly after you read Chapter 13 in this book you got into a discussion the Chief Financial Officer (CFO) at Coral Gables about weighted average cost of calculations. She pointed out that, just as the beta of the assets of a firm equals a weighted average of the betas for the individual assets (as shown in Equation 7.11

bn Asset portfolio = å xi bi = x1b1 +x2 b2 + x3b3 +...+ xn bn i=1

the beta of the assets of a firm also equals a weighted average of the betas for the preferred equity, and common equity of a firm: n

bn Asset portfolio = å xi bi = xDebt bDebt + xPref Equity bPref Equity + xCommon EquitybCommon Equity i=1

Why must this be true?

Solution: Since, collectively, the debt and equity holders are entitled to receive al cash flows that the assets of the firm are expected to produce, the systematic risk cash flows that they are entitled to receive must be the same as the systematic risk the cash flows the assets are expected to produce.

a privately owned manufacturing you got into a discussion with weighted average cost of capital assets of a firm equals a as shown in Equation 7.11):

verage of the betas for the debt,

ommon Equity Common Equity

s are entitled to receive all of the oduce, the systematic risk of the ame as the systematic risk of

13.36

The CFO described in problem 13.35 asks you to estimate the beta for Coral Gable Since the common stock is not publicly traded, you do not have the data necessary beta using regression anlaysis. However, you have found a company with publicly has operations which are exactly like those at Coral Gables. Using stock returns fo comparable you estiamte the beta for the comparable company's stock to be 1.06. of that company's common equity is $45 million and it has one debt issue outstand value of $15 million and an annual pretax of 4.85 percent. The comparable compa preferred stock. If the risk free rate is0.0395 and the market risk premium is 0.0601 of the comparable company?

If the total market value of Coral Gables' financing consists of 0.35 equity (this is what the CFO estimates the market values to be) and the pretax cos What is the beta for Coral Gables' common stock? Beta cs Common equity Debt Total capital Pretax rate

1.06 45 15 60 0.0485

Xdebt Xcs

0.25 0.75

Solution: You can solve this problem using the equation: n

 n Asset portfolio =  xi i = xDebt  Debt + xps  ps + xcs  cs i =1

Since neither company has preferred stock, the equation in this case has o terms:

n Asset portfolio = xDebt  Debt + xcs cs

a. To calculate the beta of the assets of the comparable company, you must firat e the beta of the comparable firm's debt and the fractions of the total market value the comparable firm's financing which is represented by the debt and equity. The beta of the comparable firm's debt can be estimated using the CAPM formula

E(Ri ) = Rrf + β i [E(Rm) – Rrf] Since this formual can be used to calculate the expected return on debt, it ca E(RDebt) = Rrf + β Debt[E(Rm) – Rrf] If we assume that the market is pricing the debt correctly, the pretax cost of d expected return on debt in this equation. Therefore, substituting the informat problem statement into this equation yields: Beta of debt = 0.15 Finally, the beta of the assets of the cpmparable company is: Beta of asset portfolio = Xdebtβdebt + Xcsβcs 0.8324 = b. Since the comparable company is exactly like Coral Gables, this is a good estimate of asset beta for Coral Gables. To calculate the beta for Coral Gables' common equity, you use the following equation with the beta of the assets for the comparable company and the beta of debt and financing fractions for Coral Gables. Beta of Asset Portfolio = XdebtBdebt + XcsBcs The beta of the Coral Gables debt is: Beta of debt = 0.25 Beta of equity = 1.1463

e the beta for Coral Gables' common stock. have the data necessary to estiamte the a company with publicly traded stock that es. Using stock returns for this pure-paly mpany's stock to be 1.06. The market value one debt issue outstanding with a market The comparable company has no , what is the beta of the assets

debt and 0.65 o be) and the pretax cost of its debt 0.0545 is

ation:

equation in this case has only two

ompany, you must firat estimate of the total market value of y the debt and equity.

using the CAPM formula (Equation 7.10):

ected return on debt, it can be written as:

rectly, the pretax cost of debt equals the substituting the information from the

ables, this is a good beta for Coral th the beta of the and financing

13.37

Estimate the weighted average cost of capital for Coral Gables using your estimate information in the problem statement in Problem 13.36? Assume that the average rates for Coral Gables are both 25 percent. Marginal and Average tax rate = Risk free rate = Beta of cs = Risk Premium =

25.00% 3.95% 1.15 6.01%

Expected Return on cs = Rrf + Beta of cs[Risk Premium] Expected Return on cs 1 =0.86% The weighted average cost of capital is: WACC = 0.0849

Coral Gables using your estimated beta and the 3.36? Assume that the average and marginal tax

Xdebt 35.00% Xcs 65.00% pretax cost of debt 5.45%

13.38 The cost of equity is equal to the a. expected market return. b. rate of return required by stockholders. c. cost of retained earnings plus dividends. d. risk the company incurs when financing.

Answer

13.39 Dot.Com has determined that it could issue $1,000 face value bonds with an 8 percen paid semiannually and a five-year maturity at $900 per bond. If Dot.Com’s marginal ta percent, its after-tax cost of debt is closest to: a. 6.2 percent. b. 6.4 percent. c. 6.6 percent. d. 6.8 percent.

Face value of bonds Coupon rate Coupon frequency Maturity (years) Corporate tax rate Current bond price

$1,000 8% 2 5 38% $900

Bond yield to maturity 10.91% After-tax cost of debt 6.77% Answer d.

ue bonds with an 8 percent coupon d. If Dot.Com’s marginal tax rate is 38

13.40 Morgan Insurance Ltd. issued a fixed-rate perpetual preferred stock three years ago and placed it privately with institutional investors. The stock was issued at $25.00 per share with a $1.75 dividend. If the company were to issue preferred stock today, the yield would be 6.5 percent.The stock’s current value is: a. $25.00. b. $26.92. c. $37.31. d. $40.18.

Preferred stock price (at issuance) Annual preferred dividend Current preferred dividend yield

$ 25.00 $1.75 6.50%

Current value of preferred stock

$26.92

Answer: b

erred stock three years ago ck was issued at $25.00 per e preferred stock today, the

13.41 The Gearing Company has an after-tax cost of debt capital of 4 percent, a cost of pref stock of 8 percent, a cost of equity capital of 10 percent, and a weighted average cost capital of 7 percent. Gearing intends to maintain its current capital structure as it raise additional capital. In making its capital-budgeting decisions for the average-risk projec relevant cost of capital is: a. 4 percent. b. 7 percent. c. 8 percent. d. 10 percent.

Answer b

of 4 percent, a cost of preferred d a weighted average cost of capital structure as it raises or the average-risk project, the

13.42

Suppose the cost of capital of the Gadget Company is 10 percent. If Gadget ha structure that is 50 percent debt and 50 percent equity, its before-tax cost of de its marginal tax rate is 20 percent, then its cost of equity capital is closest to: a. 10 percent. b. 12 percent. c. 14 percent. d. 16 percent.

Capital component Debt Equity

Weighted BeforeAfter-tax cost Weight tax cost Tax rate 50% 5% 20% 2.00% 50% WACC 10%

Cost of equity capital= Answer:

16%

ny is 10 percent. If Gadget has a capital uity, its before-tax cost of debt is 5 percent, and equity capital is closest to:

STP #13.1 Howard Power and Telecommunications Corporation has three divisions. The nam with the after-tax cost of capital for each division and the market value of the assets follows: Division Name Cost of Capital Infrastructure development 8.75 Power 7.5 Telecommunications 8.25

What is the overall after-tax cost of capital for Howard Power and Telecommunicat

The overall after-tax cost of capital for a firm is a value-weighted average of the afte projects (assets) in that firm. We can calculate the overall after-tax cost of capital u

kFirm = å xi ki = x1k1 + x2 k2 + x3k3 +...+ xn kn i=1

$250,000,000 + $325,000,000 + $675,000,000 = $1,250,000,000 X1 = X2 = X3 =

$250,000 / $1,250,000 = $325,000 / $1,250,000 = $675,000 / $1,250,000 =

0.20 0.26 0.54

(0.20 × 0.0875) + (0.26 × 0.0750) + (0.54 × 0.0825) = 0.0816 = 8.1

as three divisions. The names of these divisions, along e market value of the assets in each division are as MV of Assets $250,000,000 $325,000,000 $675,000,000

Power and Telecommunications?

weighted average of the after-tax cost of capital for the all after-tax cost of capital using Equation 13.2 as

+...+ xn kn

4 × 0.0825) = 0.0816 = 8.16%

STP #13.2 Quarri Industries has eight percent coupon bonds outstanding. These bonds have a of $954.41, pay interest semiannually, and will mature in 6 years. If the tax rate is 3 are the pre-tax cost and after-tax cost of this debt?

é æ öù $40 1 $1,000 ÷ú + $954.41 = ê ´ ç1êë kDebt pretax çè (1+ kDebt pretax )12 ÷øúû (1+ kDebt pretax )12 Þ kDebt pretax = 0.045 = 4.5% The annualized pretax cost is: kDebt pretax = (1+ 0.045)2 -1 = 0.0920 = 9.20% and the after-tax cost is: kDebt after-tax = 0.0920 ´ (1- 0.035) = 0.0598 = 5.98%

g. These bonds have a market price ears. If the tax rate is 35 percent, what

$1,000 + kDebt pretax )12

STP #13.3 Quarri Industries has a beta of 1.6. If the market risk free rate is 4 percent and the expected return on the market is 9 percent, what is Quarri's cost of common stock?

kcs = R rf + bcs (E(R M ) - R rf ) kcs = 0.04 +1.6 ´(0.09 - 0.04) = 0.12 =12%

STP #13.4 Miron's Copper Corp. management expects its common stock dividends to grow 1. for the indefinite future. The firm's shares are currently selling for $18.45, and the fi dividend of $3.00 yesterday. What is the cost of common stock for this firm?

P0 =

D (1+ g) D1 D Þ kcs = 1 + g = 0 +g kcs - g P0 P0

Þ kcs =

$3.00 ´ (1+ 0.015) + 0.015 = 0.18 = 18% $18.45

ck dividends to grow 1.5 percent per year g for $18.45, and the firm just paid a ock for this firm?

STP #13.5 Use the information in questions 13.2 and 13.3 as well as the following information WACC for Quarri Industries. In addition to common stock, Quarri has $500,000 pre outstanding that pay a quarterly dividend of $0.50 per share and are currently tradin share. The company's outstanding bonds have a face value of $209,553,546. Ther shares of common stock outstanding with a current market price of $98.00 per sha

The total value of the outstanding debt, preferred stock and common stock are as f Debt = $209,553,546 × 0.95441 = $200,000,000 Preferred stock = $20 × 500,000 = $10,000,000 Common stock = $98 × 2,000,000 = $196,000,000 Total capital = $406,000,000 x Debt = $200 / $406 = 0.4926 x ps = $10 / $406 = 0.0246 x cs = $196 / $406 = 0.4828 The cost for the individual types of capital are: After-tax cost of debt (from problem 13.2): k Debt after-tax = 5.98% Cost of preferred stock: k ps = D / P ps = 4 × $0.50 / $20 = 0.10 = 10% Cost of common equity (from problem 13.3): k cs = 12% WACC calculation: WACC = x Debtk Debt after-tax + x psk ps + x csk cs

WACC = (0.4926 × 0.0598) + (0.0246 × 0.10) + (0.4828 × 0.12) = 0.0899

as the following information to compute the k, Quarri has $500,000 preferred shares hare and are currently trading for $20.00 a alue of $209,553,546. There are 2 million ket price of $98.00 per share.

and common stock are as follows:

+ (0.4828 × 0.12) = 0.0899 = 8.99%

14.1 Cash conversion cycle: Wolfgang’s Masonry estimates that it takes the company 27 da its suppliers. It also knows that it has days’ sales in inventory of 64 days and days’ sales How does Wolfgang’s cash conversion cycle compare with the industry average of 75 da

Cash conversion cycle = Days Sales Outstanding + Days Sales in Inventory - Days Payab Days Payables Outstanding (DPO) Days Sales in Inventory (DSI) Days Sales Outstanding (DSO)

27 days 64 days 32 days

Industry average Cash Conversion cycle

75 days

Firm's Cash Conversion Cycle =

69 days

The firm has a shorter cash conversion cycle

akes the company 27 days on average to pay off 64 days and days’ sales outstanding of 32 days. dustry average of 75 days?

nventory - Days Payables Outstanding

14.2 Cash conversion cycle: Northern Manufacturing Company found that during the last yea 47 days to pay its suppliers, while it took 63 days to collect its receivables.The company’s was 49 days.What is Northern’s cash conversion cycle?

Cash conversion cycle = Days Sales Outstanding + Days Sales in Inventory - Days Payabl Days Payables Outstanding (DPO) Days Sales in Inventory (DSI) Days Sales Outstanding (DSO)

47 days 49 days 63 days

Firm's Cash Conversion Cycle =

65 days

nd that during the last year, it took an average of ceivables.The company’s days’ sales in inventory

nventory - Days Payables Outstanding

14.3 Cash conversion cycle: Devon Automotive estimates that it takes the company about 6 from customers on finished goods from the day it receives raw materials, and it takes abo suppliers.What is the company’s cash conversion cycle? Interpret your answer. Days sales outstanding + Days in inventory Days payables outstanding

62 days 65 days

= Operating cycle

Cash conversion cycle = -3 days The company is able to pay its suppliers, on average, 3 days after it receives cash from c

takes the company about 62 days to collect cash w materials, and it takes about 65 days to pay its rpret your answer.

= Operating cycle

after it receives cash from customers.

14.4 Operating cycle: Lilly Bakery distributes its products to more than 75 restaurants and delis. The company’s average collection period is 27 days, and it keeps its inventory for an average of four days. What is Lilly’s operating cycle? Days sales outstanding =

27 days

Days in inventory =

4 days

Operating cycle

31 days

re than 75 restaurants and and it keeps its inventory for

14.5 Operating cycle: NetSpeed Technologies is a telecom component manufacturer. The firm typically has a collection period of 44 days and days’ sales in inventory of 29 days. What is the operating cycle for NetSpeed? Days sales outstanding =

44 days

Days in inventory =

29 days

Operating cycle

73 days

ponent manufacturer. The les in inventory of 29 days.

14.7 Cost of trade credit: Sybex Corp. sells its goods with terms of 2/10 EOM, net 30.What is the implicit cost of the trade credit? Discount for paying cash # of days to make payment for getting discount Number of days of trade credit allowed Implicit cost of trade credit

2% 10 days 30 days 44.59%

14.8 Cost of trade credit: Mill Street Corporation sells its goods with terms of 4/10 EOM, net 60.What is the implicit cost of the trade credit? Discount for paying cash # of days to make payment for getting discount Number of days of trade credit allowed Implicit cost of trade credit

4% 10 days 60 days 34.72%

14.9 Lockbox: Rosenthal Design has daily sales of $59,000. The financial management team determined that a lockbox would reduce the collection time by 1.6 days. Assuming the co can earn 5.2 percent interest per year, what are the savings from the lockbox? Average daily sales Expected reduction in collection time Annual rate of return on savings Increase in collections due to lock box Annual savings due to lock box

$59,000 1.6 days 5.20% $94,400 $4,908.80

inancial management team 1.6 days. Assuming the company om the lockbox?

14.10 Lockbox: Pacific Traders has annual sales of $1,895,000. The firm’s financial manager determined that using a lockbox will reduce collection time by 2.3 days. If the firm’s oppo cost on savings is 5.25 percent, what are the savings from using the lockbox? Annual sales Expected reduction in collection time Annual rate of return on savings

$1,895,000 2.3 days 5.25%

Average daily sales Increase in collections due to lock box Annual savings due to lock box

$5,191.78 $11,941 $626.91

e firm’s financial manager has 2.3 days. If the firm’s opportunity ng the lockbox?

8% $ 340,000 7%

Annual interest to be paid Amount of loan that can be used Effective interest rate

$ 23,800 312800 7.61%

ers to keep an 8 340,000 at a 7 he loan?

12% $ 17,500,000 10%

Annual interest to be paid Amount of loan that can be used Effective interest rate

$ 1,785,000 $ 15,400,000 11.59%

14.13 Factoring: Maltz Landscaping has an average collection period of 38 days for its acco receivable. Currently, maltz factors all of its receivables at a 2.04 percent discount. W effective annual interest rate on the financing from the factor?

The terms of this factor indicate that for every dollar of receivables sold to the factor to the firm receives 98 cents today and 38-days later the factor receives the dollar in rece The cost to maltz in percentage terms is 2.04 percent over a 38 day period. Days in year 365 Period 38 m periods 9.605263

Factor Discount rate =

2.04%

Effective annual rate = [( 1 + Factor Discount rate) ^ m periods] - 1 Effective annual rate =

21.41%

eriod of 38 days for its accounts a 2.04 percent discount. What is the or?

ivables sold to the factor today, or receives the dollar in receivables. a 38 day period.

14.14 Formal line of credit:Winegartner Cosmetics is setting up a line of credit at its bank f for up to two years.The loan rate is 5.875 percent and the loan agreement calls for an of 40 basis points on any unused balance for the year. If the firm borrows $2 million on loan agreementis signed, what is the effective rate for the line of credit? Line of credit limit = Loan rate = Annual fee on used balance = Amount borrowed =

$5,000,000 5.875% 0.40% $2,000,000

Unused balance = Annual fee = Interest expense = Effective interest rate=

$3,000,000 $12,000 $117,500 6.475%

up a line of credit at its bank for $5 million he loan agreement calls for an annual fee f the firm borrows $2 million on the day the he line of credit?

14.15 Cash conversion cycle: Your boss asks you to compute the company’s cash conversi financial statements, you see that the average inventory for the year was $26,300, acco $17,900, and accounts payable were $15,100. You also see that the company had sale cost of goods sold was $122,000. Interpret your firm’s cash conversion cycle. Note: All sales are assumed to be credit sales. Accounts receivables $17,900 Accounts payables $15,100 Sales $154,000 Inventory $26,300 Cost of goods sold $122,000 Days sales outstanding (DSO)

42.43 days

Days in Inventory (DSI)

78.68 days

Days payables outstanding (DPO)

45.18 days

Firm's cash conversion cycle

75.93 days

The firm takes nearly 76 days from the time it pays for its raw materials to the time it reali credit sales. By taking a couple of more days to pay it suppliers relative to the time it take receivables, it reduces the cash conversion cycle.

e the company’s cash conversion cycle. Looking at the for the year was $26,300, accounts receivable were see that the company had sales of $154,000 and that sh conversion cycle.

w materials to the time it realizes cash from its ers relative to the time it takes to collect on its

14.16 Cash conversion cycle: Blackwell Automotive, Inc., reported the following financial in fiscal year.

Assets Cash and marketable sec. Accounts Receivable Inventories Other current assets Total current assets Net sales Cost of goods sold

Blackwell Automotive, Inc. As of 3/31/2008 $23,015 $141,258 $212,444 $11,223 $387,940 $912,332 $547,400

Calculate the firm’s cash conversion cycle and operating cycle. Note: All sales are assumed to be credit sales. Accounts receivables $141,258 Accounts payables $163,257 Sales $912,332 Inventory $212,444 Cost of goods sold $547,400 Days sales outstanding (DSO)

56.51

Days in Inventory (DSI)

141.66

Days payables outstanding (DPO)

108.86

Firm's operating cycle = Firm's cash conversion cycle =

198.17 89.31

omotive, Inc., reported the following financial information for the last

ckwell Automotive, Inc. Liabilities and Equity Accounts payable and accruals Notes payable

$163,257 $21,115

Total current liabilities

$184,372

perating cycle.

days days days days days

14.17 Cash conversion cycle: Elsee, Inc., has net sales of $13 million, and 75 percent of the credit sales. Its cost of goods sold is 65 percent of annual sales. The firm’s cash conver is 41.3 days. The inventory balance at the firm is $1,817,344, while its accounts payable is $2,171,690.What is the firm’s accounts receivable balance? Net sales $13,000,000 % credit sales 75% of net sales Cost of goods sold 65% of annual sales Cash conversion cycle 41.3 days Inventory $ 1,817,344 Accounts payable $ 2,171,690 Credit sales = $9,750,000 Cost of goods sold $8,450,000 Days payables outstanding (DPO) 93.81 days Days in Inventory (DSI) 78.50 days Cash conversion cycle = DSO + DSI - DPO ==> DSO = CCC-DSI+DPO DSO =

==>

56.61 days

DSO = Accounts Receivables/( Credit sales/365) Accounts Receivables = DSO*(Credit sales/365) Accounts Receivable =

$1,512,079.95

, and 75 percent of these are The firm’s cash conversion cycle le its accounts payable balance

14.18 Cash conversion cycle: Joanna Handicrafts, Inc., has net sales of $4.23 million with 50 percent being credit sales. Its cost of goods sold is $2.54 million.The firm’s cash conversion cycle is 47.9 days, and its operating cycle is 86.3 days.What is the firm’s accounts payable? Net sales Credit sales = Cash conversion cycle Operating cycle Cost of goods sold

$4,230,000 50% of net sales 47.9 days 86.3 days $2,540,000

==> ==>

Credit sales = $2,115,000 Cash conversion cycle = Operating cycle - Days payables outstanding Days payables outstanding = Operating cycle-Cash conversion cycle Days payables outstanding (DPO)= 38.4 days

==> ==>

DPO = [Accounts payable / (COGS/365)] Accounts payable = DPO*(COGS/365) Accounts payable = $267,221.92

of $4.23 million million.The firm’s 3 days.What is the

14.19 Operating cycle: Aviva Technology’s operating cycle is 81 days. Its inventory was $134,000 at the end of last year, and the company had a $1.1 million cost of goods sold How long does it take Aviva to collect on its receivables on average? Operating cycle Inventory Cost of goods sold

81 days $ 134,000 $1,100,000

Days sales in Inventory (DSI) 44.46 days Operating cycle = Days sales outstanding (DSO) + DSI ==> DSO = Operating cycle - DSI ==> DSO = 36.54 days

81 days. Its inventory was $1.1 million cost of goods sold. n average?

