SOLUTIONS MANUAL for Financial Management Theory & Practice 17th Edition by Eugine and Michael by StudyGuide

TABLE OF CONTENTS 1. Chapter 1. An Overview of Financial Management and the Financial Environment 2. Chapter 2. Financial Statements, Cash Flow, and Taxes 3. Chapter 3. Analysis of Financial Statements 4. Chapter 4. Time Value of Money 5. Chapter 5. Bonds, Bond Valuation, and Interest Rates 6. Chapter 6. Risk and Return 7. Chapter 7. Corporate Valuation, Stock Valuation, and Stock Market Equilibrium Rates 8. Chapter 8. Financial Options and Applications in Corporate Finance 9. Chapter 9. The Cost of Capital 10. Chapter 10. The Basics of Capital Budgeting: Evaluating Cash Flows 11. Chapter 11. Cash Flow Estimation and Risk Analysis 12. Chapter 12. Corporate Valuation and Financial Planning 13. Chapter 13. Corporate Governance 14. Chapter 14. Distributions to Shareholders: Dividends and Repurchases 15. Chapter 15. Capital Structure Decisions 16. Chapter 16. Supply Chains and Working Capital Management 17. Chapter 17. Multinational Financial Management 18. Chapter 18. Public and Private Financing: Initial Offerings, Seasoned Offerings, and Investment Banks

19. Chapter 19. Lease Financing 20. Chapter 20. Hybrid Financing: Preferred Stock, Warrants, and Convertibles 21. Chapter 21. Dynamic Capital Structures and Corporate Valuation 22. Chapter 22. Mergers and Corporate Control 23. Chapter 23. Enterprise Risk Management 24. Chapter 24. Bankruptcy, Reorganization, and Liquidation 25. Chapter 25. Portfolio Theory and Asset Pricing Models

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

SOLUTION MANUAL Financial Management Theory and Practice 17th EditionEugene F. Brigham, Michael C. Ehrhardt

Solution and Answer Guide CHAPTER 1: AN OVERVIEW OF FINANCIAL MANAGEMENT AND THE FINANCIAL ENVIRONMENT

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS ............................................................................... 1 MINI CASE ................................................................................................................................................. 5

ANSWERS TO END-OF-CHAPTER QUESTIONS 1-1

Define each of the following terms: a. Proprietorship; partnership; corporation; charter; bylaws b. Limited partnership; limited liability partnership; professional corporation c. Stockholder wealth maximization d. Money market; capital market; primary market; secondary market e. Private markets; public markets; derivatives f. Investment bank; financial services corporation; financial intermediary g. Mutual fund; money market fund h. Open outcry auction; dealer market; automated trading platform i. Production opportunities; time preferences for consumption j. Foreign trade deficit k. Algorithmic trading; high-frequency trading Answer: a. A proprietorship, or sole proprietorship, is a business owned by one individual. A partnership exists when two or more persons associate to conduct a business. In contrast, a corporation is a legal entity created by a state. The corporation is separate and distinct from its owners and managers. A company must file a charter to become a corporation. A charter includes the following information: (1) name of the proposed corporation, (2) types of activities it will pursue, (3) amount of capital stock, (4) number of directors, and (5) names and addresses of directors. The bylaws are a set of rules drawn up by the founders of the corporation. Included are such points as: (1) how directors are to be elected (all elected each year or perhaps one-third each year for 3-year terms), (2) whether the existing stockholders will have the first right to buy any new shares the firm issues, and (3) procedures for changing the bylaws themselves, should conditions require it.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

In a limited partnership, limited partners’ liabilities, investment returns and control are limited, while general partners have unlimited liability and control. In limited partnership, at least one partner is liable for all the debts in the partnership. A limited liability partnership (LLP), sometimes called a limited liability company (LLC), combines the limited liability advantage of a corporation with the tax advantages of a partnership. A professional corporation (PC), known in some states as a professional association (PA), has most of the benefits of incorporation but the participants are not relieved of professional (malpractice) liability.

Stockholder wealth maximization is the appropriate goal for management decisions. The risk and timing associated with expected earnings per share and cash flows are considered in order to maximize the price of the firm’s common stock. Maximizing shareholder’s wealth is a duty that needs to be fulfill by corporations.

A money market is a financial market for debt securities with maturities of less than 1 year (shortterm). The New York money market is the example of money market. Capital markets are the financial markets for long-term debt and corporate stocks. The New York Stock Exchange is an example of a capital market. Primary markets are the markets in which newly issued securities are sold for the first time. Secondary markets are where securities are resold after initial issue in the primary market. The New York Stock Exchange is a secondary market.

In private markets, transactions are worked out directly between two parties and structured in any manners that appeal to them. Bank loans and private placements of debt with insurance companies are examples of private market transactions. In public markets, standardized contracts are traded on organized exchanges. Securities that are issued in public markets, such as common stock and corporate bonds, are ultimately held by a large number of individuals. Private market securities are more tailor-made but less liquid, whereas public market securities are more liquid but subject to greater standardization. Derivatives are those underlying asset that derives their value from other traded assets. Futures, options, forwards are the examples of derivative market. Therefore, the value of a derivative security is derived from the value of an underlying real asset.

An investment banker is a facilitator between businesses and savers. Investment banking houses assist in the design of corporate securities and then sell them to savers (investors) in the primary markets. Financial service corporations offer a wide range of financial services such as brokerage operations, insurance, and commercial banking. A financial intermediary buys security with funds that is obtained by issuing its own securities. An example is a common stock mutual fund that buys common stocks with funds obtained by issuing shares in the mutual fund.

A mutual fund is an organization that pools the money deposited by savers to buy financial instruments. These instruments receive dividends and interest on it. The resulting dividends, interest, and capital gains are distributed to the fund’s shareholders after the deduction of operating expenses. Different funds are designed to meet different objectives. Money market funds are mutual funds which invest in short-term securities carry low-risk and also offer their shareholders interest-bearing checking accounts.

An open outcry auction is a method where traders meet face to face at particular location at an agreed price and quantity. These traders communicate with each other through hand signals and shouts. In a dealer market, a dealer holds an inventory of the security and makes a market by offering to buy or sell. Others who wish to buy or sell can see the offers made by the dealers, and can contact the dealer of their choice to arrange a transaction. An automated trading platform is a computer system in which buyers and sellers post orders and in which trades are automatically executed for matching orders.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

be demanded now. Consumption time preferences refer to the preferred pattern of consumption. Consumers’ time preferences for consumption establish how much consumption they are willing to save or consume at different levels of interest. It majorly impacts required rate of return.

1-2

A foreign trade deficit occurs when businesses and individuals in the United States import more goods from foreign countries compared to exports. This cause an increase in an interest rate. Trade deficits must be financed, and the main source of financing is debt. Foreign trade surplus occurs when exports are more than imports. As the trade deficit increases, the debt financing increases, driving up interest rates. U.S. interest rates must be competitive with foreign interest rates; if the Federal Reserve attempts to set interest rates lower than foreign rates, foreigners will sell U.S. bonds, decreasing bond prices, resulting in higher U.S. rates.

Algorithmic trading occurs when computers are programed to buy or sell stocks on behalf of stockholders if a particular event or sequence of events happens. High frequency trading (HFT) is a type of algorithmic trading in which HFT traders, which are computers, buy and sell hundreds or thousands of times a day. Most HFT is done by firms that are created for this purpose because HFT requires expensive computer systems and highly paid programmers.

What are the three principal forms of business organization? What are the advantages and disadvantages of each? Answer: Sole proprietorship, partnership, and corporation are the three principal forms of business organization. The advantages of the Sole proprietorship and partnership includes ease and low cost of formation. The advantages of the corporation include limited liability, indefinite life, ease of ownership transfer, and access to capital markets. The disadvantages of a sole proprietorship are (1) difficulty in obtaining large sums of capital, (2) unlimited personal liability for business debts, and (3) limited life. The disadvantages of a partnership are (1) unlimited liability, (2) limited life, (3) difficulty of transferring ownership, and (4) difficulty of raising large amounts of capital. The disadvantages of a corporation are (1) double taxation of earnings and (2) requirements to file state and federal reports for registration, which are expensive, complex, and time-consuming.

1-3

What is a firm’s fundamental value (which is also called its intrinsic value)? What might cause a firm’s intrinsic value to be different from its actual market value? Answer: A firm’s fundamental, or intrinsic, value is the present value of its free cash flows when discounted at the weighted average cost of capital. If the market price reflects all relevant information, then the observed price is also the intrinsic price. Intrinsic value depends on all of its expected future cash flows.

1-4

Edmund Corporation recently made a large investment to upgrade its technology. Although these improvements won’t have much of an impact on performance in the short run, they are expected to reduce future costs significantly. What impact will this investment have on Edmund’s earnings per share this year? What impact might this investment have on the company’s intrinsic value and stock price? Answer: Earnings per share in the current year will decline due to cost of the investment made in the current year and no significant performance impact in the short run. However, the company’s stock price should increase due to the significant cost savings expected in the future.

1-5

Describe the ways in which capital can be transferred from suppliers of capital to those who are demanding capital. Answer:

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

In a well-functioning economy, capital will flow efficiently from those who supply capital to those who demand it. This transfer of capital can take place in three different ways:

1-6

Direct transfers of money and securities occur when a business sells its stocks or bonds directly to savers, without going through any type of financial institution. The business delivers its securities to savers, who in turn give the money to the firm it needs.

Capital can also be transferred indirectly through an investment bank that underwrites the issue. An underwriter serves as a middleman and facilitates the issuance of securities. The company sells its stocks or bonds to the investment bank, which in turn sells these same securities to savers. The businesses’ securities and the savers’ money merely ―pass through‖ the investment banking house.

Transfers can also be made through a financial intermediary. Here, the intermediary obtains funds from savers in exchange for its own securities. The intermediary uses this money to buy and hold businesses’ securities. Intermediaries literally create new forms of capital. The existence of intermediaries greatly increases the efficiency of money and capital markets.

What are financial intermediaries, and what economic functions do they perform? Answer: Financial intermediaries are business organizations that receive funds in one form and repackage them for the use of those who need funds. Through financial intermediation, resources are allocated more effectively, and the real output of the economy is thereby increased.

1-7

Is an initial public offering an example of a primary or a secondary market transaction? Answer: A primary market is the market in which corporations raise capital by issuing new securities. An initial public offering is a stock issue where privately held firms go to public. Therefore, an IPO would be an example of a primary market transaction. A secondary offering of stock by a publicly traded company is also a primary market transaction. Other examples include bond issuances by companies or governments. A secondary market is for buying and selling securities that have already been issued. For example, a stock exchange is a secondary market.

1-8

Contrast and compare trading in face-to-face auctions, dealer markets, and automated trading platforms. Answer: Traders meet face to face in an open outcry auction at a particular location at an agreed rate. In a dealer market, there are ―market makers‖ who keep an inventory of the stock. These dealers list the prices at which they are willing to buy or sell. In a traditional dealer market, computerized quotation systems keep track of all bid and ask quotes, but they don’t actually match buyers and sellers. Instead, traders must contact a specific dealer to complete the transaction. An automated trading platform is a computer system in which buyers and sellers post their orders and then let the computer automatically determine whether a match exists. If a match exists, the computer automatically executes and reports the trade.

1-9

Describe some similarities and differences among broker-dealer networks, alternative trading systems (ATSs), and registered stock exchanges. Answer: Broker-dealer networks are registered with the SEC but are much less regulated than alternative trading systems (ATS) and registered stock exchanges. In a typical broker-dealer network, the broker-dealer purchases the stock being offered for sale by a client and then immediately sells it to another client who wished to buy the stock. The broker-dealer is the counterparty to each of the clients. The broker-dealer must report the transactions, but not any information prior to the trade. An alternative trading system is a broker-dealer that registers with the SEC as an ATS. An ATS usually has an automated trading platform to match orders from clients, so the owner of the ATS is not always the counterparty, in contrast to a

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

broker-dealer network. The ATS must report trades, but not any pre-trade information. Therefore, an ATS is often called a dark pool. Stocks can only be listed at a registered stock exchange, although they may be traded elsewhere. A stock exchange must comply with more regulations than an ATS. In addition to reporting trades, a stock exchange must also report pre-trade information regarding bids and quotes. 1-10 What are some similarities and differences between the NYSE and the NASDAQ Stock Market? Answer: The NYSE and NASDAQ are the two largest registered stock exchange around the globe. These stock exchange provides trading platform for securities situated in New York. The NYSE is a market that uses designated markets makers. NASDAQ is a dealer market where every makers is in competition with each other. The NASDAQ Stock Market has the most listings because it is willing to list smaller corporations than the NYSE. However, the NYSE’s listings have a much bigger market value than NASDAQ’s listed stocks.

MINI CASE Assume that you recently graduated and have just reported to work as an investment advisor at the brokerage firm of Balik and Kiefer, Inc. One of the firm’s clients is Michelle DellaTorre, a highly ranked professional tennis player who has just come to the United States from Chile. DellaTorre would like to start a company to produce and market apparel she designs. She also expects to invest substantial amounts of money through Balik and Kiefer. DellaTorre is very bright, and she would like to understand in general terms what will happen to her money. Your boss has developed the following set of questions you must answer to explain the U.S. financial system to DellaTorre. a.

Why is corporate finance important to all managers? Answer: Corporate finance provides the skills that is required by managers. Such as:(1) identify and select the corporate strategies and individual projects that add value to their firm; and (2) forecast the funding requirements of their company, and devise strategies for acquiring those funds.

Describe the organizational forms a company might have as it evolves from a start-up to a major corporation. List the advantages and disadvantages of each form. Answer: The three main forms of business organization are (1) sole proprietorships, (2) partnerships, and (3) corporations. In addition, several hybrid forms are gaining popularity. These hybrid forms are the limited partnership, the limited liability partnership, the professional corporation, and the s corporation. The proprietorship has three important advantages: (1) it is easily and inexpensively formed, (2) it is subject to few government regulations, and (3) the business pays no corporate income taxes. The proprietorship also has three important limitations: (1) it is difficult for a proprietorship to obtain large sums of capital, (2) the proprietor has unlimited personal liability for the business’s debts, and (3) the life of a proprietorship is limited to the life of the individual who created it. The major advantage of a partnership is its low cost and ease of formation. The disadvantages are similar to those associated with proprietorships: (1) unlimited liability, (2) limited life of the organization, (3) difficulty of transferring ownership, and (4) difficulty of raising large amounts of capital. The tax treatment of a partnership is similar to that for proprietorships, which is often an advantage. The corporate form of business has three major advantages: (1) unlimited life, (2) easy transferability of ownership interest, and (3) limited liability. While the corporate form offers significant advantages over proprietorships and partnerships, it does have two primary disadvantages: (1) corporate earnings may be

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

subject to double taxation and (2) setting up a corporation and filing the many required state and federal reports is more complex and time-consuming than for a proprietorship or a partnership. In a limited partnership, the limited partners are liable only for the amount of their investment in the partnership; however, the limited partners typically have no control. The limited liability partnership form of organization combines the limited liability advantage of a corporation with the tax advantages of a partnership. Professional corporations provide most of the benefits of incorporation but do not relieve the participants of professional liability. S-corporations are similar in many ways to limited liability partnerships, but LLPS frequently offer more flexibility and benefits to their owners. c.

How do corporations go public and continue to grow? What are agency problems? What is corporate governance? Answer: A company goes public when it sells stock to the public as the firm grows, it might issue additional stock or debt. An agency problem occurs when the managers of the firm act in their own self-interests and not in the interests of the shareholders. Corporate governance is the set of rules that control a company’s behavior towards its directors, managers, employees, shareholders, creditors, customers, competitors, and community.

What should be the primary objective of managers? Answer: The corporation’s primary goal is stockholder’s wealth maximization, which translates to maximizing the price of the firm’s common stock. 1.

Do firms have any responsibilities to society at large? Answer: Firms have an ethical responsibility to provide a safe working environment, to avoid polluting the air or water, and to produce safe products. However, the most significant cost-increasing actions will have to be put on a mandatory rather than a voluntary basis to ensure that the burden falls uniformly on all businesses.

Is stock price maximization good or bad for society? Answer: The same actions that maximize stock prices also benefit society. Stock price maximization requires efficient, low-cost operations that produce high-quality goods and services at the lowest possible cost. Stock price maximization requires the development of products and services that consumers want and need, so the profit motive leads to new technology, to new products, and to new jobs. Also, stock price maximization necessitates efficient and courteous service, adequate stocks of merchandise, and welllocated business establishments. All these factors are necessary to generate sales revenues, which are necessary to generate profits.

Should firms behave ethically? Answer: Yes, results of a recent study indicate that the executives of most major firms in the United States believe that firms do try to maintain high ethical standards in all of their business dealings. Furthermore, most executives believe that there is a positive correlation between ethics and long-run profitability. Conflicts often arise between profits and ethics. Companies must deal with these conflicts on a regular basis, and a failure to handle the situation properly can lead to huge product liability suits and even can lead to bankruptcy. There is no room for unethical behavior in the business world.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

What three aspects of cash flows affect the value of any investment? Answer: (1) amount of expected cash flows, (2) timing of the cash flow stream, and (3) riskiness of the cash flows

What are free cash flows? Answer: Free cash flows are the cash flows available for distribution to all investors (stockholders and creditors) after paying expenses (including taxes) and making the necessary investments to support growth. FCF = Sales revenues – Operating costs - Operating taxes − Required investments in Operating Capital

What is the weighted average cost of capital? Answer: The weighted average cost of capital (WACC) is the average rate of return required by all of the company’s investors (stockholders and creditors). It is affected by the firm’s capital structure, interest rates, the firm’s risk, and the market’s overall attitude toward risk.

How do free cash flows and the weighted average cost of capital interact to determine a firm’s intrinsic value? Answer: A firm’s intrinsic value is the sum of all future expected free cash flows, converted into today’s dollars. Value 

FCF1 (1  WACC)1



FCF2 (1  WACC) 2

 ....

FCF

(1  WACC) 

Who are the providers (savers) and users (borrowers) of capital? How is capital transferred between savers and borrowers? Answer: Households are net savers. Most governments are net borrowers. The United States, Italy, and France have been net borrowers each year from 2001–2020. A relatively small number of countries during this period were not net borrowers but instead were net lenders. These countries include Norway (borrowed 1 year), South Korea (borrowed 4 years), New Zealand (borrowed in 6 years), and Luxemburg (borrowed 5 years). Non-financial corporations are net borrowers. Financial corporations (i.e., financial intermediaries including banks) are slightly net borrowers, but they are almost breakeven. Capital is transferred through: (1) direct transfer (e.g., corporation issues commercial paper to insurance company), (2) an investment banking house (e.g., IPO, seasoned equity offering, or debt placement), and (3) a financial intermediary (e.g., individual deposits money in bank, bank makes commercial loan to a company).

What is a required rate of return? What components make up the required rates of return on debt and stocks? What is the cost of debt and what is the cost of equity? Answer: A required rate of return is the rate that an investor expects from an investment in order to compensate the risk involved in investment. An investor’s expected rate of return is comprised of expected payments to the investor and expected changes in the investment’s value. For debt, the lender’s expected rate of return consists of expected interest payments and expected changes in the debt’s value.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

For stock, the shareholder’s expected rate of return consists of expected dividend payments and expected changes in the stock’s price. Providing expected required returns to lenders and shareholders is usually difficult and costly. Therefore, the required expected rate of return on debt is also called the cost of debt and the required expected rate of return on equity is also called the cost of equity. In other words, the required rate of return on a source of capital is equal to the cost of using the capital. k.

What are some economic conditions that affect interest rates, which subsequently affect required rates of return? Answer: Interest rates are influenced by (1) Federal Reserve policy, (2) the federal budget deficit or surplus, (3) the level of business activity, and (4) foreign trade balances. (1) Federal Reserve Policy: The Federal Reserve sets a target interest rate and often acts to keep interest rates close to the target. If the Federal Reserve wishes to keep interest rates low, then it usually implements open market operations. The Fed will purchase Treasury securities held by banks, which increases the demand for Treasury securities, which in turn increases the prices of Treasury securities. When the price of any bond goes up and the payments remain unchanged, the bond’s rate of return goes down. If the Fed wishes to increase interest rates, it reverses this policy and sells Treasury securities. This increases supply which causes the prices of Treasury securities to fall. When the price goes down and the payments remain unchanged, the subsequent rate of return goes up. (2) Federal Budget Deficits or Surpluses: A budget deficit occurs when the federal government spends more than it collects from tax revenues. To fund excess spending, the government either must borrow or increase the money supply. The government borrows by issuing new Treasury securities (or by selling ones that it had previously repurchased). This creates a greater supply of Treasury securities than currently is demanded, which causes a decrease in prices of Treasury securities until there is no more excess supply. When the price of a bond goes down and the payments remain unchanged, the rate of return (i.e., the interest rate) goes up. If a miracle were to occur and the government had a surplus, then the government could repurchase some of its debt. This demand for Treasury securities would cause their prices to go up, which would reduce their rate of return. (3) Level of Business Activity: An increase in the level of business activity means that the demand for borrowing also increases. This creates a temporary imbalance in which the supply of loans is less than the demand for loans. When supply exceeds demand, the ―price‖ must change until supply and demand are equal. In this situation, the interest rate will increase until the demand decreases and the supply increases to the point that both are equal. The reverse is true if a decrease in the level of business activity reduces the demand for loans. If the interest rate doesn’t fall, the supply of loans will exceed the demand for loans. Therefore, the interest rate must fall until the supply and demand for loans are equal. (4) Foreign Trade Deficits or Surpluses: A foreign trade deficit occurs when a country imports more than it exports. If people and companies in the United States import more goods and services than they export, then they must spend more money on the imports than they make on the exports. The U.S. companies and individuals usually borrow to finance this additional net spending. Higher demand for borrowing will cause interest rates to go up, all else held equal. The reverse is true for a country with foreign trade surpluses.

What four fundamental factors affect required rates of return? Answer: The required rate of return depends on these four fundamental factors: (1) production opportunities, (2) time preferences for consumption, (3) risk, and (4) inflation.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Production opportunities are the cash generating activity that require cash in the present but have the ability to generate more cash in future. The higher the production opportunities, the more cash will be demanded now. Time preference for consumption refers to consumers’ preferences for current consumption versus savings for future consumption: consumers with low preferences for current consumption will be willing to lend at a lower rate than consumers with a high preference for current consumption. Inflation refers to the tendency of prices to rise, and the higher the expected rate of inflation, the larger the required rate of return. Risk, in a money and capital market context, refers to the chance that the future cash flows will not be as high as expected—the higher the perceived default risk, the higher will be the required rate of return. Risk is also linked to the maturity and liquidity of a security. The longer the maturity and the less liquid (marketable) the security, the higher the required rate of return, other things constant. m. What are financial instruments? Describe the major types of financial instruments with respect to risk, original maturity, and rates of return. Answer: Financial instruments are documents (either on paper or on computers) with contractual obligations. Some are short-term (i.e., they mature within a year) and have low default risk, such as U.S. Treasury bills, commercial paper, and CDs. Short-term financial instruments usually have low risk and low rates of return. Commercial loans (which have maturities up to 7 years) have rates that are usually tied to the prime rate (i.e., the rate that U.S. banks charge to their best customers) or SOFR (Secured Overnight Financing Rate, which is based on actual overnight loans that use Treasury securities as collateral). U.S. Treasury notes and bonds have maturities from 2 to 30 years; they have no default risk. Mortgages have maturities up to 30 years. Municipal bonds have maturities of up to thirty years; their interest is exempt from most taxes. Corporate bonds have maturities up to 40 years. Municipal and corporate bonds are subject to default risk. Some preferred stocks have no maturity date; some do have a specific maturity date. Common stock has no maturity date, and is riskier than preferred stock. n.

What is a financial institution? List some financial institutions. Answer: A financial institution acts as an intermediary between providers of funds and users of funds and provides; in other words, a financial institution facilitates transfers of capital. There are many types of financial institutions, including commercial banks, savings and loan associations (S&Ls), mutual savings banks, credit unions, life insurance companies, mutual fund companies, pension funds, hedge funds, and private equity funds. Following are definitions of these institutions: 1.

Commercial banks: Financial intermediaries whose primary purpose is to take deposits and make loans to businesses and individuals.

Savings and loan associations (S&Ls): Financial institutions that accept deposits from small savers and lend this money to homeowners and consumers.

Mutual savings banks: Similar to S&Ls, but they operate primarily in the northeastern states.

Credit unions: Cooperative associations that take deposits from members and then make loans only to other members, generally for auto purchases, home-improvement loans, and home mortgages.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Life insurance companies: Take premiums from customers, invest these funds in stocks, bonds, real estate, and mortgages, and then make payments to beneficiaries.

Mutual fund companies: Corporations that sell shares in the fund and use the proceeds to buy stocks, long-term bonds, or short-term debt instruments. The resulting dividends, interest, and capital gains are distributed to the fund’s shareholders after the deduction of operating expenses. Some funds specialize in certain types of securities, such as growth stocks, international stocks, or municipal bonds.

Pension funds: Retirement plans funded completely or partially by a corporation or government agency.

Hedge funds: Raise money from institutional investors and a relatively small number of high-net-worth individuals, and then engage in a variety of investment activities.

Private equity funds: Raise money from institutional investors and a relatively small number of highnet-worth individuals. Private equity funds primarily invest in stock of private companies.

What is a financial market? What are some types of financial markets? Answer: A market is a method of exchanging one asset (usually cash) for another asset. Some types of markets are: physical assets vs. financial assets; spot versus future markets; money versus capital markets; and primary versus secondary markets. Physical asset markets include markets for such products as wheat, autos, real estate, computers, and machinery. Financial asset markets included stock markets, bond markets, and other means of trading financial instruments. Spot markets require payment when the transaction takes place, such as purchases of groceries, stocks, and bonds. Future markets are for futures contracts in which no money changes hands until the price of the underlying asset changes. There are futures markets for many commodities, including agricultural products like wheat or oil. Financial assets with an original maturity of less than a year are traded in money markets; those with an original maturity of more than a year trade in capital markets. Primary markets are where new securities are created and first sold. Secondary markets are for trading securities that have already been created.

What are some differences between primary markets and secondary markets? Why are secondary markets important? Answer: Primary markets are where new securities are created and sold, providing cash to the issuer of the security. For example, new shares of stock are created when a company has an IPO. New shares can also be created if a company sells additional shares to the public (this is called a secondary offering). Another example of primary markets is a company issuing (i.e., selling) bonds. After a new security has been created, it can be sold in a secondary market. For example, previously issued shares of stock are traded on stock exchanges. Notice that the original issuer of the security is not involved in a secondary market transaction. One reason that secondary markets are important is that they allow entrepreneurs to reap rewards for their efforts in creating a company. They can do this by selling some shares of their own stock in the secondary market. Then they can use the cash they receive from the secondary market transaction for other purposes. For example, they might buy a new car, buy a better house, or go on a scuba diving trip. Secondary markets also allow investors to buy or sell stock if they need a change. For example, many investors have a target for the percent of their wealth that is invested in stock or bonds. If stock prices increase, investors can use secondary markets to rebalance their portfolios to get back to the target.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Secondary markets allow investors to determine the value of their investments by looking at current prices of stocks.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

What are the three major U.S. stock exchanges? Compare and contrast them with respect to the number of listed stocks and the market values of the listed stocks. Answer: The three major exchanges are the New York Stock Exchange (NYSE), NASDAQ, and the NYSE American Exchange. Their listing and market value of listings are shown below.

Exchange

Market Value of Listings (Trillions)

Percent of Total Market Value

NYSE

2,199

$36.0

57.0%

NASDAQ

2,027

27.1

42.8%

0.1

0.2%

4,288

$63.2

100%

NYSE American Total r.

