SOLUTIONS MANUAL for Finance Essentials, 1st Edition by Kidwell, Brimble, Kingsbury, Mazzola & James

Module 1: Finance in business Self-study problems 1.1

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

Financing decisions determine how a company will raise capital. Examples of financing decisions would be securing a bank loan or the sale of debt in the public capital markets.

Capital budgeting involves deciding which productive assets the company invests in, such as buying a new plant or investing in a renovation of an existing facility.

1.2

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

Financial managers should only select a capital project if the value of the project’s future cash flows exceeds the cost of the project. In other words, managers should only take on investments that will increase the company’s value and thus increase the shareholders’ wealth.

1.3

What are some ways to manage working capital?

Working capital is the day-to-day management of a company’s short-term assets and liabilities. It can be managed through maintaining the optimal level of inventory, keeping track of all the receivables and payables, deciding to whom the company should extend credit, and making appropriate investments with excess cash.

1.4

Which one of the following characteristics does not pertain to companies? a. Can enter into contracts b. Can borrow money c. Are the easiest type of business to form d. Can be sued e. Can own shares in other companies c. Are the easiest type of business to form – companies have a complex business structure.

1.5

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

The three main components of an executive compensation package are: base salary, bonus based on accounting performance, and some compensation tied to the company’s share price.

Module 1: Finance in business

Critical thinking questions 1.1

Describe the cash flows between a company and its stakeholders.

Cash flows are generated by a company’s productive assets that were purchased through either issuing debt or raising equity. These assets generate revenues through the sale of goods 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 shareholders in the form of dividends.

1.2

What are the three fundamental decisions the financial management team is concerned with, and how do they affect the company’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 company needs to buy productive assets. This is typically accomplished by selling longterm debt and equity. Finally, working capital decisions involve how companies manage their current assets and liabilities. The focus here is seeing that a company has enough money to pay its bills and that any spare money is invested to earn interest.

1.3

What is the difference between shareholders and stakeholders?

Shareholders are the owners of the company. A stakeholder, on the other hand, is anyone with a claim on the assets of the company, including, but not limited to, shareholders.

Stakeholders are the company’s employees, suppliers, creditors, and the government.

1.4

Explain why profit maximisation is not the best goal for a company. What is an appropriate goal?

Although profit maximisation 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 profit for similar companies can vary widely. Second, accounting profits do not exactly equal cash flows. Third, profit maximisation 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 maximise the value of the company’s current share 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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

1.5

In determining the price of a company’s shares, what are some of the external and internal factors that affect price? What is the difference between these two types of variables?

External factors that affect the company’s share 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 share price can be controlled by management to some degree, because they are company specific, such as financial management decisions, product quality and cost, and the line of business management has selected to enter.

Finally, perhaps the most important internal variable that determines the share price is the expected cash flow stream: its magnitude, timing, and riskiness.

1.6

Identify the sources of agency costs. What are some ways a company can control these factors?

Agency costs are the costs that result from a conflict 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 or 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 labour market.

1.7

What is CLERP 9 and what are its main goals?

CLERP 9 is the outcome of a review of corporate reporting and disclosure laws in Australia. The main goal of CLERP 9 is to strengthen the law in the areas of corporate governance, disclosure and regulation of audit and financial reporting. Among others, CELRP 9 will strengthen the standard for auditor independence, including requiring the rotation of auditors of listed companies after 5 years, strengthen the obligations of auditors to report breaches of the law to ASIC, and enhance disclosure and accountability to shareholders, including on executive and director remuneration.

Module 1: Finance in business

1.8

Give an example of a conflict of an interest in a business setting other than the one involving the real estate agent discussed in the text.

For example, imagine a situation in which you are a financial officer at a growing software company and your company has decided to hire outside consultants to formulate a global expansion strategy. Coincidentally, your wife works for one of the major consulting companies 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 company, because it will benefit your family’s financial situation if she lands the contract, regardless of whether it makes the best sense for your company.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Questions and problems BASIC 1.1

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

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

1.2

Management role: What is working capital management?

It is the management of current assets, such as inventory, and current liabilities, such as money owed to suppliers.

1.3

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

A profitable company is able to generate more than enough cash through its productive assets to cover its operating expenses, taxes, and payments to creditors. Unprofitable companies fail to do this, and therefore they may be forced to declare insolvency.

1.4

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

Financial managers are most concerned about the capital budgeting decision, the financing decision, and the working capital decision.

1.5

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

A company should undertake a capital project only if the value of its future cash flows exceeds the cost of the project. For example: undertaking a capital project that requires a cash outlay of $10,000 when the present value of all future cash flows from the project is more than the initial outlay of $10,000.

1.6

Management role: What is capital structure, and why is it important to a company?

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.

Module 1: Finance in business

1.7

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

Working capital management is the day-to-day management of a company’s current assets and liabilities to make sure that there is enough cash to cover operating expenses and there is spare cash to earn interest. The financial manager has to make decisions about the inventory levels or terms of collecting payments (receivables) from customers.

1.8

Organisational form: What are the three basic forms of business organisation discussed in this module?

The three basic forms of business organisation we discussed are sole trader, partnership, and company.

1.9

Organisational form: What are the advantages and disadvantages of becoming a sole trader?

Advantages: • It is the easiest business type to start.

• It is the least regulated.

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

Disadvantages: • The sole trader has an unlimited liability for all business debt and financial obligations of the company.

• The amount of capital that can be invested in the company is limited by the sole trader’s wealth.

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

1.10

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

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 organisation’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 contributed to the partnership.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

1.11

Organisational form: Who are the owners of a company, and how is their ownership represented?

The owners of a company are its shareholders, and the evidence of their ownership is represented by proportions of ordinary shares. Other types of ownership do exist and include preferred shares.

Module 1: Finance in business

MODERATE 1.12

Organisational form: Explain what is meant by shareholders’ limited liability.

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

1.13

Organisational form: What is the business organisation form preferred by companies that require a large capital base, and why?

A company can list on securities exchange, such as the Australian Securities Exchange (ASC) as a public company to gain access to the public markets.

1.14

Finance function: What is the most important governing body within a business organisation? What responsibilities does it have?

The most important governing body within an organisation is the board of directors. Its main role is to represent the shareholders. The board also hires (and occasionally fires) the CEO and advises him or her on major decisions.

1.15

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

An independent public accounting firm that performs an audit of a company 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 company’s performance.

1.16

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

• • •

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.

It ignores the uncertainty of risk of cash flows.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

1.17

Company’s goal: What is the appropriate goal of financial managers? Can managers’ decisions affect this goal in any way? If so, how?

The appropriate goal of financial managers should be to maximise the current value of the company’s share price. Managers’ decisions affect the share price in many ways as the value of the share is determined by the future cash flows the company 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.

Module 1: Finance in business

CHALLENGING 1.18

Company’s goal: What are the major factors affecting share price?

The following factors affect the share price: the company, the economy, economic shocks, the business environment, expected cash flows, and current market conditions.

1.19

Agency conflicts: What is an agency relationship, and what is an agency conflict?

How can agency conflicts be reduced in a company?

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

1.20

Company’s goal: What can happen if a company is poorly managed and its share price falls substantially below its maximum?

If the share 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.

1.21

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

Some of the regulations include: a. The majority of board members must be outsiders. b. A separation of the CEO and chairman of the board positions is recommended. c. The CEO and CFO must certify all financial statements.

1.22

Business ethics: How could business dishonesty and low integrity cause an economic downfall? Give an example.

Business dishonesty and lack of transparency lead to corruption, which in turn creates inefficiencies in an economy, inhibits the growth of capital markets, and slows the rate of economic growth. For example, until the mid-1990s the Russian market had a difficult time attracting investors as there was no reliable financial information on any of the companies. Only after the Russians made a conscious decision to make their records and motives transparent were they able to draw foreign investments.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

1.23

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

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 company, 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 parties. This is, for example, the case with accounting companies not being allowed to serve as consultants to companies for which they perform audits.

1.24

Business ethics: What ethical conflict does insider trading present?

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.

Module 2: The financial system Self-study problems 2.1

Economic units that need to borrow money are said to be: a. lender–savers. b. borrower–spenders. c. balanced budget keepers. d. none of the above.

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

2.2

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

Marketability refers to the ease or difficulty with which securities can be sold in the market. The level of marketability depends on many factors, such as the security’s coupon and maturity, as well as all the transaction costs: cost of trading, physical transfer cost, and search and information cost. The lower these costs are, the greater the security’s marketability.

2.3

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

OTC is a market for securities that are not listed on one of the organised exchanges. It differs from organised exchanges in that there is no central trading location, but rather the securities transactions are made via phone or computer as opposed to the floor of an exchange. Usually, small companies that could not qualify for one of the exchanges trade their share OTC.

2.4

What are the most important international financial markets for Australian firms?

The most important international financial markets for Australian firms are the short-term US market and eurocurrency market, and the long-term Eurobond market. In these markets, domestic and overseas firms can borrow or lend large amounts of Australian dollars that have been deposited in overseas banks.

Module 2: The financial system

2.5

Discuss three forms of financial market efficiency. Why is it important that financial markets be efficient?

The three forms of financial market efficiency are: 1) strong-form efficiency; 2) semistrong-form efficiency; and 3) weak-form efficiency. For a market to be strong-form efficient, all information about a security is reflected in its price. Therefore it would not be possible to earn abnormal returns by trading on private information as it would already be reflected in security prices.

A weaker form of the efficient market hypothesis, the semistrong-form, holds only that all public information is reflected in security prices. In this situation, investors who have access to private information would be able to profit by trading on this information before it becomes public.

The weakest form of the efficient market efficiency is know as the weak-form. It holds that all information contained in past prices of a security is reflected in current prices but there is both public and private information that is not. In a weak-form efficient market, it would not be possible to earn abnormal profits by looking for patterns in security prices, but it would be possible to do so by trading on public or private information.

Market efficiency is important to investors because it assures them that the securities they buy and priced close to their true value.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Critical thinking 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.

2.2

Why don’t small businesses make greater use of the direct credit markets since these markets enable companies to finance themselves at 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 business. Small businesses are better off borrowing money from financial intermediaries, such as commercial banks.

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. 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.

2.4

What are the two basic services that investment banks provide in the economy?

Investment banks specialise in helping companies sell new debt or equity as well as provide other services such as broker and dealer services.

2.5

Many large companies sell commercial paper as a source of funds. From time to time, some of these companies find that they are unable to issue commercial paper.

Why is this true?

Generally, only a small number of large companies with high credit ratings have access to the market at any given time. During economic expansion, the number of companies that can issue commercial paper increases. When the economy is slow, however, companies with lower credit rating tend to be excluded from the market, as investors are looking primarily for low-risk investments that are provided by companies with high credit rating.

Module 2: The financial system

2.6

How do large companies adjust their liquidity in the money markets?

Large companies 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 notes. Large companies with cash surplus can invest in short-term securities, while companies 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.

2.7

Why is globalisation of the international markets important to the Australian financial system?

This is important due to the small size of the Australian system in global terms. Hence internationalisation offers both additional sources of funds (from international investors), opportunities for Australian investors and institutions to diversify into offshore investments, and also a source of competition for domestic institutions which leads to improved efficiency of the domestic system. The impact of these was seen in the GFC where international concerns heavily impacted the Australian financial system. These impacts continued to a number of years as the higher cost of capital in the international markets (which the Australian banks rely upon for funding) put pressure on margins.

2.8

You believe that you can make abnormally profitable trades by observing that the CFO of a certain company always wears his green suit on days that the company is about to release positive information about itself. Describe which form of market efficiency is consistent with your belief.

You believe that the share price of this company is affected by the choice of the CFO’s wardrobe and that this private information will grant you 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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

2.9

Describe the informational differences that separate the three forms of market efficiency.

The strong-form of market efficiency states that all information is reflected in the security’s price. 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.

Module 2: The financial system

Questions and problems BASIC 2.1

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

The role of the financial system is to gather money from businesses and individuals and to channel funds to those who need them. The financial system consists of financial markets and financial institutions.

2.2

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

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 companies with good credit ratings and projects with high rates of return will be financed.

2.3

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

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, although households are important mortgage borrowers.

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?

Funds can flow directly through financial markets or indirectly through intermediation markets where funds flow through financial institutions first.

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 would this mean for the security’s marketability and liquidity?

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 value to the owner. Marketability refers to the ease to which a security can be sold or converted to cash. The information in the problem does mention a drastically lower price and so we must conclude that the security’s marketability in not affected.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

2.6

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

The financial markets are also called wholesale markets because the minimum transaction or security denomination is $1 million or more.

2.7

Financial markets: Tinker Pty Ltd is a $300 million company, as measured by asset value, and Horst Pty Ltd is a $35 million company. Both are privately held companies. Explain which company is more likely to go public and list on the ASX, and why.

Tinker Pty Ltd is more likely to go public. Going through an IPO is a very expensive process, and given Tinker’s higher worth, they are more likely to be positioned to go through with it.

2.8

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

A primary market is where new securities are sold for the first time. IPO stands for initial public offering.

2.9

Primary markets: Identify whether the following transactions are primary market or secondary market transactions. a. Jim Hendry bought 300 shares of AGL Energy through his share broker. b. Candy How bought $5,000 of AGL Energy bonds from the company. c. Hathaway Insurance Company bought 500,000 shares of AGL Energy when the company issued shares. a. Secondary. b. Secondary. c. Primary.

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?

To underwrite a new security issue means that the investment banker guarantees the amount the company wishes to raise in the issue. Any unsold securities are then purchased by the underwriter at the offer price less an underwriting spread and then on sold in the market. In addition to underwriting new securities, investment banks also provide other services, such as preparing the prospectus and other legal documents to be lodged with ASIC, and providing general financial advice to the issuer.

Module 2: The financial system

MODERATE 2.11

Investment banking: Cranbourne Ltd 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. a. What is the underwriting spread for this issue? b. What is the percentage underwriting cost? c. How much did Cranbourne raise? a. $300,000 ($10,150,000 – $985 x 10,000) b. 3.05 per cent ($30/$985) c. $9,850,000 ($985 x 10,000)

2.12

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

A financial intermediary can raise money through the sale of financial products that individuals or businesses will purchase, such as cheque and savings accounts, life insurance policies, or superannuation funds.

2.13

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

Financial intermediation is the process whereby borrowing occurs indirectly from a financial institution that has converted financial securities with one set of characteristics into securities with another set of characteristics for the borrower’s specific need.

2.14

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

The primary financial intermediaries are commercial banks, life and general insurance companies, superannuation funds, and 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.

2.15

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

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 sold.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

2.16

Money markets: What are Australian government Treasury notes?

Treasury notes are a money market instruments issue by the Australian government to meet short term liquidity needs. Money market instruments are lower in risk than other securities because of their high liquidity and low default risk.

2.17

Money markets: Besides Treasury notes, what are other money market instruments?

Other common money market instruments include commercial paper, bank accepted bills, bank negotiable CDs, and other marketable short-term securities.

2.18

Money markets: What is the primary role of money markets? How do money markets work?

Money markets provide an option for large companies to adjust their liquidity positions.

Since only seldom are cash receipts and cash expenditures perfectly synchronised, money markets allow companies to temporarily invest idle cash in Treasury notes or bank accepted bills. If a company is short on cash, it can borrow the money from money markets by selling commercial paper at lower interest rates than borrowing through commercial banks.

2.19

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

Capital market instruments are less liquid or marketable, they have longer maturities, usually between 1 and 30 years, and they carry more financial risk.

2.20

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

Public markets are organised financial markets where the public buys and sells securities through their share brokers. In contrast, private markets involve direct transactions between two parties. ASIC regulates both public and private securities markets in Australia.

2.21

Financial instruments: Explain the two risk-hedging instruments discussed in the module.

The two risk-hedging instruments discussed are futures contracts and options.

Module 2: The financial system

2.22

Market efficiency: Define operational efficiency.

Operational efficiency focusses on bringing buyers and sellers together at the lowest possible cost. That is, it is the market situation in which the costs of conducting transactions are as low as possible.

2.23

Market efficiency: What will happen to market prices if transaction costs are high?

If transaction costs are high, market prices will be more volatile, fewer financial transactions will take place and prices will not reflect the knowledge and expectations of investors as accurately.

2.24

Market efficiency: What costs are associated with a markets operational efficiency?

The costs associated with a markets operational efficiency are called transaction costs.

Transaction costs include broker commissions and other fees and expenses of bringing buyers and sellers together.

2.25

Market efficiency: Why is it important to the broader economy to have an efficient and effective financial system?

A well-developed financial system is critical for the operation of a complex economy such as that of Australia as it facilitates commercial, retail and government transactions in a timely, low cost and reliable way. An economy cannot function efficiently without a competitive and sound financial system that gathers money and channels it into the best investment opportunities. An efficient and effective financial system will also produce actual and timely information to enable effective financial decision making, which is also important in the complex financial world of today.

Module 3: Financial markets Critical thinking questions 3.1

What are the characteristics of money-market instruments? Why must a financial claim possess these characteristics to function as a money-market instrument?

The three fundamental characteristics of money market instruments are: (a) low default risk, (b) short-term to maturity, and (c) high marketability. These characteristics give money market instruments their characteristic of being low risk.

3.2

What types of firms issue commercial paper? What are the characteristics critical to being able to issue commercial paper?

Large high-credit rated businesses issue commercial paper as an inexpensive source of short-term direct borrowing. Commercial paper is an alternative to prime rate borrowing from a commercial bank and, typically, the rates are lower than rates charged by banks.

Most investors, an in attempt to protect their principal, only want paper issued by firms highly rated by rating agencies. Rating agencies will quickly write down or remove their ratings for commercial paper if the financial conditions of a company decease. The number of companies issuing commercial paper in the economic boom of the late 1990s, shrunk considerably by 2001 as rating agencies pulled their commercial paper ratings.

3.3

Explain how a three-for-five rights issue works. Provide an example.

A rights issue is where a company’s shareholders are given the right to purchase additional shares at a slightly below-market price in proportion to their current ownership in the company. Therefore, a three-for-five rights offer at a subscription price of $3 per share allows a shareholder with 5,000 shares to subscribe to another 3,000 shares at $3 each.

3.4

What is a dividend reinvestment scheme? Explain why the record date is important.

A dividend reinvestment scheme allows shareholders to increase their shareholdings gradually by automatically reinvesting their dividends in extra shares as each dividend is ‘paid’. The issued shares are normally issued at either the market price averaged over several days’ trading (often just after the record date for the dividend is declared) or at a slight discount to this price.

Module 3: Financial markets

3.5

Explain the difference between a long sale and a short sale in secondary equity markets.

The investor who buys shares is said to be long, meaning that they have bought and are holding the shares in their portfolio. On the other hand, a short sale is when a speculator thinks they might profit from a fall in the market and sells a security before buying it, waits for the market to fall and then buys the security to make the delivery required from their initial sale.

3.6

Is it true that an Australian government bond is risk-free? Discuss.

Australian government bonds are backed by the full faith and credit of the Commonwealth Government. They are considered to be free of default risk.

3.7

List three types of hybrid securities and the features they might have.

Convertible securities: Debt instruments that can be converted to shares at the discretion of the holder.

Stapled securities: Equity shares and bonds stapled together and cannot be traded separately.

Preference shares: Rank ahead of shares but behind debentures and other forms of debt.

3.8 What are the differences between the futures and the forward markets? What are the pros and cons associated with using each one?

Forward market:

Futures market:

•

The forward market is unstructured and trades over the counter.

Numerous dealers match individual buyers and sellers and/or trade for their own accounts.

No maintenance margin is required.

•

Most forward contracts are settled by delivery.

The forward market is useful when a set amount of currency is needed on a specific date.

No marking to market

•

• • • • •

• •

• •

Futures transactions are conducted on an organised exchange.

Contracts are made between buyers or sellers and the exchange.

Margin requirements are imposed to ensure no one will default when prices move adversely.

Very few contracts are settled by delivery.

The futures market is useful when it is necessary to hedge price risk over a period of time.

Marked to market daily.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

•

All elements of the contract are negotiated.

•

•

Highly illiquid because of customized features.

Default potential is quite high.

•

•

3.9

•

All elements of the contract are standardised (Only price is variable).

Trades on exchanges, and are very liquid.

Clearing house guarantees delivery and payment. Low default risk.

Of the two parties to an option contract, the buyer and the seller, who has a right and who has an obligation?

An option buyer has a right to buy or sell an asset. On the other hand, the option seller (or writer) has an obligation if the other party exercises the option.

3.10

Assume that Australia and Canada are both initially in an economic recession and that Australia begins to recover before Canada. What would you expect to happen to the Australian dollar – Canadian dollar exchange rate? Why? If the Australian economy grew faster than Canada’s, Australians would have higher income and GDP than Canada. The increased income would cause Australian imports to increase causing a trade deficit and possibly a later decline in the AUD.

Module 3: Financial markets

Questions and problems BASIC 3.1

Money markets: Outline the basic operation and economic role of the money markets.

The money markets are where financial and nonfinancial businesses adjust their liquidity positions by borrowing or investing for short periods. The instruments traded in the money markets have low default risk, have low price risk (short terms to maturity), are highly marketable (i.e. they can be bought or sold quickly) and are sold in large denominations, so the per-dollar cost for executing transactions is very low. The most important economic function of the money markets is to provide an efficient means for economic units to conduct liquidity management when their cash expenditures and receipts are not perfectly synchronised.

3.2

Money markets: Describe the cash market.

The cash market is one of the most important financial markets in Australia. It is the market in which commercial banks and other financial institutions lend each other excess funds from their ESAs. Essentially, cash-market transactions are unsecured loans between banks for short periods, in denominations of $1 million or more. The most important role of the cash market is that it facilitates the conduct of monetary policy by the RBA when it conducts open-market operations. The RBA uses repos to affect the amount of liquidity in banks’ ESAs.

3.3

Money markets: Describe the market for Treasury notes.

The most important money-market instrument issued by the Australian Office of Financial Management is the Treasury note (T-note). The government uses T-notes to finance short-term deficits and to refinance maturing government debt. T-notes have maturities of less than a year, are highly marketable and are virtually free of default risk because they are backed by the Commonwealth government. T-notes are considered to be the ideal money-market instrument.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

3.4

Money markets: Outline the market for commercial papers.

Commercial paper is a short-term promissory note issued by a large corporation to finance short-term working capital needs. Commercial paper is viewed as an open-market alternative to bank borrowing, and firms use the commercial paper market to achieve interest savings over otherwise similar bank loans. Commercial paper maturities commonly range from one to 180 days. It is sold in denominations for $100,000 to $1 million. Only firms of good credit quality can issue commercial paper because it is unsecured.

3.5

Money markets: Describe the market for bank-accepted bills.

A bank-accepted bill is a time draft drawn on and accepted by a commercial bank. After repos, they are the most heavily traded instrument in the money market. Often, bankaccepted bills arise inn international trade. The secondary market consists primarily of Australian-dollar acceptance financing in which the acceptor is an Australian bank and the draft is denominated in Australian dollars. Bank-accepted bills typically trade in lots of $100,000, $500,000 and $1 million, and mature in 90, 120 or 180 days. The default risk on bank-accepted bills is very low.

3.6

Equity markets: Describe the major differences between ordinary shares and preference shares.

Dividends Dividends Voting rights Ranking for dividends Claim to assets in liquidation

Ordinary shares Variable Not cumulative Yes Last Last (traditionally)

Preference shares Fixed May be cumulative Mostly no First Second last

Module 3: Financial markets

3.7

Equity markets: Define the following terms as they relate to secondary markets: depth, breadth and resiliency.

Depth – the existence of orders to buy at prices below the current market price and to sell at prices above the current price.

Breadth – the buy and sell orders are in appropriate volume to stabilize the market.

Resilience – new orders flow in to respond to price changes.

3.8

Equity markets: Why are convertible securities more attractive to investors than simply holding a firm’s preference shares or corporate bonds?

Depends on investors’ needs. Convertible securities behave like debt – fixed return, no capital appreciation or loss, but can be converted into shares later (perhaps when company has proven to be successful). Thus, holders retain the opportunity to convert to ordinary shares and share in successes, but enjoy a lower initial risk situation than with direct purchase of shares.

3.9

Bond markets: Which bonds are issued by the Australian Office of Financial Management? Discuss their riskiness.

The AOFM issues Treasury bonds for the Commonwealth Government. They are backed by the full faith and credit of the Commonwealth Government, making them free of default risk.

3.10

Bond markets: What is the main difference between the bond markets and share markets?

The bond market is a decentralised network of market participants, while the stock market is highly centralised consisting of only a few exchanges. Most secondary trading of corporate bonds occurs through dealers, although a few are traded on the ASX. The secondary market for corporate bonds is thin compared with the share markets. This means secondary market trades of corporate bonds are relatively infrequent. As a result, the bid-ask spread quoted by dealers of corporate bonds is quite high compared with those of other more marketable securities such as shares.

3.11

Derivative markets: Explain the difference between a put and a call.

A call is an option to buy at the strike price; a put is an option to sell at the strike price.

Diagrams as per the text.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

3.12

Derivative markets: What is the difference between an American and European option?

An American option is an option that can be exercised at any time until the option expires whereas, European options can only be exercised at expiry.

3.13

Derivative markets: What is the role of the clearinghouse in a futures market?

The clearinghouse acts as the counterparty to all buyers and all sellers. This means that traders need not worry about the creditworthiness of the party they trade with but only about the wisdom of the transaction itself.

3.14

Foreign exchange markets: Discuss the globalisation of financial markets.

A complex interaction of historical, political and economic factors drive the globalisation of financial markets. Historical and political factors include the demise of the Bretton Woods system of fixed exchange rates and the fail of the Soviet Union. Economic factors include the disruption caused by widely fluctuating oil prices, the large trade deficits experienced by the United States, Japan’s rise of financial pre-eminence during the 1980s and its weakness in the 1990s and early 2000s, the global economic expansion that began in late 1982, the Asian economic crisis in the late 1990s and the adoption of the euro in 1999.

Long-term economic and technological factors that have promoted the internationalisation of financial markets include the global trend towards financial deregulation, standardisation of business practices and process, ongoing integration of international product and service markets, and breakthroughs in telecommunications and computer technology.

Module 3: Financial markets

MODERATE 3.15

Money markets: Describe the steps in a typical banker’s acceptance transaction.

Why is the banker’s acceptance form of financing ideal in foreign transactions?

Banker’s acceptance provides two basic services: (a) financing, and (b) services and expertise specifically related to an international transaction. It is the latter that makes banker’s acceptances an attractive means of financial international transactions.

3.16

Equity markets: Why are convertible securities more attractive to investors than simply holding a firm’s preference shares or corporate bonds?

Depends on investors’ needs. Convertible securities behave like debt – fixed return, no capital appreciation or loss, but can be converted into shares later (perhaps when company has proven to be successful). Thus, holders retain the opportunity to convert to ordinary shares and share in successes, but enjoy a lower initial risk situation than with direct purchase of shares.

3.17

Bond markets: Explain what Commonwealth government securities (CGS) and semi-government securities (semis) are, where they are issued and their relative liquidity.

CGS are Treasury bonds and T-notes, issued by the Australian Office of Financial Management. Semis are bonds issued by state and territory borrowing authorities backed by their respective governments. The amount of CGS on issue has been declining from 1996. However, this trend is now reversed as the federal government is expected to run budgetary deficits for the next several years and needs to fund these by issuing new CGS. The Commonwealth government has decided to support the Treasury bond futures market by maintaining current levels of securities in the market. Treasury bonds are important instruments because they carry no default risk and are useful in managing interest rate risk across the economy. Semis are often issued offshore and can be exchanged for domestic issues Although they are not as liquid as CGS domestically, the ability to exchange them raises their liquidity offshore and makes them more attractive to investors.

Also dissimilarly to CGS, semis are issued through dealer panels and not an open tender.

3.18

Derivative markets: Explain how financial-market participants use futures.

Financial-market participants use futures to insulate themselves against changes in interest rates and asset prices. Financial futures can be used to reduce the systematic risk of share portfolios or to guarantee future returns or costs.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

3.19

Derivative markets: Why do you think some futures contracts are more widely traded than others?

Because price volatility is wider for some markets than others and some contracts involve financial instruments or commodities in which a great number of people have an interest in reducing price risk. Also, some contracts are more popular because of exchange encouragement and others have greater appeal to speculators.

3.20

Derivative markets: Explain how options can be used to manage a company'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 received for products that will be delivered in the future can purchase put options to partially or totally eliminate that risk.

3.21

Derivative markets: Define a call option and describe its pay-off function.

A call option is the right, but not the obligation, to buy an asset for a given price on or before a specific date. The price is called the exercise or trike price, and the date is called the exercise date or expiration date of the option. The pay-off from a call option equals $0 if the value of the underlying asset is less than the exercise price at expiration. If the value of the underlying asset is higher than the exercise price at expiration, then the payoff from a call option is equal to the value of the asset minus the exercise price.

3.22

Derivative markets: Define a put option and describe its pay-off function.

A put option is the right, but not the obligation, to sell an asset for a given price on or before a specific date. The price is called the exercise or trike price, and the date is called the exercise date or expiration date of the option. The pay-off from a put option is $0 if the value of the underlying asset is greater than the exercise price at expiration. If the value is lower than the exercise price, then the pay-off from a put option equals the exercise price minus the value of the underlying asset.

3.23

Derivative markets: Futures contracts on share indices are very popular. Why do you think that is so? How do you think they might be used?

By buying index futures an individual can predict the trend of the market without buying individual shares. These also allow individuals to neutralise their portfolios if they expect temporary share price declines without incurring the transaction costs associated with selling shares.

Module 3: Financial markets

3.24

Derivative markets: Your company, 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?

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. Since the price of oil went down, you would let the call option expire without exercising it. Of course, the benefit your company receives from the drop in oil prices will be reduced by the amount that you paid to purchase the option.

3.25

Derivative markets: How can a credit union guarantee its costs of funds for a period of time by using the futures market?

By selling 90-day BAB, 3-year bond or 10-year bond futures short for up to several years in the future, it can guarantee that its net costs of funds will approximately equal the rates at which it sold short plus the usual risk premium it pays on its CDs.

3.26

Foreign exchange markets: Describe several of the factors which have promoted the internationalization of financial markets during the past 15 years. Are any of these factors reversible?

The following factors have, in a variety of ways contributed to the internationalisation of financial markets.

1.

2.

3.

4.

5.

6.

7.

8.

The demise of fixed exchange rates in Eastern Europe and in Asia.

The revitalisation of Eastern Europe.

The extraordinary budget and trade deficits of the United States since 2001.

The slowdown of Japan’s growth being offset by the developing economies in Asia, Eastern Europe and Latin America.

The development toward a unified European Economic Community, a common central bank, and currency has begun to congregate a powerful economic force, especially since 2003.

The global trends toward financial deregulation.

The continuing integration of international product and service markets.

Improved telecommunications and computer technology leading to round the clock trading.

Despite the events of September 11, 2001 in the U. S., continuing growth of terrorism in the Middle east, and Europe, the ongoing conflict in Iraq and in the Palestine region, the increasing economic dependence upon other countries, growing environmental problems requiring cooperation, and continued improvements in telecommunications and computer technology are moving world trade and financial markets toward 24-hour, continuous trading.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

3.27

Foreign exchange markets: How does inflation affect a country's spot and forward exchange rates? Why? Is it absolute inflation or inflation relative to other countries that is important?

Inflation causes forward exchange rates to depreciate relative to spot exchange rates - if countries' prices are expected to be stable. Again, it is relative inflation that is important.

If other countries' prices were expected to inflate at the same rate, forward rates would still equal spot rates - assuming all countries' interest rates were the same.

Module 4: The Reserve Bank of Australia and interest rates Self-study problems 4.1

Will a drop in the cash rate affect inflation? Explain.

Theoretically a lower cash rate will cause inflation to rise. This occurs through the following mechanism: a drop in the cash rate will stimulate borrowing, investment and economic activity. The increased demand for resources will put upward pressure on the prices of resources and may lead to inflation.

4.2

What defensive actions do you suppose the RBA takes during days when pensions are paid and cash holdings by the public increase? In other words, how does the RBA offset these cash increases?

Given that the crediting of pensions to pensioners’ bank accounts causes an injection of funds into the money supply; the monetary base increases and the cash interest rate falls.

The RBA would undertake offsetting actions so that there would be no change to the cash interest rate and it would aim to reduce the excess cash holdings. They achieve this by “mopping up” the excess cash holdings by selling commonwealth government securities (CGS) to the public. As the public pay for these securities their bank accounts are debited and there is a transfer of funds from the public to the RBA reducing the amount of cash in circulation.

4.3

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

An increase in the demand for business goods and services will cause the desired borrowing schedule to shift to the right, thus increasing the real rate of interest. Other factors that contribute to increases in the real interest rate are, for example, increases in technological inventions and a reduction of corporate tax rates. Demographic factors, such as growth and age of the population, as well as cultural differences, also affect the real rate of interest.

4.4

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

Both the interest and inflation rates follow the business cycle; that is, they rise with economic expansion and fall in time of recession.

Module 4: The Reserve Bank of Australia and interest rates

4.5

Define the concept of the real rate of interest and explain what causes it to rise and fall.

The real rate of interest is the fundamental long-run interest rate in the economy. At the market equilibrium interest rate, desired savings by savers equal desired investments by producers. The real rate of interest prevails under the assumption that there is no inflation in the economy. Any economic factor that causes a shift in desired lending or borrowing will cause a change in the equilibrium rate of interest.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Critical thinking questions 4.1

When you arrive home from an overseas trip, you have $US500 left in $100 bills.

You exchange these at the airport for Australian dollars. Has money supply increased?

No. The AUD you receive was previously part of MS - that is, part of the notes and coins in circulation and remains so.

4.2

Why does the RBA restrict its trading transactions to government and semigovernment securities in the main?

The RBA is risk-averse and needs to deal in low-risk, highly traded securities where the pricing mechanism is likely to work well and adjust efficiently virtually instantaneously.

There has been an ongoing shortage of low risk securities over the period June 1997 through to June 2008 as the Australia Federal Government had paid off much of its public debt by the sale of public assets and by running budget surpluses (where tax receipts are greater than government expenditures). The shortage of CGS on issue and available for trading forced the government to expand the range of securities it would accept for repo agreements In 1997, it agreed to accept state government securities and, in 2001 and 2002, it decided to accept some other low-risk securities issued abroad but denominated in Australian dollars (euro-Australian dollars). In 2004, it expanded the list of acceptable securities even further.

4.3

Does an increase in the age pension payments affect money supply? Explain.

Yes. The total amount of transfer payments including pensions will increase, thus increasing MS.

Module 4: The Reserve Bank of Australia and interest rates

4.4

The more goals you have, the less likely you will achieve all to the same degree. Which goals do you think are the most important for the RBA to achieve? Why? The RBA is charged with the responsibility to use monetary policy to best achieve: (a) the stability of the currency of Australia; (b) the maintenance of full employment in Australia; and (c) the economic prosperity and welfare of the people of Australia.

Inflation control and steady economic growth are considered the most important goals but there are a number of political and social goals which centre on preserving individual rights, freedom of choice, equality of opportunity, equitable distribution of wealth, individual health and welfare and the safety of individuals and society as a whole.

Economically, the goals typically centre on obtaining the highest overall level of material wealth for society as a whole and for each of its members. Some under-employment of resources is often inevitable and can stem from factors other than monetary policy.

4.5

Why is rampant inflation considered “a bad thing” for an economy when obviously house prices rises and home owners receive windfall gains?

Rampant inflation severely affects the distribution of welfare and wealth within an economy. Physical asset holders and the indebted are favoured as these asset prices tend to rise with inflation (example gold, house prices); whereas debt holders are punished as they receive a fixed repayment over the life of the loan. Workers with market power are favoured, that is they can negotiate higher wages to take account of the higher inflation; fixed-income recipients are punished as they cannot change their income so have lost purchasing power.

4.6

In your view, has the RBA’s monetary policy management been successful in the past decade? Explain your answer.

Yes. The RBA is charged to keep inflation within check while at the same time endeavour to have Australia’s resources fully employed and the economy steadily growing. It has achieved all these things despite the global financial crisis.

4.7

If the RBA thinks the Australian dollar is selling for a good price in US dollars and decides to sell $100 million, what is the likely (micro) effect on the exchange rate and on money supply?

Every sale of AUD and purchase of USD marginally puts pressure on the price of each currency – downward on the AUD and upward on the USD. If the RBA sells $A100 million to Australian market dealers for USD, the MS will rise by $100 million.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

4.8

Shouldn’t the nominal rate of interest (equation 4.3) 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.

4.9

When determining the real interest rate, what happens to businesses that find themselves with unfunded capital projects whose rate of return exceeds the companies’ 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 company such as introducing a new technology that will increase the rate of return on projects for the company.

4.10

How does figure 4.5 help explain why interest rates were so high during the 1980s as compared to the relatively low interest rates in the early 2000s?

The nominal rate of interest is determined by the real rate of interest plus the expected rate of inflation, and during the late 1970s and 1980s, the Australian economy experienced a very high rate of inflation and, thus, high interest rates. Looking at figure 4.5, we can see that the inflation increased from less than 5 per cent in 1970 to almost average 13 per cent in the 1980s. This was a result of the oil price shocks of the 1970s and the monetary policy setting of the Government at that time.

Module 4: The Reserve Bank of Australia and interest rates

Questions and problems BASIC 4.1

Money supply: If the RBA bought $3.5 billion in CSG and the public withdrew $2 billion from their transaction deposits in the form of cash, by how much would the money base change? By how much would financial institutions’ reserves change?

The RBA’s purchase put $3.5 billion into MS. The public’s withdrawals do not change MS. The FIs’ aggregated reserves were affected only by the change in MS - $3.5 billion.

4.2

Money supply: Do payments received by Australian cotton growers for their direct exports of cotton affect money supply? Explain your answer.

No. If the payments are received in forex, then they exchange the currency for AUD already in the MS; if the payments are received in AUD, then other agents have already exchanged the forex for AUD.

4.3

Money supply: What is likely to happen to the monetary base when: (a) Centrelink credits age pensions to pensioners’ bank accounts (b) the RBA buys government securities from Australian investors (c) banks raise funds by an overseas note issue?

The money base is one measure of the money supply circulating in the economy at any one time.

Centrelink crediting age pensions to pensioners’ bank accounts is a government transfer payment, hence causes an injection into the money supply and the monetary base increases.

When the RBA buys back government securities from Australian investors, the investors receive the funds and the money supply increases.

When private banks raise funds by an overseas note issue they essentially borrow funds from overseas. If these are not Euro-Australian dollars then the bank will be required to change them in the Forex market into existing Aussie dollars. There will be no change to the money supply in this scenario.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

4.4

Money supply: Why are there so many measures of money?

Each measure has a different purpose and measures (slightly or largely) different concepts. We have M1, M3, Broad Money and the Money Base.

M1 consists of financial assets that people hold to buy things with (such as currency and current accounts at depository institutions).

M3 is M1 plus all other bank deposits of the private nonbank sector (including savings deposits, money-market deposit accounts, overnight repurchase agreements, moneymarket managed funds and term deposits).

Broad money is M3 plus borrowings from the private sector by nonbank financial institutions (NBFIs) less currency and bank deposits of NBFIs. M3 and broad money are the concepts of money that emphasise the role that money plays as a ‘store of value’.

Money base is the value of currency held by the private sector plus the value of the deposits made by banks with the RBA (ESAs) and any other liabilities to the private sector held by the RBA.

4.5

RBA & interest rates: Why do the financial markets pay so much attention to the cash rate?

Financial markets consider the cash rate to be the base interest rate in the economy and it is the most closely watched of all interest rates. It is the unsecured overnight interbank lending rate and represents the primary costs of short-term loanable funds. This interest rate underpins all the different interest rates charged for loans of various types. A margin for risk and illiquidity are added to the various interest rates such as mortgage interest rates, 10-year bond interest rates, and personal loan rates. The greater the risk the greater the margin added to the cash rate.

Module 4: The Reserve Bank of Australia and interest rates

4.6

RBA and interest rates: What is the essential difference between the Keynesian and the monetarist views on how money affects the economy?

Keynesians trace changes in money supply to changes in interest rates. They believe that when people and banks have more money, they will tend to buy more securities and make more loans, driving down interest rates and increasing credit availability which in turn affect activity in the economy (lower interest rates stimulate borrowing and investment).