14.20 Operating cycle: Premier Corp. has sales of $812,344, and its cost of goods sold equa of sales. Assume all sales are credit sales. If the firm’s accounts receivable total $113,9 operating cycle is 81.6 days, how much inventory does the firm have? Sales COGS Accounts receivable Operating cycle

$812,344 (all on credit) 70% of sales $113,902 81.6 days

Operating cycle = Days sales outstanding (DSO) + Days sales in inventory (DSI) DSO =[ Accounts receivable/(Credit sales/365)]

==> ==>

DSO = 51.18 days DSI = Operating cycle - DSO DSI = 30.42 days

DSI = [Average inventory/(COGS/365)] ==> Average inventory = DSI*(COGS/365) COGS = $568,640.80 ==> Average inventory = $ 47,394.87

4, and its cost of goods sold equal to 70 percent accounts receivable total $113,902 and its s the firm have?

in inventory (DSI)

14.21 Operating cycle: Telecraft Enterprises carries 45 days of inventory in its stores. Last Telecraft reported net sales of $1,400,000 and had receivables of $325,000 at the end the year. What is the operating cycle at Telecraft? Sales Receivables Days of Inventory Days in year

Receivables Turnover = DSO DSI Operating Cycle =

1,400,000 325,000 45 365

4.3077 84.73 days 45 days 129.73 days

nventory in its stores. Last year bles of $325,000 at the end of

14.22

Operating Cycle: Given the data for Telecraft Enterprises in problem 14.21, re-e operating cycle if days sales outstanding decreased to 75 days? For the same leve is the implied dollar value of receivables with 75 days sales outstanding?

14.21

Operating cycle: Telecraft Enterprises carries 45 days of inventory in its stores. L Telecraft reported net sales of $1,400,000 and had receivables of $325,000 at the What is the operating cycle at Telecraft? Sales Receivables Days of Inventory Days in year

Receivables Turnover = DSO DSI Operating Cycle =

1,400,000 325,000 45 365

4.3077 84.73 days 45 days 129.73 days

If the DSO = 75 days, solve for the accounts receivable fig 75 days = 365 days / (sales of $1,400,000/accounts recei Accounts Receivable = $287,671.23

prises in problem 14.21, re-estimate the firm's to 75 days? For the same level of sales, what s sales outstanding?

ys of inventory in its stores. Last year eceivables of $325,000 at the end of the year.

75.0 days 45 days 120.0 days

for the accounts receivable figure. of $1,400,000/accounts receivable)

14.23 Economic order quantity: Longhorn Traders is one of the largest RV dealers in Austin Texas, and sells about 2,800 recreational vehicles a year. The cost of placing an order Longhorn’s supplier is $800, and the inventory carrying costs are $150 for each RV. The company likes to maintain safety stock of 12 RVs. Most of its sales are made in either th spring or the fall. How many orders will the firm need to place this year? Annual sales (units) 2,800 Ordering cost $800 per order Carrying cost $150 per RV Safety stock level 12 RVs Economic order quantity (EOQ) = Number of orders =

EOQ = 173 RVs

2  Reorder costs Sales per period Carrying costs

rgest RV dealers in Austin, e cost of placing an order with are $150 for each RV. The sales are made in either the this year?

costs Sales per period arrying costs

14.24 Effective interest rate: The Clarkson Designer Company wants to borrow $750,000. Th loan at an APR of 6.875. Since the loan calls for a compensating balance, the effective i percent. What is the compensating balance on this loan? Desired loan amount Interest rate (APR) Effective interest rate (due to compensating balance) Interest expense =

$750,000 6.875%

Effective interest rate =

Interest expense Effective borrowing amo

9.25% $51,562.50

Effective borrowing amount=(Interest expense/Effective interest rate) Effective borrowing amount=

==>

$557,432.43

Effective borrowing amount = Loan amount - Compensating balance Compensating balance = Loan amount - Effective borrowing amount Compensating balance =

$192,567.57 or

25.68%

to borrow $750,000. The bank will provide the balance, the effective interest rate is actually 9.25

Interest expense Effective borrowing amount

14.25 Effective interest rate: The Colonial Window Treatments Company is borrowing $1.5 m The loan requires a 10 percent compensating balance, and the effective interest rate on is 9.75 percent.What is the stated APR on this loan? Loan amount Compensating balance Effective interest rate

$1,500,000 10% 9.75%

Effective interest rate =

Compensating balance= $150,000 Effective borrowing amount= $1,350,000 Interest expense = Effective interest rate * Effective borrowing amount Interest expense = $131,625 Stated APR = Interest expense/Loan amount =

8.78%

Interest expen Effective borrowing

ny is borrowing $1.5 million. fective interest rate on the loan

t rate =

Interest expense Effective borrowing amount

$10,000,000 Interest expense + Annual fee 6.25% Effective interest rate = Borrowed amount 0.60% $7,500,000

Unused balance Annual fee Interest expense Effective interest rate

$2,500,000 $15,000.0 $468,750 6.45%

al line of credit of $10 million s good for up to five years. percent on the loan, and in n the unused balance. The came available. What is the

rate =

Interest expense + Annual fee Borrowed amount

14.27 Formal line of credit: Lansdowne Electronics has a formal line of credit of $1 million to three years with HND Bank. The interest rate on the loan is 5.3 percent, and under agreement, Lansdowne has to pay 50 basis points on the unused amount as the annu fee. Suppose the firm borrows $675,000 the first day of the agreement. What is the fe company must pay? What is the effective interest rate? Line of credit limit $1,000,000 Loan rate 5.30% Annual fee on used balance 0.50% Amount borrowed $675,000 Unused amount Annual fee Interest expense Effective interest rate =

$325,000 $1,625 $35,775 5.54%

Effective interest rate =

Interest expense + Annual fee Borrowed amount

ine of credit of $1 million for up s 5.3 percent, and under the used amount as the annual greement. What is the fee the

e =

Interest expense + Annual fee Borrowed amount

14.28 Lockbox: Jennifer Electrical is evaluating whether a lockbox it is currently using is worth estimates that the lockbox reduces the mail float by 1.8 days and the processing by half average $50,000 a day for Jennifer Electrical, with the average check being for $500. Th processed check. Assume that there are 270 business days in a year and that the firm’s funds is 6 percent.What will the firm’s savings be from using the lockbox? Average daily sales No. of business days Opportunity cost of funds Average check amount Collection time saved Processing time saved Per check processing fee

$50,000 270 6% $500 1.8 days 0.5 days $0.34

No. of checks processed per day 100 The cost of a lockbox = # of checks processed per day* per check processing fee*# of b The cost of a lockbox = $9,180 Savings from mail float = Savings from processing float Total savings = Total savings =

Savings from lockbox

90,000 $25,000 (Savings from mail float + Savings from processing f $ 115,000 $ 6,900

Decision: Since the savings from using the lockbox are lower than the cost, it sho

urrently using is worth keeping. Management he processing by half a day.The remittances eck being for $500. The bank charges $0.34 per ear and that the firm’s opportunity cost for these ckbox?

processing fee*# of business days in a year

ngs from processing float)

than the cost, it should not be used.

14.29 Lockbox: Hazel Corp. has just signed up for a lockbox. Management expects the lockb Hazel Corp.’s remittances average $37,000 a day for Hazel, and the average check is $ processed check. Assume that there are 270 business days in a year.What will the firm the opportunity cost for these funds is 12 percent?

Average daily sales No. of business days Opportunity cost of funds Average check amount Collection time saved Per check processing fee

$37,000 270 12% $125 2.1 days $0.37

Number of checks processed per day 296 The cost of a lockbox = # of checks processed per day* per check processing fee*# of business The cost of a lockbox = $29,570.40 Savings from reducing mail float $77,700 Savings from lockbox = $9,324 Decision: The lockbox is way too expensive compared to the savings it generates

x. Management expects the lockbox to reduce the mail float by 2.1 days. Hazel, and the average check is $125. The bank charges $0.37 per s days in a year.What will the firm’s savings be from using the lockbox is

heck processing fee*# of business days in a year

ared to the savings it generates

14.30

Aging schedule: Ginseng Company collects 50 percent of its receivables in 10 days percent in 11 to 30 days, 7 percent in 31 to 45 days, 7 percent in 46 to 60 days, and more than 60 days.The company has $1,213,000 in accounts receivable. Prepare an schedule for Ginseng Company. Ginseng Company's Aging Schedule Age of Account (in days) 0–10 11–30 31–45 46–60 More than 60 Total

% of Total Account

Value of Account ($)

50.00% 31.00% 7.00% 7.00% 5.00% 100.00%

$606,500 $376,030 $84,910 $84,910 $60,650 $1,213,000

ts receivables in 10 days or fewer, 31 nt in 46 to 60 days, and 5 percent in s receivable. Prepare an aging

14.31 Aging schedule: A partial aging of accounts receivable for Lincoln Cleaning Services i in the accompanying table. What percent of receivables are in the 45-day range? Deter the firm’s effective days’ sales outstanding. How does it compare with the industry aver 35 days? Age of Account (in days) 10 30 45 60 75 Total

Value of Account % of Total ($) Account $ 271,000 46.0% $ 145,220 24.6% $ 87,773 14.9% $ 53,980 9.2% $ 31,245 5.3% $ 589,218 100.0%

Effective DSO = Age of the account category ´ Percent of AR for the account category Effective DSO =

28.2 days

r Lincoln Cleaning Services is given e in the 45-day range? Determine mpare with the industry average of

e account category

14.32

Aging schedule: Keswick Fencing Company collects 45 percent of its receivables in days or fewer, 34 percent in 10 to 30 days, 12 percent in 31 to 45 days, 5 percent in 4 60 days, and 4 percent in more than 60 days. The company has $937,000 in its accou receivable account. Prepare an aging schedule for Keswick Fencing.

Keswick Fencing Company % of Total Age of Account (in days) Account 0–10 11–30 31–45 46–60 More than 60 Total

45.00% 34.00% 12.00% 5.00% 4.00% 100.00%

Value of Account ($) $421,650 $318,580 $112,440 $46,850 $37,480 $937,000

45 percent of its receivables in 10 in 31 to 45 days, 5 percent in 46 to pany has $937,000 in its accounts swick Fencing.

14.33 Factoring: Zenex, Inc., sells $250,000 of its accounts receivable to factors at a 3 perce The firm’s average collection period is 90 days. What is the dollar cost of the factoring s What is the simple annual interest cost of the factors loan? Accounts receivables sold Factor discount Average collection period

$250,000 3% 90 days

Dollar cost of factoring per month Dollar cost over 90 days Simple monthly interest cost of factoring Simple interest cost of factoring

$7,500 $22,500 3.09% 37.11%

able to factors at a 3 percent discount. ollar cost of the factoring service?

14.34 Factoring: A firm sells $100,000 of its accounts receivable to factors at a 2 percent disc firm’s average collection period is one month. What is the dollar cost of the factoring ser Accounts receivables sold Factor discount Average collection period Dollar cost of factoring per month

$100,000 2% 30 days $2,000

e to factors at a 2 percent discount. The dollar cost of the factoring service?

14.35 What impact would the following actions have on the operating and cash conversion cy the cycles increase, decrease, or remain unchanged? a. More raw material than usual is purchased. b. The company enters into an off season, and inventory builds up. c. Better terms of payment are negotiated with suppliers. d. The cash discounts offered to customers are decreased. e. All else remaining the same, an improvement in manufacturing technique decreases the cost of goods sold.

Situation a. More raw material than usual is purchased. b. The company enters into an off season, and inventory builds up. c. Better terms of payment are negotiated with suppliers. d. The cash discounts offered to customers are decreased.

ating and cash conversion cycles? Would

acturing technique decreases

Operating cycle Increase

Cash conversion cycle Increase

Increase No change Increase

Increase Decrease Increase

14.36 What impact would the following actions have on the operating and cash conversion c Would the cycles increase, decrease, or remain unchanged? a. b. c. d. e.

Less raw material than usual is purchased. The company encounters unseasonable demand, and inventory declines rapidly. Tighter terms of payment are demanded by suppliers. The cash discounts offered to customers are increased. All else remaining the same, due to labor turnover and poor efficiency, the cost of goo

Situation a. Less raw material than usual is purchased. b. The company encounters unseasonable demand, and inventory declines rapidly. c. Tighter terms of payment are demanded by suppliers. d. The cash discounts offered to customers increased. e. All elseare remaining the same, due to labor turnover and poor efficiency, the cost of goods sold increases.

e on the operating and cash conversion cycles? ain unchanged?

mand, and inventory declines rapidly.

increased. nover and poor efficiency, the cost of goods sold increases.

Operating cycle

Cash conversion cycle

Decrease

No change

Increase

Decrease

Unchanged

14.37 Morgan Sports Company just reported the following financial information. Morgan Sports Equipment Company ASSETS Cash Accounts Receivable Inventories Total current assets

$ 677,423 $ 1,845,113 $ 1,312,478 $ 3,835,014

Net sales Cost of goods sold

$ 9,912,332 $ 5,947,399

a. b. c. d. e.

Calculate the firm’s days’ sales outstanding. What is the firm’s days’ sales in inventory? What is the firm’s days’ payables outstanding? What is the firm’s operating cycle? How does it compare with the industry average of 72 What is the firm’s cash conversion cycle? How does it compare with the industry averag

Days' sales outstanding (DSO) =

67.9

Days' sales in inventory (DSI) =

80.5

Days' payables outstanding (DPO) =

105.7

Firm's operating cycle =

148.5

Cash convesrion cycle =

42.83

following financial information.

LIABILITIES AND EQUITY Accounts payable Notes payable

$ 1,721,669 $ 2,113,345

Total current liabilities

$ 3,835,014

es it compare with the industry average of 72 days? How does it compare with the industry average of 42 days?

days days days days = DSO + DSI

Comment Inefficient

days = DSO + DSI - DPO

On par

14.38 Jackson Electricals, one of the largest generator dealers in Phoenix, sells about 2,000 generators a year. The cost of placing an order with its supplier is $750, and the inventory carrying costs are $170 for each generator. Jackson likes to maintain safety stock of 15 at all times. a. What is the firm’s EOQ? b. How many orders will the firm need to place this year? c. What is the average inventory for the season?

Annual sales Cost of placing an order Inventory carrying cost per generator Safety stock

EOQ =

2  Reorder costs Sales per period Carrying costs

2,000 units $750 $170 15 generators

133 generators

b) Number of orders that the firm will need to place =

15 orders

82 generators

Average inventory for the season =

Phoenix, sells about 2,000 ier is $750, and the n likes to maintain safety

14.39 Tanzaniqe, Inc., sells $200,000 of its accounts receivable to factors at a 5 percent discount. The firm’s average collection period is 90 days. a. b. c.

What is the dollar cost of the factoring service? What is the simple annual interest cost of the loan? What is the effective annual interest cost of the loan?

Accounts receivables sold Factor discount Average collection period

$200,000 5% 90 days

Dollar cost of factoring per month= Dollar cost over 90 days =

$10,000 $30,000

Monthly simple interest cost of factoring the loan Annual simple interest cost =

5.26% 63.16%

Effective annual interest cost =

85.06%

e to factors at a 5 90 days.

14.40 A company increasing its credit terms for customers from 1/10, net 30 to 1/10, net 60 experience a. b. c. d.

Answer:

an increase in cash on hand. an increase in the average collection period. higher net income. a higher level of uncollectible accounts.

b, since with the extended period allowed, more customers will avail of th

m 1/10, net 30 to 1/10, net 60 will likely

ore customers will avail of the credit

14.41 Suppose a company uses trade credit with the terms of 2/10, net 50. If the company pays their account on the 50th day, the effective borrowing cost of skipping the discount on day 10 is closest to a. 14.6 percent. b. 14.9 percent. c. 15.0 percent. d. 20.2 percent.

Credit terms = 2% Payment due in 50

discount if paid within days

Effective borrowing cost of skipping the cash discount = Answer:

10 days

20.24%

2/10, net 50. If the ve borrowing cost

The following information relates to Problems 14.42 through 14.44. Mary Gonzales is evaluating companies in the office supply industry and has compiled the following information: 20X1 Company

14.42

20X2

Credit

Average Receivables

Credit

Sales

Balance

Sales

5,000,000

1,000,000

6,000,000

3,000,000

1,200,000

4,000,000

2,500,000

800,000

3,000,000

D Industry

$ 500,000 $ 25,000,000

$ $

100,000 5,000,000

$ $

600,000 28,000,000

Which of the companies has the lowest accounts receivable turnover in the year 20X2 a. Company A b. Company B c. Company C d. Company D

14.43

The industry average receivables collection period a. increased from 20X1 to 20X2. b. decreased from 20X1 to 20X2. c. did not change from 20X1 to 20X2. d. increased along with the increase in the industry accounts receivable turnover.

14.44

Which of the companies reduced the average time it took to collect on accounts recei from 20X1 to 20X2? a. Company A b. Company B c. Company C d. Company D

ough 14.44. pply industry and has compiled

20X2 Average Receivables

20X1

20X2

A/R TO

Balance

20X1

20X2

DSO

(days) (days)

1,200,000

73.0

1,500,000

2.5

2.67

146

136.9

1,000,000

3.125

3.00 116.8

121.7

$ $

200,000 5,400,000

5 5

3.00 5.19

121.7 70.4

receivable turnover in the year 20X2?

y accounts receivable turnover.

e it took to collect on accounts receivable

73 73

STP #14.1 The Whole Foods Market, Inc. balance sheet for the fiscal year ending September assets of $1,980 million, total assets of $5,538 million, total current liabilities of $1,0 the company's net working capital on September 29, 2013? What does this tell us? Net Working Capital = Total Current Assets − Total Current Liabilities = $1,980,000,000 − $1,088,000,000 = $892,000,000

This tells us that Whole Foods could pay off all its current liabilities (those that will c that could reasonably be expected to be converted to cash within the next year and

year ending September 29, 2013 included included the following: total current current liabilities of $1,088 million, and total liabilities of $1,660 million. What was ? What does this tell us?

abilities (those that will come due in the next year) with the cash and other assets within the next year and still have $892 million left over.

STP #14.2 Last year Perpetual Plastics Company took an average of 46 days to pay suppliers days to collect its receivables. The company's average days' sales in inventory was What was Perpetual's operating cycle and cash conversion cycle last year? DPO = 46 days DSO = 38 days DSI = 52 days Perpetual's operating cycle = DSO + DSI38 = days + 52 days = 90 days

Perpetual's cash conversion cycle = DSO + DSI − DPO = 38 days + 52 days − 46 d = 44 days

age of 46 days to pay suppliers and 38 ge days' sales in inventory was 52 days. version cycle last year?

PO = 38 days + 52 days − 46 days

STP #14.3 Montrose, Inc. sells its products with terms of 3/15 EOM, net 30. What is the cost of the trade credit it provides its customers? Credit terms = 3/15 EOM, net 30

æ Discount ö Effective annual rate (EAR) = ç1+ ÷ è Discounted rate ø

365/days credit

(

= 1+ 3

97)

365

-1

= (1.030928)24.333333 -1 = 2.0984 -1 = 1.0984 = 109.84%

-1

STP #14.4 FRA Manufacturing Company purchases 9,000 units of Part 3BX each year. The co placing an order is $5 and the cost of carrying one part in inventory for a year is $1 the Economic Order Quantity (EOQ) for part 3BX if the company carries a safety st 200 units? How many orders will the company need to place this year? Annnual purchases = 9,000 units Cost of placing an order = $5 Inventory carrying cost per part = $1 Safety stock = 200 parts

EOQ = =

2 ´ Reorder costs ´ Sales (or purchases) per period Carrying costs

2 ´ $5´ 9,000 = 300 parts $1

The number of orders that the firm should place each year is 300 / 9,000 =

s 9,000 units of Part 3BX each year. The cost of rrying one part in inventory for a year is $1. What is part 3BX if the company carries a safety stock of mpany need to place this year?

(or purchases) per period ng costs

d place each year is 300 / 9,000 =

STP #14.5 Rosemary Corporation has daily sales of $139,000. The financial manager at the fi has determined that a lockbox would reduce collection time by 2.2 days. Assuming the company can earn 5.5 percent interest per year, what are the potential annual savings from the lockbox? Average daily sales = Collection time saved = Savings from mail float = Annual savings if invested =

$139,000 2.2 days 2.2 days × $139,000 = $305,800 $305,800 × 0.055 = $16,819

inancial manager at the firm me by 2.2 days. Assuming are the potential annual

STP #14.6 Sunny Way Landscaping has a formal line of credit of $500,000 with First Commen The interest rate on this loan is 6 percent, and under the agreement, Sunny Way m an annual fee of 75 basis points on the unused amount. The amount currently outs on the loan is $325,000. What is the annual fee the company must pay on the curre unused balance? What is the effective interest rate? Line of credit limit = $500,000 Interest rate = 6% Annual fee on unused balance = 0.75% Amount borrowed = $325,000 Unused balance = $175,000 Annual fee = $175,000 × 0.0075 =$1,312.50 Interest expense for amount borrowed = $325,000 × 0.06 = Effective interest rate =

$19,500.00

Interest expense + Annual fee Borrowed amount ($19,500.00 + $1,312.50) $325,000.00

,000 with First Commenrce Bank. reement, Sunny Way must pay e amount currently outstanding ny must pay on the current

$19,500.00

0.0640 = 6.40%

15.8

IPO pricing: Trajax, Inc., a high-technology firm in Portland, raised a total of $91 millio company received $27 of the $33 per share offering price. The firm’s legal fees, SEC r other administrative costs were $450,000. The firm’s stock price increased 17 percent trading. What was the total cost to the firm of issuing the securities? Offer Price Issuer receives Legal fees and other costs Underpricing Issue size

$33 $27 $450,000 17% $91,000,000

Calculation of total issue costs Number of shares issued Underwriting Spread Price after increase Undervaluation Cost Total Issue Cost

2,757,575.758 $16,545,454.55 38.61 15,470,000.00 $32,465,454.55

aised a total of $91 million in an IPO. The e firm’s legal fees, SEC registration fees, and ice increased 17 percent on the first day of rities?

15.9

IPO pricing: Myriad Biotech plans a $114 million IPO in which the offering price to the per share. The company will receive $43 per sahre. The firm's legal fees, SEC registr other administrative costs will total $525,000. If the stock price increases 14 percent o trading, what will be the total cost of issuing the securities? Offer Price Issuer receives Legal fees and other costs Underpricing Issue size

$51 $43 $525,000 14% $114,000,000

Calculation of total issue costs Number of shares issued Underwriting Spread Price after increase Undervaluation Cost Total Issue Cost

2235294.118 $17,882,352.94 58.14 15,960,000.00 $34,367,352.94

hich the offering price to the public will be $51 firm's legal fees, SEC registration fees, and price increases 14 percent on the first day of ?

15.16 Prime rate lending: Suppose two firms want to borrow money from a bank for a period Firm A has excellent credit, whereas Firm B’s credit standing is such that it would pay p percent. The current prime rate is 6.75 percent, the 30-year Treasury bond yield is 4.35 three-month Treasury bill yield is 3.54 percent, and the 10-year Treasury note yield is 4 What are the appropriate loan rates for each customer?