Number of Listings

What is a full-service brokerage account? What are two other types of brokerage accounts? Answer: A client at a full-service broker usually can call a person at the firm to discuss their portfolio and get advice. A client with a full-service broker usually must pay fees to open the account, pay annual fees maintain the account, and pay additional commissions for each stock purchase of sale. The minimum balance required for a full-service brokerage account is usually between $50,000 to $100,000. Two other types of accounts are online-only accounts and robo-advisor accounts. An online-only account is much less expensive than a full-service account and requires a much lower minimum balance, but it offers significantly fewer services. A customer doesn’t have access to a personal broker, but an online account has lots of educational material available for its account holders. Another type of online-only account provides a robo-advisor, which is a fully automated computer system that automatically makes trades on a client’s behalf based on the answers to a detailed questionnaire that the client filled out that has questions about the client’s financial situation, goals, and degrees of risk tolerance.

What are the differences between market orders and limit orders? Explain how orders from buyers and sellers are matched and executed at open outcry auctions, in dealer markets, and by automated trading platforms. Answer: Market orders instruct the broker to transact as quickly as possible at the current price. Limit orders instruct brokers to transact only if a specific situation occurs. For example, buy 100 shares if the price drops to $50 or below during the next two hours. Open outcry auctions have a physical location at which human traders meet face to face and execute trades. For example, there is still some stock trading on the floor of the NYSE. Derivatives and options also trade at physical exchanges. Dealers (i.e., market makers) buy from and sell to clients from an inventory of stocks. Orders are usually, but not always, automatically matched by computers. Automated trading platforms match orders and execute trades automatically.

What is a broker-dealer network? What is an Alternative Trading System (ATS)? What is a Trade Reporting Facility (TRF)? Answer:

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Broker-dealer networks are registered with the SEC but are much less regulated than registered stock exchanges. In a typical broker-dealer network, the broker-dealer purchases the stock being offered for sale by a client and then immediately sells it to another client who wished to buy the stock. Because the brokerdealer is the counterparty to each of the clients, this is called internalization. The broker-dealer must report the transactions, but not any information prior to the trade. Trades in broker-dealer networks are called ―off exchange‖ or over-the-counter (OTC). Trades can be with individuals (called retail trades) or with institutions. Large trades (10,000 shares or more) are called block trades and are sometimes called ―upstairs‖ trades. An alternative trading system (ATS) is a broker-dealer that registers with the SEC as an ATS. An ATS usually has an automated trading platform to match orders from clients, so the owner of the ATS is not always the counterparty, in contrast to a broker-dealer network. The ATS must report trades, but not any pre-trade information. Therefore, an ATS is often called a dark pool. Off-exchange trades are reported to the trade reporting facility (TRF) for the exchange, The situation is very different today. Both exchanges have about the same number of listed stocks: 2,199 for the NYSE and 2,027 for NASDAQ. The total market values of stocks listed on each exchange are also similar: $36 trillion for the NYSE and $27 trillion for NASDAQ. u.

What are the dollar volumes of trading at major stock trading venues, including Trade Reporting Facilities? Answer: Trade reporting facilities have the most dollar volume of trading, as shown in the table below.

Trading Venues

Dollar Volume (Trillions)

Percentage of Dollar Volume

Off-Exchange Trade Reporting Facilities (TRF)

$53

38%

NASDAQ

21%

Intercontinental Exchange

21%

Cboe Global Markets

15%

Other Exchanges

$142

100%

Total

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Solution and Answer Guide CHAPTER 2: FINANCIAL S TATEMENTS , CASH F LOWS, AND TAXES

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS............................................................................. 14 SOLUTIONS TO END-OF-CHAPTER PROBLEMS .......................................................................... 17 Easy Problems 1-9 .................................................................................................................................. 17 Intermediate Problems 10-17 .................................................................................................................. 20 Challenging Problems 18-19................................................................................................................... 25 SOLUTION TO SPREADSHEET PROBLEM ..................................................................................... 29 MINI CASE ............................................................................................................................................... 32

ANSWERS TO END-OF-CHAPTER QUESTIONS 2-1

Define each of the following terms: a. Annual report; balance sheet; income statement b. Common stockholders’ equity, or net worth; retained earnings c. Statement of stockholders’ equity; statement of cash flows d. Depreciation; amortization; EBITDA e. Operating current assets; operating current liabilities; net operating working capital; total net operating capital f. Accounting profit; net cash flow; NOPAT; free cash flow; return on invested capital g. Market Value Added; Economic Value Added h. Progressive tax; taxable income; marginal and average tax rates i. Capital gain or loss; tax loss carryforward j. Improper accumulation; S corporation Answer: a. The annual report is a report issued annually by a corporation to its stockholders. It contains basic financial statements, as well as management’s opinion of the past year’s operations and the firm’s future prospects. A firm’s balance sheet is a statement of the firm’s financial position at a specific point in time. It specifically lists the firm’s assets on the left-hand side of the balance sheet, while the right-hand side shows its liabilities and equity, or the claims against these assets. An income statement is a statement summarizing the firm’s revenues and expenses over an accounting period. Net sales are shown at the top of each statement, after which various costs, including income taxes, are subtracted to obtain the net income available to common stockholders. The bottom of the statement reports earnings and dividends per share. b.

Common stockholders’ equity (net worth) is the capital supplied by common stockholders–capital stock, paid-in capital, retained earnings, and, occasionally, certain reserves. Paid-in capital is the difference between the stock’s par value and what stockholders paid when they bought newly issued

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shares. Retained earnings is the portion of the firm’s earnings that have been saved instead of paying out as dividends. c.

The statement of stockholders’ equity shows how much of the firm’s earnings were retained in the business rather than paid out in dividends. It also shows the resulting balance of the retained earnings account and the stockholders’ equity account. Note that retained earnings represents a claim against assets, not assets per se. Firms retain earnings primarily to expand the business, not to accumulate cash in a bank account. The statement of cash flows reports the impact of a firm’s operating, investing, and financing activities on cash flows over an accounting period. It shows the inflow and outflow of the cash occurred in an accounting year.

Depreciation is a non-cash expense against tangible assets, such as buildings or machines. It is taken for the purpose of showing an asset’s estimated dollar cost of the capital equipment used up in the production process. Amortization is a non-cash expense against intangible assets, such as goodwill. EBITDA is earnings before interest, taxes, depreciation, and amortization.

Operating current assets are the current assets used to support operating activities, such as cash, accounts receivable, and inventory. It does not include short-term investments. Operating current liabilities are the current liabilities that are a natural consequence of the firm’s operations, such as accounts payable and accruals. It does not include notes payable or any other short-term debt that charges interest. Net operating working capital is operating current assets minus operating current liabilities. Total net operating capital is sum of net operating working capital and operating longterm assets, such as net plant and equipment. Operating capital also is equal to the net amount of capital raised from investors. This is the amount of interest-bearing debt plus preferred stock plus common equity minus short-term investments.

Accounting profit is a firm’s net income as reported on its income statement. Net cash flow, as opposed to accounting net income, is the sum of net income plus non-cash adjustments. NOPAT (net operating profit after taxes), is the amount of profit a company would generate if it had no debt and no financial assets. Free cash flow is the cash flow actually available for distribution to investors after the company has made all investments in fixed assets and working capital necessary to sustain ongoing operations. Return on invested capital is equal to NOPAT divided by total net operating capital. It shows the rate of return that is generated by assets.

Market value added is the difference between the market value of the firm (i.e., the sum of the market value of common equity, the market value of debt, and the market value of preferred stock) and the book value of the firm’s common equity, debt, and preferred stock. If the book values of debt and preferred stock are equal to their market values, then MVA is also equal to the difference between the market value of equity and the amount of equity capital that investors supplied. Economic value added represents the residual income that remains after the cost of all capital, including equity capital, has been deducted.

A progressive tax means the higher one’s income, the larger the percentage paid in taxes. Taxable income is defined as gross income less a set of exemptions and deductions which are spelled out in the instructions to the tax forms individuals must file. Marginal tax rate is defined as the tax rate on the last unit of income. Average tax rate is calculated by taking the total amount of tax paid divided by taxable income.

Capital gain (loss) is the profit (loss) from the sale of a capital asset for more (less) than its purchase price. Ordinary corporate operating losses can be carried backward for 2 years forward for indefinitely and used to offset future taxable income.

Improper accumulation is the retention of earnings by a business for the purpose of enabling stockholders to avoid personal income taxes on dividends. An S corporation is a small corporation

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which, under Subchapter S of the Internal Revenue Code, elects to be taxed as a proprietorship or a partnership yet retains limited liability and other benefits of the corporate form of organization. 2-2

What four statements are contained in most annual reports? Answer: The four financial statements contained in most annual reports are the balance sheet, income statement, statement of stockholders’ equity, and statement of cash flows.

2-3

If a ―typical‖ firm reports $20 million of retained earnings on its balance sheet, can the firm definitely pay a $20 million cash dividend? Answer: No, because the $20 million of retained earnings doesn’t mean the company has $20 million in cash. The retained earnings figure represents cumulative amount of net income that the firm has not paid out as dividends during its entire history. Thus, most of the reinvested earnings were probably spent on the firm’s operating assets, such as buildings and equipment.

2-4

Explain the following statement: ―Whereas the balance sheet can be thought of as a snapshot of the firm’s financial position at a point in time, the income statement reports on operations over a period of time.‖ Answer: The income statement shows the amount sales, costs, taxes, net income, and other items that have occurred during a specific time interval, such as a year, quarter, or month. For example, it would show the interest expense that a company paid in a year. In contrast, the balance sheet reports the actual amount of cash, inventory, fixed assets, and other assets that a company owns on a specific date. It also shows the amounts of current liabilities, debt, and other liabilities as of a specific date. For example, it might show the balance of accounts payable on the date the balance sheet was constructed.

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2-5

What is operating capital, and why is it important? Answer: Operating capital is the amount of interest-bearing debt, preferred stock, and common equity used to acquire the company’s net operating assets. Without this capital, a firm cannot exist, as there is no source of funds with which to finance operations.

2-6

Explain the difference between NOPAT and net income. Which is a better measure of the performance of a company’s operations? Answer: NOPAT is the amount of net income a company would generate if it had no debt and held no financial assets. NOPAT is a better measure of the performance of a company’s operations because debt lowers income. In order to get a true reflection of a company’s operating performance, one would want to take out debt to get a clearer picture of the situation.

2-7

What is free cash flow (FCF)? Why is it the most important measure of cash flow? Answer: Free cash flow is the cash flow actually available for distribution to investors after the company has made all the investments in fixed assets and working capital necessary to sustain ongoing operations. It is the most important measure of cash flows because it shows the exact amount available to all investors.

2-8

Explain the differences between net cash flow, cash flow from operations (also called operating cash flow), and free cash flow. Answer: Net cash flow is net income plus non-cash expenses less non-cash income. Usually, this amounts to net income plus depreciation. It is an adjustment to net income that reflect non-cash items. Cash flow from operations is the cash flow given in the operating section of the statement of cash flows. It also adjusts net income for depreciation and other non-cash expenses but also adjusts for the required investment in current assets less cash provided by operating current liabilities. So, it extends the definition of cash flow to include some, but not all investments. Free cash flow is NOPAT minus investment in operating assets. FCC is different from net cash flow and operating cash flow as it starts with EBIT (not net income) and adjusts it for investment in all net operating assets (not just the short-term assets like in operating cash flow).

2-9

If you were starting a business, what tax considerations might cause you to prefer to set it up as a proprietorship or a partnership rather than as a corporation? Answer: If the business were organized as a partnership or a proprietorship, its income could be passed to the owners without being subject to taxation at the business level. Also, if you expected to have losses for a few years while the company was getting started, if you were not incorporated, and if you had outside income, the business losses can be used to offset your other income and reduce your total tax bill. These factors would lead you to not incorporate the business. An alternative would be to organize it as an S Corporation, if requirements are met.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1-9 2-1

Personal After-Tax Yield. An investor recently purchased a corporate bond that yields 7.68%. The investor is in the 25% federal-plus-state tax bracket. What is the bond’s after-tax yield to the investor?

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Solution: Corporate yield = 7.68%; Tax = 25% After Tax yield = (Pre-tax yield) (1 – Tax) = 7.68%(0.75) = 5.76% 2-2

Personal After-Tax Yield. Corporate bonds issued by Johnson Corporation currently yield 8.0%. Municipal bonds of equal risk currently yield 5.5%. At what personal tax rate would an investor be indifferent between these two bonds? Solution: Corporate bond yields 8%. Municipal bond yields 6%.

Equivalent pretax yield  Yield on municipal bond on taxable bond (1  Tax) 8% 

5.5% (1  T )

0.08  0.08T  0.055 0.08T  0.025 T  .3125  31.25%. 2-3

Income Statement. Holly's Art Galleries recently reported $7.9 million of net income. Its EBIT was $13 million, and its federal tax rate was 21% (ignore any possible state corporate taxes). What was its interest expense? (Hint: Write out the headings for an income statement and then fill in the known values. Then divide $7.9 million net income by 1 – T = 0.79 to find the pre-tax income. The difference between EBIT and taxable income must be the interest expense. Use this procedure to work some of the other problems.) Solution: NI = $7,900,000; EBIT = $13,000,000; T = 21%; Interest = ? Set up an income statement, plug in the given values, and work in the order of the steps shown below. (As with most problems, there are alternative ways of solving the problem.

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EBIT = $13,000,000 (3)

(Given)

−Interest= 3,000,000 EBT =$10,000,000

(1) (2)

EBT = $10,000,000

NI = EBT(1 − T)  EBT =

NI (1  T)

$7,900,000

 $10,000,000

0.79

−Taxes (21%)= 2,100,000 = EBT(T)= $10,000,000) (0.21) = $2,100,000. NI = $7,900,000

(Given)

More directly, use algebra to determine: Interest = EBIT – [NI/ (1 – T)] = $13,000,000 − $7,900,000/ (1 − 0.21) = $3,000,000. 2-4

Income Statement. Nicholas Health Care Systems recently reported an EBITDA of $25.0 million and net income of $15.8 million. It had $2.0 million of interest expense, and its federal tax rate was 21% (ignore any possible state corporate taxes). What was its charge for depreciation and amortization? Solution: EBITDA = $25,000,000; NI = $15,800,000; Int = $2,000,000; T = 21% ; D&A = ? Set up an income statement, plug in the given values, and work in the order of the steps shown below. (As with most problems, there are alternative ways of solving the problem. EBITDA = $25,000,000

(Given)

(4)

−D&A = 3,000,000

EBITDA – D&A = EBIT  D&A = EBITDA – EBIT

(3)

EBIT

= $22,000,000

EBIT = EBT + Int = $20,000,000 + $2,000,000

−Int

= 2,000,000

(Given)

EBT

= $20,000,000

NI = EBT(1 − T)  EBT =

(1)

(2) −Taxes (21%) NI

NI (1  T)

$15, 800, 000

= $20, 000, 000

0.79

= 4,200,000 = $15,800,000

(Given)

More directly, D&A = EBITDA – Int – (NI/ (1 – T)) = $25,000,000 – $2,000,000 – ($15,800,000/ (1 – 0.21)) = $3,000,000. 2-5

Net Cash Flow. Kendall Corners Inc. recently reported net income of $3.1 million and depreciation of $500,000. What was its net cash flow? Assume it had no amortization expense. Solution: NI = $3,100,000; DEP = $500,000; AMORT = 0 ; NCF = ? NCF = NI + DEP and AMORT = $3,100,000 + $500,000 = $3,600,000.

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2-6

Statement of Retained Earnings. In its most recent financial statements, Del-Castillo Inc. reported $70 million of net income and $900 million of retained earnings. The previous retained earnings were $855 million. How much in dividends did the firm pay to shareholders during the year? Solution: NI = $70,000,000; R/EY/E = $900,000,000; R/EB/Y = $855,000,000; Dividends =? R/EB/Y + NI – Div = R/EY/E $855,000,000 + $70,000,000 – Div = $900,000,000 $925,000,000 – Div = $900,000,000 $25,000,000 = Div

2-7

Net Operating Profit after Taxes (NOPAT). Zucker Inc. recently reported $4 million in earnings before interest and taxes (EBIT). Its federal-plus-state tax rate is 25%. What is its net operating profit after taxes (NOPAT)? Solution: NOPAT = EBIT (1 – T) = $4,000,000(1 – 0.25) = $3,000,000.

2-8

Total Net Operating Capital. Jenn Translation (JT) Inc. reported $10 million in operating current assets, $15 million in net fixed assets, and $3 million in operating current liabilities. How much total net operating capital does JT have? Solution: Total net operating capital = Net fixed assets + Net operating working capital = Net fixed assets + (Operating CA – Operating CL) = $15,000,000 + ($10,000,000 – $3,000,000) = $22,000,000.

2-9

Free Cash Flow (FCF). Carter Swimming Pools has $16 million in net operating profit after taxes (NOPAT) in the current year. Carter has $12 million in total net operating assets in the current year and had $10 million in the previous year. What is its free cash flow? Solution: Free cash flow = NOPAT – Net investment in total operating capital = NOPAT – (Total net operating capital in current year – Total net operating capital in previous year) = $16,000,000 – ($12,000,000 − $10,000,000) = $14,000,000.

INTERMEDIATE PROBLEMS 10-17 2-10 Corporate Tax Liability. The Talley Corporation had taxable operating income of $365,000 (i.e., earnings from operating revenues minus all operating costs). Talley also had (1) interest charges of $50,000, (2) dividends received of $15,000, and (3) dividends paid of $25,000. Its federal tax rate was 21% (ignore any possible state corporate taxes). Recall that 50% of dividends received are tax exempt. What is the taxable income? What is the tax expense? What is the after-tax income?

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Solution: Pre-tax operating earnings

$365,000

Less: Interest deduction

50,000

Plus: Taxable dividends received

Taxable income

7,500 $322,500

For a corporation, 50% of dividends received are excluded from taxes; therefore, taxable dividends are calculated as $15,000(1 – 0.5) = $7,500. Tax expense = 21%($322,500) = $67,725.00. After-tax income: Taxable income

$322,500.00

Minus taxes

67,725.00

Net income before non-taxable dividends Plus taxable dividends received

Net income

$254,775.00 7,500.00 $262,275.00

Non-taxable dividends are calculated as $15,000 − $7,500 = $7,500.

2-11 Corporate Tax Liability. The Wendt Corporation reported $50 million of taxable income. Its federal tax rate was 21% (ignore any possible state corporate taxes). a. What is the company’s federal income tax bill for the year? b. Assume the firm receives an additional $1 million of interest income from some bonds it owns. What is the additional tax on this interest income? c. Now assume that Wendt does not receive the interest income but does receive an additional $1 million as dividends on some stock it owns. Recall that 50% of dividends received are tax exempt. What is the additional tax on this dividend income? Solution: a. Tax = $50,000,000)(0.21) = $10,500,000. b.

Tax = $1,000,000(0.21) = $210,000.

Tax = ($1,000,000)(1 − 0.50)(0.21) = $105,000.

2-12 Corporate After-Tax Yield. The Shrieves Corporation has $10,000 that it plans to invest in marketable securities. It is choosing among AT&T bonds (which yield 6.6%), AT&T preferred stock (with a dividend yield of 6.0%), and State of Florida municipal bonds (which yield 5% but are not taxable). The federal tax rate is 21% (ignore any possible state corporate taxes). Recall that 50% of dividends received are tax exempt. Find the after-tax rates of return on all three securities after paying federal corporate taxes. Solution: A-T yield on AT&T bond = 6.6% − Taxes = 6.6% − 6.6%(0.21) = 5.214%. Check: Invest $10,000 @ 6.6% = $660 interest. Pay 21% tax, so A-T income = $660(1 − T) = $660(0.79) = $521.4. A-T rate of return = $521.40/$10,000 = 5.214%. A-T yield on AT&T preferred stock:

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A-T yield = 6% − Taxes = 6% − (50%)(6%)(0.21) = 6% − 0.630% = 5.370%. A-T yield on FLA bond = 5.000%. Therefore, invest in AT&T preferred stock. 2-13 Net Cash Flows. The Moore Corporation has operating income (EBIT) of $750,000. Its depreciation expense is $200,000. Moore is 100% equity financed. The federal tax rate is 21% (ignore any possible state corporate taxes). What is the company’s net income? What is its net cash flow? Solution: EBIT = $750,000; DEP = $200,000; 100% Equity; T = 21% Set up an income statement, plug in the given values, and work in the order of the steps shown below. (As with most problems, there are alternative ways of solving the problem.) EBIT Interest

$750,000 0

EBT

$750,000

Taxes (21%)

157,500

$592,500

Given No debt with 100% equity

NCF = NI + DEP = $592,500 + $200,000 = $792,500. 2-14 Income and Cash Flow Analysis. The Berndt Corporation expects to have sales of $12 million. Costs other than depreciation are expected to be 75% of sales, and depreciation is expected to be $1.5 million. All sales revenues will be collected in cash, and costs other than depreciation must be paid for during the year. The federal tax rate is 21% (ignore any possible state corporate taxes). Berndt has no debt. a. Set up an income statement. What is Berndt’s expected net income? Its expected net cash flow? b. Suppose Congress changed the tax laws so that Berndt’s depreciation expenses doubled. No changes in operations occurred. What would happen to reported profit and to net cash flow? c. d.

Now suppose that Congress changed the tax laws such that, instead of doubling Berndt’s depreciation, it was reduced by 50%. How would profit and net cash flow be affected? If this were your company, would you prefer Congress to cause your depreciation expense to be doubled or halved? Why?

Solution: a.

Sales revenues

Income Statement

$12,000,000 Given

Costs except depreciation

9,000,000 = 75%($12,000,000)

EBITDA

3,000,000

Interest

Depreciation EBT Taxes (21%)

1,500,000 Given $ 1,500,000 = Sales – (cost except depr) – depr 315,000

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Sales revenues

$12,000,000 Given

Net income

$ 1,185,000

Add back depreciation

1,500,000

Net cash flow b.

$ 2,685,000

If depreciation doubled, depreciation would increase to 2($1,500,000) = $3,000,000. Taxable income (EBT) would fall EBITDA – Depr = $3,000,000 – $3,000,000 = 0; taxes would be zero. Thus, net income would decrease to zero, but net cash flow would rise to NI + Depr = $0 + $3,000,000. The company would save $315,000 in taxes, thus increasing its cash flow. Alternatively: ∆CF = T(∆Depreciation) = 0.21($1,500,000) = $315,000. Net cash flow = Previous net cash flow + ∆CF = $2,685,000 + $315,000 = $3,000,000.

If depreciation were halved, depreciation would fall to 0.5($1,500,000) = $750,000. Taxable income (EBT) would increase to EBITDA – Depr = $3,000,000 – $750,000 = $2,250,000; taxes would increase to T(EBT) = 0.21($2,250,000) = $472,500 Therefore, net income would rise to EBT – Tax = $2,250,000 – $472,500 = $1,177,500. However, net cash flow would fall to NI + Depr = $1,177,500 + $750,000 = $2,527,500.

You should prefer to have higher depreciation charges and higher cash flows. Net cash flows are the funds that are available to the owners to withdraw from the firm and, therefore, cash flows should be more important to them than net income.

2-15 Net Operating Profit after Tax (NOPAT). Use the following income statement of Elliott Game Theory Consulting to determine its net operating profit after taxes (NOPAT). Use 25% as the tax rate.

Elliot Game Theory Consulting: Income Statement for Year Ending December 31 2023 Sales

$800,000

Operating costs excluding depreciation

700,000

Depreciation and amortization

20,000

Earnings before interest and taxes Less interest Pre-tax income Taxes (25%) Net income available to common stockholders

$ 80,000 2,000 $ 78,000 19,500 $ 58,500

Solution: NOPAT = EBIT(1 – T) = $80,000(1 – 0.25) = $60,000. 2-16 Net Operating Working Capital (NOWC). Using the following balance sheets of Mimi’s Gymnastics Inc., what is the net operating working capital (NOWC) for 2023?

Mimi’s Gymnastics Inc.: Balance Sheets as of December 31 (Millions of Dollars)

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2023 Assets Cash

Short-term investments

110

Accounts receivable

1,200

Inventories

900

Total current assets

$2,300

Net plant and equipment

2,200

Total assets

$4,500

Liabilities and Equity Accounts payable

600

Accruals

200

Notes payable

180

Total current liabilities Long-term debt Total liabilities

980 800

$ 1,780

Common stock

2,200

Retained earnings

520

Total common equity

$ 2,720

Total liabilities and equity

$4,500

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Solution: NOWC = Operating CA – Operating CL = (Cash + AR + INV) – (AP + Accruals) = ($90 + $1,200 + $900) – ($600 + $200) = $1,390 million. 2-17 Investment in Total Net Operating Capital. Athenian Venues Inc. just reported the following selected portion of its financial statements for the end of 2023. Your assistant has already calculated the 2023 end-of-year net operating working capital (NOWC) from the full set of financial statements (not shown here), which is $13 million. The total net operating capital for 2022 was $50 million. What was the 2023 net investment in operating capital?

Athenian Venues Inc.: Selected Balance Sheet Information as of December 31 (Millions of Dollars) Assets

2023

Cash

$ 1

Short-term investments

Accounts receivable

Inventories Total current assets

11 $24

Net plant and equipment

Total assets

$75

Solution: Net investment in operating capital = (NOWC + Op LT assets) – (Total net Op Cap. in previous year) = ($13 + $51) – ($50) = $14 million.

CHALLENGING PROBLEMS 18-19 2-18 Free Cash Flows. Rhodes Corporation’s financial statements are shown after part f. Suppose the federalplus-state tax corporate tax is 25%. Answer the following questions: a. What is the net operating profit after taxes (NOPAT) for 2023? b. What are the amounts of net operating working capital for both years? c. What are the amounts of total net operating capital for both years? d. What is the free cash flow for 2023? e. What is the ROIC for 2023? f. How much of the FCF did Rhodes use for each of the following purposes: after-tax interest, net debt repayments, dividends, net stock repurchases, and net purchases of short-term investments? (Hint: Remember that a net use can be negative.)

Rhodes Corporation: Income Statements for Year Ending December 31 (Millions of Dollars)

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Sales

2023

2022

$11,000

$10,000

9,612

8,728

380

360

Operating costs excluding depreciation Depreciation and amortization Earnings before interest and taxes

$ 1,008

Less interest Pre-tax income

Taxes (25%)

912

120

100

888

$812

222

203

Net income available to common stockholders

666

609

Common dividends

202

200

Rhodes Corporation: Balance Sheets as of December 31 (Millions of Dollars) 2023

2022

Assets

Cash

550

500

Short-term investments

110

100

Accounts receivable

2,750

2,500

Inventories

1,650

1,500

Total current assets

$5,060

$4,600

Net plant and equipment

3,850

3,500

$ 8,910

$ 8,100

$ 1,100

$ 1,000

Accruals

550

500

Notes payable

384

200

$2,034

$ 1,700

1,100

1,000

$ 3,134

$ 2,700

Common stock

4,312

4,400

Retained earnings

1,464

1,000

Total common equity

$ 5,776

$5,400

Total liabilities and equity

$ 8,910

$ 8,100

Total assets Liabilities and Equity

Accounts payable

Total current liabilities Long-term debt Total liabilities

Solution: a.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

2023 EBIT

$1,008

x (1 − Tax rate)

75.0%

Net operating profit after taxes (NOPAT)

$ 756

2023

2022

$ 550

$ 500

+ Accounts receivable

2,750

2,500

+ Inventories

1,650

1,500

Operating current assets

$4,950

$4,500

Accounts payable

$ 1,100

$ 1,000

550

500

Operating current liabilities

$ 1,650

$ 1,500

Operating current assets

$4,950

$4,500

− Operating current liabilities

1,650

1,500

$3,300

$3,000

2023

2022

$3,300

$3,000

3,850

3,500

$ 7,150

$6,500

Cash

+ Accruals

Net operating working capital (NOWC) c.

Net operating working capital (NOWC) + Net plant and equipment Total net operating capital d.