Monetarist economists, on the other hand, believe that when people have more money relative to their needs, they will spend more freely and thus will stimulate the economy directly. Conversely, if people have less money than they need, given their income and expenditure levels, they will spend less so they can accumulate more cash. So for monetarists, the key variable that drives changes in economic activity in the economy is the money supply as measured by the monetary base. Monetarists therefore believe increases in MS directly affect spending and therefore economic activity.

4.7

RBA & interest rates: In what direction is the cash rate likely to move under the scenarios in the previous question, if no balancing open-market operations take place?

The cash interest rate underpins all interest rates in the economy. It measures the “price” of bank reserves (i.e. the cost of borrowing money) hence it directly reflects the available reserves in the banking system. Any increase (decrease) in monetary base reflects an increase (decrease) in the money supply. If no balancing open-market operation takes place to offset the increase (decrease) in the money supply, then as in any demand/supply situation, an excess supply of money would cause the price (cash rate) of money to fall and vice a versa. a. Crediting pension payments causes an increase in the money supply so the cash rate (price of borrowing) is likely to move downwards. b. The RBA buying back securities injects more funds into the banking system, with the excess supply of funds, the cash rate is likely to fall. c. If private banks raise funds overseas, because they required swapping in the forex market there was no change to existing money supply. There would be no pressure on the cash rate to move either upward or downward, rather it would remain the same.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

4.8

RBA policies: Describe the likely consequences for GDP growth when the RBA sells CGS to raise funds for the Commonwealth Government.

If the RBA conducts sales of CGS the sequence of events that occurs in both the financial sector and the real sector of the economy is the reverse of the process demonstrated in the text. The sale of CGS is a means whereby the government borrows funds from the public.

As this occurs the money supply (notes and coins in the hands of the public) decreases.

The shortage of money stimulates interest rates to rise, business investment and consumer borrowing and spending all fall with the subsequent impact causing GDP growth to decrease. The exchange rate is likely to increase (as the higher interest rate attracts capital inflow from the rest of the world), exports decrease and imports increase.

4.9

Cash rate: Why would active investors in fixed-interest securities such as bonds watch the cash rate closely and try to ‘read between the lines’ of RBA announcements?

The traded prices of bonds are affected by market interest rates which in turn are affected by the cash rate. As there is an inverse relationship between bond prices and interest rates, active investors would attempt to predict which way the RBA will move the cash rates. If investors believe the cash rate is likely to rise, then the price of bonds will fall.

Active investors would either like to sell their securities before the price falls or postpone purchases and buy securities after the interest rate rise and price fall.

4.10

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

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.

4.11

Interest rates: Define the concept of an interest rate and explain the role of interest rates in the economy.

Interest rates represent the ‘price’ of renting money from another party for a fixed amount of time. Interest rates, and movements therein, are a key factor that influences the economy. Interest rates are similar to other prices in the economy in that they allocate funds between savers (SSUs) and borrowers (DSUs) among financial markets.

Module 4: The Reserve Bank of Australia and interest rates

MODERATE 4.12

Money supply: If the RBA is highly risk averse in its open-market operations, why has it moved into the forex market?

Forex, as currency issued and backed by foreign national governments, is virtually the equivalent of national government securities. The inclusion of forex into their trading operations has expanded the pool of acceptable trading ‘products’.

4.13

Monday supply: Why do holders of ESAs try to minimise their daily balances, subject to precautionary levels?

Even though the RBA pays interest nowadays on ESA balances, the interest rate is not as high as the holders can earn by using those funds in the market. Hence there is an opportunity cost in holding ESA balances and holders try to optimise their balances.

4.14

Money supply: Outline the effect an RBA unsterilised intervention in foreign currency markets would have on the money supply and cash interest rates? Why would the RBA want to sterilise these actions?

Occasionally the RBA trades in the forex market with the intention of directly influencing or supporting the value of the Australian dollar (AUD). These forex interventions do have an impact on the money supply and the cash interest rate. An unsterilised intervention occurs when the RBA enters the Forex Market with either a purchase or a sale of AUD. If the monetary effects are not offset it is considered an unsterilised intervention. For example, if the RBA believes the AUD value is too high it may sell AUD (and purchase foreign currency) in the forex market, increasing the amount of AUD in circulation. This increases the money supply and causes a fall in the cash interest rate or vice versa if they consider the AUD value is too low. In this case, the RBA buys AUD (sells foreign currency) in the forex market reducing the money supply with a subsequent increase in the cash interest rate. This strategy is considered an unsterilised forex intervention by the RBA. The RBA would want to sterilise these actions if they wished to influence the value of the AUD without the liquidity effects on the money supply and interest rates. Sterilised intervention or the neutralisation of the RBA’s intervention in the Forex market is achieved by taking offsetting sales or purchases of CGS. When the RBA is selling (buying) AUD it would sell (buy) CGS and reduce (increase) liquidity and the money supply thereby sterilising or neutralising its actions in the forex market and the impact on the money supply and interest rates.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

4.15

RBA & interest rates: The RBA raises $500 million from money-market dealers in ten-day repos. Explain the cash flows involved and the effects on money supply.

To raise the funds with repos, the RBA sells the dealers securities with provisions to buy back in 10 days. At the expiry of the 10 days, the RBA buys the securities back again.

MS is first reduced and then increased.

4.16

RBA & interest rates: What would happen to the money base if the Commonwealth government collected $1 billion in taxes and the RBA bought 0.5 billion in the CGS in a single day? How would the cash rate become involved in these transactions? $1 billion paid out of money supply (MS) and $0.5 billion paid into MS, making a $0.5 billion net reduction. The reduction in funds theoretically reduces loanable funds and therefore puts upward pressure on the cash rate. The cash rate is involved through the clearing mechanism between banks and the ESA accounts held with the RBA.

4.17

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

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

4.18

Interest rates: What is the Fisher equation, and how is it used? How does it affect the nominal rate of interest?

The Fisher equation is the equation relating the expected, not the reported or actual, annualised change in prices (∆Pe) and the real rate of interest to the nominal rate of interest. It is used to protect 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.

4.19

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

The only time the nominal and real interest rates are equal is when the expected rate of inflation over the contract period is zero.

Module 4: The Reserve Bank of Australia and interest rates

4.20

Interest rates: If demand for money (loanable funds) increases, what happens to the level of interest rates?

An increase in the demand for money will shift the demand for loanable funds up and to the right, increasing interest rates (at least in the short term).

4.21

Interest rates: If the money supply is increased, what happens to the level of interest rates?

An increase in the money supply shifts the supply of loanable funds to the right, lowering interest rates (again at least in the short term).

4.22

Interest rates: The one-year real rate of interest is currently estimated to be 5 per cent. The current annual rate of inflation is 2 per cent, and market forecasts predict the annual rate of inflation to be 4 per cent. What is the current 1-year nominal rate of interest?

Assuming the Fisher effect, the current 1-year nominal rate should be 9 percent, the sum of the real rate (5%) plus the expected inflation rate (4%), an approximate but illustrative way of estimating the answer. The correct way to deal with compounding rates is to multiply (1+.05)(1+.04) - 1 = 9.20%.

4.23

Interest rates: Under what conditions is the loss of purchasing power on interest in the Fisher effect an important consideration?

Retired individuals, church endowments, or foundations with fixed interest rate returns on long-term CD or bond investment portfolios are hurt with actual or anticipated inflation. With expected inflation, market interest rates increase, and the value of the investment declines. With inflation and fixed interest income, less can be purchased each period.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

4.24

Interest rates: Can interest rates be negative? If so, under what circumstances and has this ever happened?

Yes, however they are rarely observed in global financial markets. The Fischer equation suggests that a negative interest rate could occur when the expected rate of deflation (a negative term) exceeds the real rate of interest. The real rate of interest is always positive because we assume that human nature is such that nearly all market participants have a positive time preference for consumption. Practically speaking, negative interest rates might occur when a country is in a deep and prolonged recession. During such a time, the real rate of interest should be low and the economy could suffer falling asset prices (deflation).

In November 1998, the interest rate on Japanese Treasury bills declined to a negative interest rate. At that time the Japanese economy was in the depths of a 10-year recession, which ended in 2004. The Treasury rate became negative because large investors did not want to buy bank liabilities because of their concerns over the stability of Japan’s fragile banking system. More recently, a similar story of negative yields across a number of Europe’s major economies was unfolding in 2011-12 during the depths of the European sovereign debt crisis, as a massive flight for safety occurred from the EU’s Southern states to its Northern neighbours. Historically, the Great Depression (1929–33) in the United States serves as a textbook illustration of an observed negative yield for (U.S. Treasury) securities amid concerns over the stability of the U.S. banking system.

4.25

Interest rates: Imagine you borrow $500 from your roommate, agreeing to pay her back the $500 plus 7 per cent nominal interest in 1 year. Assume inflation over the life of the contract is expected to be 4.25 per cent. What is the total amount you will have to pay her back in a year? How much of the interest payment is the result of the real rate of interest?

You will pay her back $535 ($500 x 1.07) in one year, of which $13.75 will be a result of the real interest rate ($500 x 0.0275). (Real interest rate is calculated as 7% nominal rate – 4.25% inflation =2.75%)

4.26

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 term deposit that pays 6.75 per cent interest. You know that the trip costs $1,025 right now and that the inflation for the year is predicted to be 4 per cent.

Will you have enough money in a year to purchase the trip?

Yes. The term deposit will be worth $1,067.50 at the end of the year ($1,000 x 6.75% + $1000), and the price of the trip will be $1,066 ($1,025 x 4% + $1,025). The term deposit will be able to cover the trip.

Module 4: The Reserve Bank of Australia and interest rates

4.27

Interest rates: If the realised real rate of return turns out to be positive, would you rather have been a borrower or a lender? Explain in terms of the purchasing power of the money used to repay a loan.

The answer depends upon whether the lender (borrower) earns (pays) their expected real rate. If inflation were originally underestimated, borrowers would benefit at the cost of lenders – their actual cost of borrowing would be less. If inflation were overestimated, lenders would benefit at the cost of borrowers – actual returns (borrowing costs) would higher than originally anticipated.

4.28

Interest rates: Explain how forecasters use the flow-of-funds approach to determine future interest rate movements.

Using the loanable funds theoretical constructs, forecasters predict funds flow through sectors looking for significant supply/demand or sources/uses variations, which may signal changes in rates.

4.29

An investor purchased a one-year Treasury security with a promised yield of 6 per cent. The investor expected the annual rate of inflation to be 2 per cent; however, the actual rate turned out to be 6 per cent. What were the expected and the realised real rates of return for the investor?

The expected real rate is re = i - Pe = 6% - 2% = 4%; the realized real rate is rr = i - Pa = 6% - 6% = 0.

Module 5: Time value of money Self-study problems 5.1

Amit Patel is planning to invest $10 000 in a bank term deposit for 5 years. The term deposit will pay interest of 9 per cent per annum. What is the future value of Amit’s investment?

Present value of the investment = PV = $10000 Interest rate on CD = i = 9% No. of years = n = 5.

0 1 2 3 4 5 ├───┼───┼───┼────┼───┤ -$10,000 FV=?

FV = PV (1 + i ) n = 10000(1 + 0.09) 5 = $15386.24

5.2

Megan Watts expects to need $50 000 as a deposit on a house in 6 years. How much does she need to invest today in an account paying 7.25 per cent per annum?

Amount Megan will need in 6 years = FV6 = $50000 No. of years = n = 6 Interest rate on investment = i = 7.25% Amount needed to be invested now = PV = ?

0 1 2 3 4 5 6 ├───┼───┼───┼────┼───┼───┤ PV = ?

FV = $50,000

FV n (1 + i ) n 50000 = (1 + 0.0725) 6 = $32853.84

PV =

Module 5: Time value of money

5.3

Mun Ngai has $10 000 that he can deposit into a savings account for 5 years. Bank A pays compounds interest annually, Bank B twice a year, and Bank C quarterly.

Each bank has a stated interest rate of 6 per cent. What amount would Mun have at the end of the fifth year if he left all the interest paid on the deposit in each bank?

Present value = PV = $10000 No. 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 1 2 3 4 5 ├───┼───┼───┼────┼───┤ -$10,000 FV = ?

5.4

A:

FVn = PV x (1 + i/m)m x n FV5 = 10000 x (1 + 0.06/1)1x5 FV5 = $13382.26

B:

FV5 = 10000 x (1 + 0.06/2)2x5 FV5 = $13439.16

C:

FV5 = 10000 x (1 + 0.06/4)4x5 FV5 = $13468.55

You have an opportunity to invest $2500 today and receive $3000 in 3 years. What will be the return on your investment?

Investment today = PV = $2500 Amount to be received back = FV3= $3000 Time of investment = n = 3 Return on the investment = i = ?

FVn = PV (1 + i)n 3000 = 2500 (1 + i)3 (3000/2500)1/3 = 1 + i i = 6.27%

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.5

Emily Smith deposits $1200 in her bank today. If the bank pays 7 per cent simple interest, how much money will she have at the end of 5 years? What if the bank pays compound interest? How much of the earnings will be interest on interest?

Deposit today = PV = $1200 Interest rate = i = 4% No. of years = n = 5 Amount to be received back = FV5 = ? a. Future value with simple interest Simple interest per year = 1200 (0.07) = $84.00 Simple interest for 5 years = 84 x 5 = $420.00 FV5 = 1200 + 420 = $1620.00 b. Future value with compound interest FV5 = 1200 (1 + 0.07)5 FV5 = $1683.06 Simple interest = (1620 – 1200) = $420 Interest-on-interest = 1683.06 – 1200 – 420 = $63.06

Module 5: Time value of money

Critical thinking 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.

5.2

Explain the importance of a time line.

Time lines are important tools used to analyse 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.

5.3

Differentiate future value from 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).

5.4

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.

5.5

Differentiate 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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.6

Explain how compound interest differs from simple interest.

Suppose you invest $100 for three years at a rate of 10 percent. Simple interest would imply that you will earn $10 for each of the three years for a total of $30 interest. At the end of three years you would have $130. Compound interest recognises 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 you would have at the end of three years would be: $100(1.10) 3 = $133.10 .

By compounding, you 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.

5.7

If you were given a choice of investing in an account that paid quarterly interest and one that paid monthly interest, which one should you choose 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.

5.8

Growth rates are 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.

5.9

The process of compounding a present amount to the future is the opposite of doing what?

The opposite of calculating the future value is the process of discounting a future amount to the present, that is, determining the current value (or present value) of a future cash flow.

Module 5: Time value of money

5.10

You are planning to take a mid-year trip to Bali in your last year of university. The trip is exactly 2 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 trip comes.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Questions and problems BASIC 5.1

Future value: George Paps is planning to invest $25 000 today in an investment fund that will provide a return of 8 per cent each year. What will be the value of the investment in 10 years?

0 5 years ├────────────────────┤ PV = $25000 FV = ?

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 = 25000 × (1.08)10 = $53973.12

5.2

Future value: Hin Liang is investing $7 500 in a bank term deposit that pays a 6.5 per cent annual interest. How much will the term deposit be worth at the end of 5 years?

0 5 years ├────────────────────┤ PV = $7500 FV = ?

Amount invested today = PV = $7500 Return expected from investment = i = 6.5% Duration of investment = n = 5 years Value of investment after 5 years = FV5

FV5 = PV × (1 + i) n = 7500 × (1.065) 5 = $10275.65

Module 5: Time value of money

5.3

Future value: Your aunt is planning to invest in a bank deposit that will pay 8.5 per cent interest compounding semiannually. If she has $5 000 to invest, how much will she have at the end of 4 years?

0 4 years ├────────────────────┤ PV = $5000 FV = ?

Amount invested today = PV = $5000 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 FV 4 = PV × 1 + m

mn

0.085 = 5000 × 1 + 2

2×4

= 5,000 × (1.0425) 8 = $6975.55

5.4

Future value: Alison Green received a graduation present of $5000 that she is planning on investing in an investment fund that earns 10.5 per cent each year. How much money can she collect in 3 years?

0 3 years ├────────────────────┤ PV = $5000 FV = ?

Amount Alison invested today = PV = $5000 Return expected from investment = i = 10.5% Duration of investment = n = 3 years Value of investment after 3 years = FV3

FV3 = PV × (1 + i) n = 5000 × (1.105) 3 = $6746.16

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.5

Future value: Your bank pays 5 per cent interest semiannually on your savings account. You don’t expect the current balance of $2700 to change over the next 4 years. How much money can you expect to have at the end of this period?

0 4 years ├────────────────────┤ PV = $2700 FV = ?

Amount invested today = PV = $2700 Return expected from investment = i = 5% Duration of investment = n = 4 years Frequency of compounding = m = 2 Value of investment after 4 years = FV4 i FV 4 = PV × 1 + m

mn

0.05 = 2700 × 1 + 2

2×4

= 2700 × (1.025) 8 = $3289.69

5.6

Future value: Your birthday is coming up, and instead of any presents, your parents promised to give you $1000 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 term deposit that pays 7.2 per cent compounding quarterly for the next 2 years. How much money can you expect to gain in this period of time?

0

2 years

├────────────────────┤ PV = $1000

FV = ?

Amount invested today = PV = $1000 Return expected from investment = i = 7.2% Duration of investment = n = 2 years Frequency of compounding = m = 4 Value of investment after 2 years = FV2

i FV2 = PV × 1 + m

mn

= 1000 × (1.018)8 = $1153.41

0.072 = 1000 × 1 + 4

4× 2

Module 5: Time value of money

5.7

Multiple compounding periods: Find the future value of an investment of $100 000 made today for 5 years and paying 8.75 per cent for the following compounding periods: a. quarterly. b. monthly. c. daily. d. continuous.

0 5 years ├────────────────────┤ PV = $100,000 FV = ?

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 Value of investment after 5 years = FV5

i FV5 = PV × 1 + m

mn

0.0875 = 100000 × 1 + 4

4×5

= 100000 × (1.021875) 20 = $154154.24 b.

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

i FV5 = PV × 1 + m

mn

0.0875 = 100000 × 1 + 12

12×5

= 100000 × (1.00729) 60 = $154637.37 c.

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

i FV5 = PV × 1 + m

mn

0.0875 = 100000 × 1 + 365

= 100000 × (1.00024)1825 = $154874.91 d.

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

FV5 = PV × e in = 100000 × e 0.0875 ×5 = 100000 ×1.5488303 = $154883.03

365×5

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.8

Growth rates: Luke Hughes, the designated hitter for the Perth Heat, is expected to hit 12 home runs in 2011. If his home-run-hitting ability is expected to grow by 12 per cent every year for the next 5 years, how many home runs is he expected to hit in 2016?

0 5 years ├────────────────────┤ PV = 12 FV = ?

Number of home runs hit in 2011 = PV = 12 Expected annual increase in home runs hit = i = 12% Growth period = n = 5 years No. of home runs after 5 years = FV5 FV5 = PV × (1 + i ) n = 12 × (1.12) 5 ≈ 21 home runs

5.9

Present value: Roy Goss is considering an investment that pays 7.6 per cent per annum. How much will he have to invest today so that the investment will be worth $25 000 in 6 years?

0 6 years ├────────────────────┤ PV = ?

FV = $25 000 Value of investment after 6 years = FV5 = $25 000 Return expected from investment = i = 7.6% Duration of investment = n = 6 years Amount to be invested today = PV FV n 25000 n = (1 + i ) (1.076) 6 = $16108.92

PV =

Module 5: Time value of money

5.10

Present value: Maria Lukas has been offered a future payment of $750 2 years from now. If her opportunity cost is 6.5 per cent compounded annually, what should she pay for this investment today?

0 2 years ├────────────────────┤ PV = ?

FV = $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 FV n 750 n = (1 + i ) (1.065) 2 = $661.24

PV =

5.11

Present value: Your brother has asked you for a loan and has promised to pay back $7750 at the end of 3 years. If you normally invest to earn 6 per cent per annum, how much will you be willing to lend to your brother?

0 3 years ├────────────────────┤ PV = ?

FV = $7750 Loan repayment amount after 3 years = FV3 = $7750 Return expected from investment = i = 6% Duration of investment = n = 3 years Amount to be invested today = PV PV =

FV n

(1 + i )

n

=

= $6507.05

7750 (1.06) 3

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.12

Present value: Tracy Chapman is saving to buy a house in 5 years. She plans to have a 20 per cent deposit at that time, and she believes that she will need $70 00 for the deposit. If Tracy can invest in a fund that pays 9.25 per cent annually, how much will she need to invest today?

0 5 years ├────────────────────┤ PV = ?

FV = $70 000 Amount needed for down payment after 5 years = FV5 = $70 000 Return expected from investment = i = 9.25% Duration of investment = n = 5 years Amount to be invested today = PV FV n

70000 (1 + i ) (1.0925) 5 = $44977.03

PV =

5.13

n

=

Present value: You want to buy some zero coupon bonds that have a value of $1000 at the end of 7 years. The bonds are said to pay 4.5 per cent interest per annum.

How much should you pay for them today?

0 7 years ├────────────────────┤ PV = ?

FV = $1000 Face value of bond at maturity = FV7 = $1000 Appropriate discount rate = i = 4.5% Number of years to maturity = n = 7 years.

Present value of bond = PV FV n 1000 n = (1 + i ) (1.045) 7 = $734.83

PV =

Module 5: Time value of money

5.14

Present value: Elizabeth Sweeney wants to accumulate $24 000 by the end of 12 years. If the interest rate is 7 percent per annum, how much will she have to invest today to achieve her goal?

0 12 years ├────────────────────┤ PV = ?

FV = $24 000 Amount Ms. Sweeney wants at end of 12 years = FV12 = $24 000 Interest rate on investment = i = 7% Duration of investment = n = 12 years.

Present value of investment = PV FV n 24000 n = (1 + i ) (1.07)12 = $10656.29

PV =

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 $1300 and agree to pay back $1500 in 2 years. Alternatively, you could borrow from your bank that is charging 6.5 per cent interest per annum. Should you go with your uncle or the bank?

0 2 years ├────────────────────┤ PV = $1300 FV = $1500 Amount to be borrowed = PV = $1300 Amount to be paid back after 2 years = FV2 = $1500 Interest rate on investment = i = ?

Duration of investment = n = 2 years.

Present value of investment = PV

FV n (1 + i ) n 1500 1300 = (1 + i ) 2 1500 (1 + i ) 2 = = 1.1538 1300 i = 1.1538 1 PV =

i = 7.42% You should go with the bank borrowing, as the bank is offering a lower lending rate.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.16

Time to attain goal: You invest $150 in an investment fund today that pays 9 per cent interest per annum. How long will it take to double your money?

0 n years ├────────────────────┤ PV = $150 FV = $300 Value of investment today = PV = $150 Interest on investment = n = 9% Future value of investment = FV = $300 Number of years to double investment = n FV n = 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) = 8.043 years ln(1.09)

Module 5: Time value of money

MODERATE 5.17

Simple interest versus compound interest: First State Bank pays 6 per cent simple interest on its savings account balances, whereas First United Bank pays 6 per cent interest compounded annually. If you made an $8000 deposit in each bank, how much more money would you earn from your First United Bank account at the end of 7 years?

FV FirstState Bank = P0 + (P0  i  n )

= $8,000 + ($8,000  0.06  7 ) = $8,000 + $3,360 = $11,360

FV FirstUnite dBank = PV  (1 + i ) n = $8,000  (1.06) 7 = $8,000  1.50363 = $12,029.04 Difference = $12,029.04 - $11,360 = $669.04 If you invested in First United Bank you would earn an additional $669.04 by the end of 7 years.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.18

Growth rate: Your finance textbook sold 12 250 copies in its first year. The publishing company expects the sales to grow at a rate of 20 per cent for the next 3 years and by 10 per cent in year 4. 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 4 years.

Number of copies sold in its first year = PV = 12 250 Expected annual growth in the next 3 years = i = 20% Number of copies sold after 3 years = FV3 =

FV n = PV × (1 + i) n = 12250 × (1.20) 3 = 21168 copies Number of copies sold in the fourth year = FV4

FV n = PV × (1 + i ) n = 21168 × (1.10) = 23285 copies 0 3 4 years ├───────────┼────────┤ PV = 12 250 21 168 23 285 copies

Module 5: Time value of money

5.19

Growth rate: CelebNav Ltd had sales last year of $700 000, and the analysts are predicting a good year for the start-up, with sales growing 20 per cent a year for the next 3 years. After that, the sales should grow 11 per cent per year for 2 years, at which time the owners are planning to sell the company. What are the projected sales for the last year of the company’s operation?

0 1 2 3 4 5 years ├───────┼────────┼───────┼────────┼───────┤ g1 = 20% g2 = 11% PV = $700 000 FV=?

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

FV 5 = PV (1 + g1 ) 3 (1 + g 2 ) 2 = $700000(1.20) 3 (1.11) 2 = $1,490,348.16

5.20 Growth rate: You decide to set up an online dating web site. You know that you have 450 people who will sign up immediately and, through careful marketing research and analysis, determine that membership can grow by 27 per cent in the first 2 years, 22 per cent in year 3, and 18 per cent in year 4. How many members do you expect to have at the end of 4 years?

0 1 2 3 4 years ├───────┼────────┼───────┼────────┤ g1-2=27% g3=22% g4=18% PV = 450 FV = ?

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

FV 4 = PV (1 + g1 ) 2 (1 + g 3 )(1 + g 4 ) = 450(1.27) 2 (1.22)(1.18) = 1,045 members

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.21

Multiple compounding periods: Find the future value of an investment of $2500 made today for the following rates and periods: a. 6.25 per cent compounded semiannually for 12 years. b. 7.63 per cent compounded quarterly for 6 years. c. 8.9 per cent compounded monthly for 10 years. d. 10 per cent compounded daily for 3 years. e. 8 per cent compounded continuously for 2 years.

a.

0.0625 FV12 = PV × 1 + 2 = $5232.09

2×12

= 2500 × (2.0928)

4×6

b.

c.

d.

e.

5.22

0.0763 FV12 = PV × 1 + = 2500 × (2.4768) 4 = $3934.48 12×10 0.089 FV12 = PV × 1 + = 2500 × (2.4271) 12 = $6067.86 0.010 FV12 = PV × 1 + 365 = $3374.51

365×3

= 2500 × (1.3498)

FV3 = PV × e in = $3,000 × e 0.08×2 = 2500 ×1.1735 = $2933.78

Growth rates: Xenix Ltd had sales of $353 866 in 2011. If it expects its sales to be at $476 450 in 3 years, what is the rate at which the company’s sales are expected to grow?

Sales in 2011 = PV = $353 866 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 476450 = 353866(1 + g ) 3 (1 + g ) 3 =

476450 = 1.3464 353866 1

g = (1.3464) 3 1 = 10.42%

Module 5: Time value of money

5.23

Growth rate: Infosys Technologies Ltd, an Indian technology company, reported a profit of $419 million this year. Analysts expect the company’s earnings to be $1.468 billion in 5 years. What is the expected growth rate in the company’s earnings?

Earnings in current year = PV = $419 million Expected earnings five years from now = $1,468 million To calculate the expected earnings growth rate, we set up the future value equation.

FV 5 = PV  (1 + g ) 5 1468 = 419(1 + g ) 5 (1 + g ) 5 =

1468 = 3.5036 419 1

g = (3.5036) 5 − 1 = 28.5%

5.24

Time to attain goal: Zephyr Sales Ltd has currently reported sales of $1.125 million.

If the company expects its sales to grow at 6.5 per cent annually, how long will it be before the company can double its sales? Use a financial calculator to solve this problem.

Enter: 6.5

I/Y

-1.125

PV

2.25

FV

0

PMT Answer: 11.007 years

COMP N

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.25

Time to attain goal: You are able to deposit $850 into a bank term deposit today, and you will withdraw the money once the balance is $1000. If the bank pays 7 per cent interest per annum, how long will it take you to attain your goal?

Amount invested today = PV = $850 Expected amount in the future = FV = $1000 Interest rate on the term deposit = i = 5% To calculate the time needed to reach the target FV, we set up the future value equation.

FV n = PV  (1 + i ) n $1,050 = $700  (1.07) n $1,050 = 1.50 700 n  ln(1.07) = ln(1.50) (1.07) n =

n=

5.26

ln(1.50) = 5.99 years ln(1.07)

Time to attain goal: Skipping Girl is a private company with sales of $1.3 million a year. They want to go public but have to wait until the sales reach $2 million.

Providing that they are expected to grow at a steady 12 per cent annually, when is the earliest that Skipping Girl can start selling their shares?

Current level of sales = PV = $1.3 million Target sales level in the future = FV = $2 million Projected growth rate = g = 12% To calculate the time needed to reach the target FV, we set up the future value equation.

FV 3 = PV  (1 + g ) n 2 = 1.3  (1.12) n 2 = 1.5385 1 .3 n  ln(1.12) = ln(1.5385) (1.12) n =

n=

ln(1.5385) = 3.801 years ln(1.12)

Module 5: Time value of money

5.27

Present value: Thang Nguyen needs to decide whether to accept a bonus of $1900 today or wait 2 years and receive $2100 then. She can invest at 6 per cent per annum. What should she do?

0 2 years ├────────────────────┤ PV = $1900 FV = ?

Amount to be received in 2 years = FV2 = $2100 Return expected from investment = i = 6% Duration of investment = n = 2 years Present value of amount today = PV FV 2 2100 = n (1 + i ) (1.06) 2 = $1868.99

PV =

Since the amount to be received today ($1900) is greater than the present value of the $2100 to be received in 2 years, Thang should choose to receive the amount of $1900 today

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.28

Multiple compounding periods: Find the present value of $3500 under each of the following rates and periods. a. 8.9 per cent compounded monthly for 5 years. b. 6.6 per cent compounded quarterly for 8 years. c. 4.3 per cent compounded daily for 4 years. d. 5.7 per cent compounded continuously for 3 years.

0 n years ├────────────────────┤ PV = ?

FV = $3500

a.

Return expected from investment = i = 8.9% Duration of investment = n = 5 years Frequency of compounding = m = 12 Present value of amount = PV FV 5

PV =

mn

=

3500

i    0.089  1 +  1 +  12   m  3500 = = $2246.57 1.5579

b.

Return expected from investment = i = 6.6% Duration of investment = n = 8 years Frequency of compounding = m = 4 Present Value of amount = PV PV =

FV8 mn

=

3500

i    0.066  1 +  1 +  4   m  3500 = = $2073.16 1.6882

c.

48

Return expected from investment = i = 4.3% Duration of investment = n = 4 years Frequency of compounding = m = 365 Present Value of amount = PV PV =

FV 4 mn

=

3500

i    0.043  1 +  1 +  365   m  3500 = = $2946.96 1.1877

365 4

125

Module 5: Time value of money

d.

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 3500  = 0.057 3 in e e 3500 = = $2949.88 1.1865

PV =

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.29

Multiple compounding periods: Kylie wants to invest some money so she can collect $5500 at the end of 3 years. Which investment should she make given the following choices? a. 4.2 per cent compounded daily b. 4.9 per cent compounded monthly c. 5.2 per cent compounded quarterly d. 5.4 per cent compounded annually 0 3 years ├────────────────────┤ PV = ?

FV = $5500

a.

Return expected from investment = i = 4.2% Duration of investment = n = 3 years Frequency of compounding = m = 365 Present value of amount = PV PV =

FV 3 mn

=

5500

i    0.042  1 +  1 +  365   m  5500 = = $4848.92 1.1343

365 3

Kylie should invest $4848.92 today to reach her target of $5500 in 3 years. b.

Return expected from investment = i = 4.9% Duration of investment = n = 5 years Frequency of compounding = m = 12 Present value of amount = PV PV =

FV 3 mn

=

5500

i    0.049  1 +  1 +  12   m  5500 = = $4749.54 1.5579

123

Kylie should invest $4749.54 today to reach her target of $5500 in 3 years.

Module 5: Time value of money

c.

Return expected from investment = i = 5.2% Duration of investment = n = 3 years Frequency of compounding = m = 4 Present Value of amount = PV PV =

FV 3 mn

=

5500

i    0.052  1 +  1 +  4   m  5500 = = $4710.31 1.1677

43

Kylie should invest $4710.31 today to reach her target of $5500 in 3 years. d.

Return expected from investment = i = 5.4% Duration of investment = n = 3 years Frequency of compounding = m = 1 Present value of amount = PV

PV =

FV3 5500 = = $4697.22 3 (1 + i) (1.054) 3

Kylie should invest $4697.22 today to reach her target of $5500 in 3 years.

Kylie should invest in choice D as it is the cheapest price for the FV of $5500.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.30

You have $2500 you want to invest in your classmate’s start-up business. You believe the business idea to be great and hope to get $3700 back at the end of 3 years. If all goes according to the plan, what will be your return on investment?

0 3 years ├────────────────────┤ PV = $2500 FV = $3700 Amount invested in project = PV = $2500 Expected return three years from now = FV =$3700 To calculate the expected rate of return, we set up the future value equation.

FV 3 = PV  (1 + i ) 3 3700 = 2500(1 + i ) 3 (1 + i ) 3 =

3700 = 1.4800 2500 1

i = (1.4800) 3 − 1 = 0.1396 = 13.96%

5.31

Jason has $2400 that he is hoping to invest. His brother approached him with an investment opportunity that could double his money in 4 years. What interest rate would the investment have to yield in order for Jason’s brother to deliver on his promise?

0 4 years ├────────────────────┤ PV = $2400 FV = $4800 Amount invested in project = PV = $2400 Expected return three years from now = FV =$4800 Investment period = n = 4 years To calculate the expected rate of return, we set up the future value equation.

FV 4 = PV  (1 + i ) 4 4800 = 2400(1 + i ) 4 (1 + i ) 4 =

4800 = 1.4800 2400 1

i = (2.000) 4 − 1 = 0.1892 = 18.92%

Module 5: Time value of money

5.32

You have $12 000 in cash. You can deposit it today in an investment fund earning 8.2 per cent semiannually; or you can wait, enjoy some of it, and invest $11 000 in your brother’s business in 2 years. Your brother is promising you a return of at least 10 per cent 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 will you choose?

Option A: Invest in account paying 8.2 per cent semiannually for 10 years.

0 10 years ├────────────────────┤ PV = $12 000 FV = ?

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  0.082  FV10 = PV  1 +  2   = $26803.77

210

= 12000  (2.23365)

Option B: Invest in brother’s business to earn 10 percent for eight years.

0 8 years ├────────────────────┤ PV = $11000 FV = ?

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 = FV10

FV8 = PV  (1 + 0.10) = 11000  (2.14359) 8

= $23579.48 You are $3224.29 better off by investing today in the mutual fund and earn 8.2 per cent semiannually for 10 years.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.33

When you were born your parents set up a bank account in your name with an initial investment of $5000. You are turning 21 in a few days and will have access to all your funds. The account was earning 7.3 per cent for the first 7 years, and then the rates went down to 5.5 per cent for 6 years. The economy then did well and your account was earning 8.2 per cent for 3 years in a row. Unfortunately, the next 2 years you only earned 4.6 per cent. Finally, as the economy recovered, your return jumped to 7.6 per cent for the last 3 years. a.

How much money was in your account before the rates went down drastically (end of year 16)? b.

How much money is in your account now, end of year 21? c.

What would be the balance now if your parents made another deposit of $1200 at the end of year 7?

0 1 7 13 14 15 16 21 years ├───┼∙∙∙∙∙∙∙∙∙∙┼∙∙∙∙∙∙∙∙∙∙∙∙────┼────┼───┼───∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙──┤ PV = $5,000 FV = ? i1 = 7.3% i2 = 5.5% i3 = 8.2% i4 = 4.6% i5 = 7.6%

a.

Initial investment = PV = $5000 Interest rate for first 7 years = i1 = 7.3% Interest rate for next 6 years = i2 = 5.5% 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 = 5000  (1 + 0.073)  (1.055) 6  (1.082) 3 7

= 5000  (1.6376)  (1.3788)  (1.2667 ) = $14300.94

b.

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 = $14 300.94 Investment value at age 21 years = FV21 FV 21 = FV16  (1 + i4 ) 2  (1 + i5 ) 3 = 14300.55  (1 + 0.046 )  (1.076) 3 2

= 14300.55  (1.0941)  (1.2458)) = $19492.38

Module 5: Time value of money

c.

Additional investment at start of 8th year = $1,200 Total investment for next 6 years = $8187.82 + $1200 = $9387.82 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 FV 21 = FV 7  (1 + i2 ) 6  (1 + i3 ) 3  (1 + i4 ) 2  (1 + i5 ) 3 = 9387.82  (1.055) 6  (1.082) 3  (1.046 )  (1.076) 3 2

= 9387.82  (1.3788)  (1.2667 )  (1.0941)  (1.2458) = $22349.16

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.34

Brett Holman and his agent are evaluating three contract options to return to play in the A-League after a successful career with Dutch Ereduvusue team, Feyenoord.

Each option offers a signing bonus and a series of payments over the life of the contract. Wilkshire uses a 10.25 per cent rate of return to evaluate the contracts.

Given the cash flows for each option, which one should he choose?

Year 0 1 2 3 4

Cash Flow Type Signing Bonus Annual Salary Annual Salary Annual Salary Annual Salary

Option A $3 500 000 $ 700000 $ 750 000 $ 800 000 $ 850 000

Option B $3 500 000 $ 850 000 $ 800 000 $ 750 000 $ 700 000

Option C $3 500 000 $ 775 000 $ 775 000 $ 775 000 $ 775 000

To decide on the best contract from Luke Wilkshire’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

700000 750000 800000 850000 + + + 1 2 3 (1.1025) (1.1025) (1.1025) (1.1025) 4 = 3500000 + 634921 + 617027 + 596972 + 575313 = $5924233

PV A = $3500,000 +

Option B: Discount rate to be used = i= 10.25% Present value of contract = PVB

850000 800000 750000 700000 + + + 1 2 3 (1.1025) (1.1025) (1.1025) (1.1025) 4 = 3500000 + 770975 + 658162 + 559662 + 473788 = $5962586

PV B = $3500000 +

Module 5: Time value of money

Option C: Discount rate to be used = i= 10.25% Present value of contract = PVC

775000 775000 775000 775000 + + + 1 2 3 (1.1025) (1.1025) (1.1025) (1.1025) 4 = 3500000 + 702948 + 637594 + 578317 + 524551 = $5943410

PVC = 3500000 +

Option B is the best choice for Tim Cahill as it provides the highest PV

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

5.35

Jimmal Bolts Ltd reported earnings of $2.1 million last year. The company’s primary business line is manufacturing nuts and bolts. Since this is a mature industry, the analysts are certain that the sales will grow at a steady rate of 7 per cent a year for as far as they can tell. The company reports profit 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 Jimmal Bolts Ltd be able to buy the new fleet of trucks? What will the sales and profit be that year?

Current level of sales for Jimmal = PV = $2 100 000 Profit margin = 23% Profit for the year = 0.23 x 2100000 = $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.

FV n = PV  (1 + g ) n 620000 = 483000  (1.07) n 620000 = 1.2836 483000 n  ln(1.07) = ln(1.2836) (1.07) n =

n=

ln(1.2836) = 3.7 years ln(1.12)

The company achieves its profit target during the fourth year.

Sales level at end of year 4 = FV4

FV n = PV  (1 + g ) n = 2100000  (1.07) 4 = $2752671.62 Profit for the year = $2752671.62 x 0.23 = $633114.47

Module 5: Time value of money

5.36

You are graduating in 2 years and you start thinking about your future. You know that you will want to buy a house 5 years after you graduate and that you will want a deposit of $70 000. As of right now, you have $8000 in your savings account. You are also fairly certain that once you graduate, you can work in the family business and earn $42 000 a year, with a 5 per cent raise every year. You plan to live with your parents for the first 2 years after graduation, which will enable you to minimise your expenses and put away $15 000 each year. The next 3 years, you will have to live out on your own, as your younger sister will be graduating from an interstate university and has already announced her plan to move back into the family house. Thus, you will only be able to save 13 per cent of your annual salary.

Assume that you will be able to invest savings from your salary at 7.2 per cent. 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 7 years from now and your first salary will be in year 3.