Firm A's credit rating Excellent Firm B's credit rating Prime +2 Current Prime rate 6.75% 30-year bond yield 4.35% 3-month Treasury bill yield 3.54% 10-year Treasury note yield 4.22% Appropriate Loan rate calculation Firm A Prime Rate 6.75% Default Premium 0 Maturity Risk Premium 0

Firm B 6.75% 2% 0

One -year Loan Rate

8.75%

6.75%

15.17 Prime rate lending: Now suppose that Firm B from Problem 15.16 decides to get a te years. How does this affect the company’s borrowing cost? Firm A's credit rating Excellent Firm B's credit rating Prime +2 Current Prime rate 6.75% 30-year bond yield 4.35% 3-month Treasury bill yield 3.54% 10-year Treasury note yield 4.22% Appropriate Loan rate calculation Firm A Prime Rate 6.75% Default Premium 0 Maturity Risk Premium 0.68%

Firm B 6.75% 2% 0.68%

One -year Loan Rate

7.43%

9.43%

y from a bank for a period of one year. s such that it would pay prime + 2 easury bond yield is 4.35 percent, the r Treasury note yield is 4.22 percent.

15.16 decides to get a term loan for 10

15.18

Prime-rate lending: Cartco needs to borrow $5 million for an upgrade to its headq and manufacturing facility. Management has decided to borrow using a five-year t from its existing commercial bank. The prime rate is 3.25 percent, and Cartco's cu rating is prime + 2.48 percent. The yield on a five-year U.S. treasury note is 2.01 p and the three-month U.S. Treasury bill rate is 0.09 percent. What is the estimated for the five-year bank loan? Ki = PR + DRP + MAT PR = 3.25% DRP = 2.48% 5yr Tbill 2.01% 3-month Tbill 0.09%

PR 3.25%

DRP 2.48%

MAT 1.92%

Ki 7.65%

an upgrade to its headquarters row using a five-year term loan ercent, and Cartco's current treasury note is 2.01 percent, What is the estimated loan rate

15.20

IPO: On August 19th, 2004 Google issued its IPO of 19.6 million shares to the init $85.00 per share. The closing price of the stock that same day was $100.34. Wha dollar value of the underpricing associated with the Google IPO? The closing price of Google was $100.34 Number of shares issued 19,600,000 Market Value of Google after issue $1,966,664,000.00 IPO price Market value befor issue

$85.00 $1,666,000,000.00

Total Underpricing

$300,664,000.00

6 million shares to the initial investors at me day was $100.34. What was the gle IPO?

15.21 IPO: Deere and Bros. is a broker that brings new issues of small firms to the market. Their most recent deal for Dextra, Inc., had the following characteristics: Number of shares: 1,000,000; Price to public: $15 per share; Proceeds to Dextra: $13,500,000. The legal fees were $150,000, printing costs were $56,000, and all the other expenses were $72,000. What is the profit or loss for Deere Bros.? Number of shares Offer Price Proceeds to issuing company (Dextra, Inc.) Legal fees Printing costs Other expenses

1,000,000 $15 13,500,000 150,000 $56,000 $72,000

Calculation of Profit or loss to Broker (Deere and Bros.) Gross Proceeds from issue of 1,000,000 shares @ $15 per share $15,000,000 Less Proceeds to Dextra Inc. 13,500,000 Gross Profit to Deere and Bros. from the new issue deal $1,500,000 Less legal, printing and other costs $278,000 Net Profit to Broker $1,222,000

of small firms to the market. characteristics: Number of eds to Dextra: $13,500,000. 00, and all the other ere Bros.?

15.22 IPO: When Global Partners went public in September 2008, the offer price was $22.00 per share and the closing price at the end of the first day was $23.90. The firm issued million shares. What was the loss to the company due to underpricing? Offer Price $22.00 Closing Price $23.90 Number of shares issued 4,900,000 $ Per share Underpricing $1.90 % underpricing 8.64% Loss due to underpricing $9,310,000

offer price was $22.00 3.90. The firm issued 4.9 ricing?

15.23 IPO: Bellex Technologies agreed to complete its IPO on a best-effort basis. The company’s investment bank demanded a spread of 17 percent of the offer price, which was set at $30 per share. Three million shares were issued. However, the bank was overly optimistic and eventually was able to sell the stock for only $28 per share. What are the proceeds for the issuer and the underwriter? Offer Price Number of shares issued Underwriter's spread Selling Price Proceeds from sale of shares Proceeds to underwriter Proceeds to Issuer

$30 3,000,000 17% $28 $84,000,000 $15,300,000 $68,700,000

n a best-effort basis. The percent of the offer price, which ued. However, the bank was k for only $28 per share. What

15.24 IPO: Suppose a biotech company in Boston, Massachusetts, completes an $85 million priced to te public at $75 per share. The firm receives $72 per share and the out-of-po expenses are $340,000. The stock’s closing price at the end of the first day is $84. Wh total cost to the firmof issuing the securities? Total Value of IPO Offer Price Net Price to Issuer Closing Price at end of 1st day Out-of-pocket expenses Number of shares sold Underwriter's Commission Out-of-pocket expenses Under pricing cost Total Cost of issue

$85,000,000 $75 $72 $84 $340,000 1133333 $ 3,400,000 $340,000 $ 10,200,000 $13,940,000

completes an $85 million IPO er share and the out-of-pocket of the first day is $84. What is the

15.25

IPO: An online medical advice company just completed an IPO with an investment commitment basis. The firm issued 5 million shares of common stock, and the und were $4.20 per share. The offering price was $26 per share. a. What were the total proceeds from the common stock sale? b. How much money did the company actually make from the deal? c. How much money did the investment bank make?

Number of shares issued Offer price Underwriting fees

5,000,000 $26 $4.20

Total proceeds from the common stock sale Proceeds to company Proceeds to Investment bank

$130,000,000 $109,000,000 $21,000,000

n IPO with an investment bank on a firmmmon stock, and the underwriting fees re.

15.26 IPO underpricing: Suppose that a biotech firm in Baltimore raised $120 million in an IPO. The firm received $23 per share and the stock sold to the public for $25 per share. The firm’s legal fees, SEC registration fees, and other administrative costs were $270,000. The firm’s stock price increased 17.5 percent on the first day. What was the total cost to the firm of issuing the securities?

Total Value of IPO Offer Price Net Price to Issuer Premium on Closing Price at end of 1st day Legal fees, SEC reg. fees, other admin. Costs

Number of shares sold Underwriter's Commission Out-of-pocket expenses Under pricing cost Total Cost of issue

$120,000,000 $25 $23 17.50% $270,000

$ $

4,800,000 9,600,000 $270,000 21,000,000 $30,870,000

e raised $120 million in an the public for $25 per er administrative costs were n the first day. What was

STP 15.1 Why are traditional sources of funding not usually available for new or emerging busin

There are three reasons such businesses often have little or no access to traditional f

1) The high degree of risk associated with them. 2) Their primary assets are often intangible assets that are not as well understood by other potential investors as tangible assets. 3) Potential investors often have limited knowledge of highly specialized technologies business areas and therefore find it difficult to assess the quality of their managemen prospects.

or new or emerging businesses?

no access to traditional funding:

ot as well understood by lenders or

specialized technologies or new ality of their management teams or their

STP 15.2 A firm is making an initial public offering. The investment bankers agree to a firm underwriting commitment for 500,000 shares that would be priced to the public at $36 a share. The underwriter's spread is 7 percent. What were the proceeds for the issuer and the underwriter? $18,000,000 Gross proceeds from offer = $36 × 500,000 = Underwriter's spread = Proceeds to Underwriter = $18,000,000 × 0.07 = Proceeds to issuer = ($36 × 500,000) − $1,260,000 =$16,740,000

ment bankers agree to a firm ould be priced to the public at What were the proceeds for

$1,260,000

STP15.3 Hilton Worldwide Holdings Inc. completed an initial public offering on December 12, 20 offer price was $20.00 per share and the closing price at the end of the first day was $ firm issued 117.6 million shares. What was the loss to Hilton due to underpricing? Wh this value? Change in price on the first day of trading = $21.50 − $20.00 = Number of shares outstanding = 117.6 million Loss due to underpricing = $1.50 × 117.6 million = 176.4 The initial investor, who purchased the shares allocated by the underwriters of the IPO received this value.

ic offering on December 12, 2013. The t the end of the first day was $21.50. The Hilton due to underpricing? Who received

$1.50 million

ed by the underwriters of the

STP15.5 Management of Southern Parts Company has decided to sell 10-year bonds to finance expansion into the Pacific Northwest. The loan rate on these bonds is 8 percent and the 3-month Treasury bill rate is 2.1 percent. The firm's credit rating is B, and the yield on 10-year Treasury bonds is 2.5 percent higher than that on 3month Treasury bills. How much of a premium over the 10-year Treasury bond are those Southern Parts bonds selling for? k t = PR + DRP + MAT 8.0% = 2.1% + DRP + 2.5% DRP = 3.4%

ed to sell 10-year bonds to n rate on these bonds is 8 ent. The firm's credit rating is cent higher than that on 3he 10-year Treasury bond are

16.4

M&M Proposition 1: Cerberus Security produces a cash flow of $200 and is expected to continue doing so in the infinite future. The cost of equity capital for Cerberus is 20 percent, and the firm is financed totally with equity. The firm would like to repurchase $100 in shares by borrowing $100 at a 10 percent rate (assume that the debt will also be outstanding into the infinite future). Using Modigliani and Miller’s Proposition 1, what is the value of the firm today, and what will be the value of the claims on the firm’s assets after the stock repurchase? What will be the rate of return on common stock required by investors after the share repurchase?

Annual Cash Flow generated by the firm Cost of Equity Capital of the 100% equity financed firm Repurchase of equity = Debt used to buyback equity Interest rate on debt

$200 20% $100 $100 10%

Based on Modigliani and Miller's Proposition I: Value of the firm today Amount of Debt after restructuring Amount of Equity after restructuring Interest cost of debt Residual income to holders of common stock Rate of Return on common stock (kcs) ALTERNATIVE METHOD Formula to calculate Cost of Equity

V  kcs = kAssets +  Debt  (kAssets − kDebt )  Vcs  KAssets

20%

Vdebt / Vcs kAssets − kDebt

0.11111 10%

kcs

21.11%

$1,000 $100 $900 $10 $190 21.11%

sh flow of $200 and is cost of equity capital for with equity. The firm would a 10 percent rate (assume ure). Using Modigliani and y, and what will be the value hase? What will be the rate of share repurchase?

16.5

M&M Proposition 1: A firm financed completely with equity currently has a cost of capital equal to 15 percent. If Modigliani and Miller’s Proposition 1 holds and the firm is thinking about changing its capital structure to 50 percent debt and 50 percent equity, then what will be the cost of equity after the change if the cost of debt is 10 percent?

All-Equity Firm's Cost of Capital Proposed Capital Structure Debt Equity Cost of Debt (after restructuring)

15% 50% 50% 10%

Cost of Equity (after restructuring)

æV ö kcs = kAssets + çç Debt ÷÷ kAssets - kDebt è Vcs ø

(

KAssets VDebt/Vcs (kAssets-kDebt) kcs

) 15%

100% 5% 20.0%

currently has a Proposition 1 holds 50 percent debt er the change if

16.6

M&M Proposition 1: Swan Specialty Cycles is currently financed with 50 percent debt 50 percent equity. The firm pays $125 each year to its debt investors (at a 10 percent c debt), and the debt has no maturity date. What will be the value of the equity if the firm repurchases all of its debt and raises the funds by issuing equity? Assume that all of th assumptions in Modigliani and Miller’s Proposition 1 hold.

Current Capital Structure Debt Equity

50% 50%

Annual interest cost Cost of Debt (%)

$125 10%

Proposed Capital Structure Debt 0% Equity 100%

Current Value of Debt $1,250 Current Value of Equity $1,250 After repurchase of debt: Value of Equity

$2,500

nced with 50 percent debt and nvestors (at a 10 percent cost of ue of the equity if the firm uity? Assume that all of the

16.7

10% 8% 80%

æV ö kcs = kAssets + çç Debt ÷÷ kAssets - kDebt è Vcs ø

(

Equity Ratio Cost of Equity

)

20% 18%

Check WACC

10%

apital for a firm, hold, is 10 percent. the cost of debt for the percent debt?

16.8 Interest tax shield benefit: Legitron Corporation has $350 million of debt outstanding at interest rate of 9 percent. What is the dollar value of the tax shield on that debt, just for thi year, if Legitron is subject to a 35 percent marginal tax rate? Amount of Debt outstanding Interest rate on debt Corporate tax rate

$350,000,000 9% 35%

Annual interest cost on debt Annual tax shield on interest expense

$31,500,000 $11,025,000

on of debt outstanding at an ld on that debt, just for this

16.9 Interest tax shield benefit: FAJ Inc. has $500 million of debt outstanding at an interest rate of 9 percent. What is the present value of the tax shield on that debt if it has no maturity and if FAJ is subject to a 30 percent marginal tax rate? Amount of Debt outstanding $500,000,000 Interest rate on debt 9% Corporate tax rate 30% Annual interest cost $45,000,000 Annual tax shield on interest $13,500,000 Present Value of tax shield $150,000,000

n of debt outstanding at an interest x shield on that debt if it has no al tax rate?

16.10

Interest tax shield benefit: Springer Corp. has $250 million of debt outstanding at an interest rate of 11 percent. What is the present value of the debt tax shield if the debt no maturity and if Springer is subject to a 40 percent marginal tax rate? Amount of Debt outstanding Interest rate on debt Corporate tax rate

$250,000,000 11% 40%

Annual interest cost Annual tax shield on interest Present Value of tax shield

$27,500,000 $11,000,000 $100,000,000

million of debt outstanding at an f the debt tax shield if the debt has marginal tax rate?

16.11 Interest tax shield benefit: Structural Corp. currently has an equity cost of capital equal to 15 percent. If the Modigliani and Miller Proposition I assumptions hold, with the exception of the assumption that there are no taxes, and the firm’s capital structure is made up of 50 percent debt and 50 percent equity, then what is the weighted average cost of capital for the firm if the cost of debt is 10 percent and the firm is subject to a 40 percent marginal tax rate? Cost of equity Cost of debt Proportion of Debt Proportion of Equity Corporate Tax rate

15% 10% 50% 50% 40%

Calculation of Weighted Average Cost of Capital (WACC) After-tax cost of debt WACC

6% 10.50%

n equity cost of capital assumptions hold, with d the firm’s capital ty, then what is the bt is 10 percent and the

16.13 M&M Proposition 1: Keyboard Chiropractic Clinics produces $300,000 of cash flow each year. The firm has no debt outstanding, and its cost of equity capital is 25 percent. The firm's management would like to repurchase $600,000 of its equity by borrowing a similar amount at a rate of 8 percent per year. If we assume that the debt will be perpetual, find the cost of equity capital for Keyboard after it changes its capital structure. Assume that Modigliani and Miller Proposition 1 holds. Annual Cash Flow generated by the firm Cost of Equity Capital of the 100% equity financed firm Repurchase of equity = Debt used to buyback equity Interest rate on debt

$300,000 25% $600,000 $600,000 8%

æV ö kcs = kAssets + çç Debt ÷÷ kAssets - kDebt è Vcs ø

(

KAssets

25%

VDebt/Vcs kAssets-kDebt

1 17%

kcs

42.00%

)

$1,200,000 $600,000 $600,000 $48,000 $252,000 42.00%

300,000 of cash flow uity capital is 25 ,000 of its equity by e assume that the debt er it changes its capital s.

16.14 M&M Proposition 1: Marx and Spender has a current WACC of 21 percent. If the cost of debt capital for the firm is 12 percent and the firm is currently financed with 25 percent debt, then what is the current cost of equity capital for the firm? Assume that the assumptions in Modigliani and Miller’s Proposition 1 hold. WACC Cost of debt capital Proportion of debt

21% 12% 25%

Formula to calculate Cost of Equity

V  kcs = kAssets +  Debt  (kAssets − kDebt )  Vcs  KAssets

21%

VDebt/Vcs kAssets-kDebt

33.33% 9%

kcs

24.00%

CC of 21 percent. If the cost ently financed with 25 for the firm? Assume that ld.

50% 10% 15%

Formula to calculate Cost of Equity

V  kcs = kAssets +  Debt  (kAssets − kDebt )  Vcs  KAssets

15%

Vdebt / Vcs kAssets − kDebt

100.00% 5%

kcs

20.00%

for a firm y) is 15 percent. ost of debt is 10 e firm is 0.5?

16.17 M&M Proposition 2: Mikos Processed Foods is currently valued at $500 million. Mikos will be repurchasing $100 million of its equity by issuing a nonmaturing debt issue at a 10 percent annual interest rate. Mikos is subject to a 30 percent marginal tax rate. If all of the Modigliani and Miller assumptions apply, except the assumption that there are no taxes, what will be the value of Mikos after the recapitalization? Current market value of the firm Proposed restructuring: Equity buyback Nonmaturing Debt issue Cost of Debt Marginal tax rate

$500,000,000

Annual interest cost on debt Tax shield Present value of tax shield

$10,000,000 $3,000,000 $30,000,000

Value of firm after recapitalization

$530,000,000

$100,000,000 $100,000,000 10% 30%

ued at $500 million. Mikos nmaturing debt issue at a ent marginal tax rate. If all sumption that there are no n?

16.18 M&M Proposition 2: Backwards Resources has a WACC of 12.6 percent, and it is subject to a 40 percent marginal tax rate. Backwards has $250 million of debt outstanding at an interest rate of 9 percent and $750 million of equity (market value) outstanding. What is the expected return of the equity given this capital structure? WACC Tax rate Value of Debt outstanding Cost of Debt Value of Equity

12.60% 40% $250,000,000 9% $ 750,000,000

Debt/Equity ratio Expected Return on equity

33.33% 15.00%

Check WACC

12.60%

PMT PVIF $11,000,000 0.593451328

$250,000,000 11% 40% $27,500,000 $11,000,000 5 $40,654,867.19

PVIFA 3.695897018

PVA $40,654,867.19

erest rate of 11 percent. t will mature in five years t Finite is subject to a 40

$900,000,000 $300,000,000 30%

Value of Tax shield due to interest Value of equity before paying off debt

$90,000,000 $600,000,000

Value of equity after paying off debt

$510,000,000

STP 16.1 Central Grocers Inc. produces annual cash flows of $ 175,000, which are expected to company is financed entirely with equity capital at an annual cost of 12 percent. Mana borrowing $400,000 at an annual interest rate of 6 percent to repurchase $400,000 of outstanding stock (You can assume that the debt will be outstanding into the indefinite value of Central Grocers' stock before the stock repurchase? Under Modigliani and Mi would be the value of the total claims on the company's assets after the stock repurch of return on common stock required by investors after the repurchase?

Using the perpetuity formula, we can compute the value of Central Grocers' stock befo $175,000/0.12 = $1,458,333 if the cash flow is expected to be produced into the infinit

Under M&M Proposition 1, the value of the firm will be the same before and after the r since the value of the debt claim will be $400,000 at the time of the transaction, the va equity after the repurchase must be $1,458,333 - $400,000 = $1,058,333.

Since interest of $400,000 x 0.06 = $24,000 must be paid to the debt holders each ye available for the stockholders each year will equal $175,000 - $24,000 = $151,000. Th cost of equity capital for the firm will be $1,058,333 = $151,000/k cs, or kcs = 0.1427, or

which are expected to continue indefinitely. The ost of 12 percent. Management is considering epurchase $400,000 of the company's nding into the indefinite future.). What is the total Under Modigliani and Miller's Proposition 1, what after the stock repurchase? What will be the rate rchase?

ntral Grocers' stock before the repurchase to be produced into the infinite future.

e before and after the repurchase. Therefore, f the transaction, the value of the outstanding 1,058,333.

e debt holders each year, the amount that will be $24,000 = $151,000. This implies that the new /k cs, or kcs = 0.1427, or 14.27%.

STP 16.2 The required rate of return on the assets of a firm is 12 percent, the firm has a deb common-stock ratio of 40 percent, and the cost of debt is 6 percent. If the firm has preferred stock and the three conditions specified by M&M hold, what is the expec of return on the firm's common stock? Using the equation for M&M Proposition 2, Equation 16.3, we get: k cs = k Assets + (VDebt /Vcs) × (k Assets - k Debt) = 0.12 + [(0.4) × (0.12 - 0.06)] = 0.144 = 14.4%

cent, the firm has a debt-to6 percent. If the firm has no hold, what is the expected rate

STP 16.3 Your boss at Box and Freight Company asks you how much additional debt the company would have to add through a capital restructuring in order to create $9 million in present value from the resulting interest tax shields. What would you tell him if the debt will have no maturity and if Box and Freight is subject to a 32 percent marginal tax rate? The present value of Box & Freight's additional tax shield will be tc x D = 0.32 x D = $9,000,000 Therefore D = $28,125,000

ch additional debt the g in order to create hields. What would Freight is subject to

17.2

Dividends: Marx Political Consultants has decided to discontinue all of its business op debt of $7 million, and the liquidation value of its assets is $10 million. If the book valu million, then what will be the amount of the liquidating dividend when the firm liquidate

Total debts = Liquidation value of assets = Book value of equity =

$ 7,000,000 $ 10,000,000 $ 5,000,000

Residual value of assets =

3,000,000

Liquidating dividend =

3,000,000

ontinue all of its business operations. The firm has total $10 million. If the book value of the firm’s equity is $5 dend when the firm liquidates all of its assets?

17.7

Dividends: Scintilla, Inc., is trading for $10.00 per share on the day before the exdividend date. If the amount of the dividend is $0.25 and there are no taxes, what should the price of the shares be on the ex-dividend date? Price on day before the ex-dividend date = Dividend per share paid =

$ 10.00 $0.25

Price on ex-dividend date =

$ 9.75

on the day before the exthere are no taxes, what e?

17.8

Dividends: A company announces that it will make a $1.00 dividend payment. Assuming all investors are subject to a 15 percent tax rate on dividends, how much should the company’s share price drop on the ex-dividend date? Dividend per share declared = Investors' Tax rate on dividends =

$1.00 15%

Drop in share price on ex-dividend date =

$ 0.85

ividend payment. dividends, how end date?

17.27 The Saguaro Company currently has 30,000 shares outstanding. Each share has a market value of $20. If the firm pays $5 per share in dividends, what will each share be worth after the dividend payment? Ignore taxes. # of shares outstanding = Market value of stock = Dividends paid per share = Price per share (ex-dividend) =

30,000 $20 $5 $15

nding. Each share has a nds, what will each share

17.28 The Cholla Company currently has 30,000 shares outstanding. Each share has a market value of $20. If the firm repurchases $150,000 worth of shares, then what will be the value of each share outstanding after the repurchase? Ignore taxes. # of shares outstanding = Market value of stock = Value of shares repurchased= # of shares repurchased = # of shares outstanding after repurchase = Market value of equity before repurchase = Market value of equity after repurchase = Value of each share after repurchase =

30,000 $20 $150,000 7500 22,500

$600,000 $450,000 $20 i.e., there is no change in

ding. Each share has a th of shares, then what will se? Ignore taxes.

i.e., there is no change in the market value of the shares.