2023 NOPAT − Investment in total net operating capital Free cash flow

$756 650 $ 106

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

2023 NOPAT

$756

÷ Total net operating capital

7,150

Return on invested capital (ROIC)

10.57%

Uses of FCF

2023

After-tax interest payment =

$ 90

Reduction (increase) in debt =

-$284

Payment of dividends =

$202

Repurchase (Issue) stock =

$ 88

Purchase (Sale) of short-term investments =

$ 10

Total uses of FCF =

$ 106

2-19 Loss Carryforward. The Bookbinder Company had $500,000 cumulative operating losses prior to the beginning of last year. It had $100,000 in pre-tax earnings last year before using the past operating losses and has $300,000 in the current year before using any past operating losses. It projects $350,000 pre-tax earnings next year. a. How much taxable income was there last year? How much, if any, cumulative losses remained at the end of the last year? b. What is the taxable income in the current year? How much, if any, cumulative losses remain at the end of the current year? c. What is the projected taxable income for next year? How much, if any, cumulative losses are projected to remain at the end of next year? Solution: a. Last year:

Cumulative losses prior to beginning of last year =

$500,000

Last year's pre-tax earnings =

$ 100,000

Amount of last year's pre-tax earnings that may be offset by past operating losses = MIN[80% × $100,000, $500,000) =

$ 80,000

Last year's taxable earnings after offset =

$ 20,000

Remaining cumulative losses = MAX[0,Prior cumulative losses – amount of offset] =

$420,000

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Current year:

Cumulative losses prior to beginning of current year =

$420,000

Current year's pre-tax earnings =

$300,000

Amount of current year's pre-tax earnings that may be offset by past operating losses = MIN[80% × $300,000, $420,000) =

$240,000

Last year's taxable earnings after offset =

$ 60,000

Remaining cumulative losses = MAX[0,Prior cumulative losses – amount of offset] =

$ 180,000

Projections for next year:

Cumulative losses prior to end of next year =

$ 180,000

Next year's projected pre-tax earnings =

$350,000

Amount of next year's pre-tax earnings that may be offset by past operating losses = MIN[80% × $350,000, $180,000) =

$ 180,000

Next year's projected taxable income after offset =

$ 170,000

Remaining cumulative losses = MAX[0,Prior cumulative losses – amount of offset] =

SOLUTION TO SPREADSHEET PROBLEM 2-20 Build a Model: Financial Statements. Begin with the partial model in the file Ch02 P20 Build a Model.xlsx on the textbook’s website. a. Britton String Corp. manufactures specialty strings for musical instruments and tennis racquets. Its most recent sales were $880 million; operating costs (excluding depreciation) were equal to 85% of sales; net fixed assets were $300 million; depreciation amounted to 10% of net fixed assets; interest expenses were $22 million; the state-plus-federal corporate tax rate was 25%; and it paid 40% of its net income out in dividends. Given this information, construct its income statement. Also calculate total dividends and the addition to retained earnings. Report all dollar figures in millions. b. Britton String’s partial balance sheets follow. Britton issued $36 million of new common stock in the most recent year. Using this information and the results from part a, fill in the missing values for common stock, retained earnings, total common equity, and total liabilities and equity.

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Britton String Corp.: Balance Sheets as of December 31 (Millions of Dollars) 2023

2022

Cash and cash equivalents

$ 70

$ 60

Short-term investments

Accounts receivable

120

140

Inventories

264

196

$ 500

$438

Net fixed assets

300

262

Total assets

$800

$700

$ 73

$ 64

Accruals

Notes payable

$ 152

$ 163

217

178

$ 369

$ 341

Common stock

285

249

Retained earnings

146

110

Total common equity

$ 431

$359

Total liabilities and equity

$800

$700

Assets

Total current assets

Liabilities and Equity Accounts payable

Total current liabilities Long-term debt Total liabilities

Construct the statement of cash flows for 2023.

Solution: The detailed solution for the spreadsheet problem, Ch02 P20 Build a Model Solution.xlsx is available at the textbook’s website. 2-21 Build a Model: Free Cash Flows, EVA, and MVA. Begin with the partial model in the file Ch02 P21 Build a Model.xlsx on the textbook’s website. a. Using the financial statements shown here for Lan & Chen Technologies, calculate net operating working capital, total net operating capital, net operating profit after taxes, free cash flow, and return on invested capital for 2023. The federal-plus-state tax rate is 25%. b. Assume there were 15 million shares outstanding at the end of 2023, the year-end closing stock price was $65 per share, and the after-tax cost of capital was 10%. Calculate EVA and MVA for 2023.

Lan & Chen Technologies: Income Statements for Year Ending December 31 (Millions of Dollars) 2023

2022

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

2023

2022

Sales

$945,000

$900,000

Expenses excluding depreciation and amortization

812,700

774,000

$ 132,300

$ 126,000

33,100

31,500

EBIT

$ 99,200

$ 94,500

Interest expense

10,400

8,900

$ 88,800

$85,600

22,200

21,400

Net income

$ 66,600

$ 64,200

Common dividends

$ 43,300

$ 41,230

Addition to retained earnings

$ 23,300

$ 22,970

EBITDA Depreciation and amortization

Pre-tax earnings Taxes (25%)

Lan & Chen Technologies: December 31 Balance Sheets (Millions of Dollars) 2024

2023

$ 47,250

$ 45,000

Short-term investments

3,800

3,600

Accounts receivable

283,500

270,000

Inventories

141,750

135,000

Total current assets

$476,300

$453,600

Net fixed assets

330,750

315,000

$807,050

$768,600

$ 94,500

$ 90,000

Accruals

47,250

45,000

Notes payable

17,400

9,000

$ 159,150

$ 144,000

90,000

Total liabilities Common stock

$ 249,150 444,600

$234,000 444,600

Retained earnings

113,300

90,000

Total common equity

$557,900

$534,600

Total liabilities and equity

$807,050

$768,600

Assets Cash and cash equivalents

Total assets Liabilities and Equity Accounts payable

Total current liabilities Long-term debt

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Solution: The detailed solution for the spreadsheet problem, Ch02 P21 Build a Model Solution.xlsx is available at the textbook’s website.

MINI CASE Jenny Cochran, a graduate of the University of Tennessee with 4 years of experience as an equities analyst, was recently brought in as assistant to the chairman of the board of Computron Industries, a manufacturer of computer components. During the previous year, Computron had doubled its plant capacity, opened new sales offices outside its home territory, and launched an expensive advertising campaign. Cochran was assigned to evaluate the impact of the changes. She began by gathering financial statements and other data. Note: These are available in the file Ch02 Tool Kit.xlsx in the Mini Case tab. Balance Sheets

2022

2023

Assets Cash and equivalents

Short-term investments

100

Accounts receivable

400

520

Inventories

620

820

$ 1,180

$ 1,400

$3,900

$4,820

1,000

1,320

Net plant and equipment

$ 2,900

$ 3,500

Total assets

$4,080

$4,900

$ 300

$ 400

Notes payable

250

Accruals

200

240

$550

$ 890

Long-term bonds

800

1,100

Total liabilities

$ 1,350

$1,990

Common stock

1,000

Retained earnings

1,730

1,910

Total equity

$ 2,730

$ 2,910

$4,080

$4,900

Total current assets Gross fixed assets Less: Accumulated depreciation

Liabilities and Equity Accounts payable

Total current liabilities

Total liabilities and equity

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Income Statement

2022

2023

Net sales

$ 5,500

$6,000

Cost of goods sold (Excluding depr. & amort.)

4,300

4,800

Depreciation and amortizationa

290

320

Other operating expenses

350

420

Total operating costs

$4,940

$5,540

$ 560

$ 460

108

$ 492

$ 352

Taxes (25%)

123

Net Income

$ 369

$ 264

Other Data

2022

2023

Stock price

$50.00

$30.00

100

Earnings before interest and taxes (EBIT) Less interest Pre-tax earnings

Note: a

Computron has no amortization charges.

Shares outstanding Common dividends Tax rate Weighted average cost of capital (WACC)

25%

10.00%

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Statement of Cash Flows

2023

Operating Activities Net Income before preferred dividends

$ 264

Noncash Adjustments Depreciation and amortization

320

Due to Changes in Working Capital Change in accounts receivable

(120)

Change in inventories

(200)

Change in accounts payable

100

Change in accruals

Net cash provided by operating activities

$ 404

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Statement of Cash Flows (continued)

2023

Investing Activities Cash used to acquire fixed assets

$(920)

Change in short-term investments

Net cash provided by investing activities

$(830)

Financing Activities Change in notes payable

$ 200

Change in long-term debt

300

Payment of cash dividends

(84)

Net cash provided by financing activities

$ 416

Net change in cash and equivalents

$ (10)

Cash and securities at beginning of the year Cash and securities at end of the year a.

60 $

What effect did the expansion have on sales and net income? What effect did the expansion have on the asset side of the balance sheet? What effect did it have on liabilities and equity? Answer: Sales increased by $500 million (9% growth), but net income fell by $105 million. Current assets and net plant and equipment each grew by over 20%. Large increases in debt funded the expansion, causing a 59% increase in interest payments.

What do you conclude from the statement of cash flows? Answer: Net CF from operations was positive, but was dragged down by a large net increase in working capital. Net CF from investing was negative even though the firm sold short-term investments. This was because the expenditures in fixed assets were so high. Net CF from financing shows heavy borrowing. Even after borrowing, the cash account fell.

What is free cash flow? Why is it important? What are the five uses of FCF? Answer: FCF is the amount of cash available from operations for distribution to all investors (including stockholders and debtholders) after making the necessary investments to support operations. A company’s value depends upon the amount of FCF it can generate. 1.

Pay interest on debt.

Pay back principal on debt.

Pay dividends.

Buy back stock.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

5. d.

Buy nonoperating assets (e.g., marketable securities, investments in other companies, etc.)

What is Computron’s net operating profit after taxes (NOPAT)? What are operating current assets? What are operating current liabilities? How much net operating working capital and total net operating capital does Computron have? Answer: NOPAT = EBIT(1 − TAX RATE) Current year: NOPAT = 460(1 − 0.25) = $345. Previous year: NOPAT = $420. Operating current assets are the CA needed to support operations. OP CA include: cash, inventory, receivables. OP CA exclude: short-term investments, because these are not a part of operations. Operating current liabilities are the CL resulting as a normal part of operations. OP CL include: accounts payable and accruals. OP CA exclude: notes payable, because this is a source of financing, not a part of operations. NOWC = operating CA – operating CL Current year: NOWC = ($50 + $520 + 820) – ($400 + $240) = $1,390 – $640 = $750. Previous year: NOWC = $580. Total operating working capital = NOWC + net fixed assets. Current year: Operating capital = $750 + $3,500 = $4,250. Previous year: Operating capital = $3,480.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

What is Computron’s free cash flow (FCF)? What are Computron’s ―net uses‖ of its FCF? Answer: FCF = NOPAT − Net investment in capital = $345 − ($4,250 − $3,480) = $345 − $770 = –$425.

Uses of FCF:

After-tax interest payment =

$ 81

Reduction (increase) in debt =

−$500

Payment of dividends =

$ 84

Repurchase (Issue) stock =

Purchase (Sale) of short-term investments =

−$ 90

Total uses of FCF =

−$ 425

Calculate Computron’s return on invested capital (ROIC). Computron has a 10% cost of capital (WACC). What caused the decline in the ROIC? Was it due to operating profitability or capital utilization? Do you think Computron’s growth added value? Answer: ROIC = NOPAT/Total Net operating capital. Current year: ROIC = $345/$4,250 = 8.1%. Previous year: ROIC = 12.1%. Current year: OP = $345/$6,000 = 5.8%. Previous year: OP = 7.0%. Current year: CR = $4,250/$6,000 = 70.8%. Previous year: CR = 58.0%.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

The current ROIC dropped from the previous year. This decline was due to worse operating profitability (5.8% versus 7.0%) and worse capital utilization (CR ratio of 70.8% versus a CR ratio of 58.0%). The ROIC is less than the WACC of 10%. Investors did not get the return they require. Note: high growth usually causes negative FCF (due to investment in capital), but that’s OK if ROIC > WACC. g.

Cochran also has asked you to estimate Computron's economic value added (EVA). She estimates that the after-tax cost of capital was 10% in both years. Answer: EVA = NOPAT − (WACC)(CAPITAL). Current year: EVA = $345 − (0.1)($4,250) = $345 − $425 = –$80. Previous year: EVA = $420 − (0.10)($3,480) = $420 − $348 = $72.

What happened to Computron's market value added (MVA)? Answer: MVA = Market value of the firm − Book value of the firm. Market value = (# shares of stock)(Price per share) + Value of debt. Book value = Total common equity + Value of debt. If the market value of debt is close to the book value of debt, then MVA is market value of equity minus book value of equity. Assume market value of debt equals book value of debt. Current year: Market value of equity = (100)($30.00) = $3,000. Book value of equity = $2,910. MVA = $3,000 − $2,910 = $90. Previous year: MVA = 100($50.00) − $2,730 = $2,270.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

What are the differences between progressive tax rates and flat tax rates? Are U.S. corporate tax rates progressive or flat? Answer: Progressive tax rates increase as taxable income increases. Flat rates do not change as income increases. Corporate tax rates were progressive before 2018, but the 2017 Tax Cuts and Jobs Act changed them to a flat rate. A small corporation with a taxable income of $100,000 pays the same tax rate as a giant corporation with a taxable income of $100 million.

How are corporations taxed on: (1) pre-tax profits from operations (including sales of equipment that it no longer needs), (2) interest received from bank accounts and other investments that pay interest, (3) and capital gains from the sale of a financial security? Answer: The federal tax rate of 21% is applied to the following sources of pre-tax operating profits:

Sales of products to customers.

Services provided to customers.

Capital gains on sales of equipment that the company no longer needs.

What is the corporate net operating loss (NOL) carryforward provision? Answer: Corporations can carry forward operating losses to reduce taxable income in current years: 1.

Applies to cumulative past operating losses.

Carry forward to offset future taxable income and taxes.

Carry forward indefinitely.

Prior to TCJA: Could carry forward only 20 years). Could carry back losses and receive refunds from past paid taxes.

Suppose a company has taxable income of $80 billion. However, the company has $72 billion in prior unused net operating losses. What is the company's taxable income after the carryforward adjustment, the tax on the adjusted income, and any remaining unused prior loss? The corporate tax rate is 25% and the carryforward limitation percentage is 80%. Answer: The maximum amount of loss that can be carried forward in the current year is 80% of the taxable income of $80 billion: 80%($80) = $64 billion. The remaining taxable income after the carryforward adjustment is: $80 − $64 = $16 billion The tax on adjusted profit is: 25%($16) = $4 billion

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

The remaining unused prior loss that can be carried forward is: $72 − $64 = $8 billion. m. A corporation has $50 billion of earnings before interest and taxes (EBIT) and $20 billion in interest expenses this year. How much interest expense can the company deduct from its EBIT in the current year? What happens if the company can't deduct all of its interest expenses in the current year? Answer: Corporations can deduct interest expenses in a single year up to 30% of EBIT. Deduction in current year = 30%($50) = $15 billion. The company started with $20 billion in interest expenses. After deducting $15 billion, the company has $5 billion remaining unused interest expenses ($20 − $15 = $5). It can deduct the remaining unused interest expense in future years, subject to the 30% limitation. n.

Compare the corporate tax treatments of interest that a company pays versus dividends that a company pays. Do the tax treatments cause a company to prefer financing with equity or debt, all else held equal? Answer: Companies can deduct interest payments, subject to the annual limit of 30% of EBIT. However, companies may not deduct dividends. All else held equal, companies have an incentive to finance with debt instead of equity.

How is a company taxed on interest it receives from bank accounts and other financial investments that pay interest? How is a company taxed on a capital gain if it sells a financial security for a profit? If a company owns shares of stock issued by another company, how is the company taxed on dividends it receives from those shares? Answer: A company pays the standard 21% tax rate on interest it receives. It also pays 21% on capital gains from financial investments just like it does on capital gains from sales of operating assets. The tax treatment of dividends is different. Suppose a company pays dividends from its after-tax income. Now suppose a second company owns some shares of the first company’s stock. The dividends that this second company receives are part of its taxable income, so these dividends are taxed as part of the second company’s taxable income. Notice that this is the second time that the original pre-tax income that the first company needed to pay a dividend has been taxed: It was taxed as part of the first company’s taxable income, and it was taxed as part of the second company’s taxable income. Suppose the second company pays a dividend to its shareholders. A shareholder must pay tax on the dividend. This is the third time that a portion of the original company’s income gets taxed: It was taxed as part of the first company’s taxable income, it was taxed as part of the second company’s taxable income, and it is taxed as part of the shareholder’s income. This is called the triple taxation of dividends. To mitigate the triple taxation of dividends, the second company can exclude from its own taxable income 50% of the dividends that it received from the first company.

A company has $40 million in cash and has decided to invest it in another company's bonds or preferred stock, which it considers to be equally risky. The bonds pay an interest rate of 5.4% and the preferred stock pays a dividend rate of 5%. The corporate tax rate is 25%. Which investment has the higher after-tax return?

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Answer: The preferred stock’s total pre-tax dividend payments are: 5%($40) = $2.0 million. To mitigate triple taxation of dividends, 50% of dividends are exempt from taxation. Therefore, only 50%($2.0) = $1.0 million of the dividends will be taxed. The tax on these dividends is 25%($1.0) = $0.25 million. Therefore, the after-tax income from the preferred stock is $2.0 − $0.25 = $1.75 million. The after-tax rate of return is $1.75/$40 = 4.38%. The total interest payments on the bonds equals 5.4%($40) = $2.16 million. The tax on the interest payments equals 25%($2.16) = $0.54 million. The after-tax payments equal $2.16 – $0.54 = $1.62 million. The after-tax rate of return on the bonds is: $1.62/$40 = 4.05%. Therefore, the preferred stock has a higher after-tax return than the bond even though it has a lower pre-tax return. In this example, the after-tax return on the preferred stock is greater than the after-tax return on the bond. An investor would be indifferent between preferred stock and a perpetual bond if they have the same risk and the same after-tax return. Let rd be the expected return on the debt and rps be the expected return on the preferred stock. If both investments are selling at par, then r d and rps the pre-tax expected returns. The interest rate on the bond that produces the same after-tax return as the after-tax return on the preferred stock is: rd = rps + {[(rps )(X)(T)]/(1 – T)}. Applying this formula to this example gives the result: rd = 0.05 + {[(0.05)(0.5)(0.25)]/(1 – 0.25)} = 0.0583 = 5.83%. q.

A corporation has $166 million of taxable income from operations. It also received interest income of $20 million and dividend income of $28 million from an unrelated company. The federal tax rate is 21% and the dividend exclusion rate is 50%. What is the company's federal tax liability? Answer: Calculation of the company’s tax liability: Taxable dividend income = Dividends(1 – Exclusion rate) = $28(1 – 0.5) = $14

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Taxable operating income = $166 million Taxable interest income = $20 million Taxable dividend income = $14 million Total taxable income = $200 million Tax = 21%($200)= $42.0. r.

If a U.S. company has a foreign subsidiary, how are the subsidiary’s profits taxed by the United States? Answer: Foreign profits are earned by a subsidiary of a U.S. company that is located overseas. They are taxed at subsidiary’s legal residence (e.g., Ireland because it has favorable tax laws). Before 2018, they were not taxed by the United States until they were repatriated to the United States, where they were taxed. Therefore, many companies kept their foreign profits overseas rather than bring them to the United States and get taxed. The 2018 TCJA changed this and imposed a 15.5% tax on foreign profits held overseas as cash or cash equivalents. It imposed an 8% tax on foreign profits invested in other ways. Companies can spread the tax out between 2018 and 2025. Now the United States doesn’t tax a U.S. company on foreign profits earned after 2018.

Briefly describe key provisions for personal taxes. Answer: The TCJA made changes to personal taxes for 2018−2025. Unless Congress acts, these changes will expire and the personal tax code will revert to its pre-TCJA form. Following are key provisions in the tax code for individual and married filers. 1.

For most people, ordinary income comes primarily from wages.

The marginal tax rate is the rate applied to the next dollar of taxable income.

There are seven tax brackets. The marginal tax rate for taxable income within a bracket is constant. But as taxable income increases and goes into a higher bracket, the tax rate applied to taxable income within the bracket goes up.

Tax brackets with increasing tax rates cause personal taxes to be progressive, which means that the average tax rate ―progresses‖ upward as taxable income increases. In other words, filers with higher taxable incomes pay higher proportions of their taxable income in taxes.

The top of the first bracket for 2022 is $10,275. Income below this is taxed at 10%. The bottom of the last bracket is $539,900. Income over this is taxed at a rate of 37%. Income within the other brackets is taxed at a rate between 12% and 35%.

Ordinary income consists of salary and wages. Short-term capital gains (assets are owned for less than a year) are taxed like ordinary income.

Assets held for more than 1 year are taxed as long-term gains. If the gain is less than $41,675, then it is taxed at the ordinary income tax rate. There is a 15% tax on long-term gains that are between $41,675 and $459,750. The tax rate for gains over $459,750 is 20%.

The tax on dividends depends on whether it is ―qualified‖ to be taxed as a capital gain or whether it is ―ordinary.‖ (The word ―ordinary‖ has nothing to do with common stock versus preferred stock.)

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Loosely speaking, a qualified gain is one on a stock that was owned for at least 60 days before the dividend was paid and for at least 60 days after the dividend was paid. An ―ordinary‖ dividend is one that is not qualified. An ordinary dividend is taxed as though it were ordinary income. There are exceptions, so be sure to consult a professional tax advisor. t.

Assume that you are in the 24% marginal tax bracket. You have narrowed your investment choices down to municipal bonds yielding 5% or equally risky corporate bonds with a yield of 6.4%. Which one should you choose and why? At what marginal personal tax rate would you be indifferent? Answer: After-tax return income at T = 24%: After-tax interest on corporate bond = 0.064(1 – 0.24) = 0.0486 = 4.86% This is less than the 5% rate on the muni because the muni isn’t taxed. Alternatively, calculate after-tax yields: At what marginal tax rate would you be indifferent? Solve for T in this equation: Muni yield = Corp yield(1 – T) T = 1 – (Muni yield/Corp yield) T = 1 – (5.0%/6.4%) = 21.88%.

Solution and Answer Guide CHAPTER 3: ANALYSIS OF FINANCIAL S TATEMENTS

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS............................................................................. 43 SOLUTIONS TO END-OF-CHAPTER PROBLEMS .......................................................................... 46 Easy Problems 1-5 .................................................................................................................................. 46 Intermediate Problems 6-10 .................................................................................................................... 47 Challenging Problems 11-14................................................................................................................... 50 SOLUTION TO SPREADSHEET PROBLEM ..................................................................................... 56 MINI CASE ............................................................................................................................................... 57

ANSWERS TO END-OF-CHAPTER QUESTIONS 3-1

Define each of the following terms: a. Profitability ratios: profit margin on sales; basic earning power (BEP) ratio; return on total assets (ROA); return on common equity (ROE)

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

b. c. d. e. f. g.

Asset management ratios: inventory turnover ratio; days sales outstanding (DSO); fixed assets turnover ratio; total assets turnover ratio Liquidity ratios: current ratio; quick ratio Financial leverage ratios: debt ratio; times-interest-earned (TIE) ratio; EBITDA coverage ratio Market value ratios: price/earnings (P/E) ratio; price/free cash flow ratio; market/book (M/B) ratio; book value per share Trend analysis; comparative ratio analysis; benchmarking DuPont equation; window dressing; seasonal effects on ratios

Answer: a. A liquidity ratio is a ratio that shows the relationship of a firm’s cash and other current assets to its current liabilities. The current ratio is found by dividing current assets by current liabilities. It indicates the extent to which current liabilities are covered by those assets expected to be converted to cash in the near future. The quick, or acid test, ratio is found by (1) subtracting inventories from current assets and (2) dividing by current liabilities. b.

Asset management ratios are a set of ratios that measure how effectively a firm is managing its assets. The inventory turnover ratio is COGS divided by inventories. It indicates how effective a company is at managing its inventory. A larger turnover rate usually is a sign that a company is doing well at managing its inventory. The days sales outstanding (DSO) ratio is used to appraise accounts receivable and indicates the length of time the firm must wait after making a sale before it receives cash. It is found by dividing receivables by average sales per day. A smaller DSO ratio is preferred, all else equal. However, some companies may give their customers longer to pay as a way to increase sales. The fixed assets turnover ratio measures how effectively the firm uses its plant and equipment. It is the ratio of sales to net fixed assets. In general, a lower ratio is better than a higher ratio. The total assets turnover ratio measures the turnover of all the firm’s assets; it is calculated by dividing sales by total assets. In general, a higher ratio is preferred.

Financial leverage ratios measure the use of debt financing. The debt ratio is the ratio of total debt, which usually is the sum of notes payable and long-term bonds, to total assets, it measures the percentage of assets financed by debtholders. The debt-to-equity ratio is the total debt divided by the total common equity. The times-interest-earned ratio is determined by dividing earnings before interest and taxes by the interest charges. This ratio measures the company’s ability to meet its annual interest costs. It is also called the Interest Coverage Ratio. The EBITDA coverage ratio is similar to the times-interest-earned ratio, but it recognizes that many firms lease assets and also must make sinking fund payments. It is found by adding EBITDA and lease payments then dividing this total by the sum of interest charges, lease payments, and sinking fund payments over one minus the tax rate.

Profitability ratios are a group of ratios, which show the combined effects of liquidity, asset management, and debt on operations. The profit margin on sales, calculated by dividing net income by sales, gives the profit per dollar of sales. Basic earning power is calculated by dividing EBIT by total assets. This ratio shows the raw earning power of the firm’s assets, before the influence of taxes and leverage. Return on total assets is the ratio of net income to total assets. Return on common equity is found by dividing net income by common equity.

Market value ratios relate the firm’s stock price to its earnings and book value per share. The price/earnings ratio is calculated by dividing price per share by earnings per share; this shows how much investors are willing to pay per dollar of reported profits. The price/free cash flow is calculated by dividing price per share by free cash flow per share. This shows how much investors are willing to pay per dollar of free cash flow. Market-to-book ratio is simply the market price per share divided by the book value per share. Book value per share is common equity divided by the number of shares outstanding.

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3-2

Trend analysis begins with comparing past ratios with the present ratios. Because it indicates how a firm’s financial ratios are evolving over time, it can be used to estimate the improvement or deterioration in a company’s financial situation. Comparative ratio analysis shows a firm’s ratios and the same ratios for a group of other compares. This is helpful in determining how well a company is doing relative to its competitors. This type of analysis is also known as benchmarking.

The DuPont equation is a formula that expresses the return on equity ratio as a function of three drivers. These are: (1) the assets turnover ratio, (2) the profit margin, and (3) the amount of financial leverage. It is useful in identifying how much a company’s ROE will change if a company changes its operations and/or its capital structure. Window dressing is a technique employed by firms to make their financial statements look better than they really are. Seasonal factors can distort ratio analysis. For example, at certain times of the year a firm may have high inventories in preparation of a ―season‖ of high sales. Therefore, an inventory turnover ratio taken at this time will be relatively large compared to its ratio during other periods in the year.

Financial ratio analysis is conducted by managers, equity investors, long-term creditors, and short-term creditors. What is the primary emphasis of each of these groups in evaluating ratios?

Answer: The emphasis by the various types of analysts is by no means uniform nor should it be. Management is interested in all types of ratios for two reasons. First, the ratios point out weaknesses that should be strengthened; second, management recognizes that the other parties are interested in all the ratios and that financial appearances must be kept up if the firm is to be regarded highly by creditors and equity investors. Equity investors are interested primarily in profitability, but they examine the other ratios to get information on the riskiness of equity commitments. Long-term creditors are more interested in: (1) the debt ratio, (2) the times-Interest-earned (TIE) ratio, (3) the fixed-charge coverage ratios, and (4) the profitability ratios. Short-term creditors emphasize liquidity and look most carefully at the liquidity ratios. 3-3

Over the past year, M. D. Ryngaert & Co. has realized an increase in its current ratio and a drop in its total assets turnover ratio. However, the company’s sales, quick ratio, and fixed assets turnover ratio have remained constant. What explains these changes? Answer: Given that sales have not changed, a decrease in the total assets turnover ratio means that the company’s assets have increased. Also, the fact that the fixed assets turnover ratio remained constant implies that the company increased its current assets. Since the company’s current ratio increased without a commensurate change in the quick ratio, this means that the company has increased its inventories.