Starting salary in year 3 = $42000 Annual pay increase = 5% Savings in first 2 years = $15000 Savings rate for years 3 to 7 = 13%

Year

1

2

3

4

5

6

Salary

$0.00

$0.00

$42,000.00 $44,100.00 $46,305.00 $48,620.25 $51,051.26

Savings

$0.00

$0.00

$15,000.00 $15,000.00 $6,019.65

$6,320.63

Investment rate = i = 7.2% Future value of savings from salary = FV7

FV 7 = $0 + $0 + 15000  (1.072) 4 + 15000  (1.072) 3 + 6019.65  (1.072) 2 + 6320.63  (1.072)1 + 6636.66  (1.072) 0 = 19809.36 + 18478.88 + 6917.68 + 6775.72 + 6636.66 = $58618.30 Target deposit = $70000 Amount needed to reach target = $70000 – 58618.30 = FV = $11381.70 Current savings balance = PV $8,000 Time to achieve target = n = 7 years.

7

$6,636.66

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

To solve for the investment rate needed to achieve target, we need to set up the future value equation: FV = PV  (1 + i ) 7 11381.70 = 8000  (1 + i ) 7 11381.70 = 1.4227 8000 i = (1.4227 )1 7 − 1

(1 + i ) 7 =

= 1.05166 − 1 = 5.17%

Module 6: Discounted cash flows and valuation Self-study problems 6.1

Kronya Ltd is expecting cash flows of $13 000, $11 500, $12 750, and $9635 over the next 4 years. What is the present value of these cash flows if the appropriate discount rate is 8 per cent?

The time line for the cash flows and their present value is as follows: 0 8% 1 2 3 4 ├─────────┼─────────┼─────────┼─────────┤ $13000 $11500 $12750 $9635

13000 11500 12750 9635 + + + 2 3 (1.08) (1.08) (1.08) (1.08) 4 = 12037.04 + 9859.40 + 10121.36 + 7082.01

PV 4 =

= $39,099.81

6.2

Your grandfather has agreed to deposit a certain amount of money each year into an account paying 7.25 per cent annually to help you go to university. Starting next year, and for the following 4 years, he plans to deposit $2250, $8150, $7675, $6125, and $12 345 into the account. How much will you have at the end of the 5 years?

The time line for the cash flows and their future value is as follows: 0 7.25% 1 2 3 4 5 ├─────────┼─────────┼─────────┼──────────┼─────────┤

$2250

$8150

$7675

$6125

FV5 = 2250(1.0725) 4 + 8150(1.0725) 3 + 7675(1.0725) 2 + 6125(1.0725) 2 + 12345 = 2976.95 + 10054.25 + 8828.22 + 6569.06 + 12345 = $40,773.48

$12345

Module 6: Discounted cash flows and valuation

6.3

Mike White is planning to save up for a trip to Europe in 3 years. He will need $10 000 when he is ready to make the trip. He plans to invest the same amount at the end of each of the next 3 years in an account paying 6 per cent annually. What is the amount he will have to save every year to reach his goal of $10 000 in 3 years?

Amount Mike White will need in three years = FVA3 = $10000 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 ├────┼────┼────┤ FVA = $10000 FVAn = CF ( FVIFA i ,n )  (1 + i ) n − 1 = CF   i    (1 + 0.06) 3 − 1 10000 = CF   0.06   = CF * 3.1836 10000 3.1836 = $3141.10

CF =

Mike will have to save $3141.10 every year for the next 3 years.

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 so?

Present value of investment = Amount needed annually = This is a perpetuity!

CF PVA = i i=

CF $12500 = PVA $150000

i = 8.33%

$150000 $12500

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.5

Dynamo Ltd is expecting annual payments of $34 225 for the next 7 years from a customer. What is the present value of this annuity if the discount rate is 8.5 per cent?

0 8.5% 1 2 3 4 5 6 7 ├───┼───┼────┼───┼───┼───┼───┤ PVA= ? $34225 $34225 $34225 $34225 $34225 $34225 $34225   1   1 −  (1 + i ) n     PVA7 = CF   i        1  1 −  7  ( 1 .

085 )   = 34225    0.085     = $34225  5.1185 = $175181.14

Module 6: Discounted cash flows and valuation

Critical thinking questions 6.1

Identify the steps involved in calculating 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.

6.2

What is the key economic principle involved in calculating the present value and 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.

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 is called an annuity. If the same payments are made periodically forever, the contract is called a perpetuity.

6.4

Define annuity due. Would an investment be worth more if it was 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 (price or present value) than an ordinary annuity because each cash flow will accrue an extra interest payment.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.5

Raymond Liu is trying to choose between two equally risky annuities, each paying $5000 per year for 5 years. One is an ordinary annuity, and 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.

Answer 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.

6.6

Which of the following investments will have the highest future value at the end of 3 years? Assume that the effective annual rate for all investments is the same. a. You earn $3000 at the end of three years (a total of one payment). b. You earn $1000 at the end of every year for the next 3 years (a total of three payments). c. You earn $1000 at the beginning of every year for the next 3 years (a total of three payments).

Answer 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.

6.7

Explain whether or not each of the following statements is correct. a. A 15-year home loan will have larger monthly payments than a 30-year loan of the same amount and same interest rate. b. If an investment pays 10 per cent interest compounded annually, its effective rate will also be 10 per cent. a. This is a true statement. The 15-year home loan will have higher monthly payments since more of the principal will have to be paid each month than in the case of a 30year home loan. Common-sense will tell us that the 15 year loan repayments will be double if we do not account for the time value of money (i = 0). b. This 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.

Module 6: Discounted cash flows and valuation

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.

6.9

Why is the EAR superior to the 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 per cent. 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 per cent, but the second investment actually provides a return of 10.38 per cent because of the quarterly compounding. Thus, this is the superior investment!

6.10 Suppose two investments have equal lives and multiple cash flows. A high discount rate tends to favour: a. the investment with large cash flows early. b. the investment with large cash flows late. c. the investment with even cash flows. d. neither investment since they have equal lives.

Answer 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 favoured.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Questions and problems BASIC 6.1

Future value with multiple cash flows: Somerset Ltd, expects to earn cash flows of $10 875, $10 798, $11 595, and $17 128 over the next 4 years. If the company uses an 6.3 per cent discount rate, what is the future value of these cash flows at the end of year 4?

0 6.3% 1 2 3 4 ├───────┼────────┼───────┼────────┤ $10875 $10798 $11595 $17128 FV 4 = 10875(1.063) 3 + 10798(1.063) 2 + 11595(1.063)1 + 17128 = 13062.58 + 12201.41 + 12325.49 + 17128 = $54,717.48

6.2

Future value with multiple cash flows: Greg Wool has an investment that will pay him the following cash flows over the next five years: $4947, $5157, $6131, $4024, and $9549. If his investments typically earn 8.25 per cent, what is the future value of the investment’s cash flows at the end of 5 years?

0 8.25% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ $4947 $5157 $6131 $4024 $9549

FV 5 = 4947 (1.0825) 4 + 5157 (1.0825) 3 + 6131(1.0825) 2 + 4024(1.0825)1 + 9549 = 6792.87 + 6541.55 + 7184.34 + 4355.98 + 9549 = $34,423.74

Module 6: Discounted cash flows and valuation

6.3

Future value with multiple cash flows: You are first year at university and are planning a trip to Canada when you graduate at the end of 4 years. You plan to save the following amounts annually, starting today: $781, $627, $895 and $920. If the account pays 6.03 per cent annually, how much will you have at the end of 4 years?

0 6.03% 1 2 3 4 ├───────┼────────┼───────┼────────┤ $781 $627 $895 $920

FV 4 = 781(1.0603) 4 + 627(1.0603) 3 + 895(1.0603) 2 + 920(1.0603) = 987.11 + 747.40 + 1006.19 + 975.48 = $3,716.18

6.4

Present value with multiple cash flows: Peter Garcia has just purchased some equipment for his landscaping business. He plans to pay the following amounts at the end of each of the next 5 years: $11 009, $14 501, $11 298, $8 704 and $12 973. If he uses a discount rate of 11.534 per cent, what is the cost of the equipment he purchased today?

0 11.534% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ $11 009 $14 501 $11 298 $ 8 704 $12 973 PV =

11009 14501 11298 8704 12973 + + + + 2 3 4 (1.11534) (1.11534) (1.11534) (1.11534) (1.11534) 5

= 9870.53 + 11656.91 + 8142.91 + 5624.58 + 7516.30 = $42,811.23

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.5

Present value with multiple cash flows: Akram Motavalli borrowed a certain amount from his friend and promised to repay him the amounts of $2079, $1933, $2107, $1396, and $1578 over the next 5 years. If the friend normally discounts investments at 6.2 per cent annually, how much did Andrew borrow?

0 6.2% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ $2079 $1933 $2107 $1396 $1578 PV =

2079 1933 2107 1396 1578 + + + + 2 3 4 (1.062) (1.062) (1.062) (1.062) (1.062) 5

= 1957.63 + 1713.89 + 1759.10 + 1097.46 + 1168.11 = $7,696.19

6.6

Present value with multiple cash flows: Biosynthetics Pty Ltd expects the following cash flow stream over the next 5 years. The company discounts all cash flows at a 17.9 per cent discount rate. What is the present value of this cash flow stream?

0 17.9% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ -$1,035,546 -$1,094,678 $293,427 $822,105 $1,873,588

PV =

− 1,035,549 − 1,094,678 293,427 822,105 1,873,588 + + + + (1.179) (1.179) 2 (1.179) 3 (1.179) 4 (1.179) 5

= −878,325.70 − 787,514.90 + 179,043.54 + 425,473.06. + 822,441.60 = −$238,882.40

Module 6: Discounted cash flows and valuation

6.7

Present value of an ordinary annuity: An investment opportunity requires a payment of $592 for 12 years, starting a year from today. If your required rate of return is 8.8 per cent, what is the value of the investment today?

0 8.8% 1 2 3 11 12 ├───────┼────────┼───────┼………………┼───────┤ $592 $592 $592 $592 $592 Annual payment = PMT = $592 No. of payments = n = 12 Required rate of return = 8.8% Present value of investment = PVA12

PVA n = =

PMT  1   1 − n  i  (1 + i )   592  1  1 − 12  0.088  (1.088) 

= $4,282.17

6.8

Present value of an ordinary annuity: Dynamics Telecoconference Pty Ltd has made an investment in another company that will guarantee it a cash flow of $21 846 each year for the next 5 years. If the company uses a discount rate of 10 per cent on its investments, what is the present value of this investment?

0 10% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ $21846 $21846 $21846 $21846 $21846 Annual payment = PMT = $21846 No. of payments = n = 5 Required rate of return = 10% Present value of investment = PVA5

PVA n =

PMT  1   1 − n  i  (1 + i ) 

=

21846  1   1 − 5 0.1  (1.1) 

= $82,813.82

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.9

Future value of an ordinary annuity: Cecilia Fortuna plans to invest $23 004 a year at the end of each year for the next 7 years in an investment that will pay her a rate of return of 12.5 per cent per annum. How much money will Cecilia have at the end of 7 years?

0 12.5% 1 2 3 6 7 ├───────┼────────┼───────┼………………┼───────┤ $23004 $23004 $23004 $23004 $23004 Annual investment = PMT = $23,004 No. of payments = n = 7 Investment rate of return = 12.5% Future value of investment = FVA7





PMT  (1 + i ) n − 1 i 23004 =  (1.125) 7 − 1 0.125 = $235,689.30

FVA n =



6.10



Future value of an ordinary annuity: Silas Yeung is a sales executive at a Brisbane company. She is 25 years old and plans to invest $2296 every year in a retirement savings account, beginning at the end of this year until she turns 65 years old. If the retirement savings investment will earn 11.31 per cent annually, how much will she have in 40 years when she turns 65 years old?

0 11.31% 1 2 3 39 40 ├───────┼────────┼───────┼………………┼───────┤ $2296 $2296 $2296 $2296 $2296 Annual investment = PMT = $2,296 No. of payments = n = 40 Investment rate of return = 11.31% Future value of investment = FVA40





PMT  (1 + i ) n − 1 i 2296 =  (1.1131) 40 − 1 0.1131 = $1,454,986.63

FVA n =





Module 6: Discounted cash flows and valuation

6.11

Future value of an annuity. Refer to Problem 6.10. If Silas Yeung starts saving at the beginning of each year, how much will she have at age 65?

0

11.31% 1

2

3

39

40

├───────┼────────┼───────┼………………┼───────┤ $2296 $2296 $2296 $2296 $2296 Annual investment = PMT = $2296 No. of payments = n = 40 Type of annuity = Annuity due Investment rate of return = 11.31% Future value of investment = FVA40





PMT  (1 + i ) n − 1 (1 + i ) i 2296 =  (1.1131) 40 − 1 (1.1131) = 1,619,545.62  1.1131 0.1131 = $1,802,716.23

FVA n =





Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.12

Calculating annuity payment: Anthony Whitlam is saving for a European holiday in 3 years. He estimates that he will need $4229 to cover his airfare and all other expenses for a week-long holiday. If he can invest his money in an S&P/ASX500 equity index fund that is expected to earn an average return of 11.4 per cent over the next 3 years, how much will he have to save every year, starting at the end of this year?

0 11.4% 1 2 3 ├───────┼────────┼───────┤ PMT PMT PMT FVAn = $4,229 Future value of annuity = FVA = $4,229 Return on investment = i = 11.4% Payment required to meet target = PMT Using the FVA equation:





PMT  (1 + i ) n − 1 i PMT 4229 =  (1.114) 3 − 1 0.114 4229  0.114 482.106 PMT = = (1.114) 3 − 1 0.38247

FVA n =





= $1,260.51 Anthony has to save $1,260.51 every year for the next three years to reach his target of $4,229.

Module 6: Discounted cash flows and valuation

6.13

Calculating annuity payment: The Bridge Bar & Grill has a 7-year loan of $23 500 with Bankwest. It plans to repay the loan in 7 equal instalments starting today. If the rate of interest is 8.4 per cent per annum, how much will each payment be worth?

0 1 2 3 6 7 ├───────┼────────┼───────┼………………┼───────┤ 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:

PVAn =

PMT é 1 ù ´ ê1ú(1+ i) i ë (1+ i)n û

23500 ´ 0.084 23500 ´ 0.084 = é 1 ù 0.431415 ´1.084 (1.084) ê17ú ë (1.084) û = $4, 221.07

PMT =

Each payment made by Bridge Bar & Grill will be $4221.07, starting today.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.14 Calculating the number of periods: Michael Jones currently owes $3 450 on a car loan. If he is charged 11.6 per cent per annum, how long will it take him to pay off the loan assuming he pays $600 per year.

PVAn = CF  $3 450 = $600 

1 − 1/(1 + i)n i 1 − 1/(1.116)n 0.116

1 − 1/(1.116)n 0.116 0.667 = 1 − 1/(1.116)n 1/(1.116)n = 1 − 0.667 1.116n = 1/0.333 n × ln 1.116 = ln 3.003003003 n × 0.109750864= 1.0996 n = 10 payments n = 10 years 5.75 =

Using a financial calculator, the steps are: Enter

11.6

3450 [+/-]

600

0

Keys Solve for

6.15

10

Perpetuity: Your grandfather is retiring at the end of next year. He would like to ensure that he, and after he dies, his heirs receive a payment of $11 309 a year forever, starting when he retires. If he can invest at 9.9 per cent per annum, how much does need to invest to receive the desired cash flow?

Annual payment needed = PMT = $11,309 Investment rate of return = i = 9.9% Term of payment = Perpetuity Present value of investment needed = PV PMT 11309 = i 0.099 = $114,232.32

PV of Perpetuity =

Module 6: Discounted cash flows and valuation

6.16

Perpetuity: Calculate the perpetuity payments for each of the following cases: a. $250 000 invested at 6 per cent per annum. b. $50 000 invested at 12 per cent per annum. c. $100 000 invested at 10 per cent per annum. a.

Annual payment = PMT Investment rate of return = i = 6% Term of payment = Perpetuity Present value of investment needed = PV = $250 000 PMT i PMT = PV  i = 250000  0.06

PV of Perpetuity =

= $15000

b.

Annual payment = PMT Investment rate of return = i = 12% Term of payment = Perpetuity Present value of investment needed = PV = $50 000 PMT i PMT = PV  i = 50000  0.12

PV of Perpetuity =

= $6000

c.

Annual payment = PMT Investment rate of return = i = 10% Term of payment = Perpetuity Present value of investment needed = PV = $100 000 PMT i PMT = PV  i = $100000  0.10

PV of Perpetuity =

= $10000

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.17

Effective annual rate: Rajesh Sachdeva bought a Honda Civic for a price of $17 345.

He deposited $6000 and financed the rest through the dealer at an APR of 9.3 per cent for 4 years. What is the effective annual rate (EAR) if payments are made monthly?

Loan amount = PV = $17,345 Interest rate on loan = i = 9.3% Frequency of compounding = m = 12 Effective annual rate = EAR m

12

i   0.093  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0971 − 1 = 9.71%

6.18

Effective annual rate: Cyclone Rentals borrowed $15 550 from a bank for 3 years. If the quoted rate (APR) is 6.75 per cent, and the compounding is daily, what is the effective annual rate (EAR)?

Loan amount = PV = $15550 Interest rate on loan = i = 6.75% Frequency of compounding = m = 365 Effective annual rate = EAR m

i   0.0675  EAR = 1 +  − 1 = 1 + 365   m  = 1.0698 − 1 = 6.98%

365

−1

Module 6: Discounted cash flows and valuation

MODERATE 6.19

Future value with multiple cash flows: Tricord Ltd is expecting to invest cash flows of $1 175 227, $754 321, $1 162 092, $818 400, $1 239 644 and $1 617 848 in research and development over the next 6 years. If the appropriate interest rate is 8.17 per cent per annum, what is the future value of these investment cash flows?

0 8.17% 1 2 3 4 5 6 ├───────┼────────┼───────┼────────┼───────┼────────┤ $1,175,227 $754,321 $1,162,092 $818,400 $1,239,644 $1,617,848 FV 6 = 1,175,227(1.0817 ) 5 + 754,321(1.0817 ) 4 + 1,162,092(1.0817 ) 3 + 818,400(1.0817 ) 2 + 1,239,644(1.0817 )1 + 1,617,848 = 1,740,427.39 + 1,032,722.21 + 1,470,824.99 + 957,589.29 + 1,340,922.91 + 1,617,848 = $8,160,344.79

6.20

Future value with multiple cash flows: Stephanie Holland plans to adopt the following investment pattern beginning next year. She will invest $2719 in each of the next 3 years and will then make investments of $3650, $3725, $3875 and $4000 over the following 4 years. If the investments are expected to earn 7.3 per cent annually, how much will she have at the end of the 7 years?

Expected rate of return = i = 7.3% Investment period = n = 7 years Future value of investment = FV FV 7 = 2719(1.073) 6 + 2719(1.073) 5 + 2719(1.073) 4 + 3650(1.073) 3 + 3725(1.073) 2 + 3875(1.073) 1 + 4000 = 4149.61 + 3867.30 + 3604.19 + 4509.12 + 4288.70 + 4157.88 + 4000 = $28,576.80

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.21

Present value with multiple cash flows: Polly Chan, a lottery winner, will receive the following payments over the next 7 years. If she can invest her cash flows in a fund that will earn 10.5 per cent annually, what is the present value of her winnings?

Expected rate of return = i = 10.5% Investment period = n = 7 years Future value of investment = FV 200000 250000 275000 300000 350000 400000 550000 + + + + + + (1.105)1 (1.105) 2 (1.105) 3 (1.105) 4 (1.105) 5 (1.105) 6 (1.105) 7 = 180995 .48 + 204746.01 + 203819.56 + 201220.46 + 212449.96

FV7 =

+ 219728.47 + 273417.77 = $1,496,377.71

6.22

Calculating annuity payment: Marco Boncordo is a Year 9 student. He currently has $7500 in a savings account paying 5.65 per cent annually. Marco plans to use his current savings plus what he can save over the next 4 years to buy a car. He estimates that the car will cost him $12 000 in 4 years. How much money should Marco save each year if he wants to buy the car?

Cost of car in four years = $12000 Amount invested in money market account now = PV = $7500 Return earned by investment = i = 5.65% Value of current investment in 4 years = FV4

FV4 = PV (1 + i) 4 = 7500(1.0565) 4 = $9,344.14 Balance of money needed to buy car = 12000 – 9344.14 = $2655.86 = FVA Payment needed to reach target = PMT

PMT é ´ ë(1+ i)n -1ùû i FVA ´ i 2655.86 ´ 0.0565 150.0561 PMT = = = n é(1+ i) -1ù (1.0565)4 -1 0.245885 ë û FVA =

= $610.27

Module 6: Discounted cash flows and valuation

6.23 Calculating number of periods: Johnny Johnson borrowed $75 000 to purchase a caravan. The terms of his loan require him to make quarterly payments of $3434 over 7 years. The discount rate is 7.2 per cent per annum (compounding quarterly). How much sooner will he pay off the loan if he makes quarterly payments of $3876 instead?

PVAn =

CF 

$75 000 = $3 876

1 − 1/(1 + i)n i 1 − 1/(1.018)n 0.018

1 − 1/(1.018)n 0.018 0.348297213 = 1 − 1/(1.018)n 1/(1.018)n = 1 − 0.348297213 1.018n = 1/0.651702786 n × ln 1.018 = ln 1.534441806 n × 0.017839918 = 0.42816667 n = 24 payments n = 6 years 19.3498452 =

Using a financial calculator, the steps are:

Enter Keys Solve for

1.8

75000 [+/]

3876

0

24

Note: don’t forget to convert the value of N to the number of years by dividing by 4.

If he makes the higher payments, he will pay off the loan in six years, thus one year sooner than the original term.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.24

Future value of an annuity due: Joshua Lipscombe plans to save $4613 every year for the next 8 years, starting today. At the end of 8 years, Jeremy will turn 30 years old and plans to use his savings toward the deposit on a house. If his investment in an investment fund will earn him 9.5 per cent annually, how much will he have saved in 8 years when he will need the money to buy a house?

0 9.5% 1 2 3 7 8 ├───────┼────────┼───────┼………………┼───────┤ $4,613 $4,613 $4,613 $4,613 $4,613 Annual investment = PMT = $4,613 No. of payments = n = 8 Type of annuity = Annuity due Investment rate of return = 9.5% Future value of investment = FVA8





PMT  (1 + i ) n − 1 (1 + i ) i 4613 =  (1.095) 8 − 1  (1.095) = 48557.89  1.066869009  1.095 0.095 = $56,726.38

FVA n =



6.25



Present value of an annuity due: Grant Productions has borrowed a huge sum from the Esanda Finance Ltd at a rate of 17.5 per cent annually for a 7-year period. The loan calls for a payment of $1 540 862.19 each year beginning today. What is the amount borrowed by this company?

0 17.5% 1 2 3 6 7 ├───────┼────────┼───────┼………………┼───────┤ PMT =$1540862.19 at the beginning of each year Annual payment = PMT = $1540862.19 Type of annuity = Annuity due No. of payments = n = 7 Required rate of return = 17.5% Present value of investment = PVA8

PMT é 1 ù ´ ê1ú(1+ i) i ë (1+ i)n û 1540862.19 é 1 ù = ´ ê1ú(1.175) = 8804926.8 ´ 0.6766 ´1.175 0.175 ë (1.175)7 û = $6,999,999.98 @ $7,000,000

PVAn =

Module 6: Discounted cash flows and valuation

6.26

Present value of an annuity due: Sharon Lance has won a lottery and will receive a payment of $85 950.97 every year, starting today for the next 20 years. If she invests the proceeds at a rate of 5.52 per cent per annum, what is the present value of the cash flows that she will receive?

0 5.52% 1 2 3 19 20 ├───────┼────────┼───────┼………………┼───────┤ PMT = $85,950.97 at the beginning of each year Annual payment = PMT = $85,950.97 Type of annuity = Annuity due No. of payments = n = 20 Required rate of return = 5.52% Present value of investment = PVA20

PVA n = =

PMT  1   1 − (1 + i ) n  i  (1 + i )   85,950.97  1  1 − (1.0552) = 1557082 .79  0.6585679  1.0552 20  0.0552  (1.0552) 

= $1,082,049.30  $1,082,049

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.27

Perpetuity: Calculate the present value of the following perpetuities: a. $1250 discounted to the present at 7 per cent. b. $7250 discounted to the present at 6.33 per cent. c. $850 discounted to the present at 20 per cent. a.

Annual payment = PMT =$1250 Investment rate of return = i = 7% Term of payment = Perpetuity Present value of investment needed = PV PMT 1250 = i 0.07 = $17,857.14

PV of Perpetuity =

b.

Annual payment = PMT =$7250 Investment rate of return = i = 6.33% Term of payment = Perpetuity.

Present value of perpetuity = PV PMT 7250 = i 0.0633 = $114,533.97

PV of Perpetuity =

c.

Annual payment = PMT =$850 Investment rate of return = i = 20% Term of payment = Perpetuity.

Present value of investment needed = PV PMT 850 = i 0.20 = $4,250

PV of Perpetuity =

Module 6: Discounted cash flows and valuation

6.28

Effective annual rate: Find the effective annual interest rate (EAR) on each of the following: a. 6 per cent compounded quarterly. b. 4.99 per cent compounded monthly. c. 7.25 per cent compounded semi-annually. d. 5.6 per cent compounded daily. a.

Interest rate = i = 6% Frequency of compounding = m = 4 Effective annual rate = EAR m

4

i   0.06  EAR = 1 +  − 1 = 1 + −1 4   m  = 1.06136 − 1 = 6.14% b.

Interest rate = i = 4.99% Frequency of compounding = m = 12 Effective annual rate = EAR m

12

i   0.0499  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0511 − 1 = 5.11% c.

Interest rate = i = 7.25% Frequency of compounding = m = 2 Effective annual rate = EAR m

2

i   0.0725  EAR = 1 +  − 1 = 1 + −1 2   m  = 1.0738 − 1 = 7.38% d.

Interest rate = i = 5.6% Frequency of compounding = m = 365 Effective annual rate = EAR m

i   0.056  EAR = 1 +  − 1 = 1 + 365   m  = 1.0576 − 1 = 5.76%

365

−1

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.29

Effective annual rate: Which of the following investments has the highest effective annual rate (EAR)? a. A bank term deposit that pays 8.25 per cent compounded quarterly. b. A bank term deposit that pays 8.25 per cent compounded monthly. c. A bank term deposit that pays 8.45 per cent compounded annually. d. A bank term deposit that pays 8.25 per cent compounded semiannually. e. A bank term deposit that pays 8 per cent compounded daily (on a 365-day basis). a.

Interest rate on term deposit = i = 8.25% Frequency of compounding = m = 4 Effective annual rate = EAR m

4

i   0.0825  EAR = 1 +  − 1 = 1 + −1 4   m  = 1.08509 − 1 = 8.51% b.

Interest rate on term deposit = i = 8.25% Frequency of compounding = m = 1 Effective annual rate = EAR m

12

i   0.0825  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0857 − 1 = 8.57% c.

Interest rate on term deposit = i = 8.45% Frequency of compounding = m = 12 Effective annual rate = EAR m

1

i   0.0845  EAR = 1 +  − 1 = 1 + −1 1   m  = 1.0845 − 1 = 8.45% d.

Interest rate on term deposit = i = 8.25% Frequency of compounding = m = 2 Effective annual rate = EAR m

2

i   0.0825  EAR = 1 +  − 1 = 1 + −1 2   m  = 1.0842 − 1 = 8.42%

Module 6: Discounted cash flows and valuation

e.

Interest rate on term deposit = i = 8% Frequency of compounding = m = 365 Effective annual rate = EAR m

i   0.08  EAR = 1 +  − 1 = 1 +  m  365  = 1.0833 − 1 = 8.33%

365

−1

The bank term deposit that pays 8.25 per cent monthly has the highest yield of 8.57%.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.30

Effective annual rate: You are considering three alternative investments: (1) a 3year bank term deposit paying 7.5 per cent interest compounded quarterly; (2) a 3year bank term deposit paying 7.3 per cent interest compounded monthly; and (3) a 3-year bank term deposit paying 7.75 per cent interest compounded annually.

Which investment has the highest effective annual rate?

(1)

Interest rate on term deposit = i = 7.5% Frequency of compounding = m = 4 Effective annual rate = EAR m

4

i   0.075  EAR = 1 +  − 1 = 1 + −1 4   m  = 1.0771 − 1 = 7.71% (2)

Interest rate on term deposit = i = 7.3% Frequency of compounding = m = 12 Effective annual rate = EAR m

12

i   0.073  EAR = 1 +  − 1 = 1 + −1 12   m  = 1.0755 − 1 = 7.55% (3)

Interest rate on term deposit = 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% The three-year bank term deposit paying 7.75 per cent interest compounded annually has the highest effective yield.

Module 6: Discounted cash flows and valuation

CHALLENGING 6.31

Joshua Kennedy, a professional football player, 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. Joshua and his agent came up with a counter offer.

What are the present values of each of the contracts using a 14 per cent discount rate? Which of the three contacts has the highest present value?

Current Contract 812500 365000 271500 182225 + + + (1.14) (1.14) 2 (1.14)3 (1.14) 4 = 712719.30 + 280855.65 + 183254.77 + 107891.83

PV =

= $1,284,721.54

Team’s Offer

400000 382500 385000 392500 + + + (1.14) (1.14) 2 (1.14) 3 (1.14) 4 = 350877.19 + 294321.33 + 259864.03 + 232391.51

PV =

= $1,137,454.07 Counteroffer

525000 755000 362500 280000 + + + (1.14) (1.14) 2 (1.14) 3 (1.14) 4 = 460526.32 + 580947.98 + 244677.17 + 165782.48

PV =

= $1.451.933.95 The counteroffer has the best value for the player.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.32

Gary Dahl will turn 30 years old next year. He comes up with a plan to save for his retirement at 67 years of age. Currently, he has saved $40 000 in a balanced superannuation account earning 8.3 per cent annually. He also currently has invested an inheritance of $50 000 in a money market account earning 5.25 per cent per annum and plans to leave it as part of his retirement savings. He has set himself a retirement target of $2 000 000. How much must be deposited in his superannuation account each year to reach his target? If Gary is earning $60 000 a year and 9 per cent of his salary is deposited into his superannuation by his employer, would Gary have to make further contributions to enable him to reach his goal?

Investment (1) Balance in superannuation = PV = $40000 Return on superannuation account = i = 8.3% Time to retirement = n = 37 years Value of superannuation at age 67 = FVIRA

FV IRA = PV (1 + i ) n = 40000(1.083) 37 = $764,386.29 Investment (2) Balance in money market investment = PV = $50000 Return on money market account = i = 5.25% Time to retirement = n = 37 years Value of money market at age 67 = FVMMA

FV MMA = PV (1 + i ) n = 50000(1.0525) 37 = $332,038.06 Target retirement balance = $2,000,000 Future value of current savings = 764386.29 + 332038.06 = $1,096,424.35 Amount needed to reach retirement target = FVA = $903,575.65 Annual payment needed to meet target = PMT Expected return on superannuation = i = 8.3%

PMT é n ë(1+ i) -1ùû i FVA ´ i 903575.65´ 0.083 74996.78 PMT = = = éë(1+ i)n -1ùû éë(1.083)37 -1ùû 18.10966 FVA =

= $4,141.26 As Gary’s employer superannuation contribution is $5400 ($60000 x 0.09 = $5400) each year Gary will not have to make any additional payments to meet his goal.

Module 6: Discounted cash flows and valuation

6.33

Babu Baradwaj is planning to save for his son’s university education. His son is currently 11 years old and will begin university in 7 years. Babu has an index fund investment of $17 500 earning 9.5 per cent annually. Total expenses currently at the University of Sydney where his son says he plans to go, are expected to be $35 000 per year. Babu plans to invest a certain amount in an investment fund that will earn 11 per cent annually to make up the difference between the education expenses and his current 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 university. a. What will be the present value of the 4 years of education expenses at the time that Babu’s son starts university? Assume a discount rate of 6 per cent. b. What will be the value of the index fund when his son just starts university? 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 university expenses? d. How much will Babu have to invest every year in order for him to have enough funds to cover all his son’s expenses?

Annual cost of university education today (t = 0) = $35 000 Expected increase in annual tuition costs = g = 4% a.

Four-year tuition costs (t = 7 to t = 10) Discount rate = i = 6% Need Present value of tuition costs in year 7 not year 6 = PV

PVAn = =

PMT  1   1 − (1 + i ) n  i  (1 + i )  35, 000  1   1 −  (1.06) = 583, 333.33  0.207906336  1.06 0.06  (1.06)4 

= $128, 555.42 b.

Future value of the index mutual fund at t = 7 Present value of index fund investment = PV = $17500 Return on fund = i = 9.5% Future value of investment = FV

FV = PV (1 + i )n = 17, 500(1.095)7 = $33, 032.15

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

c.

Target savings needed at t = 7 PV of tuition costs – Future value of investment

= $128, 555.42 − 33, 032.15 = $95, 523.27

d.

Annual savings needed Return on fund = i = 11% Amount that needs to be saved = FVA = $95,523.27 Annuity payment needed = PMT

 (1 + i )n − 1  FVA = PMT   (1 + i ) i   FVA 95, 523.27 95, 523.27 PMT = = = n 7 9.783274117  1.11  (1 + i ) − 1   (1.11) − 1    (1 + i )    (1.11) i    0.11  = $8, 796.34

Module 6: Discounted cash flows and valuation

6.34

You are now 50 years old and plan to retire at age 67. You currently have a share portfolio worth $150 000, a superannuation plan worth $250 000, and a money market account worth $50 000. Your share portfolio is expected to provide you annual returns of 12 per cent, your superannuation investment will earn you 9.5 per cent annually, and the money market account earns 6.25 per cent, compounded monthly. a. If you do not save another cent, what will be the total value of your investments when you retire at age 67? b. Assume that your superannuation contribution is $12 000 per year for the next 17 years (starting 1 year from now). How much will your investments be worth when you retire at 67? c. Assume that you expect to live another 23 years after you retire (until age 90). At age 67, you now take all of your investments and place them in an account that pays 8 per cent (use the scenario from part b in which you continue saving). If you start withdrawing funds starting at age 68, how much can you withdraw every year (e.g., an ordinary annuity) and leave nothing in your account after a 23th and final withdrawal at age 90? d. At age 67, you want your 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 (at 8 per cent per year)? a.

Share Portfolio Current value of share portfolio = $150,000 Expected return on portfolio = i = 12% Time to retirement = n = 17 years Expected value of portfolio at age 67 = FVShares

FVShare = PV (1 + i)17 = 150000(1.12)17 = $1,029,906.13 Superannuation Investment Current value of Superannuation portfolio = $250,000 Expected return on portfolio = i = 9.5% Time to retirement = n = 17 years Expected value of portfolio at age 67 = FVSuper

FVSuper = PV (1 + i)17 = 250000(1.095)17 = $1,169,445.63

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Money market account Current value of savings = $50,000 Expected return on portfolio = i = 6.25% Time to retirement = n = 17 years Frequency of compounding = m = 12 Expected value of portfolio at age 67 = FVMMA mn

1217

i    0.0625  FV MMA = PV 1 +  = 500001 +  12   m  = 50000  2.8856 = $144,281.41

Total value of all three investments = $1,029,906.13+ $1,169,445.63+$144,281.41 = $2,343,633.17 b.

Planned annual investment in superannuation plan = $12,000 Future value of annuity = FVA

PMT é ´ ë(1+ i)n -1ùû i 12, 000 é = ´ ë(1.095)17 -1ùû = 126315.78 ´ 3.67778 0.095 = $464,562.00

FVAn =

Total investment amount at retirement = $2,343,633.174+ $464,562.001 = $2,808,195.18 c.

Amount available at retirement = PVA = $2,808,195.18 Length of annuity = n = 23 Expected return on investment = i = 8% Annuity amount expected = PMT Using the PVA equation:

PVAn =

PMT é 1 ù ´ ê1ú i ë (1+ i)n û

2,808,195.18 ´ 0.08 224655.6144 = é 1 ù 0.829685 ê123 ú ë (1.08) û = $270772.27

PMT =

Each payment received for the next 23 years will be $270,772.27.

Module 6: Discounted cash flows and valuation

d.

Type of payment = Perpetuity Present value of perpetuity = PVA = $2,808,195.18 Expected return on investment = i = 8%

PMT i PMT 2,808,195.18 = 0.08 PMT = $2,808,195.18  0.08 = $224655.61

PV of Perpetuity =

You could receive an annual payment of $224,655.61 forever.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.35

Trevor Richardson is looking to purchase a Mercedes Benz SL600 Roadster which has a total cost of $335 000. Trevor plans to deposit $120 000 and will pay the rest by taking on a 7.75% per annum 5-year bank loan. What is the monthly payment on this car loan? Prepare an amortisation table using Excel. Assume interest compounds monthly.

Cost of new car = $335000 Deposit = $20,000 Loan amount = $385000-$120000 = $215000 Interest rate on loan = i = 7.75% Term of loan = 5 years Frequency of payment = m = 12 n = 12 x 5 = 60 Monthly payment on loan = PMT

PVAn =

PMT é 1 ù ´ ê1ú i ë (1+ i)n û

215000 ´ 0.0775 12 = 1388.542 PMT = é ù 0.3204 ê ú 1 ê1ú ê æ 0.0775 ö12´5 ú ÷ ú ê ç1+ 12 ø û ë è = $4, 333.75

Module 6: Discounted cash flows and valuation

6.36

The Harding's are buying a new 4 bedroom house in Albury-Wodonga and will borrow $337 000 from Westpac at a rate of 8.375 per cent per annum for 25 years.

What is their monthly loan payment? Prepare an amortisation schedule using Excel.

Assume interest compounds monthly.

Home loan amount = $337,000 Interest rate on loan = i = 8.375% Term of loan = 25 years Frequency of payment = m = 12 n = 25 x 12 = 300 Monthly payment on loan = PMT

PVAn = PMT =

=

PMT é 1 ù ´ ê1ú i ë (1+ i)n û 337000 ´ 0.08375 12

é ù ê ú 1 ê1ú ê æ 0.08375 ö12´25 ú ÷ ê ç1+ ú 12 ø ë è û 2351.98 = $2685.29 0.87588

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

6.37

Assume you will start on a job as soon as you graduate (at 22) and that saving for your retirement through superannuation starts at that time. Currently, you plan to retire when you turn 67 years old. 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 18 years). The average inflation rate is likely to be 4 per cent. a. Calculate the lump sum you need to have accumulated in your superannuation by the age of 67 to be able to draw the desired income. Assume that your return on the portfolio investment is likely to be 10 per cent per annum. b. What is the dollar amount you need to invest every year, starting at age 22 and ending at age 67 (i.e. for 45 years) to reach the target lump sum at age 67? c. Now answer questions a and b assuming your rate of return to be (i) 8 per cent per year and (ii) 15 per cent per year. d. Assume you do not start working until you finish your PhD when you are 28 years old and your superannuation saving starts then. Analyse the situation under rate of return assumptions of (i) 8 per cent per year, (ii) 10 per cent per year, and (iii) 15 per cent per year.

RETIREMENT ANALYSIS SUMMARY INVESTMENT AGE = 22 INVESTMENT AGE = 28

Rate of Return Inflation rate Retirement Income Level Lump sum needed at age 67 Annuity payment needed

8%

10%

15%

8%

10%

15%

5% $40,000 $2,995,139

$2,574,263 $1,847,416

$2,995,139

$2,574,263

$1,847,416

$7,749.28

$3,580.81

$12,535.05

$6,412.45

$1,194.84

$515.30

Module 7: Risk and return 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?

Part 1: E(cash flow) = (0.5 x –$15) + (0.5 x $15) = 0 σ2cash flow = [0.5 x (–$15 - $0)2] + [0.5 x ($15 – $0)2] = $225 Part 2: E(cash flow) = (0.5 x –$15) + (0.5 x $20) = $2.50 σ2cash flow = [0.5 x (–$15 – $2.50)2] + [0.5 x ($20 – $2.50)2] = $306.25

7.2

You know that the price of a CSR Ltd share will be $12 exactly 1 year from today.

Today the price of the share is $11. Describe what must happen to the price of CSR Ltd today in order for an investor to generate a 20 per cent return over the next year.

Assume that CSR does not pay dividends.

The expected return for CFI based on today’s share price is ($12 – $11)/$11 = 9.09%.