17.29 You purchased 1,000 shares of Koogal five years ago at $30 per share. Today Kooga shares through a fixed-price tender offer price of $80 per share.What is the amount of that you will get to keep if only the capital gain is taxed at a 15 percent rate? Number of shares of Koogal you own = Purchase price of each share purchased 5 years ago = Tax rate on capital gains = Repurchase tender offer price =

1000 $30 15% 80

Proceeds from tendering the shares = Taxes on capital gains =

$ 80,000 $ 7,500

After-tax proceeds =

$ 72,500

$30 per share. Today Koogal is repurchasing its share.What is the amount of after-tax proceeds a 15 percent rate?

17.30

You purchased 1,000 shares of Zebulon Copper Co. five years ago at $50 per share. decide whether to repurchase shares at $70 per share through a fixed-price tender off per share. If capital gains are taxed at a 15 percent rate, then at what rate must divide indifferent between receiving the dividend and selling your shares back to Zebulon? # of shares purchased five years ago = Purchase price five years ago = Repurchase tender offer price = Cash dividend per share = Tax rate on capital gains =

1000 $ 50 $ 70 $ 70 15%

Capital gains per share if tendered = After tax proceeds =

$ 20 $ 67

After-tax proceeds on dividends = Cash dividend *(1-tax rate) To be indifferent between the 2 options…After-tax proceeds from both should be the s ==> (1-tax rate) = After-tax proceeds / Cash dividend ==> Tax rate = 1-(After-tax proceeds/ Cash dividend) = 4.286%

ago at $50 per share. Today Zebulon is trying to a fixed-price tender offer or pay a $70 cash dividend at what rate must dividends be taxed for you to be res back to Zebulon?

om both should be the same,$67.00 i.e.,

17.29 The Llama Substitute Wool Company is trying to do some financial planning for the co $10,000 in new equity this year and wants to pay a dividend to stockholders of $30,00 $20,000 interest during the year and will also pay down principal on its debt obligation with its capital budgeting plan, it will require $100,000 for capital expenditures during t information, how much cash must be provided from operations for the firm to meet its

Sources

Uses

CF Opnst + Equityt + Debt t = Divt + Interest t + Principal t + Cap Expt where: CF Opnst = net cash flow from operations in period t Equity t = proceeds from the sale of stock in period t Debt t = proceeds from the sale of debt in period t Div t = dividends paid in period t Interest t = interest payments in period t Principal t = principal payments in period t CapExp t = capital expenditures in period t Equityt = Principalt = Interestt = Divt = Cap. Expt =

$10,000 $10,000 $20,000 $30,000 $100,000

CF Opnst

$150,000

me financial planning for the coming year. Llama plans to raise dend to stockholders of $30,000 in total. The firm must pay principal on its debt obligations by $10,000. If the firm continues or capital expenditures during the year. Given the above erations for the firm to meet its plan?

pal t + Cap Expt

STP#17.1 Shares of Convoy West, Inc. are trading for $55.45 on the day before the ex-dividend quarterly dividend is $0.16 per share and there are no taxes, how will the share price ex-dividend date? Since there are no taxes, the value of the shares would drop by the $0.16, the amount of the dividend. Therefore, the shares should trade for $55.29 ($55.45 − $0.16 = $55.29) on the exdividend date if no other information relevant to the price of the stock becomes public.

5 on the day before the ex-dividend date. If the no taxes, how will the share price change on the

by the $0.16, the amount of the 45 − $0.16 = $55.29) on the exhe stock becomes public.

STP#17.2 Three years ago, you purchased 4,000 shares of Metwa Inc. for $17 per share. Tod is repurchasing its shares trhough a fixed-price tender offer at a price of $45 per sh are the after-tax proceeds that you will receive if capital gains are taxed at a rate of percent? The tax on the stock would be 4,000 × ($45 − $17) × 0.20 = $22,400. Your after-tax proceeds would equal (4,000 × $45) − $22,400 = $157,600.

wa Inc. for $17 per share. Today Metwa offer at a price of $45 per share. What al gains are taxed at a rate of 20

STP#17.5 Mastercard, Inc. completed a ten-for-one stock split on January 22, 2014. Immedia stock split there were 120.38 million shares outstanding at a price of $826.00 per s split, how many shares were outstanding and at what price would you expect them stock split cause any substantial change for Mastercard or the investors? Why wou management choose to split the company's stock?

After the stock split, there would be 120.38 million × 10 = 1,203.8M shares outstanding at a pric $82.60 per share. Nothing substantially changed for Mastercard or the investors. There were te many shares outstanding after the split, but each was worth only one tenth as much as a share before the split. Mastercard management might split the stock to lower their share price, hoping stock more accessible to investors. Mastercard management might also split the stock to send a signal to investors about management's outlook for the company's future.

uary 22, 2014. Immediately before the price of $826.00 per share. After the would you expect them trade? Did the he investors? Why would Mastercard

es outstanding at a price of $826/10 = nvestors. There were ten times as nth as much as a share was worth heir share price, hoping to make the split the stock to send a positive e.

18.8 Multiples analysis: It is April 4, 2015, and your company is considering the possibility o manufacturing business. Managers of Fiat, the Italian automobile manufacturer that own interested in selling the firm. Since Chrysler does not have publicly traded shares of its o Company as a comparable company to help you determine the market value of Chrysle

This morning Ford’s common stock was trading at $16.69 per share, and the company h estimated that the market value of all of the company’s other outstanding securities (exc special shares owned by the Ford family) is $100 billion and that its revenues from auto Chrysler’s revenue in 2014 was $50.0 billion. Based on the enterprise value/revenue rat implied by the Ford market values?

Ford's common stock price Ford's # of shares outstanding Ford's last year's revenues from auto sales Ford's market value of all other outstanding securities Chrysler's revenue in 2006 Ford's enterprise value(VF) =

VF = VEquity + VOther Securities

Ford's value of equity = Ford's enterprise value =

$ $

Ford's enterprise value/revenue ratio =

57.91 157.91 118.38%

Chrysler's total value as implied by Ford's market values =

mpany is considering the possibility of purchasing the Chrysler automobile an automobile manufacturer that owns Chrysler, have hinted that they might be ot have publicly traded shares of its own, you have decided to use Ford Motor etermine the market value of Chrysler.

$16.69 per share, and the company had 3.47 billion shares outstanding. You ny’s other outstanding securities (excluding the common stock but including llion and that its revenues from auto sales were $133.4 billion last year. d on the enterprise value/revenue ratio, what is the total value of Chrysler that is

16.69 3.47 $133.40 100 $50.00

uity + VOther Securities

billion billion

$59.19

18.10 Dividend discount approach: You want to estimate the total intrinsic value of a large g company. This company has publicly traded stock and has been paying a regular divide decide that, due to the predictability of the dividend that this company pays, you can use valuation approach. The company is expected to pay a dividend of $1.25 per share nex expected to grow at a rate of 3 percent per year thereafter. You estimate that the approp future dividends is 12 percent. In addition, you know that the company has 46 million sh market value of its debt is $350 million. What is the total value of the company? Dividend expected next year = Dividend growth rate (constant)= Appropriate discount rate= # of shares outstanding = Market value of company's debt =

$1.25 3% 12% 46 million $350 million

Intrinsic value of a share of common stock= Market value of equity =

$ 13.89 $ 638.89 million

Market value of the firm = MVequity + Mvdebt =

$ 988.89 million

total intrinsic value of a large gas and electric utility s been paying a regular dividend for many years. You is company pays, you can use the dividend discount vidend of $1.25 per share next year, and the dividend is r. You estimate that the appropriate rate for discounting he company has 46 million shares outstanding and that the alue of the company?

18.15 Break-even: You have started a business that sells a home gardening system that all vegetables on the countertop in their kitchens.You are considering two options for ma product.The first is to advertise on local TV.The second is to distribute flyers in the loc option, which costs $50,000 annually, will promote the product more effectively and cr 1,200 units per year. The flyer advertisement costs only $6,000 annually but will create 250 units per year. The price per unit of the indoor gardening system is $100, and the per unit. Assume that the production capacity is not limited and that the marketing cos involved in your business.What are the breakeven points for both marketing options? choose?

Cost of TV advertising Demand created by TV ad Cost of flyer advertising Demand created by flyer ad Selling price per unit Variable cost per unit

$50,000 per year 1200 units per year $6,000 per year 250 units per year $100 $60

Breakeven point for TV option =

1,250 units

Breakeven point for Flyer option =

150 units

Since the breakeven point for the flyer ad is lower than the demand it will create, choo

ome gardening system that allows people to grow considering two options for marketing your is to distribute flyers in the local community.The TV product more effectively and create a demand for y $6,000 annually but will create a demand for only ening system is $100, and the variable cost is $60 ted and that the marketing cost is the only fixed cost ts for both marketing options? Which one should you

the demand it will create, choose the flyer option.

18.16 Going-concern value: Aggie Motors is a chain of used car dealerships that has publi traded stock. Using the adjusted book value approach, you have estimated the value o Aggie Motors to be $45,646,000.The company has $40.5 million of debt outstanding. I stock price is $5.5 per share, and there are 1,378,000 shares outstanding. What is the going concern value of Aggie Motors? Adjusted book value of firm Value of debt outstanding Current stock price # of shares outstanding

$ 45,646,000 $40,500,000 $5.50 1,378,000

Going concern value = Market value of firm - Adjusted book value of firm Market value of stock = $7,579,000 Market value of firm = Market value of stock + Market value of debt = Going concern value = $2,433,000

sed car dealerships that has publicly ch, you have estimated the value of $40.5 million of debt outstanding. Its 00 shares outstanding. What is the

alue of firm $48,079,000

Use the following information concerning Johnson Machine Tool Company in Problems 18.17, 18.18, and 18.19. Johnson’s income statement from the fiscal year that ended this past December is:

All dollar values are in millions. Depreciation and amortization expenses last year were $42 mill the company has $533 million of debt outstanding. 18.17

All dollar values are in millions. Billy’s had depreciation and amortization expenses of $71 millio and 200 million shares and $600 million of debt outstanding as of the end of the year. Its stock trading at $12.25 per share. Using the P/E multiple, what is the value of Johnson’s stock? What total value of Johnson Machine Tool Company?

18.17

18.18

18.19

Use the following information concerning Johnson Machine Tool Company in Problems 18.17, 18.18, and 18.19. Johnson’s income statement from the fiscal year that ended this past December is: Revenue Cost of goods sold Gross profit Selling, general, and administrative expenses Operating profit (EBIT) Interest expense Earnings before taxes Taxes Net income All dollar values are in millions. Depreciation and amortization expenses last year were $42 million, and the company has $533 million of debt outstanding. Multiples analysis: You are an analyst at a private equity firm that buys private companies, improves their operating performance, and sells them for a profit. Your boss has asked you to estimate the fair market value of the Johnson Machine Tool Company. Billy’s Tools is a public company with business operations that are virtually identical to those at Johnson. The most recent income statement for Billy’s Tools is as follows: Revenue Cost of goods sold Gross profit Selling, general, & administrative expenses Operating profit (EBIT) Interest expense Earnings before taxes Taxes Net income All dollar values are in millions. Billy’s had depreciation and amortization expenses of $71 million last year and 200 million shares and $600 million of debt outstanding as of the end of the year. Its stock is currently trading at $12.25 per share. Using the P/E multiple, what is the value of Johnson’s stock? What is the total value of Johnson Machine Tool Company? Billy Tools' depreciation and amortization expenses

Billy Tools' number of shares outstanding Billy Tools' value of outstanding debt Billy Tools' current stock price Johnson Machine Tools' depreciation and amortization expense Johnson Machine Tools' value of outstanding debt Billy Tools P/E ratio = Johnson Machine Tools value of equity = Billy Tools' P/E ratio * JMT's Net Income JMT's total value = Value of Equity + Value of Debt Multiples analysis: Using the enterprise value/EBITDA multiple, what is the total value of Johnson Machine Tool Company? What is the per share value of Johnson’s stock?

Billy Tools' enterprise value = Billy Tools' equity value + Billy Tools' debt value Billy Tools EBITDA = Billy Tools' EBIT + Depreciation and amortization expenses Billy Tools' Enterprise value/EBITDA multiple = Johnson's EBITDA = Johnson's implied firm value = Johnson's value of stock = Its Firm value - Its value of outstanding debt Multiples analysis: Which of the above multiples analyses do you believe is more appropriate?

While the value estimates in the previous questions are reasonably similar, the enterprise value/EBITDA multiple is more appropriate for this analysis. The reason is that the capital structu of Johnson and Billy’s differ considerably and the enterprise value/EBITDA multiple is less sensit Billy Tools' debt ratio = Johnson's debt ratio =

December is: $ $

995 652

$ $

343 135

$ $

208 48

$ $

160 64

year were $42 million, and

buys private companies, Your boss has asked you to any. Billy’s Tools is a public se at Johnson. The most

$ $

1,764 1,168

$ $

596 211

$ $

385 12

$ $

373 147

226

enses of $71 million last year the year. Its stock is currently nson’s stock? What is the

$71 million

200 million $600 million $12.25 per share $42 million $533 million

$ $

10.84 1,040.71 million 1,573.71 million

what is the total value of Johnson’s stock?

$ $ $ $

$3,050 million 456 million 6.69 times 250 million 1,672.15 million 1,139.15 million

believe is more appropriate?

nably similar, the enterprise he reason is that the capital structures value/EBITDA multiple is less sensitive to 19.67% 31.88%

18.20 Income approaches: You are using the FCFF approach to value a business. You hav for next year will be $123.65 million and that it will increase at a rate of 8 percent for e years. After that point, the FCFF will increase at a rate of 3 percent forever. If the WAC and it has no NOA, what is it worth?

Present Value of Firm = PV of the free cash flows during Years 1−5 + PV of the Terminal Value Present Value of the 5-year growing annuity (PVAn ): n

PVAn = [CF1/(WACC − g) ] x [1 − {(1 + g)/(1 + WACC)} ] Present Value of the Terminal Value in Year 5 (PV(TV 5)): PV(TV5) = [CF1*(1+g1)4*(1+g2)]/[(WACC-g2)]*[1/(1+WACC)5]

Next year's FCF = $123,650,000 Growth rate of FCF in Years 1−5 (g 1)= 8% Number of years of 8% growth= 5 years Growth rate in second phase (g2)= 3% per year, forever WACC = 10% PVAn

541,975,672

PV(TV5) =

$ 1,536,968,269

PVFirm

$ 2,078,943,942

ue a business. You have estimated that the FCFF rate of 8 percent for each of the following four ent forever. If the WACC for this firm is 10 percent

of the Terminal Value at the end of Year 5

18.21 Valuing a private business: You want to estimate the value of a privately owned resta entirely with equity. Its most recent income statement is as follows: Revenue Cost of goods sold

$ $

3,000,000 600,000

Gross profit Salaries and wages Selling expenses

$ $ $

2,400,000 1,400,000 100,000

Operating profit (EBIT) Taxes

$ $

900,000 315,000

Net income

585,000

You note that the profitability of this restaurant is significantly lower than that of compar primarily due to high salary and wage expenses. Further investigation reveals that the a owner and his wife, the firm’s accountant, are $900,000 and $300,000, respectively. Th higher than the industry median salaries for these two positions of $100,000 and $50,00 Compensation for other employees ($200,000 in total) appears to be consistent with the median P/E ratio of comparable restaurants with no debt is 10. What is the total value o

Owner's annual salary Owner's wife's salary

$900,000 $300,000

Median PE ratios (no-debt firms)

The Income statement must be adjusted to reflect "realistic" salaries and wages Revenue Cost of Goods Sold Gross Profit Salaries and Wages Selling Expenses Operating Profit (EBIT) Taxes Net Income

$ $ $ $ $ $ $ $

3,000,000 600,000 2,400,000 350,000 100,000 1,950,000 682,500 1,267,500

The Firm's value can then be estimated by multiplying the adjusted net income by the Industry m Firm's total value = Net Income * Industry median PE ratio $ =12,675,000

e value of a privately owned restaurant that is financed is as follows:

ificantly lower than that of comparable restaurants, her investigation reveals that the annual salaries for the 00 and $300,000, respectively. These salaries are much o positions of $100,000 and $50,000, respectively. ) appears to be consistent with the market rates. The ebt is 10. What is the total value of this restaurant?

Industry median $100,000 $50,000

alaries and wages

usted net income by the Industry median PE ratio

18.23 You plan to start a business that sells waterproof sun block with a unique formula that damage of UVA radiation 30 percent more effectively than similar products on the mar

You expect to invest $50,000 in plant and equipment to begin the business. The tar the sun block is $15 per bottle.You forecast that unit sales will total 1,500 bottles in the and will increase by 20 percent in each of the following months during the first year.Yo cost of raw materials to be $3 per bottle. In addition, monthly gross wages and payroll be $13,000, rent is expected to be $3,000, and other expenses are expected to total $ Advertising costs are estimated to be $35,000 in the first month but to remain constan month during the following eleven months.

You have decided to finance the entire business at one time using your own saving investment of $75,000 adequate to avoid a negative cash balance in any given month much more do you need to invest up front? How much do you need to invest up front minimum cash balance of $5,000? What is the break-even point of the business?

Initial investment for plant and equipment Unit selling price Unit sales in first month Growth in sales after 1st month (for Year1) Cost of raw materials per bottle Monthly gross wages and payroll Rent per month Other expense per month Advertising costs (1st month) Monthly advertsing costs (Months 2-12) Initial cash balance Desired minimum monthly cash balance Monthly Cash Budget Month Beginning Cash Balance Cash Receipts Cash Sales Total Cash Available Cash Payments Operations Raw Material Gross Wages and Payroll Advertising

1 $75,000

2 ($9,000)

22,500 $97,500

27,000 $18,000

4,500 13,000 35,000

5,400 13,000 5,000

Rent Other Expenses Operations Total Financing and Investments Capital Expenditures Total Cash Payments Ending Cash Balance

3,000 1,000 $56,500

3,000 1,000 $27,400

50,000 $106,500 ($9,000)

$27,400 ($9,400)

Answer: No, a beginning cash balance of $75,000 is not adequate to avoid a negative balance even in the first three months. Since, Youthere will need is a maximum to invest an shortfall additional of $9400 amounin to avoid the shortfall in Month 2, i.e. $84,400. If a $5,000 desired minimum cash bala needed, the initial cash balance will have to be increased by that amount, i.e. to $89,4 Break-even point calculation: In Month 1 Total fixed costs = Contribution margin = Break-even sales =

Expected sales per month Cumulative sales per month Cumulative break-even

Month 1 Months 2-12 $ 52,000 22,000 $ 12 $ 12 4333 Month 1 1500 1500 4333

1833 bottles Month 2 1800 3300 6167

Month 3 2160 5460 8000

Note: The firm will reach break-even point during the 6th month when its cumul

k with a unique formula that reduces the similar products on the market.

begin the business. The targeted price of will total 1,500 bottles in the first month onths during the first year.You expect the hly gross wages and payroll are expected to nses are expected to total $1,000. month but to remain constant at $5,000 per

time using your own savings. Is an initial balance in any given month? If not, how you need to invest up front to keep a n point of the business?

$ 50,000 $ 15.00 1500 bottles 20% per month $ 3.00 $13,000 3000 1000 $35,000 $5,000 $75,000 $5,000

3 ($9,400)

4 ($5,480)

32,400 $23,000

38,880 $33,400

6,480 13,000 5,000

7,776 13,000 5,000

3,000 1,000 $28,480

3,000 1,000 $29,776

$28,480 ($5,480)

$29,776 $3,624

adequate to avoid a negative cash invest an additional amount of $9400 desired minimum cash balance is by that amount, i.e. to $89,400

Month 4 2592 8052 9833

Month 5 Month 6 3110.4 3732.48 11162.4 14894.88 11667 13500

6th month when its cumulative unit sales equals its cumulative breakeven sales.

18.24 For the previous question, assume that you do not have sufficient savings to cover the e sun-block business. You are going to have to get external financing. A local banker who month loan of $20,000 at an APR of 12 percent.You will pay interest each month and re six months.

Assume that instead of making a single up-front investment, you are going to finance th investments as cash is needed in the business. Assuming the proceeds from the loan g first day and are therefore available to pay for some of the capital expenditures, how mu your savings account every month to run the business and keep the cash balances pos

Bank loan = Monthly interest payment =

$ 20,000 Interest rate= $ 200 Loan paid off in Month Monthly Cash Budget

Month Beginning Cash Balance Cash Receipts Investments by owner Cash Sales Total Cash Available Cash Payments Operations Raw Material Gross Wages and Payroll Advertising Rent Other Expenses Operations Total Financing and Investments Capital Expenditures Debt/Interest Payment Total Cash Payments

$ 20,000

($64,200)

($64,800)

22,500 $42,500

27,000 ($37,200)

32,400 ($32,400)

4,500 13,000 35,000 3,000 1,000 $56,500

5,400 13,000 5,000 3,000 1,000 $27,400

6,480 13,000 5,000 3,000 1,000 $28,480

50,000 200

200

$106,700

$27,600

$28,680

Ending Cash Balance

($64,200) ($64,800)

($61,080)

Answer: Based on the cash budget above, you will need to withdraw $64,200 in M $600 in Month 2, after which the cash balance will be positive.

ufficient savings to cover the entire amount required to start your financing. A local banker whom you know has offered you a sixay interest each month and repay the entire principal at the end of

nt, you are going to finance the business by making monthly the proceeds from the loan go directly into the business on the capital expenditures, how much money do you need to pull out of keep the cash balances positive?