3-4

Profit margins and turnover ratios vary from one industry to another. What differences would you expect to find between a grocery chain and a steel company? Think particularly about the turnover ratios, the profit margin, and the DuPont equation. Answer: Differences in the amounts of assets necessary to generate a dollar of sales cause asset turnover ratios to vary among industries. For example, a steel company needs a greater number of dollars invested in fixed assets to produce a dollar in sales than does a grocery store chain. Also, profit margins and turnover ratios may vary due to differences in the amount of expenses incurred to produce sales. For example, one would expect a grocery store chain to spend more per dollar of sales than does a steel company. Often, a large turnover will be associated with a low profit margin, and vice versa.

3-5

How might (a) seasonal factors and (b) different growth rates distort a comparative ratio analysis? Give some examples. How might these problems be alleviated?

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Answer: a. Cash, receivables, and inventories, as well as current liabilities, vary over the year for firms with seasonal sales patterns. Therefore, those ratios that examine balance sheet figures will vary unless averages (monthly ones are best) are used. b.

3-6

Common equity is determined at a point in time, say December 31 of a particular year. Profits are earned over time, say during that particular year. If a firm is growing rapidly, year-end equity will be much larger than beginning-of-year equity, so the calculated rate of return on equity will be different depending on whether end-of-year, beginning-of-year, or average common equity is used as the denominator. Average common equity is conceptually the best figure to use. In public utility rate cases, people are reported to have deliberately used end-of-year or beginning-of-year equity to make returns on equity appear excessive or inadequate. Similar problems can arise when a firm is being evaluated.

Why is it sometimes misleading to compare a company’s financial ratios with those of other firms that operate in the same industry? Answer: Firms within the same industry may employ different accounting techniques, which make it difficult to compare financial ratios. More fundamentally, comparisons may be misleading if firms in the same industry differ in their other investments. For example, comparing PepsiCo and Coca-Cola may be misleading because apart from their soft drink business, Pepsi also owns other businesses such as FritoLay, Pizza Hut, Taco Bell, and KFC.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1-5 3-1

DSO. Greene Sisters has a DSO of 20 days. The company’s average daily sales are $20,000. What is the level of its accounts receivable? Assume there are 365 days in a year. Solution: DSO = 20 days; ADS = $20,000; AR = ?

AR S 365 AR 20 = $20,000 AR = $400,000. DSO =

3-2

Debt Ratio. Vigo Vacations has $200 million in total assets, $5 million in notes payable, and $25 million in long-term debt. What is the debt ratio? Solution: TA = $200 million, notes payable = $5 million, and LT debt = $25 million. Debt ratio = Debt-to-assets ratio =

3-3

$5  $25 Total debt = = 15%. $200 Total assets

Market/Book Ratio. Winston Watch’s stock price is $75 per share. Winston has $10 billion in total assets. Its balance sheet shows $1 billion in current liabilities, $3 billion in long-term debt, and $6 billion

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in common equity. It has 800 million shares of common stock outstanding. What is Winston’s market/book ratio? Solution: TA = $10,000,000,000; CL = $1,000,000,000; LT debt = $3,000,000,000; CE = $6,000,000,000; Shares outstanding = 800,000,000; P0 = $75; M/B = ? Book value per share =

M/B = 3-4

$6,000,000,000 = $7.50. 800,000,000

$75.00 = 10. $7.50

Price/Earnings Ratio. Reno Revolvers has an EPS of $1.50, a free cash flow per share of $3.00, and a price/free cash flow ratio of 8.0. What is its P/E ratio? Solution: Earnings per share = $1.50; FCF per share = $3.00; P/FCF = 8.0; P/E = ? P/FCF = 8.0 P/$3.00 = 8.0 P = $24.00. P/E = $24.00/$1.50 = 16.0

3-5

ROE. Needham Pharmaceuticals has a profit margin of 3% and an equity multiplier of 2.0. Its sales are $100 million, and it has total assets of $50 million. What is its ROE? Solution: PM = 3%; EM = 2.0; Sales = $100,000,000; Assets = $50,000,000; ROE = ? ROE = PM  TATO  EM = NI/S  S/TA  A/E = 3%  $100,000,00/$50,000,000  2 = 12%.

INTERMEDIATE PROBLEMS 6-10 3-6

DuPont Analysis. Gardial & Son has an ROA of 12%, a 5% profit margin, and a return on equity equal to 20%. What is the company’s total assets turnover? What is the firm’s equity multiplier? Solution: ROA = 12%; PM = 5%; ROE = 20%; S/TA = ?; A/E = ? ROA = NI/A; PM = NI/S; ROE = NI/E ROA = PM  S/TA NI/A = NI/S  S/TA 12% = 5%  S/TA

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S/TA = 2.40. ROE = PM  S/TA  TA/E NI/E = NI/S  S/TA  TA/E 20% = 5%  2.4  TA/E 20% = 12%  TA/E TA/E = 1.67. 3-7

Current and Quick Ratios. Ace Industries has current assets equal to $3 million. The company’s current ratio is 1.5, and its quick ratio is 1.0. What is the firm’s level of current liabilities? What is the firm’s level of inventories? Solution:

CA CA  I nv = 1.5; = 1.0; CL CL

CA = $3,000,000; CL = ?; I = ?

CA = 1.5 CL $3,000,000 = 1.5 CL 1.5CL = $3,000,000 CL = $2,000,000.

CA  Inv = 1.0 CL $3, 000, 000  Inv = 1.0 $2, 000, 000 $3,000,000 – Inv = $2,000,000 Inv = $1,000,000 3-8

Profit Margin and Debt Ratio. Assume you are given the following relationships for the Haslam Corporation: Sales/total assets Return on assets (ROA) Return on equity (ROE)

1.2 4% 7%

Calculate Haslam’s profit margin and liabilities-to-assets ratio. Suppose half its liabilities are in the form of debt. Calculate the debt-to-assets ratio. Solution: We are given ROA = 4%, ROE = 7%, and TAT = Sales/Total assets = 1.2. From DuPont equation: ROA = Profit margin  Total assets turnover 4% = Profit margin (1.2)

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Profit margin = 4%/1.2 = 3.33%. We can also calculate the company’s liabilities-to-assets (L/TA) ratio in a similar manner, given the facts of the problem. We are given ROA = NI/TA and ROE = NI/E. We begin by finding the percentage of assets financed by equity, E/TA:

E  NI  E   1  =    ROA    ROA/ROE TA  TA  NI   ROE 

E = ROA/ROE = 4%/7% = 57.14%. TA By definition, L + E = Total liabilities & Equity = TA. Therefore, the percentage of the firm financed by liabilities is equal to 1 minus the percentage financed by equity:

L E =1− = 1 − 57.14% = 42.86%. TA TA To find the debt-to-total asset (i.e., the debt ratio), begin with the total liabilities-to-assets ratio of 42.86%. We are given that half of the liabilities are debt, so the debt ratio is: Debt ratio = Debt-to-total assets = (0.5)(L/TA) = (0.5)(42.86%) = 21.43%. 3-9

Current and Quick Ratios. The Nelson Company has $1,312,500 in current assets and $525,000 in current liabilities. Its initial inventory level is $375,000, and it will raise funds as additional notes payable and use them to increase inventory. How much can Nelson’s short-term debt (notes payable) increase without pushing its current ratio below 2.0? What will be the firm’s quick ratio after Nelson has raised the maximum amount of short-term funds? Solution: Present current ratio =

$1,312,500 = 2.5. $525,000

Minimum current ratio =

$1,312,500 + Δ NP = 2.0. $525,000 + Δ NP

$1,312,500 + ∆NP = $1,050,000 + 2∆NP ∆NP = $262,500. Short-term debt can increase by a maximum of $262,500 without violating a 2 to 1 current ratio, assuming that the entire increase in notes payable is used to increase current assets. Since we assumed that the additional funds would be used to increase inventory, the inventory account will increase to $637,500, and current assets will total $1,575,000. Quick ratio = ($1,575,000 – $637,500)/$787,500 = $937,500/$787,500 = 1.19. 3-10 Times-Interest-Earned Ratio. The Morrit Corporation has $600,000 of debt outstanding, and it pays an interest rate of 8% annually. Morrit’s annual sales are $3 million, its average tax rate is 25%, and its net profit margin on sales is 3%. If the company does not maintain a TIE ratio of at least 5 to 1, then its bank will refuse to renew the loan, and bankruptcy will result. What is Morrit’s TIE ratio? Solution: TIE = EBIT/INT, so find EBIT and INT.

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Interest = $600,000  0.08 = $48,000. Net income = $3,000,000  0.03 = $90,000. Pre-tax income = $90,000/(1 – T) = $90,000/0.75 = $120,000. EBIT = $120,000 + $48,000 = $168,000. TIE = $168,000/$48,000 = 3.5. The loan will not be renewed and they will go bankrupt!

CHALLENGING PROBLEMS 11-14 3-11 Balance Sheet Analysis. Complete the balance sheet and sales information in the table that follows for J. White Industries, using the following financial data: Total assets turnover: 1.5 Gross profit margin on sales: (Sales – Cost of goods sold)/Sales = 25% Total liabilities-to-assets ratio: 40% Quick ratio: 0.80 Days sales outstanding (based on 365-day year): 36.5 days Inventory turnover ratio: 3.75 Partial Income Statement Information Sales

_______

Cost of goods sold

_______

Balance Sheet Information Cash

_______

Accounts payable

_______

Accounts receivable

_______

Long-term debt

50,000

Inventories

_______

Common stock

_______

Fixed assets

_______

Retained earnings

100,000

Total assets

$400,000

Total liabilities and equity

_______

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Solution: 1. Sales = (1.5)(Total assets) = (1.5)($400,000) = $600,000. 2.

Cost of goods sold = (Sales)(1 – 0.25) = ($600,000)(0.75) = $450,000.

Accounts receivable = (Sales/365)(DSO) = ($600,000/365)(36.5) = $60,000.

Inventory = COGS/3.75 = $450,000/3.75 = $120,000.

TL = (0.40)(Total assets) = (0.40)($400,000) = $160,000.

Total liabilities and equity = Total assets = $400,000. (TA given in problem statement.)

Accounts payable = TL – Long-term debt = $160,000 – $50,000 = $110,000

Common stock = Total liabilities and equity – TL – Retained earnings = $400,000 – $160,000 – $100,000 = $140,000.

Cash + Accounts receivable = (0.80)(Accounts payable) Cash + $60,000 = (0.80)($110,000) Cash = $88,000 – $60,000 = $28,000.

10. Fixed assets = Total assets – (Cash + Accts rec. + Inventories) = $400,000 – ($28,000 + $60,000 + $120,000) = $192,000. 3-12 Comprehensive Ratio Calculations. The Kretovich Company had a quick ratio of 1.4, a current ratio of 3.0, a days sales outstanding of 36.5 days (based on a 365-day year), total current assets of $810,000, and cash and marketable securities of $120,000. What were Kretovich’s annual sales? Solution: 1.

Current assets $810,000 = 3.0 = 3.0 Current liabilities Current liabilities Current liabilities = $810,000/3 = $270,000.

Current assets  Inventories $810,000  Inventories = 1.4  = 1.4 Current liabilities $270,000 Inventories = $810,000 – (1.4)($270,000) = $432,000.

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Current = Cash + Marketable + Accounts + Inventories assets Securities receivable $810,000 = $120,000 + Accounts receivable + $432,000 Accounts receivable = $810,000 − $120,000 − $432,000 = $258,000.

DSO =

Accounts receivable Sales/365

36.5 =

$258,000 Sales /365

Sales = ($258,000  365)/36.5 = $2,580,000. 3-13 Comprehensive Ratio Analysis. The following financial statements show data for Lozano Chip Company and its industry averages. (Note: The statements and other data also are in the file Ch03 Tool Kit.xlsx. They are in the worksheet named Data for Problem 3-13.) a. Calculate the indicated ratios for Lozano. Use the book value of debt for all ratios. b. Construct the extended DuPont equation for both Lozano and the industry. c. Outline Lozano’s strengths and weaknesses as revealed by your analysis. Lozano Chip Company: Balance Sheet as of December 31, 2023 (Thousands of Dollars) Cash

$ 225,000

Accounts payable

Receivables

1,575,000

Notes payable

100,000

Inventories

1,125,000

Other current liabilities

525,000

Total current assets

$2,925,000

Total current liabilities

$1,225,000

Net fixed assets

1,350,000

Long-term debt

400,000

Common equity

2,650,000

Total liabilities and equity

$4,275,000

Total assets

$4,275,000

$ 600,000

Lozano Chip Company: Income Statement for Year Ended December 31, 2023 (Thousands of Dollars) Sales

$7,500,000

Cost of goods sold

6,375,000

Selling, general, and administrative expenses

933,000

Earnings before interest and taxes (EBIT)

$ 192,000

Interest expense Earnings before taxes (EBT) Federal and state income taxes (25%) Net income

40,000 $ 152,000 38,000 $ 114,000

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Ratio

Lozano

Industry Average

Current assets/Current liabilities

__________

2.0

Days sales outstanding (365-day year)

__________

35.0 days

COGS/Inventory

__________

6.7

Sales/Fixed assets

__________

12.1

Sales/Total assets

__________

3.0

Net income/Sales

__________

1.2%

Net income/Total assets

__________

3.6%

Net income/Common equity

__________

9.0%

Total debt/Total assets

__________

30.0%

Total liabilities/Total assets

__________

60.0%

Solution: a. (Dollar amounts in thousands.)

Current assets Current liabilities

Accounts receivable Sales/365

COGS Inventory

Sales Fixed assets

Sales Total assets

Net income Sales

Net income Total assets

Net income Common equity

Total debt Total assets

Total liabilities Total assets

$2, 925, 000 $1, 225, 000 $1,575,000 $7,500,000/365 $6,375,000 $1,125,000 $7,500,000 $1,350,000 $7,500,000 $4,275,000

$114,000 $7,500,000 $114,000 $4,275,000 $114,000 $2,650,000

$100,000+$400,000 $4,275,000 $1,225,000+$400,000 $4,275,000

Firm

Industry Average

2.39

2.0

77 days

35 days

5.67

6.7

5.56

12.1

1.754

3.0

1.52%

1.2%

2.67%

3.6%

4.30%

9.0%

11.70%

30.0%

38.01%

60.0%

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For the firm, Equity multiplier (EM) =

$4,275,000 $2,650,000

= 1.61%.

ROE = PM  T.A. turnover  EM = 1.52%  1.754  1.61 = 4.3%. For the industry, ROE = 1.2%  3  2.5 = 9%. Note: To find the industry ratio of assets to common equity, recognize that 1 minus the Liabilities-toassets ratio = common equity/total assets. So, common equity/total assets = 1 – 60% = 40%, and 1/0.40 = 2.5 = total assets/common equity. c.

The firm’s days sales outstanding is more than twice as long as the industry average, indicating that the firm should tighten credit or enforce a more stringent collection policy. The total assets turnover ratio is well below the industry average so sales should be increased, assets decreased, or both. While the company’s profit margin is higher than the industry average, its other profitability ratios are low compared to the industry; net income should be higher given the amount of equity and assets. However, the company seems to be in an average liquidity position and financial leverage is similar to others in the industry.

3-14 Comprehensive Ratio Analysis. The Jimenez Corporation’s forecasted 2024 financial statements follow, along with some industry average ratios. Calculate Jimenez’s 2024 forecasted ratios, compare them with the industry average data, and comment briefly on Jimenez’s projected strengths and weaknesses. (Note: The statements and other data also are in the file Ch03 Tool Kit.xlsx. They are in the worksheet named Data for Problem 3-14.) Jimenez Corporation: Forecasted Balance Sheet as of December 31, 2024 Assets Cash

$72,000

Accounts receivable

439,000

Inventories Total current assets

894,000 $1,405,000

Fixed assets

431,000

Total assets

$1,836,000

Liabilities and Equity Accounts payable

$332,000

Notes payable

100,000

Accruals

170,000

Total current liabilities

$602,000

Long-term debt

404,290

Common stock

575,000

Retained earnings

254,710

Total liabilities and equity

$1,836,000

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Jimenez Corporation: Forecasted Income Statement for 2024 Sales

$4,290,000

Cost of goods sold

3,580,000

Selling, general, and administrative expenses

406,456

Earnings before taxes (EBT)

$ 184,544

Interest expense

40,000

Earnings before taxes (EBT)

$ 144,544

Taxes (25%)

36,136

Net income

108,408

Jimenez Corporation: Per Share Data for 2022 EPS

$4.71

Cash dividends per share

$0.95

P/E ratio

5.0

Market price (average)

$23.57

Number of shares outstanding

23,000

Ratio Quick ratio Current ratio Inventory turnover

Days sales outstanding

Jimenez

Industry Averagea

________________

1.0

________________

2.7

________________

7.0

________________

32.0 days

________________

13.0

________________

2.6

Return on assets

________________

9.1%

Return on equity

________________

18.2%

Profit margin on sales

________________

3.5%

Debt-to-assets ratio

________________

21.0%

Liabilities-to-assets ratio

________________

50.0%

P/E ratio

________________

6.0

Market/Book ratio

________________

3.5

Fixed assets turnover Total assets turnover

Notes: a Industry average ratios have been stable for the past 4 years. b Based on year-end balance sheet figures. c Calculation is based on a 365-day year.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Solution: Here are the firm’s base case ratios and other data as compared to the industry: Firm

Industry

Comment

Quick

$511,000/$602,000

= 0.85

1.0

Weak

Current

$1,405,000/$602,000

= 2.33

2.7

Weak

Inventory turnover

$3,580,000/$894,000

= 4.00

7.0

Poor

Days sales outstanding

$439,000/$11,753

= 37.35 days

32 days

Poor

Fixed assets turnover

$4,290,000/$431,000

= 9.95

13.0

Poor

Total assets turnover

$4,290,000/$1,836,000

= 2.34

2.6

Poor

Return on assets

$108,408/$1,836,000

= 5.90%

9.1%

Bad

Return on equity

$108,408/$829,710

= 13.07%

18.2%

Bad

Profit margin on sales

$108,408/$4,290,000

= 2.53%

3.5%

Bad

Debt ratio

$504,290/$1,836,000

= 27.47%

21.0%

High

Liabilities-to-assets

$1,006,290/$1,836,000

= 54.81%

50.0%

High

EPS

$4.71

n.a.

Stock price

$23.57

n.a.

P/E ratio

$23.57/$4.71

= 5.00

6.0

Poor

M/B ratio

$23.57/$36.07

= 0.65

n.a.

The firm appears to be badly managed–all of its ratios are worse than the industry averages, and the result is low earnings, a low P/E, P/CF ratio, a low stock price, and a low M/B ratio. The company needs to do something to improve.

SOLUTION TO SPREADSHEET PROBLEM 3-15 Build a Model: Ratio Analysis. Start with the partial model in the file Ch03 P15 Build a Model.xlsx from the textbook’s website. Joshua & White (J&W) Technology’s financial statements are also shown here. Answer the following questions. (Note: Industry average ratios are provided in Ch03 P15 Build a Model.xlsx.) a. Has J&W’s liquidity position improved or worsened? Explain. b. Has J&W’s ability to manage its assets improved or worsened? Explain. c. How has J&W’s profitability changed during the last year? d. Perform an extended DuPont analysis for J&W for 2022 and 2023. What do these results tell you? e. Perform a common size analysis. What has happened to the composition (that is, percentage in each category) of assets and liabilities? f. Perform a percentage change analysis. What does this tell you about the change in profitability and asset utilization?

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Joshua & White Technology: December 31 Balance Sheets (Thousands of Dollars) Assets

2023

2022

Liabilities & Equity

2023

2022

Cash

$21,000

$20,000

Accounts payable

$33,600

$32,000

Short-term investments

3,759

3,240

Accruals

12,600

12,000

Accounts receivable

52,500

48,000

Notes payable

19,929

6,480

Inventories

84,000

56,000

Total current liabilities

$66,129

$50,480

Total current assets

$161,259

$127,240

Long-term debt

67,662

58,320

Net fixed assets

223,097

200,000

Total liabilities

$133,791

$108,800

Total assets

$384,356

$327,240

Common stock

178,440

Retained earnings

72,125

40,000

Total common equity

$250,565

$218,440

Total liabilities & equity

$384,356

$327,240

Joshua & White Technology: Income Statements for Year Ending on December 31 (Thousands of Dollars) 2023

2022

Sales

$420,000

$400,000

COGS excluding depr. & amort.

300,000

298,000

Depreciation and amortization

19,660

18,000

Other operating expenses

27,600

22,000

EBIT

$72,740

$62,000

5,740

4,460

EBT

$67,000

$57,540

Taxes (25%)

16,750

14,385

Net income

$50,250

$34,524

Common dividends

$18,125

$17,262

Additions to retained earnings

$32,125

$17,262

Interest expense

Other Data

2023

2022

Year-end stock price

$90.00

$96.00

Number of shares (Thousands)

4,052

4,000

Lease payment (Thousands of Dollars)

$20,000

Sinking fund payment (Thousands of Dollars)

$5,000

Solution: The detailed solution for the problem is available in the file Ch07 P15 Build a Model Solution.xlsx and is available at the textbook’s website.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

The first part of the case, presented in the previous chapter, discussed the situation of Computron Industries after an expansion program. A large loss occurred in 2021, rather than the expected profit. As a result, its managers, directors, and investors are concerned about the firm’s survival. Jenny Cochran was brought in as assistant to Computron’s chairman, who had the task of getting the company back into a sound financial position. Cochran must prepare an analysis of where the company is now, what it must do to regain its financial health, and what actions to take. Your assignment is to help her answer the following questions by using the recent and projected estimates shown next. Provide clear explanations, not yes or no answers. Balance Sheets

2022

2023

2024E

$ 50

Short-term investments

100

Accounts receivable

400

520

530

Inventories

620

820

660

Total current assets

$1,180

$1,400

$1,300

Net Fixed Assets

2,900

3,500

3,700

Total Assets

$4,080

$4,900

$5,000

Liabilities and Equity

2022

2023

2024E

Accounts payable

$ 300

$ 400

$ 330

Notes payable

250

100

Accruals

200

240

270

$ 550

$ 890

Long-term bonds

800

1,100

Total liabilities

$1,350

$1,990

$1,800

Common stock (100,000 shares)

1,000

Retained earnings

1,730

1,910

2,200

Total common equity

$2,730

$2,910

$3,200

Total liabilities and equity

$4,080

$4,900

$5,000

Assets Cash and equivalents

Total current liabilities

700

Note: ―E‖ denotes the ―estimated forecast.‖

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Income Statements

2022

2023

2024E

Net sales

$5,500

$6,000

$6,600

Cost of goods sold (Excluding depr.)

4,300

4,800

5,210

Depreciation

290

320

370

Other operating expenses

350

420

400

$ 560

$ 460

$ 620

108

100

Pre-tax earnings

$ 492

$ 352

$ 520

Taxes (25%)

123

130

Net income

$ 369

$ 264

$ 390

Earnings before interest and taxes (EBIT) Less interest

Note: ―E‖ denotes the ―estimated forecast.‖ Also, Computron has no amortization. Other Data

2022

2023

2024E

EPS

$3.69

$2.64

$3.90

DPS

$0.90

$0.84

$1.00

Book Value Per Share

$27.30

$29.10

$32.00

Dividends

$90

$84

$100

Additions to retained earnings

$279

$180

$290

Per Share Information

Additional Information

Year-end shares outstanding

100

Year-end common stock price

$50.00

$30.00

$49.00

Lease payments

$20

Tax rate

25%

Note: ―E‖ denotes the ―estimated forecast.‖

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Ratio Analysis

2022

2023

2024E

Industry Average

Profit margin

6.7%

4.4%

____________

7.2%

Operating profit margin

10.2%

7.7%

____________

10.4%

Basic earning power

13.7%

9.4%

____________

15.6%

ROA

9.0%

5.4%

____________

10.8%

ROE

13.5%

9.1%

____________

15.4%

Inventory turnover

7.4

6.2

____________

9.0

Days sales outstanding

26.5

31.6

____________

28.0

Fixed assets turnover

1.9

1.7

____________

3.0

Total assets turnover

1.348

1.224

____________

1.5

Current

2.1

1.6

____________

2.5

Quick

1.0

0.7

____________

1.9

20.8%

27.6%

____________

15.0%

0.31

0.46

____________

0.22

Debt ratio Debt-to-equity ratio Liabilities-to-assets ratio

33.1%

40.6%

____________

32.0%

Equity multiplier

1.5

1.7

____________

1.5

TIE

8.2

4.3

____________

13.0

EBITDA coverage

9.9

6.3

____________

17.2

Price/earnings (P/E)

13.6

11.4

____________

16.8

Market/book

1.8

1.0

____________

2.7

Note: ―E‖ denotes the ―estimated forecast.‖ a.

Why are ratios useful? What three groups use ratio analysis and for what reasons? Answer: Ratios facilitate comparison of (1) one company over time and (2) one company versus other companies. Ratios are used by (1) managers to help improve the firm’s performance, (2) lenders to help evaluate the firm’s likelihood of repaying debts, and (3)stockholders to help forecast future earnings and cash flows.

Calculate the projected profit margin, operating profit margin, basic earning power (BEP), return on assets (ROA), and return on equity (ROE). What can you say about these ratios? Answer: Calculations for projected ratios: Profit Margin = Net Income/Sales = $390/$6,600 = 5.9%. Operating Profit Margin = EBIT/Sales = $620/$6,600 = 9.4%. Basic Earning Power = EBIT/Total Assets = $620/$5,000 = 12.4%. ROA = Net Income/Total Assets = $390/$5,000 = 7.8%. ROE = Net Income/Common Equity = $390/$3,200 = 12.2%.

Profitability Ratios

2022

2023

2024E

Industry Average

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Profitability Ratios

2022

2023

2024E

Industry Average

Profit margin

6.7%

4.4%

5.9%

7.4%

Operating profit margin

10.2%

7.7%

9.4%

10.5%

Basic earning power

13.7%

9.4%

12.4%

15.8%

ROA

9.0%

5.4%

7.8%

11.1%

ROE

13.5%

9.1%

12.2%

15.5%

The projected profit projected profitability ratios are improved but still are below the industry average. c.

Calculate the projected inventory turnover, days sales outstanding (DSO), fixed assets turnover, and total assets turnover. How does Computron’s utilization of assets stack up against that of other firms in its industry? Answer: Projected Inventory Turnover = COGS/Inventory = ($5,210 + $370)/$660 = 8.45 Projected DSO = Receivables/(Sales/365) = $530/($6,600/365) = 29.3 days. Projected Fixed Assets Turnover = Sales/Net Fixed Assets = $6,600/$3,700 = 1.8. Projected Total Assets Turnover = Sales/Total Assets = $6,600/$5,000 = 1.320  1.3. Asset Management Ratios Inventory turnover

2022 7.4

2023 6.2

2024E 8.45

Industry 9.0

Days sales outstanding

26.5

31.6

29.3

28.0

Fixed asset turnover

1.9

1.7

1.8

3.0

Total asset turnover

1.348

1.224

1.320

1.5

All the asset management ratios are projected to improve, but they still are not as good as the industry’s ratios. d.

Calculate the projected current and quick ratios based on the projected balance sheet and income statement data. What can you say about the company’s liquidity position and its trend? Answer: Projected Current Ratio = Current Assets/Current Liabilities = $1,300/$700 =1.86

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Projected Quick Ratio = (Current Assets – Inventory)/Current Liabilities = ($1,300 – $660)/$700 = 0.91 Liquidity Ratios Current ratio

2022 2.1

2023 1.6

2024E 1.86

Industry 2.1

Quick ratio

1.0

0.7

0.91

1.3

The company’s current and quick ratios are below the industry average. e.