Therefore, you require a higher return. Since the share price one year from today is fixed, then the only way that you will generate a 20 per cent return is if the price of the share drops today. Consequently, the price of the share today must drop to $10. It is found by solving the following: 0.2 = ($12 – x)/ x, or x = $10.

7.3

Two men are making a bet according to the outcome of a coin toss. You know that the expected outcome of the bet is that one man will lose $20. Suppose you know that if that same man wins the coin toss, he will receive $80. How much will he pay out if he loses the coin toss?

Since you know that the probability of any coin toss outcome is equal to 0.5, you can solve the problem by setting up the following equation: –$20 = (0.5 x $80) + (0.5 x x) And solving for x: 0.5 x x = -$20 – (0.5 x $80) x = [-$20 – (0.5 x $80)]/0.5 = $120

Module 7: Risk and return

This means that he pays $120 if he loses the bet.

7.4

The expected value of a normal distribution of prices for a share is $50. If you are 90 per cent sure that the price of the share will be between $40 and $60, then what is the variance of the prices for the share?

Since you know that 1.645 standard deviations around the expected return captures 90 per cent 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

7.5

The Solahart Industries Pty Ltd common shares have an expected return of 25 per cent and a coefficient of variation of 2.0. What is the variance of Solahart ordinary share returns?

Since the coefficient of variation = CVi = σRi /E(Ri), substituting in the coefficient of variation and E(Ri) allows us to solve for σ2return as follows: 2.0 = σRi/0.25 σRi = 0.5 σ2Ri = (0.5)2 = 0.25

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Critical thinking questions 7.1

Given that you know the risk as well as the expected return for two shares, discuss what process you might utilise to determine which of the two shares is a better buy.

You may assume that the two shares will be the only assets held in your portfolio.

You should be looking to maximise 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 shares. If the shares have the same expected return, then choose the share with the lower risk. If the shares have the same risk, then choose the share 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 share contains the least risk per unit of expected return.

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 realised. 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.

7.3

Suppose that the standard deviation of the returns on the shares of share at two different companies is exactly the same. Does this mean that the required rate of return will be the same for these two shares? How might the required rate of return on the share of a third company be greater than the required rates of return on the shares of the first two companies even if the standard deviation of the returns of the third company’s share is lower?

No. Because some risk can be diversified away, it is possible that two shares with the same standard deviation of returns can have different required rates of return. One of these shares can have a higher systematic risk than the other share and, therefore, a higher required rate of return. The third share can have a higher required rate of return if its systematic risk is greater than the systematic risk of the share in the other two companies.

Module 7: Risk and return

7.4

The correlation between Shares A and B is 0.50, while the correlation between Shares A and C is –0.5. You already own Share A and are thinking of buying either Share B or Share C. If you want your portfolio to have the lowest possible risk, would you buy Share B or C? Would you expect the share you choose to affect the return that you earn on your portfolio?

You would buy share C because it would result in your portfolio having a lower beta. If you buy share C, the required return for your portfolio would be lower than the required return would be if you bought share B. If the expected returns on shares C and B equal their required returns, then you would expect your portfolio to earn less with share C.

7.5

The idea that we can know the return on a security for each possible outcome is overly simplistic in many ways. 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 Australian 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.

7.6

Which investment category has shown the greatest degree of risk in Australia since 1974? Explain why that makes sense in a world where the price of a small share is likely to be more adversely affected by a particular negative event than the price of a government bond. Use the same type of explanation to help explain other investment choices since 1974.

Small shares have generally been riskier than large shares, 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 realise that shares in small companies 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.

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 company. You do believe, however, that the company 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 company’s cash?

The risk of Shifty embezzling is a non-systematic 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).

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

7.8

The CAPM is used to price the risk in any asset. Our examples have focused on shares, but we could also price the expected rate of return for bonds. Explain how debt securities are also subject to systematic risk.

A company’s ability to repay its debt obligations will be affected in a very similar, and yet lessened, way than the company’s share 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.

7.9

In recent years, investors have correctly agreed that the market portfolio consists of more than just a group of Australian shares and bonds. If you are an investor who only invests in Australian shares, describe the effects on the risk in your portfolio.

If the market portfolio is composed of all assets, then the Australia-only portfolio will probably have a small amount of non-systematic risk that is not providing return compensation for that risk. Therefore, the portfolio is bearing too much risk given its expected returns.

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 per cent of your assets in the early part of your investment life. Evaluate omitting it from your portfolio 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.

Module 7: Risk and return

Questions and problems BASIC 7.1

Returns: Describe the difference between a total holding period return and an expected return.

The holding period return is the total return over some investment or “holding” period. It consists of a capital appreciation component and an income component. The holding period return reflects past performance. The 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: Barry is watching an old game show on rerun television called Let’s Make a Deal in which you have to choose a prize behind one of two curtains.

One of the curtains will yield a gag prize worth $179, and the other will give a car worth $5640. 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 per cent. What is the expected value of the selection, and what is the standard deviation of that selection?

E(prize) =0 .75($179) + (0.25) ($5,640) = $1,544.25 σ2prize = 0.75($179 – $1,544.25)2 + (0.25) ($5,640 – $1,544.25)2 = $5,591,722.687500 => σprize

7.3

= ($5,591,722.687500)1/2 = $2,364.68

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 into medical school is about 18 per cent. If you are accepted into medical school, then your starting salary when you graduate will be $346 085 per year.

However, if you are not accepted, then you would choose to work in a zoo, where you will earn $42 530 per year. Without considering the additional educational years or the time value of money, what is your expected starting salary as well as the standard deviation of that starting salary?

E(salary) = 0.82($42,530) + (0.18) ($346,085) = $97,169.90 σ2salary = 0.82($42,530 – $97,169.90)2 + (0.18) ($346,085 – $97,169.90)2 = $13,600,696,172.4900 σsalary = ($13,600,696,172.4900)1/2 = $116,622.02

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

7.4

Historical market: Describe the general relation between risk and return that we observe in the historical bond and share market data.

The general axiom that the greater the risk, the greater the return describes the historical returns of the bond and share market. If we look in module 7 of the text, we see that small shares have averaged the greatest returns but that they also have the greatest standard deviation for the returns. When compared to large shares, the average return and standard deviation of the small shares are greater. Large share 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 Australian notes or bonds. 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: Shares A, B, and C have expected returns of 17.12 per cent, 12.62 per cent, and 11.34 per cent, respectively, while their standard deviations are 41.54 per cent, 26.55 per cent, and 34.63 per cent, respectively. If you were considering the purchase of each of these shares as the only holding in your portfolio, then which share should you choose?

Since the holding will be made in a completely undiversified portfolio, then we can calculate the risk per unit of return for each share, the coefficient of variation, and choose the share with the lowest value.

CV(RA) = 0.4154/0.1712 = 2.43 CV(RB) = 0.2655/0.1262 = 2.10 CV(RC) = 0.3463/0.1134 = 3.05 ===> Choose B 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 Share B is superior.

7.6

Diversification: Describe how investing in more than one asset can reduce risk through diversification.

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.

Module 7: Risk and return

7.7

Systematic risk: Define systematic risk.

Risk that cannot be diversified away is called 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.

7.8

Measuring systematic risk: Susan is expecting the returns on the market portfolio to be negative in the near term. Since she is managing an equity investment fund, she must remain invested in a portfolio of shares. However, she is allowed to adjust the beta of her portfolio. What kind of beta would you recommend for Susan’s portfolio?

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 an Australian government bond should be.

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 government note or bond. If we purchased a government bond five years ago and held the same bond 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 government bond has no systematic risk. That is logical given that we know that a government bond has no risk at all since it is a riskless asset.

7.10

Measuring systematic risk: If the expected rate of return for the market is not much greater than the risk-free rate of return, what is the general level of compensation for bearing systematic risk?

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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

7.11

CAPM: Describe the Capital Asset Pricing Model (CAPM) and what it tells us.

The CAPM is a model that 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 risk-free rate. As systematic risk increases, the expected return increases linearly with beta. The CAPM is written as E(Ri) = Rrf + i(E(Rm) – Rrf) .

7.12

The Security Market Line: If the expected return on the market is 6.18 per cent and the risk-free rate is 4 per cent, what is the expected return for a share with a beta equal to 1.11? What is the market risk premium for the set of circumstances described?

Following the CAPM prediction: (Rcs) = Rrf + β (E(RM) – Rrf) = 0.04 + 1.11(0.0618 – 0.04) = 0.0642 The market risk premium is (E(RM) – Rrf)

= 0.0618 – 0.04 = 0.0218

Module 7: Risk and return

MODERATE 7.13

Expected returns: Nikhil is thinking about purchasing a soft drink machine and placing it in a business office. He knows that there is a 12 per cent 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 Nikhil expects 1387 people per day to pass by the machine and requires a complete return of his investment in 1 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 tax and the time value of money.

E(Revenue) = 1,387 x 0.12 x $.10 x 250 days = $4,161 Therefore, the most Nikhil should pay for the machine is $4,161.

7.14

Interpreting the variance and standard deviation: The distribution of results in an introductory finance class is normally distributed, with an expected grade of 68. If the standard deviation of grades is 6, in what range would you expect 90 per cent of the grades to fall?

90% is 1.645 standard deviations from the mean 68 + (6 x 1.645) = 77.870 68 – (6 x 1.645) = 58.13 Range = 77.870 – 58.13 = 19.74

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

7.15

Calculating the variance and standard deviation: You are considering purchasing shares in Lake Awoonga Scenic Tours Ltd. You have observed the following returns on this share over the last four years: Year Return

1 – 8%

2 3%

3 16%

4 5%

What is the expected return and standard deviation of the return on Awoonga Scenic Tours shares?

The average return is: n

 (R )

R1 + R2 + + Rn n n −8 + 3 + 16 + 5 16 = = = 4% 4 4 i

E(R Asset ) = i =1

=

The variance of returns is:

n

  R − E(R)

2

i

 R2 = i =1

n −1

2 2 2 2 R i − E(R)  +  R i − E(R)  +  R i − E(R)  +  R i − E(R)   =

4 −1

 −8 − 4 + 3 − 4 + 16 − 4 + 5 − 4 2

=

2

2

3

−12 − 1 + 12 + 1 144 + 1 + 144 + 1 = 3 3 290 = = 96.67% 2 3

=

2

2

2

2

The standard deviation of returns is: 1

 R = ( R2 ) 2 =  R2 = 96.67 = 9.83%

2

Module 7: Risk and return

Note: You may find it easier to calculate the variance of returns using a table format as shown below.

(1) Actual Return Ri –8 3 16 5 16

Year 1 2 3 4 Totals

n

(2) Average Return E(R) 4 4 4 4

(3) Deviation (1) – (2) Ri – E(R) – 12 –1 12 1 0.0

(4) Squared Deviation [Ri – E(R)]2 144 1 144 1 290

  R − E(R) = 290 i =1

2

i

 R2 =

7.16

290 290 = = 96.67% 2 n −1 3

Calculating the variance and standard deviation: Kayla recently invested in real estate with the intention of selling the property 1 year from today. She has modelled 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 per cent return.

However, if the economy softens, as predicted, the return will be 10 per cent, while the return will be –25 per cent if the economy slips into a recession. If the probabilities of the healthy, soft and recessionary states are 0.2, 0.6 and 0.2, respectively, then what are the expected return and the standard deviation on Kayla’s investment?

E(Ri)

= (0.2)(0.3) + (0.6) (0.1) + (0.2) (–.25) = 0.0700

σ2return = (0.2)(0.3 – 0.0700)2 + (0.6) (0.1 – 0.0700)2 + (0.2) (–0.25 – 0.0700)2 = 0.031600 σreturn = (0.031600)1/2 = 0.1778

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

7.17

Calculating the variance and standard deviation: Sandra is considering investing in a share 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 Sandra’s investment.

Probability Return Boom 0.3 25.00% Good 0.4 15.00% Level 0.2 10.00% Slump 0.1 -5.00%

E(Ri) = 0.3(0.25) + (0.4) (0.15) + (0.2) (0.1) + (0.1) (–o.05) = 0.1500 σ2return = 0.3(0.25 – 0.1500)2 + (0.4) (0.15 – 0.1500)2 + (0.2) (0.1 – 0.1500)2 + (0.1) (–0.5 – 0.1500)2

= 0.007500 σreturn = (0.007500)1/2 = 0.0866

7.18

Calculating the variance and standard deviation: James 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 on James’s gold investment.

Probability Return Boom 0.1 34.00% Good 0.2 25.00% OK 0.3 13.00% Level 0.2 1.00% Slump 0.2 -17.00%

E(Ri) = 0.1(0.34) + (0.2) (0.25) + (0.3) (0.13) + (0.2) (0.01) + (0.2) (–0.17) = 0.0910 σ2return = 0.1(0.34 – 0.0910)2 + (0.2) (0.25 – 0.0910)2 + (0.3) (0.13 – 0.0910)2 + (0.2) (0.01 – 0.0910)2 + (0.2) (–0.17 – 0.0910)2 = 0.026649 σreturn = (0.026649)1/2 = 0.1632

Module 7: Risk and return

7.19

Single-asset portfolios: Using the information from Problems 7.15, 7.16, and 7.17, calculate each coefficient of variation.

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 = 0.083707 (using the exact values rather than the printed) Problem 17: 0.16759/0.125 = 1.34069 (using the exact values rather than the printed)

7.20

Portfolios with more than one asset: Andrea is analysing a two-share portfolio that consists of a utility share and a commodity share. She knows that the return on the utility has a standard deviation of 40 per cent, and the return on the commodity has a standard deviation of 30 per cent. However, she does not know the exact covariance in the returns of the two shares. Andrea would like to plot the variance of the portfolio for each of three cases—covariance of 0.17, 0 and –0.17—in order to understand how the variance of such a portfolio would react. Do the calculation for each of the extreme cases (0.17 and –0.17), assuming an equal proportion of each share in Andrea’s portfolio.

Var ( R2 asset port ) = x12 12 + x22 22 + 2 x1 x2 12 Part 1, σ12 = 0.12: (0.5)2 (0.4)2 + (0.5)2 (0.3)2 + 2(0.5)(0.5)(0.17) = 0.1475 Part 2, ρ = 0.0: (0.5)2 (0.4)2 + (0.5)2 (0.3)2 + 2(0.5)(0.5)(0.0) = 0.0625 Part 3, σ12 = -0.12: (0.5)2 (0.4)2 + (0.5)2 (0.3)2 + 2(0.5)(0.5)(-0.17) = -0.0225

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

7.21 Portfolios with more than one asset: Given the returns and probabilities for the three possible states listed here, calculate the covariance between the returns of Share A and Share B. For convenience, assume that the expected returns of Share A and Share B are 11.75 per cent and 18 per cent, respectively.

Probability 0.30 0.50 0.2

Good OK Poor

Return(A) 0.30 0.10 -0.25

Return(B) 0.50 0.10 -0.30

Cov ( RA , RB ) =  AB = 0.30(0.3 − 0.1175)(0.5 − 0.18) + 0.5(0.1 − 0.1175)(0.1 − 0.18) + 0.2(−0.25 − 0.1175)(−0.3 − 0.18) = 0.0535

7.22

Compensation for bearing systematic risk: You have constructed a diversified portfolio of shares 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.

Your portfolio contains no non-systematic risk but it does in fact contain systematic risk.

Therefore, the market should compensate the holder of this portfolio for the systematic risk that the investor bears. The risk-free security has no risk and therefore requires no compensation for risk bearing. The expected return of the portfolio should therefore be greater than the return of the risk-free security.

7.23

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.

Cov(Return1 , Return 2 ) =  R12 n

(

=  pi x (Return1,i − E(Return1 )  x (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.

Module 7: Risk and return

7.24

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 note.

The statement is false. Even if we could afford such a portfolio and thus completely diversify our portfolio, we would only be eliminating non-systematic risk. The systematic risk generated by the portfolio would remain. Otherwise, the expected rate of return on the market portfolio would be equal to the risk-free rate of return. We know that to be a false statement.

7.25

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 per cent. What is the expected return on Damien’s portfolio?

Following the CAPM prediction: (Rcs) = Rrf + β (E(RM) – Rrf) = Rrf + E(RM) – Rrf = E(RM) = 0.08

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

CHALLENGING 7.26

David is going to purchase two shares to form the initial holdings in his portfolio.

Iron share has an expected return of 14 per cent, while Copper share has an expected return of 28 per cent. If David plans to invest 30 per cent 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 per cent of his funds in Iron shares?

Part 1: E(Rport) = (0.3)(0.14) + (0.7)(0.28) = 0.2380 Part 2: E(Rport) = (0.7)(0.14) + (0.3)(0.28) = 0.1820

7.27

Sumeet 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.

The covariance measure is dependent on the expected return of the two assets in questions, so without the expected return of the two assets, it is difficult to characterise 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.

7.28

In order to fund her retirement, Gwen requires a portfolio with an expected return of 10.3 per cent per year over the next 30 years. She has decided to invest in Shares 1, 2 and 3, with 25 per cent in Share 1, 50 per cent in Share 2 and 25 per cent in Share 3. If Shares 1 and 2 have expected returns of 9 per cent and 10 per cent per year, respectively, then what is the minimum expected annual return for Share 3 that will enable Gwen to achieve her investment requirement?

The formula for the expected return of a three-share portfolio is:

E ( R3 asset port ) = x1 E ( R1 ) + x2 E ( R2 ) + x3 E ( R3 ) Therefore, we can solve as in the following: 0.103 = 0.25(0.09) + 0.5(0.1) + 0.25E(R3) 0.122 = E(R3)

Module 7: Risk and return

7.29

Tonalli is putting together a portfolio of 10 shares in equal proportions. What is the relative importance of the variance for each share versus the covariance for the pairs of shares in her portfolio? For this exercise, ignore the actual values of the variance and covariance terms and explain their importance conceptually.

The variance of the portfolio will be composed of 10 (n = 10) individual share 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.

7.30

Explain why investors who have diversified their portfolios will determine the price and, consequently, the expected return on an asset.

If we assume that all investors will seek to be compensated (generate returns) for the level of risk that they are bearing, then we can see that undiversified investors will require a greater return for a given investment than diversified investors will. Given that, we can see that diversified investors will be willing to pay a greater price for an asset than undiversified investors. Therefore, the diversified investor is the marginal investor whose purchase will determine the equilibrium price, and therefore the equilibrium return for an asset.

7.31

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.

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 non-systematic risk inherent in the returns of the asset and will consequently not affect the beta of the asset.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

7.32

The beta of an asset is equal to 0. Discuss what the asset must be.

Following the CAPM prediction: (Rcs) = Rrf + β (E(RM) – Rrf) = Rrf + 0 (E(RM) – Rrf) = Rrf Therefore, the expected return on the asset is equal to the risk-free rate of return. The only way an asset could generate a risk-free rate of return is if the asset had no systematic risk (otherwise the asset would have to compensate an investor for such risk bearing). This implies that the asset must be the riskless asset, or, practically speaking, it must be a Tbill.

7.33

The expected return on the market portfolio is 17 per cent, and the return on the risk-free security is 5 per cent. What is the expected return on a portfolio with a beta equal to 1.7?

E(Ri) = Rrf + β(E(RM) – Rrf) = 5 + 1.7(17-5) = 25.4%

7.34

Draw the Security Market Line (SML) for the case where the market risk premium is 5 per cent and the risk-free rate is 7 per cent. Now suppose an asset has a beta of –1.0 and an expected return of 4 per cent. 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 per cent. 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.

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 per cent, and the market is expected to return 5 per cent more than this. Therefore, the expected rate of return for the market (a beta one asset) is 12 per cent. To draw this SML, we need only connect the dots: We can see from the following diagram that an asset with expected return of 4 per cent and a beta of –1.0 is under-priced (its expected return is too high). As the market becomes aware of this under-pricing, 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.)

Module 7: Risk and return

Expected Return

18% 15% 12% 9% 6% 3% 0% 0

1

2

Beta

18%

Expected Return

15% 12% 9% 6% 3% 0% -1

0

1

2

Beta

As we can see from the following diagram, an asset with a beta of 3.0 should have an expected return of 7% + (3)(5%) = 22%. The asset only has an expected return of 20 per cent. 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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

23%

Expected Return

18% 14%

The investment will fall here in this plot

9% 5% 0% 0

1

2 Beta

3

Module 8: Bond valuation Self-study problems 8.1

Calculate the price of a 5-year bond that has a coupon of 6.5 per cent and pays annual interest. The current market rate is 5.75 per cent.

Please note: the bond has a face value of $1000.

0 5.75% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ PB=? $65 $65 $65 $65 $1,065

PB = =

Fn C 1  1 −  + i  (1 + i )n  (1 + i )n

 65  1 1000 1 − + 5  0.0575  (1.0575)  (1.0575)5

= 275.68 + 756.13 = $1031.81 8.2

Billabong International Ltd issued a 5-year bond 1 year ago with a coupon of 8 per cent and a face value of $1000. The bond pays interest semi-annually. If the yield to maturity on this bond is 9 per cent, what is the price of the bond?

0 9% 1 2 3 4 5 6 7 8 ├───┼───┼───┼────┼───┼───┼───┼────┤ PB=?

PB =

 C m 1 Fmn 1 − + mn  i m  (1 + i m )  (1 + i m )mn

=

 80 2  1 1000 1 − + 24  0.09 2  (1 + 0.09 2 )  (1 + 0.09 2 )2  4

=

40  1  1000 1 − + 8  0.045  (1.045)  (1.045)8

= 263.835 + 703.185 = $967.02

Module 8: Bond valuation

8.3

Westpac Banking Corporation has a 3-year bond outstanding that pays a 7.25 per cent coupon and is currently priced at $913.88. What is the yield to maturity of this bond? Assume annual coupon payments and a face value of $1000.

0 1 2 3 ├───────┼────────┼───────┤ PB = $913.88 $72.50 $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%: PB =

C 1  Fn 1 − + n  i  (1 + i )  (1 + i )n

72.50  1  1000 1 − + 0.10  (1.10 )3  (1.10 )3 = 180.30 + 751.31 ≠ 931.61 913.88 =

We need a lower price, so try a higher rate, say YTM = 11%: PB =

C 1  Fn 1 − + n  i  (1 + i )  (1 + i )n

72.50  1  1000 1 − + 0.11  (1.11)3  (1.11)3 = 177.17 + 731.19 ≠ 908.36 913.88 =

Since this is less than the price of the bond, we know that the YTM is between 10 and 11% and closer to 11%.

Try YTM = 10.75% PB =

C 1  Fn 1 − + n  i  (1 + i )  (1 + i )n

 72.50  1 1000 1 − + 3  0.1075  (1.1075 )  (1.1075 )3 = 177.94 + 736.15 ≈ 914.09 913.88 =

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Thus, the YTM is approximately 10.75 per cent. Using a financial calculator provides an exact YTM of 10.7594 per cent. (Calculator inputs are as follows: 1000 FV, -913.88 PV, 3 N, 72.5 PMT, COMP I/Y)

8.4

Wesfarmers Ltd has a 10-year bond that is priced at $1100.00. It has a coupon of 8 per cent paid semiannually and a face value of $1000. What is the yield to maturity on this bond? What is the effective annual yield?

0 1 2 3 4 5 6 ├───┼────┼───┼───┼───┼────┼── $40 $40 $40 $40 $40 $40

20 ─────┤ $40 $1,000

The easiest way to calculate the yield to maturity is with a financial calculator. The inputs are as follows: Procedure Enter cash flow data

Key Operation 1,000 [FV]

Display 1,000=>FV

20 [N]

20=>N

1,000.00 20.00 -1100[PV]

(-1100)=>PV

40 [PMT]

40 =>PMT

[COMP] [I/Y]

I/Y=

-1100.00 40.00 Calculate I/Y

3.31

The answer we get is 3.31%, which is the semi-annual interest rate. To obtain an annualised yield to maturity, we multiply this by 2: YTM = 3.31% × 2 = 6.62% However, we can only use this YTM to compare against similar bonds, to compare against other investments we need to calculate the effective annual yield (EAY): m

 Quoted interest rate  EAY = 1 +  −1 m   2

 0.0662  = 1 +  −1 2   = 0.0673 or 6.73%

Module 8: Bond valuation

8.5

Highland Corporation Pty Ltd, an Australian company, has a 5-year bond whose yield to maturity is 6.5 per cent. The bond has no coupon payments. The bond has a face value of $1000. What is the price of this zero coupon bond?

You are given the following information: YTM = 6.5%; m = 1 No coupon payments Most Australian bonds pay interest semi-annually. Thus m x n = 5 x 2 = 10 and i/2 = 0.065/2 = 0.0325. Using Equation 8.4, we obtain the following calculation: PB = Fmn/(1 + i/m)mn PB = $1,000/(1 + 0.0325)10 PB = $726.27

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Critical thinking questions 8.1

Differentiate between Treasury bonds and Treasury indexed bonds.

Treasury bonds are coupon instruments paying fixed interest semiannually and pay the face value at maturity. Treasury indexed bonds (TIBs) adjust for inflation and pay interest quarterly. The principal amount of TIBs adjusts in response to changes in the Consumer Price Index (CPI). Therefore as the principal is adjusted for inflation prior to making coupon payments, the amount of each coupon will vary depending on changes in the CPI. In addition, at maturity the investor receives the greater of the final principal amount or the initial par-amount.

8.2

Who issues semis and what is the purpose of the funds raised?

Semis are bonds issued by state and territory borrowing authorities backed by their respective governments. The funds raised are used to develop infrastructure assets and provide government-administered services such as hospitals, schools, policing, roads, electricity and water.

8.3

What economic conditions would prompt investors to take advantage of a bond’s convertibility feature?

A bond’s convertibility feature becomes attractive when the company’s share price rises above the bond’s price. This usually happens in times of economic expansion when the share market is booming and interest rates are decreasing, hence lowering the bond’s price.

Module 8: Bond valuation

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) 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 realised gain equal to the yield to maturity. If the investor sells before the maturity date, then realised 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!

8.5

Define interest rate risk. How can the CFOs manage this risk?

The change in a bond's price 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 per cent change in the market interest rates.

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 lowcoupon 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 raise more for longerterm 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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.6

Explain why bond prices and interest rates are negatively related. What is the role of the coupon rate and term-to-maturity in this relationship?

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.

8.7

•

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 will be lower due to the compounding effect. 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.

If rates are expected to increase, should investors look to long-term bonds or shortterm 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.

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.

Module 8: Bond valuation

8.9

An investor holds a 10-year bond paying a coupon of 9 per cent. The yield to maturity of the bond is 7.8 per cent. Would you expect the investor to be holding a par-value, premium or discount bond? What if the yield to maturity was 10.2 per cent? Explain.

Since the bond’s coupon of 9 per cent 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 per cent 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 per cent, 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 per cent bond will decline, driving its price below the face value. This will be a discount bond.

8.10

a.

b.

Investor A holds a 10-year bond while investor B has an 8-year bond. If interest rate increases by 1 per cent, which investor will have the higher interest rate risk? Explain.

Investor A holds a 10-year bond paying 8 per cent a year, while investor B also has a 10-year bond that pays a 6 per cent coupon. Which investor will have the higher interest rate risk? Explain.

a.

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 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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Questions and problems BASIC 8.1

Bond price: AR Australasia Ltd is issuing a 10-year bond with a coupon rate of 8.89 per cent. The interest rate for similar bonds is currently 5.97 per cent. Assuming annual payments and a face value of $1000, what is the present value of the bond?

Years to maturity = n = 10 Coupon rate = C = 8.89% Annual coupon = $1,000 x 0.0889 = $88.90 Current market rate = i = 5.97% Present value of bond = PB

0 5.97% 1 2 3 4 5 6 ├───┼────┼───┼───┼───┼────┼── $88.90 $88.90 $88.90 $88.90 $88.90 $88.90

F C  1  n P =  1 − + B i  (1 + i ) n  (1 + i ) n =

 88.90  1 1000  1 − + 10  0.0597  (1 + 0.0597 )  (1 + 0.0597 )10

= $655.2427 + $559.9776 = $1,215.22

10 ─────┤ $88.90 $1,000

Module 8: Bond valuation

8.2

Bond price: Alex Simmonds just received a gift from her grandfather. She plans to invest in a 5-year bond issued by Nucorp Pty Ltd that pays annual coupons of 4.81 per cent. If the current market rate is 9.11 per cent, what is the maximum amount Alex should be willing to pay for this bond? Assume it has a face value of $1000.

0 9.11% 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ $48.10 $48.10 $48.10 $48.10 $1,000 Years to maturity = n = 5 Coupon rate = C = 4.81% Annual coupon = $1,000 x 0.0481 = $48.10 Current market rate = i = 9.11% Present value of bond = PB

F C  1  n P =  1 − +  B i  (1 + i ) n  (1 + i ) n =

 48.10  1 1000  1 − + 5  0.0911  (1 + 0.0911)  (1 + 0.0911) 5

= $186.5595 + $646.6618 = $833.22

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.3

Bond price: Choice Pty Ltd has issued a 3-year bond with a face value of $1000 that pays a coupon of 4.90 per cent. Coupon payments are made semiannually. Given the market rate of interest of 4.70 per cent, what is the market value of the bond?

Years to maturity = n = 3 Coupon rate = C = 4.90% Frequency of payment = m = 2 Semi-annual coupon = $1,000 x (0.0490/2) = $24.50 Current market rate = i = 4.70% Present value of bond = PB 0 4.70% 1 2 3 4 5 6 ├───┼────┼───┼───┼───┼────┤ $24.50 $24.50 $24.50 $24.50 $24.50 $24.50 $1,000

F  C/m  1 mn P =  1 − + B i / m  (1 + i/m) mn  (1 + i/m) mn =

  49 / 2 1 1000  1 − + 2 x3  0.047 / 2  (1 + 0.047 / 2)  (1 + 0.047 / 2) 2 x 3

= $135.6287 + $869.9072 = $1,005.54

Module 8: Bond valuation

8.4

Bond price: National Australia Bank Ltd has 7-year bonds outstanding that pay an 11.03 per cent coupon rate. Investors buying the bond today can expect to earn a yield to maturity of 6.72 per cent. What is the current value of these bonds? Assume annual coupon payments and a face value of $1000.

Years to maturity = n = 7 Coupon rate = C = 11.03% Annual coupon = $1,000 x 0.1103 = $110.30 Current market rate = i = 6.72% Present value of bond = PB 0 1 2 3 4 5 6 7 ├───┼────┼───┼───┼───┼────┼───┤ $110.30 $110.30 $110.30 $110.30 $110.30 $110.30 $1,000

F C  1  n P =  1 − + B i  (1 + i ) n  (1 + i ) n =

 110.30  1 1000  1 − + 7  0.0672  (1 + 0.0672)  (1 + 0.0672) 7

= $600.2856 + $634.2775 = $1,234.59

$110.30

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.5

Bond price: You are interested in investing in a 5-year bond with a face value of $1000 that pays a 6.33 per cent coupon with interest to be received semiannually.

Your required rate of return is 9.69 per cent. What is the most you would be willing to pay for this bond?

Years to maturity = n = 5 Coupon rate = C = 6.33% Frequency of payment = m = 2 Semi-annual coupon = $1,000 x (0.0633/2) = $31.65 Current market rate = i = 9.69% Present value of bond = PB 0 9.69% 1 2 3 4 5 6 ├───┼────┼───┼───┼───┼────┼── $31.65 $31.65 $31.65 $31.65 $31.65 $31.65

F  C/m  1 mn P =  1 − +  B i / m  (1 + i/m) mn  (1 + i/m) mn =

 63.30 / 2  1 1000  1 − + 2 x5  0.0969 / 2  (1 + 0.0969 / 2)  (1 + 0.0969 / 2) 2 x 5

= $246.2430 + $623.0498 = $869.29

10 ─────┤ $31.65 $1,000

Module 8: Bond valuation

8.6

Zero coupon bonds: Chelsea Carter is interested in buying a 5-year zero coupon bond whose face value is $1,000. She understands that the market interest rate for similar investments is 7.96 per cent. Assume annual compounding for payments.

What is the current price of this bond?

Years to maturity = n = 5 Coupon rate = C = 0% Current market rate = i = 7.96% 0 1 2 3 4 5 ├───┼────┼───┼───┼───┤ $0 $0 $0 $0 $0 $1,000

F mn P = B (1 + i/m) mn 1000 (1 + 0.0796) 5 = $681.84

=

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.7

Zero coupon bonds: 10-year zero coupon bonds issued by the Queensland Treasury have a face value of $1000 and interest is compounded semi-annually. If similar bonds in the market yield 11.32 per cent, what is the value of these bonds?

Years to maturity = n = 10 Frequency of payment = m = 2 Coupon rate = C = 0% Current market rate = i = 11.32% 0 1 2 3 4 5 6 ├───┼────┼───┼───┼───┼────┼── $0 $0 $0 $0 $0 $0

F mn P = B (1 + i/m) mn 1000 (1 + 0.1132 / 2) 2 x10 1000 = (1.05660) 20 = $332.50

=

20 ─────┤ $0 $1,000

Module 8: Bond valuation

8.8

Zero coupon bonds: ELM Property Group is planning to fund a development project by issuing 10-year zero coupon bonds with a face value of $1000. Assuming semiannual compounding, what will be the price of these bonds if the appropriate discount rate is 12.53 per cent?

Years to maturity = n = 10 Coupon rate = C = 0% Current market rate = i = 14% Assume semi-annual coupon payments.

0 1 2 3 4 5 6 ├───┼────┼───┼───┼───┼────┼── $0 $0 $0 $0 $0 $0

F mn P = B (1 + i/m) mn 1000 (1 + 0.1253 / 2) 2 x10 1000 = (1.0627 ) 20 = $296.34

=

20 ─────┤ $0 $1,000

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.9

Yield to maturity: Jessica Thompson is looking to invest in a 3-year bond with a face value of $1000 that pays semi-annual coupons at a coupon rate of 10.35 per cent. If these bonds have a market price of $957.02, what yield to maturity and effective annual yield can she expect to earn?

Years to maturity = n = 3 Coupon rate = C = 10.35% Frequency of payment = m = 2 Semi-annual coupon = $1,000 x (0.1035/2) = $51.75 Yield to maturity = i Present value of bond = PB = $957.02 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 = 10.4%.

957.02 

 51.75  1 1000 + 1 − 6  0.0518  (1 + 0.0518 )  (1 + 0.0518 )6

 260.9739 + 737.7438  998.72

Try a higher rate, say YTM = 12.10%.

957.02 

 51.75  1 $1,000 + 1 − 6  0.0605  (1 + 0.0605 )  (1 + 0.0605 )6

 254.0513 + 702.9687  957.02

The YTM is approximately 12.10 per cent.

Using a financial calculator provides an exact YTM of 12.10 per cent.

Procedure Enter cash flow data

Key Operation 1,000 [FV]

Display 1,000=>FV

6 [N]

6=>N

-957.02 [PV]

(-957.02)=>PV

51.75 [PMT]

51.75 =>PMT

1,000.00 6.00 -957.02 51.75 Calculate I/Y

[COMP] [I/Y]

I/Y= 6.05

Module 8: Bond valuation

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

The effective annual yield can be calculated as: m  Quoted interest rate  EAY = 1 +  −1 m   2

 0.1210  = 1 +  −1 2   = 0.1247 = 12.47%

YtM = 12.10% EaY = 12.47%

Module 8: Bond valuation

8.10

Yield to maturity: Ruth Jones wants to invest in 4-year bonds with a face value of $1000 that are currently priced at $772.89. These bonds have a coupon rate of 4.15 per cent and pay semiannual coupons. What is the current market yield on this bond?

Years to maturity = n = 4 Coupon rate = C = 4.15% Frequency of payment = m = 2 Semi-annual coupon = $1,000 x (0.0415/2) = $20.77 Yield to maturity = i Present value of bond = PB = $772.89 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 = 4.2%.

772.89 

 20.77  1 1000 + 1 − 8  0.0208  (1 + 0.0208 )  (1 + 0.0208 )8

 151.5298 + 846.8258  998.36

Try a higher rate, say YTM = 11.38%.

772.89 

 20.77  1 1000 + 1 − 8  0.0569  (1 + 0.0569 )  (1 + 0.0569 )8

 130.6035 + 642.2865  772.89

The YTM is approximately 11.38 per cent. Using a financial calculator provides an exact YTM of 11.38 per cent.

Procedure Enter cash flow data

Key Operation 1,000 [FV]

Display 1,000=>FV

8 [N]

8=>N

-772.89 [PV]

(-772.89)=>PV

20.77 [PMT]

20.77 =>PMT

1,000.00 8.00 -772.89 20.77 Calculate I/Y

[COMP] [I/Y]

I/Y= 5.69

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Module 8: Bond valuation

8.11

Realised yield: James Millett bought 10-year, 14.92 per cent coupon bonds issued by the Australian government 3 years ago at $913.44. If he sells these bonds, which have a face value of $1000, at the current price of $771.37, what is the realised yield on the bonds? Assume annual coupons on similar coupon-paying bonds.

Purchase price of bond = $913.44 Years investment held = n = 3 Coupon rate = C = 14.92% Frequency of payment = m = 1 Annual coupon = $1,000 x (0.1492) = $149.20 Realised yield = i Selling price of bond = PB = $771.37 To calculate the realised 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 realised return is going to be less than the bond’s coupon. Try rates lower than the coupon rate.

Try i = 10%.

PB = 913.44 =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n  $771.37 149.20  1 + 1 − 3 0.1492  (1.1492)  (1.1492) 3

= 341.1854 + 508.5137  849.70 Try a lower rate, i = 11.71%.

PB = 913.44 =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n  149.20  1 771.37 + 1 − 3 0.1171  (1.1171)  (1.1171) 3

= 360.1070 + 553.3330  913.44

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

The realised rate of return is approximately 11.71 per cent. Using a financial calculator provides an exact yield of 11.71 per cent.

Procedure Enter cash flow data

Key Operation 771.37 [FV]

Display 771.37=>FV

3 [N]

3=>N

771.37 3.00 -913.44 [PV]

(-913.44)=>PV

149.20 [PMT]

149.20 =>PMT

-913.44 149.20 Calculate I/Y

[COMP] [I/Y]

I/Y= 11.71

Module 8: Bond valuation

8.12

Realised yield: Four years ago, Lisa Hampson bought 6-year, 11.63 per cent coupon bonds issued by Flight Centre Ltd for $947.68. If she sells these bonds at the current price of $903.47, what is the realised yield on the bonds? Assume annual coupons on similar coupon-paying bonds and a face value of $1000.

Purchase price of bond = $947.68 Years investment held = n = 4 Coupon rate = C = 11.63% Frequency of payment = m = 1 Annual coupon = $1,000 x (0.1163) = $116.34 Realised yield = i Selling price of bond = PB = $903.47 To calculate the realised 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 realised return is going to be less than the bond’s coupon. Try rates lower than the coupon rate.

Try i = 11.6%.

PB = 947.68 =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n  116.34  1 903.47 + 1 − 4  0.1163  (1.1163)  (1.1163) 4

= 356.3633 + 582.4477  $938.81

Try i = 11.29%.

PB = 947.68 =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n  116.34  1 903.47 + 1 − 4  0.1129  (1.1129)  (1.1129) 4

= 358.7154 + 588.9646  $947.68

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

The realised rate of return is approximately 9.5 per cent. Using a financial calculator provides an exact yield of 11.29 per cent.

Procedure Enter cash flow data

Key Operation 903.47 [FV]

Display 903.47=>FV

4 [N]

4=>N

903.47 4.00 -947.68 [PV]

(-947.68)=>PV

116.34 [PMT]

116.34 =>PMT

-947.68 116.34 Calculate I/Y

[COMP] [I/Y]

I/Y= 11.29

Module 8: Bond valuation

MODERATE 8.13

Bond price: The International Publishing Group Pty Ltd is raising $10 million by issuing 15-year bonds with a coupon rate of 7.57 per cent and a face value of $1000.

Coupon payments will be annual. Investors buying the bond currently will earn a yield to maturity of 10.00 per cent. At what price will the bonds sell in the marketplace? Explain.