12% 6

y Cash Budget 4

($61,080) ($52,176)

($37,051)

38,880 ($22,200)

46,656 ($5,520)

55,987 $18,936

7,776 13,000 5,000 3,000 1,000 $29,776

9,331 13,000 5,000 3,000 1,000 $31,331

11,197 13,000 5,000 3,000 1,000 $33,197

200

20,200

$29,976

$31,531

$53,397

($52,176) ($37,051)

ed to withdraw $64,200 in Month 1, and an additional

($34,461)

18.29 At the end of 2014 the value of the S&P 500 Index divided by the estimated 2014 earn 500 firms (the S&P 500 P/E multiple) was 18.66. Assume that the long-term Treasury was 3.72 percent, the market risk priemium was 5.17 percent, and firms in the S&P 50 expected to pay out an average of 37.6 percent of their earnings as dividends in the fu rate were dividends paid by S&P 500 firms expected to grow in the future? Equation 18.1 can be used to answer this question. Po/E1 = b / (Kcs − g) Recognize that E1 = Eo x (1 + g) Rewrite equation. Po/Eo = (1 + g)b/(Kcs − g) Use CAPM to find Kcs. Kcs = Rrf + beta × market premium

Since the S&P 500 represents more than 70% of the amrket capitalization of all stocks U.S., the beta will be relatively close to 1.0. Rrf market premium beta Kcs

3.72% 5.17% 1 8.89%

Po/Eo

18.66 given

Dividend payout percent (b) 37.60% given Write the formula for the P/E as follows: Po/Eo = (1 + g)b/(Kcs − g) Po/Eo 18.66 b 37.60% Kcs 8.89% 1.6589 − 18.66g Collect terms. 1.2829 Solve for g. 7.895%

= = =

The S&P 500 index value at the end of 2010 implied that the market expected dividen firms in the S&P 500 to increase at an average annual rate of 7.9 percent forever.

ed by the estimated 2014 earnings for S&P me that the long-term Treasury bond yield ercent, and firms in the S&P 500 were earnings as dividends in the future. At what grow in the future?

mrket capitalization of all stocks traded in the

0.3760 + .409g 19.069 g g

at the market expected dividends paid by ate of 7.9 percent forever.

18.31

You own a company that produces and distributes course packets for classes at l via the Internet. You have asked a friend to invest $35,000 in the business. Your know what the business is worth so that he can determine how much of equity (e. percentage) he should expect to receive for his investment. You offer to help him business. The business is expected to generate revenue of $110,000 and incur cash ope expenses of $70,000 next year. Over the following three years, revenue and cash expenses are expected to increase 15 percent, 10 percent, and 7 percent. After y expected to grow 2 percent per year forever. Depreciation and amortization, capi expenditures, and additions to working capital are expected to equal 5 percent, 6 percent of revenue, respectively, in the future. You have determined that a target structure of 10 percent is reasonable for this business. With this capital structure, of debt will be 6 percent and the beta for the equity will be 1.30. The average tax business is 10 percent, and the marginal rate is 20 percent. The risk-free rate is 4 and the market risk premium is 6.01 percent. What is a 100 percent equity intere business worth? What percentage of the equity should your friend get for his inve

Value the equity of this business using the FCFF Income approach. First, estimate the required rate of retrun using the CAPM. Rrf beta Market premium 4.25% 1.3 6.01% Second, determine the WACC from Equation 13.7. Xdebt 10.00% Kdebt pretax 6.00% Tax rate 10.00% Xcs 90.00% Kcs 12.06% WACC 11.397%

Third, forecast the FCFF and discount them to the present using the WACC to ob

Revenues Operating costs Depreciation and amortization Operating profit Taxes

10.00%

Year 1 1 110,000 70,000 5.00% 5,500 34,500 3,450

NOPAT Depreciation and amortization

31,050 5,500 6.0% 6,600 1.00% 165 29,785

Capital expenditures Additions to working capital FCFF PVIFA Terminal Value with 2% growth FFCF + TV PVIF PV(FCFF) @WACC

2.00%

11.390%

Enterprise Value Less: 10% debt Equity value

0 29,785 0.8977 26,739 393,877 39,388 354,490

Note: Terminal value in year 4 is determined by discounting Year 5 cash flow growth rate

The equity value calculated does not take into account any adjustments for Since there is no information in the problem statement , we do not consider With this caveat, we can calculate the percentage of the equity that your frie Investment of $35,000.00 Equity value $354,489.53 Percentage of equity received 9.87%

urse packets for classes at local universities 35,000 in the business. Your friend wants to mine how much of equity (e.g., what tment. You offer to help him value the

$110,000 and incur cash operating ree years, revenue and cash operating rcent, and 7 percent. After year 4 they are iation and amortization, capital pected to equal 5 percent, 6 percent, and 1 ave determined that a target capital s. With this capital structure, the pretax cost ill be 1.30. The average tax rate for the ercent. The risk-free rate is 4.25 percent, s a 100 percent equity interest in the ld your friend get for his investment?

ome approach. Kcs 12.06%

esent using the WACC to obtain the enterprise value. 15% 10% 7% 2% Year 2 Year 3 Year 4 Year 5 Year 6 2 3 4 5 126,500 139,150 148,891 151,868 80,500 88,550 94,749 96,643 5.00% 5.00% 5.00% 5.00% given 6,325 6,958 7,445 7,593 39,675 43,643 46,697 47,631 3,968 4,364 4,670 4,763

2% 6

35,708 6,325 6.0% 7,590 1.00% 127 34,316

39,278 6,958 6.0% 8,349 1.00% 97 37,789

0 34,316 0.8059 27,657

0 37,789 0.7235 27,342

42,028 7,445 6.0% 8,933 1.00% 30 40,509 0.0939 440,034 480,543 0.6496 312,139

42,868 7,593 6.0% given 9,112 1.00% given 30 41,319

41,319 0.5831 24,095

scounting Year 5 cash flow by the differential of WACC of 11.39% and 2%

count any adjustments for control, lack of marketability, or key people. ment , we do not consider them here. of the equity that your friend should receive as:

STP #18.1 You plan to start a business to produce and sell custom kitchen cabinets. The targe order of cabinets is $10,000. You estimate that you will receive orders for cabinets each of the first two months, nine kitchens in the third month, and ten kitchens in th cost of the equipment necessary to produce the cabinets is $105,000. You expect t materials to be $3,000 per order. In addition, you expect monthly gross wages and rent to be order. In addition, you expect monthly gross wages and payroll to be $27 $10,000 in the first month, but to remain constant at $1,000 per month during the fo How much will you have to initially invest ensure that you have a cash balance of $ beginning of the second month? If you invest this amount, what will be your cash b the fourth month?

m kitchen cabinets. The targeted price for each ll receive orders for cabinets for eight kitchens in month, and ten kitchens in the fourth month. The ets is $105,000. You expect the cost of raw ect monthly gross wages and payroll to be $27,000, wages and payroll to be $27,000, rent to be 1,000 per month during the following three months. you have a cash balance of $10,000 at the unt, what will be your cash balance at the end of

STP #18.3 Sessler Corporation is a private company that had EBIT of $186 million and deprec and amortization of $22 million in the most recent fiscal year. At the end of that yea similar, competing firm has an Enterprise Value/EBITDA multiple of 4.3. What is the enterprise value of Sessler?

IT of $186 million and depreciation al year. At the end of that year, a DA multiple of 4.3. What is the implied

STP #18.4 Winters Inc. management estimates that the company will generate free cash flows firm (FCFF) of $12.5 million, $16.8 million and $19.7 million, respectively, over the three years. After that, FCFF will grow at a constant five percent per year forever. T company has $5 million in non-operational assets. If the appropriate W ACC is 8 pe what is the enterprise value of this business?

y will generate free cash flows from the million, respectively, over the next ve percent per year forever. The he appropriate W ACC is 8 percent,

19.7

Addition to retained earnings: Northwood, Inc., has revenue of $455,316 and costs and pays taxes at a rate of 31 percent. If the firm pays out 45 percent of its earnings a every year, how much earnings are retained and what is the firm's retention ratio? Revenue Tax rate

455316 Costs 31% Payout ratio

$316,487 45%

Retained earnings = (Revenues - Costs)*(1-Tax rate)*(1-Payout ratio) Retained earnings =

$ 52,686 Retention ratio =

55%

of $455,316 and costs of $316,487 ercent of its earnings as dividends m's retention ratio?

19.8

Payout and retention ratio: Goodwin Corp. has revenues of $12,112,659, costs of $9 interest payment of $412,375, and a tax rate of 34 percent. It paid dividends of $1,025 stockholders. Find the firm’s dividend payout ratio and retention ratio. Revenues Costs Interest exp. Tax rate Dividends paid

$ 12,112,659 $ 9,080,545 $ 412,375 34% $ 1,025,000

Goodwin Corp. Amount Revenues $ 12,112,659 Costs $ 9,080,545 EBIT $ 3,032,114 Interest $ 412,375 EBT $ 2,619,739 Taxes (34%) $ 890,711 NET INCOME $ 2,141,403 Dividends paid $ 1,025,000 Retained earnings $ 1,116,403 Dividend payout ratio 47.9% Retention ratio 52.1%

es of $12,112,659, costs of $9,080,545, nt. It paid dividends of $1,025,000 to its tention ratio.

19.9

Percent of sales: Cattail Corporation's financial statements for the fiscal year just ended are shown below: Cattail Corporation Financial Statements for the Fiscal Year Just Ended ($ thousands) Income Statement Net Sales $1,500 Costs 350 Net Income $1,150

Assets Total

Balance Sheet $ 700 Debt Equity $ 700 Total

Cattail management expects sales to increase by 14 percent next year. Assume that the financial statement accounts vary directly with changes in sales and that management has no financing plan at this time. Given this information, develop a pro forma income statement for Cattail for the next fiscal year. Expected growth rate in sales Net sales Projected Sales Costs Projected Costs

14.00% 1,500,000 $1,710,000 350,000 $399,000

Cattail Corporation Pro Forma Income Statement ($ thousands) Net Sales $1,710,000 Costs $399,000 Net Income $1,311,000

nts for the fiscal year

heet $ $

600 100 700

cent next year. ly with changes in time. Given this attail for the next fiscal

19.10

Percent of sales: Given the data for Cattail Corporation in Problem 19.9, if you as balance sheet items also vary with the change in sales, develop a pro forma balan for the next fiscal year. Assuming that the firm did not sell or repurchase stock, wh cash dividend implied by the pro forma income statement and balance sheet?

19.9

Percent of sales: Cattail Corporation's financial statements for the fiscal year just

Cattail Corporation Financial Statements for the Fiscal Year Just Income Statement Net Sales $ 1,500,000 Costs 350,000 Net Income $ 1,150,000

Assets Total

Cattail management expects sales to increase by 14 percent next year. Assume t sales and that management has no financing plan at this time. Given this informat fiscal year.

Expected growth rate in sales Net sales Projected Sales Costs Projected Costs Cattail Corporation Pro Forma Income Statement Net Sales Costs Net Income

14.00% 1,500,000 $1,710,000 350,000 $399,000

$1,710,000 $399,000 $1,311,000

Pro forma net income is $1,311,000 and the change in the equity account is $ the difference ($1,311,000 - $14,000 = $1,297,000) is the amount of the cash d

Net income Expected Equity-Equity Cash Dividend

$1,311,000 $14,000 $1,297,000

Problem 19.9, if you assume that all velop a pro forma balance sheet for Cattail or repurchase stock, what is the nd balance sheet?

s for the fiscal year just ended are shown below:

il Corporation or the Fiscal Year Just Ended Balance Sheet Debt Equity Total

$ 700,000 $ 700,000

$ $

600,000 100,000 700,000

nt next year. Assume that the financial statement accounts vary directly with changes in me. Given this information, develop a pro forma income statement for Cattail for the next

Assets Expected Assets

700,000 $798,000

Debt Equity Expected Debt Expected Equity

600,000 100,000 $684,000 $114,000

Cattail Corporation Pro Forma Balance Sheet Assets Total

he equity account is $14,000, therefore amount of the cash dividend that must be paid.

$798,000 Debt Equity $798,000 Total

$684,000 $114,000 $798,000

19.12 Capital intensity ratio: Tantrix Confectioners has total assets of $3,257,845 and sales of $5,123,951. What is the firm’s capital intensity ratio? Total assets = Sales = Capital intensity ratio =

$ 3,257,845 $ 5,123,951 63.58%

s of $3,257,845 atio?

19.13 Capital intensity ratio: McDonald Metal Works has been able to generate sales of $13,445,196 on assets of $9,145,633. What is the firm’s capital intensity ratio? Total assets = Sales = Capital intensity ratio =

$ 9,145,633 $ 13,445,196 68.02%

been able to generate sales of m’s capital intensity ratio?

19.14 Capital intensity ratio: For McDonald Metal Works in Problem 19.13, how much mus sales grow if the capital intensity ratio has to drop to 60 percent? Indicate your answer both percent of sales and dollar sales increase. Total assets = Sales = Desired capital intensity ratio =

Sales level required to reach desired capital intensity ratio Increase in sales required = Percentage increase in sales required =

$ $

9,145,633 13,445,196 60%

$ 15,242,721.67 $

1,797,525.67 13.37%

em 19.13, how much must ent? Indicate your answer in

19.15 Internal growth rate: Swan Supply Company has net income of $1,212,335, assets o retains 70 percent of its income every year. What is the company’s internal growth rat Net income Total assets Plowback ratio

$1,212,335 $12,522,788 70%

Internalgrowth rate (IGR) = Plowback ratio  ROE  Equity ratio Net income Equity  Equity Total assets Net income = Plowback ratio  Total assets

= Plowback ratio 

IGR =

6.78%

me of $1,212,335, assets of $12,522,788 and mpany’s internal growth rate?

19.16 Sustainable growth rate: If Newell Corp. has a ROE of 13.7 percent and a dividend payout ratio of 32 percent, what is its sustainable growth rate? ROE Dividend payout ratio

13.70% 32%

Plowback ratio =1- Payout ratio SGR = Plowback ratio ´ ROE Sustainable growth rate (SGR) =

9.32%

percent and a wth rate?

19.17 EFN and growth: Refer to Exhibits 19.10 and 19.11 in the text. The EFNs for several growth rates for Empire Enterprises are as follows: Growth Rate(%) 0% 5 9.6 10 15 20

EFN($) (4.80) (2.30) 0.20 2.70 5.20

As a drill, you may want to check the calculations and plot the line to replicate the graph in Exhibit 19.11.

External Funds Needed (EFN($)) 6.00

EFN($)

4.00 2.00 (2.00)

9.6

(4.00) (6.00) Growth rate (%)

he text. The EFNs for ws:

ot the line to replicate the

EFN($)

19.18 Retention ratio: Refer to Problem 19.7. Northwood expects to increase its sales by 15 costs vary directly with sales. If Northwood wants to retain $65,000 of earnings next yea its dividend payout ratio? If so, what will be the new dividend payout ratio and retention

Last year's revenue $455,316 Tax rate 31% Expected growth rate in sales Expected retained earnings

Last year's costs Last year's payout ratio 15% $65,000

Retained earnings = (Revenues − Costs)*(1 − Tax rate)*(1 − Payout ratio) Expected revenue = 523613.4 Expected costs Expected retained earnings (based on current dividend policy) =

To reach its desired retained earnings goal of $65,000 , the firm will have to reduce its dividend Since, ==> ==> ==> ==>

Retained earnings = (Revenues − Costs)*(1 − Tax rate)*(1 − Payout ratio) (1 − Payout ratio) = [(Retained earnings)]/[(Revenues − Costs)*(1 − Tax rate)] (1 − Payout ratio) = 59% = Retention ratio Payout ratio = (1 − 0.59) Payout ratio = 41% ,i.e., it will decline from 45% to 41%

o increase its sales by 15 percent next year. All 5,000 of earnings next year, will it have to change payout ratio and retention ratio for the firm?

$316,487 45%

Payout ratio) $

363960.05 60,588.45

ave to reduce its dividends and its payout ratio

Payout ratio) sts)*(1 − Tax rate)]

19.20 Percent of sales: Tomey Supply Company’s financial statement for the most recent fi that sales will increase by 20 percent next year. Assume that all costs and assets incre percent dividend payout ratio and has no plans to issue new equity. Any financing nee forma financial statements for the coming year based on this information, and determi Tomey Supply Company Revenues Costs EBT Taxes (35%) NET INCOME

$ 1,768,121 $ 1,116,487 $ 651,634 $ 228,072 $ 423,562

Growth rate of sales 20% Costs and assets Proportional to sales Dividend payout ratio 33% External financing needed = Increase in Long-term debt Tax rate 35% Sales Change

Tomey Supply Company Revenues Costs EBT Taxes (35%) NET INCOME Dividends paid Addition to retained earnings

$ 1,768,121 $ 1,116,487 $ 651,634 $ 228,072 $ 423,562

1.2 1.2

ASSETS Current assets Net fixed assets Total assets

$ $ $

280,754 713,655 994,409

1.2 1.2

LIABILITIES Currrent liabilities

167,326

1.2

Long-term debt Common stock Retained earnings Total Liabilities & Equity

$ $ $ $

319,456 200,000 307,627 994,409

External Financing Needed

(175,127)

Internal Growth Rate

34.2%

Note: The EFN is negative meaning that the firm will have funds available to pay off some long-t

19.21 Internal growth rate: Using the pro forma financial statements for Tomey Supply Com developed in Problem 19.20, find the internal growth rate for Tomey Supply Company Internal Growth rate (IGR) = Change in RE/Total Assets (See above)

al statement for the most recent fiscal year is shown in this problem. The company projects me that all costs and assets increase directly with sales. The company has a constant 33 ue new equity. Any financing needed will be in the form of long-term debt. Prepare pro d on this information, and determine the EFN.

Supply Company ASSETS Current assets Net fixed assets Total Assets

$ 280,754 $ 713,655 $ 994,409

LIABILITIES Currrent liabilities Long-term debt Common stock Retained earnings Total Liabilities & Equity

$ 167,326 $ 319,456 $ 200,000 $ 307,627 $ 994,409

Pro Forma $ $ $ $ $ $ $

2,121,745 1,339,784 781,961 273,686 508,275 167,731 340,544

$ $ $

336,905 856,386 1,193,291

200,791

$ $ $ $

144,329 200,000 648,171 1,193,291

unds available to pay off some long-term debt

tatements for Tomey Supply Company rate for Tomey Supply Company.

Assets (See above)

19.22 Sustainable growth rate: Use the following pro forma information for Tomey Supply C year: net income = $508,275; addition to retained earnings = $340,544; common equity sales = $2,121,745. Assume that management does not want the ratio of long-term deb exceed the current long-term debt to equity ratio of 63 percent and does not want to iss What level of sales growth can it sustain? Calculate the new sales level. Next year's net income = Addition to retained earnings= Common equity = Net sales = Desired LTD/Equity ratio =

$ $ $ $

508,275 340,544 848,171 2,121,745 63%

Sustainable growth rate (SGR) = Plowback ratio X ROE

SGR =

Addition to Retained earnings Net income ´ Net income Equity

40.15%

Level of sales it can sustain =

$ 2,973,633.98

ormation for Tomey Supply Company for next s = $340,544; common equity = $848,171; net want the ratio of long-term debt to equity to cent and does not want to issue new equity. ew sales level.

19.23 Sustainable growth rate: Rowan Company has a net profit margin of 8.3 percent, de percent, total assets of $4,157,550, and sales of $6,852,654. If the company has a div ratio of 67 percent, what is its sustainable growth rate? Net profit margin Debt ratio Total assets Sales Dividend payout ratio

8.30% 45% $ 4,157,550 $ 6,852,654 67%

Sustainable growth rate (SGR) = Plowback ratio X ROE Plowback ratio = (1-Dividend payout ratio) = ROE = Net Income/ Equity Net income = Net profit margin * Sales = Equity = (1-Debt ratio)*Total assets = ROE = SGR =

19.24 Sustainable growth rate: Refer to the information for Rowan Company in Problem 19 management desires a growth rate (SGR) of 10 percent but does not wish to change i its payout ratio. What will the firm’s new net profit margin have to be in order to achiev growth rate? Desired SGR = Dividend payout ratio= Debt ratio =

10% 67% 45%

Sustainable growth rate (SGR) = Plowback ratio X ROE ==> 10% = (1-0.67) * ROE ==> ROE = 10%/(1-0.67) ==> ROE= 30.30% Now, ROE = Net Profit Margin * (Sales/Equity) Sales = Equity =

$ 6,852,654 $ 2,286,653

==> ==>

Sales/Equity = 3.00 Net Profit margin = ROE/(New Sales/Equity) Net Profit margin = 10.11%

et profit margin of 8.3 percent, debt ratio of 45 852,654. If the company has a dividend payout e?

33%

$ 568,770.28 $ 2,286,652.50 24.87% 8.21%

or Rowan Company in Problem 19.23. The firm’s ent but does not wish to change its level of debt or rgin have to be in order to achieve the desired

19.25 Sustainable growth rate: Rocky Sales, Inc., has current sales of $1,215,326 and net in $211,253. It has a debt ratio of 25 percent and a dividend payout ratio of 75 percent. Th company has total assets of $712,455. What is its sustainable growth rate? Current sales Net income Debt ratio Dividend payout ratio Total assets

$ 1,215,326 $ 211,253 25% 75% $ 712,455

Sustainable growth rate (SGR) = Plowback ratio X ROE Plowback ratio = (1 - Dividend payout ratio) = ROE =

Net income / Equity

Equity = Total assets * (1-Debt ratio) ROE = SGR =

25.00%

$ 534,341 39.54%

9.9%

sales of $1,215,326 and net income of payout ratio of 75 percent. The able growth rate?