Calculate the projected debt ratio, debt-to-equity ratio, liabilities-to-assets ratio, times-interestearned ratio, and EBITDA coverage ratios. How does Computron compare with the industry with respect to financial leverage? What can you conclude from these ratios? Answer: Projected Debt Ratio = Total Debt/Total Assets = ($100+ $1,100)/$5,000 = 24.0%. Projected Debt-to-Equity Ratio = Total Debt/Common Equity = ($100 + $1,100)/$3,200 = 0.38. Projected Liabilities-to-Assets Ratio = Total Liabilities/Total Assets = $1,800/$5,000 = 36.0%. Projected Earnings Multiplier = Total Assets/Common Equity = $5,000/$3,200 = 1.5625 Projected TIE = EBIT/Interest = $620/$100 = 6.2.



Proj. EBITDA Cov. =  EBITDA 



Lease   Loan Lease    /  Interest   Payments   Repayments Payments 

= ($620 + $370 + $20)/($100 + $20) = 8.4.

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Debt Management Ratios

2022

2023

2024E

Industry

Debt ratio

20.8%

27.6%

24.0%

15.0%

0.31

0.46

0.38

0.21

33.1%

40.6%

36.0%

28.0%

Earnings multiplier

1.49

1.68

1.56

1.4

Times interest earned

8.2

4.3

6.2

17.5

EBITDA coverage ratio

9.9

6.3

8.4

24.2

Debt-to-equity ratio Liabilities-to-assets ratio

The projected debt management ratios are lower than in the previous year but are higher than the industry average. f.

Calculate the projected price/earnings ratio and market/book ratio. Do these ratios indicate that investors are expected to have a high or low opinion of the company? Answer: EPS = Net Income/Shares Outstanding = $390/100 = $3.90. Projected Price/Earnings = Price Per Share/Earnings Per Share = $49.00/$3.90 = 12.6. Projected BVPS = Common Equity/Shares Outstanding = $3,200/100 = $32.00. Projected Market/Book = Market Price Per Share/Book Value Per Share = $49.00/$32.00 = 1.53.

$2.64

2024E $3.90

Industry Average na

13.6

11.4

12.6

20.0

$27.30

$29.10

$32.00

1.8

1.0

1.5

3.1

Market Value Ratios Earnings per share

2022 $3.69

Price/earnings (P/E) Book value per share Market/book

2023

All the market value ratios are projected to improve, but the P/E ratio and BVPS still are below the industry average. g.

Perform a common size analysis and percent change analysis. What do these analyses tell you about Computron? Answer: For the common size balance sheets, divide all items in a year by the total assets for that year. For the common size income statements, divide all items in a year by the sales in that year.

Common Size Balance Sheets

2022

2023

2024E

Industry

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Common Size Balance Sheets

2022

2023

2024E

Industry

Cash and equivalents

1.5%

1.0%

1.2%

2.0%

Short-term investments

2.5%

0.2%

1.0%

5.0%

Accounts receivable

9.8%

10.6%

14.0%

Inventories

15.2%

16.7%

13.2%

13.0%

Total current assets

28.9%

28.6%

26.0%

34.0%

Net fixed assets

71.1%

71.4%

74.0%

66.0%

Total assets

100.0%

Common Size Balance Sheets

2022

2023

2024E

Industry

Accounts payable

7.4%

8.2%

6.6%

6.0%

Notes payable

1.2%

5.1%

2.0%

3.0%

Accruals

4.9%

5.4%

7.0%

Total current liabilities

13.5%

18.2%

14.0%

16.0%

Long-term bonds

19.6%

22.4%

22.0%

12.0%

Total liabilities

33.1%

40.6%

36.0%

28.0%

Common

24.5%

20.4%

20.0%

27.2%

Retained earnings

42.4%

39.0%

44.0%

44.8%

Total common equity

66.9%

59.4%

64.0%

72.0%

Total liabilities and equity

100.0%

Assets

Liabilities and Equity

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Common Size Income Statements Net sales

2022 100.0%

2023 100.0%

2024E 100.0%

Industry 100.0%

COGS except depr.

78.2%

80.0%

78.9%

71.0%

Depreciation

5.3%

5.6%

4.0%

Other expenses

6.4%

7.0%

6.1%

14.5%

EBIT

10.2%

7.7%

9.4%

10.5%

Less interest

1.2%

1.8%

1.5%

0.6%

Pre-tax earnings

8.9%

5.9%

7.9%

9.9%

Taxes (25%)

2.2%

1.5%

2.0%

2.5%

Net income

6.7%

4.4%

5.9%

7.4%

Computron has higher proportion of net fixed assets than the industry. Computron’s total debt is 24% (the combined percentages of notes payable and long-term bonds) of its assets, which is higher than the industry’s combined debt percentage of 20%. Computron’s profit margin is less than the industry ratio because Computron has much higher costs of goods sold, even though it has lower other costs. For the percent change analysis, divide all items in a row by the value in the first year of the analysis. Percentage Change Income Statements Net sales

2023 9.1%

2024E 20.0%

Costs of goods sold

11.6%

21.2%

Depreciation

10.3%

27.6%

Other expenses

20.0%

14.3%

EBIT

–17.9%

10.7%

Less interest

58.8%

47.1%

Pre-tax earnings

–28.5%

5.7%

Taxes (25%)

–28.5%

5.7%

Net income

–28.5%

5.7%

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Percentage Change Balance Sheets Assets

2023

2024E

Cash and equivalents

–16.7%

0.0%

Short-term investments

–90.0%

–50.0%

Accounts receivable

30.0%

32.5%

Inventories

32.3%

6.5%

Total current assets

18.6%

10.2%

Net fixed assets

20.7%

27.6%

Total assets

20.1%

22.5%

Percentage Change Balance Sheets Liabilities and Equity

2023

2024E

Accounts payable

33.3%

10.0%

Notes payable

400.0%

100.0%

Accruals

20.0%

35.0%

Total current liabilities

61.8%

27.3%

Long-term bonds

37.5%

Total liabilities

47.4%

33.3%

Common stock

0.0%

Retained earnings

10.4%

27.2%

Total common equity

6.6%

17.2%

Total liabilities and equity

20.1%

22.5%

We see that in the most recent year, total assets grew by 20.1% relative to the baseline (with inventory growing by 32.3%). However, actual sales only grew by 9.1%, which indicates trouble, with unsold inventory causing much of the problem. Other expenses also grew rapidly, causing a steep decline in net income (–28.5%). Part of this decline is due to the 58.8% increase in interest expense. For the projected year, sales are projected to grow by a factor of 20.0% relative to the baseline year, which is about the same as total assets are projected to grow (22.5%). Note that net income is projected to grow by 5.7% from the baseline year. Much work remains, but the projections reflect the turnaround plans. h.

Use the extended DuPont equation to provide a breakdown of Computron’s projected return on equity. How does the projection compare with the previous years and with the industry’s DuPont equation? Answer: DuPont Equation:

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ROE =

ROE

Profit  Total Assets  Equity Margin Turnover Multiplier =

Net income Equity

Net income Total assets

Total assets Equity

Net income Sales

Sales Total assets

Total assets Equity

Profit margin

Total asset turnover

Equity multiplier

ROE2022 = (6.7%)(1.348)(1.495) = 13.5% ROE2023 = (4.4%)(1.224)(1.684) = 9.1% ROE2024E = (5.9%)(1.320)(1.563) = 12.2% ROEInd = (7.4%)(1.5)(1.39) = 15.4% Computron’s profit margin and total assets turnover ratio were below the industry average. It had a higher equity multiplier because it had more debt, which boosted its ROE. Otherwise, its ROE would have been even lower than the industry ROE. i.

What are some potential problems and limitations of financial ratio analysis? Answer: Some potential problems are listed below:

Comparison with industry averages is difficult if the firm has different divisions operating in different industries.

Different operating and accounting practices distort comparisons.

Sometimes it is hard to tell whether a specific ratio is ―good‖ or ―bad.‖

Sometimes it is difficult to tell whether company is, on balance, in a strong or weak position.

―Average‖ performance is not necessarily good.

Seasonal factors can distort ratios.

―Window dressing‖ techniques can make statements and ratios look better.

What are some qualitative factors that analysts should consider when evaluating a company’s likely future financial performance? Answer: Top analysts recognize that certain qualitative factors must be considered when evaluating a company. These factors, as summarized by the American Association of Individual Investors (AAII), are as follows: 1.

Are the company’s revenues tied to one key customer?

To what extent are the company’s revenues tied to one key product?

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

To what extent does the company rely on a single supplier?

What percentage of the company’s business is generated overseas?

Competition

Future prospects

Legal and regulatory environment

Solution and Answer Guide CHAPTER 4: T IME VALUE OF MONEY

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS............................................................................. 68 SOLUTIONS TO END-OF-CHAPTER PROBLEMS .......................................................................... 70 Easy Problems 1-8 .................................................................................................................................. 70 Intermediate Problems 9-29 .................................................................................................................... 73 Challenging Problems 30-34................................................................................................................... 84 SOLUTION TO SPREADSHEET PROBLEM ..................................................................................... 87 MINI CASE ............................................................................................................................................... 88 Web Extension 4B Continuous Compounding and Discounting Solutions to Problems .................. 102

ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1

Define each of the following terms: a. PV; I; INT; FVN; PVAN; FVAN; PMT; M; INOM b. Opportunity cost rate c. Annuity; lump-sum payment; cash flow; uneven cash flow stream d. Ordinary (or deferred) annuity; annuity due e. Perpetuity f. Outflow; inflow; time line; terminal value g. Compounding; discounting h. Annual, semiannual, quarterly, monthly, and daily compounding i. Effective annual rate (EAR or EFF%); nominal (quoted) interest rate; APR; periodic rate j. Amortization schedule; principal versus interest component of a payment; amortized loan Answer: a. PV (present value) is today’s value of a future payment, or stream of payments, discounted at the appropriate rate of interest. PV is also the beginning amount that will grow to some future value. The parameter i is the periodic interest rate that an account pays. The parameter INT is the dollars of interest earned each period. FVn (future value) is the ending amount in an account, where n is the number of

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periods the money is left in the account. PVAn is today’s value of a future stream of equal payments (an annuity) and FVAn is the ending value of a stream of equal payments, where n is the number of payments of the annuity. PMT is equal to the dollar amount of an equal, or constant cash flow (an annuity). In the EAR equation, m is used to denote the number of compounding periods per year, while iNom is the nominal, or quoted, interest rate. The opportunity cost rate (i) of an investment is the rate of return available on the best alternative investment of similar risk.

An annuity is a series of payments of a fixed amount for a specified number of periods. A single sum, or lump sum payment, as opposed to an annuity, consists of one payment occurring now or at some future time. A cash flow can be an inflow (a receipt) or an outflow (a deposit, a cost, or an amount paid). We distinguish between the terms cash flow and PMT. We use the term cash flow for uneven streams, while we use the term PMT for annuities, or constant payment amounts. An uneven cash flow stream is a series of cash flows in which the amount varies from one period to the next. The PV (or FVn) of an uneven payment stream is merely the sum of the present values (or future values) of each individual payment.

An ordinary annuity has payments occurring at the end of each period. A deferred annuity is just another name for an ordinary annuity. An annuity due has payments occurring at the beginning of each period. Most financial calculators will accommodate either type of annuity. The payment period must be equal to the compounding period.

A perpetuity is a series of payments of a fixed amount that last indefinitely. In other words, a perpetuity is an annuity where n equals infinity.

An outflow is a deposit, a cost, or an amount paid, while an inflow is a receipt. A time line is an important tool used in time value of money analysis; it is a graphical representation which is used to show the timing of cash flows. The terminal value is the future value of an uneven cash flow stream.

Compounding is the process of finding the future value of a single payment or series of payments. Discounting is the process of finding the present value of a single payment or series of payments; it is the reverse of compounding.

Annual compounding means that interest is paid once a year. In semiannual, quarterly, monthly, and daily compounding, interest is paid 2, 4, 12, and 365 times per year, respectively. When compounding occurs more frequently than once a year, you earn interest on interest more often, thus increasing the future value. The more frequent the compounding, the higher the future value.

The effective annual rate is the rate that, under annual compounding, would have produced the same future value at the end of 1 year as was produced by more frequent compounding, say quarterly. The nominal (quoted) interest rate, iNom, is the rate of interest stated in a contract. If the compounding occurs annually, the effective annual rate and the nominal rate are the same. If compounding occurs more frequently, the effective annual rate is greater than the nominal rate. The nominal annual interest rate is also called the annual percentage rate, or APR. The periodic rate, i PER, is the rate charged by a lender or paid by a borrower each period. It can be a rate per year, per 6-month period, per quarter, per month, per day, or per any other time interval (usually 1 year or less).

An amortization schedule is a table that breaks down the periodic fixed payment of an installment loan into its principal and interest components. The principal component of each payment reduces the remaining principal balance. The interest component is the interest payment on the beginning-ofperiod principal balance. An amortized loan is one that is repaid in equal periodic amounts (or ―killed off‖ over time).

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4-2

What is an opportunity cost rate? How is this rate used in discounted cash flow analysis, and where is it shown on a time line? Is the opportunity rate a single number that is used to evaluate all potential investments? Answer: The opportunity cost rate is the rate of interest one could earn on an alternative investment with a risk equal to the risk of the investment in question. This is the value of i in the TVM equations, and it is shown on the top of a time line, between the first and second tick marks. It is not a single rate—the opportunity cost rate varies depending on the riskiness and maturity of an investment, and it also varies from year to year depending on inflationary expectations.

4-3

An annuity is defined as a series of payments of a fixed amount for a specific number of periods. Thus, $100 a year for 10 years is an annuity, but $100 in Year 1, $200 in Year 2, and $400 in Years 3 through 10 does not constitute an annuity. However, the entire series does contain an annuity. Is this statement true or false? Answer: True. The second series is an uneven payment stream, but it contains an annuity of $400 for 8 years. The series could also be thought of as a $100 annuity for 10 years plus an additional payment of $100 in Year 2, plus additional payments of $300 in Years 3 through 10.

4-4

If a firm’s earnings per share grew from $1 to $2 over a 10-year period, the total growth would be 100%, but the annual growth rate would be less than 10%. True or false? Explain. Answer: True, because of compounding effects—growth on growth. The following example demonstrates the point. The annual growth rate is I in the following equation:

$1(1 + I)10 = $2. The term (1 + I)10 is the FVIF for I percent, 10 years. We can find I in one of two ways:

4-5

Using a financial calculator input N = 10, PV = –1, PMT = 0, FV = 2, and I/YR = ?. Solving for I/YR you obtain 7.18%.

Using a financial calculator, input N = 10, I/YR = 10, PV = –1, PMT = 0, and FV = ?. Solving for FV you obtain $2.59. This formulation recognizes the ―interest on interest‖ phenomenon.

Would you rather have a savings account that pays 5% interest compounded semiannually or one that pays 5% interest compounded daily? Explain. Answer: For the same stated rate, daily compounding is best. You would earn more ―interest on interest.‖

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1-8 4-1

Future Value of a Single Payment. If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in your account after 5 years? Solution:

0 10% 1

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| | PV = 10,000

| FV5 = ?

FV5 = $10,000(1.10)5 = $10,000(1.61051) = $16,105.10. Alternatively, with a financial calculator enter the following: N = 5, I/YR = 10, PV = –10,000, and PMT = 0. Solve for FV = $16,105.10. 4-2

Present Value of a Single Payment. What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7% annually? Solution:

0 7% | PV = ?

5 |

10 |

15 |

20 | FV20 = 5,000

With a financial calculator enter the following: N = 20, I/YR = 7, PMT = 0, and FV = 5000. Solve for PV = $1,292.10. 4-3

Interest Rate on a Single Payment. Your parents will retire in 18 years. They currently have $250,000, and they think they will need $1 million at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds? Solution:

0 I/YR = ? | PV = 250,000

18 | FV18 = 1,000,000

With a financial calculator enter the following: N = 18, PV = –250,000, PMT = 0, and FV = 1.000,000. Solve for I/YR = 8.01% ≈ 8%. 4-4

Number of Periods of a Single Payment. If you deposit money today in an account that pays 6.5% annual interest, how long will it take to double your money? Solution:

0 6.5% | PV = 1

N=? | FVN = 2

$2 = $1(1.065)N.

4-5

With a financial calculator enter the following: I/YR = 6.5, PV = –1, PMT = 0, and FV = 2. Solve for N = 11.01 ≈ 11 years. Number of Periods for an Annuity. You have $42,180.53 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $250,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal? Solution:

0 12% | PV = 42,180.53

1 | 5,000

2 | 5,000



N–2 | 5,000

N–1 | 5,000

N | FV = 250,000

Using your financial calculator, enter the following data: I/YR = 12; PV = –4,2180.53; PMT = –5,000; FV = 250,000; N = ? Solve for N = 11. It will take 11 years to accumulate $250,000.

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4-6

Future Value: Ordinary Annuity versus Annuity Due. What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year? If this were an annuity due, what would its future value be? Solution: Ordinary annuity:

0 7% |

1 | 300

2 | 300

3 | 300

4 5 | | 300 300 FVA5 = ?

With a financial calculator enter the following: N = 5, I/YR = 7, PV = 0, and PMT = −300. Solve for FV = $1,725.22. Annuity due:

0 7% 1 | | 300 300

2 | 300

3 | 300

4 | 300

5 | FVA5 = ?

With a financial calculator, switch to ―BEG‖ and enter the following: N = 5, I/YR = 7, PV = 0, and PMT = −300. Solve for FV = $1,845.99. Don’t forget to switch back to ―END‖ mode. 4-7

Present and Future Value of an Uneven Cash Flow Stream. An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 8% annually, what is this investment’s present value? Its future value? Solution:

0 8% | PV = ?

1 | 100

2 | 100

3 | 100

4 | 200

5 | 300

6 | 500 FV = ?

Using a financial calculator, enter the following: CF0 = 0; CF1 = 100; Nj = 3; CF4 = 200 (Note calculator will show CF2 on screen.); CF5 = 300 (Note calculator will show CF3 on screen.); CF6 = 500 (Note calculator will show CF4 on screen.); and I/YR = 8. Solve for NPV = $923.98. To solve for the FV of the cash flow stream with a calculator that doesn’t have the NFV key, do the following: Enter N = 6, I/YR = 8, PV = –923.98, and PMT = 0. Solve for FV = $1,466.24. 4-8

Annuity Payment and EAR. You want to buy a car, and a local bank will lend you $20,000. The loan would be fully amortized over 5 years (60 months), and the nominal interest rate would be 12%, with interest paid monthly. What is the monthly loan payment? What is the loan’s EFF%? Solution: Using a financial calculator, enter the following: N = 60, I/YR = 1, PV = –20,000, and FV = 0. Solve for PMT = $444.89. M

I   EAR = 1  NOM  – 1.0 M  

= (1.01)12 – 1.0 = 12.68%.

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Alternatively, using a financial calculator, enter the following: NOM% = 12 and P/YR = 12. Solve for EFF% = 12.6825%. Remember to change back to P/YR = 1 on your calculator.

INTERMEDIATE PROBLEMS 9-29 4-9

Present and Future Values of Single Cash Flows for Different Periods. Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can ―override‖ the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.) a. An initial $500 compounded for 1 year at 6% b. An initial $500 compounded for 2 years at 6% c. The present value of $500 due in 1 year at a discount rate of 6% d. The present value of $500 due in 2 years at a discount rate of 6% Solution:

a. 0 6% | –500

1 | FV = ?

$500(1.06) = $530.00.

b. 0 6% 1 | | –500 FV = ? c. 0 6% | PV = ?

d. 0 6% | PV = ?

2 $500(1.06)2 = $561.80.

1 | 500

$500(1/1.06) = $471.70.

1 |

2 |

$500(1/1.06)2 = $445.00. 500

4-10 Present and Future Values of Single Cash Flows for Different Interest Rates. Use both the TVM equations and a financial calculator to find the following values. See the Hint for Problem 4-9. a. An initial $500 compounded for 10 years at 6% b. An initial $500 compounded for 10 years at 12% c. The present value of $500 due in 10 years at a 6% discount rate d. The present value of $500 due in 10 years at a 12% discount rate Solution: a.

0 1 | | –500

2 |

0 12%1 | | –500

2 |

3 |

4 |

5 |

$500(1.06)10 = $895.42.

| FV = ?

3 |

4 |

5 |

6 |

7 |

8 |

9 |

$500(1.12)10 = $1,552.92.

10 | FV = ?

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0 6%1 | | PV = ?

0 12%1 | | PV = ?

2 |

3 |

4 |

5 |

6 |

7 |

8 |

9 |

10 $500(1/1.06)10 = $279.20

| 500

2 |

3 |

4 |

5 |

6 |

7 |

8 |

9 |

10 $500(1/1.12)10 = $160.99

| 500

4-11 Time for a Lump Sum to Double. To the closest year, how long will it take to double $200 if it is deposited and earns the following rates? [Notes: (1) See the Hint for Problem 4-9. (2) Some financial calculators will round up and give an integer answer to the problem, and others will give the exact decimal solution. This problem is asking for the closest integer. For example, if the answer is less than 5.5 years, then round down to 5. If the answer is greater than or equal to 5.5 years, round up to 6. a. 7% b. 10% c. 18% d. 100% Solution: a. 7% | –200

? | 400

With a financial calculator, enter I/YR = 7, PV = –200, PMT = 0, and FV = 400. Then press the N key to find N = 10.24 ≈ 10. b. 10% | –200

? | 400

With a financial calculator, enter I/YR = 107, PV = –200, PMT = 0, and FV = 400. Then press the N key to find N = 7.27 ≈ 7. c.

18% | –200

| 400

With a financial calculator, enter I/YR = 18, PV = –200, PMT = 0, and FV = 400. Then press the N key to find N = 4.19 ≈ 4. d.

100% | –200

? | 400

With a financial calculator, enter I/YR = 100, PV = –200, PMT = 0, and FV = 400. Then press the N key to find N = 1.00 ≈ 1. 4-12 Future Value of an Annuity. Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities. (Notes: See the Hint to Problem 49. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.) a. $400 per year for 10 years at 10% b. $200 per year for 5 years at 5% c. $400 per year for 5 years at 0%

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Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

Solution: a.

0 10% 1 2 3 4 5 6 7 8 9 10 | | | | | | | | | | | 400 400 400 400 400 400 400 400 400 400 FVA10 = ? With a financial calculator, enter N = 10, I/YR = 10, PV = 0, and PMT = –400. Then press the FV key to find FV = $6,374.97.

b. 0 |

5% 1 2 3 4 5 | | | | | 200 200 200 200 200 FVA5 = ?

With a financial calculator, enter N = 5, I/YR = 5, PV = 0, and PMT = –200. Then press the FV key to find FV = $1,105.13. c.

0 0%1 | | 400

2 3 4 5 | | | | 400 400 400 400 FVA5 = ?

With a financial calculator, enter N = 5, I/YR = 0, PV = 0, and PMT = –400. Then press the FV key to find FV = $2,000. d.

To solve part d using a financial calculator, repeat the procedures discussed in parts a, b, and c, but first switch the calculator to ―BEG‖ mode. Make sure you switch the calculator back to ―END‖ mode after working the problem. (1) 0 10%1 2 | | | 400 400 400

3 | 400

4 5 6 7 8 9 10 | | | | | | | 400 400 400 400 400 400 FVA10 = ?

With a financial calculator set to ―BEG‖ mode, enter N = 10, I/YR = 10, PV = 0, and PMT = – 400. Then press the FV key to find FV = $7,012.46. (2) 0 5% 1 | | 200 200

2 | 200

3 | 200

4 | 200

5 | FVA5 = ?

With a financial calculator set to ―BEG‖ mode, enter N = 5, I/YR = 5, PV = 0, and PMT = –200. Then press the FV key to find FV = $1,160.38. (3) 0 0% 1

| 400

| FVA5 = ?

| 400

With a financial calculator set to ―BEG‖ mode, enter N = 5, I/YR = 0, PV = 0, and PMT = –400. Then press the FV key to find FV = $2,000. 4-13 Present Value of an Annuity. Find the present value of the following ordinary annuities (see the Notes to Problem 4-12):

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a. b. c. d.

$400 per year for 10 years at 10% $200 per year for 5 years at 5% $400 per year for 5 years at 0% Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

Solution: a. 0 10%1 2 3 4 5 6 7 8 9 10 | | | | | | | | | | | PV = ? 400 400 400 400 400 400 400 400 400 400 With a financial calculator, enter N = 10, I/YR = 10, PMT = –400, and FV = 0. Then press the PV key to find PV = $2,457.83. b.

0 1 5% | | PV = ? 200

2 | 200

3 | 200

4 | 200

5 | 200

With a financial calculator, enter N = 5, I/YR = 5, PMT = –200, and FV = 0. Then press the PV key to find PV = $865.90. c.

0 1 2 | | | PV = ? 400 400

3 | 400

4 5 | | 400 400

$400(5) = $2,000.00.

With a financial calculator, enter N = 5, I/YR = 0, PMT = –400, and FV = 0. Then press the PV key to find PV = $2,000. d.

(1)

| 400 PV = ?

| | | | | | | | | | 400 400 400 400 400 400 400 400 400

With a financial calculator set to ―BEG‖ mode, enter N = 10, I/YR = 10, PMT = –400, and FV = 0. Then press the PV key to find PV = $2,703.61. (2) 0 5% 1 2 3 4 5 | | | | | | 200 200 200 200 200 PV = ? With a financial calculator set to ―BEG‖ mode, enter N = 5, I/YR = 5, PMT = –200, and FV = 0. Then press the PV key to find PV = $909.19. (3) 0 0% 1 2 3 4 5 | | | | | | 400 400 400 400 400 PV = ? With a financial calculator set to ―BEG‖ mode, enter N = 5, I/YR = 0, PMT = –400, and FV = 0. Then press the PV key to find PV = $2,000.00. 4-14 Uneven Cash Flow Stream. a. Find the present values of the following cash flow streams. The appropriate interest rate is 8%. (Hint: It is fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows

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such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course. Note that, when working with the calculator’s cash flow register, you must enter CF0 = 0. Note also that it is quite easy to work the problem with Excel, using procedures described in the file Ch04 Tool Kit.xlsx.)

Year

Cash Stream A

Cash Stream B

$100

$300

400

300

100

What is the value of each cash flow stream at a 0% interest rate?

Solution: a. Cash Stream A 0

Cash Stream B 3

| | | | | | PV = ? 100 400 400 400 300

2 |

PV = ? 300

| | 400 400

5 | 400

| 100

With a financial calculator, simply enter the cash flows (be sure to enter CF 0 = 0), enter I/YR = 8, and press the NPV key to find NPV = PV = $1,251.25 for the first problem. Override I = 8 with I = 0 to find the next PV for Cash Stream A. Repeat for Cash Stream B to get NPV = PV = $1,300.32. b.

PVA = $100 + $400 + $400 + $400 + $300 = $1,600. PVB = $300 + $400 + $400 + $400 + $100 = $1,600.

4-15 Effective Rate of Interest. Find the interest rate (or rates of return) in each of the following situations: a. You borrow $700 and promise to pay back $749 at the end of 1 year. b. You lend $700 and receive a promise to be paid $749 at the end of 1 year. c. You borrow $85,000 and promise to pay back $201,229 at the end of 10 years. d. You borrow $9,000 and promise to make payments of $2,684.80 at the end of each of the next 5 years. Solution: These problems can all be solved using a financial calculator by entering the known values shown on the time lines and then pressing the I/YR button. a.

0 | +700

I=?

1 | –749

With a financial calculator, enter N = 1, PV = 700, PMT = 0, and FV = –749. Then press the I/YR key to find I/YR = 7%. b.

0 | –700

I=?

1 | +749

With a financial calculator, enter N = 1, PV = –700, PMT = 0, and FV = 749. Then press the I/YR key to find I/YR = 7%. c.

0 |

I=?

10 |

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–201,229

+85,000

With a financial calculator, enter N = 10, PV = 85,000, PMT = 0, and FV = –201,229. Then press the I/YR key to find I/YR = 9%. d.