Years to maturity = n = 15 Coupon rate = C = 7.57% Annual coupon = $1,000 x 0.0757 = $75.70 Current market rate = i = 10% Present value of bond = PB 0 1 2 3 4 ├───┼────┼───┼───┼─── $75.70 $75.70 $75.70 $75.70

15 ─────┤ $75.70 $1,000

n = 15;

PB = =

C = 7.57%;

i = YTM = 7.57%

C 1  F + 1 − n  i  (1 + i )  (1 + i ) n  75.70  1 1000 + 1 − 15  0.1000  (1.1000)  (1.1000)15

= $575.7802 + $239.3920 = $815.17

This answer should have been intuitive. Since the bond is paying a coupon equal to the going market rate of 10 per cent, the bond should be selling at its par value of $815.17.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

15 [N]

15=>N

1000.00 15.00 10[I/Y]

10=>I/Y

75.70 [PMT]

75.70 =>PMT

[COMP] [PV]

PV=

10 75.70 Calculate PV

-815.17

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.14

Bond price: Pacific Brands Ltd issued 10-year bonds 4 years ago with a coupon rate of 9.375 per cent. At the time of issue, the bonds sold at par. Today bonds of similar risk and maturity will pay a coupon rate of 6.25 per cent. Assuming semiannual coupon payments and a face value of $1000, what will be the current market price of the company’s bonds?

Years to maturity = n = 6 Coupon rate = C = 9.375% Semi-annual coupon = $1,000 x (0.09375/2) = $46.875 Current market rate = i = 6.25% Present value of bond = PB

0 1 2 3 4 ├───┼────┼───┼───┼─── $46.875 $46.875………

12 ─────┤ $46.875 $1,000

n = 6; m = 2; C = 9.375%; i = YTM = 6.25%

PB = =

 Fmn C m 1 1 − + mn mn i m  (1 + i m )  (1 + i m ) 

 93.75 2  1 1000 1 − + 26 26 0.0625 2  (1 + 0.0625 2 )  (1 + 0.0625 2 ) 

 46.875  1 1000 1 − + 12 12 0.03125  (1.03125)  (1.03125)  = 463.13 + 691.25

=

= $1154.38 Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

12[N]

12=>N

1000.00 12.00 3.125[I/Y]

3.125=>I/Y

46.875 [PMT]

46.875 =>PMT

3.125 46.875 Calculate PV

[COMP] [PV]

PV= -1154.38

Module 8: Bond valuation

8.15

Bond price: Metasale Ltd is issuing 8-year bonds with a coupon rate of 7.99 per cent and semiannual coupon payments. If the current market rate for similar bonds is 9.53 per cent, what will be the bond price? Assume each bond has a face value of $1000. If the company wants to raise $1.25 million, how many bonds does the it have to sell?

Years to maturity = n = 8 Coupon rate = C = 7.99% Semi-annual coupon = $1,000 x (0.0799/2) = $39.95 Current market rate = i = 9.53% Present value of bond = PB 0 9.53% 1 2 3 4 ├───┼────┼───┼───┼─── $39.95

$39.95………..$39.95

16 ─────┤ $39.95 $1,000

PB = =

 C/m  1 Fmn + 1 − mn  i / m  (1 + i/m)  (1 + i/m) mn  79.90 / 2  1 1000 + 1 − 2 x8  0.0953 / 2  (1 + 0.0953 / 2)  (1 + 0.0953 / 2) 2 x8

= 110.0757 + 474.8326 = $915.14 To raise $1.25million bonds, the company would have to sell: Number of bonds = $1,250,000 / $915.14 = 1,366 bond contracts Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

16[N]

16=>N

4.77[I/Y]

4.77=>I/Y

39.95 [PMT]

39.95 =>PMT

[COMP] [PV]

PV=

1000.00 16.00 4.77 39.95 Calculate PV

-915.14

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.16

Bond price: QBE Insurance Group Ltd has outstanding bonds with a face value of $1000 that will mature in 6 years and pay an 8 per cent coupon, interest being paid semiannually. If you paid $1036.65 today, and your required rate of return was 6.6 per cent, did you pay the right price for the bond?

Years to maturity = n = 6 Coupon rate = C = 8% Semi-annual coupon = $1,000 x (0.08/2) = $40 Current market rate = i = 6.6% Present value of bond = PB 0 1 2 3 ├───────┼────────┼────────┼── $40 $40 $40

PB =

12 ─────────┤ $40 $1,000

 Fmn C m 1 1 − + mn i m  (1 + i m )  (1 + i m )mn

=

 80 2  1 1000 1 − + 2  6   0.066 2  (1 + 0.066 2 )  (1 + 0.066 2 )26

=

 40  1 1000 1 − + 12   0.033  (1.033)  (1.033)12

= 391.123 + 677.323 = 1068.45  1036.65

You paid less than what the bond is worth. That was a good price!

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV 1000.00

12[N]

12=>N

3.3[I/Y]

3.3=>I/Y

12.00 3.30 40 [PMT]

40 =>PMT

[COMP] [PV]

PV=

40.00 Calculate PV

-1068.45

Module 8: Bond valuation

8.17

Bond price: SLG Ltd has a bond issue maturing in 7 years and paying a coupon rate of 7.78 per cent (semiannual payments). The company wants to retire a portion of the issue by buying the securities in the open market. If it can refinance at 9.60 per cent, how much will SLG Ltd pay to buy back its current outstanding bonds?

Assume each bond has a face value of $1000.

Years to maturity = n = 7 Coupon rate = C = 7.78% Semi-annual coupon = $1,000 x (0.0778/2) = $38.90 Current market rate = i = 9.60% Present value of bond = PB 0 1 2 3 ├───────┼────────┼────────┼── $38.90 $38.90 $38.90

PB = =

14 ─────────┤ $38.90 $1000

 C/m  1 Fmn + 1 − mn  i / m  (1 + i/m)  (1 + i/m) mn  77.80 / 2  1 1000 + 1 − 14  0.0960 / 2  (1 + 0.0960 / 2)  (1 + 0.0960 / 2)14

= 390.0286 + 518.7308 = $908.76 The company will be willing to pay no more than $1,079.22 for their bond.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

14[N]

14=>N

4.8[I/Y]

4.8=>I/Y

38.90 [PMT]

38.90 =>PMT

[COMP] [PV]

PV=

1000.00 14.00 4.8 38.90 Calculate PV

-908.76

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.18

Zero coupon bonds: Kip McGrath Education Centres Ltd wants to raise $1 million by issuing 6-year zero coupon bonds with a face value of $1000. Its investment banker states that investors would use an 11.4 per cent discount rate on such bonds.

At what price would these bonds sell in the marketplace? How many bonds would the company have to issue to raise $1 million? Assume semiannual coupon payments.

Years to maturity = n = 6 Coupon rate = C = 0% Current market rate = i = 11.4% Assume semiannual coupon payments.

0 1 2 3 4 5 6 ├───┼────┼───┼───┼───┼────┼── $0 $0 $0 $0 $0 $0

PB =

(

Fmn

1+ i

m

)

mn

=

(

$1, 000

1 + 0.114

2

)

26

=

$1, 000

(1.057 )

12

12 ─────┤ $0 $1,000

= $514.16

At the price of $514.16, the company needs to raise $1 million. To do so, the company will have to issue: Number of contracts = $1,000,000 / $514.16 = 1,945 contracts

Module 8: Bond valuation

8.19

Zero coupon bonds: Rheochem Ltd plans to issue 7-year zero coupon bonds with a face value of $1000. It has learnt that these bonds will sell today at a price of $439.76. Assuming annual compounding for payments, what is the yield to maturity on these bonds?

Years to maturity = n = 7 Coupon rate = C = 0% Current market rate = i Assume annual coupon payments.

Present value of bond = PB = $439.76 0 1 2 3 4 5 6 7 ├───┼────┼───┼───┼───┼────┼───┤ $0 $0 $0 $0 $0 $0 $0 $1,000 Fmn PB = n (1 + i ) 439.76 =

(1 + i ) = 7

1000

(1 + i )

7

1000 439.76 1

1 + i = ( 2.2740 ) 7 1 + i = 1.124525 i = 1.124525 − 1 i = 0.124525 = 12.45%

No need for trial and error.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

7 [N]

7=>N

1000.00 7.00 -439.76[PV]

-439.76=>PV

0 [PMT]

0 =>PMT

[COMP] [I/Y]

I/Y=

-439.76 0 Calculate I/Y

12.4525

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.20

Yield to maturity: Elders Ltd has 4-year bonds with a face value of $1000 outstanding that pay a coupon rate of 6.6 per cent 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?

Years to maturity =4 hence n = 4x2=8 Coupon rate = C = 6.6% Current market rate = i Semi-annual coupon payments = $1,000 x (0.066/2) = $33 Present value of bond = PB = $914.89 0 1 2 3 ├───────┼────────┼────────┼── $33 $33 $33

8 ─────────┤ $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 per cent (3.3 per cent per 6 months).

Try i = 8% or i/2 = 4%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

33  1  1000 1− +  0.04  (1.04) 8  (1.04) 8

= 222.18 + 730.69 = 952.87  914.89 Try a higher rate, i = 9%, i/2 = 4.5%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

33  1  1000 1− +  8 0.045  (1.045)  (1.045) 8

= 217.66 + 703.19 = 920.85  914.89 Try a higher rate, i = 9.2%, i/2 = 4.6%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

33  1  1000 1− +  8 0.046  (1.046)  (1.046) 8

= 216.78 + 697.82 = 914.60  914.89

Module 8: Bond valuation

The yield to maturity is approximately 9.2 per cent (4.6 x 2 = 9.2). The effective annual yield can be approximately calculated as: EAY = (1 + Quoted rate m) m − 1  (1.046 ) − 1 2

 0.0941  9.41%

However, using the financial calculator provides us with the exact YTM Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

8 [N]

8=>N

1000.00 8.00 -914.89[PV]

-914.89=>PV

33 [PMT]

33 =>PMT

-914.89 33.00 Calculate I/Y

[COMP] [I/Y]

I/Y= 4.5954

The effective annual yield can be calculated as: EAY = (1 + Quoted rate m) m − 1 = (1.045954 ) − 1 2

= 0.09402 = 9.402%

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.21

Yield to maturity: Sonic Healthcare Ltd has 5-year bonds outstanding that pay a coupon of 8.8 per cent. If these bonds are priced at $1064.86, what is the yield to maturity on these bonds? Assume semiannual coupon payments and a face value of $1000. What is the effective annual yield?

Years to maturity = 5 Hence n=5x2=10 Coupon rate = C = 8.8% Current market rate = i Semi-annual coupon payments = $1,000 x (0.088/2) = $44 Present value of bond = PB = $1,064.86 0 1 2 3 ├───────┼────────┼────────┼── $44 $44 $44

10 ─────────┤ $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 per cent.

Try i = 7% or i/2 = 3.5%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

 44  1 1000 1− +  10  0.035  (1.035)  (1.035)10

= 365.93 + 708.92 = 1074.85  1064.86 Try a higher rate, i = 7.2%, i/2 = 3.6%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

 44  1 1000 1− +  10  0.036  (1.036)  (1.036)10

= 364.09 + 702.11 = 1066.20  1064.86 The YTM is approximately 7.2 per cent. The effective annual yield can be calculated as: EAY = (1 + Quoted rate m) m − 1  (1.036 ) − 1 2

 0.0733  7.33%

Module 8: Bond valuation

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

10 [N]

10=>N

-1064.86[PV]

-1064.86=>PV

44 [PMT]

44 =>PMT

[COMP] [I/Y]

I/Y=

1000.00 10.00 -1064.86 44.00 Calculate I/Y

3.6156

The effective annual yield can be calculated as: EAY = (1 + Quotedrate m )m − 1 = (1.036156 ) − 1 2

= 0.07362 = 7.36%

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.22

Yield to maturity: Claire Brownell is planning to buy 10-year zero coupon bonds issued by the Queensland Treasury. If these bonds with a face value of $1000 are currently selling at $404.59, what is the expected return on these bonds? Assume that interest compounds semiannually on similar coupon-paying bonds.

Years to maturity = 10 Hence n= 10x2=20 Coupon rate = C = 0% Current market rate = i Assume semi-annual coupon payments.

Present value of bond = PB = $404.59 0 1 2 3 ├───────┼────────┼────────┼── $0 $0 $0

PB = 404.59 =

(1 + i )

20

=

20 ─────────┤ $0 $1,000

Fmn

(1 + i m)

mn

1000

(1 + i )

20

1000 404.59 1

1 + i = ( 2.47164 ) 20 = 1.046283 i = 4.6283% The YTM is 9.2566%.

EAY = (1 + Quoted rate m) m − 1 = (1.046283 ) − 1 2

= 0.0947085 = 9.471%

The expected return from this investment is 9.471 per cent.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV 1000.00

20 [N]

20=>N

-404.59[PV]

-404.59=>PV

20.00 -404.59 0 [PMT]

0 =>PMT

[COMP] [I/Y]

I/Y=

0 Calculate I/Y

4.6283

Module 8: Bond valuation

8.23

Realised yield: Bell Financial Group Ltd issued 7-year bonds 2 years ago that can be called after 5 years. The bond makes semiannual coupon payments at a coupon rate of 7.875 per cent and has a face value of $1000. The bond has a market value of $1053.40, and the call price is $1078.75. If the bonds are called by the company, what is the investor’s realised yield?

Assuming you bought today: Purchase price of bond = $1053.40 Years investment held = 3 hence n=3x2=6 Coupon rate = C = 7.875% Frequency of payment = m = 2 Semi-annual coupon = $1,000 x (0.07875/2) = $39.375 Realised yield = i Selling price of bond = PB = 1078.75 To calculate the realised return, either the trial-and-error approach or the financial calculator can be used. The realised return is going to be greater than the bond’s coupon as the market price and the call price are higher than the par value. Try rates higher than the coupon rate.

Try i = 8%, or i/2 = 4%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

39.375  1  1078.75 1− +  0.04  (1.04) 6  (1.04) 6

= 206.41 + 852.55 = 1058.96  1053.40 Try a higher rate, i = 8.2% or i/2 = 4.1%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

39.375  1  1078.75 1− +  0.041  (1.041) 6  (1.041) 6

= 205.74 + 847.65 = 1053.39  1053.40 EAY = (1 + Quoted rate m) m − 1 = (1.041) − 1 2

= 0.08368 = 8.37%

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

The realised rate of return to call is approximately 8.37 per cent. Using a financial calculator provides an exact yield of 8.368 per cent.

Procedure Enter cash flow data

Key Operation 1078.75 [FV]

Display 1078.75=>FV

6 [N]

6=>N

1078.75 6.00 -1053.40[PV]

-1053.40=>PV

39.375 [PMT]

39.375 =>PMT

-1053.40 39.375 Calculate I/Y

[COMP] [I/Y]

I/Y= 4.099795

EAY = (1 + Quoted rate m )m − 1 = (1.04099795) − 1 2

= 0.08368 = 8.37%

Module 8: Bond valuation

8.24

Realised yield: Kevin Phan bought 10-year bonds issued by Harvey Norman 5 years ago for $936.05. The bonds make semiannual coupon payments at a rate of 8.4 per cent and have a face value of $1000. If the current price of the bond is $1048.77, what is the yield that Kevin would earn by selling the bonds today?

Purchase price of bond = $936.05 Years investment held = 5 Hence n= 5x2=10 Coupon rate = C = 8.4% Frequency of payment = m = 2 Annual coupon = $1,000 x (0.084/2) = $42 Realised yield = i Selling price of bond = PB = $1,048.77 To calculate the realised 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 realised return is going to be greater than the bond’s coupon. Try rates higher than the coupon rate.

Try i = 11%, or i/2 = 5.5%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

 1048.77 42  1 1− +  10  0.055  (1.055)  (1.055)10

= 316.58 + 613.98 = 930.56  936.05 Try a lower rate, i = 10.85% or i/2 = 5.425%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

 42  1 1048.77 1− +  10  0.05425  (1.05425)  (1.05425)10

= 317.722 + 618.364 = 936.09  936.05 EAY = (1 + Quoted rate m )m − 1 = (1.05425) − 1 2

= 0.11144 = 11.14%

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

The realised rate of return is approximately 11.144 per cent. Using a financial calculator provides an exact yield of 11.145 per cent.

Procedure Enter cash flow data

Key Operation 1048.77 [FV]

Display 1048.77=>FV

10 [N]

10=>N

1048.77 10.00 -936.05[PV]

-936.05=>PV

42 [PMT]

42 =>PMT

-936.05 42 Calculate I/Y

[COMP] [I/Y]

I/Y= 5.42549

The effective annual yield can be calculated as: EAY = (1 + Quoted rate m) m − 1 = (1.054249 ) − 1 2

= 0.11145 = 11.145%

Module 8: Bond valuation

8.25

Realised yield: You bought a 6-year bond issued by Seven Network Ltd 4 years ago.

At that time, you paid $974.33 for the bond. The bond pays a coupon rate of 7.375 per cent, and interest is paid semi-annually. Currently, the bond is priced at $1023.56. What yield can you expect to earn on this bond if you sell it today?

Assume the bond has a face value of $1000.

Purchase price of bond = $974.33 Years investment held = 4 Hence n=4x2=8 Coupon rate = C = 7.375% Frequency of payment = m = 2 Annual coupon = $1,000 x (0.07375/2) = $36.875 Realised yield = i Selling price of bond = PB = $1,023.56 To calculate the realised 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 realised return is going to be greater than the bond’s coupon. Try rates higher than the coupon rate.

Try i = 9%, or i/2 = 4.5%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

36.875  1  1023.56 1− +  0.045  (1.045) 8  (1.045) 8

= 243.23 + 719.75 = 962.98  974.33 Try a lower rate, i = 8.6% or i/2 = 4.3%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

36.875  1  1023.56 1− +  0.043  (1.043) 8  (1.043) 8

= 245.22 + 730.87 = 976.09  974.33 EAY = (1 + Quoted rate m) m − 1  (1.043) − 1 2

 0.08785  8.79%

The realised rate of return is approximately 8.79 per cent. Using a financial calculator provides an exact yield of 8.84 per cent.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Procedure Enter cash flow data

Key Operation 1023.56 [FV]

Display 1023.56=>FV

8 [N]

8=>N

-974.33[PV]

-974.33=>PV

36.875 [PMT]

36.875 =>PMT

[COMP] [I/Y]

I/Y=

1023.56 8.00 -974.33 36.875 Calculate I/Y

4.32666

The effective annual yield can be calculated as: EAY = (1 + Quoted rate m) m − 1 = (1.0432666 ) − 1 2

= 0.088405 = 8.84%

Module 8: Bond valuation

CHALLENGING 8.26

Lend Lease Corporation Ltd is planning to issue 10-year bonds with a face value of $1000. The going market rate for such bonds is 8.125 per cent. Assume that coupon payments will be semiannual. The company is trying to decide between issuing an 8 per cent coupon bond or a zero coupon bond. The company needs to raise $1 million. a.

What will be the price of the 8 per cent coupon bonds? b.

How many coupon bonds would have to be issued? c.

What will be the price of the zero coupon bonds? d.

How many zero coupon bonds will have to be issued?

a.

Years to maturity = 10 hence n=10x2=20 Coupon rate = C = 8.125% Semi-annual coupon = $1,000 x (0.08/2) = $40 Current market rate = 8.125% Hence i = 8.125/2=4.0625 semi annual Present value of bond = PB 0 1 2 3 ├───────┼────────┼────────┼── $40 $40 $40

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

  40 1 1000 1− +  20  0.040625  (1.040625)  (1.040625) 20

14 ─────────┤ $40 $1,000

= 540.617 + 450.936 = 991.55 The company can sell these bonds at $991.55.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

20 [N]

20=>N

4.0625[I/Y]

4.0625=> I/Y

40 [PMT]

40 =>PMT

1000.00 20.00 4.0625 40 Calculate PV

[COMP] [PV]

PV= -991.55

b.

Amount needed to be raised = $1,000,000 Number of bonds sold = $1,000,000 / $991.55 = 1,009

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

c.

Years to maturity = 10 Hence n=10x2=20 Coupon rate = C = 0% Current market rate = i = 8.125% Assume semi-annual coupon payments.

0 1 2 3 4 5 6 ├───┼────┼───┼───┼───┼────┼── $0 $0 $0 $0 $0 $0

PB =

(

Fmn

1+ i

m

)

mn

=

(

Procedure Enter cash flow data

$1, 000

1 + 0.08125

2

)

210

=

20 ─────┤ $0 $1,000

$1, 000

(1.040625)

20

= $450.94

Key Operation 1000 [FV]

Display 1000=>FV

20 [N]

20=>N

4.0625[I/Y]

4.0625=> I/Y

0 [PMT]

0 =>PMT

[COMP] [PV]

PV=

1000.00 20.00 4.0625 0 Calculate PV

-450.94

d.

At the price of $450.94, the company needs to raise $1 million. To do so, the company will have to issue: Number of contracts = $1,000,000 / $450.94 = 2,218 contracts

Module 8: Bond valuation

8.27

Sunny Times Pty Ltd has issued 8-year bonds with a coupon of 6.375 per cent and semiannual coupon payments. The market’s required rate of return on such bonds is 7.65 per cent and the face value is $1000. a.

What is the market price of these bonds? b.

Now assume that the above bond is callable after 5 years at an 8.5 per cent premium on the face value. What is the expected return on this bond?

a.

Years to maturity = 8 Hence n= 8x2=16 Coupon rate = C = 6.375% Semi-annual coupon = $1,000 x (0.06375/2) = $31.875 Current market rate = 7.65% Hence i=7.65/2=3.825% Present value of bond = PB 0 1 2 3 ├───────┼────────┼────────┼── $31.875 $31.875 $31.875

PB =

C 1  FV 1− + n   i  (1 + i )  (1 + i ) n

PB =

 31.875  1 1000 1− + 16   0.03825  (1.03825)  (1.03825)16

16 ─────────┤ $31.875 $1,000

= 376.26 + 548.49 = $924.75 The company can sell these bonds at $924.75. b.

Assume purchase price of bond = market price from part (a) = $924.75 Years investment held = 5 hence n= 5x2=10 Coupon rate = C = 6.375% Semi-annual coupon = $1,000 x (0.06375/2) = $31.875 Frequency of payment = m = 2 Realised yield = i Call price of bond = PB = 1085 = $1000x(1.085) To calculate the realised return, either the trial-and-error approach or the financial calculator can be used. Since the call price is higher than the market price, the realised rate must be higher than current market rates. Try rates higher than the current YTM.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Try i = 9%, or i/2 = 4.5%.

PB =

C 1  FV 1− +  n i  (1 + i )  (1 + i ) n

PB =

 31.875  1 1085 1− +  10  0.045  (1.045)  (1.045)10

= 252.22 + 698.66 = 950.88  924.75 Try a higher rate, i = 9.6% or i/2 = 4.8%.

PB =

C 1  FV 1− +  n i  (1 + i )  (1 + i ) n

PB =

 31.875  1 1085 1− +  10  0.048  (1.048)  (1.048)10

= 248.54 + 678.92 = 927.46  924.75 EAY = (1 + Quoted rate m )m − 1  (1.048 ) − 1 2

 0.0983  9.83%

The realised rate of return is approximately 9.83 per cent. Using a financial calculator provides an exact yield of 9.90 per cent.

Procedure Enter cash flow data

Key Operation 1085 [FV]

Display 1085=>FV

10 [N]

10=>N

-924.75[PV]

-924.75=>PV

1085 10.00 -924.75 31.875 [PMT]

31.875 =>PMT

[COMP] [I/Y]

I/Y=

31.875 Calculate I/Y

4.8352

The effective annual yield can be calculated as: EAY = (1 + Quotedrate m) m − 1 = (1.048352 ) − 1 2

= 0.09904 = 9.90%

Module 8: Bond valuation

8.28

Probiotec Ltd has 7-year bonds outstanding. The bonds pay a coupon of 8.375 per cent semiannually and are currently worth $1063.49. The bonds can be called in 3 years at a price of $1075. The bond has a face value of $1000. a.

What is the yield to maturity on the bond? b.

What is the effective annual yield? c.

What is the realised yield on the bonds if they are called? d.

If you plan to invest in this bond today, what is the expected yield on the investment? Explain.

a.

Years to maturity =7 hence n = 7x2=14 Coupon rate = C = 8.375% Current market rate = i Semi-annual coupon payments = $1,000 x (0.08375/2) = $41.875 Present value of bond = PB = $1,063.49 0 1 2 3 ├───────┼────────┼────────┼── $41.875 $41.875 $41.875

14 ─────────┤ $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 per cent.

Try i = 8% or i/2 = 4%.

PB =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n

PB =

41.875  1  1000 + 1 − 14  0.04  (1.04)  (1.04) 14

= 442.33 + 577.48 = 1019.81  1063.49

Try a lower rate, i = 7.2%, or i/2 = 3.6%.

PB =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n

PB =

 41.875  1 1000 + 1 −  0.036  (1.036) 14  (1.036) 14

= 454.24 + 609.49 = 1063.73  1063.49

The yield-to maturity is approximately 7.2 per cent.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

b.

The effective annual yield can be calculated as: EAY = (1 + Quoted rate m) m − 1 = (1.036021) − 1 2

= 0.073292 = 7.33% Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

14 [N]

14=>N

-1063.49[PV]

-1063.49=>PV

41.875 [PMT]

41.875 =>PMT

[COMP] [I/Y]

I/Y=

1000.00 14.00 -1063.49 41.875 Calculate I/Y

3.6021

c.

Purchase price of bond = $1063.49 Years investment held = 3 hence n = 3x2=6 Coupon rate = C = 8.375% Semi-annual coupon payments = $1,000 x (0.08375/2) = $41.875 Frequency of payment = m = 2 Realised yield = i Selling price of bond = PB = $1075 To calculate the realised return, either the trial-and-error approach or the financial calculator can be used. Since the call price has is higher than the par value the realised yield to call will be higher than the YTM. Try rates higher than the YTM calculated in parts a and b.

Try i = 8%, or i/2 = 4%

PB =

C 1  FV 1− + n   i  (1 + i )  (1 + i ) n

PB =

41.875  1  1075 1− +  0.04  (1.04)6  (1.04) 6

= 219.51 + 849.59 = 1069.10  1063.49

Module 8: Bond valuation

Try a higher rate, i = 8.2% or i/2 = 4.1%.

PB =

C 1  FV 1− + n   i  (1 + i )  (1 + i ) n

PB =

41.875  1  1075 1− + 6  0.041  (1.041)  (1.041)6

= 218.80 + 844.70 = 1063.50  1063.49 EAY = (1 + Quoted rate m )m − 1 = (1.041) − 1 2

= 0.083681 = 8.37%

The realised rate of return is approximately 8.37 per cent. Using a financial calculator provides an exact yield of 8.37 per cent.

Procedure Enter cash flow data

Key Operation 1075 [FV]

Display 1075=>FV

6 [N]

6=>N

-1063.49[PV]

-1063.49=>PV

1075.00 6.00 -1063.49 41.875 [PMT]

41.875 =>PMT

[COMP] [I/Y]

I/Y=

41.875 Calculate I/Y

4.10026

The effective annual yield can be calculated as: EAY = (1 + Quoted rate m )m − 1 = (1.0410026 ) − 1 2

= 0.083686413 = 8.37%

d.

If we purchased the bond today, then the expected return on the bond will be at least the annualised YTM of 7.33 per cent, if the bond is not called and is held until maturity in 7 years. If the bond is however, is called in 3 years we realise a yield to call of 8.37 per cent.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.29

New South Wales Treasury has issued 25-year bonds that pay semiannual coupons at a rate of 9.875 per cent. The current market rate for similar securities is 11 per cent. Assume the bond has a face value of $1000. a.

What is the bond’s current market value? b.

What will be the bond’s price if rates in the market (i) decrease to 9 per cent or (ii) increase to 12 per cent? c.

Refer to your answers in part b. How do the interest rate changes affect premium bonds and discount bonds? d.

Suppose the bonds were to mature in 12 years. How do the interest rate changes in part b affect the bond prices?

a.

Years to maturity =25 hence n = 2x2=50 Coupon rate = C = 9.875% Semi-annual coupon = $1,000 x (0.09875/2) = $49.375 Current market rate = i = 11% Present value of bond = PB 0 1 2 3 ├───────┼────────┼────────┼── $49.375 $49.375 $49.375 PB =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n

PB =

 49.375  1 1000 + 1 − 50  0.055  (1.055)  (1.055) 50

50 ─────────┤ $49.375 $1,000

= 835.99 + 68.77 = 904.76

The NSW Treasury bonds will sell at $904.76.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV 1000.00

50 [N]

50=>N

5.5[I/Y]

5.5=> I/Y

50.00 5.5 49.375 [PMT]

49.375 =>PMT

[COMP] [PV]

PV=

49.375 Calculate PV

-904.76

Module 8: Bond valuation

b.

(i)

Current market rate = i = 9%

PB =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n

PB =

 49.375  1 1000 + 1 − 50  0.045  (1.045)  (1.045) 50

= 975.75 + 110.71 = 1086.46

The NSW Treasury bonds will increase in price to sell at $1,086.46.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

50 [N]

50=>N

1000.00 50.00 4.5[I/Y]

4.5=> I/Y

49.375 [PMT]

49.375 =>PMT

4.5 49.375 Calculate PV

[COMP] [PV]

PV= -1086.46

(ii)

Current market rate = i = 12% PB =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n

PB =

49.375  1  1000 + 1 − 50  0.06  (1.06)  (1.06) 50

= 778.24 + 54.29 = 832.53

The NSW Treasury bonds will decrease in price to sell at $832.53.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

50 [N]

50=>N

1000.00 50.00 6[I/Y]

6=> I/Y

49.375 [PMT]

49.375 =>PMT

[COMP] [PV]

PV=

6 49.375 Calculate PV

-832.53

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

c.

Bonds, in general, decrease in price when interest rates go up. When interest rates decrease, bond prices increase.

d.

(i)

Current market rate = i = 9% Term to maturity = 12 years

PB =

C 1  FV 1− + n   i  (1 + i )  (1 + i ) n

PB =

 49.375  1 1000 1− + 24   0.045  (1.045)  (1.045) 24

= 715.714 + 347.703 = 1063.42 The NSW Treasury bonds will increase in price to sell at $1,063.42.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

24 [N]

24=>N

1000.00 24.00 4.5[I/Y]

4.5=> I/Y

49.375 [PMT]

49.375 =>PMT

[COMP] [PV]

PV=

4.5 49.375 Calculate PV

-1063.42

(ii)

Current market rate = i = 12% PB =

C 1  FV + 1 − n  i  (1 + i )  (1 + i ) n

PB =

49.375  1  1000 + 1 − 24  0.06  (1.06)  (1.06) 24

= 619.67 + 246.98 = 866.65

Module 8: Bond valuation

The NSW Treasury bonds will decrease in price to sell at $866.65.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

24 [N]

24=>N

6[I/Y]

6=> I/Y

1000.00 24.00 6.00 49.375 [PMT]

49.375 =>PMT

[COMP] [PV]

PV=

49.375 Calculate PV

-866.65

The Maryland bonds will drop in price to $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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

8.30

The Wattyl Group has 18-year bonds outstanding. These bonds, which have a face value of $1000 and pay semiannual coupons, have a coupon rate of 9.735 per cent and a yield to maturity of 7.95 per cent. a.

Calculate the bond’s current price. b.

If the bonds can be called after 5 more years at a premium of 13.5 per cent over par value, what is the investor’s realised yield? c.

If you bought the bond today, what is your expected rate of return? Explain.

a.

Years to maturity = 18 hence n = 18x2=36 Coupon rate = C = 9.735% Semi-annual coupon = $1,000 x (0.09735/2) = $48.675 Current market rate = i = 7.95% Present value of bond = PB 0 1 2 3 ├───────┼────────┼────────┼── $48.675 $48.675 $48.675

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

 48.675  1 1000 1− +  36  0.03975  (1.03975)  (1.03975) 36

30 ─────────┤ $48.675 $1,000

= 923.555 + 245.787 = 1169.34 The bond’s current price is at $1169.34.

Procedure Enter cash flow data

Key Operation 1000 [FV]

Display 1000=>FV

36 [N]

36=>N

1000.00 36.00 3.975[I/Y]

3.975=> I/Y

48.675 [PMT]

48.675 =>PMT

[COMP] [PV]

PV=

3.975 48.675 Calculate PV

-1169.34

Module 8: Bond valuation

b.

Purchase price of bond = $1169.34 from part a Years investment held = 5 hence n = 5x2=10 Coupon rate = C = 9.735% Semi-annual coupon = $1,000 x (0.09735/2) = $48.675 Frequency of payment = m = 2 Realised yield = i Call price of bond = FV = $1000 x 1.135 = 1135 To calculate the realised return, either the trial-and-error approach or the financial calculator can be used. Since the call price is lower than the current price, the realised yield to call will be lower than the current market rate. So, try rates lower than the current YTM rate.

Try i = 7.8%, or i/2 = 3.9%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

 48.675  1 1135 1− +  10  0.039  (1.039)  (1.039)10

= 396.77 + 774.18 = 1170.95  1169.34 Try a higher rate, i = 7.84 or i/2 = 3.92%.

PB =

C 1  FV 1− +  n  i  (1 + i )  (1 + i ) n

PB =

 48.675  1 1135 1− +  10  0.0392  (1.0392)  (1.0392)10

= 396.37 + 772.69 = 1169.06  1169.34 EAY = (1 + Quoted rate m) m − 1  (1.0392 ) − 1 2

 0.0.79937  7.99%

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

The realised rate of return is approximately 7.99 per cent. Using a financial calculator provides an exact yield of 7.9876 per cent.

Procedure Enter cash flow data

Key Operation 1135 [FV]

Display 1135=>FV

10 [N]

10=>N

1135.00 10.00 -1169.34[PV]

-1169.34=> PV

48.675 [PMT]

48.675 =>PMT

-1169.34 48.675 Calculate I/Y

[COMP] [I/Y]

I/Y = -3.91706

The effective annual yield can be calculated as: EAY = (1 + Quoted rate m) m − 1 = (1.0391706 ) − 1 2

= 0.079876 = 7.9876%

c.

If we purchased the bond today, then the expected return on the bond will be the annualised YTM of 8.108 per cent, if the bond is not called and is held until maturity in 18 years. If the bond is however, called in 5 years we realise a yield to call of 7.9876 per cent.

The effective annual yield can be calculated as: EAY = (1 + Quoted rate m) m − 1 = (1.03975 ) − 1 2

= 0.08108 = 8.108%

Module 9: Share valuation Self-study problems 9.1

Ted McKay has just bought ordinary shares of Ryland Pty Ltd. The company expects to grow at the following rates for the next 3 years: 30 per cent, 25 per cent, and 15 per cent. Last year the company paid a dividend of $2.50. Assume a required rate of return of 10 per cent. Calculate the expected dividends for the next 3 years and also the present value of these dividends.

Expected dividends for Ryland Pty Ltd and their present value: 0 10% 1 2 3 ├─────────┼─────────┼─────────┼─────────┼──────────› D0 = $2.50 D1 D2 D3

g1 = 30%

g2 = 25%

D1 = D0 (1 + g1 ) = $2.50 (1 + 0.30 ) = $3.25 D2 = D1 (1 + g 2 ) = $3.25 (1 + 0.25) = $4.063 D3 = D2 (1 + g3 ) = $4.063 (1 + 0.15) = $4.672 PVDividends = PVD1 + PVD 2 + PVD 3 3.25 4.063 4.672 + + 1.11 1.12 1.13 PVDividends = 2.95 + 3.36 + 3.51 = $9.82

PVDividends =

The present value of Ryland’s dividends is $9.82.

g3 = 15%

Module 9: Share valuation

9.2

Centrogen Manufacturing Pty Ltd has been growing at a rate of 6 per cent for the past 2 years, and the company’s 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 of return was 14 per cent, what is the maximum price that you would be willing to pay for this company’s shares?

Present value of Centrogen shares: 0

14%

1

2

3

├─────────┼─────────┼─────────┼─────────┼──────────› D0 = $1.20 D1 D2 D3

g = 6% D1 = D0(1 + g) = $1.20(1 + 0.06) = $1.272 P0 =

D1 $1.272 $1.272 = = = $15.90 ( R − g ) ( 0.14 − 0.06) 0.08

The maximum price you should be willing to pay for this share is $15.90.

9.3

Clarion Australia Pty Ltd has been selling electrical supplies for the past 20 years.

The company’s product line has seen very little change in the past 5 years, and the company does not expect to add any new items for the foreseeable future. Last year, the company paid a dividend of $4.45 to its ordinary shareholders. The company is not expected to grow its revenues for the next several years. If your required rate of return for such companies is 13 per cent, what is the current value of this company’s shares?

Present value of Clarion Australia Pty Ltd’s shares: 0

13%

1

2

3

├─────────┼─────────┼─────────┼─────────┼──────────› D0 = $4.45 D1 D2 D3

g = 0% Since the company’s dividends are not expected to grow, D0 = D1 =D2=……..D∞ = $4.45 = D Present value of the share

= = =

D/R $4.45/0.13 $34.23

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

The current value of Clarion’s shares is $34.23.

9.4

Cooper Communications Pty Ltd 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 2 years. Last year the company’s growth accelerated, and they expect to grow at a rate of 35 per cent for the next 5 years before slowing down to a more stable growth rate of 7 per cent for the next several years. In the third year, the company has forecasted a dividend payment of $1.10. Calculate the share price of the company at the end of its rapid growth period (that is, at the end of 5 years). Your required rate of return for such shares is 17 per cent. What is the current price of these shares?

Present value of Cooper Communications Pty Ltd’s share: 0 17% 1 2 3 4 5 6 7 8 ├────┼────┼────┼────┼────┼────┼────┼────┤ D0 D1 D2 D3 D4 D5 D6

g1 – g5 = 35% D0 = D3 = D4 = D5 = D6 =

g6 = 7%

D1 = D2 = 0 $1.10 D3(1 + g4) = $1.10(1 + 0.35) = $1.485 D4(1 + g5) = $1.485(1 + 0.35) = $2.005 D5(1 + g6) = $2.005(1 + 0.07) = $2.145

Price of share at t = 5 P5: D6 $2.145 $2.145 = = ( R − g ) ( 0.17 − 0.07) 0.1 = $21.45

P5 =

Present value of the dividends 

= t =1

Dt

(1 + R )

= $0 + $0 +

t

=

= PV(D1) + PV(D2) + PV(D3) + PV(D4) + PV(D5)

D1

(1 + R )

1

+

D2

(1 + R )

2

+

D3

(1 + R )

$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 Present value (price) of shares = PV(Dividends) + PV(P5) = $2.39 + [$21.45/(1.17)5] = $2.39 + $9.78

3

+

D4

(1 + R )

4

+

D5

(1 + R )

5

Module 9: Share valuation

= $ 12.17

9.5

The current price of Cooper Communications’ shares is $12.17.

You are interested in buying the preference shares of a bank that pays a dividend of $1.80 semiannually. If you discount such cash flows at 8 per cent, what is the price of this share?

Present value of preferred bank share: semiannual dividend on preference shares = D = $1.80 Required rate of return = 8% Current price of share = = = The price of this share is $45.

(D/R ) $1.80/(0.08/2) $45.00

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Critical thinking questions 9.1

Why can the market price of a security differ from its true value?

Let us start by first defining the market equilibrium price or true value of a security as the price that equates the demand for a security with the supply of the security. The role of the security markets is to bring buyers and sellers together in the most efficient way such that securities are bought and sold at the true equilibrium price. In reality, however, barriers of various kinds including the geographic separation of the two parties make the market price of a security slightly different than the true equilibrium price. The more efficient the market place, the smaller the deviation between the two.

9.2

Why are investors and managers concerned about market efficiency?

The role of secondary markets is to bring buyers and sellers together. Ideally, we would like security 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 equilibrium price (true value).

The more efficient the market, the more likely this is to happen. This makes it easier for managers to price the securities close to the equilibrium price.

What investors are most concerned about is having complete information regarding a security’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 equilibrium price than otherwise possible.

Thus, both investors who provide funds and managers (companies) who raise money are concerned when high transaction costs lead to inefficient markets.

9.3

Why are ordinary shareholders considered to be more at risk than the holders of other types of securities?

In the hierarchy of lenders (suppliers) of funds to a company, ordinary shareholders have the most to lose. In the event of a company becoming bankrupt, the law requires that creditors of different types, including bondholders, be paid off first. Next, preference shareholders are paid off. Finally, ordinary shareholders receive their investment if any funds are still available. Thus, ordinary shareholders receive their money back last and are placed at most risk. This feature of ordinary equity is referred to as residual claim.