19.26 Sustainable growth rate: Ellicott Textile Mills management has reported the following for the year ended September 30, 2008. The company generated a net income of $915 profit margin of 6.4 percent. It has a dividend payout ratio of 50 percent. The company h intensity ratio of 62 percent and a debt ratio of 45 percent. What is the company’s susta

Net income Net profit margin Dividend payout ratio Capital intensity ratio Debt ratio

915,366 6.40% = Net Income/Sales 50% 62% =Total assets/Sales 45% =Total Debt/Total assets

Sustainable growth rate (SGR) = Plowback ratio X ROE Plowback ratio = (1 − Dividend payout ratio) = ROE = Net income/Equity Equity = Total Assets * (1 − Debt ratio) Total Assets = Capital intensity ratio * Sales Sales = Net income/Net profit margin = ==> Total assets = ==> Equity = ==> ROE = ==> SGR =

19.27 Internal growth rate: Given the information in Problem 19.26, what is the internal grow Textile Mills? Internal growth rate (IGR) = Plowback ratio X ROA IGR =

5.2%

management has reported the following financial information mpany generated a net income of $915, 366 reflecting a net ayout ratio of 50 percent. The company has a capital 45 percent. What is the company’s sustainable growth rate?

come/Sales

ssets/Sales Debt/Total assets

50%

$ $ $

14,302,594 8,867,608 4,877,184 18.77% 9.4%

Problem 19.26, what is the internal growth rate of Ellicott

19.28 Internal growth rate: Fantasy Travel Company has a return on equity of 17.5 percent equity ratio of 65 percent, and a dividend payout ratio of 75 percent. What is the comp internal growth rate? ROE = Equity ratio = Dividend payout ratio =

17.50% = Net income/Equity 65% = Equity/Total assets 75%

Internal growth rate = Plowback ratio * Return on Assets Plowback ratio = 25% Return on Assets = Net income/Total assets = (Net income/Equity)*(Equity/Total Asse Return on Assets =

11.4%

IGR =

2.84%

equity of 17.5 percent, an ent. What is the company’s

ty)*(Equity/Total Assets)

19.29 EFN: Maryland Micro Brewers generated revenues of $12,125,800 with a 72 percent c ratio during the year ended September 30, 2011. Its net income was $873,058. With of a half dozen new specialty beers, the brewery expects to grow sales by 15 percent Assume that all costs vary directly with sales and that the firm maintains a dividend pa percent. What will be the EFN needed by this firm? If the company wants to raise no m $750,000 externally and is not averse to adjusting its payout policy, what will be the ne payout ratio? Revenues (2008)= $ 12,125,800 Capital intensity ratio= 72% Net income = $ 873,058 Next year's expected growth rate in sales = 15% Dividend payout ratio= 70% Target EFN desired = $ 750,000 Total Assets = Capital intensity ratio * Sales revenues =

$ 8,730,576

Addition to Retained Earnings = Net Income *(1 − dividend payout ratio) = EFN =

(Growth rate * Total assets) − Addition to retained earnings =

Amount of EFN exceeding target EFN at current retention rate = Amount of retained earnings neccesary to achieve target EFN = Retention ratio that would be needed to reach target EFN = New dividend payout that would be warranted =

800 with a 72 percent capital intensity e was $873,058. With the introduction ow sales by 15 percent next year. maintains a dividend payout ratio of 70 any wants to raise no more than olicy, what will be the new dividend

261,917.40

1,047,669.00

297,669.00

559,586.40 64.1% 35.9%

19.30 EFN: Ritchie Marble Company has total assets of $12,899,450, sales of $18,174,652, income of $4,589,774. Management expects its sales to grow by 25 percent next year costs (including taxes) vary directly with sales, and management expects to maintain a 65 percent. Calculate the EFN. Total assets $ 12,899,450 Sales $ 18,174,652 Net income $ 4,589,774 Sales growth rate 25% Payout ratio 65% Expected net income next year = This years's net income * (1 + Sales growth rate) = Addition to Retained Earnings =

Expected Net income * (1 − Payout ratio) =

EFN = (Sales growth rate * Total assets) − Addition to retained earnings =

899,450, sales of $18,174,652, and net o grow by 25 percent next year. All assets and agement expects to maintain a payout ratio of

Sales growth rate) = $ 2,008,026.13 $ 1,216,836.38

$ 5,737,217.50

19.31 EFN: Norton Group, Inc., expects to add $1,213,777 to retained earnings and currentl assets of $23,159,852. If the company has the ability to borrow up to $1 million, how m can the firm support if it is willing to borrow to its maximum capacity? Addition to retained earnings = Total assets = Borrowing capacity =

$ 1,213,777 $ 23,159,852 $ 1,000,000

EFN = (Growth rate * Total assets) − Addition to retained earnings If maximum borrowing capacity is used ==>

EFN =

1,000,000

(Growth rate * $23,159,852) − $1,213,777

==>

1,000,000 =

==>

(Growth rate * $23,159,852)= 1,000,000 + 1,213,777

==>

Growth rate =

9.56%

tained earnings and currently has total orrow up to $1 million, how much growth m capacity?

19.32

EFN: Capstone Marketing Group has total assets of $5,568,000, sales of $3,008,7 income of $822,000. The company expects its sales to grow by 12 percent next ye and costs (including taxes) vary directly with sales, and the firm expects to maintai of 55 percent. Calculate Capstone's EFN. Growth rate in sales Net income Projected Income

12.00% $822,000 $920,640

Payout ratio Addition to Retained earnings

55.00% $414,288

Total assets EFN

$5,568,000 $ 253,872.00

,568,000, sales of $3,008,725, and net grow by 12 percent next year. All assets the firm expects to maintain a payout ratio

19.33

Maximum sales growth: Given the data for Capstone Marketing Group in Problem Capstone's payout ratio have to be in order for the firm's EFN to be zero?

19.32

EFN: Capstone Marketing Group has total assets of $5,568,000, sales of $3,008,7 of $822,000. The company expects its sales to grow by 12 percent next year. All (including taxes) vary directly with sales, and the firm expects to maintain a payout Calculate Capstone's EFN. Growth rate in sales Net income Projected Income

12.00% $822,000 $920,640

Payout ratio Addition to Retained earnings

55.00% $414,288

Total assets EFN

$5,568,000 $253,872

EFN will be equal to zero

Net Income Projected change in asset Now solve for the payout r zero = $668,160 - $822,00 Projected change in asset Net income Net income Payout ratio

Marketing Group in Problem 19.32, what would EFN to be zero?

568,000, sales of $3,008,725, and net income 12 percent next year. All assets and costs pects to maintain a payout ratio of 55 percent.

EFN will be equal to zero if the change in assets is equal to the change in retained earnings.

Net Income $822,000 Projected change in assets$668,160 Now solve for the payout ratio such that the EFN is exactly equal to zero. zero = $668,160 - $822,000(1 − payout ratio) Projected change in assets ($668,160) Net income $822,000 $153,840 Net income $822,000 Payout ratio 18.72%

19.34 Maximum sales Growth: Rockville Consulting Group expects to add $271,898 to retained earnings this year. The company has total assets of $3,425,693 and wishes t add no new external funds for the coming year. If assets and costs vary directly with sales, how much sales growth can the company support while retaining an EFN of zer What is the firm’s internal growth rate? Expected addition to retained earnings = Total assets = Desired EFN =

Maximum growth rate =

271898 3425693 0

EFN + Addition to Retained earnings Total assets 7.94%

Internal growth rate = (Addition to Retained earnings/Total assets) =7.94%

xpects to add $271,898 to sets of $3,425,693 and wishes to ts and costs vary directly with ort while retaining an EFN of zero?

19.35 The financial statements for the year ended June 30, 2011, are given for Morgan Con Company. The firm’s revenues are projected to grow at a rate of 25 percent next year statement accounts will vary directly with sales. Based on that projection, develop a pr sheet and an income statement for the 2012 fiscal year.

Morgan Construction Company Balance Sheet as of June 30, 2011 ASSETS

Cash Accounts Receivables Inventories Total Current Assets

$ $ $ $

3,349,239 5,830,754 22,267,674 31,447,666

Net Fixed Assets Other Assets

$ $

43,362,482 1,748,906

76,559,054

TOTAL ASSETS

Morgan Construction Company Income Statement for the Fiscal Year Ended Jun Revenues $ 193,212,500 Costs $ 145,265,625 EBITDA $ 47,946,875 Depreciation $ 23,318,750 EBIT $ 24,628,125 Interest $ 11,935,869 EBT $ 12,692,256 Taxes (35%) $ 4,442,290 NET INCOME $ 8,249,967

Morgan Construction Company - Pro Forma Balance Sheet for year ended June 2012

ASSETS

Cash

3,349,239

1.25

4,186,548

Accounts Receivables Inventories Total Current Assets

$ $ $

5,830,754 22,267,674 31,447,666

1.25 1.25

$ $ $

7,288,442 27,834,593 39,309,583

Net Fixed Assets Other Assets

$ $

43,362,482 1,748,906

1.25 1.25

$ $

54,203,102 2,186,133

76,559,054

95,698,818

TOTAL ASSETS

Expected growth rate of sales =

25%

Morgan Construction Company Pro Forma Income Statement for year ended Jun Revenues $ 193,212,500 1.25 $ 241,515,625 Costs $ 145,265,625 1.25 $ 181,582,031 EBITDA $ 47,946,875 $ 59,933,594 Depreciation $ 23,318,750 1.25 $ 29,148,438 EBIT $ 24,628,125 $ 30,785,156 Interest $ 11,935,869 1.25 $ 14,919,836 EBT $ 12,692,256 $ 15,865,320 Taxes (35%) $ 4,442,290 $ 5,552,862 NET INCOME $ 8,249,967 $ 10,312,458

11, are given for Morgan Construction a rate of 25 percent next year, and all financial n that projection, develop a pro forma balance

June 30, 2011 LIABILITIES

Accounts Payables Notes Payables

$ $

Total Current Liabilities

$ 13,899,174

Long Term Debt Common Stock Retained Earnings

$ 29,731,406 $ 19,987,500 $ 12,940,974

TOTAL LIABILITIES & EQUITY

9,041,679 4,857,496

$ 76,559,054

or the Fiscal Year Ended June 30, 2011

e Sheet for year ended June 30, 2012 LIABILITIES

Accounts Payables

9,041,679

1.25

$ 11,302,098

Notes Payables

Total Current Liabilities

$ 13,899,174

Long Term Debt Common Stock Retained Earnings

$ 29,731,406 $ 19,987,500 $ 12,940,974

TOTAL LIABILITIES & EQUITY

Statement for year ended June 30, 2012

4,857,496

$ 76,559,054

1.25

6,071,869

$ 17,373,968 1.25 1.25 1.25

$ 37,164,258 $ 24,984,375 $ 16,176,217 $ 95,698,818

19.36 Use the financial information for Morgan Construction Company from Problem 19.35. change when retained earnings change or new equity is issued. The company pays 75 company plans to expand production capacity by expanding the current facility and ac has no plans to issue new equity this year. Prepare a pro forma balance sheet using t in current liabilities) will be in the form of long-term debt. What is the external financing Dividend payout ratio =

75%

Morgan Construction Company Balance Sheet as of June 30, 2011 ASSETS

Cash Accounts Receivables Inventories Total Current Assets

$ $ $ $

3,349,239 5,830,754 22,267,674 31,447,666

Net Fixed Assets Other Assets

$ $

43,362,482 1,748,906

76,559,054

TOTAL ASSETS

Morgan Construction Company Income Statement for the Fiscal Year Ended Ju Revenues $ 193,212,500 Costs $ 145,265,625 EBITDA $ 47,946,875 Depreciation $ 23,318,750 EBIT $ 24,628,125 Interest $ 11,935,869 EBT $ 12,692,256 Taxes (35%) $ 4,442,290 NET INCOME $ 8,249,967

Morgan Construction Company - Pro Forma Balance Sheet for year ended June ASSETS

2012

Cash Accounts Receivables Inventories Total Current Assets

$ $ $ $

3,349,239 5,830,754 22,267,674 31,447,666

1.25 1.25 1.25

$ $ $ $

4,186,548 7,288,442 27,834,593 39,309,583

Net Fixed Assets $ Addition to Fixed Assets Other Assets $

43,362,482

1.25

1,748,906

1.25

$ $ $

54,203,102 10,000,000 2,186,133

TOTAL ASSETS

76,559,054

Expected growth rate of sales =

$ 105,698,817.50 25%

Pro Forma Income Statement for year ended June 30, 2012 Revenues $ 193,212,500 1.25 $ 241,515,625 Costs $ 145,265,625 1.25 $ 181,582,031 EBITDA $ 47,946,875 $ 59,933,594 Depreciation $ 23,318,750 1.25 $ 29,148,438 EBIT $ 24,628,125 $ 30,785,156 Interest $ 11,935,869 1.25 $ 14,919,836 EBT $ 12,692,256 $ 15,865,320 Taxes (35%) $ 4,442,290 $ 5,552,862 NET INCOME $ 8,249,967 $ 10,312,458

ny from Problem 19.35. Assume now that equity accounts do not vary directly with sales but d. The company pays 75 percent of its income as dividends every year. In addition, the he current facility and acquiring additional equipment. This will cost the firm $10 million. The firm ma balance sheet using this information. Any funds that need to be raised (in addition to changes is the external financing needed in this case? Additional equipment cost

$10,000,000

30, 2011 LIABILITIES

Accounts Payables Notes Payables

$ $

9,041,679 4,857,496

Total Current Liabilities

13,899,174

Long Term Debt Common Stock Retained Earnings

$ $ $

29,731,406 19,987,500 12,940,974

TOTAL LIABILITIES & EQUITY

76,559,054

e Fiscal Year Ended June 30, 2011

et for year ended June 30, 2012 LIABILITIES

Accounts Payables Notes Payables

$ $

9,041,679 4,857,496

Total Current Liabilities

13,899,174

$ 17,373,967.81

Long Term Debt

29,731,406

52,818,262

Common Stock Retained Earnings

$ $

19,987,500 12,940,974

$ $

19,987,500 15,519,088

TOTAL LIABILITIES & EQUITY

76,559,054

Addition to Retained Earnings =

2,578,114.55

Total Assets (2012) Total Current liabilities Shareholders' equity Long-term debt

$ 105,698,817.50 $ 17,373,967.81 $35,506,588.05 $ 52,818,261.64

EFN =

23,086,855.39

1.25 1.25

$ $

11,302,098 6,071,869

$105,698,817.50 $ $ $

2,578,114.55 76,559,054 8,249,967 0.25 $32,928,473.50

Addition to RE Initial TA Net income Plowback ratio Shareholders equity

19.37 Using the information for Morgan Construction Company in the preceding problem, ca growth rate and sustainable growth rate.

Addition to Retained earnings Initial assets SGR = Plowback ratio ´ ROE IGR =

Addition to Retained earnings = $ Initial assets = $ Plowback ratio = Net Income (2011)= $ Common stock (2011)= $ Retained earnings (2011) = $ Shareholders equity (2011) = $ ROE = IGR =

3.37%

SGR =

6.26%

2,578,114.55 76,559,054.00 0.25 8,249,966.56 19,987,500.00 12,940,973.50 32,928,473.50 25.05%

preceding problem, calculate the firm’s internal

19.38 Use the information for Morgan Construction Company from Problems 19.35 and 19.3 sales, but change when retained earnings change or new equity is issued. The compa percent, and its equity-to-total assets ratio is about 43 percent. The company wishes t percent. It is willing to reduce its payout ratio, but will retain no more than 40 percent o funds needed including funds for expansion in new equity. No new long-term debt will scenario. a. What is the external financing needed to accommodate the expected growth? b. What is the firm’s internal growth rate? c. What is the firm’s sustainable growth rate? d. How much new equity will the firm have to issue? e. What is the firm’s new equity ratio and debt-to-equity ratio? Long-term debt-to-equity ratio = Equity-to-total assets ratio = Desired equity-to-total assets ratio = Maximum retention rate desired = Expected growth rate of sales = Net income = a) EFN = (Growth rate * Total assets) - Addition to retained earnings EFN =

IGR =

25% *

$76,559,054

Addition to Retained earnings Initial assets

b) Addition to Retained earnings = IGR =

SGR = Plowback ratio´ROE c) ROE = SGR =

25.05% 10.02%

d) Retained earnings (2011) = Addition to retained earnings (2012)= Retained earnings (2012)=

Maximum plowback ratio =

Total liabilities and Equity (2012)= Current liabilities (2012) = Long-term debt (2011) = Shareholders' equity (2012) = Common stock (2011) = Common stock (2012) = New equity issued in 2012 = e) Long-term debt to equity ratio (2012)= Equity to total assets ratio (2012) =

Morgan Construction Company - Pro forma Balance Sheet for the year ended Se

$ $ $ $

2011 3,349,239 1.25 $ 5,830,754 1.25 $ 22,267,674 1.25 $ 31,447,666 $

2012 4,186,548 7,288,442 27,834,593 39,309,582.81

Net fixed assets $ Addition to fixed assets Other assets $

43,362,482 1.25 $ $ 1,748,906 1.25 $

54,203,102 10,000,000 2,186,133

76,559,054

105,698,818

Cash Accounts receivables Inventories Total current assets

TOTAL ASSETS

Pro forma Income Statement for year ended Sep. 30, 2012 2011 2012 Revenues $ 193,212,500 1.25 $ 241,515,625 Costs $ 145,265,625 1.25 $ 181,582,031 EBITDA $ 47,946,875 $ 59,933,594 Depreciation $ 23,318,750 1.25 $ 29,148,438 EBIT $ 24,628,125 $ 30,785,156 Interest $ 11,935,869 1.25 $ 14,919,836 EBT $ 12,692,256 $ 15,865,320 Taxes (35%) $ 4,442,290 1.25 $ 5,552,862 NET INCOME $ 8,249,967 $ 10,312,458

roblems 19.35 and 19.36. Assume that equity accounts do not vary directly with ty is issued. The company’s long-term debt-to-equity ratio is approximately 90 . The company wishes to increase its equity-to-total assets ratio to at least 50 more than 40 percent of its retained earnings. The company will raise any additional new long-term debt will be issued. Prepare pro forma statements to reflect the new

expected growth?

90% 43% 50% (at least) 40% 25% $10,312,458.20

$4,124,983 =

$4,124,983 5.39%

plowback ratio =

$ $ $

40%

12,940,973.50 4,124,983.28 17,065,956.78

$15,014,780.22

$ $ $ $ $ $ $

105,698,817.50 17,373,967.81 29,731,406.25 58,593,443.44 19,987,500.00 21,539,986.66 1,552,486.66 50.74% 55.43%

t for the year ended Sep. 30, 2012 2011 9,041,679 1.25 $ 4,857,496 1.25 $

2012 11,302,098 6,071,869

Accounts payables Notes payables

$ $

Total Current Liabilities

$ 13,899,174

17,373,968

Long-term debt Common stock Retained earnings

$ 29,731,406 $ 19,987,500 $ 12,940,974

$ $ $

29,731,406 41,527,487 17,065,957

TOTAL LIABILITIES & EQUITY

$ 76,559,054

$ 105,698,818

19.39 Munson Communications Company has just reported earnings for the year ended Jun last 10 years and does not plan to change this policy. Based on internal forecasts, the percent. Assume that equity accounts and long-term debt do not vary directly with sale

a. What is the firm’s internal growth rate (IGR)? b. What is the firm’s sustainable growth rate (SGR)? c. What is the external financing needed (EFN) to accommodate the expected growth? d. Construct the firm’s 2008 pro forma financial statements under the assumption that all external financing will be done with long-term debt. Net income in 2011 = Sales Growth rate expected= Projected Net income for 2012= Plowback ratio for 2012 =

Projected addition to RE = ROE = IGR = (Addition to RE/Initial Total assets) = SGR = EFN =

Munson Communications Company - Pro forma Balance Sheet for the year ende

Cash Accounts Receivables Inventories Total Current Assets Net Fixed Assets Other Assets

TOTAL ASSETS

Pro forma Income Statemen Revenues Costs EBITDA Depreciation EBIT Interest EBT Taxes (35%) NET INCOME

ust reported earnings for the year ended June 30, 2011. Given in this problem are the firm’s income statement and b this policy. Based on internal forecasts, the company expects the demand for its products to grow at a rate of 20 pe long-term debt do not vary directly with sales, but change when retained earnings change or additional capital is iss Munson Communications Company Income Statement for the Fiscal Year Ended June 30, Revenues Costs EBITDA Depreciation EBIT Interest EBT Taxes (35%) NET INCOME Munson Communications Company -Balance Sheet as of June. 30, 2011

Cash Accounts Receivables Inventories Total Current Assets Net Fixed Assets Other Assets

TOTAL ASSETS

FN) to accommodate the expected growth? cial statements under the assumption that g-term debt.

Plowback ratio * ROE [(Growth rate*Total Assets) - Addition to RE]

ro forma Balance Sheet for the year ended June. 30, 2012 2011

1,728,639.35 3,009,421.16 11,492,993.03 16,231,054 22,380,635.61

1,748,906

40,360,595

Pro forma Income Statement for year ended June 30, 2012 2011 79,722,581 $ 59,358,499 $ 20,364,082 $ 7,318,750 $ 13,045,332 $ 3,658,477 $ 9,386,855 $ 3,285,399 $ 6,101,456

ed June 30, 2011. Given in this problem are the firm’s income statement and balance sheet. The company has a 55 ts, the company expects the demand for its products to grow at a rate of 20 percent for the next year and has projec th sales, but change when retained earnings change or additional capital is issued.

ns Company Income Statement for the Fiscal Year Ended June 30,

$ $ $ $ $ $ $ $

79,722,580.65 59,358,499 20,364,082 7,318,750 13,045,332 3,658,477 9,386,855 3,285,399 6,101,456

s Company -Balance Sheet as of June. 30, 2011

1,728,639.35 3,009,421.16 11,492,993.03 16,231,054 22,380,635.61

1,748,906

40,360,595

6,101,456 20% 7,321,747 45%

3,294,786 30.75% 8.16% 13.84%

) - Addition to RE]

4,777,333

r ended June. 30, 2012

1.20 1.20 1.20

2012 $ 2,074,367 $ 3,611,305 $ 13,791,592 $ 19,477,264.26

1.20

26,856,763

1.20

2,098,688

48,432,714

$ $ $ $ $ $ $ $ $

2012 95,667,097 71,230,199 24,436,898 8,782,500 15,654,398 4,390,172 11,264,226 3,942,479 7,321,747

ement for year ended June 30, 2012 1.20 1.20 1.20 1.20 1.20

ce sheet. The company has a 55 percent dividend payout ratio for the for the next year and has projected the sales growth for 2012 to be 20

Dividend payout ratio Projected sales growth rate for 2012 Equity accounts and long-term debt do not vary with sales

55% 20%

Accounts Payables Notes Payables

4,666,673 2,507,094

Total Current Liabilities

Long Term Debt Common Stock Retained Earnings

$ 13,345,242 $ 10,165,235 $ 9,676,351

TOTAL LIABILITIES & EQUITY

7,173,767

$ 40,360,595

2011 4,666,673 2,507,094

Accounts Payables Notes Payables

$ $ $

8,608,521

Total Current Liabilities

Long Term Debt Common Stock Retained Earnings

$ 13,345,242 $ 10,165,235 $ 9,676,351

$ 19,982,608 $ 10,165,235 $ 9,676,351

$ 40,360,595

$ 48,432,714

TOTAL LIABILITIES & EQUITY

7,173,767

1.20 1.20

2012 5,600,007 3,008,513

$ 6,637,366 $

$ 6,637,366

STP#19.1 Mars Company had net sales of $18 million in the year that just ended. Next year, th company's management expects a 15 percent increase in sales. If cost of goods sol percent of sales and inventory is 25 percent of sales, what would you estimate sales and cost of goods sold to be next year?

hat just ended. Next year, the n sales. If cost of goods sold is 60 at would you estimate sales, inventory

STP#19.2 Lavaca Inc. management expects net sales to be $855,000, total costs to be $647,0 taxes at an average rate of 32 percent this year. If the Lavaca pays out 38 percent o dividends, what is its retention ratio? How much will Lavaca's retained earnings incre

000, total costs to be $647,000, and to pay avaca pays out 38 percent of its earnings as aca's retained earnings increase?