1 I=? | | +9,000 –2,684.80

2 | –2,684.80

3 4 5 | | | –2,684.80 –2,684.80 –2,684.80

With a financial calculator, enter N = 5, PV = 9,000, PMT = –2,684.8, and FV = 0. Then press the I/YR key to find I/YR = 15%. 4-16 Future Value for Various Compounding Periods. Find the amount to which $500 will grow under each of the following conditions: a. 12% compounded annually for 5 years b. 12% compounded semiannually for 5 years c. 12% compounded quarterly for 5 years d. 12% compounded monthly for 5 years Solution: a. 0 12% 1 | | -500

5 | FV = ?

With a financial calculator, enter N = 5, I/YR = 12, PV = –500, and PMT = 0, and then press FV to obtain FV = $881.17. b.

0 6%1 | | –500

2 |

3 |

4 |

5 |

6 |

7 |

8 |

9 |

10 | FV = ?

With a financial calculator, enter N = 10, I/YR = 6, PV = –500, and PMT = 0, and then press FV to obtain FV = $895.42. c.

0 4 3% | | –500

8 |

12 |

16 |

20 | FV = ?

With a financial calculator, enter N = 20, I/YR = 3, PV = –500, and PMT = 0, and then press FV to obtain FV = $903.06. d.

0 1%12 | | –500

24 |

36 |

48 |

60 | ?

With a financial calculator, enter N = 60, I/YR = 1, PV = –500, and PMT = 0, and then press FV to obtain FV = $908.35. 4-17 Present Value for Various Compounding Periods. Find the present value of $500 due in the future under each of the following conditions: a. 12% nominal rate, semiannual compounding, discounted back 5 years b. 12% nominal rate, quarterly compounding, discounted back 5 years c. 12% nominal rate, monthly compounding, discounted back 1 year Solution: a. 0

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| | PV = ?

| 500

With a financial calculator, enter N = 10, I/YR = 6, PMT = 0, and FV = –500. Then press the PV key to find PV = $279.20. Alternatively, mn

   1  PV = FVn    1 i     m

    1 = $500    1  0.12     2 

2(5)

 1    1.06 

= $500  b.

0 4 3% | | PV = ?

8 |

12 |

16 |

= $500(PVIF6%, 10) = $500(0.5584) = $279.20.

20 | 500

With a financial calculator, enter N = 20, I/YR = 3, PMT = 0, and FV = –500. Then press the PV key to find PV = $276.84, or

    1 PV = $500    1  0.12     4  c.

0 1%1 | | PV = ?

2 |



4(5)

 1  = $500    1.03 

= $276.84.

12 | 500

With a financial calculator, enter N = 12, I/YR = 1, PMT = 0, and FV = –500. Then press the PV key to find PV = $443.72, or 12(1)

    1 PV = $500    1  0.12     12  12

 1    1.01

= $500 

= $500(1.01)-12 = $443.72.

4-18 Future Value of an Annuity for Various Compounding Periods. Find the future values of the following ordinary annuities: a. Payments of $400 every 6 months for 5 years at a nominal rate of 12%, compounded semiannually b. Payments of $200 every 3 months for 5 years at a nominal rate of 12%, compounded quarterly c. The annuities described in parts a and b have the same total amount of money paid into them during the 5-year period, and both earn interest at the same nominal rate, yet the annuity in part b earns $101.75 more than the one in part a over the 5 years. Why does this occur?

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Solution: a. 0 6% 1 | | 400

2 |

3 |

400



9 |

10 |

400

400 FVA10 = ?

Enter N = 5  2 = 10, I/YR = 12/2 = 6, PV = 0, PMT = –400, and then press FV to get FV = $5,272.32. b.

Now the number of periods is calculated as N = 5 × 4 = 20, I/YR = 12/4 = 3, PV = 0, and PMT = –200. The calculator solution is $5,374.07. Note that the solution assumes that the nominal interest rate is compounded at the annuity period.

The annuity payments in part b occur more frequently than those in part a, which means that interest is earned on interest more frequently. In addition, the first annuity payment for part b occurs earlier in the year than the first payment for the annuity in part a, so interest on part b’s Month-3 payment begins compounding before interest begins compounding on part a’s Month-6 semiannual payment. The same is true for part b’s Month-9 payment relative to part a’s Month-12 end-of-year payment.

4-19 Effective versus Nominal Interest Rates. Universal Bank pays 7% interest, compounded annually, on time deposits. Regional Bank pays 6% interest, compounded quarterly. a. Based on effective interest rates, in which bank would you prefer to deposit your money? b. Could your choice of banks be influenced by the fact that you might want to withdraw your funds during the year as opposed to at the end of the year? In answering this question, assume that funds must be left on deposit during an entire compounding period in order for you to receive any interest. Solution: a. Universal Bank: Effective rate = 7%. Regional Bank: 4

 0.06  Effective rate =  1   – 1.0 = (1.015)4 – 1.0 4   = 1.0614 – 1.0 = 0.0614 = 6.14%. With a financial calculator, you can use the interest rate conversion feature to obtain the same answer. You would choose the Universal Bank. b.

If funds must be left on deposit until the end of the compounding period (1 year for Universal and 1 quarter for Regional), and you think there is a high probability that you will make a withdrawal during the year, the Regional account might be preferable. For example, if the withdrawal is made after 10 months, you would earn nothing on the Universal account but (1.015) 3 – 1.0 = 4.57% on the Regional account. Ten or more years ago, most banks and S&Ls were set up as described above, but now virtually all are computerized and pay interest from the day of deposit to the day of withdrawal, provided at least $1 is in the account at the end of the period.

4-20 Amortization Schedule. Consider a $25,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 10%. a. Set up an amortization schedule for the loan. b. How large must each annual payment be if the loan is for $50,000? Assume that the interest rate remains at 10% and that the loan is still paid off over 5 years.

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How large must each payment be if the loan is for $50,000, the interest rate is 10%, and the loan is paid off in equal installments at the end of each of the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Why are these payments not half as large as the payments on the loan in part b?

Solution: a. With a financial calculator, enter N = 5, I/YR = 10, PV = –25,000, and FV = 0, and then press the PMT key to get PMT = $6,594.94. Then go through the amortization procedure as described in your calculator manual to get the entries for the amortization table.

Year 1 2 3 4 5

Repayment Interest $2,500.00 2,090.51 1,640.06 1,144.58 599.54 $7,974.69

Payment $ 6,594.94 6,594.94 6,594.94 6,594.94 6,594.93* $32,974.69

Remaining of Principal $ 4,094.94 4,504.43 4,954.88 5,450.36 5,995.39 $25,000.00

Balance $20,905.06 16,400.63 11,445.75 5,995.39 0

*The last payment must be smaller to force the ending balance to zero. b.

Here the loan size is doubled, so the payments also double in size to $13,189.87: enter N = 5, I/YR = 10, PV = –50,000, and FV = 0, and then press the PMT key to get PMT = $13,189.87.

The annual payment on a $50,000, 10-year loan at 10 percent interest would be $8,137.27: enter N = 10, I/YR = 10, PV = –50,000, and FV = 0, and then press the PMT key to get PMT = $8,137.27. Because the payments are spread out over a longer time period, more interest must be paid on the loan, which raises the amount of each payment. The total interest paid on the 10-year loan is 10($8,137.27) – $50,000 = $31,372.70 versus interest of 5($6,594.94) – $50,000 = $15,949.37 on the 5-year loan.

4-21 Growth Rates. Sales for Hanebury Corporation’s just-ended year were $12 million. Sales were $6 million 5 years earlier. a. At what rate did sales grow? b. Suppose someone calculated the sales growth for Hanebury in part a as follows: ―Sales doubled in 5 years. This represents a growth of 100% in 5 years; dividing 100% by 5 results in an estimated growth rate of 20% per year.‖ Explain what is wrong with this calculation. Solution: a. 0 I = 1? | | –6

2 |

3 |

4 |

5 | 12 (in millions)

With a calculator, enter N = 5, PV = –6, PMT = 0, FV = 12, and then solve for I/YR = 14.87% ≈ 15%. b.

The calculation described in the quotation fails to take account of the compounding effect. It can be demonstrated to be incorrect as follows: $6,000,000(1.20)5 = $6,000,000(2.4883) = $14,929,800, which is greater than $12 million. Thus, the annual growth rate is less than 20 percent; in fact, it is about 15 percent, as shown in part a.

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4-22 Expected Rate of Return. Washington-Pacific (W-P) invested $4 million to buy a tract of land and plant some young pine trees. The trees can be harvested in 10 years, at which time W-P plans to sell the forest at an expected price of $8 million. What is W-P’s expected rate of return? Solution: 0 1 2 I=? | | | –4

3 |

4 |

5 |

8 |

9 |

10 | 8 (in millions)

With a calculator, enter N = 10, PV = –4, PMT = 0, FV = 8, and then solve for I/YR = 7.18%. 4-23 Effective Rate of Interest. A mortgage company offers to lend you $85,000; the loan calls for payments of $8,273.59 at the end of each year for 30 years. What interest rate is the mortgage company charging you? Solution: 0 I=? 1 | | 85,000 –8,273.59

2 | –8,273.59

3 | –8,273.59

4 | –8,273.59

30 

| –8,273.59

With a calculator, enter N = 30, PV = 85,000, PMT = –8273.59, FV = 0, and then solve for I/YR = 9%. 4-24 Required Lump-Sum Payment. To complete your last year in business school and then go through law school, you will need $10,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $10,000 one year from today). Your uncle offers to put you through school, and he will deposit in a bank paying 7% interest a sum of money that is sufficient to provide the four payments of $10,000 each. His deposit will be made today. a. How large must the deposit be? b. How much will be in the account immediately after you make the first withdrawal? After the last withdrawal? Solution: a. 0 7% 1 | | PV = ? –10,000

2 3 4 | | | –10,000 –10,000 –10,000

With a calculator, enter N = 4, I/YR = 7, PMT = –10,000, and FV = 0. Then press PV to get PV = $33,872.11. b.

(1) At this point, we have a 3-year, 7% annuity of $10,000 whose present value is $26,243.16: N = 3, I/YR = 7, PMT = –10,000, and FV = 0. Then press PV to get PV = $26,243.16. You can also think of the problem as follows: (Beginning balance)(1+I) – PMT = Ending balance $33,872.11 (1.07) – $10,000 = $26,243.16.

(2) Zero after the last withdrawal. 4-25 Repaying a Loan. While Mary Corens was a student at the University of Tennessee, she borrowed $12,000 in student loans at an annual interest rate of 9%. If Mary repays $1,500 per year, then how long (to the nearest year) will it take her to repay the loan? Solution: 0 1 9% | | 12,000 –1,500

2 | –1,500



? | –1,500

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With a calculator, enter I/YR = 9, PV = 12,000, PMT = –1,500, and FV = 0. Press N to get N = 14.77  15 years. Therefore, it will take approximately 15 years to pay back the loan. 4-26 Reaching a Financial Goal. You need to accumulate $10,000. To do so, you plan to make deposits of $1,250 per year—with the first payment being made a year from today—into a bank account that pays 12% annual interest. Your last deposit will be less than $1,250 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal, and how large will the last deposit be? Solution: 0 1 | 12% | 1,250

2 |

3 |

1,250

? FV = 10,000

With a financial calculator, get a ―ballpark‖ estimate of the years by entering I/YR = 12, PV = 0, PMT = – 1250, and FV = 10,000, and then pressing the N key to find N = 5.94 years. This answer assumes that a payment of $1,250 will be made 94/100th of the way through Year 5. Now find the FV of $1,250 for 5 years at 12%; N = 5, I/YR = 12, PV = 0, and PMT = –1250. Press FV to get FV = $7,941.06. Compound this value for 1 year at 12% to obtain the value in the account after 6 years and before the last payment is made; it is $7,941.06(1.12) = $8,893.99. Thus, you will have to make a payment of $10,000 – $8,893.99 = $1,106.01 at Year 6, so the answer is: it will take 6 years, and $1,106.01 is the amount of the last payment. 4-27 Present Value of a Perpetuity. What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7%? If interest rates in general were to double and the appropriate discount rate rose to 14%, what would happen to the present value of the perpetuity? Solution: PV = $100/0.07 = $1,428.57. PV = $100/0.14 = $714.29. When the interest rate is doubled, the PV of the perpetuity is halved. 4-28 PV and Effective Annual Rate. Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling securities that call for four payments of $50 (one payment at the end of each of the next 4 years) plus an extra payment of $1,000 at the end of Year 4. Your friend says she can get you some of these securities at a cost of $900 each. Your money is now invested in a bank that pays an 8% nominal (quoted) interest rate but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you? (Hint: Do not round intermediate calculations to less than six decimal places.) Solution: 0 1 8.24% | | PV = ? 50

2 | 50

3 | 50

4 | 1,050

Discount rate: Effective rate on bank deposit: EFF% = (1 + 0.08/4)4 – 1 = 8.2432%. Find PV of above stream at 8.2432%: with a financial calculator, N = 4, I/YR = 8.2432, PMT = 50, and FV = 1,000, then press the PV key to get PV = $893.16.

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4-29 Loan Amortization. Assume that your aunt sold her house on December 31, and to help close the sale she took a second mortgage in the amount of $10,000 as part of the payment. The mortgage has a quoted (or nominal) interest rate of 10%; it calls for payments every 6 months, beginning on June 30, and is to be amortized over 10 years. Now, 1 year later, your aunt must inform the IRS and the person who bought the house about the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) a. To the closest dollar, what is the remaining balance at the end of the first year? b. To the closest dollar, what is the total amount of interest that was paid during the first year? Solution: This can be done with a calculator by specifying an interest rate of 5% per period for 20 periods with 1 payment per period to get the payment each 6 months: N = 10  2 = 20, I/YR = 10%/2 = 5, PV = –10,000. FV = 0. Solve for PMT = $802.43. Set up amortization table as shown next:

Principal

$802.43

Pmt of Interest $500.00

$302.43

Pmt of End Bal $9,697.57

802.43

484.88

$317.55

$9,380.02

Period

Beg Bal

Payment

$10,000.00

9,697.57

$984.88 You can also work the problem with a calculator having an amortization function. Find the interest in each 6-month period, sum them, and you have the answer. Even simpler, with some calculators such as the HP-10B, allow you to find the interest paid during a particular period of time.

CHALLENGING PROBLEMS 30-34 4-30 Loan Amortization. Your company is planning to borrow $1 million on a 5-year, 15%, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? Solution: First, find PMT by using a financial calculator: N = 5, I/YR = 15, PV = –1,000,000, and FV = 0. Solve for PMT = $298,315.55. Then set up the amortization table:

Year

Beginning Balance

Payment

Interest

Ending Principal

Balance

$1,000,000.00

$298,315.55

$150,000.00

$148,315.55

$851,684.45

851,684.45

298,315.55

127,752.67

170,562.88

681,121.57

Fraction that is principal = $170,562.88/$298,315.55 = 0.5718 = 57.18%. 4-31 Non-annual Compounding. It is now January 1. You plan to make a total of five deposits of $100 each, one every 6 months, with the first payment being made today. The bank pays a nominal interest rate of 12% but uses semiannual compounding. You plan to leave the money in the bank for 10 years. a. How much will be in your account after 10 years? b. You must make a payment of $1,432.02 in 10 years. To get the money for this payment, you will make five equal deposits, beginning today and for the following four quarters, in a bank that pays a nominal interest rate of 12% with quarterly compounding. How large must each of the five payments be?

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Solution: a. Begin with a time line: 6-mos. 0

Years 0

6% |

100 100 100 100 100 FVA Since the first payment is made today, we have a five-period annuity due. The applicable interest rate is I = 12/2 = 6 per period, N = 5, PV = 0, and PMT = –100. Setting the calculator on ―BEG,‖ we find FVA (Annuity due) = $597.53. That will be the value at the fifth 6-month period, which is t = 2.5. Now we must compound out to t = 10, or for 7.5 years at an EAR of 12.36%, or 15 semiannual periods at 6%. $597.53  20 – 5 = 15 periods @ 6%  $1,432.02, or $597.53  10 – 2.5 = 7.5 years @ 12.36%  $1,432.02. b.

1 0 3% 1 | | PMT PMT

2 |

4 |

| PMT

PMT

5 | PMT



10 years 40 quarters | FV = 1,432.02

The timeline depicting the problem is shown above. Because the payments only occur for five periods throughout the 40 quarters, this problem cannot be immediately solved as an annuity problem. The problem can be solved in two steps: (1) Discount the $1,432.02 back to the end of Quarter 5 to obtain the PV of that future amount at Quarter 5. (2) Then solve for PMT using the value solved in Step 1 as the FV of the five-period annuity due. Step 1:

Input the following into your calculator: N = 35, I/YR = 3, PMT = 0, FV = 1432.02, and solve for PV at Quarter 5. PV = $508.92.

Step 2:

The PV found in Step 1 is now the FV for the calculations in this step. Change your calculator to the BEGIN mode. Input the following into your calculator: N = 5, I/YR = 3, PV = 0, FV = 508.92, and solve for PMT = $93.07.

4-32 Nominal Rate of Return. Anne Lockwood, manager of Oaks Mall Jewelry, wants to sell on credit, giving customers 3 months to pay. However, Anne will have to borrow from her bank to carry the accounts receivable. The bank will charge a nominal rate of 15% and will compound monthly. Anne wants to quote a nominal rate to her customers (all of whom are expected to pay on time) that will exactly offset her financing costs. What nominal annual rate should she quote to her credit customers? Solution: Here we want to have the same effective annual rate on the credit extended as on the bank loan that will be used to finance the credit extension. First, we must find the EAR = EFF% on the bank loan. Enter NOM% = 15, N = P/YR = 12, and press EFF% to get EAR = 16.08%. Now recognize that giving 3 months of credit is equivalent to quarterly compounding interest is earned at the end of the quarter, so it is available to earn interest during the next quarter. Therefore, enter P/YR = 4, EFF% = EAR = 16.08%, and press NOM% to find the nominal rate of 15.19 percent.

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Therefore, if a 15.19% nominal rate is charged and credit is given for 3 months, the cost of the bank loan will be covered. Alternative solution: We need to find the effective annual rate (EAR) the bank is charging first. Then, we can use this EAR to calculate the nominal rate that should be quoted to the customers. Bank EAR: EAR = (1 + INOM/M)M – 1 = (1 + 0.15/12)12 – 1 = 16.08%. Nominal rate that should be quoted to customers: 16.08% = (1 + INOM/4)4 – 1 1.1608 = (1 + INOM/4)4 1.0380 = 1 + INOM/4 INOM = 0.0380(4) = 15.19%. 4-33 Required Annuity Payments. Assume that your father is now 50 years old, plans to retire in 10 years, and expects to live for 25 years after he retires—that is, until age 85. He wants his first retirement payment to have the same purchasing power at the time he retires as $40,000 has today. He wants all of his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: Your father realizes that if inflation occurs the real value of his retirement income will decline year by year after he retires.) His retirement income will begin the day he retires, 10 years from today, and he will then receive 24 additional annual payments. Inflation is expected to be 5% per year from today forward. He currently has $100,000 saved and expects to earn a return on his savings of 8% per year with annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal? (Note: Neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.) Solution: Information given: 1.

Will save for 10 years, then receive payments for 25 years.

Wants payments of $40,000 per year in today's dollars for first payment only. Real income will decline. Inflation will be 5%. Therefore, to find the inflated fixed payments, we have this time line: 0 5% | | 40,000

5 |

10 |

| FV = ?

Enter N = 10, I/YR = 5, PV = –40,000, PMT = 0, and press FV to get FV = $65,155.79. 3.

He now has $100,000 in an account that pays 8%, annual compounding. We need to find the FV of the $100,000 after 10 years. Enter N = 10, I/YR = 8, PV = –100,000, PMT = 0, and press FV to get FV = $215,892.50.

He wants to withdraw, or have payments of, $65,155.79 per year for 25 years, with the first payment made at the beginning of the first retirement year. So, we have a 25-year annuity due with PMT = 65,155.79, at an interest rate of 8%. (The interest rate is 8% annually, so no adjustment is required.) Set the calculator to ―BEG‖ mode, then enter N = 25, I/YR = 8, PMT = 65,155.79, FV = 0, and press PV to get PV = $751,165.35. This amount must be on hand to make the 25 payments.

Since the original $100,000, which grows to $215,892.50, will be available, we must save enough to accumulate $751,165.35 – $215,892.50 = $535,272.85.

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The $535,272.85 is the FV of a 10-year ordinary annuity. The payments will be deposited in the bank and earn 8% interest. Therefore, set the calculator to ―END‖ mode and enter N = 10, I/YR = 8, PV = 0, FV = 535,272.85, and press PMT to find PMT = $36,949.61.

4-34 Growing Annuity Payments. You want to accumulate $1 million by your retirement date, which is 25 years from now. You will make 25 deposits in your bank, with the first occurring today. The bank pays 8% interest, compounded annually. You expect to receive annual raises of 3%, which will offset inflation, and you will let the amount you deposit each year also grow by 3% (i.e., your second deposit will be 3% greater than your first, the third will be 3% greater than the second, etc.). How much must your first deposit be if you are to meet your goal? Solution: Information given: The nominal time line is shown below, with a different payment each period and a FV of a nominal $1 million: 0 1 2 3 4 5 8% | | | | | | PMT1 PMT2 PMT3 PMT4 PMT5

 PMT6

24 | PMT25

25 | FV = $1 million

The key is to ―rewrite‖ this as a real time line (i.e., a time line based on today’s purchasing power). First, the purchasing power of $1 million in 25 years with an inflation rate of 3% per year is: $1,000,000 / (1 + Inflation)N = $1,000,000 / (1 + 0.03)25 = $477,605.57. This is a growing annuity, with a nominal rate of 8% and an inflation rate of 3%. You should use the real rate in the calculator: rr = [(1 + rNOM)/(1 + Inflation)] – 1.0 = [1.08/1.03] – 1.0 = .0485437 = 4.85437%. So the ―real‖ time line in expressed in today’s purchasing power is:

4.85437%

0 | PMT

1 | PMT

2 | PMT

3 |

4 | PMT

5 | PMT

PMT

24 25  | | PMT FV = $477,605.57

Set the financial calculator to the ―BEG‖ mode, N = 25, I/YR = 4.85437, PV = 0, FV = 477,605.57, and press PMT for PMT = $9,736.96. Thus, an initial payment of $9,736.96 that grows at 3% each year for 24 more payment, invested at a rate of 8% per year, will accumulate $1 million at Year 25.

SOLUTION TO SPREADSHEET PROBLEM 4-35 Build a Model: The Time Value of Money. Start with the partial model in the file Ch04 P35 Build a Model.xlsx from the textbook’s website. Answer the following questions, using the spreadsheet model to do the calculations: a. Find the FV of $1,000 invested to earn 10% annually 5 years from now. Answer this question first by using a math formula and then by using the Excel function wizard. b. Now create a table that shows the FV at 0%, 5%, and 20% for 0, 1, 2, 3, 4, and 5 years. Then create a graph with years on the horizontal axis and FV on the vertical axis to display your results. c. Find the PV of $1,000 due in 5 years if the discount rate is 10% per year. Again, first work the problem with a formula and then by using the function wizard. d. A security has a cost of $1,000 and will return $2,000 after 5 years. What rate of return does the security provide?

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e. f. g. h. i.

Suppose California’s population is 30 million people and its population is expected to grow by 2% per year. How long would it take for the population to double? Find the PV of an ordinary annuity that pays $1,000 at the end of each of the next 5 years if the interest rate is 15%. Then find the FV of that same annuity. How would the PV and FV of the above annuity change if it were an annuity due rather than an ordinary annuity? What would the FV and PV for parts a and c be if the interest rate were 10% with semiannual compounding rather than 10% with annual compounding? Find the PV and FV of an investment that makes the following end-of-year payments. The interest rate is 8%. Year

Payment

$100

200

400

Suppose you bought a house and took out a mortgage for $50,000. The interest rate is 8%, and you must amortize the loan over 10 years with equal end-of-year payments. Set up an amortization schedule that shows the annual payments and the amount of each payment that repays the principal and the amount that constitutes interest expense to the borrower and interest income to the lender. (1) Create a graph that shows how the payments are divided between interest and principal repayment over time. (2) Suppose the loan called for 10 years of monthly payments, 120 payments in all, with the same original amount and the same nominal interest rate. What would the amortization schedule show now?

Solution: The detailed solution for the spreadsheet problem, Ch04 P35 Build a Model Solution.xlsx, is available on the textbook’s website.

MINI CASE Assume that you are nearing graduation and have applied for a job at a prestigious company. The company's evaluation process requires you to take an examination that covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the following questions. a.

Draw time lines for (a) a $100 lump sum cash flow at the end of Year 2, (b) an ordinary annuity of $100 per year for 3 years, and (c) an uneven cash flow stream of –$50, $100, $75, and $50 at the end of Years 0 through 3. Answer: (Begin by discussing basic discounted cash flow concepts, terminology, and solution methods.) A time line is a graphical representation which is used to show the timing of cash flows. The tick marks represent end of periods (often years), so time 0 is today; time 1 is the end of the first year, or 1 year from today; and so on.

0 | 0

1 | 1

2 | 100

year cash flow

lump sum

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| 0 | –50

| 100

1 | 100

2 | 75

3 | 50

annuity

uneven cash flow stream

A lump sum is a single flow; for example, a $100 inflow in Year 2, as shown in the top time line. An annuity is a series of equal cash flows occurring over equal intervals, as illustrated in the middle time line. An uneven cash flow stream is an irregular series of cash flows which do not constitute an annuity, as in the lower timeline; –50 represents a cash outflow rather than a receipt or inflow. b.

What is the future value of an initial $100 after 3 years if it is invested in an account paying 10% annual interest?

Answer: Show dollars corresponding to question mark, calculated as follows:

0 | 100

10%

1 |

2 |

3 | FV = ?

After 1 year:

FV1 = PV + I1 = PV + PV(I) = PV(1 + I) = $100(1.10) = $110.00. Similarly:

FV2 = FV1 + I2 = FV1 + FV1(I) = FV1(1 + I) = PV(1 + I)(1 + I) = PV(1 + I)2 = $110(1.10) = $121.00 FV3 = FV2 + I3 = FV2 + FV2(I) = FV2(1 + I) = PV(1 + I)2(1 + I) = PV(1 + I)3. = $121(1.10) = $133.10 In general, we see that: FVn = PV(1 + I)N, Therefore, the future value at t = 3 is: FV3 = $100(1.10)3 = $100(1.3310) = $133.10. Note that this equation has four variables: FVN, PV, I, and N. Here we know all except FVN, so we solve for FVN. We will, however, often solve for one of the other three variables. By far, the easiest way to work all time value problems is with a financial calculator or Excel. Just plug in any three of the four values and find the fourth.

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Finding future values (moving to the right along the timeline) is called compounding. Note that there are three ways of finding FV3: using a regular calculator, financial calculator, or spreadsheets. For simple problems, we show only the regular calculator and financial calculator methods. (1) regular calculator: 1.

$100(1.10)(1.10)(1.10) = $133.10.

$100(1.10)3 = $133.10.

(2) financial calculator: This is especially efficient for more complex problems, including exam problems. Input the following values: N = 3, I/YR = 10, PV = –100, PMT = 0, and solve for FV = $133.10. b.

What is the present value of $100 to be received in 3 years if the appropriate interest rate is 10%?

Answer: Finding present values, or discounting (moving to the left along the time line), is the reverse of compounding, and the basic present value equation is the reciprocal of the compounding equation:

0 10%1 | | PV = ?

2 |

3 | 100

FVn = PV(1 + I)N transforms to:

PV =

1  = FVN   N (1  I) 1 I 

FVN

= FVN(1 + I)-N

thus: 3

 1   = $100 = (0.7513) = $75.13. PV = $100   1.10  The same methods used for finding future values are also used to find present values. Using a financial calculator input N = 3, I/YR = 10, pmt = 0, FV = 100, and then solve for PV = $75.13. c.