Module 9: Share valuation

9.4

How can individual shareholders avoid double taxation?

Double taxation refers to the fact that in most of the world a company’s income is taxed first and then any dividends paid to investors get taxed at the personal tax rate. Thus, investors pay tax twice. Some investors who desire to get around this problem try to invest in growth companies that do not pay out dividends but instead reinvest in the company. This allows the companies to grow with internal capital and leads to the company’s value (price) growing faster. Shareholders benefit from rising share prices and can sell some or all of their holdings and generate capital gains, which are taxed at a lower rate than income.

In Australia, however, under dividend imputation tax is paid only once. Under the imputation tax system the company’s profits are still subject to company tax but the company tax paid is passed on as a franking credit to resident shareholders. This franking credit can be used to offset the investor’s other sources of taxable income. Thus investors are effectively only taxed once at their marginal personal tax rate.

9.5

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 company has good prospects for earnings growth in the future. In fact, they believe that the company will have higher growth potential than companies 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, companies like Cochlear and CSL had very high P/E ratios. As these companies matured and settled to annual growth rates of 20 per cent or less, their P/E ratios have declined.

9.6

Preference shares are considered to be non-participating because: a. investors do not participate in the election of the company’s directors. b. investors do not participate in the determination of the dividend payout policy. c. investors do not participate in the company’s earnings growth. d. none of the above. c. Non-participating implies that the preference share dividend remains constant regardless of any increase in the company’s earnings. Thus, investors in a company’s preference shares will not see higher dividends when the company’s earnings increase.

Nor will they see a decrease if the company’s earnings decrease.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

9.7

Explain why preference shares are considered to be a hybrid of equity and debt securities.

The law considers preference shares as equity. Thus, holders are treated as the company’s owners. Also, like ordinary shareholders, preference shareholders have to pay tax on their dividend income. However, preference shareholders do not have any voting rights. In addition, they receive only a fixed dividend just like bondholders. If a company is liquidated, then they receive a stated value (par value) similar to bondholders. Preference shares are rated by credit rating agencies just like bonds. Some preference share issues are convertible to the company’s ordinary shares just like convertible bonds. Some preference share issues are not perpetual and have a fixed maturity just like bonds.

Thus preference shares are a hybrid security—like equity in some ways and like debt security in others.

9.8

Why is share valuation more difficult than bond valuation?

Despite the availability of mathematical models to value shares, it is more difficult to apply valuation techniques to shares than to bonds. First, unlike bonds, companies are not in default if dividends are not declared. This makes it difficult to determine the size and timing of the cash flows. Second, ordinary shares, unlike bonds, do not have a fixed maturity, and hence, it is difficult to determine a terminal value unlike bonds, which have a maturity (par) 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 shares, it is rather difficult to estimate a required rate of return for many shares and classify them into different risk groups.

9.9

You are currently thinking about investing in a share valued at $25.00. The share recently paid a dividend of $2.25 and is expected to grow at a rate of 5 per cent for the foreseeable future. You normally require a return of 14 per cent on shares of similar risk. Is the share overpriced, under-priced or correctly priced?

This share is under-priced at $25. Using the constant-growth model, we can arrive at a 2.25(1.05) = 26.25 ) for this share. This makes the share underprice of $26.25 ( P0 = 0.14 − 0.05 priced, and it should be considered a good buy.

Module 9: Share valuation

9.10

Share A and Share B are both priced at $50 per share. Share A has a P/E ratio of 17, while Share B has a P/E ratio of 24. Which is the more attractive investment, considering everything else to be the same, and why?

Share 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 share price. This makes Share A a more attractive investment than Share B.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Questions and problems BASIC 9.1

Present value of dividends: Outback Yards Pty Ltd is a fast-growing company. The company expects to grow at a rate of 22 per cent over the next 2 years and then slow down to a growth rate of 18 per cent for the following 3 years. If the last dividend paid by the company was $2.15, estimate the dividends for the next 5 years.

Calculate the present value of these dividends if the required rate of return was 14 per cent.

0 1 2 3 4 5 ├───────┼────────┼───────┼────────┼───────┤ D0 = $2.15 g1-2 = 22%; g3-5 = 18%; kCS = 14% D1 = D0(1 + g1) = $2.15(1.22) = $2.623 D2 = D1(1 + g2) = $2.623(1.22) = $3.200 D3 = D2(1 + g3) = $3.200(1.18) = $3.776 D4 = D3(1 + g4) = $3.776(1.18) = $4.456 D5 = D4(1 + g5) = $4.456(1.18) = $5.258

$2.623 $3.200 $3.776 $4.456 $5.258 + + + + (1.14)1 (1.14) 2 (1.14)3 (1.14) 4 (1.14)5 = $2.30 + $2.46 + $2.55 + $2.64 + $2.73 = $12.68

PV ( Dividends) =

9.2

Zero growth: Nicnet Australia Ltd paid a dividend of $3.54 last year. The company does not expect to increase its dividend for the next several years. If the required rate of return is 13 per cent, what is the current share price?

D0 = $3.54; g = 0; R = 13.0% D $3.54 P0 = = = $27.23 R 0.13

Module 9: Share valuation

9.3

Zero growth: Armour Supply Pty Ltd has seen no growth for the last several years and expects the trend to continue. The company last paid a dividend of $3.67. If you require a rate of return of 18.5 per cent, what is the current share price?

D0 = $3.67; g = 0; R = 18.5% D $3.67 P0 = = = $19.84 R 0.185

9.4

Zero growth: Sam Gripple is interested in buying the shares of Bank of Queensland Ltd. While the bank expects no growth in the near future, Sam is attracted by the dividend income. Last year, the bank paid a dividend of $5.88. If Sam requires a return of 16.5 per cent on such shares, what is the maximum price he should be willing to pay?

D0 = $5.88; g = 0; R = 16.5% D $5.88 P0 = = = $35.64 R 0.165

9.5

Zero growth: The current share price of Coral Pty Ltd is $41.45. If the required rate of return is 18 per cent, what is the dividend paid by this company, which is not expected to grow in the near future?

P0 = $41.45; R = 18%; D P0 = R D $41.45 = 0.18 D = $41.45  0.18 = $7.46

D = ?;

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

9.6

Constant growth: Happy Optical Pty Ltd declared a dividend of $2.15 yesterday.

The company is expected to grow at a steady rate of 5 per cent for the next several years. If shares such as these require a rate of return of 21 per cent, what should be the market value of this share?

D0 = $2.15;

g = 5%;

R = 21%

D1 D (1 + g ) = 0 R−g R−g = $2.15 x 1.05 0.21 – 0.05 = $2.258 0 0.21 – 0.05 = $14.11

P0 =

9.7

Constant growth: Maurica Ltd is a consumer products company growing at a constant rate of 6.5 per cent. The company’s last dividend was $3.36. If the required rate of return was 14 per cent, what is the market value of this share?

D0 = $3.36;

g = 6.5%;

D1 D (1 + g ) = 0 R−g R−g = $3.36 x 1.065 0.14 – 0.065 = $47.71

P0 =

R = 14%

Module 9: Share valuation

9.8

Constant growth: Tarco Pty Ltd is expected to pay a dividend of $2.32 next year.

The forecast for the share price a year from now is $41.50. If the required rate of return is 17.5 per cent, what is the current share price? Assume constant growth.

D1 = $2.32;

P1 = $41.50;

R = 17.5%

D2 D (1 + g ) = 1 R−g R−g 2.32(1 + g ) 41.50 = 0.175 − g 41.50(0.175 − g ) = 2.32 + 2.32 g P1 =

7.26250 − 41.50 g = 2.32 + 2.32 g 7.26250 − 2.32 = 41.50 g + 2.32 g 4.94250 = 11.28% 43.82 D1 P0 = R−g $2.32 = = $37.30 0.175 − 0.1128 g=

9.9

Constant growth: Lavfield Pty Ltd is expected to grow at a constant rate of 8.25 per cent. If the company’s next dividend is $1.83 and its current price is $22.35, what is the required rate of return on this share?

D1 = $1.83;

P0 = $22.35;

g = 8.25%

D1 R−g 1.83 22.35 = R − 0.0825 22.35 x( R − 0.0825) = 1.83 P0 =

− 1.8439 − 1.83 = −22.35 xR 3.6739 22.35 R = 16.44%

R=

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

9.10

Preference share valuation: Keystone Energy Pty Ltd has issued perpetual preference shares with a par of $100 and an annual dividend of 5.5 per cent. If the required rate of return is 11.75 per cent, what is the share’s current market price?

D = 5.5% ($100) = $5.50;

P0 =

9.11

R = 11.75%

D $5.50 = = $46.81 R 0.1175

Preference share valuation: Icelock (Australia) Pty Ltd has issued perpetual preference shares with a $100 par value. The bank pays a quarterly dividend of $1.65 on a share. What is the current price of this preference share given a required rate of return of 10 per cent, compounding quarterly?

Semiannual dividend = $1.65 Required rate of return = R = 10.0%

P0 =

9.12

1.65 x 4 = $66.00 0.1

Preference shares: The preference shares of Queensland Tours Pty Ltd are selling currently at $54.56. If your required rate of return is 11.5 per cent, what is the dividend paid by this share?

P0 = $54.56;

R = 11.5%

D D $54.56 = R 0.115 D = $54.56 x 0.115 = $6.27

P0 =

Module 9: Share valuation

9.13

Preference shares: Each quarter, Top Brewers Pty Ltd pays a dividend on its perpetual preference shares. Today, the share is selling at $62.33. If the required rate of return for such shares is 14.5 per cent, compounding quarterly, what is the quarterly dividend paid by this company?

P0 = $62.33;

R = 14.5%

D R D $62.33 = 0.145 D = $62.33 x 0.145 P0 =

D = $9.04 Annual dividend = $9.04 Quarterly dividend = $9.04 / 4 = $2.26

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

MODERATE 9.14

Constant growth: Kathleen Ferrero is interested in purchasing the ordinary shares of Vespertine Pty Ltd which is currently priced at $39.96. The company expects to pay a dividend of $2.58 next year and expects to grow at a constant rate of 8 per cent. a. What should the market value of the share be if the required rate of return is 14 per cent? b. Is this a good buy? Why or Why not? a.

P0 =

b.

9.15

D1 $2.58 = = $43.00 R − g 0.14 − 0.08

The share at $39.96 is a good buy, as the projected dividend and growth rate justify a share price of $43.00.

Constant growth: The required rate of return is 23 per cent. Gnangara Pty Ltd has just paid a dividend of $3.12 and expects to grow at a constant rate of 5 per cent.

What is the expected price of the share 3 years from now?

R = 23%; D0 = $3.12; D (1 + g ) 4 D4 P3 = = 0 R−g R−g

g = 5%

3.12(1.05) 4 3.7924 = = $21.07 0.23 − 0.05 0.18 or

=

Calculate price now and then the price in year 3.

D (1 + g ) D1 = 0 R−g R−g 3.12(1.05) 3.276 = = = $18.20 0.23 − 0.05 0.18

P0 =

P3 = P0 (1 + g )

3

= 18.2 (1.053 ) = $21.07

Module 9: Share valuation

9.16

Constant growth: Pedro Sanchez is interested in buying shares in TreeTop Pty Ltd which is growing at a constant rate of 8 per cent. Last year, the company paid a dividend of $2.65. The required rate of return is 18.5 per cent. What is the current price for this share? What would be the price of the share in year 5? g = 8%,

D0 = $2.65,

D1 R−g D (1 + g ) P0 = 0 R−g $2.65 x 1.08 P0 = 0.185 − 0.08 P0 = $27.26

P0 =

or P5 =

D6 R−g

P5 =

D0 (1 + g )6 R−g

$2.65 (1.08)6 0.185 − 0.08 P5 = $40.05

P5 =

R = 18.5%

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

9.17

Non-constant growth: Anittel Pty Ltd is a fast growing technology company. The company projects a rapid growth of 30 per cent for the next 2 years, then a growth rate of 17 per cent for the following 2 years. After that, the company expects a constant growth rate of 8 per cent. The company expects to pay its first dividend of $2.45 a year from now. If your required rate of return on such shares is 22 per cent, what is the current price of the share? g1 = g2 = 30%,

g3 = g4 = 17%,

g = 8%,

D1 = $2.45, D2 = $2.45(1.30) = $3.185 D3 = $3.185(1.17) = $3.726 D4 = $3.726(1.17) = $4.359 D5 = 4.359(1.08) = $4.708 D5 4.708 4.708 = = = 33.63 R − g 0.22 − 0.08 0.14 D3 D1 D2 D4 P4 P0 = + + + + 1 2 3 4 (1 + R ) (1 + R ) (1 + R ) (1 + R ) (1 + R ) 4 P4 =

P0 =

2.45 3.185 3.726 4.359 33.63 + + + + 2 3 4 1.22 (1.22) (1.22) (1.22) (1.22) 4

P0 = 2.01 + 2.14 + 2.05 + 1.97 + 15.18 P0 = $23.35

D1 = $2.45,

R = 22%

Module 9: Share valuation

9.18

Non-constant growth: Agenix Ltd a biotech company, forecast the following growth rates for the next 3 years: 35 per cent, 28 per cent and 22 per cent. The company then expects to grow at a constant rate of 9 per cent for the next several years. The company paid a dividend of $1.75 last week. If the required rate of return is 20 per cent, what is the market value of this share? g1 = 35%; g2 = 28%; g3 = 22%; g4 = 9% forever; D0 = $1.75; R = 20% D1 = D0 (1 + g 1 ) = $1.75(1.35) = $2.363 D2 = D1 (1 + g 2 ) = $2.363(1.28) = $3.024 D3 = D2 (1 + g 3 ) = $3.024(1.22) = $3.689 D4 = D3 (1 + g ) = $3.689(1.09) = $4.021 P3 =

D4 4.021 4.021 = = = $36.55 R − g 0.20 − 0.09 0.11

P0 =

D3 P3 D1 D2 + + + 2 3 (1 + R ) (1 + R ) (1 + R ) (1 + R ) 3

P0 =

2.363 3.024 3.689 36.55 + + + 2 3 1.20 (1.20) (1.20) (1.20) 3

P0 = $1.97 + $2.10 + $2.13 + $21.15 P0 = $27.35

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

9.19

Non-constant growth: Nillahcootie Outdoor Centre Pty Ltd is on a fast-growth share and expects to grow at a rate of 23 per cent for the next 4 years. It then will settle to a constant-growth rate of 6 per cent. The first dividend will be paid in year 3 and be equal to $4.25. If the required rate of return is 17 per cent, what is the current price of the share? g1-4 = 23%;

g5 = 6%; D3 = $4.25;

R = 17%

D4 = D3 (1.23) = 4.25(1.23) = $5.228 D5 = D4 (1.06) = 5.228 (1.06) = $5.542

P4 =

D5 5.542 5.542 = = = $50.38 R − g 0.17 − 0.06 0.11

P0 =

D3 D1 D2 D + P4 + + + 4 2 3 (1 + R ) (1 + R ) (1 + R ) (1 + R ) 4

4.25 5.228 50.38 + + 3 4 (1.17) (1.17) (1.17) 4 P0 = $2.65 + $2.79 + $26.89 = $32.33

P0 = 0 + 0 +

9.20

Non-constant growth: Quoin Hill Vineyard expects to pay no dividends for the next 6 years. It has projected a growth rate of 25 per cent for the next 7 years. After 7 years, the company will grow at a constant rate of 5 per cent. Its first dividend to be paid in year 7 will be worth $3.25. If your required rate of return is 24 per cent, what is the share worth today? gconstant = 5%; R = 24%; D7 = $3.25; D1 – D6 = 0

P7 =

D8 3.25(1.05) 3.413 = = = $17.96 R − g 0.24 − 0.05 0.19

D7 + P7 3.25 + 17.96 21.21 = = = $4.71 7 7 4.5077 (1 + R ) (1.24) or

P0 =

D7 3.25 3.25 = = = $17.105 R − g 0.24 − 0.05 0.19 P6 17.105 P1 = = = $4.71 6 6 (1 + R ) 1.24

P6 =

Module 9: Share valuation

9.21

Non-constant growth: Serventy Organic Wines Pty Ltd will pay dividends of $5.00, $6.25, $4.75 and $3.00 for the next 4 years. Thereafter, the company expects its growth rate to be at a constant rate of 6 per cent. If the required rate of return is 18.5 per cent, what is the current market price of the share?

D1 = $5;

D2 = $6.25;

D3 = 4.75;

D4 = $3;

g = 6%;

P0 =

D3 D1 D2 D4 P4 + + + + 2 3 4 (1 + R ) (1 + R ) (1 + R ) (1 + R ) (1 + R ) 4

P4 =

D5 3(1.06) 3.18 = = = $25.44 R − g 0.185 − 0.06 0.125

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 + $2.85 + $14.42 = $25.94

9.22

Non-constant growth: Devil’s Lair Pty Ltd is growing rapidly at a rate of 35 per cent for the next 7 years. The first dividend to be paid 3 years from now will be worth $5. After 7 years, the company will settle to a constant growth rate of 8.5 per cent. What is the market value for this share given a required rate of return of 14 per cent? 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) = $9.113 D6 = 9.113 (1.35) = $12.303 D7 = $12.303(1.35) = $16.609 D8 = 16.609(1.085) = $18.021 D8 $18.021 18.021 P7 = = = = $327.65 R − g 0.14 − 0.085 0.055

P0 =

D3 D5 D6 D + P7 D1 D2 D4 + + + + + + 7 2 3 4 5 6 (1 + R ) (1 + R ) (1 + R ) (1 + R ) (1 + R ) (1 + R ) (1 + R ) 7

5 6.75 9.113 12.303 16.609 327.65 + + + + + 3 4 (1.14) (1.14) (1.14)5 (1.14)6 (1.14)7 (1.14) 7 = 3.37 + 4.00 + 4.73 + 5.61 + 6.64 + 130.94

=0+0+

= $155.29

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

9.23

Non-constant growth: Tim Adams Wines Pty Ltd is growing rapidly. Dividends are expected to grow at rates of 30 per cent, 35 per cent, 25 per cent and 18 per cent over the next 4 years. Thereafter the company expects to grow at a constant rate of 7 per cent. The shares are currently selling at $47.85, and the required rate of return is 16 per cent. Calculate the dividend for the current year (D0). g1 = 30%; g2 = 35%; g3 = 25%; g4 = 18%; g = 7%; R = 16%; P0 = $47.85 P0 = $47.85 =

D3 D1 D2 D4 P4 + + + + 2 3 4 (1 + R ) (1 + R ) (1 + R ) (1 + R ) (1 + R ) 4 D0 (1.30) D0 (1.30)(1.35) D0 (1.30)(1.35)(1.25) D0 (1.30)(1.35)(1.25)(1.18) + + + 1.16 (1.16) 2 (1.16) 3 (1.16) 4

D0 (1.30)(1.35)(1.25)(1.18)(1.07) 0.16 − 0.07 + (1.16) 4 1.30 1.755 2.19375 2.588625 = D0 + D0 + D0 + D0 1.16 1.3456 1.560896 1.81063936 30.775875 + D0 1.81063936 = D0 [1.120689655 + 1.304250892 + 1.405442771 + 1.429674543 + 16.99724179] = D0  22.25729965

D0 =

$47.85 = $2.15 $22.25729965

Module 9: Share valuation

CHALLENGING 9.24

Wineries stores has forecast a high growth rate of 40 per cent for the next 2 years, followed by growth rates of 25 per cent and 20 per cent for the following 2 years. It then expects to stabilise its growth to a constant rate of 7.5 per cent for the next several years. The company paid a dividend of $3.80 recently. If the required rate of return is 15 per cent, what is the current market price of the share? g1-2 = 40%; g3 = 25%; g4 = 20%; g = 7.5%; D0 = $3.80; R = 15% D1 = D0(1 + g1) = $3.80(1.40) = $5.320 D2 = D1(1 + g2) = $5.320(1.40) = $7.448 D3 = D2(1 + g3) = $7.448(1.25) = $9.310 D4 = D3(1 + g4) = $9.310(1.20) = $11.172 D5 = D4(1 + g5) = $11.172(1.075) = $12.010

D5 R−g $12.010 P4 = 0.15 − 0.075 P4 = $160.133 D1 D2 D3 D4 P4 P0 = + + + + 1 2 3 4 (1 + R) (1 + R) (1 + R ) (1 + R ) (1 + R ) 4 $5.320 $7.448 $9.310 $11.172 $160.133 P0 = + + + + (1.15)1 (1.15) 2 (1.15)3 (1.15) 4 (1.15) 4 P0 = $4.626 + $5.632 + $6.121 + $6.388 + $91.557

P4 =

P0 = $114.32

9.25

Chambers Rosewood Pty Ltd issued perpetual preference shares a few years ago.

The company pays an annual dividend of $4.27, and your required rate of return is 12.2 per cent. a.

What is the value of the share given your required rate of return? b.

Should you buy this share if its current market price is $34.41? Explain. a.

D = $4.27; R = 12.2% D $4.27 P0 = = = $35.00 R 0.122

b.

Since the share is worth $35.00 but can be bought for $34.41in the marketplace and thus is undervalued, you should buy this share.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

9.26

Gerald Neut owns shares in Patina Pty Ltd. Currently, the market price of the share is $36.34. The company expects to grow at a constant rate of 6 per cent for the foreseeable future. Its last dividend was worth $3.25. Gerald’s required rate of return for such shares is 16 per cent. He wants to find out whether he should sell his shares or add to his holdings. a.

What is the value of this share? b.

Based on your answer to part a, should Gerald buy additional shares in Patina Pty Ltd? Why or why not? a.

g = 6% D0 = $3.25 R = 16% D1 $3.25(1.06) 3.445 P0 = = = = $34.45 R − g 0.16 − 0.06 0.1

b.

No, he should not buy more shares. This share is overpriced with the share selling at a higher price in the market than what it is worth. Gerald should sell his shares.

Module 9: Share valuation

9.27

Parri Holdings Pty Ltd declared a dividend of $2.50 yesterday. You are interested in investing in this company, which has forecast a constant growth rate of 7 per cent for the next several years. The required rate of return is 18 per cent. a.

Calculate the expected dividends D1, D2, D3 and D4. b.

Find the present value of these four dividends. c.

What is the price of the share 4 years from now (P4)? d.

Calculate the present value of P4. Add the answer you got in part b. What is the price of the share today? e.

Use the equation for constant growth (equation 9.4) and calculate the price of the share today. a.

D0 = $2.50 g = 7% R = 18% D1 = $2.50(1.07) = $2.675 D2 = $2.50(1.07) 2 = $2.862 D3 = $2.50(1.07)3 = $3.063 D4 = $2.50(1.07) 4 = $3.277

2.675 2.862 3.063 $3.277 + + + 1 2 (1.18) (1.18) (1.18)3 (1.18) 4 = $2.27 + 2.06 + $1.86 + $1.69 = $7.88

PV ( Dividends ) =

b.

D5 = D4 (1 + g ) = $3.277(1.07) = $3.506

c.

P4 =

D5 $3.506 3.506 = = = $31.88 R − g 0.18 − 0.07 0.11

$31.88 = $16.44 (1.18) 4 P0 = PV ( Dividends ) + PV ( P4 )

PV ( P4 ) =

d.

= $7.88 + $16.44 = $24.32

e.

For a constant-growth share: D1 $2.675 2.675 P0 = = = = $24.32 R − g 0.18 − 0.07 0.11

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

9.28

Aspen Australia Pty Ltd is a fast-growing drug company. The company forecasts that in the next 3 years, its growth rates will be 30 per cent, 28 per cent, and 24 per cent, respectively. Last week it declared a dividend of $1.67. After 3 years, the company expects a more stable growth rate of 8 per cent for the next several years.

Your required rate of return is 14 per cent. a.

Calculate the dividends for the next 3 years, and find its present value. b.

Calculate the price of the share at the end of year 3 when the company settles to a constant growth rate. c.

What is the current price of the share? g1 = 30%; g2 = 28%; g3 = 24%; g = 8%; D0 = $1.67; R = 14% D1 = D0 (1 + g 1 ) = $1.67(1.30) = $2.171 D2 = D1 (1 + g 2 ) = $2.171(1.28) = $2.779 D3 = D2 (1 + g3 ) = $2.779(1.24) = $3.446

a.

PV ( Dividends ) = =

D3 D1 D2 + + 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 D4 = D3 (1 + g ) = $3.446(1.08) = $3.722

b.

P3 =

D4 $3.722 = = $62.03 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 = $48.24

Module 9: Share valuation

9.29

Trentham Estate Pty Ltd expects to grow at a rate of 22 per cent for the next 5 years and then settle to a constant-growth rate of 6 per cent. The company’s most recent dividend was $2.35. The required rate of return is 15 per cent. a.

Find the present value of the dividends during the rapid growth period. b.

What is the price of the share at the end of year 5? c.

What is the price of the share today? g1-5 = 22%; g = 6%; D0 = $2.35; R = 15%

D1 = D0 (1 + g 1 ) = $2.35(1.22) = $2.867 D2 = D1 (1 + g 2 ) = $2.867(1.22) = $3.498 D3 = D2 (1 + g3 ) = $3.498(1.22) = $4.268 D4 = D3 (1 + g 4 ) = $4.268(1.22) = $5.207 D5 = D4 (1 + g ) = $5.207(1.22) = $6.353 a.

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 $4.268 $5.207 6.353 + + + + 1.15 (1.15) 2 (1.15)3 (1.15) 4 (1.15)5

= $2.49 + $2.64 + $2.81 + $2.98 + $3.16 = $14.08 D6 = D5 (1 + g ) = $6.353(1.06) = $6.734

b.

P5 =

D6 $6.734 = = $74.82 R − g 0.15 − 0.06

$74.82 = $37.20 (1.15)5 P0 = PV ( Dividends ) + PV ( P5 )

PV ( P5 ) =

c.

= $14.08 + $37.20 = $51.28

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

9.30

Comwin Pty Ltd is expanding very fast and expects to grow at a rate of 25 per cent for the next 4 years. The company recently declared a dividend of $3.60 but does not expect to pay any dividends for the next 3 years. In year 4, they intend to pay a $5 dividend and thereafter grow it at a constant-growth rate of 6 per cent. The required rate of return on such shares is 20 per cent. a.

Calculate the present value of the dividends during the fast growth period. b.

What is the price of the share at the end of the fast growth period (P4)? c.

What is the share price today? d.

Would today’s share price be driven by the length of time you intend to hold the share? a.

g1-4 = 25% g5 = 6% D0 = $3.60 D4 = $5.00 kcs = 20% $5 PV ( Dividends ) = 0 + 0 + 0 + = $2.41 (1.20) 4

b.

P4 =

D5 $5.00(1.06) = = $37.86 R − g 0.20 − 0.06

$37.86 (1.20)4 = $2.41 + 18.26 = $20.67 P0 = $2.41 +

c.

d.

No, the length of the holding period has no bearing on today’s share price.

Module 10: Capital budgeting and cash flows Self-study problems 10.1

Premium Manufacturing Ltd is evaluating two forklift systems to use in its plant that produces the towers for a wind farm. The costs and the cash flows from these systems are shown here. 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 Forklifts Craigmore Forklifts

Year 0 −$3 123 450 −$4 137 410

Year 1 $979 225 $875 236

Year 2 $1 358 886 $1 765 225

a. NPV for Otis Forklifts: n

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

= −$3,123,450 +

= $337,075

b. NPV for Craigmore Forklifts: n

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

= −$4,137,410 +

= $90,606

Premium should purchase the Otis forklift since it has a larger NPV.

Year 3 $2 111 497 $2 865 110

Module 10: Capital budgeting and cash flows

10.2

Perryman Crafts Ltd is evaluating two independent capital projects that will each cost the company $250 000. The two projects will provide the following cash flows: Year 1 2 3 4

Project A $80 750 $93 450 $40 235 $145 655

Project B $32 450 $76 125 $153 250 $96 110

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?

Payback periods for Perryman projects A and B: Project A Year 0 1 2 3 4

Cumulative Cash Flow Cash Flows $(250,000) $(250,000) 80,750 (169,250) 93,450 (75,800) 40,235 (35,565) 145,655 110,090

Project B Year 0 1 2 3 4

Cash Flow $(250,000) 32,450 76,125 153,250 96,110

Cumulative Cash Flows $(250,000) (217,550) (141,425) 11,825 107,935

Payback period for Project A: PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 3 + ($35,565 / $145,655) = 3.24 years Payback period for Project B: PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 2 + ($141,425/ $153,250) = 2.92 years If the payback period is three years, project B will be chosen. If the payback criterion is five years, then both A and B will be chosen.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.3

Terrell Ltd is looking into purchasing a machine for its business that will cost $117 250 and will be depreciated on a straight-line basis over a 5-year period. The sales and expenses (excluding depreciation) for the next 5 years are shown in the following table.

The company’s tax rate is 30 percent.

Sales Expenses

Year 1 $123 450 $137 410

Year 2 $176 875 $126 488

Year 3 $242 455 $141 289

Year 4 $255 440 $143 112

Year 5 $267 125 $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?

Evaluation of Terrell Ltd project:

Sales Expenses Depreciation EBIT Tax (30%) Net Income Beginning Book Value Less: Depreciation Ending Book Value

Year 1 $123,450 137,410 23,450 ($37,410) 11,223 (26,187) 117,250 (23,450) $93,800

Year 2 $176,875 126,488 23,450 $26,937 8,081 18,856 93,800 (23,450) $70,350

Year 3 $242,455 141,289 23,450 $77,716 23,315 54,401 70,350 (23,450) $46,900

Year 4 $255,440 143,112 23,450 $88,878 26,663 62,215 46,900 (23,450) $23,450

Year 5 $267,125 133,556 23,450 $110,119 33,036 77,083 23,450 (23,450) $0

Average net income = (-$26,187+18,856+54,401+62,215+77,083)/5 =$37,274 Average book value = ($93,800+$70,350+$46,900+$23,450+$0)/5 = $46,900 Accounting rate of return (ARR) = $37,274/$46,900 = 79.48% The company should accept the project because the project has a higher ARR than 45%.

Module 10: Capital budgeting and cash flows

10.4

You are considering opening another restaurant in BigBurgers chain. The new restaurant will have annual revenue of $300 000 and operating expenses of $150 000. The annual depreciation and amortisation 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 company tax rate will be 30 per cent.

Calculate the incremental annual free cash flow for the project.

The incremental annual free cash flow is calculated as: FCF = ($300,000-$150,000-$50,000) x (1-0.3) + $50,000-$10,000 = $110,000

10.5

Bes Manufacturing Ltd 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 per cent. Which air-conditioning system should Bes purchase?

The equivalent annual cost for each system is: EAC1 = (0.1)($50,000)[((1.1)10)/((1.1)10-1)] = $8,137.27 EAC2 = (0.1)($72,000)[((1.1)15)/((1.1)15-1)] = $9,466.11 Therefore Be2 should purchase the first one.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Critical thinking questions 10.1

Explain why the cost of capital is referred to as the 'hurdle' rate in capital budgeting.

The cost of capital is the minimum required return on any new investment that allows a company 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.

10.2

Explain why we use discounted cash flows instead of actual market price data.

While market price data would be preferable to estimating future cash flows in determining an asset’s value, it is often not available. Thus, the discounted cash flow approach is used as a proxy for actual market price of an asset’s value.

10.3

Identify the weaknesses of the payback period method.

There are several critical weaknesses in the payback period approach of evaluating capital projects.

• • • •

10.4

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 company 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 projects.

What are the strengths and weaknesses of the accounting rate of return (ARR) approach?

The biggest advantage of ARR is that it is easy to calculate 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 cut-off 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.

Module 10: Capital budgeting and cash flows

10.5

Under what circumstances might the IRR and NPV approaches have conflicting results?

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 of a project—then multiple IRRs can be obtained as solutions. We would be unable to identify the correct IRR for decision making. 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 uses an unrealistically higher rate as proxy.

10.6

Do you agree or disagree with the following statement given the techniques discussed in this module? We can calculate future cash flows precisely and obtain an exact value for the NPV of an investment.

The statement is not true. Given the nature of the real business world, it is almost certain that the cash flows generated by a project will differ from the forecasts used to decide whether to proceed with the project. However, techniques discussed in this module provide an important and useful framework that helps minimise errors and ensures that forecasts are internally consistent.

10.7

What are the differences between forecast 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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.8

RetroMusic Ltd is a producer of MP3 players which currently have either 20 gigabytes or 30 gigabytes of storage. Now the company is considering launching a new production line making mini MP3 players with 5 gigabytes of storage. Analysts forecast that RetroMusic will be able to sell 1 million such mini MP3 players if the investment is taken. In making the investment decision, discuss what the company should consider other than the sales of the mini MP3 players.

The company’s launch of the new mini MP3 players may reduce its current sales of MP3 players of bigger storage. This impact has to be considered. This is consistent with our Rule 2 for incremental cash flow calculations: Include the impact of the project on cash flows from other product lines.

10.9

High-End Fashions Ltd bought a production line of ankle-length skirts last year at a cost of $500 000. This year, however, miniskirts are hot in the market and anklelength skirts are completely out of fashion. High-End has the option to rebuild the production line and use it to produce miniskirts, with a cost of $300 000 and expected revenue of $700 000. How should the company treat the cost of $500 000 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.

10.10 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 value, NPV perpetuity 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.

Module 10: Capital budgeting and cash flows

Questions and problems BASIC 10.1

Net present value: Ridge Ltd is planning to spend $650 000 on a new marketing campaign. It believes that this action will result in additional cash flows of $334 897 over the next three years. If the discount rate is 17.5 percent, what is the NPV on this project?

Initial investment = $650,000 Annual cash flows = $334,897 Length of project = n = 3 years Required rate of return = k = 17.5% Net present value = NPV n

NCFt $334,897 $334,897 $334,897 = −$650,000 + + + t (1.175)1 (1.175) 2 (1.175) 3 t =0 (1 + k ) = −$650,000 + 285,018.7234 + $242,569.1263 + $206,441.8096

NPV = 

= $84,029.66

Module 10: Capital budgeting and cash flows

10.2

Net present value: Redcliff Ltd is looking to add a new machine at a cost of $4 268 709. The company expects this equipment will lead to cash flows of $749 583, $825 118, $905 758, $1 046 608, $1 139 940 and $1 164 240 over the next 6 years. If the appropriate discount rate is 15 per cent, what is the NPV of this investment?

Cost of new machine = $4,268,709 Length of project = n = 6 years Required rate of return = k = 15% n

NCFt t t =0 (1 + k )

NPV = 

$749,583 $825,118 $905,758 $1,046,608 $1,139,940 $1,164,240 + + + + + (1.15)1 (1.15) 2 (1.15) 3 (1.15) 4 (1.15)5 (1.15) 6 = −$4,268,709 + 651,811.3043 + $$623,907.7505 + $595,550.5877 + $598,401.5209 + $566,751.6476 + $503,333.0803

= −$4,268,709 +

= −$728,953.11

© John Wiley & Sons Australia, Ltd 2018

10.8

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.3

Net present value: Sweet Treats, a confectioner, is thinking of purchasing a new jellybean-making machine at a cost of $312 500. The company projects that the cash flows from this investment will be $89 575 for each of the next 7 years. If the appropriate discount rate is 14 percent, what is the NPV for the project?

Initial investment = $312,500 Annual cash flows = $89,575 Length of project = n = 7 years Required rate of return = k = 14% n

NCFt t t =0 (1 + k )

NPV = 

$89,575 $89,575 $89,575 $89,575 $89,575 + + + + (1.14)1 (1.14) 2 (1.14) 3 (1.14) 4 (1.14) 5 $89,575 $89,575 + + (1.14) 6 (1.14) 7 = $71,624.91

= −$312,500 +

© John Wiley & Sons Australia, Ltd 2018

10.9

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.4

Payback: Quantum Ltd is purchasing machinery at a cost of $4 128 148. The company expects, as a result, cash flows of $846 736, $1 133 275, and $2 282 632 over the next 3 years. What is the payback period?

Year 0 1 2 3

CF -$4,128,148 846,736 1,133,275 2,282,632

Cumulative Cash Flow -$4,128,148 -3,281,412 -2,148,137 134,495

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 2.94 years

10.5

Payback: Outback Specialties just purchased inventory-management computer software at a cost of $2 025 335. Cost savings from the investment over the next 6 years will be reflected in the following cash flow stream: $218 128, $293 502, $475 940, $510 510, $533 596, and $505 481. What is the payback period on this investment?

Year 0 1 2 3 4 5 6

CF -$2,025,335 218,128 293,502 475,940 510,510 533,596 505,481

Cumulative Cash Flow -$2,025,335 -1,807,207 -1,513,705 -1,037,765 -527,255 6,341 511,822

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 4.99 years

Module 10: Capital budgeting and cash flows

10.6

Accounting rate of return (ARR): State Ltd is expecting to generate after-tax income of $74 079 over each of the next 3 years. The average book value of its equipment over that period will be $168 324. If the company’s acceptance decision on any project is based on an ARR of 37.5 per cent, should this project be accepted?

Annual after-tax income = $74,079 Average after-tax income = ($74,079 +$74,079+ $74,079) / 3 = $74,079 Average book value of equipment = $168,324 Average after - tax income Average book value $74,079 = = 44.01% $168,324

Accounting rate of return =

Since the project’s ARR is above the acceptance rate of 37.5 percent, the project should be accepted.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.7

Internal rate of return: Divine chocolates, a chocolatier, is looking to purchase a new chocolate-making machine at a cost of $383 543. The company projects that the cash flows from this investment will be $122 920 for the next seven year. What is the IRR of this project?

Initial investment = $383,543 Annual cash flows = $122,920 Length of project = n = 7 years To determine the IRR, a trial-and-error approach can be used. Set NPV = 0.

Try IRR = 20.42% n

FCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 −  (1.2042) 7  0  −$383,543 + $122,920     0.2042     −$54,479.06  0

Try a higher rate, IRR = 25.52% n

FCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.2552) 7  0  −$383,543 + $122,920     0.2552    0 The IRR of the project is 25.52 percent. Using a financial calculator, we find that the IRR is 25.52 percent.

Module 10: Capital budgeting and cash flows

10.8

Internal rate of return: Holliday Ltd, a resort company, is refurbishing one of its hotels at a cost of $6 465 406. The company expects that this improvement will lead to additional cash flows of $2 092 819 for the next 6 years. What is the IRR of this project? If the appropriate cost of capital is 12 per cent, should it go ahead with this project?

Initial investment = $6,465,406 Annual cash flows = $2,092,819 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 = 18.43% n

FCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.1843) 6  0  −$6,465,406 + $2,092,819     0.1843     $774,469.36  0

Try IRR = 23.01% n

FCFt t t =0 (1 + IRR)

NPV = 0 = 

1   1 − (1.2304) 6  0  −$6,465,406 + $2,092,819     0.2304    0 The IRR of the project is 23.04. Using a financial calculator, we find that the IRR is 23.04 percent. Since IRR > k, accept the project.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.9

The FCF calculation: How do we calculate incremental after-tax free cash flow from forecast earnings of a project? What are the common adjustment items?

We need to adjust for the depreciation and amortisation tax shield, capital expenditures, and changes in working capital (including receivables and payables).

10.10 The FCF calculation: How do we adjust for depreciation when we calculate incremental after-tax free cash flow from EBITDA? What is the intuition for the adjustment?

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 flow 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 cash flows.