STP#19.3 Spurlock Inc. had net income of $266,778 in its most recent fiscal and total assets o $1,833,400 at the end of the year. The company's total debt ratio (total debt to total 35 percent and Spurlock retains 60 percent of its income every year. What is Spurlo internal growth rate? What is its sustainable growth rate?

ent fiscal and total assets of debt ratio (total debt to total assets) is every year. What is Spurlock's ?

STP#19.4 Using the information in Sample Test Probbleml9.3, what is Spurlock's capital inten the company has net sales of$3,557,100? What does this ratio tell us?

t is Spurlock's capital intensity ratio if s ratio tell us?

STP#19.5 Edgefield Excavation Company has total assets of $4,976,456, sales of $1,225,700 $587,000. The company's management expects sales to grow by 9 percent next ye taxes) and assets vary directly with sales and the firm expects to maintain a payout Calculate the external funds needed (EFN) by Edgefield. What would Edgefield's pa in order for the company's EFN to equal zero?

6,456, sales of $1,225,700, and net income of grow by 9 percent next year. All costs (including pects to maintain a payout ratio of 35 percent. What would Edgefield's payout ratio have to be

20.3

Option payoffs: What is the payoff for a call option with a strike price of $50 if the stock price at expiration is $40? What if it is $65? Call Strike Price Stock Price at expiration= OR Stock Price at expiration =

$50 $40 $65

Calculation of Call Option Payoff

Call Option Payoff at $40

Call Option Payoff at $65

rike price of $50 if

20.4

Option payoffs: What is the payoff for a put option with a strike price of $50 if the stock price at expiration is $40? What if it is $65? Put Strike Price Stock Price at expiration= OR Stock Price at expiration =

$50 $40 $65

Calculation of Put Option Payoff Put Option Payoff at $40

Put Option Payoff at $65

20.10

Option valuation: What is the value at expiration of a call option with a strike price of $65 if the stock price is $1? $50? $65? $100? $1,000?

Strike Price =

$65

Stock Price $1 $50 $65 $100 $1,000

Value of Call at expiration 0 0 0 35 935

option with a strike 000?

of Call at expiration

20.11 Option valuation: Suppose you have an option to buy a share of ABC Corp. stock for $100. The option expires tomorrow, and the current price of ABC Corp. is $95. How much is your option worth? Strike Price of Call (EP)= $100 Current Stock Price (Ps)= $95

Value of Call =

are of ABC Corp. t price of ABC

20.12 Option valuation: You hold an American option to sell one share of Zyther Co. The option expires tomorrow. The strike price of the option is $50, and the current stock pri is $49. What is the value of exercising the option today? If you wanted to sell the option instead, about how much would you expect to receive? Put's Strike Price = Current Stock Price =

$50 $49

Value of Put if exercised today =

$ 1.00

Value of Put if sold today =

$ 1.00

Reason: No time value left

hare of Zyther Co. The and the current stock price u wanted to sell the option

20.20

Option valuation: The stock of Socrates Motors is currently trading for $40 and $50 or fall to $35 in one month. The risk-free rate for one month is 1.5 percent. W a one-month call option with a strike price of $40?

Current Stock Price = Call's Strike Price = Expiration (months)= Price Expected after 1 month

$40 $40 1

Risk-free rate for 1 month=

1.50%

$50

Stock (x) Today

$35

Risk-Free Loan (y)

$40

Expiration $35

$50

$1.015

$10 = ($50 × x ) + (1.015 × y ) $0 = ($35 × x ) + (1.015 × y ) 10 = ($15 x ) + (0) 10/15 = x = 0.67 substituting x = .67 in equation 1 we get: 10 = ($50*.67) + (1.015)y

Equation 1 Equation 2 Subtracting Equation 2 from Equation 1

$50 Stock Price $35 1.015 Risk-free Loan

$1.015 $1.015

1.015 $10 Call

??? $0

0.6667

(22.9885)

Call Price

$3.68

rs is currently trading for $40 and will either rise to te for one month is 1.5 percent. What is the value of 0?

Option ?

ation 2 from Equation 1

$10

20.21

Option valuation: Again assume that the price of Socrates Motors stock will eith to $50 or fall to $35 in one month and that the risk-free rate for one month is 1.5 How much is an option with a strike price of $40 worth if the current stock price is instead of $40?

Current Stock Price = Call's Strike Price = Expiration (months)= Price Expected after 1 month

$45 $40 1

Risk-free rate for 1 month=

1.50%

$50

Stock (x) Today

$35

Risk-Free Loan (y)

$45

Expiration $35

$50

$1.015

$10 = ($50 × x ) + (1.015 × y ) $0 = ($35 × x ) + (1.015 × y ) 10 = ($15 x ) + (0) 5/15 = x = 0.6667 substituting x = .6667 in equation 1 we get: 5 = ($50*.6667) + (1.015)y

$50 Stock Price $35 1.015

$1.015

Equation 1 Equation 2 Subtracting Equation 2 from Equation 1

y = (10 − ($50*.6667))/1.015 = -22.99

Risk-free Loan 1.015 $10 Call

??? $0

0.6667

(22.9885)

Call Price

$7.01

of Socrates Motors stock will either rise sk-free rate for one month is 1.5 percent. 0 worth if the current stock price is $45

Option ?

ation 2 from Equation 1

6667))/1.015 = -22.99

$10

20.22

Assume that the stock of Socrates Motors is currently trading for $40 and will eith or fall to $35 in one month. The risk-free rate for one month is 1.5 percent. What a one-month call option with a strike price of $25?

Current Stock Price = Call's Strike Price = Expiration (months)= Price Expected after 1 month

$40 $25 1

Risk-free rate for 1 month=

1.50%

$50

Stock (x) Today

$35

Risk-Free Loan (y)

$40

Expiration $35

$50

$1.015

$25 = ($50 × x ) + (1.015 × y ) $10 = ($35 × x ) + (1.015 × y ) 15 = ($15 x ) + (0) 15/15 = x =1.0 substituting x = 1.0 in equation 2 we get: 10 = ($35*1.0) + (1.015)y

Equation 1 Equation 2 Subtracting Equation 2 from Equation 1

y = (10 − ($35*.1.0))/1.015 = -24.63

$50 Stock Price $35 1.015 Risk-free Loan

$1.015

1.015 $25 Call

??? $10

1.0000

(24.6305)

Call Price

$15.37

rrently trading for $40 and will either rise to $50 r one month is 1.5 percent. What is the value of 5?

Option ?

$10

ation 2 from Equation 1

1.0))/1.015 = -24.63

$25

20.23

Option valuation: You are considering a three-month put on Wing and a Prayer C currently trades for $10 per share and will either rise to $15 or fall to $7 in three mo three months is 2 percent. What is the appropriate price for a put with a strike price

For this problem, first calculate the price of a call with the same strike price as the put using the binomial model, and then use the put-call parity relationship to calculate the price of the put.

Current Stock Price = Call's Strike Price = Expiration (months)= Price Expected after 3 months Risk-free rate for3 month=

$10 $9 3 $15 2.00%

$15 Stock Price $7 1.02 Risk-free Loan 1.02 $6 Call

??? $0

0.7500

(5.1471)

Call Price Put Price

$2.35 P = C + Xe–rt – V

$1.31

Wing and a Prayer Construction. The company fall to $7 in three months. The risk-free rate for put with a strike price of $9?

as the put using e the price of the put.

20.24

Option valuation: You hold a European Put option on Tubes, Inc., with a strike pric $100. Things haven’t been going too well for Tubes. The current stock price is $2, a you think that it will either rise to $3 or fall to $1.50 at the expiration of your option. T appropriate risk-free rate is 5 percent. What is the value of the option? If this were a American option, would it be worth more?

NOTE: No expiration date is given

For this problem, first calculate the price of a call with the same strike price as the put using the binomial model, and then use the put-call parity relationship to calculate the price of the put.

Current Stock Price = Call's Strike Price = Expiration (months)= Price Expected after 12 months

$2 $100 12

Risk-free rate =

5.00%

$3 Stock Price $1.50 1.05 Risk-free Loan 1.05 $0 Call

??? $0

0.0000

Call Price

$0.00

Put Price

P = C + Xe–rt – V

$93.12 ?????

Exercising today would allow us to sell for $100 something worth $2, a gain o this is more than $93.12. The American option is worth more.

on Tubes, Inc., with a strike price of The current stock price is $2, and the expiration of your option. The lue of the option? If this were an

rike price as the put using o calculate the price of the put.

$1.50

something worth $2, a gain of $98. worth more.

20.28. Option Valuation: One way to extend the binomial pricing model is by including multip periods. Suppose Splittime, Inc., is currently trading for $100 per share. In one month, either increase by $10 (to $110) or decrease by $10 (to $90). The following month will The price will either increase by $10 or decrease by $10. Notice that in two months, the be $120, $100, or $80. The risk-free rate is 1 percent per month. Find the value today to buy one share of Splittime in two months for a strike price of $105. (Hint: To do this, value of the option at each of the two possible one-month prices. Then use those value payoffs at one month and find the value today.)

1-month later $110 Current Stock Price Call Strike Price 1+R

$100 $105 1.01

Qu Qd

0.5446 0.4455

Call Price at t = 0 $4.45

2-months later U 1.1

$120 $100

$90

0.9 D

$80

Call Price at t = 1 $8.17 0

The portfolio value is $4.45 and this is the value of the option.

model is by including multiple time per share. In one month, the price will . The following month will be the same. tice that in two months, the price could onth. Find the value today of an option of $105. (Hint: To do this, first find the ices. Then use those values as the

20.28B Option Valuation: One way to extend the binomial pricing model is by including multip Suppose Splittime, Inc., is currently trading for $100 per share. In one month, the price increase by $10 (to $110) or decrease by $10 (to $90). The following month will be the price will either increase by $10 or decrease by $10. Notice that in two months, the pric $120, $100, or $80. The risk-free rate is 1 percent per month. Find the value today of a one share of Splittime in two months for a strike price of $105. (Hint: To do this, first fin the option at each of the two possible one-month prices. Then use those values as the month and find the value today.) Current Stock Price = Call's Strike Price = Expiration (months)= Price Expected after 1 month

$90 $105 1

Risk-free rate for 1 month=

1.00%

$100

Stock (x) Today

$80

Risk-Free Loan (y)

$90

Expiration $80

$100

$1.01

$1.01 $1.015

$0 = ($100 × x ) + (1.01 × y ) Equation 1 $0 = ($80 × x ) + (1.01 × y ) Equation 2 0 = ($20 x ) + (0) Subtracting Equation 2 from Equation 1 0/20 = x = 0.0 substituting x = 0 in equation 2 we get: 0 = ($80*0) + (1.01)y y = (0 − 80*0)/1.01 = 0

$100 Stock Price $80 1.01 Risk-free Loan 1.01 $0 Call

??? $0

0.0000

Call Price

$0.00

del is by including multiple time periods. In one month, the price will either owing month will be the same. The t in two months, the price could be Find the value today of an option to buy (Hint: To do this, first find the value of use those values as the payoffs at one

Option ?

ation 2 from Equation 1

$20

20.28A Option Valuation: One way to extend the binomial pricing model is by including multip Splittime, Inc., is currently trading for $100 per share. In one month, the price will eithe or decrease by $10 (to $90). The following month will be the same. The price will eithe decrease by $10. Notice that in two months, the price could be $120, $100, or $80. Th per month. Find the value today of an option to buy one share of Splittime in two month (Hint: To do this, first find the value of the option at each of the two possible one-month values as the payoffs at one month and find the value today.)

Current Stock Price = Call's Strike Price = Expiration (months)= Price Expected after 1 month

$110 $105 1

Risk-free rate for 1 month=

1.00%

$120

Stock (x)

Risk-Free Loan (y)

$110

Today

$100

Expiration $100

$120

$15 = ($120 × x ) + (1.01 × y ) $0 = ($100 × x ) + (1.01 × y ) 15 = ($20 x ) + (0) 15/20 = x = 0.75 substituting x = .75 in equation 2 we get: 0 = ($100*.75) + (1.01)y

$1.01

Equation 1 Equation 2 Subtracting Equation 2 from Equation 1

y = (0 − 75)/1.01 = -74.2574

$120 Stock Price $100 1.01 Risk-free Loan 1.01 $15 Call

??? $0

0.7500

(74.2574)

Call Price

$8.24

The value of this portfolio and thereor the value of the option at this point, is $8.2

del is by including multiple time periods. Suppose onth, the price will either increase by $10 (to $110) me. The price will either increase by $10 or $120, $100, or $80. The risk-free rate is 1 percent of Splittime in two months for a strike price of $105. two possible one-month prices. Then use those

ation 2 from Equation 1

Option ?

$15

20.29

Spin the wheel Co. has assets currently worth $10 million in the form of one-year r that will return 10 percent. The company has debt with a face value of $5.5 million year. (No interest payments will be made). The stockholders decided to sell $8 m risk-free bonds and to invest the money in a very risky venture. This venture cons William Kidd taking the money now and, in one year, flipping a coin. If it comes up Kidd will pay SpinTheWheel $17.6 million. If it is tails, SpinTheWheel gets nothing this is a zero NPV investment.)

a. What is the value of the debt and equity before they make this "investment"? b. Using the binomial pricing model, with the payoff to the equity holders represen the option and the assets of the company representing the underlying asset, estimate the value of the equity after they make the investment. c. What is the new value of the debt after the investment?

a. The value of the debt today is the present value of the debt at the risk-free rate. Debt $5,500,000 risk-free rate 10.00% PVIF 0.909090909 Value of Debt today $5,000,000 Assets Debt Equity

$10,000,000 $5,000,000 $5,000,000

b. The payoffs of the option (the equity), the underlying (the firm), and the risk-free Firm Risk-Free (Y) Today $10 $1 One Year

option 1 $2,200,000 option 2 $19,800,000

The payoff for the option in the up case is The equations are: $14.3 = $19.8 × X + $1.1 × Y

$1.1 $1.1

$0 = $2.2 × X + $1.1 × Y X=

0.81250

($1,625,000) assets X Y Value of portfolio New value of equity

$10,000,000 0.81250 ($1,625,000) $6,500,000 $6,500,000

c. The current value of the firm did not change (this was a zero NPV project) and remains at $10 million. If the equity has increased in value to $6.5 million, the debt has decreased in v

million in the form of one-year risk-free bonds with a face value of $5.5 million due in one ockholders decided to sell $8 million of the isky venture. This venture consists of Mr. ar, flipping a coin. If it comes up heads, Mr. ails, SpinTheWheel gets nothing. (Notice that

they make this "investment"? ff to the equity holders representing esenting the underlying asset, e the investment.

of the debt at the risk-free rate.

rlying (the firm), and the risk-free bond are: Equity ???

$0 $14 $14,300,000

$3,500,000

20.3

The price of a non-dividend-paying stock is currently $35 and the risk-free rate is 4 percent. A European call option on the stock, with a strike price of $35 and which in six months, sells for $3.04. A European put option on the same stock with the s strike price sells for $2.35. Is there an arbitrage opportunity here? If so, what is it?

Substitute the values into the put-call parity relation and see if it holds. P = C + Xe-rt − V Put selling price $2.35 Call selling price $3.04 Xercise price of European call option $35.00 risk-free rate 4.00% Expires in how many months 6 Months in a year 12 time to maturity 50.00% Value, currently of stock $35.00 Put selling Price C X e-(.04)(.50) V C + Xe-rt − V

$2.35 $3.04 $35.00 0.98 $35.00 $2.34

Since the put-call parity relation approximately holds, there is no arbitrage opportun

and the risk-free rate is 4 price of $35 and which expires he same stock with the same y here? If so, what is it?

ee if it holds.

e is no arbitrage opportunity.

20.31

Two call options have been written on the same underlying stock. Call #1 has a st price of $42 and Call #2 has a strike price of $52. Call #1 is selling for $5.00 and C #2 is selling for $6.00. What arbitrage opportunity do these prices present investo Show the potential payoffs from this opportunity. Strike price of Call #1Cost of Call #1 $42 $5

Call #1 has a lower strike price and costs less than Call #2. You can earn an arbitrage opportunity by purchasing the less expensive Call #1 an A Payoff Table is presented below: $42 $52 Stock Price Buy $42 Call Sell $52 Call Proceeds $28 $0 $6 $6 $30 $0 $6 $6 $32 $0 $6 $6 $34 $0 $6 $6 $36 $0 $6 $6 $38 $0 $6 $6 $40 $0 $6 $6 $42 $0 $6 $6 $44 $2 $6 $8 $46 $4 $6 $10 $48 $6 $6 $12 $50 $8 $6 $14 $52 $10 $6 $16 $54 $12 $4 $16 $56 $14 $2 $16 $58 $16 $0 $16 $60 $18 ($2) $16

e underlying stock. Call #1 has a strike 2. Call #1 is selling for $5.00 and Call nity do these prices present investors? y. Strike price of Call #2 $52

Cost of Call #2 $6

han Call #2. asing the less expensive Call #1 and selling the more expensive Call #2.

20.4.

20.5. Option valuation: What are the five variables that affect the value of an option, and h 20.6.

Option valuation: Assuming nothing else changes, what happens to the value

20.7.

Option valuation: What does the seller of a put option hope will happen?

20.8.

Option valuation: What is the value of an option if the stock price is zero? Wh

20.9.

Option valuation: Like owners of stock, owners of options can lose no more th

20.1

Option valuation: What is the value at expiration of a call option with a strike p

20.11.

Option valuation: Suppose you have an option to buy a share of ABC Corp. st

20.12.

Option valuation: You hold an American option to sell one share of Zyther Co.

20.13.

Real options: What is the difference between a financial option and a real opti

20.14. Real options: List and describe four different types of real options that are associate 20.15. Agency costs: How are options related to the agency costs of debt and equity? Intermediate

20.16. Option valuation: Suppose that you own a call option and a put option on the same 20.17.

Other options: A callable bond is a bond that can be bought back by the bond

20.18.

Other options: A convertible bond is a bond that can be exchanged for stock a

20.19.

Option valuation: The seller of an option can never make any money from a c

20.20.

Option valuation: The stock of Socrates Motors is currently trading for $40 and

20.21.

Option valuation: Again assume that the price of Socrates Motors stock will ei

20.22.

Option valuation: Assume that the stock of Socrates Motors is currently tradin

20.23.

Option valuation: You are considering a three-month put on Wing and a Praye

20.24.

Option valuation: You hold a European Put option on Tubes, Inc., with a strike

20.25. Other options: A golden parachute is a part of a manager’s compensation package Advanced 20.26.

Combining options: Consider the following payoff diagram.

Value

Covered call

$10

$40

$50

$60

Stock

Find a combination of calls, puts, risk-free bonds, and stock that has this payoff. (You need

Option valuation: Consider the payoff structures of the following two portfolios 20.27. a. Buying a call option on one share in one month at a strike price of $50 and b. Buying a put option on one share in one month at a strike price of $50 and What conclusion can you draw about the relation between call prices and put prices? 20.28.

Option Valuation: One way to extend the binomial pricing model is by includin

20.29.

Option Valuation: SpinTheWheel Co. has assets currently worth $10 million in

What is the value of the debt and equity before the stockholders make this

Using the binomial pricing model, with the payoff to the equity holders repr

What is the new value of the debt after the investment?

20.30. Agency costs: The payoff function for the holder of straight debt looks like that for t Self-Test Problems 20.1.

Draw the payoff diagram representing the payoff for a combination of buying a

20.2.

Of the five variables identified as affecting the value of an option, which will hav

20.3. a. b. c.

What kinds of real options are being described? Fred’s Cheap Cars buys the empty field adjacent to its car lot. Midway through construction, MiniMax, Inc., stops construction of an office Major Deals, a discount retailer, opens its first new store in Mexico.

20.4.

If you fail to account for the real options available in a given project, what error

20.5

Suppose you are a corn farmer. Assuming that there is an active market in corn

ue of an option, and how do changes in each of these variables affect the value of a call option?

s can lose no more than the amount they invested. They are far more likely to lose that full amount, but they cannot

share of ABC Corp. stock for $100. The option expires tomorrow, and the current price of ABC Corp. is $95. How mu

e share of Zyther Co. The option expires tomorrow. The strike price of the option is $50, and the current stock price

ut option on the same stock and that these options have the same exercise price. Explain how the relative values of

ught back by the bond issuer before maturity for some pre-specified price (normally face value) at the discretion of th

exchanged for stock at the discretion of the bondholder. How would you go about finding the value of such a bond?

e any money from a change in the value of the underlying asset; he or she can only hope that the option will not be e

tly trading for $40 and will either rise to $50 or fall to $35 in one month. The risk-free rate for one month is 1.5 perce

es Motors stock will either rise to $50 or fall to $35 in one month and that the risk-free rate for one month is 1.5 perce

ors is currently trading for $40 and will either rise to $50 or fall to $35 in one month. The risk-free rate for one month

on Wing and a Prayer Construction. The company currently trades for $10 per share and will either rise to $15 or fa

bes, Inc., with a strike price of $100. Things haven’t been going too well for Tubes. The current stock price is $2, and

ompensation package that makes a large lump-sum payment in the event that the manager is fired (or loses his or h

Stock

strike price of $50 and saving the present value of $50 (so that at expiration it will have grown to $50 with interest).

g model is by including multiple time periods. Suppose Splittime, Inc., is currently trading for $100 per share. In one m

ly worth $10 million in the form of one-year risk-free bonds that will return 10 percent. The company has debt with a

he equity holders representing the option and the assets of the company representing the underlying asset, estimate

ebt looks like that for the seller of a put option. Convertible debt is straight debt plus a call option on a firm’s stock. Ho

mbination of buying a call with a strike price of $40 and selling a call with a strike price of $50. What would the buyer

option, which will have the opposite effects on the value of a put and the value of a call? That is, for which variables

n active market in corn options, what trades might you want to use to protect yourself against falling corn prices? Wh

amount, but they cannot lose more. Do sellers of options have the same limitation on their losses?

d the current stock price is $49. What is the value of exercising the option today? If you wanted to sell the option inst

ow the relative values of these two options will change as the stock price increases or decreases.

ue) at the discretion of the bondholder. How would you go about finding the value of such a bond? Would the bond b

e value of such a bond? Would the bond be worth more or less than an equivalent nonconvertible bond?

at the option will not be exercised and that and he or she will not lose any money. Given that this is the case, why do

r one month is 1.5 percent. What is the value of a one-month call option with a strike price of $40?

r one month is 1.5 percent. How much is an option with a strike price of $40 worth if the current stock price is $45 in

k-free rate for one month is 1.5 percent. What is the value of a one-month call option with a strike price of $25?

ill either rise to $15 or fall to $7 in three months. The risk-free rate for three months is 2 percent. What is the approp

ent stock price is $2, and you think that it will either rise to $3 or fall to $1.50 at the expiration of your option. The app

is fired (or loses his or her job in a merger, for example). This seems ill advised to most people first hearing about it.