We sometimes need to find out how long it will take a sum of money (or anything else, such as earnings, population, or prices) to grow to some specified amount. For example, if a company's sales are growing at a rate of 20% per year, how long will it take sales to double? Answer: We want to find out how long it will take us to double our money at an interest rate of 20%. Let X denote any amount of dollars and N denote the number of years. We can use this equation to determine the time for an amount to double. FVN = $X(1 + I)N Substitute 2X for FVN because we want X to double: 2X = X(1 + I)N Now divided both sides of the equation by X and solve for N:

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2 = (1 + I)N (1.2)N = $2/$1 = 2 N ln(1.2) = ln(2) N = ln(2)/ln(1.2) N = 0.693/0.182 = 3.8. We can show this on a timeline:

0 20%1 | | –1X

2 |

3 |

3.8 4 | | 2X

Alternatively, we could use a financial calculator. We would plug I/YR = 20, PV = –1, PMT = 0, and FV = 2 into our calculator, and then press the N button to find the number of years it would take 1 (or any other beginning amount) to double when growth occurs at a 20% rate. The answer is 3.8 years, but some calculators will round this value up to the next highest whole number. The graph also shows what is happening. FV 2

1 3.8

Year

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If you want an investment to double in 3 years, what interest rate must it earn? Answer: 0

| 2

–1 FVN = PVN (1 + I)N FV3 = $1(1 + I)3. $2 = $1(1 + I)3 (1 + I)3 = $2/$1 = 2. 1 + I = (2)1/3 = 1.2599 i = 25.99%.

Using a financial calculator to solve: enter N = 3, PV = –1, PMT = 0, FV = 2, then press the I/YR button to find I/YR = 25.99%.

Calculators can find interest rates quite easily, even when periods and/or interest rates are not even numbers, and when uneven cash flow streams are involved. (With uneven cash flows, we must use the ―CFLO‖ function, and the interest rate is called the IRR, or ―internal rate of return‖; we will use this feature in capital budgeting.) e.

What is the difference between an ordinary annuity and an annuity due? What type of annuity is shown below? How would you change the time line to show the other type of annuity?

0 |

1 | 100

2 | 100

3 | 100

Answer: This is an ordinary annuity—it has its payments at the end of each period; that is, the first payment is made one period from today. Conversely, an annuity due has its first payment today. In other words, an ordinary annuity has end-of-period payments, while an annuity due has beginning-of-period payments.

The annuity shown above is an ordinary annuity. To convert it to an annuity due, shift each payment to the left, so you end up with a payment under the 0 but none under the 3. f.

What is the future value of a 3-year ordinary annuity of $100 if the appropriate interest rate is 10%?

Answer: 0

10% 1

| 100

100 110 121 $331

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Go through the following discussion. One approach would be to treat each annuity flow as a lump sum. Here we have

= $100(1) + $100(1.10) + $100(1.10)2 = $100[1 + (1.10) + (1.10)2] = $100(3.3100) = $331.00.

FVAn

Using a financial calculator, N = 3, I/YR = 10, PV = 0, PMT = –100. This gives FV = $331.00. f.

What’s the present value of the annuity?

Answer: 0 10%1

| 100

90.9091 82.6446 75.1315 $248.6852 The present value of the annuity is $248.6852, rounded to $248.69. Using a financial calculator, input N = 3, I/YR = 10, PMT = 100, FV = 0, and press the PV button.

Spreadsheets are useful for time lines with multiple cash flows. The following spreadsheet shows this problem:

100

2 3

248.6852

The Excel formula in cell A3 is = NPV(10%,B2:D2). This gives a result of 248.6852. Note that the interest rate can be either 10% or 0.10, not just 10. Also, note that the range does not include any cash flow at time zero.

Excel also has special functions for annuities. For ordinary annuities, the Excel formula is = PV(interest rate, number of periods, payment). In this problem, = PV(10%, 3,–100), gives a result of 248.69. For the future value, it would be = FV(10%,3,–100), with a result of 331. f.

What would the future and present values be if the annuity were an annuity due?

Answer: If the annuity were an annuity due, each payment would be shifted to the left, so each payment is compounded over an additional period or discounted back over one less period. To find the future value of an annuity due, use the following formula:

FVAn(Annuity Due) = FVAn(1 + I). In our situation, the future value of the annuity due is $364.10:

FVA3(Annuity Due) = $331.00(1.10)1 = $364.10. This same result could be obtained by using the time line: $133.10 + $121.00 + $110.00 = $364.10. The best way to work annuity due problems is to switch your calculator to ―BEG‖ or beginning or

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

―DUE‖ mode, and go through the normal process. Note that it's critical to remember to change back to ―END‖ mode after working an annuity due problem with your calculator. This formula could be used to find the present value of an annuity due:

PVAn(Annuity Due) = PVAn(1 + I). In our situation, the present value of the annuity due is $273.55:

PVA3(Annuity Due) = $248.685(1.10)1 = $273.55. The Excel function is = PV(10%,3,–100,0,1). The fourth term, 0, tells Excel there are no additional cash flows. The fifth term, 1, tells Excel it is an annuity due. The result is $273.55. A similar modification gives the future value: = FV(10%,3,–100,0,1), with a result of 364.10. g.

What is the present value of the following uneven cash flow stream? The appropriate interest rate is 10%, compounded annually.

0 | 0

1 | 100

2 3 4 years | | | 300 300 –50

Answer: Here we have an uneven cash flow stream. The most straightforward approach is to find the PVs of each cash flow and then sum them, as shown below:

0 |

10% 1 | 100

2 | 300

3 | 300

4 years | –50

90.909 247.934 225.394 −34.151 530.087 Note (1) that the $50 outflow Year 4 remains an outflow even when discounted. There are numerous ways of finding the present value of an uneven cash flow stream. But by far the easiest way to deal with uneven cash flow streams is with a financial calculator or a spreadsheet. Calculators have a function which on the HP 17B is called ―CFLO,‖ for ―cash flow.‖ Other calculators could use other designations such as cf0 and CFi, but they explain how to use them in the manual. You would input the cash flows, so they are in the calculator's memory, then input the interest rate, I, and then press the NPV or PV button to find the present value. Spreadsheets are especially useful for uneven cash flows. The following spreadsheet shows this problem:

100

300

–50

2 3

530.087

The Excel formula in cell A3 is = NPV(10%,B2:E2), with a result of 530.087.

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Define the nominal rate (INOM), which also is called the stated rate and the quoted rate. Also define the periodic rate (IPER). If the nominal rate is 6% and is compounded quarterly, what is the periodic rate (IPER)? If it is compounded monthly?

Answer: The nominal rate, the stated rate, and the quoted rate are names used to denote the annual percentage rate of return specified in a contract. If compounding occurs more than once a year, the nominal rate is not used in calculations or shown on time lines. The periodic rate is the rate charged by a lender or paid by a borrower each period: IPER = INOM/M, where M is the number of times the rate is compounded during the year. The quarterly periodic rate is: INOM/M = 6%/4 = 1.5%; The monthly periodic rate is: INOM/M = 6%/12 = 0.5%. h.

If the stated interest rate is constant, will the future value be larger or smaller if we compound an initial amount more often than annually (for example, semiannually)? Why?

Answer: Accounts that pay interest more frequently than once a year, for example, semiannually, quarterly, or daily, have larger future values because interest is earned on interest more often. Virtually all banks now pay interest daily, so they use daily compounding. h.

What is the future value of $100 after 5 years under 12% annual compounding? Semiannual compounding? Quarterly compounding? Monthly compounding? Daily compounding?

Answer: Under annual compounding, the $100 is compounded over five annual periods at a 12.0% periodic rate:

INOM = 12%.

I FVN = PV1  NOM  M  

 0.12   = $100 1  1  

1*5

= $100(1.12)5 = $176.23.

Under semiannual compounding, the $100 is compounded over 10 semiannual periods at a 6.0% periodic rate:

INOM = 12%.

I FVN = PV1  NOM  M  

 0.12   = $100 1  2  

2*5

= $100(1.06)10 = $179.08.

quarterly: FVN = $100(1.03)20 = $180.61. monthly: FVN = $100(1.01)60 = $181.67. daily: FVN = $100(1+ 0.12/365)365*5 = $182.19.

What is the effective annual rate (EFF%), also called the annual equivalent rate (AER)? What is the EFF% for a nominal rate of 12%, compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily? Answer: The effective annual rate is the annual rate that causes the PV to grow to the same FV as under multi-period compounding; it is sometime denoted as the annual equivalent rate (AER). For 12% semiannual compounding, the ear is 12.36%:

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

1  I NOM  EFF% = Annual Equivalent Rate =   M  

 1.0.

If iNom = 12% and interest is compounded semiannually, then: 2

 0.12    1.0 = (1.06)2 – 1.0 = 1.1236 – 1.0 = 0.1236 = 12.36%. EFF% = 1  2  

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

For quarterly compounding, the effective annual rate is:

EFF% = (1.03)4 – 1.0 = 12.55%. For monthly compounding, the effective annual rate is:

EFF% = (1.01)12 – 1.0 = 12.68%. For daily compounding, the effective annual rate is:

EFF% (1 + 0.12/365)365 – 1.0 = 12.75%. h.

Can the effective annual rate ever be equal to the nominal (quoted) rate?

Answer: If annual compounding is used, then the effective annual rate will be equal to the nominal rate. If more frequent compounding is used, the effective annual rate will be greater than the nominal rate. i.

Define the annual percentage rate (APR). Suppose you borrow $3,621.15 and take out a loan with an 8% nominal interest rate. You must repay the loan with 48 monthly payments of $90 each. In addition, you must pay an initial loan processing fee of $100. What is the APR for this loan? Answer: The Consumer Credit Protection Act of 1968 has Truth in Lending provisions to help borrowers understand the true costs of loans. One major provision is that lenders must disclose the annual percentage rate (APR) of the loan, which is the nominal annual interest rate actually charged on loans after taking into account any fees charged by the lender. To find the APR, calculate the monthly periodic rate based on the loan’s actual cash flows, including the initial fee. With a financial calculator, enter N = 48, PV = 3,621.15 − 100 = 3,521.15, PMT = −90, and FV = 0. The resulting periodic rate is 0.8675%. Multiply the periodic rate by 12 to get the APR: 12(0.8675) = 0.1041 = 10.41%.

Explain when you should use the: nominal rate (INOM), periodic rate (IPER), effective annual rate (EFF%), and annual percentage rate (APR). Can you think of a more useful rate than the APR that should be reported on all contracts? If so, how would you calculate that rate? Answer: The nominal rate is shown on contracts. You should use the nominal rate and the number of compounding periods per year to calculate the periodic rate. If there is no compounding, the nominal rate and the periodic rate are equal. You should use the periodic rate in all calculations. The effective annual rate takes into consideration the impact of compounding frequency, so you should use it to compare loan terms that have different payment frequencies, such as quarterly payments versus monthly payments. However, it ignores any fees that the lender might charge the borrower. The APR does include the impact of fees when calculating an adjusted periodic rate, which makes it useful in comparing loans with different fees. However, the APR ignores compounding and simply multiplies the adjusted periodic rate by the number of periods. A more useful rate would be to modify the APR to include the impact of compounding. You can do this yourself by dividing the APR by 12 to get the monthly rate and then compound the monthly rate for 12 periods to get a more useful version of the APR. As we calculated previously, the monthly periodic rate that incorporates the initial loan processing fee is

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

0.8675%. For monthly compounding, the modified APR is:

Modified APR = (1.008675)12 – 1.0 = 10.92%. k.

Construct an amortization schedule for a $1,000, 10% annual rate loan with three equal installments.

During Year 2, what is the annual interest expense for the borrower, and what is the annual interest income for the lender? Hint: Construct an amortization schedule.

Answer: To begin, note that the face amount of the loan, $1,000, is the present value of a 3-year annuity at a 10% rate:

0 10% 1 | | –1,000 PMT 1

PVA3

| PMT

PMT 2

1   1  + PMT  1  = PMT   + PMT     1 I  1 I  1 I 

$1,000 = PMT(1 + I)-1 + PMT(1 + I)-2 + PMT(1 + I)-3 = PMT(1.10)-1 + PMT(1.10)-2 + PMT(1.10)-3. We have an equation with only one unknown, so we can solve it to find PMT. The easy way is with Excel, using the PMT function: = PMT(10,3, –1,000). The results is 402.11. With a financial calculator, input N = 3, I/YR = 10, PV = –1,000, FV = 0, and then press the PMT button to get PMT = 402.1148036, rounded to $402.11. These facts regarding the amortization schedule are important: 

The $402.11 annual payment includes both interest and principal. Interest in the first year is calculated as follows: 1st year interest = I  beginning balance = 0.1  $1,000 = $100.



The repayment of principal is the difference between the $402.11 annual payment and the interest payment: 1st year principal repayment = $402.11 – $100 = $302.11.



The loan balance at the end of the first year is: 1st year ending balance = beginning balance – principal repayment = $1,000 – $302.11 = $697.89.



We would continue these steps in the following years. Here is the full table:

N 1 2 3 Total

Beg. Amt. $1,000.00 $697.89 $365.56

Payment $402.11 $402.11 $402.11 $1,206.34

Interest $100.00 $69.79 $36.56 $206.34

Principal $302.11 $332.33 $365.56 $1,000.00

End. Amt. $697.89 $365.56 $0.00

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach



Notice that the interest each year declines because the beginning loan balance is declining. Since the payment is constant, but the interest component is declining, the principal repayment portion is increasing each year.



The interest component is an expense which is deductible to a business or a homeowner, and it is taxable income to the lender. If you buy a house, you will get a schedule constructed like ours, but longer, with 30  12 = 360 monthly payments if you get a 30-year, fixed rate mortgage.



The payment may have to be increased by a few cents in the final year to take care of rounding errors and make the final payment produce a zero ending balance.



The lender received a 10% rate of interest on the average amount of money that was invested each year, and the $1,000 loan was paid off. This is what amortization schedules are designed to do.



Most financial calculators have amortization functions built in.

Suppose on January 1 you deposit $100 in an account that pays a nominal (or quoted) interest rate of 11.33463%, with interest added (compounded) daily. How much will you have in your account on October 1, or 9 months (273 days) later? Answer: The daily periodic interest rate is IPER = 11.3346%/365 = 0.031054%. There are 273 days between January 1 and October 1. Calculate FV as follows:

FV273 = $100(1.00031054)273 = $108.85. Using a financial calculator, input N = 273, I/YR = 0.031054, PV = –100, and PMT = 0. Pressing FV gives $108.85.

An alternative approach would be to first determine the effective annual rate of interest, with daily compounding, using the formula:

 0.1133463   EFF% = 1  365  

365

– 1 = 0.12 = 12.0%.

(Some calculators, e.g., the HP 10b and 17b, have this equation built in under the ICNV [interest conversion] function.)

Thus, if you left your money on deposit for an entire year, you would earn $12 of interest, and you would end up with $112. The question, though, is this: how much will be in your account on October 1? Here you will be leaving the money on deposit for 9/12 = 3/4 = 0.75 of a year.

0 12% 0.75 | | –100 FV = ?

1 | 112

You would use the regular setup, but with a fractional exponent:

FV0.75 = $100(1.12)0.75 = $100(1.088713) = $108.87. This is slightly different from our earlier answer, because n is actually 273/365 = 0.7479 rather than 0.75. m. 1.

Consider the time line shown here. Is the stream of cash flows an annuity?

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

0 |

1 | 100

2 | 100

3 Years | 100

Answer: The payments occur annually, but compounding occurs each 6 months. Therefore, the payment stream is an annuity in the sense of constant amounts at regular intervals, but the intervals do not correspond with the compounding periods. Thus, we cannot use normal annuity valuation techniques. This kind of situation occurs often. m. 2.

What is the value at the end of Year 3 of the following cash flow stream if the quoted interest rate is 10%, compounded semiannually?

0 5% 1 2 3 Years  100 100 100 110.25 = 100(1.05)2 121.55 = 100(1.05)4 331.80 Here we have a different situation. The payments occur annually, but compounding occurs each 6 months. Thus, we cannot use normal annuity valuation techniques. There are two approaches that can be applied: (1) treat the cash flows as lump sums, as was done above, or (2) treat the cash flows as an ordinary annuity, but use the effective annual rate:

 

 M 

 

EFF% = 1 + I N OM   1 =  1 +

0.10    1 = 10.25%. 2 

Now we have this three-period annuity:

FVA3 = $100(1.1025)2 + $100(1.1025)1 + $100 = $331.80. You can plug in N = 3, I/YR = 10.25, PV = 0, and PMT = –100, and then press the FV button to find FV = $331.80. m. 3.

What is the PV of the same stream?

Answer:

0 5% 1 2 3 Years  100 100 100 2 90.70 = 100/(1.05) 82.27 = 100/(1.05)4 74.62 = 100/(1.05)6 247.59 To use a financial calculator, input N = 3, I/YR = 10.25, PMT = 100, FV = 0, and then press the PV key to find PV = $247.59. m. 4.

An important rule is that you should never show a nominal rate on a time line or use it in calculations unless what condition holds? (Hint: Think of annual compounding, when INOM =

10 0

Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

EFF% = IPER.) What would be wrong with your answer to parts (1) and (2) if you used the nominal rate of 10% rather than the periodic rate (INOM /2 = 10%/2 = 5%)? Answer: iNom can only be used in the calculations when annual compounding occurs. If the nominal rate of 10% was used to discount the payment stream, the present value would be overstated by $272.32 – $247.59 = $24.73. n.

You have the chance to buy a guaranteed promissory note for $850. The note pays $1,000 in 15 months (i.e., exactly 456 days). You have $850 in a bank account that pays a 7% nominal rate compounded daily. Which is a better investment, the note or the bank account? Answer this question using three approaches: (1) compare your future value if you buy the note versus leaving your money in the bank; (2) compare the PV of the note with your current bank balance; and (3) compare the effective rate or return on the note with that of the bank account. Answer: The timeline, based on daily compounding, is shown next.

0 7%/365 365 465 | | | –850 1,000 The solutions using three methods are explained next.

(1) To find the future value of leaving your money in the bank, first calculate the daily interest rate: 0.07/365 = 0.00019178. Use this daily rate to calculate the future value after 465 days: FV = $850(1 + 0.00019178)365 = $927.67. This is less than the $1,000 future value if you buy the note, so you should buy the note. With a financial calculator, set N = 465, I/YR = 0.019178 (recall that the financial calculator requires the entry as a percentage), PV = −850, and PMT = 0. Solve for FV = 927.67. (2) To find the PV of the note, use the daily interest rate to discount the $1,000 future value for 456 days: PV = $1,000/(1 + 0.00019178)456 = $916.27. The present value of the note is greater than the $850 cost, so you should buy the note. With a financial calculator, set N = 465, I/YR = 0.019178 (recall that the financial calculator requires the entry as a percentage), PMT = 0, and FV = 1,000. Solve for PV = 916.27; the same result obtained by the first method. (3) To calculate the note’s effective rate of return with a financial calculator, set N = 456, PV = −850, PMT = 0, and FV = 1,000. Solve for I/YR = 0.035646%. This is greater than the daily rate of the bank account (0.019178%), so you should buy the note. To see this same result using the annualized value, first calculate the annual effective rate of the note based on the daily rate; the result is 13.89%: (1 + 0.00035646)365 – 1 = 0.1389 = 13.89%. The effective rate of the bank, based on its 7% nominal rate compounded daily, is 7.25%: (1 + 0.07/365)365 – 1 = 0.0725 = 7.25%. The note’s annual effective rate is greater than the bank’s annual effective rate, so you should buy the note. Because there are no payments but only a present value and a future value, there is another way to solve this problem. To see this, we rewrite the note’s time line base on years and the annual nominal rate, as shown next. Note that 456 days are equal to 1.2493 years (456/365 =

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

1.2493). 0 1 1.2493 7% | | | –850 1,000 As calculated previously, the 7% nominal rate is an effective rate of 7.25%. The FV of 850 when compounded at the effective rate of 7.25% for 1.2493 years is FV N = 850(1 + 0.0725)1.2493 = 927.67, the same result as calculate previously. Because this is less than the $1,000 future value of the note, you should buy the note. We can also find the present value of the $1,000 future value using the effective rate and the actual number of years. The result is PVN = 1,000/(1 + 0.0725)1.2493 = 916.27, the same result as calculated using previously. To find the rate of return, we use a financial calculator and set N = 1.2493, PV = −850, PMT = 0, and FV = 1,000. We press the I/YR key and the answer is 13.89%, the same result we obtained previously.

WEB EXTENSION 4B CONTINUOUS COMPOUNDING AND DISCOUNTING SOLUTIONS TO PROBLEMS (4B-1) FV Continuous Compounding If you receive $15,000 today and can invest it at a 6% annual rate compounded continuously, what will be your ending value after 15 years? Solution: FV15 = $15,000e0.06(15) = $36,894.05. (4B-2) PV Continuous Compounding In 7 years, you are scheduled to receive money from a trust established for you by your grandparents. When the trust matures, there will be $200,000 in the account. If the account earns 9% compounded continuously, how much is in the account today? Solution: PV = FVN/eIN = $200,000/e0.09(7) = $200,000/1.8776 = $106,518.36. (4B-3) FV Continuous Compounding Bank A offers a nominal annual interest rate of 7% compounded daily, while Bank B offers continuous compounding at a 6.9% nominal annual rate. If you deposit $1,000 with each bank, what will be the difference in the two bank account balances after 2 years? Solution: Daily compounding: FV2 = PV(1 + 0.07/365)365(2) = $1,000(1.15026) = $1,150.26 Continuous compounding: FV2 = PVeIN = $1,000e0.069(2) = $1,000(1.14798) = $1,147.98 Difference between accounts

$ 2.28

(4B-4) Continuous Compounded Interest Rate

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

In order to purchase your first home, you need a down payment of $40,000 six years from today. You currently have $20,000 to invest. In order to achieve your goal, what nominal interest rate, compounded continuously, must you earn on this investment? Solution: Calculate the growth factor using PV and FV which are given: FVN = PVeIN; $40,000 = $20,000eI6 eI6

= 2.0.

Take the natural logarithm of both sides: I(6)ln e = ln 2.00. The natural log of e = 1.0. Inputs: 2.0. Press LN key. Output: LN = 0.6931. I(6)ln e I(6) I

= ln 2.0 = 0.6931 = 0.1155 = 11.55%.

(4B-5) Continuous Compounding You have the choice of placing your savings in an account paying 10.25% compounded annually, an account paying 10.0% compounded semiannually, or an account paying 9.5% compounded continuously. In order to maximize your return, which would you choose? Solution: Determine the effective annual rates. a.

10.25% annually = 10.25%. 2

0.10    – 1.0 = 0.1025 = 10.25%. b. 10.0% semiannually = 1  2   c.

9.8% continuously = e0.098 – 1.0 = 0.10296 = 10.30%.

(4B-6) Continuous Compounding You have $11,572.28 in an account that has been paying an annual rate of 9% compounded continuously. If you deposited some funds 15 years ago, how much was your original deposit? Solution: (Constant e

= 2.7183 rounded.)

$11,572.28

= PVe0.09(15)

$11,572.28

= PVe1.35

= $11,572.28/e1.35 = $11,572.28/3.85743 = $3,000.

(4B-7) Continuous Compounding

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

For a 10-year deposit, what annual rate payable semiannually will produce the same effective rate as 3% compounded continuously? Solution: e

INOM    = 1  2  

(0.03)(10)

INOM    = 1  2  

0.3

=1+

INOM 2

1.01511 = 1 +

INOM 2

e0.3/20

INOM = 0.01511 2 INOM = 0.0302 = 3.02%. (4B-8) Payment and Continuous Compounding You place $2,000 in an account that pays 8% interest compounded continuously. You plan to hold the account exactly 3 years. At the same time, in another account you deposit money that earns 9% compounded semiannually. If you want the accounts to have the same amount at the end of the 3 years, how much of an initial deposit do you need to make now in the account that pays 9% interest compounded semiannually? Solution: Step 1: Calculate the FV of the $2,000 deposit at 8% with continuous compounding: Using ex key: Inputs:

X = 0.24; press ex key.

Output:

ex = 1.27125.

FVN = $2,000e0.08(3) = $2,000(1.27125) = $2,542.50. Step 2:

Calculate the PV or initial deposit: Input the following data into your calculator: N = 6; I/YR = 4.5; PMT = 0; FV = 2542.50; and then solve for PV = $1,952.37.

Solution and Answer Guide CHAPTER 5: BONDS, BOND VALUATION, AND INTEREST RATES

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 105 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 109 Easy Problems 1-6 ................................................................................................................................ 109 Intermediate Problems 7–20 ................................................................................................................. 111 Challenging Problems 21–23 ................................................................................................................ 117 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 120 MINI CASE ............................................................................................................................................. 120 Web Extension 5A ................................................................................................................................... 132 Answers to Questions ........................................................................................................................... 132 Solutions to Problems ........................................................................................................................... 133 Web Extension 5E ................................................................................................................................... 136 Solutions to Problems ........................................................................................................................... 136

ANSWERS TO END-OF-CHAPTER QUESTIONS 5-1

Define each of the following terms: a. Bond; Treasury bond; corporate bond; municipal bond; foreign bond b. Par value; maturity date; coupon payment; coupon interest rate c. Floating-rate bond; zero coupon bond; original issue discount bond (OID) d. Call provision; redeemable bond; sinking fund e. Convertible bond; warrant; income bond; indexed bond (also called a purchasing power bond) f. Premium bond; discount bond g. Current yield (on a bond); yield to maturity (YTM); yield to call (YTC) h. Indentures; mortgage bond; debenture; subordinated debenture i. Development bond; municipal bond insurance; junk bond; investment-grade bond j. Real risk-free rate of interest, r*; nominal risk-free rate of interest, rRF k. Inflation premium (IP); default risk premium (DRP); liquidity; liquidity premium (LP) l. Interest rate risk; maturity risk premium (MRP); reinvestment rate risk m. Term structure of interest rates; yield curve n. ―Normal‖ yield curve; inverted (―abnormal‖) yield curve Answer: a. A bond is a promissory note issued by a business or a governmental unit. Treasury bonds, sometimes referred to as government bonds, are issued by the Federal government and are not exposed to default risk. Corporate bonds are issued by corporations and are exposed to default risk. Different corporate bonds have different levels of default risk, depending on the issuing company’s characteristics and on the terms of the specific bond.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Municipal bonds are issued by state and local governments. The interest earned on most municipal bonds is exempt from federal taxes, and also from state taxes if the holder is a resident of the issuing state. Foreign bonds are issued by foreign governments or foreign corporations. These bonds are not only exposed to default risk but are also exposed to an additional risk if the bonds are denominated in a currency other than that of the investor’s home currency. b.

The par value is the nominal or face value of a stock or bond. The par value of a bond generally represents the amount of money that the firm borrows and promises to repay at some future date. The par value of a bond is often $1,000 but can be $5,000 or more. The maturity date is the date when the bond’s par value is repaid to the bondholder. Maturity dates generally range from 10 to 40 years from the time of issue. A call provision may be written into a bond contract, giving the issuer the right to redeem the bonds under specific conditions prior to the normal maturity date. A bond’s coupon, or coupon payment, is the dollar amount of interest paid to each bondholder on the interest payment dates. The coupon is so named because bonds used to have dated coupons attached to them, which investors could tear off and redeem on the interest payment dates. The coupon interest rate is the stated rate of interest on a bond.

In some cases, a bond’s coupon payment may vary over time. These bonds are called floating-rate bonds. Floating-rate debt is popular with investors because the market value of the debt is stabilized. It is advantageous to corporations because firms can issue long-term debt without committing themselves to paying an unusually high interest rate for the entire life of the loan. Zero coupon bonds pay no coupons at all, but are offered at a substantial discount below their par values and hence provide capital appreciation rather than interest income. In general, any bond originally offered at a price significantly below its par value is called an original issue discount bond (OID).