10.11 Calculating terminal-year FCF: Perfect Health Ltd, a pharmaceutical company bought a machine that produces pain-reliever medicine at a cost of $2 million 5 years ago. The machine has been depreciated over the past 5 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 company tax rate is 35 per cent. 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 include the sale price of the machine, as well as the tax on the capital gain: 1,000,000 – 0.35(1,000,000 – 800,000) = $930,000 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+ 0.35(800,000 – 600,000) = $670,000

Module 10: Capital budgeting and cash flows

MODERATE 10.12 Net present value: Champion Ltd is investigating two computer systems. The Alpha 8300 costs $3 122 300 and will generate annual cost savings of $1 345 500 over the next 5 years. The Beta 2100 system costs $3 750 000 and will produce cost savings of $1 125 000 in the first 3 years and then $2 million for the next 2 years. If the company’s discount rate for similar projects is 14 per cent, what is the NPV for the two systems? Which one should be chosen based on the NPV? 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−  FCFt (1.14)5  NPV =  = − $ 3 , 122 , 300 + $ 1 , 345 , 500    t t = 0 (1 + k )  0.14    = −$3,122,300 + $4,619,210 n

= $1,496,910

Cost of Beta 2100 = $3,750,000 Length of project = n = 5 years Required rate of return = k = 14% 1   1 −  (1.14)3  $2,000,000 $2,000,000 n FCFt NPV =  = − $ 3 , 750 , 000 + $ 1 , 125 , 500  +  + t (1.14) 4 (1.14)5 t = 0 (1 + k )  0.14    = −$3,750,000 + $2,611,836 + $1,184,161 + 1,038,737 = $1,084,734

Based on the NPV, the Alpha 8300 system should be chosen.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.13 Net present value: Stonefield Condiments is a spice-making company. Recently, it developed a new process for producing spices. This calls for acquiring machinery that would cost $2 183 602. The machine will have a life of 5 years and will produce cash flows as shown in the table. What is the NPV if the company uses a discount rate of 16.35 percent?

Year 1 2 3 4 5

Cash Flow $420 452 -$213 205 $646 352 $772 329 $661 617

Cost of equipment = $2,183,602 Length of project = n = 5 years Required rate of return = k = 16.35% n

FCFt t t =0 (1 + k )

NPV = 

= −$12,183,602 + = −$837,627.32

$420,452 − $213,205 $646,352 $772,329 $661,617 − + + + (1.1635)1 (1.1635) 2 (1.1635) 3 (1.1635) 4 (1.1635) 5

Module 10: Capital budgeting and cash flows

10.14 Net present value: Emporium Ltd is evaluating two heating systems. Costs and projected energy savings are given in the following table. The company uses 14.21 per cent to discount such project cash flows. Which system should be chosen?

Year 0 1 2 3 4

System 100 -$1 881 250 $341 277 $488 411 $678 072 $661 238

System 200 -$1 657 793 $737 025 $752 640 $651 058 $332 586

Required rate of return = 14.21% System 100: Cost of product line expansion = $1,881,250 n

FCFt $341,277 $488,411 $678,072 $661,238 = −$1,881,250 + − + + t (1.1421)1 (1.1421) 2 (1.1421)3 (1.1421) 4 t =0 (1 + k ) = −$364,205.30

NPV = 

System 200: Cost of product line expansion = $1,657,793 n

FCFt $737,025 $752,640 $651,058 $332,586 = −$1,657,793 + − + + t (1.1421)1 (1.1421) 2 (1.1421)3 (1.1421) 4 t =0 (1 + k ) = $197,034.99

NPV = 

Since System 200 has a positive NPV, select that system. Reject System 100 as it has negative NPV.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.15 Payback: Creative Circle Ltd has invested $5 751 125 in equipment. The company uses payback period criteria of not accepting any project that takes more than 4 years to recover costs. The company anticipates cash flows of $751 354, $666 148, $1 101 278, $1 113 292, $2 216 006, and $2 599 238 over the next 6 years. Does this investment meet the company’s payback criteria?

Year 0 1 2 3 4 5 6

CF -$5,751,125 751,354 666,148 1,101,278 1,113,292 2,216,006 2,599,238

Cumulative Cash Flow -$5,751,125 -4,999,771 -4,333,623 -3,232,345 -2,119,053 96,953 2,696,191

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 4.96 years Since the project payback period exceeds the company’s target of four years, it should not be accepted.

Module 10: Capital budgeting and cash flows

10.16 Internal rate of return: Calculate 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. b.

An initial investment of $1 million followed by a single cash flow of $1 650 000 in year 4. c.

An initial investment of $2 million followed by cash flows of $1 650 000 and $1 250 000 in years 2 and 4, respectively a.

Try IRR = 7%

FCFt t t = 0 (1 + IRR ) $37,450 0  −$25,000 + (1.07)6  −$25,000 + $24,955  −$45 n

NPV = 0 = 

Try IRR = 6.97%

FCFt t t = 0 (1 + IRR ) $37,450 0  −$25,000 + (1.0697 )6  −$25,000 + $24,997  −$3 n

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. b.

Try IRR = 12%

FCFt t t = 0 (1 + IRR ) $1,650,000 0  −$1,000,000 + (1.12) 4  −$1,000,000 + $1,048,605  $48,605 n

NPV = 0 = 

Try IRR = 13%

FCFt t t = 0 (1 + IRR ) $1,650,000 0  −$1,000,000 + (1.13) 4  −$1,000,000 + $1,011,976  $11,976 n

NPV = 0 = 

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Try IRR = 13.3%

FCFt t t = 0 (1 + IRR ) $1,650,000 0  −$1,000,000 + (1.133) 4  −$1,000,000 + $1,1,001,300  $1,300 n

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. c.

Try IRR = 15%

FCFt 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 n

NPV = 0 = 

Try IRR = 14%

FCFt 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 n

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.

Module 10: Capital budgeting and cash flows

10.17 Internal rate of return: Calculate the IRR for the following project cash flows. a.

An initial outlay of $3 125 000 followed by annual cash flows of $565 325 for the next 8 years. b.

An initial investment of $33 750 followed by annual cash flows of $9430 for the next 5 years. c.

An initial outlay of $10 000 followed by annual cash flows of $2500 for the next 7 years. a.

Initial investment = $3,125,000 Annual cash flows = $565,325 Length of investment = n = 8 years Try IRR = 8% 1   1−  FCFt (1.08)8  NPV =  = − $ 3 , 125 , 000 + $ 565 , 325    t t = 0 (1 + k )  0.08    = −$3,125,000 + $3,249,006 n

= $124,006

Try a higher rate, IRR = 9% 1   1−  FCFt (1.09)8  NPV =  = − $ 3 , 125 , 000 + $ 565 , 325    t t = 0 (1 + k )  0.09    = −$3,125,000 + $3,129,248 n

= $4,248

The IRR of the project is approximately 9 percent. Using a financial calculator, we find that the IRR is 9.034 percent.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

b.

Initial investment = $33,750 Annual cash flows = $9,430 Length of investment = n = 5 years Try IRR = 12%

1   1 −  (1.12)5  n FCFt NPV =  = − $ 33 , 750 + $ 9 , 430    t t = 0 (1 + k )  0.12    = −$33,750 + $33,993 = $243 Try IRR = 12.3%

1   1 − 5   n FCFt (1.123) NPV =  = −$33,750 + $9,430    t t = 0 (1 + k )  0.123    = −$33,750 + $33742 = −$8  0 The IRR of the project is approximately 12.3 percent. Using a financial calculator, we find that the IRR is 12.29 percent. c.

Initial investment = $10,000 Annual cash flows = $2,500 Length of investment = n = 7 years Try IRR = 16%

1   1−  FCFt (1.16)7  NPV =  = − $ 10 , 000 + $ 2 , 500    t t = 0 (1 + k )  0.16    = −$10,000 + $10,096 n

= $96

Module 10: Capital budgeting and cash flows

Try IRR = 16.3%

1   1− 7   FCFt (1.163) NPV =  = −$10,000 + $2,500    t t = 0 (1 + k )  0.163    = −$10,000 + $10,008 n

= $8  0 The IRR of the project is approximately 16.3 percent. Using a financial calculator, we find that the IRR is 16.327 percent.

10.18 Investment cash flows: Wellbeing Potions Ltd. 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 $5000 at the beginning of the project. Wellbeing Potions will recover these changes in working capital at the end of the project 10 years later.

Assume the appropriate discount rate to be 12 per cent. What are the relevant present values of the cash flows?

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 + 12%)10 = $19,318.39

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.19 Cash flows from operations: Given the soaring price of petrol, Ford is considering introducing a new production line of petrol-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 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 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 company tax rate is 30 per cent. What is the incremental annual cash flow from operations?

Step One: Revenue: $22,000 x 30,000 machines =$660,000,000 Step Two: Op Exp: $10,000 x 30,000 machines = $300,000,000 Plus lost net revenue from regular sedans = ($20,000 – $12,000) x 10,000 = $80,000,000 Total Op Exp = $380,000,000 Step Three: D&A: $50,000 Step Four: Plug information into the template below. ∆NR = = x = + = =

660,000,000 ∆OpEx 380,000,000 ∆EBITDA 280,000,000 ∆D&A -50,000 ∆EBIT 279,950,000 (1-t) 0.70 ∆NOPAT 195,965,000 ∆D&A 50,000 ∆CFO 196,015,000 ∆CapEx 0 ∆AWC 0 ∆FCF 196,015,000

Module 10: Capital budgeting and cash flows

Alternatively, the incremental annual cash flow from operations is: ((22,000-10,000)*30,000-(20,000-12,000)*10,000)*(1-0.3) + 50,000*0.3 = 196,015,000 Note that the fixed costs are not included in the incremental cash flows calculations, since they exist regardless of the hybrid sedan investment.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.20 FCF and NPV for a project: Highland Ltd is considering buying a new farm that it plans to operate for 10 years. The farm will require an initial investment of $12 million. The 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 at a price of $5 million, $2 million above book value.

The farm is expected to produce revenue of $2 million each year, and annual cash flow from operation equals $1.8 million. The company tax rate is 30 per cent, and the appropriate discount rate is 10 per cent. Calculate the NPV of this investment.

Cash flow of investment in year 0 is: $(12,000,000) PV of annual investment year 1 to 10 is found using the present value factor for an annuity: Payment * (1 – {1 / (1 + i)n}) / i) $(1,800,000*0.7+1,200,000*0.3)( 1 – {1 / (1.1)10}) / 0.1) = $9,954,199 PV of sales and tax on capital gain in year 10 is: (5,000,000-[2,000,000*0.3]) / (1.1)10 = 1,696,390 Therefore, PV of investment cash flows = $(349,411) The company should not buy the farm.

Module 10: Capital budgeting and cash flows

CHALLENGING 10.21 Dravid Ltd is currently evaluating three projects that are independent. The cost of funds can be either 13.6 per cent or 14.8 per cent 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 per cent? What if the discount rate was 13.6 per cent?

Year 1 2 3 4

Project 1 $ 0 125 000 150 000 375 000

Project 2 $ 0 0 500 000 500 000

Project 3 $245 125 212 336 112 500 74 000

Cost of projects = $500,000 Length of project = n = 4 years Required rate of return = k = 14.8% Project 1: FCFt $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 n

NPV = 

Project 2: FCFt $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 n

NPV = 

Project 3: FCFt $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 n

NPV = 

At a discount rate of 14.8 per cent, only project 2 will be accepted. At a discount rate of 13.6 per cent, 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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Year 0 1 2 3 4 NPV

Project 1 $(500,000) − 125,000 150,000 375,000

PVCF $(500,000) − 96,862 102,319 225,175 (75,645)

Project 2 $(500,000) − − 500,000 500,000

PVCF $(500,000) − − 341,063 300,232 141,295

Project 3 $(500,000) 245,125 212,336 112,500 74,000

PVCF $(500,000) 215,779 164,538 76,739 44,434 1,491

Module 10: Capital budgeting and cash flows

10.22 Intrepid Ltd wants to invest in two or three independent projects. The costs and the cash flows are given in the following table. The appropriate cost of capital is 14.5 per cent. Calculate the IRRs and identify the projects that will be accepted.

Year 0 1 2 3 4

Project 1 –$275 000 63 000 85 000 85 000 100 000

Project 2 –$312 500 153 250 167 500 112 000

Project 3 –$500 000 212 000 212 000 212 000 212 000

Project 1: Cost of Project 1 = $275,000 Length of project = n = 4 years Required rate of return = k = 14.5% FCFt t t = 0 (1 + k ) n

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

= −$275,000 +

= −$40,338

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% FCFt t t = 0 (1 + IRR ) $63,000 $85,000 $85,000 $100,000 0 = −$275,000 + + + + (1.075)1 (1.075) 2 (1.075)3 (1.075) 4 = −$275,000 + 58,550 + $73,417 + $68,231 + $74,602 n

NPV = 0 = 

= −$200  0

The IRR of the project is approximately 7.6 percent. Using a financial calculator, we find that the IRR is 7.57 percent.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Project 2: Cost of Project 2 = $312,500 Length of project = n = 3 years Required rate of return = k = 14.5% FCFt $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 n

NPV = 

At the required rate of return of 14.5 percent, Project 1 has a NPV of $23,717. To find the IRR, try higher rates.

Try IRR =19% FCFt 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 n

NPV = 0 = 

= $1,027

Try IRR=19.2% FCFt 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 n

NPV = 0 = 

= $80  0

The IRR of the project is approximately 19.2 percent. Using a financial calculator, we find that the IRR is 19.22 percent.

Module 10: Capital budgeting and cash flows

Project 3: Cost of Project 3 = $500,000 Length of project = n = 4 years Required rate of return = k = 14.5% 1   1 −  (1.145) 4  n FCFt NPV =  = −$500,000 + $212,000    t t = 0 (1 + k )  0.145    = −$500,000 + $611,429 = $111,429

At the required rate of return of 14.5 percent, Project 1 has a NPV of $111,429. To find the IRR, try higher rates.

Try IRR =25% FCFt t t = 0 (1 + IRR ) n

NPV = 0 = 

1   1 − (1.25) 4  0 = −$500,000 + $212,000     0.25    = −$500,000 + $500,659  $659

Try IRR=25.1% FCFt t t = 0 (1 + IRR ) n

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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Only Projects 2 and 3 will be accepted as the IRRs exceed the required rate of return of 14.5 percent.

Module 10: Capital budgeting and cash flows

10.23 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 per cent. Calculate the IRRs based on the given cash flows, and state which project(s) will be accepted.

Year 0 1 2 3 4

Project 1 –$475 000 300 000 110 000 125 000 140 000

Project 2 –$500 000 117 500 181 300 244 112 278 955

Project 1: Cost of project = $475,000 Length of project = n = 4 years Required rate of return = k = 17% FCFt t t = 0 (1 + k ) n

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

= −$475,000 +

= $14,524

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% FCFt t t = 0 (1 + k ) n

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

= −$475,000 +

 −$1,230

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Try IRR = 18.8% FCFt t t = 0 (1 + k ) n

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

= −$475,000 +

= $302  0

The IRR of the project is approximately 18.8 percent. Using a financial calculator, we find that the IRR is 18.839 percent.

Project 2: Cost of project = $500,000 Length of project = n = 4 years Required rate of return = k = 17% FCFt t t = 0 (1 + k ) n

NPV = 

$117,500 $181,300 $244,312 $278,955 + + + (1.17)1 (1.17) 2 (1.17)3 (1.17) 4 = −$475,000 + $100,427 + $132,442 + $152,416 + $148,864

= −$500,000 +

= $34,150

At the required rate of return of 17 percent, Project 1 has an NPV of $34,150. To find the IRR, try higher rates.

Try IRR = 20% FCFt t t = 0 (1 + IRR ) $117,500 $181,300 $244,312 $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 n

NPV = 0 = 

= −$385  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.

Module 10: Capital budgeting and cash flows

10.24 Calculate the IRR for each of the following cash flow streams: Year 0 1 2 3 4 5

Project 1 –$10 000 4 750 3 300 3 600 2 100

Project 2 –$10 000 1 650 3 890 5 100 2 750 800

Project 3 –$10 000 800 1 200 2 875 3 400 6 600

Project 1: Cost of project = $10,000 Length of project = n = 4 years FCFt 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 n

NPV = 0 = 

= $13  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 FCFt 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 + $1,545 + $421 n

NPV = 0 = 

= −$4  0

The IRR of the project is approximately 13.7 percent. Using a financial calculator, we find that the IRR is 13.685 percent.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Project 3: Cost of project = $10,000 Length of project = n = 5 years FCFt 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 n

NPV = 0 = 

= −$13  0

The IRR of the project is approximately 10.9 percent. Using a financial calculator, we find that the IRR is 10.862 percent.

Module 10: Capital budgeting and cash flows

10.25 Primus Ltd is planning to convert an existing warehouse into a new plant that will increase its production capacity by 45 per cent. 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. a.

What is the payback period? b.

What is the NPV for this project? c.

What is the IRR? a.

Year 0 1 2 3 4 5 6 7 8

Project 1 $(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

Cumulative CF $(7,125,000) (5,250,000) (3,375,000) (1,500,000) 375,000 2,250,000 4,125,000 6,000,000 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 b.

Cost of this project = $7,125,000 Required rate of return = 12% Length of project = n = 8 years

FCFt t t = 0 (1 + k ) n

NPV = 

1   1 − (1.12)8  = −$7,1250,000 + $1,875,000     0.12    = −$7,125,000 + $9,314,325 = $2,189,325

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

c.

To calculate the IRR, try rates higher than 12 percent.

Try IRR = 20%

FCFt t t = 0 (1 + k ) n

NPV = 0 = 

1   1 − (1.20)8  0 = −$7,1250,000 + $1,875,000     0.20    = −$7,125,000 + $7,194,675 = $69,675 Try IRR = 20.3%

FCFt t t = 0 (1 + k ) n

NPV = 0 = 

1   1 − (1.203)8  0 = −$7,1250,000 + $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.

Module 10: Capital budgeting and cash flows

10.26 Quasar Tech Ltd. 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 3 years and then increase to $2.4 million for 3 more years. The project is expected to last 6 years and cost the company annually $898 620 (excluding depreciation). The machinery will be depreciated to zero by year 6 using the straight-line method. The company’s tax rate is 30 per cent, and its cost of capital is 16 per cent. a.

What is the payback period? b.

What is the average accounting return (ARR)? c.

Calculate the project NPV. d.

What is the IRR for the project? a.

Year 0 1 2 3 4 5 6

Net Income $(104,034) $(104,034) $(104,034) 350,966 350,966 350,966

Project 1 Depreciation Cash Flows $(6,000,000) $1,000,000 895,966 $1,000,000 895,966 $1,000,000 895,966 $1,000,000 1,350,966 $1,000,000 1,350,966 $1,000,000 1,350,966

Cumulative CF $(6,000,000) (5,104,034) (4,208,068) (3,312,102) (1,961,136) (610,170) 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.

Sales Expenses Depreciation EBIT Tax (30%) Net income Beginning BV Less: Depreciation Ending BV

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

$ 1,750,000 898,620 1,000,000 $(1,48,620) 44,586 $ (104,034) 6,000,000 1,000,000 $ 5,000,000

$ 1,750,000 898,620 1,000,000 $(1,48,620) 44,586 $ (104,034) 5,000,000 1,000,000 $ 4,000,000

$ 1,750,000 898,620 1,000,000 $(1,48,620) 44,586 $ (104,034) 4,000,000 1,000,000 $ 3,000,000

$ 2,400,000 898,620 1,000,000 $ 501,380 (150,414) $ 350,966 3,000,000 1,000,000 $ 2,000,000

$ 2,400,000 898,620 1,000,000 $ 501,380 (150,414) $ 350,966 2,000,000 1,000,000 $ 1,000,000

$ 2,400,000 898,620 1,000,000 $ 501,380 (150,414) $ 350,966 1,000,000 1,000,000 $ 0

Average after-tax income = 123,466 Average book value of equipment = $2,500,000 Average after - tax income Accounting rate of return = Average book value $123,466 = = 4.9% $2,500,000

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

c.

Cost of this project = $6,000,000 Required rate of return = 16% Length of project = n = 6 years

FCFt t t = 0 (1 + k ) n

NPV = 

1  1    1 − (1.16)3  1 − (1.16)3  1 = −$6.000,000 + $895,966    + $1,350,966    3  0.16   0.16  (1.16)     = −$6,000,000 + $2,012,241 + $1,943,833 = −$2,043,927 d.

To calculate the IRR, try rates lower than 16 percent.

Try IRR = 3%

FCFt t t = 0 (1 + IRR ) n

NPV = 0 = 

1  1    1 − 1 − 3  (1.03)   (1.03)3  1 0 = −$6.000,000 + $895,966   + $ 1 , 350 , 966     3  0.03   0.03  (1.03)     = −$6,000,000 + $2,534,340 + $3,497,084 = $31,424

Try IRR = 3.1%

FCFt t t = 0 (1 + IRR ) n

NPV = 0 − 

1 1     1 − 1 − 3  (1.031)   (1.031)3  1 0 = −$6.000,000 + $895,966    + $1,350,966    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.

Module 10: Capital budgeting and cash flows

10.27 Tyler Ltd. is looking to move to a new technology for its production. The cost of equipment will be $4 million. The company normally uses a discount rate of 12 per cent. Cash flows that the company expects to generate are as follows.

Years 0 1-2 3–5 6–9 a. b.

CF –$4 000 000 0 845 000 1 450 000

Calculate the payback and discounted payback period for the project.

What is the NPV for the project? Should the company go ahead with the project?

What is the IRR, and what would be the decision under the IRR?

c. a.

Year 0 1 2 3 4 5 6 7 8 9

Cash Flows $(4,000,000) --845,000 845,000 845,000 1,450,000 1,450,000 1,450,000 1,450,000

PVCF $(4,000,000) --601,454 537,013 479,476 734,615 655,906 585,631 522,885

Cumulative CF $(4,000,000) $(4,000,000) $(4,000,000) (3,155,000) (2,310,000) (1,465,000) (15,000) 1,435,000 2,885,000 4,335,000

Cumulative PVCF $(4,000,000) $(4,000,000) $(4,000,000) (3,398,546) (2,861,533) (2,382,057) (1,647,442) (991,536) (405,905) 116,979.48

PB = Years before cost recovery + (Remaining cost to recover/ Cash flow during the year) = 6 + ($15,000 / $1,450,000) = 6.01 years Discount PB

= Years before Recovery + (Remaining Cost / Next Year’s CF) = 8 + ($405,905 / $522,885) = 8.8 years

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

b.

Cost of this project = $4,000,000 Required rate of return = 12% Length of project = n = 9 years 1   1 −  (1.12)3  n FCFt 1 NPV =  = − $ 4 .

000 , 000 + 0 + 0 + $ 845 , 000    t 2 t = 0 (1 + k )  0.12  (1.12)   1   1 − (1.12) 4  1 + $1,450,000    5  0.12  (1.12)   = −$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 calculate the IRR, one should try rates higher than 12 percent.

Try IRR = 12.5% 1   1− 3   FCFt 1 (1.125) NPV =  = −$4.000,000 + 0 + 0 + $845,000    t 2 t = 0 (1 + k )  0.125  (1.125)   1   1 −  (1.125) 4  1 + $1,450,000    5  0.125  (1.125)   = −$4,000,000 + 0 + 0 + $1,589,915 + $2,418,479 n

= $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.

Module 10: Capital budgeting and cash flows

10.28 Given the following cash flows for a capital project, calculate the NPV and IRR. The required rate of return is 8 per cent.

Years Cash flows

a. b. c. d.

0 –50 000

NPV $1905 $1905 $3379 $3379

1 15 000

2 15 000

3 20 000

4 10 000

5 5 000

IRR 10.9% 26.0% 10.9% 26.0%

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.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.29 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 per cent. The net present value is closest to: a. $42.22 b. $58.33 c. $68.52 d. $98.95

B is correct.

3

CFt 40 80 120 = −100 + + + = $58.33 t 2 1.20 1.20 1.203 t = 0 (1 + r )

NPV = 

10.30 An investment of $150 000 is expected to generate an after-tax cash flow of $100 000 in 1 year and another $120 000 in 2 years. The cost of capital is 10 per cent. What is the internal rate of return? a.

28.19 per cent b.

28.39 per cent c.

28.59 per cent d.

28.79 per cent

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.

Year

Cash Flow

0 1 2 Total

–150,000 100,000 120,000

Present Value 28.19% 28.39% –150,000 –150,000 78,009 77,888 73,025 72,798 1,034 686

28.59% –150,000 77,767 72,572 338

28.79% –150,000 77,646 72,346 –8

A more precise IRR of 28.7854 percent has a total PV closer to zero.

Module 10: Capital budgeting and cash flows

10.31 An investment has an outlay of 100 and after-tax cash flows of 40 annually for 4 years. A project enhancement increases the outlay by 15 and the annual after-tax cash flows by 5. As a result, the vertical intercept of the NPV profile of the enhanced project shifts: a. up and the horizontal intercept shifts left. b. up and the horizontal intercept shifts right. c. down and the horizontal intercept shifts left. d. down and the horizontal intercept shifts right.

A is correct. The vertical intercept changes from 60 to 65, and the horizontal intercept changes from 21.86 percent to 20.68 percent.

10.32 You are the CFO of SlimBody Ltd a retailer of the exercise machine Bodyslim and related accessories. Your company is considering opening up a new store in Perth.

The store will have a life of 20 years. It will generate annual sales of 5000 exercise machines, and the price of each machine is $2500. The annual sales of accessories will be $600 000, and the operating expenses of running the store, including labour and rent, will amount to 50 per cent 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 company will need to invest $2 million in additional working capital immediately, and recover it at the end of the investment. Your company’s tax rate is 30 per cent. The opportunity cost of opening up the store is 10 per cent. What are the incremental cash flows from this project at the beginning of the project as well as in years 1-19 and 20? Should you approve it?

Step One: Initial outlay = $30,000,000 + $2,000,000 (WC requirement) = $32,000,000 Step Two: ΔNR for years 1- 20: $2,500 x 5,000 machines = $12,500,000 plus $600,000 = $13,100,000 Step Three: ΔOpExp for years 1- 20: $1,250 x 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 template below.

Step Six: Yr 20 recapture of WC requirements that were funded in year 0.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Yrs 1-19 ΔNR Δ

O

p

E

Δ

E

B

I

Δ

D

&

Δ

(

E

1

B

-

t

1

3

x

T

D

A

6

-

1

6

A

I

,

-

T

5

,

,

1

0

2

8

5

5

3

0

5

0

0

5

,

0

,

0

0

,

Yr 20

0

0

0

0

0

0

0

0

0

0

0

0

0

)

0

0

Δ

N

O

Δ

D

&

Δ

C

F

Δ

C

a

p

Δ

A

W

Δ

F

C

P

A

3

,

-

6

-

1

6

5

,

,

1

0

2

8

5

5

3

0

5

0

0

5

,

0

,

0

0

,

0

0

0

0

0

0

0

0

0

0

0

0

0

7

0

0

0

.

7

3

,

7

4

5

,

0

0

0

3

,

7

4

5

,

0

0

0

A

1

,

5

0

0

,

0

0

0

1

,

5

0

0

,

0

0

0

O

5

,

2

4

5

,

0

0

0

5

,

2

4

5

,

0

0

0

E

T

0

.

1

x

-

3

C

F

-

-

3

0

,

0

0

0

,

0

0

0

0

2

,

0

0

0

,

0

0

0

0

2

,

0

0

0

,

0

0

0

2

,

0

0

0

,

0

0

0

0

7

,

2

4

5

,

0

0

0

5

,

2

4

5

,

0

0

0

Therefore the NPV of the project is: NPV = -32,000,000+5,245,000*(((1.1)20-1)/ ((1.1)20*0.1))+2,000,000/(1.1)20 =12,950,929 You should approve the project since it has a positive NPV.

Alternative solution: Incremental cash flows in year 0 is: ΔFCF0 = -30,000,000-2,000,000= -32,000,000 Annual incremental cash flows through the life of the investment are: ΔFCFt = (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: NPV = -32,000,000+5,245,000*(((1.1)20-1)/ ((1.1)20*0.1))+2,000,000/(1.1)20 =12,950,929 You should approve the project since it has a positive NPV.

Module 10: Capital budgeting and cash flows

10.33 Snowy Hills Lumber Ltd is considering purchasing a new wood saw that costs $50 000. The saw will generate revenues of $100 000 per year for 5 years. The cost of materials and labour 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 $1000 at the end of its 5-year life and will be depreciated on a straight-line basis over 5 years to zero. Snowy Hills Lumber’s tax rate is 30 per cent, and its opportunity cost of capital is 10 per cent. Should the company purchase the saw?

Explain why or why not.

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 template below.

Step Six: Yr 5: Capital recovery = $1,000 – (.30 x 1,000 gain on sale) = $700.

Yr 0

Yrs 1-4 100,000 -70,000 30,000 -10,000 20,000 0.70 14000 10,000 24000

∆NR ∆OpEx ∆EBITDA ∆D&A ∆EBIT (1-t) ∆NOPAT ∆D&A ∆CFO ∆CapEx -50,000 ∆AWC 0 0 ∆FCF -50000 24000

Yr 5 100,000 -70,000 30,000 -10,000 20,000 0.70 14000 10,000 24000 700 0 24700

Therefore, NPV of investment is: -50,000+24,000 /(1.1)1+24,000 /(1.1)2+24,000 /(1.1)3+24,000 /(1.1)4 +(24,000 +700)/(1.1)5= $41,414 Therefore the company should buy the machine.

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

Alternatively: The annual operating cash flows from year 1 to 5 are: (100,000-60,000-10,000)*(1-0.3)+0.3*10,000=24,000 The after-tax terminal value in year 5 is: 1,000 -(0.3)(1,000-0) = 700 Therefore, NPV of investment is: -50,000+24,000 /(1.1)1+ 24,000 /(1.1)2+ 24,000 /(1.1)3+24,000 /(1.1)4 +(24,000 + 700 )/(1.1)5=$41,414 Therefore the company should buy the machine.

Module 10: Capital budgeting and cash flows

10.34 A beauty product company is developing a new fragrance named Beautiful. There is a probability of 0.5 that consumers will love Beautiful 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 weird 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 costs are $1.2 million. Assume that the tax rate is 30 per cent. What are the expected annual incremental cash flows from the new fragrance?

Step One: Expected sales units: (.5)1,000,000 + (.4)200,000 + (.1)50,000 = 585,000 units Step Two: ΔNR: 585,000 units x $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 template below.

= = x = + = =

∆NR ∆OpEx ∆EBITDA ∆D&A ∆EBIT (1-t) ∆NOPAT ∆D&A ∆CFO ∆CapEx ∆AWC ∆FCF

22,230,000 -5,680,000 16,550,000 -1,200,000 15,350,000 0.70 10,745,000 1,200,000 11,945,000 0 0 11,945,000

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)*(10.3)+1,200,000*0.3 = 11,945,000

Solutions manual to accompany: Finance essentials 1e by Kidwell et al.

10.35 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 5-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 5 years. An inventory investment of $73 000 is required during the life of the investment. The company tax rate is 30 per cent, and its cost of capital is 10 per cent. What is the project NPV? a. $100 753 b. $120 359 c. $136 844 d. $153 666 C 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 – 0.30) + 92,000 CF = $155,000 The terminal year after-tax non-operating cash flow in Year 5 is: TNOCF = Sal5 + NWCInv – T(Sal5 – B5) = 85,000 + 73,000 – 0.30(85,000 – 0) TNOCF = $132,500 The NPV is: 5

155,000 132,500 + = $136,844 t 1.10 5 t =1 1.10

NPV = −533,000 + 

Module 10: Capital budgeting and cash flows

10.36 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 straightline over an 8-year life. The tax rate is 30 per cent and the required rate of return is 10 per cent. No changes in cash operating revenues, cash operating expenses, or salvage value are expected. What is the effect on the project NPV? a. $100 000 decrease b. $79 994 decrease c. $59 988 decrease d. No change B is correct. The additional annual depreciation is $100,000/8 = $12,500. The depreciation tax savings is 0.30 ($12,500) = $3,750. The change in project NPV is: 8

3,750 = −$79,994 t t −1 (1.10)

− 100,000 + 

Module 11: Cost of capital and working capital management

Module 11: Cost of capital and working capital management Self-study problems 11.1 Comics‘R’Us Ltd has borrowed $100 million and is required to pay investors $8 million in interest this year. If the corporate tax rate is 30 per cent, then what is the after-tax cost of debt (in dollars as well as in annual interest) to Comics‘R’Us? Since Comics enjoys a tax deduction for its interest charges, the after-tax interest expense for Comics is $8 million × (1 – 0.30) = $5.6 million, which translates into an annual interest expense of $5.6/$100 = 0.056, or 5.6 per cent.

11.2 Explain why the after-tax cost of equity (preference or ordinary shares) does not have to be adjusted by the corporate tax rate for the company.

The Australian tax code allows a deduction for interest expense incurred on borrowing.

Preference and ordinary 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.

11.3 Dempsey’s Ltd has debt claims of $400 (market value) and equity claims of $600 (market value). If the cost of debt financing (after tax) is 11 per cent and the cost of equity is 17 per cent, then what is Dempsey’s weighted average cost of capital?

Dempsey’s Ltd total company value = $400 + $600 = $1,000. Therefore: Debt = 40 per cent of financing Equity = 60 per cent of financing WACC = xDebtkDebt(1-t) + xpskps + xcskcs WACC = (0.4 x 0.11) + (0.6 x 0.17) = 0.146, or 14.6%

11.4

You are provided the following working capital information for the Blue Ridge Ltd: 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 sales

$19 630

If all sales are on credit, what are the company’s operating and cash conversion cycles?

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 sales = $19,630 DSO =

DSI =

Accounts receivable $2,800 = = 41.6 days Credit sales 365 $24,589 365

Inventory $2,890 = = 53.7 days COS 365 $19, 630 365

DPO =

Accounts Payable $2,670 = = 49.6 days COS 365 $19,630 365

Operating cycle = DSO + DSI = 41.6 + 53.7 = 95.3 days

Cash conversion cycle = DSO + DSI - DPO = 41.6 + 53.7 − 49.6 = 45.7 days

11.5

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 raw materials are received at Merrifield Cosmetics until the finished products they are used to produce are sold?

The following information describes Merrifield’s inventory management: Operating cycle = 76 days Accounts receivables = $230,000 Net sales = $1,920,000, assume all sales are credit sales.

DSO =

Accounts receivable s $230,000 = = 43.7 days Credit sales 365 $1,920,000 365

Operating cycle = DSO + DSI 76 = 43.7 + DSI DSI = 32.3 days Merrifield Cosmetics takes 32.3 days to move the inventory through as finished products.

Critical thinking questions 11.1

Explain why the required rate of return on a company’s assets must be equal to the weighted average cost of capital associated with its liabilities and equity.

In order to conceptualise the answer to this question, it helps to think of the case in which the company 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 company. Assume that this source has no other 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 company since that is the ultimate source of the returns. Therefore the weighted return of that portfolio, which is the weighted average cost of capital for the company (if for the time being we abstract away tax effects), is the return on the assets of the company.

11.2

Which is easier to calculate directly, the expected rate of return on the assets of a company or the expected rate of return on the company’s debt and equity? Assume that you are an outsider to the company.

As an outsider to the company, you will not be privy to the complete information about the projected cash flows of each of the company’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 company, 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 company is much easier than finding the expected return on the assets of the company, although that return can then be calculated from the expected return on the financing claims of the company.

11.3

Your friend has recently told you that the Commonwealth Government effectively subsidises the cost of debt (compared to equity use) for companies. Do you agree with that statement? Explain.

Your friend is correct. Because interest expense on debt is tax deductible, whereas dividend payments on equity are not, the company effectively gets a rebate on interest paid through a lowered tax bill. Two companies with identical EBIT amounts with different interest expenses will have different cash flow available to its collective set of investors. The company with greater interest expense (assuming it is less than the EBIT amount) will have greater cash flow available to all of its investors.

11.4

Describe why it is not usually appropriate to use the coupon rate on a company’s bonds to estimate the pre-tax cost of debt for the company.

The pre-tax cost of debt for the company is the current annual economic cost of borrowing for the company (before any tax effects). That cost is better measured by the current yield to maturity on the company’s debt than by the coupon rate that is currently paid on that debt. Since most companies 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 company 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.

11.5

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 company.

In order to be completely correct, a company 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.

11.6

Your manager just finished calculating your company’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 company is considering for the next 4 years. Evaluate that statement.

Your manager is incorrect. A company is always subject to revisions to its cost of capital due to current market and company conditions. In addition, the company 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, preference shares, and ordinary shares) with which the entire company is currently financed. In addition, the future projects must contain the same level of systematic risk as that of the average project that the company is currently operating.

11.7

How are customers and suppliers affected by a company’s working capital management decisions?

Customers like companies 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 they can be a costly item on a company’s balance sheet. Management’s decisions on the company’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 company is selling durable goods, the terms of credit are likely to be more generous. The terms of sale are also affected by the creditworthiness of the customer. If the company 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 company 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 company—sales should increase, relationships with vendors and suppliers should improve, and work or manufacturing stoppages should be less likely.

11.8

How do the following circumstances affect the cash conversion cycle: (a) favourable credit terms allow the company to pay its accounts payable more slowly, (b) inventory turnover increases and (c) accounts receivable turnover decreases? (a)

(b) (c)

11.9

Favourable credit terms from suppliers allow the company to use the suppliers’ funds to finance their working capital. It also reduces the company’s cash conversion cycle.

An increase in the inventory turnover, that is, the DSI decreases, reduces both the company’s operating cycle and the cash conversion cycle.

As the accounts receivables turnover (DSO) decreases, the company improves its receivables management and reduces its operating cycle and hence, its cash conversion cycle.

Why are promissory notes available only to the most creditworthy companies?

Promissory notes are available only to 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 company. Thus, companies that are the most creditworthy are able to raise funds in this market at costs that are lower than bank loans.

Questions and problems BASIC 11.1

WACC: What is the weighted average cost of capital?

The weighted average cost of capital (WACC) is the weighted average of the costs to the different sources of capital used to fund a company, The WACC is often used as an estimate of the cost of financing a new project given the company’s current mix of debt and equity.

11.2

Current cost of a bond: You are analysing the cost of debt for a company. You know that the company’s 14-year maturity, 10.55 per cent coupon bonds are selling at a price of $1050.24. The bonds pay interest semiannually and have a face value of $1000. If these bonds are the only debt outstanding for the company, what is the after-tax cost of debt for this company if the corporate tax is 30 per cent?

The current YTM for the bonds can be calculated as follows. $1050.24 = $52.75 x PVIFA(28, YTM/2) + $1,000 x PVIF(28, YTM/2) Solving, we find that YTM = 0.11, and therefore the after-tax cost of debt is equal to: 0.0988 x (1 – 0.3) = 0.0692, or 6.92%

11.3

Tax and the cost of debt: How is tax accounted for when we calculate the cost of debt?

When we calculate the cost of debt for an Australian company, we must take into account the tax subsidy given in Australia for interest payments on debt. For every dollar the company pays in interest, the company’s tax bill will decline by ($1 * t), where t is the company tax rate. We adjust for this tax benefit by multiplying the pre-tax 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.

11.4

Tax and the cost of debt: Fafincare Ltd has earnings before interest and tax equal to $500. If the company incurred interest expense of $200 and pays tax at the corporate rate of 30 per cent, what amount of cash is available for Fafincare Ltd’s investors?

EBIT Interest Exp EBT Tax (30%) Profit Interest expense Cash for investors

11.5

$500 200 $300 90 $210 200 $410

Cost of ordinary equity: List and describe each of the three methods used to calculate the cost of ordinary equity.

1) The Capital Asset Pricing Model (CAPM) formula for the cost of ordinary shares can be used to calculate the return investors will demand on investment in the company’s ordinary shares.

2) The constant-growth dividend model can be used to calculate the cost of equity implied by the company’s current share price. In an efficient market, the current price of the company’s shares should reflect the cash flows (dividends) that investors will receive in the future from holding equity in the company, discounted by an appropriate rate (the cost of equity). By knowing the current dividend paid by the company and the expected growth rate of dividends, we can compute the cost of capital that is implied in the company’s current share price. The constant-growth dividend model is only appropriate when there is a reasonable expectation that the company’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—for example, a small, fast growing company whose growth will certainly slow as the company becomes larger.

11.6

Cost of ordinary shares: Hallmark Tyre Ltd just paid a $1.70 dividend on its ordinary shares. If Hallmark is expected to increase its annual dividend by 6.90 per cent per year into the foreseeable future and the current price of Hallmark Tyre Ltd’s ordinary shares is $17.25, what is the cost of ordinary equity for Hallmark Tyre Ltd? The cost of ordinary equity for Hallmark can be found using the constant-growth assumption equation: Pcs =

D (1 + g ) $1.70(1 + 0.069) D1 = 0 = = $17.25 k cs − g k cs − g k cs − 0.069

Solving for kcs, we find it is equal to 0.1744 or 17.44 per cent.