$100 per share. In one month, the price will either increase by $10 (to $110) or decrease by $10 (to $90). The follow

ompany has debt with a face value of $5.5 million due in one year. (No interest payments will be made.) The stockho

tion on a firm’s stock. How does the addition of a call option to straight debt affect the concern that lenders have abo

at is, for which variables will a given change increase the value of a call and decrease the value of a put (or vice vers

n of your option. The appropriate risk-free rate is 5 percent. What is the value of the option? If this were an American

ple first hearing about it. Explain how a golden parachute can help reduce agency costs between stockholders and m

$10 (to $90). The following month will be the same. The price will either increase by $10 or decrease by $10. Notice

l be made.) The stockholders decided to sell $8 million of the risk-free bonds and to invest the money in a very risky

decrease by $10. Notice that in two months, the price could be $120, $100, or $80. The risk-free rate is 1 percent pe

he money in a very risky venture. This venture consists of Mr. William Kid’s taking the money now and, in one year,

-free rate is 1 percent per month. Find the value today of an option to buy one share of Splittime in two months for a

y now and, in one year, flipping a coin. If it comes up heads, Mr. Kid will pay SpinTheWheel $17.6 million. If it is tails

time in two months for a strike price of $105. (Hint: To do this, first find the value of the option at each of the two pos

$17.6 million. If it is tails, SpinTheWheel gets nothing. (Notice that this is a zero-NPV investment.)

on at each of the two possible one-month prices. Then use those values as the payoffs at one month and find the val

e month and find the value today.)

STP #20.1 You own a call option on Pepsico stock with a strike price of $60 per share that expires in 60 days. The current market price of Pepsico stock is $63.50 per share. What are the limits on the value of the call option you own?

trike price of $60 per share that Pepsico stock is $63.50 per ll option you own?

STP #20.2 Assume that the current market price of Montrose Industrials stock is $28 per share and will either rise to $38 per share or fall to $21 per share in one month. The risk-free rate for one month is I percent. What is the value of a one-month call option with a strike price of $24 per share?

se Industrials stock is $28 per to $21 per share in one ent. What is the value of a per share?

STP #20.3 The market value of Whole Foods stock is currently $53.73 per share and the risk percent. A three month call option on the stock with a strike price of $55 sells for $ value of a put option on Whole Foods stock that has the same strike price and exp there are no arbitrage opportunities?

53.73 per share and the risk free rate is 3 strike price of $55 sells for $2.15. What is the the same strike price and expiration date if

21.1

Spot rate: Ryan wants to buy a pair of leather shoes at Harrods in London that is priced at £113.60. If the exchange rate that day is $1.6177/£, what is Ryan’s cost in U.S. dollars?

Price of shoes in London

£113.60

113.6

Spot exchange rate

$1.6177/£

1.6177

Cost in U.S. dollars

183.77

arrods in London that is 7/£, what is Ryan’s cost in

21.2

Spot rate: Crescent Corporation’s recent sale to a firm in Mexican produced revenues 13,144,800 Mexican pesos (MPs). If the firm sold the pesos to its bank and was credite $1,077,873.60, what was the spot rate at which the pesos were converted?

Revenues In Mexican Pesos =

13,144,800 MP

Proceeds in US$ =

1,077,873.60

Spot exchange rate of MP/$=

12.19512195

an produced revenues of s bank and was credited with converted?

21.3

Spot rate: Given the following direct quotes, calculate the equivalent indirect quotes. a) $0.0844/Mexican pesos b) £0.8513/€ c) Rs 54.64/ C$

Direct quotes 0.0844 $ /Mexican Pesos 0.8513 £/€ 54.64 Rs/C$ Equivalent Indirect quotes 11.848 Mexican Pesos/$ 1.1747 €/ £ 0.0183 C$/Rs

21.4

Spot rate: Convert the following indirect quotes to the appropriate American a) £0.6917/$ b) ¥104.28/$ c) SF 1.0769/$

Indirect quotes 0.6917 £/$ 104.28 ¥/$ 1.0769 SF/$ American quotes 1.4457 $/ £ 0.0096 $/¥ 0.9286 $/SF

appropriate American

21.5

Spot rate: Suppose a BMW 745i is priced at $68,750 in New York and € 50,267 in Berlin. In which place is the car more expensive if the spot rate is $1.3677/€?

New York Price

$68,750

Berlin Price (€)

50,267

Spot Rate $/€

1.3677

Price of BMW 745i in Berlin converted into US$ = The car is more expensive in Berlin by a whopping

68,750.18 $0.18

New York and € 50,267 in t rate is $1.3677/€?

21.6

Forward rate: Explain the relationship between each pair of currencies.

a. b. c.

Spot Rate $1.655/ £ ¥104.45/$ C$ 1.1121/$

a. b. c.

Forward Rate $1.6001/£ ¥102.33/$ C$ 1.0940/$ Spot Rate 1.655 104.45 1.1121

Forward premium (discount) =

a. b. c.

Forward Rate 1.6001 102.33 1.094 Forward rate − Spot rate Spot rate

Forward premium (discount) -3.32% forward discount 2.03% forward premium 1.63% forward premium

360 n

$/£ ¥/$ C$/$

× 100

currencies.

21.7

$/C$

1.0413

Forward rate $/C$

1.0507

Amount of currency sold C$

1,000,000

US $ proceeds at Forward Rate

$ 1,050,700

US $ proceeds at Spot Rate

$ 1,041,300

Net difference

9,400

0-day forward rate you receive by selling

21.8

Forward rate: Crane, Inc., sold equipment to an Irish firm and will receive €1,319,405 days. If the company entered a forward contract to sell at the 30-day forward rate of $1.3012/€, what is the dollar revenue received?

30-day forward rate Euro Proceeds from sale Dollar Proceeds

$/€

1.1912

€

1,301,200 $ 1,549,989.44

and will receive €1,319,405 in 30 he 30-day forward rate of

21.9

Forward rate: Brilliant Equipment purchased machinery from a Japanese firm and mu make a payment of ¥313.25 million in 45 days. The bank quotes a forward rate of ¥103.01/$ to buy the required yen. What is the cost to Brilliant in U.S. dollars?

Purchase price in Japanese Yen

313.25 million

Forward rate

103.01

Cost in US $

¥/$

$ 3.0410 million

y from a Japanese firm and must k quotes a forward rate of Brilliant in U.S. dollars?

21.10 Forward rate: Triumph Autos has contracted with an Indian software firm for design software. The payment of 22,779,750 rupees (Rs) is due in 30 days. What is the cost i dollars if the 30-day forward rate is Rs.64.39/$. Purchase price in Indian Rupees Forward rate Cost in US $

22,779,750

Rs/$

64.39 $

353,778

n software firm for design 30 days. What is the cost in

21.11

Forward rate: Use the data in Exhibit 21.5 to answer these questions: a. What is the six-month forward rate (in US dollars) for Swiss francs? Is the Swis b. What is the six-month forward rate (in US dollars) for the Japanese yen? Is the c. Given the information above, what do think will happen to the value of the U.S. d

The forward premium (discount) =

future 1.045

The forward premium (discount) =

1.0003

For both [a] and [b] remember these are six-month rates so to annualiz c.

Given the data on forward rates in [a] and [b] above, we can expect the the Canandian dollar can be expected to depreciate relative to the U.S.

swer these questions: ars) for Swiss francs? Is the Swiss franc selling for a premium or a discount? ars) for the Japanese yen? Is the Japanese yen selling for a premium or a discount? happen to the value of the U.S. dollar relative to the Japanese yen and Swiss franc? present 1.0434 1.0048

Premium (Discount) 0.003066897 so there is a forward premium on the Swiss franc. -0.008957006

so there is a forward discount on the Canadian dollar.

are six-month rates so to annualize, multiply the premium or discount by 2.

and [b] above, we can expect the Swiss franc to appreciate relative to the U.S. dollar and d to depreciate relative to the U.S. dollar.

21.12

Bid-ask spread: Nova Scotia Bank offers quotes on the Canadian dollar as given here. What is the bid-ask spread based on these quotes? Bid C$ 0.9973/$

Ask C$ 0.9978/$

Bid quote

C$/$

0.9973

Ask quote

C$/$

0.9978

Bid-Ask Spread

0.0501%

e Canadian dollar as quotes?

21.13

Bid-ask spread: A local community bank has requested foreign exchange quotes for the Swiss Franc from Citibank. Citibank quotes a bid rate of $1.0934/SF and an ask rate of $1.0997/SF. What is the bid-ask spread?

Bid quote

1.0934 $/SF

Ask quote

1.0997 $/SF

Bid-ask spread

0.573%

ted foreign exchange otes a bid rate of he bid-ask spread?

21.14

Bid-ask spread: A foreign exchange dealer is willing to buy the Danish krone (DKr) at $0.1556/DKr and will sell it at a rate of $0.1563/DKr. What is the bid-ask spread on the Danish krone?

Bid quote

0.1556 $/DKr

Ask quote

0.1563 $/DKr

Bid-ask spread

0.448%

21.15 Cross rate: Given the following quotes, calculate the €/£ cross rate. Bank of America $1.663/£ Chase $1.3914/€

Bank of America quote

1.663 $/£

Chase quote

1.3914 $/€

Cross Rate (€/£)

1.1952 €/£

21.16

Cross rate: Barclays Bank of London has offered the following exchange rate quo ¥134.64/£ and Korean won 13.8374/¥. What is the cross rate between the Korean won and the British pound? ¥/£

134.64

Korean Won/¥

13.8374

Cross Rate: Korean Won/£

1863.07

21.17

Cross Rate:

Cross rate: Bremer Corporation observes that the Swiss franc (SF) is being quoted at €0.7660/SF, while the Swedish krona (SK) is quoted at €0.1114/SK. What is the SK/SF cross rate? €/SF

0.766

€/SK

0.1114

SK/SF

6.8761

wiss franc (SF) is (SK) is quoted at

21.21

Forward premium: The spot rate on the London market was £0.05514/$, while the 90-day forward rate was £0.5589/$. What is the annualized forward premium or discount on the period?

Spot rate £/$ Term Forward rate £/$

0.5514 90 days 0.5589

Annual Forward Premium

5.441%

arket was £0.05514/$, s the annualized

21.22

Spot rate Term Forward rate

Forward premium: Bank of America quoted the 180-day forward rate on the Swiss franc at $1.0407. The spot rate was quoted at $1.0268/SF. What is the forward premium or discount on the Swiss franc? $/SF $/SF

Annual Forward Premium

1.0268 180 days 1.0407 2.707%

day forward rate on the 1.0268/SF. What is the

21.23 Forward premium: The foreign exchange department at Tokyo’s Daiwa Bank quoted rate on the Euro at €0.007269/¥. The 90-day forward rate is quoted at a premium of 5. percent on the Euro. What is the 90-day forward rate? Spot rate Term Forward rate premium

€/¥

0.007269 90 days 5.42

90-day forward rate

€/¥

0.00727

Tokyo’s Daiwa Bank quoted the spot is quoted at a premium of 5.42

21.24 Forward premium: The spot rate for the Australian dollar (A$) is A$1.1667/$. The Australian dollar is quoted at a 30-day forward of 4.90 percent against the U.S. dollar. What is the 30-day forward quote? Spot rate Rs/$ Term Forward rate premium %

1.1667 30 days 4.90

30-day forward rate

1.17146

Rs/$

alian dollar (A$) is 30-day forward of 4.90 day forward quote?

21.25

Bid Quote

Bid-ask spread: The foreign exchange department of Bank of America has a bid quote on Canadian dollars (C$) of C$1.0800/$. If the bank typically tries to earn a bid-ask spread of 0.5 percent on these foreign exchange transactions, what will the ask rate have to be? C$/$

Bid-Ask Spread Ask Rate

1.0800 0.50% 1.08543

f Bank of America has f the bank typically tries gn exchange

21.26

Bid-ask spread: Banco Santiago wants to make a bid-ask spread of 0.65 percent on its foreign exchange transactions. If the ask rate on the Mexican peso (MP) is MP10.3092/$, what does the bid rate have to be?

Ask quote MP/$

10.3092

Bid-Ask Spread

0.65%

Bid Rate

MP/$

10.2421902

k spread of 0.65 e on the Mexican be?

21.27 Cross rate: Alcor Pharma just received revenues of $3,165,300 in Australian dollars (A Management has the following exchange rates: A$1.8010/£ and $1.5906/£. What is th value of the company’s revenues? Revenues received in A$ Exchange rate

3,165,300

A$/£

1.801

$/£

1.5906

$/A$

0.883176013

US$ value of revenues

$ 2,795,517.03

Cross rate

0 in Australian dollars (A$). d $1.5906/£. What is the U.S. dollar

21.28 Cross rate: Flint Corp. recently purchased auto parts worth 17.5 million Mexican peso (MP). Management needs to find out the U.S. dollar cost of the payables. It has access to two quotes for Canadian dollars (C$): C$1.0174/$ and C$0.0820/MP. What will it co Flint to purchase 17.5 million Mexican pesos? Cost of auto parts in Mexican Pesos (MP) Exchange rate

Cross rate

17,500,000

C$/$

1.0174

C$/MP

0.0820

$/MP

US$ cost of payables

0.080597602 $ 1,410,458.03

17.5 million Mexican pesos he payables. It has access 0.0820/MP. What will it cost

21.29 Hedging: Tricolor Industries has purchased equipment from a Brazilian firm for a total Brazilian reals. The firm has to pay in 30 days. Citicorp has given the firm a 30-day forw $0.4723/real. Assume that on the day the payment is due, the spot rate is at $0.4917/r would Tricolor save by hedging with a forward contract? Cost of equipment

272,500 Brazilian reals

30-day forward quote

$/real

0.4723

Spot rate on day of payment

$/real

0.4917

Cost of purchasing dollars at forward rate

128701.75

Costof purchasing dollars at spot rate after 30-days

133988.25

Saving due to hedging with a forward contract

5,286.50

om a Brazilian firm for a total cost of 272,500 s given the firm a 30-day forward quote of the spot rate is at $0.4917/real. How much

21.30 Eurocredit loan: A Swiss sporting goods company borrows in yen in the Eurocredit m rate of 4.35 percent from Bank of America using a three-month rollover loan. Bank o assigns a default risk premium of 2 percent on the loan, and the country risk is an add 0.75 percent. The bank can borrow funds in the Euromarket at the three-month LIBO 0.40 percent. What is Bank of America's gross profit margin on the loan? K BR DRP CR

0.0435 loan rate on 3 month rollover loan frim Bank of America 0.004 Bank can borrow at the 3-month LIBOR 0.02 default risk priemium 0.0075 additional country risk priemium

GPMAR

0.012 gross profit margin on the loan

ows in yen in the Eurocredit market at a month rollover loan. Bank of America and the country risk is an additional rket at the three-month LIBOR rate of rgin on the loan? frim Bank of America

21.31 Hedging: Covington Industries sold equipment to a Mexican firm. Payment of 11,315,000 pesos will be due in 30 days. Covington has the option of selling the pesos at a 30-day forward rate of $0.09139/peso. If it waits 30 days to sell the Pesos, the expected spot rate is $0.0907/peso. In dollars, how much better off is Covington by selling the pesos in the forward market? Equipment selling price

11,315,000

90-day forward quote

0.09139

Expected Spot rate after 30 days

0.0907

Dollar revenue that will be received by selling the pesos forward Dollar revenue that will be received by selling the pesos at the spot rate Additional dollar revenue received by selling the peso forward

Mexican firm. Payment of has the option of selling the t waits 30 days to sell the llars, how much better off is ? pesos $/peso $/peso $

1,034,077.85

1,026,270.50

7,807.35

21.32 Hedging: Barrington Fertilizers, Inc., exports its specialized lawn care products to Can C$1,150,000, with the payment due in 90 days. Its banker has given it a forward quote forward rate, the firm gains an additional $8,433.25 over what it would have gotten if it the spot market 90 days later. What was the spot rate at the time the payment was rec Sale of lawn care products

1,150,000 C$

Payment due in Forward rate quote Gains due to forward hedge

90 days 0.9021 $/C$ $8,433.25

Proceeds in US$ based on 90-day forward rate

$ 1,037,415.00

Proceeds in US$ if spot rate had been used

$1,028,981.75

Spot rate of $/C$ 90 days later

$0.8948 $/C$

d lawn care products to Canada. It has just made a sale worth has given it a forward quote of $0.9021/C$. By using the what it would have gotten if it had sold the Canadian dollars in he time the payment was received?

Capital budgeting: Moon Rhee Auto Supply, a Korean supplier of parts to Kia Motors, is evaluating an opportunity to sey up a plant in Alabama, where Ki has an auto assembly plant for its SUVs. The cost of this plant will be $13.5 m The current spot rate is 1,120.318 Korean won per U.S. dollar. The firm is expe use this plant for the next five years and is expecting to generate the following c The firm uses a discount rate of 9 percent for projects in the United States.

21.33

Years Cash flows (millions of U.S. Expected exchange rate (Won/$)

1 2.3 1105.231

2 4.2 1115.632

What is the NPV of this project? Should Moon Rhee Auto Supply take on this p

(1) Year

0 1 2 3 4 5 Discount Rate NPV Decision Year 0 1 2 3 4 5

(2) Cash Flow $ (millions) -13.5 2.3 4.2 3.6 5.8 7.6

(3) EFX Rate (KWN/$)

(5) Cash Flow(KWN)

1120.318 1105.231 1115.632 1146.155 1120.221 1110.67

(15,124.29) 2,542.03 4,685.65 4,126.16 6,497.28 8,441.09

9% 4,426.79 KWN Accept the project, since NPV > 0 Cash Flows ######## 2,542.03 4,685.65 4,126.16 6,497.28 8,441.09

PVIF 1.00000 0.91743 0.84168 0.77218 0.70843 0.64993

NPV (15,124.29) 2,332.14 3,943.82 3,186.15 4,602.84 5,486.13 4,426.79

orean supplier of parts to a plant in Alabama, where Kia Motors t of this plant will be $13.5 million. U.S. dollar. The firm is expected to ng to generate the following cash flows. ects in the United States. 3 4 5 3.6 5.8 7.6 1146.155 1120.221 1110.67

ee Auto Supply take on this project?

21.34 Boeing Corp. has two different debt issues, both maturing four years from now. The dom pays semiannual coupons and has a coupon rate of 4.80 percent. The current price on The Eurobond issue is priced at $964.33 and pays an annual coupon of 4.95 percent. W maturity for each bond? Frequency Coupon rate $coupon Maturity Face Value Domestic Bond semi-annual 4.80% 24.00 4 $1,000 Eurobond

annual

4.95%

49.50

$1,000

four years from now. The domestic bond issue percent. The current price on the bond is $962.75. ual coupon of 4.95 percent. What is the yield to

Current Price $962.75

Yield to Maturity 5.94%

$964.33

5.98%

21.35 Caterpillar, Inc. management is trying to decide between selling a new bond issue in th market. In either market the bonds will be denominated in dollars and will have a three bonds will have a coupon rate of 4.1 percent and sell at a market price of $1,034.25. T coupon rate of 4 percent and will sell at $1,029.76. Which bond issue will have the low

Frequency Coupon rate $coupon Maturity Domestic Bond semi-annual 4.10% 20.50 3 Eurobond

annual

4.00%

40.00

The lower cost choice for Caterpillar is the domestic bond with a yield of 2.92%

decide between selling a new bond issue in the U.S. or the Eurodollar bond be denominated in dollars and will have a three-year maturity. The domestic rcent and sell at a market price of $1,034.25. The Eurobonds will have a $1,029.76. Which bond issue will have the lowest cost to the firm?

Face Value

Current Price $1,000 $1,034.25 $1,000

stic bond with a yield of 2.92%

$1,029.76

Yield to Maturity 2.92% 2.95%

21.36 IBM’s German unit is looking to borrow €7.5 million from Deutsche Bank. Deutsche Bank quotes a rate of three-month LIBOR plus 0.25 percent for the 90-day loan. Currently, the three-month LIBOR is 3.875 percent. What is IBM’s interest cost on the loan in Euros? If the exchange rate on the payoff date is €0.8164/$, what is the dollar cost of the loan? Proposed loan amount 7,500,000 Euros 3-month LIBOR 3.875% Add-on 0.25% Exchange rate on payoff date 0.8164 €/$ Interest cost in Euros Interest cost in dollars

77,343.75 € $ 94,737.57

21.37 Toyota is interested in borrowing $5 million for 90 days. Bank of America has quoted a rate of 1.125 percent under the prime rate of 6.25 percent. Daiwa Bank is offering Toyo a rate of 0.75 percent over the three-month LIBOR of 4.2 percent. Which is the better d for Toyota, and what is the lower interest cost in dollars? Loan Amount $5,000,000 Term 90 days Bank of America rate Prime 6.25% less 1.125% Daiwa Bank rate LIBOR plus

4.20% 0.75%

Interest cost of Bank of America Loan Interest cost of Daiwa Loan Better Deal

64,062.50 61,875

Daiwa Loan

k of America has quoted a Daiwa Bank is offering Toyota rcent. Which is the better deal

STP #21.2 If a Dell Studio laptop sells for $999 in Austin and £689 in London, what is the implied exchange rate between the U.S. dollar and the euro?

STP #21.3

A bank in India has offered a spot rate quote on Indian rupees (Rs) of Rs62.2 a 30-day forward premium of 5.22 percent against the dollar. What is the 30-

n rupees (Rs) of Rs62.2905/$. The Indian rupee is quoted at e dollar. What is the 30-day forward quote?

STP #21.4 Technocorp has purchased industrial parts from a German company for a total cost of €1,225,000. The firm has 30 days to pay. A bank has given Technocorp a 30-day forward rate of $1.355/€. Assume that on the day the payment is due, the spot rate is $1.368/€. How much would Technocorp have saved by hedging with a forward contract?

erman company for a . A bank has given me that on the day the would Technocorp have

STP #21.5 Tass Co., Ltd, a Japanese electrical parts producer, is considering building a plant in of this plant will be $20 million and the current spot exchange rate between the yen a ¥101.8/$. Tass management expects to use this plant for the next five years and exp the following cash flows during this period. Year 1 Cash flows ($ millions) $2.0 Expected exchange rate ¥101.5/$

If Tass uses a discount rate of 8 percent for projects in the United States, what is the project? Should Tass Company take on this project?

s considering building a plant in the U.S. The cost xchange rate between the yen and the U.S. dollar is nt for the next five years and expects it to generate

2 $3.6 ¥100.4/$

Year 3 $5.0 ¥98.6/$

4 $6.8 ¥95.9/$

5 $8.0 ¥92.5/$

in the United States, what is the NPV of this