11.7

Cost of ordinary shares: Fast Way Ltd is expected to pay a dividend of $1.10 in a year from today on its ordinary shares. That dividend is expected to increase by 5 per cent every year thereafter. If the price of Fast Way Ltd shares is $13.75, what is Fast Way Ltd’s cost of ordinary equity?

We can use the formula to find the cost of ordinary equity assuming constant growth. k cs =

11.8

D1 $1.10 +g= + 0.05 = 0.13, or 13% Pcs $13.75

Cost of ordinary shares: Lock Stage’s ordinary shares are expected to pay an annual dividend equal of $1.55, and it is commonly known that the company expects dividends paid to increase by 11.10 per cent for the next 2 years and by 2 per cent thereafter. If the current price of Lock Stage’s ordinary shares is $16.93, what is the cost of ordinary equity capital for the company?

Pcs =

D1 (1 + g1 ) D1 (1 + g1 ) 2 D1 (1 + g1 ) 2 (1 + g 2 ) + + 2 2 1 + kcs (1 + kcs ) ( kcs − g 2 )(1 + kcs )

$16.93 =

$1.55(1 + 0.111) $1.55(1 + 0.111) 2 $1.55(1 + 0.111) 2 (1 + 0.02) + + 1 + k cs (1 + k cs ) 2 (k cs − g 2 )(1 + k cs ) 2

Using a spreadsheet to solve for the value of kcs, we find that the cost of ordinary equity capital is 12.99 per cent.

11.9

Cost of preference shares: Luxury Cruises has preference shares outstanding that pay an annual dividend equal to $13 per year. If the current price of Luxury Cruises preference shares is $144, what is the after-tax cost of preference shares for Luxury Cruises?

Using the equation for finding the cost of preferred equity, we have: k ps =

D 13 = = 0.0903, or 9.03% Pps 144

11.10 WACC for a company: Share Ltd has a capital structure that is financed, based on current market values, with 21 per cent debt, 19 per cent preference shares and 60 per cent ordinary shares. If the return offered to the investors for each of those sources is 11 per cent, 12 per cent and 18 per cent for debt, preference shares and ordinary shares, respectively, then what is Share Ltd’s after-tax WACC? Assume that the company’s corporate tax rate is 40 per cent.

WACC = xdebt k debt (1 − t ) + x ps k ps + xcs k cs =

WACC = 0.21 x 0.11x (1-0.4) + 0.19 x 0.12 + 0.6 x 0.18 =0.1447 or 14.47%

11.11 Finance balance sheet: Describe why the total value of all of the securities financing the company must be equal to the value of the company.

The value of the company’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 prioritised by the financing of those assets. Therefore, the financing claims on the assets of the company 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.

11.12 Cash conversion cycle: Michel Masonry estimates that it takes the company 27 days on average to pay off its suppliers. It also knows that it has days’ sales in inventory of 45 days and days sales’ outstanding of 38 days. How does Michel Masonry’s cash conversion cycle compare to that of an industry average of 75 days?

DPO = 27 days DSI = 45 days DSO = 38 days Industry average for cash conversion cycle = 75 days Michel Masonry’s cash conversion cycle = Cash conversion cycle = DSO + DSI - DPO = 38 + 45 – 27 = 56 days Since the company’s cycle is less than the industry average of 75 days, the company is more efficient than other companies in the industry in managing its working capital.

11.13 Cash conversion cycle: Eastern Manufacturers Ltd found that during the last year, they took 37 days to pay off its suppliers, while they took 58 days to collect their receivables. The company’s days’ sales in inventory was 61 days. What is Eastern Manufacturers Ltd’s cash conversion cycle?

DPO = 37 days DSI = 61 days DSO = 58 days Eastern Manufacturers cash conversion cycle = Cash conversion cycle = DSO + DSI - DPO = 58 + 61 – 37 = 82 days

11.14 Operating cycle: Lillybrook Bakery distributes its products to more than 75 restaurants and delis. The company’s collection period is 25 days, and it keeps its inventory for 3 days. What is Lillybrook Bakery’s operating cycle?

DSI = 3 days DSO = 25 days Lillybrook Bakery’s operating cycle = Operating cycle = DSO + DSI = 25 + 3 = 28 days

11.15 Operating cycle: Ether Technologies is a telecom component manufacturer. The company typically has a collection period of 55 days and days’ sales in inventory of 30 days. What is the operating cycle for Ether Technologies?

DSI = 30 days DSO = 55 days Ether Technologies operating cycle = Operating cycle = DSO + DSI = 55 + 30 = 85 days

MODERATE 11.16 Current cost of a bond: You know that the after-tax cost of debt capital for Red Port is 8.9 per cent. If the company has only one issue of 5-year maturity bonds outstanding, what is the current price of the bonds if the coupon rate on those bonds is 12.71 per cent? Assume the bonds make semiannual coupon payments and the corporate tax rate is 30 per cent.

We know the after-tax cost of debt, and from that we can find the pre-tax cost of debt by multiplying by 1 minus the tax rate. This becomes 0.089 / (1 – .3.) = 0.1271 = 12.71%.

Since the YTM on the bonds is equal to the coupon rate, then we know the bonds are priced at par, or $1,000.

11.17 Current cost of a bond: Eternity Ltd has issued bonds that never require the principal amount to be repaid to investors. Correspondingly, Eternity Ltd must make interest payments into the infinite future. If the bondholders receive annual payments of $92 and the current price of the bonds is $876, what is the after-tax cost of this borrowing for Eternity Ltd if the corporate tax rate is 40 per cent?

Since the bonds represent a perpetuity, we know that the pre-tax cost of debt can be solved using the following:

k debt =

Coupon Payment $92 = = 0.1050, or 10.50% Bond Price $876

The after-tax cost is 0.1050 × (1 - .4) = 0.0630, or 6.30%

11.18 Cost of debt for a company: You are analysing the after-tax cost of debt for a company. You know that the company’s 12-year maturity, 9.5 per cent coupon bonds with a face value of $1000 are selling at a price of $1200. If these bonds are the only debt outstanding for the company, what is the after-tax cost of debt for this company if the corporate tax rate is 30 per cent? What if the bonds are selling at par?

The current YTM for the bonds can be calculated as follows. $1,200 = $47.50 x PVIFA(24, YTM/2) + $1,000 x PVIF(24, YTM/2) Solving, we find that YTM = 0.07008 and therefore the after-tax cost of debt is equal to 0.07008 x (1 – .30) = 0.049056, or 4.906% If the bonds are priced at par, then the YTM on the bonds is 9.5 per cent and then the after-tax cost of debt would be 6.65%

11.19 Cost of ordinary shares: Stronghold Ltd’s ordinary shares currently sell for $41 per share. The company believes that its shares should really sell for $54 per share. If the company just paid an annual dividend of $2 per share and the company expects those dividends to increase by 6 per cent per year forever (and this is common knowledge to the market), what is the current cost of ordinary equity for the company and what does the company believe is a more appropriate cost of ordinary equity for the company?

The current cost of equity for the company is

D1 ($2.00 x1.06) +g= + 0.06 = 0.1117, or 11.17% Pcs $41 But the company believes that its cost of capital is more appropriately k cs =

k cs =

D1 ($2.00 x1.06) +g= + 0.06 = 0.0993, or 9.93% Pcs $54

11.20 WACC for a company: A company financed totally with ordinary equity is evaluating two distinct projects. The first project has a large amount of nonsystematic risk and a small amount of systematic risk. The second project has a small amount of non-systematic risk and a large amount of systematic risk. Which project, if taken, will have a tendency to increase the company’s cost of capital?

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 company, even if it has the lowest level of non-systematic risk.

11.21 WACC for a company: Contemporary Products Ltd currently has $200 million of market value debt outstanding. The 9 per cent coupon bonds (semiannual pay) have a maturity of 15 years, a face value of $1000 and are currently priced at $1,024.87 per bond. The company also has an issue of 2 million preference shares outstanding with a market price of $20. The preference shares offer an annual dividend of $1.20.

Contemporary Products also has 14 million ordinary shares outstanding with a price of $20.00 per share. The company is expected to pay a $2.20 ordinary dividend 1 year from today, and that dividend is expected to increase by 7 per cent per year forever. If the corporate tax rate is 40 per cent, then what is the company’s weighted average cost of capital?

Step 1: Total amount of debt, ordinary equity, and preferred equity: Debt = $200,000,000 (given) Preferred equity = $20 x 2,000,000 = $40,000,000 Ordinary equity = $20 x 14,000,000 = $280,000,000 Total capital = $520,000,000 xDebt = 200/520 = 0.3846 xps = 40/520 = 0.0769 xcs = 280/520 = 0.5385 Step 2: Cost of capital components: Cost of debt: $1,024.87 = $45 x PVIFA(30, YTM/2) + $1,000 x PVIF(30, YTM/2) Solving, we find that YTM = 0.0870 (this is a pre-tax number).

Cost of preferred equity: k ps =

D $1.20 = = 0.06 Pps $20.00

Cost of ordinary equity: D1 $2.20 +g= + 0.07 = 0.18 Pcs $20.00 Step 3: Combine using the WACC formula. k cs =

WACC = xdebt kdebt (1 − t ) + x ps k ps + xcs kcs WACC =[0.3846 x 0.0870 x (1-0.4)] + (0.0769 x 0.0600) + (0.5385 x 0.18) = 0.1216 = 12.16%

Please note: Question and Problem 11.22 from the end-of-chapter questions PDF had to be omitted – this will be amended in the Learning Space Course and Vital Source eText shortly.

11.22 Choosing a discount rate: If a company anticipates financing a project with a capital mix different than the company’s current capital structure, describe in realistic terms how the company is subjecting itself to a calculation error if it chooses to use its historical WACC to evaluate the project.

Since the company is financing the project with a different capital mix than it has historically used, we know that the weights and rates for debt, preference, and ordinary 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. Therefore, we know that the WACC will be different for the overall company versus that of the individual project.

Therefore, using its historical WACC can result in an error in the NPV estimate for the project.

11.23 Cash conversion cycle: Your boss asks you to calculate the company’s cash conversion cycle. Looking at the financial statements, you see that the average inventory for the year was $25 937, accounts receivable were $17 480, and accounts payable were at $17 601. You also see that the company had sales of $154 303 and that cost of sales was $123 442. Interpret your company’s cash conversion cycle.

All sales are assumed to be credit sales.

Accounts receivable = $17,480 Accounts payable = $17,601 Sales = $154,303 Inventory = $25,937 Cost of sales = $123,442

DSO =

Accounts receivable $17,480 = = 42.4 days Credit sales/365 $154,303/3 65

DSI =

Inventory $25,937 = = 76.7 days COS/365 $123,442/3 65

DPO =

Accounts payable $17,601 = = 52.0 days COS/365 $123,442/3 65

Cash conversion cycle = DSO + DSI – DPO = 41.3 + 76.7 – 52.0 = 66.0 days

The company takes 66 days from the time it pays for its raw materials to the time it realises 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.

11.24 Cash conversion cycle: Silver Ltd has net sales of $10.7 million and 75 per cent of these are credit sales. Its cost of sales is 65 per cent of annual sales. The company’s cash conversion cycle is 53.3 days. The inventory balance at the company is $1 707 161, while its accounts payable is $2 457 447. What is the company’s accounts receivable balance?

Net sales = $10,700,000 Credit sales = (0.75 × $10,700,000) = $8,025,000 Accounts payable = $2,457,447 Inventory = $1,707,161 Cost of sales = (0.65 × Sales) = (0.65 × $10,700,000) = $6,955,000 Cash conversion cycle = 53.3 days

DPO =

Accounts payable $2,457,447 = = 129.0 days COS/365 $6,955,000/365

DSI =

Inventory $1,707,161 = = 89.6 days COS/365 $6,955,000/365

Cash conversion cycle = DSO + DSI – DPO 53.3 = DSO + 89.6 – 129.0 DSO = 92.7 days Using the DSO equation, we can solve for the accounts receivable.

DSO =

Accounts receivable AR = = 92.7 days Credit sales/365 $8,025,000/365

Accounts Receivable = 92.7 x 21,986.30 = $2,038,130.14

The company has accounts receivables of $2,038,130.

11.25 Operating cycle: Ava Technology’s operating cycle is 99 days. Its inventory level was at $110 093 last year and the company had a $1.4 million cost of sales. How long does it take Ava Technology to collect on its receivables?

Operating cycle = 99 days Inventory = $110,093 Cost of goods sold = $1,400,000

DSI =

Inventory $110,093 = = 28.7 days COS/365 $1,400,000/365

Operating cycle = DSO + DSI 99 = DSO + 28.7 DSO = 70.3 days It takes Ava 70.3 days to collect on its receivables.

CHALLENGING 11.26 You are analysing the cost of capital for MacroSwift Ltd, which develops software operating systems for computers. The company’s dividend growth rate has been a very constant 3 per cent per year for the past 15 years. Competition for the company’s current products is expected to develop in the next year, and MacroSwift Ltd is currently expanding its revenue stream into the multimedia industry.

Evaluate using a 3 per cent growth rate in dividends for MacroSwift Ltd in your cost of capital model.

While the growth in dividends has been extremely constant for Macroswift Ltd 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 Ltd will have competition for its current product list in the near future, and that could alter the company’s growth rate. In addition, the company is expanding its product line into an area that will probably not yield the same level of growth. It is therefore, unlikely that MacroSwift Ltd’s dividend growth rate will continue at a 3 per cent annual rate. This suggests that we should consider something other than constant growth in our modelling.

11.27 You know that the return of Cycles-r-us’s ordinary shares reacts to macroeconomic information 1.00 more times than the return of the market. If the risk-free rate of return is 4.80 per cent and the market risk premium is 6 per cent, what is Cycles-rus’s cost of ordinary equity capital?

We know that the beta for Cycles-r-us’s is 1.00, and we can use the remaining information in the CAPM as follows:

E ( Rcs ) = Rrf +  ( E ( Rm ) − Rrf ) = 0.048 + 1.00(0.06) = 0.1080, or 10.80%

11.28 In your analysis of the cost of capital for an ordinary share, 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.

Comparing the two formulas for the two methods, we have:

(

E(Rcs ) = Rrf + β E(Rm ) - Rrf

) and k = PD + g 1

cs

cs

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 share. If the market price is incorrect, then this might lead to a difference.

11.29 Hardy Trucks has a preference share issue outstanding that pays an annual dividend of $1.30 per year. The current cost of preference shares for Hardy Trucks is 10.80 per cent. If Hardy Trucks issues additional preference shares that pay exactly the same dividend and the investment banker retains 5.10 per cent of the sale price, what is the cost of new preference shares for Hardy Trucks?

The current cost of preference shares for Hardy Trucks is: Pps =

D $1.30 = = $12.04 k ps 0.1080

Then Hardy Trucks would receive 94.90 per cent of the proceeds. We could then adapt the cost of preferred equity to the following: k ps =

D $1.30 $1.30 = = = 0.1137 = 11.37% Pps (1 − F ) $12.04(1 − 0.0510) $11.43

11.30 The cost of equity is equal to the: a. expected market return. b. rate of return required by shareholders. c. cost of retained earnings plus dividends. d. risk the company incurs when financing.

B is correct.

The cost of equity is defined as the rate of return required by shareholders.

11.31 Dot.Com has determined that it could issue $1000 face value bonds with an 8 per cent coupon paid semiannually and a 5-year maturity at $900 per bond. If the corporate tax rate is 30 per cent, its after-tax cost of debt is closest to: a.

7.2 per cent b.

7.4 per cent. c.

7.6 per cent. d.

7.8 per cent.

B 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% rd(1 – t)= 10.6298% (1 – 0.30) = 7.44%

11.32 Morgan Insurance Ltd. issued a fixed-rate perpetual preference share 3 years ago and placed it privately with institutional investors. The share was issued at $25.00 per share with a $1.75 dividend. If the company were to issue preference shares today, the yield would be 6.5 per cent. The share’s current value is a. $25.00 b. $26.92 c. $37.31 d. $40.18 B is correct.

The company can issue preference shares at 6.5%.

Pp = $1.75/0.065 = $26.92 Note: Dividends are not tax deductible so there is no adjustment for taxes.

11.33 Gearing Ltd has an after-tax cost of debt capital of 4 per cent, a cost of preference shares of 8 per cent, a cost of equity capital of 10 per cent, and a weighted average cost of capital of 7 per cent. Gearing Ltd 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 per cent b.

7 per cent c.

8 per cent d.

10 per cent 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.

11.34 Suppose the cost of capital of Gadget Ltd is 10 per cent. If Gadget Ltd has a capital structure that is 50 per cent debt and 50 per cent equity, its before-tax cost of debt is 5 per cent, and its corporate tax rate is 30 per cent, then its cost of equity capital is closest to: a.

12 per cent b.

14 per cent c.

16 per cent d.

18 per cent

C is correct.

WACC = xdebt kdebt (1- t) + xos kos 0.1 = 0.05(0.7)(0.5) + 0.5kos 0.0825 = 0.5kos kos = 0.165 or 16.5%

11.35 What impact would the following actions have on the operating and cash conversion cycles? Would the cycles increase, decrease, or remain the 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 sales.

Situation Operating cycle a. More raw material than usual is Increase purchased. b. The company enters into an off season, Increase and inventory builds up. c. Better terms of payment are negotiated No change with suppliers. d. The cash discounts offered to customers Increase are decreased. e. All else remaining the same, an improvement in manufacturing Increase technique decreases the cost of sales

Cash conversion cycle Increase Increase Decrease Increase Unchanged

Module 12: Capital structure and dividend policy

Module 12: Capital structure and dividend policy Self-study problems 12.1

Is tax necessary for the cost of debt financing to be less than the cost of equity financing?

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 pre-tax cost to the company for debt is still lower than the cost of equity.

12.2

You would like to own ordinary shares that have a record date of Wednesday, 16 March 2014. What is the last date that you can purchase the shares and still receive the dividend if it takes 4 days to settle a share transaction?

The ex-dividend date is the first day that the share will be trading without the rights to the dividend, and that occurs four business days before the record date. Therefore, the last day that you can purchase the share and still receive the dividend will be the day before the ex-dividend date (Thursday, 10 March 2011).

12.3

You believe that the average investor is subject to a 30 per cent tax rate on dividend payments. If a company is going to pay a $0.30 fully franked at a company tax rate of 30 per cent, by what amount would you expect the share price to drop on the exdividend date?

The share price will drop by approximately $0.30 plus tax credit of ($0.30 x 0.3)/ (1-0.3), giving a total of $0.43.

12.4

Valley Ltd just announced that instead of a regular half yearly dividend, it will be buying back shares using the same amount of cash that would have been paid in the suspended dividend. Should this be a good or bad signal from the company?

Valley Ltd has replaced a committed cash flow with one that is stated but does not have to be acted on. Therefore, the company’s actions should be greeted with suspicion, and the signal is not a good one.

12.5

Bernie Sports Ltd has just declared a 3-for-1 share split. If you own 12 000 shares before the split, how many shares do you own after the split?

You will own three shares of Bernie Sports for every one share that you currently own.

Therefore, you will own 3 × 12,000 = 36,000 shares of the company.

Critical thinking questions 12.1

Consider the WACC for a company that pays tax. Explain what a company's best course of action would be to misuse its WACC and thereby maximise the company value. Use the WACC formula for your explanation.

WACC = (1 – Tc) x kDebt x (D/V) + kcs x (E/V) Since we know that kcs > kDebt, then it would make sense to increase D relative to E 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 company from its current valuation.

This highlights the effect of taxes without taking into account the other M&M assumptions.

12.2

Matsubishi Vehicles sells cars in a market where the standard car comes with a 5year/130,000-kilometre warranty on all parts and labour. Describe how an increased probability of insolvency could affect sales of cars by Matsubishi.

In a market where a warranty is a significant portion of the cost of a car, purchasing a car where the seller might not be able to completely perform on that warranty would have negative impact on the company’s future car sales. This would decrease the amount of cash flow available to the investors of the company, which would lower the value of the company.

12.3

The principal-agent problem occurs due to the divergent interests of the non-owner managers and shareholders of a company. Propose a capital structure change that might help align a portion of these divergent interests.

The managers of a company would rather work as little as possible, given a set level of compensation, whereas shareholders would rather compensate the manager for a high level of effort, with a low effort receiving very little compensation. If the company’s capital structure generates a very small probability of bankrupting the company, then increasing the proportion of debt in the capital structure would increase the probability of the company falling into insolvency. This increased probability of insolvency, and therefore the increased chance that the manager will lose his job, would then help to align

the interests of the manager and shareholders by giving the manager an additional incentive to work harder for the shareholders.

12.4

If a company increases its debt to a very high level, then the positive effect of debt in aligning the interests of management with those of shareholders tends to become negative. Explain why this occurs.

Whereas increasing the debt level for a company tends to catch management’s attention and force them to work harder, a very high level of debt can be detrimental. That is, at very high levels of debt, risk-averse managers begin to minimise the risks that a company takes on for the managers’ own job preservation needs. This risk minimisation can deter managers from taking risky, but positive-NPV projects, which are needed to help the company meet the very debt obligations that are causing the problem. In addition, the financially risky company may also bear costs not previously borne in relationships with employees, suppliers, and customers.

12.5

When we observe the capital structure of many companies, we find that they tend to utilise lower levels of debt than that predicted by the trade-off theory. Offer an explanation for this effect.

This empirical result is consistent with a company maintaining a reserve level of debt or high cash levels in order for it to have ample internally generated funds for new projects.

One explanation would be that companies like to have this “reserve” financing available for new projects when they are identified. Another explanation is that companies do not have to offer new investors an explanation 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 securities for the financing of the new projects. Both of these explanations are in line with the pecking order theory.

12.6

Suppose that you live in a country where it takes 10 days to settle a share purchase.

How many days before the record date will be the ex-dividend date?

The ex-dividend date is the first day that a share will trade without the right to a dividend.

If it takes ten business days for a share purchase to settle, then the ex-dividend date will be ten business days before the record date.

12.7

The price of a share is $15.00 on 16 February 2014. The record date for a $0.50 dividend is 10 February 2014. If there are no taxes on dividends, what would you expect the price of a share to be on 9 through 16 February? Assume that no other information that could change the price of a share arises.

The price will generally drop on the ex-dividend date by approximately the amount of the dividend plus tax credit. If there is no other information that could change the price of the share arises, the price on record date and beyond would stay at $15.00.

12.8

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 change hands very infrequently. This makes the dividend process much easier for private companies than for the public ones.

12.9

You are the CEO of a company that has been the subject of a hostile takeover.

Thibeaux Piques has been accumulating the shares of your company and now holds a substantial percentage of the outstanding shares. You would like to purchase the shares that he owns. What method of share buy-backs will you opt for?

Since Mr. Piques is hostile to your company, 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 company), 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 selective buy-back method. 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.

12.10 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 share price becomes too high for individual investors to afford. What course of action could Fled take to get its share price down without dissipating value for shareholders?

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 share split. This would increase the number of shares outstanding and decrease the value of each share outstanding. Since each shareholder would continue owning his or her prior pro-rata share of the company, shareholders would not see any of their value dissipated by the company’s actions.

Questions and problems BASIC 12.1

Interest tax shield benefit: Black Ltd has $461 million of debt outstanding at an interest rate of 9 per cent. What is the amount of the tax shield on that debt, just for this year, if Black Ltd is subject to a 34 per cent company tax rate?

Black Ltd will pay $41,490,000 ($461,000,000 × 0.09) in interest this year, which will shield Black Ltd from paying a tax amount equal to: VTax-savings debt = D × t = ($41,490,000 × 0.34) = $14,106,600 Therefore, the amount of this year’ tax shield, due to debt issuance, for Black Ltd is $14,106,600.

12.2

Interest tax shield benefit: Victoria Ltd has $307 million of debt outstanding at an interest rate of 7 per cent. What is the present value of the tax shield on that debt if it has no maturity and if Victoria Ltd is subject to a 34 per cent company tax rate?

The present value of Victoria Ltd’s tax shield is: tc × D = 0.34 x $307,000,000 = $104,380,000 An alternative calculation would be: (tc × D × kDebt ) / kDebt = (0.34 x $307,000,000 x 0.07) / 0.07 = $104,380,000

12.3

Interest tax shield benefit: Harlock Ltd has $462 million of debt outstanding at an interest rate of 13 per cent. What is the present value of the debt tax shield if the debt has no maturity and if Harlock Ltd is subject to a 37 per cent company tax rate?

The present value of Harlock Ltd’s tax shield is: tc × D = 0.37 × $462,000,000 = $170,940,000

12.4

Interest tax shield benefit: Swann Ltd currently has an equity cost of capital equal to 20 per cent. If the Modigliani and Miller assumptions hold (with the exception of the assumption that there is no tax) and the company’s capital structure is made up of 50 per cent debt and 50 per cent equity, then what is the weighted average cost of capital for the company if the cost of debt is 12 per cent and the company is subject to a 31 per cent company tax rate?

WACC = xDebt kDebt + xcs kcs = (0.5)(0.12)(1-0.31) + 0.5(0.20) = 0.1414, or 14.14% 12.5

12.6

Practical considerations in capital structure choice: List and describe three practical considerations that concern managers when they make capital structure decisions.

1.

Financial flexibility: Managers must minimise the company’s cost of capital while also ensuring that the company has the flexibility to raise new capital quickly to deal with unexpected problems or to take advantage of unexpected opportunities.

2.

Profit Risk: Increasing the leverage of a company increases the risk associated with a company’s profit, and the risk of default.

3.

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-PV project). Although financial theory suggests that neither of these effects should matter, managers often take them into account when making financing decisions.

Dividends: Artemis Shipping Ltd has paid a $0.25 dividend every 6 months for the past 3 years. Artemis Shipping Ltd just lowered its declared dividend to $0.20 for the next dividend payment. Discuss what this new information might convey concerning Artemis Shipping Ltd management’s belief concerning the future of the company.

Since dividends convey information concerning the future prospects of the company, any change in dividend levels is also believed to convey a change in management’s forecast of the company’s prospects. That is, lowering the dividend from $0.25 to $0.20 suggests that the company’s future cash flow may be reduced. This reduction could be because of a general reduced level of profitability, because the company’s projects are winding down, or even because of an increased need to invest in new positive NPV projects for the future.

12.7

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.

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.

12.8

Share buy-backs and company value: Explain how the repurchase new securities by a company can produce useful information about the issuing company. Why does this information make the shares of the company more valuable, even if this information is confirmation of existing information about the company?

When issuing new securities, the issuing company 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 company’s actual financial status. In a sense, it reduces the variability in the information that the company may already have released. If the production of this information reduces the level of risk borne by investors, then the issue of repurchasing new securities could actually increase the value of the securities issued by the company and, in turn, the total value of the company.

12.9

Dividends: Explain why holders of a company’s debt should insist on a covenant that restricts the amount of cash dividends.

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 shareholders to at least a level where bondholders will still be able to generate their expected rate of return.

12.10 Share splits and bonus share issues: Explain why companies prefer that their shares trade in a moderate price range instead of a high dollar -per -share cost. How do companies keep the share trading in a moderate price range?

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, companies 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.

12.11 Dividends: Alpha Ltd is trading for $11.80 per share on the day before the exdividend date. If the amount of the dividend is $0.25 and there is no tax, what should the price of the shares be trading for on the ex-dividend date?

Since there is no tax, the value of the shares should drop by the amount of the dividend.

Therefore, the shares should trade for $11.55 on the ex-dividend date.

MODERATE 12.12 The costs of debt: Briefly discuss costs of financial distress to a company that may arise when employees believe it is highly likely that the company will declare insolvency.

If the employees of a company understand that the company has a significant chance of filing for insolvency, then costs to the company 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 company.

2. Higher recruiting costs. New employees, understanding that working for the company is a risky venture, 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.

12.13 The costs of debt: Creswell Shoes is a retailer that has just begun having financial difficulty. Creswell’s suppliers are aware of the increased possibility of insolvency.

What might Creswell’s suppliers do based on this information?

Creswell Shoes is not certain to go into insolvency, so its suppliers would still like to do business with Creswell as long as it is profitable to do so. Therefore, the suppliers would still make sales to Creswell as long as payment for the sales was made at the time of purchase rather than on credit. This would require Creswell to maintain a higher cash balance. This requirement to hold additional cash could be viewed as a cost of financial distress to Creswell Shoes.

12.14 Shareholder-manager agency costs: The Ellison Group has determined that it will come up short by $50 million on its debt obligations at the end of this year. The business has identified a positive-NPV project that will require a great deal of effort on the part of management. However, this project is expected to generate only $40 million at the end of the year. Assume that all the members of the Ellison Group’s management team will lose their jobs if the company becomes insolvent at the end of the year. Will managers take the positive NPV project? If it declines the project, what kind of cost will the Ellison Group incur?

Managers expect to lose their jobs in one year whether they work hard and take the project or not. Although there may be a slim chance that the company will not declare insolvency, management has no incentive to take on the difficult project. This makes the shortage to the debt holders, as well as the shareholders, greater than it would be if the company followed the rule of always accepting positive-NPV projects. This is another example of agency costs that can arise from financial distress.

12.15 Two theories of capital structure: Use the following table to make a suggestion for the recommended proportion of debt that the company should utilise for 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

75% debt

$20 −$ 5 −$10

$30 −$20 −$10

By totalling the cost and benefits for each proportion of debt we find: Benefit or (Cost)

No debt

Total cost/benefit

-$11

25% debt $2

50% debt

75% debt

$5

$0

Therefore, this company can maximise company value by choosing a 50 per cent debt capital structure.

12.16 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.

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 second most expensive source in this list.

2. New issue debt—This will be the cheapest 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 do not exhaust the cheapest sources of financing before moving on to more expensive sources.

12.17 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.

That internally generated equity is utilised first as a source of financing does not mean that the internally generated funds are cheaper than debt. Internally generated funds belong to shareholders and are therefore really equity financing, which we know to be more expensive than debt. However, using internally generated funds enables the company to avoid the costs associated with borrowing or selling shares (including the costs associated with the signals that financing announcements send investors), which, in turn, can make internal funds most attractive.

12.18 The costs of debt: Discuss how the legal costs of financial distress may increase with the probability that a company will fall become insolvent, even if the company has not reached the point of insolvency.

If a company is anticipating insolvency to a greater extent, then it will increase its legal efforts to protect the company from creditors when and if the company reaches that point.

Therefore, the legal costs of insolvency will increase with financial leverage even if the company has not yet declared insolvency.

12.19 Dividend policy and company value: Explain how a share buy-back, although it places cash in the hands of its shareholders, is different from a dividend payment.

A share buy-back, 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 buy-back 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.

12.20 Dividend policy and company value: You have just encountered two identical companies with identical investment opportunities, as well as the ability to fund these opportunities. You have found that one of the companies has just announced an introductory dividend policy, whereas the other has continued with a no-dividend policy. Which of the two companies is worth more? Explain.

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 company’s real investment policy, then both companies will be worth exactly the same. That is because investors who want dividends but own a no-dividend share can liquidate their appreciated value shares to create a homemade dividend, and shareholders who do not want dividends but own a dividend-paying share can use their “unwanted” dividends to purchase additional shares of that share.

12.21 Dividend policy and company value: Cash Flow Ltd has been increasing its cash dividends each year for the past 8 years. While this may signal that the company is financially very healthy, what else could we conclude from these actions?

If we rule out the possibility that the company is just producing a high level of cash, then we must conclude that the company has more cash than it has investment opportunities to utilise that cash. In short, we might conclude that the company’s growth rate will be slowing down in the future.

12.22 Dividend policy and company value: Is it possible for a company to retain its shareholders using its dividend policy? Explain your answer.

Investors with low marginal personal tax rate would be drawn to companies that pay high level of dividends as they are able to obtain the maximum benefit from the imputation tax system. On the other hand, investors with high marginal personal tax rate might prefer some returns in the form of capital gain because their capital gain will be taxed at 50% of their personal tax rate (if the shares are held more than 12 months), resulting in a lower capital gain tax payable. The investor clientele argument suggests that if a company consistently pays a low (or high) dividend, they will be able to attract a group of clientele investors to their company. In particular, a company that pays high level of dividend is likely to attract investors with low personal tax rate.

12.23 Dividends: Undecided Ltd has additional cash on hand right now, although management is not sure about the level of cash flows going forward. If the company

would like to put cash in its shareholders’ hands, what kind of dividend should it pay, and why?

Since this is a one-time increase in cash flows, the company would not want to commit to an ongoing higher dividend rate. If the company 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 dividend would not be appropriate. A more appropriate choice would be to declare a special dividend.

12.24 Dividend policy and company value: A company can deliver a negative signal to shareholders by increasing the level of dividends or by reducing the level of dividends. Explain.

When a company reduces its dividend, the company 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 company is telling its investors that it has greater cash than it has investment uses for that cash. If the company is currently viewed as a growth company, then the market could interpret an increase in the dividend as a slowdown in the growth rate of the company precipitated by the company’s lower investment rate.

12.25 Dividend policy and company value: You own shares in a company that has enough cash on hand to distribute to shareholders. You do not want the cash. What course of action would you prefer the company take?

You would prefer that the company initiate a share buy-back. You can opt not to sell your shares to the company but still participate in the increased value of the company’s shares since your pro-rata share of the expected future cash flows generated by the company 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.

12.26 Dividend policy and company value: Share buy-backs, once announced, do not actually occur in total or in part. From a signalling perspective, why would a special dividend be better than a share buy-back?

If we ignore the preferences of individual shareholders, then a special dividend is preferred to a share buy-back. Although dividends are binding, once declared by the company’s board of directors, a share buy-back is not binding. Therefore, a special dividend is considered a stronger signal than a share buy-back.

12.27 Dividend policy and company value: Consider a company that buy-backs shares from its shareholders in the open market, and explain why this action might be

detrimental to the shareholders to whom the company is attempting to deliver value through its action.

To understand this argument, we have to consider two points. First, the company should be managed for the benefit of its shareholders. Second, the company is the ultimate insider concerning the value of its shares.

Given the above points, we must realise that any time the company is buys back its shares, it must be doing so because the company’s management believes that the company’s shares are undervalued. Therefore, by buying back its share, the company is utilising 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 company. 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 realised had they held their shares until the buy-back was complete.

12.28 Dividend policy and company value: Explain why a company might raise money to pay a cash dividend by selling equity to new shareholders.

While this process may seem circular at best, it does have the advantage of producing information concerning the company for investors. That is, the underwriting process helps additional information on the company to become public. This information production may be a credible way for the company to let the market know about its operations. So although the cash flow circularity does exist, the process is good for the investing public in that information is learned about the company.

12.29 Share buy-backs: Briefly discuss the methods available for a company to buy-back its shares and explain why you might expect the share price reactions to the announcement of each of these methods to differ.

On-market buy-backs: Listed companies can buy back their shares on-market via the securities exchange. This type of buy-backs requires an ordinary resolution if over the 10/12 rules and the securities exchange rules apply.

Equal access buy-backs: This is the most straightforward form of share buy-back where all ordinary shareholders are offered to consider the offer to buy back the same percentage of their ordinary shares. If a proposed share buy-back is over the 10/12 limit, then it can only take place following passage of an ordinary resolution. This buy-back method is usually conducted off-market.

Selective buy-backs: Offers to buy back shares are only made to some of the shareholders in the company at a specific price. The scheme must first be approved by all shareholders or by a special resolution (requiring a 75% resolution). Usually conducted off-market.

Employee share scheme buy-back: A company buy-backs shares held by or for employees or salaried directors of the company or a related company. This type of buyback requires an ordinary resolution if over the 10/12 limit.

Minimum holding buy-back: A company offer to buy unmarketable parcels of shares from shareholders. The purchased shares must be cancelled. This type of buy-back does not require a resolution.

CHALLENGING 12.30 Ruttabul Ltd has $250 million of debt outstanding at an interest rate of 11 per cent.

What is the present value of the debt tax shield if the debt will mature in 5 years (and no new debt will replace the old debt), assuming that Ruttabul is subject to a 30 per cent company tax rate?

Ruttabul will pay $27,500,000 ($250,000,000 x 0.11) in interest each year, which will shield Ruttabul from paying a tax amount equal to $8,250,000 ($27,500,000 x 0.3). The tax shield will last for five years, so the present value of receiving this amount for the next five years is: $8,250,000 × PVIFA(11%, 5) = $8,250,000 × 3.695897 = $30,491,175

12.31 Albatross Ltd is currently valued at $900 million, but management wants to completely pay off its perpetual debt of $300 million. Albatross is subject to a 30 per cent corporate tax rate. If Albatross pays off its debt, what will be the total value of its equity?

Albatross 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 x .3 = $90,000,000 Therefore, Albatross will be worth $810 million after the recapitalisation, and since it will be an all-equity company, that will be the value of the equity.

12.32 Watson Ltd has an abundant cash flow. It is so high that the managers take Fridays off for a weekly luncheon in Byron Bay using the corporate jet. Describe how altering the company’s capital structure might make the management of this company stay in the office on Fridays in order to work on new positive NPV projects.

The root of the problem is that the company’s management is too comfortable, because their weekly trip to Byron Bay is not costly enough to the managers of the company.

Watson could drastically increase the proportion of debt in the company’s capital structure. This would decrease the amount of “free” cash that Watson’s management could spend on their weekly outings. If enough debt is placed on this company, then a cash shortage, or lack of a large cash surplus, would necessitate that the managers of the company work on new positive-NPV projects rather than spend their Fridays in Byron Bay. 12.33 According to the pecking order theory: a. new debt is preferable to new equity. b. new equity is preferable to internally generated funds. c. new debt is preferable to internally generated funds. d. new equity is always preferable to other sources of capital.

A is correct. According to pecking order theory, internally generated funds are preferable to both new equity and new debt.

12.34 According to the static 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.

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.

12.35 Sampson Ltd has not issued any new debt securities in 10 years. It will begin paying cash dividends to its shareholders for the first time next year. Explain how a dividend might help the company get closer to its optimal capital structure of 50 per cent debt and 50 per cent equity.

If the company 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 company 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 company to balance out its debt-equity ratio and get closer to a 50 percent-50 per cent mix (assume that the debt was below the 50 per cent level to begin with).

12.36 Sunlight Ltd, had shares outstanding that were valued at $120 per share before a two-for-one share split. After the share split, the shares were valued at $62 per share. If we accept that the company’s financial manoeuvre did not create any new

value, then why might the market be increasing the total value of the company’s equity?

We know that the share 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, companies have a tendency to increase their dividend rate after a share split. Therefore, since a share 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 company’s equity.

12.37 White Lotus Ltd currently has 30 000 shares outstanding. Each share has a market value of $25. If the company pays $4 per share in dividends, what will the value of each share be worth after the dividend payment? Ignore tax.

The current value of all of the shares is 30,000 x $25 = $750,000. If the company pays $4 per share, then the total cash paid out will be 30,000 x $4 = $120,000. Therefore, the value of all of the shares will be worth $120,000 less or $630,000, and the price of each share will be $630,000 / 30,000 = $21 per share.

However, it seems logical that if shares were worth $25 before the dividend payout, then they should be worth $4 less after the dividend payout or $21 just as we have calculated.

12.38 Cherry Ltd currently has 30 000 shares outstanding. Each share has a market price of $28. If the company buys back $150 000 worth of shares at market price, what will be the value of each share after the repurchase? Ignore tax.

The current value of all of the shares is 30,000 × $28 = $840,000. If the company repurchases $150,000 worth of shares, then it will repurchase $150,000 / $28 = 5,357 shares. Therefore, the value of all of the shares not purchased will be worth $150,000 less, or $690,000, and the price of each share will be $690,000 / (30,000 – 5,357) = $28 per share.

It seems logical, however, that if shares were worth $28 before the repurchase, then they should be worth $28 after the repurchase since investors should be indifferent between selling their shares to the company and retaining shares.

12.39 Woolers Ltd is trying to do some financial planning for the coming year. Woolers Ltd plans to raise $10 000 in new equity this year and wants to pay a dividend to shareholders of $39 000 in total. The company must pay $20 000 interest during the year and will also pay down principal on its debt obligations by $10 000. If the company continues with its capital budgeting plan, it will require $112 793 for capital expenditures during the year. Given the above information, how much cash must be provided from operations for the company to meet its plan?

CF Opnst + Equityt + Debtt = Divt + Interestt + Principalt + Cap Expt ==> CF Opnst + $10,000 = $39,000 + $20,000 + $10,000 + $112,793 ==>

CF Opnst = $171,793