Most bonds contain a call provision, which gives the issuing corporation the right to call the bonds for redemption. The call provision generally states that if the bonds are called, the company must pay the bondholders an amount greater than the par value, a call premium. Redeemable bonds give investors the right to sell the bonds back to the corporation at a price that is usually close to the par value. If interest rates rise, investors can redeem the bonds and reinvest at the higher rates. A sinking fund provision facilitates the orderly retirement of a bond issue. This can be achieved in one of two ways: The company can call in for redemption (at par value) a certain percentage of bonds each year. The company may buy the required amount of bonds on the open market.

Convertible bonds are securities that are convertible into shares of common stock, at a fixed price, at the option of the bondholder. Bonds issued with warrants are similar to convertibles. Warrants are options which permit the holder to buy stock for a stated price, thereby providing a capital gain if the stock price rises. Income bonds pay interest only if the interest is earned. These securities cannot bankrupt a company, but from an investor’s standpoint they are riskier than ―regular‖ bonds.

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The interest rate of an indexed or purchasing power bond is based on an inflation index such as the consumer price index (CPI), so the interest paid rises automatically when the inflation rate rises, thus protecting the bondholders against inflation. f.

Bond prices and interest rates are inversely related; that is, they tend to move in the opposite direction from one another. A fixed-rate bond will sell at par when its coupon interest rate is equal to the going rate of interest, rd. When the going rate of interest is above the coupon rate, a fixed-rate bond will sell at a ―discount‖ below its par value. If current interest rates are below the coupon rate, a fixed-rate bond will sell at a ―premium‖ above its par value.

The current yield on a bond is the annual coupon payment divided by the current market price. YTM, or yield to maturity, is the rate of interest earned on a bond if it is held to maturity. Yield to call (YTC) is the rate of interest earned on a bond if it is called. If current interest rates are well below an outstanding callable bond’s coupon rate, the YTC may be a more relevant estimate of expected return than the YTM, since the bond is likely to be called.

Corporations can influence the default risk of their bonds by changing the type of bonds they issue. Under a mortgage bond, the corporation pledges certain assets as security for the bond. All such bonds are written subject to an indenture, which is a legal document that spells out in detail the rights of both the bondholders and the corporation. A debenture is an unsecured bond, and as such, it provides no lien against specific property as security for the obligation. Debenture holders are, therefore, general creditors whose claims are protected by property not otherwise pledged. Subordinated debentures have claims on assets, in the event of bankruptcy, only after senior debt as named in the subordinated debt’s indenture has been paid off. Subordinated debentures may be subordinated to designated notes payable or to all other debt.

A development bond is a tax-exempt bond sold by state and local governments whose proceeds are made available to corporations for specific uses deemed (by Congress) to be in the public interest. Municipalities can insure their bonds, in which an insurance company guarantees to pay the coupon and principal payments should the issuer default. This reduces the risk to investors who are willing to accept a lower coupon rate for an insured bond issue vis-a-vis an uninsured issue. Bond issues are normally assigned quality ratings by major rating agencies, such as Moody’s Investors Service and Standard & Poor’s Corporation. These ratings reflect the probability that a bond will go into default. Aaa (Moody’s) and AAA (S&P) are the highest ratings. Rating assignments are based on qualitative and quantitative factors including the firm’s debt/assets ratio, current ratio, and coverage ratios. Because a bond’s rating is an indicator of its default risk, the rating has a direct, measurable influence on the bond’s interest rate and the firm’s cost of debt capital. Junk bonds are high-risk, high-yield bonds issued to finance leveraged buyouts, mergers, or troubled companies. Most bonds are purchased by institutional investors rather than individuals, and many institutions are restricted to investment-grade bonds, securities with ratings of Baa/BBB or above.

The real risk-free rate is the rate that a hypothetical riskless security pays each moment if zero inflation were expected. The real risk-free rate is not constant—r* changes over time depending on economic conditions. The real risk-free rate could also be called the pure rate of interest since it is the rate of interest that would exist on very short-term, default-free U.S. Treasury securities if the

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expected rate of inflation were zero. It has been estimated that this rate of interest, denoted by r*, has fluctuated in recent years in the United States in the range of 2 to 4%. The nominal risk-free rate of interest, denoted by rRF, is the real risk-free rate plus a premium for expected inflation. The short-term nominal risk-free rate is usually approximated by the U.S. Treasury bill rate, while the long-term nominal risk-free rate is approximated by the rate on U.S. Treasury bonds. Note that while T-bonds are free of default and liquidity risks, they are subject to risks due to changes in the general level of interest rates. k.

The inflation premium (IP) is the premium added to the real risk-free rate of interest to compensate for the expected loss of purchasing power. The inflation premium is the average rate of inflation expected over the life of the security. Default risk is the risk that a borrower will not pay the interest and/or principal on a loan as they become due. Thus, a default risk premium (DRP) is added to the real risk-free rate to compensate investors for bearing default risk. Liquidity refers to a firm’s cash and marketable securities position, and to its ability to meet maturing obligations. A liquid asset is any asset that can be quickly sold and converted to cash at its ―fair‖ value. Active markets provide liquidity. A liquidity premium (LP) is added to the real risk-free rate of interest, in addition to other premiums, if a security is not liquid.

Interest rate risk arises from the fact that bond prices decline when interest rates rise. Under these circumstances, selling a bond prior to maturity will result in a capital loss, and the longer the term to maturity, the larger the loss. Thus, a maturity risk premium must be added to the real risk-free rate of interest to compensate for interest rate risk. Reinvestment rate risk occurs when a short-term debt security must be ―rolled over.‖ If interest rates have fallen, the reinvestment of principal will be at a lower rate, with correspondingly lower interest payments and ending value. Note that long-term debt securities also have some reinvestment rate risk because their interest payments have to be reinvested at prevailing rates.

m. The term structure of interest rates is the relationship between yield to maturity and term to maturity for bonds of a single risk class. The yield curve is the curve that results when yield to maturity is plotted on the Y-axis with term to maturity on the X-axis. n.

When the yield curve slopes upward, it is said to be ―normal,‖ because it is like this most of the time. Conversely, a downward-sloping yield curve is termed ―abnormal‖ or ―inverted.‖

5-2

―Short-term interest rates are more volatile than long-term interest rates, so short-term bond prices are more sensitive to interest rate changes than are long-term bond prices.‖ Is this statement true or false? Explain. Answer: False. Short-term bond prices are less sensitive than long-term bond prices to interest rate changes because funds invested in short-term bonds can be reinvested at the new interest rate sooner than funds tied up in long-term bonds.

5-3

The rate of return on a bond held to its maturity date is called the bond’s yield to maturity. If interest rates in the economy rise after a bond has been issued, what will happen to the bond’s price and to its

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YTM? Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond’s price? Why or why not? Answer: The price of the bond will fall and its YTM will rise if interest rates rise. If the bond still has a long term to maturity, its YTM will reflect long-term rates. Of course, the bond’s price will be less affected by a change in interest rates if it has been outstanding a long time and matures shortly. While this is true, it should be noted that the YTM will increase only for buyers who purchase the bond after the change in interest rates and not for buyers who purchased previous to the change. If the bond is purchased and held to maturity, the bondholder’s YTM will not change, regardless of what happens to interest rates. 5-4

If you buy a callable bond and interest rates decline, will the value of your bond rise by as much as it would have risen if the bond had not been callable? Explain. Answer: If interest rates decline significantly, the values of callable bonds will not rise by as much as those of bonds without the call provision. It is likely that the bonds would be called by the issuer before maturity, so that the issuer can take advantage of the new, lower rates.

5-5

A sinking fund can be set up in one of two ways. Discuss the advantages and disadvantages of each procedure from the viewpoint of both the firm and its bondholders. Answer: From the corporation’s viewpoint, one important factor in establishing a sinking fund is that its own bonds generally have a higher yield than do government bonds; hence, the company saves more interest by retiring its own bonds than it could earn by buying government bonds. This factor causes firms to favor the second procedure. Investors also would prefer the annual retirement procedure if they thought that interest rates were more likely to rise than to fall, but they would prefer the government bond purchases program if they thought rates were likely to fall. In addition, bondholders recognize that, under the government bond purchase scheme, each bondholder would be entitled to a given amount of cash from the liquidation of the sinking fund if the firm should go into default, whereas under the annual retirement plan, some of the holders would receive a cash benefit while others would benefit only indirectly from the fact that there would be fewer bonds outstanding. On balance, investors seem to have little reason for choosing one method over the other, while the annual retirement method is clearly more beneficial to the firm. The consequence has been a pronounced trend toward annual retirement and away from the accumulation scheme.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1-6 5-1

Bond Valuation With Annual Payments. Jackson Corporation’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8%. The bonds have a yield to maturity of 9%. What is the current market price of these bonds? Solution: With your financial calculator, enter the following: N = 12; I/YR = YTM = 9%; PMT = 0.08  1,000 = 80; and FV = 1000. Press PV key to solve for PV = $928.39. Therefore, VB = $928.39. Alternatively, VB = $80((1 – 1/1.0912)/0.09) + $1,000(1/1.0912)

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= $928.39 5-2

Yield to Maturity for Annual Payments. Wilson Corporation’s bonds have 12 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 10%. The bonds sell at a price of $850. What is their yield to maturity? Solution: With your financial calculator, enter the following: N = 12; PV = –850; PMT = 0.10  1,000 = 100; and FV = 1000. Press I/YR key to solve for I/YR = 12.48% = YTM.

5-3

Current Yield for Annual Payments. Heath Food Corporation’s bonds have 7 years remaining to maturity. The bonds have a face value of $1,000 and a yield to maturity of 8%. They pay interest annually and have a 9% coupon rate. What is their current yield? Solution: With your financial calculator, enter the following to find the current value of the bonds, so you can then calculate their current yield: N = 7; I/YR = YTM = 8; PMT = 0.09  1,000 = 90; and FV = 1000. Press PV to solve for PV = $1,052.06 = VB. Current yield = $90/$1,052.06 = 8.55%. Alternatively, VB = $90((1 – 1/1.087)/0.08) + $1,000(1/1.087) = $1,052.06. Current yield = $90/$1,052.06 = 8.55%.

5-4

Determinant of Interest Rates. The real risk-free rate of interest is 4%. Inflation is expected to be 2% this year and 4% during each of the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2-year Treasury securities? What is the yield on 3-year Treasury securities? Solution: r* = 4%; I1 = 2%; I2 = 4%; I3 = 4%; MRP = 0; rT-2 = ?; rT-3 = ? r = r* + IP + DRP + LP + MRP. Since these are Treasury securities, DRP = LP = 0. rT-2 = r* + IP2 IP2 = (2% + 4%)/2 = 3% rT-2 = 4% + 3% = 7%. rT-3 = r* + IP3 IP3 = (2% + 4% + 4%)/3 = 3.33% rT-3 = 4% + 3.33% = 7.33%.

5-5

Default Risk Premium. A Treasury bond that matures in 10 years has a yield of 6%. A 10-year corporate bond has a yield of 9%. Assume that the liquidity premium on the corporate bond is 0.5%. What is the default risk premium on the corporate bond? Solution: rT-10 = 6%; rC-10 = 9%; LP = 0.5%; DRP = ? r = r* + IP + DRP + LP + MRP.

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rT-10 = r* + IP + MRP = 6%; DRP = LP = 0. rC-10 = r* + IP + DRP + 0.5% + MRP = 8%. Because both bonds are 10-year bonds, the inflation premium and maturity risk premium on both bonds are equal. The only difference between them is the liquidity and default risk premiums. rC-10 = r* + IP + MRP + 0.5% + DRP = 9%. But we know from above that r* + IP + MRP = 6%; therefore, 6% + 0.5% + DRP DRP = 2.5%. 5-6

= 9%

Maturity Risk Premium. The real risk-free rate is 3%, and inflation is expected to be 3% for the next 2 years. A 2-year Treasury security yields 6.3%. What is the maturity risk premium for the 2-year security? Solution: r* = 3%; IP = 3%; rT-2 = 6.3%; MRP2 = ? rT-2 = r* + IP + MRP = 6.3% rT-2 = 3% + 3% + MRP = 6.3% MRP = 0.3%.

INTERMEDIATE PROBLEMS 7–20 5-7

Bond Valuation With Semiannual Payments. Renfro Rentals has issued bonds that have a 10% coupon rate, payable semiannually. The bonds mature in 8 years, have a face value of $1,000, and a yield to maturity of 8.5%. What is the price of the bonds? Solution: The problem asks you to find the price of a bond, given the following facts: N = 16; I/YR = 8.5/2 = 4.25; PMT = 50; FV = 1000. With a financial calculator, solve for PV = $1,085.80

5-8

Yield to Maturity and Call With Semiannual Payments. Thatcher Corporation’s bonds will mature in 10 years. The bonds have a face value of $1,000 and an 8% coupon rate, paid semiannually. The price of the bonds is $1,100. The bonds are callable in 5 years at a call price of $1,050. What is their yield to maturity? What is their yield to call? Solution: With your financial calculator, enter the following to find YTM: N = 10  2 = 20; PV = –1100; PMT = 0.08/2  1,000 = 40; and FV = 1000. Solve for I/YR = 3.31%. Multiply by 2 to get annual YTM: 3.31%  2 = 6.62% = YTM. With your financial calculator, enter the following to find YTC: N = 5  2 = 10; PV = –1100; PMT = 0.08/2  1,000 = 40; and FV = 1050. Press I/YR = 3.24%  2 = 6.49% = YTC.

5-9

Bond Valuation and Interest Rate Risk. The Garraty Company has two bond issues outstanding. Both bonds pay $100 annual interest plus $1,000 at maturity. Bond L has a maturity of 15 years, and Bond S has a maturity of 1 year. a. What will be the value of each of these bonds when the going rate of interest is (1) 5%, (2) 8%, and (3) 12%? Assume that there is only one more interest payment to be made on Bond S.

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Why does the longer-term (15-year) bond fluctuate more when interest rates change than does the shorter-term bond (1 year)?

Solution: a.

5%:

Bond L: Input N = 15, I/YR = 5, PMT = −100, and FV = −1000. Press PV to get PV = $1,518.98. Bond S: Change to N = 1. Press PV to get PV = $1,047.62.

8%:

Bond L: From Bond S inputs, change N = 15 and I/YR = 8. Press PV to get PV = $1,171.19. Bond S: Change to N = 1. Press PV to get PV = $1,018.52.

12%: Bond L: From Bond S inputs, change N = 15 and I/YR = 12. Press PV to get PV = $863.78. Bond S: Change N = 1; Press PV to get PV = $982.14.

Think about a bond that matures in 1 month. Its present value is influenced primarily by the maturity value, which will be received in only 1 month. Even if interest rates double, the price of the bond will still be close to $1,000. A 1-year bond’s value would fluctuate more than the 1-month bond’s value because of the difference in the timing of receipts. However, its value would still be fairly close to $1,000 even if interest rates doubled. A long-term bond paying semiannual coupons, on the other hand, will be dominated by distant receipts, receipts which are multiplied by 1/(1 + rd/2)t, and if rd increases, these multipliers will decrease significantly. Another way to view this problem is from an opportunity point of view. A 1-month bond can be reinvested at the new rate very quickly, and hence the opportunity to invest at this new rate is not lost; however, the long-term bond locks in subnormal returns for a long period of time.

5-10 Yield to Maturity and Required Returns. The Brownstone Corporation’s bonds have 5 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 9%. a. What is the yield to maturity at a current market price of (1) $829 or (2) $1,104? b. Would you pay $829 for one of these bonds if you thought that the appropriate rate of interest was 12%—that is, if rd = 12%? Explain your answer. Solution: a. Calculator solution: 1. Input N = 5, PV = –829, PMT = 90, and FV = 1000. Press I/YR to get I/YR 13.98%. 2. b.

Change PV = –1104; Press I/YR to get I/YR = 6.50%.

Yes. At a price of $829, the yield to maturity, 13.98%, is greater than your required rate of return of 12%. If your required rate of return were 12%, you should be willing to buy the bond at any price below $891.86.

5-11 Yield to Call and Realized Rates of Return. Goodwynn & Wolf Incorporated (G&W) issued a bond 7 years ago. The bond had a 20-year maturity, a 14% coupon paid annually, a 9% call premium and was issued at par, $1,000. Today, G&W called the bonds. If the original investors had expected G&W to call the bonds in 7 years, what was the yield to call at the time the bonds were issued? Solution:

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Using a financial calculator, input the following: N = 7; PV = −1000; PMT = 14%(1,000) = 140; and FV = (1 + 0.09)(1,000) = 1090. Press I/YR to get I/YR = 14.82%. 5-12 Bond Yields and Rates of Return. A 10-year, 12% semiannual coupon bond with a par value of $1,000 may be called in 4 years at a call price of $1,060. The bond sells for $1,100. (Assume that the bond has just been issued.) a. What is the bond’s yield to maturity? b. What is the bond’s current yield? c. What is the bond’s capital gain or loss yield? d. What is the bond’s yield to call? Solution: a. Using a financial calculator, input the following: N = 20, PV = –1100, PMT = 60, and FV = 1000. Solve for I/YR = 5.1849%. However, this is a periodic rate. The nominal annual rate = 5.1849%(2) = 10.3699% ≈ 10.37%. b.

The current yield = $120/$1,100 = 10.91%.

YTM = Current yield + Capital gains (loss) yield 10.37% = 10.91% + Capital loss yield Capital loss yield = –0.54%.

Using a financial calculator, input the following: N = 8, PV = –1100, PMT = 60, and FV = 1060. Solve for I/YR = 5.0748%. However, this is a periodic rate. The nominal annual rate = 5.0748%(2) = 10.1495% ≈ 10.15%.

5-13 Yield to Maturity and Current Yield. You just purchased a bond that matures in 5 years. The bond has a face value of $1,000 and an 8% annual coupon. The bond has a current yield of 8.21%. What is the bond’s yield to maturity? Solution: The problem asks you to solve for the YTM, given the following facts: N = 5, PMT = 80, and FV = 1000. In order to solve for I/YR, we need PV. However, you are also given that the current yield is equal to 8.21%. Note that ―current yield‖ does NOT mean the yield to maturity existing at the time! Given this information, we can find PV. Current yield = Annual interest/Current price 0.0821 = $80/PV PV = $80/0.0821 = $974.42. Now, solve for the YTM with a financial calculator: N = 5, PV = –974.42, PMT = 80, and FV = 1000. Solve for I/YR = YTM = 8.65%. 5-14 Current Yield With Semiannual Payments. A bond that matures in 7 years sells for $1,020. The bond has a face value of $1,000 and a yield to maturity of 10.5883%. The bond pays coupons semiannually. What is the bond’s current yield? Solution: The problem asks you to solve for the current yield, given the following facts: N = 14, I/YR = 10.5883/2 = 5.2942, PV = −1020, and FV = 1000. In order to solve for the current yield we need to find PMT. With

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a financial calculator, we find PMT = $55.00. However, because the bond is a semiannual coupon bond this amount needs to be multiplied by 2 to obtain the annual interest payment: $55.00(2) = $110.00. Finally, find the current yield as follows: Current yield = Annual interest/Current price = $110/$1,020 = 10.78%. 5-15 Yield to Call, Yield to Maturity, and Market Rates. Absalom Energy’s 14% coupon rate, semiannual payment, $1,000 par value bonds that mature in 30 years are callable 5 years from now at a price of $1,050. The bonds sell at a price of $1,353.54, and the yield curve is flat. Assuming that interest rates in the economy are expected to remain at their current level, what is the best estimate of the nominal interest rate on new bonds issued in 5 years? Solution: The bond is selling at a large premium, which means that its coupon rate is much higher than the going rate of interest. Therefore, the bond is more likely to be called than to remain outstanding until it matures. Thus, it will probably provide a return equal to the YTC rather than the YTM. So, there is no point in calculating the YTM; just calculate the YTC. Enter these values: N = 10, PV = –1353.54, PMT = 70, and FV = 1050. Solve for I/YR = 3.24%. The periodic rate is 3.24%, so the nominal YTC is 2 × 3.24% = 6.47%. This would be close to the going rate, and it is about what the firm would have to pay on new bonds. 5-16 Interest Rate Sensitivity. A bond trader purchased each of the following bonds at a yield to maturity of 8%. Immediately after she purchased the bonds, interest rates fell to 7%. What is the percentage change in the price of each bond after the decline in interest rates? Fill in the following table: Price @ 8%

Price @ 7%

Percentage Change

10-year, 10% annual coupon

_________

10-year zero

_________

5-year zero

_________

30-year zero

_________

Perpetuity, $100 annual coupon

_________

Solution: The price of a perpetuity is: Price = (Annual payment)/(Interest rate). For example, the price of a $100 perpetuity at an 8% interest rate is: $100/0.08 = $1,250. The prices for the other cases are found with a financial calculator. For example, the price of a 10-year, 10% bond is found using these inputs: N = 10, I/YR = 8, PV = ?, PMT = −(0.10 × 1000) = −100, FV = −1000; solve for PV = 1,134.20. The same approach can be used for the zero coupon bonds by substituting zero for the payment. Price at 8%

Price at 7%

$1,134.20

$1,210.71

6.75%

10-year zero

463.19

508.35

9.75%

5-year zero

680.58

712.99

4.76%

30-year zero

99.38

131.37

32.19%

$100 perpetuity

1,250.00

1,428.57

14.29%

10-year, 10% annual coupon

Percentage Change

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5-17 Bond Value as Maturity Approaches. An investor has two bonds in her portfolio. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity equal to 9.6%. One bond, Bond C, pays an annual coupon of 10%; the other bond, Bond Z, is a zero coupon bond. Assuming that the yield to maturity of each bond remains at 9.6% over the next 4 years, what will be the price of each of the bonds at the following time periods? Fill in the following table: T

Price of Bond C

Price of Bond Z

_________

Solution: Using a financial calculator, the price of Bond C is found using these inputs: N = 4 − Yeart, I/YR = 9.6, PMT = −(0.10 × 1000) = −100, FV = −1000. Solve for PV. For example, to find the price of Bond C at Year 0, enter: N = 4, I/YR = 9.6, PMT = −(0.10 × 1000) = −100, FV = −1000. Solve for PV = 1,012.79. The same approach can be used for the zero coupon bonds by substituting zero for the payment. Yeart

Price of Bond C

Price of Bond Z

$1,012.79

$ 693.04

1,010.02

759.57

1,006.98

832.49

1,003.65

912.41

1,000.00

5-18 Determinants of Interest Rates. The real risk-free rate is 2%. Inflation is expected to be 3% this year, 4% next year, and then 3.5% thereafter. The maturity risk premium is estimated to be 0.0005 × (t − 1), where t = number of years to maturity. What is the nominal interest rate on a 7-year Treasury security? Solution: r = r* + IP + MRP + DRP + LP. r* = 0.02. IP = [0.03 + 0.04 + (5)(0.035)]/7 = 0.035. MRP = 0.0005(6) = 0.003. DRP = 0. LP = 0. r = 0.02 + 0.035 + 0.003 = 0.058 = 5.8%. 5-19 Maturity Risk Premiums. Assume that the real risk-free rate, r*, is 3% and that inflation is expected to be 8% in Year 1, 5% in Year 2, and 4% thereafter. Assume also that all Treasury securities are highly liquid and free of default risk. If 2-year and 5-year Treasury notes both yield 10%, what is the difference in the maturity risk premiums (MRPs) on the two notes; that is, what is MRP5 minus MRP2? Solution: First, note that we will use the equation rt = 3% + IPt + MRPt. We have the data needed to find the IPs:

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IP5 =

8% + 5% + 4% + 4% + 4% 25% = = 5%. 5 5

IP2 =

8% + 5% = 6.5%. 2

Now we can substitute into the equation: r2 = 3% + 6.5% + MRP2 = 10%. r5 = 3% + 5% + MRP5 = 10%. Now we can solve for the MRPs, and find the difference: MRP5 = 10% – 8% = 2%. MRP2 = 10% – 9.5% = 0.5%. Difference = (2% – 0.5%) = 1.5%. 5-20 Inflation Risk Premiums. Because of a recession, the inflation rate expected for the coming year is only 3%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3%. Assume that the real risk-free rate is r* = 2% for all maturities and that there are no maturity risk premiums. If 3-year Treasury notes yield 2 percentage points more than 1-year notes, what inflation rate is expected after Year 1? Solution: Basic relevant equations: rt = r* + IPt + DRPt + MRPt + LPt. But here IP is the only premium, so rt = r* + IPt. IPt = Avg. inflation = (I1 + I2 + ...)/N. We know that I1 = IP1 = 3% and r* = 2%. Therefore, r1 = 2% + 3% = 5%. r3 = r1 + 2% = 5% + 2% = 7%. But, r3 = r* + IP3 = 2% + IP3 = 7%, So, IP3 = 7% – 2% = 5%. We also know that It = Constant after t = 1. We can set up this table: r*

Avg. I = IPt

3%/1 = 3%

(3% + I)/2 = IP2

(3% + I + I)/3 = IP3

r = r* + IPt 5%

r3 = 7%,

Therefore, IP3 = 7% − 2% = 5%.

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Avg. I = IP3 = (3% + 2I)/3 = 5% 2I = 12% I = 6%.

CHALLENGING PROBLEMS 21–23 5-21 Bond Valuation and Changes in Maturity and Required Returns. Suppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments. a. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 6%. At what price would the bonds sell? b. Suppose that 2 years after the initial offering, the going interest rate had risen to 12%. At what price would the bonds sell? c. Suppose that 2 years after the issue date (as in part a) interest rates fell to 6%. Suppose further that the interest rate remained at 6% for the next 8 years. What would happen to the price of the bonds over time? Solution: a. The bonds now have an 8-year, or a 16-semiannual period, maturity, and their value is calculated as follows: Calculator solution: Input N = 16, I/YR = 3, PMT = 50, and FV = 1000. Solve for PV = $1,251.22. b.

Calculator solution: Change inputs from Part a to I/YR = 6. Solver for PV = $898.94.

The price of the bond will decline toward $1,000, hitting $1,000 (plus accrued interest) at the maturity date at 8 years (16 six-month periods).

5-22 Yield to Maturity and Yield to Call. Arnot International’s bonds have a current market price of $1,200. The bonds have an 11% annual coupon payment, a $1,000 face value, and 10 years left until maturity. The bonds may be called in 5 years at 109% of face value (call price = $1,090). a. What is the yield to maturity? b. What is the yield to call if they are called in 5 years? c. Which yield might investors expect to earn on these bonds, and why? d. The bond’s indenture indicates that the call provision gives the firm the right to call them at the end of each year beginning in Year 5. In Year 5, they may be called at 109% of face value, but in each of the next 4 years the call percentage will decline by 1 percentage point. Thus, in Year 6 they may be called at 108% of face value, in Year 7 they may be called at 107% of face value, and so on. If the yield curve is horizontal and interest rates remain at their current level, when is the latest that investors might expect the firm to call the bonds? Solution: a. Find the YTM as follows: Input N = 10, PV = –1200, PMT = 110, and FV = 1000. Solve for I/YR = YTM = 8.02%. b.

Find the YTC, if called in Year 5 as follows:

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Input N = 5, PV = –1200, PMT = 110, and FV = 1090. Solve for I/YR = YTC = 7.59%. c.

The bonds are selling at a premium which indicates that interest rates have fallen since the bonds were originally issued. Assuming that interest rates do not change from the present level, investors would expect to earn the yield to call. (Note that the YTC is less than the YTM.)

Repeating the same process as used in step b, the YTC can be found for each subsequent year. If called in Year 6: N = 6, PV = –1200, PMT = 110, and FV = 1080. Solver for I/YR = YTC = 7.80%. If called in Year 7: N = 7, PV = –1200, PMT = 110, and FV = 1070. Solve for I/YR = YTC = 7.95%. If called in Year 8: N = 8, PV = –1200, PMT = 110, and FV = 1060. Solve for I/YR = YTC = 8.07%. If called in Year 9: N = 9, PV = –1200, PMT = 110, and FV = 1050. Solve for I/YR = YTC = 8.17%. According to these calculations, the latest investors might expect a call of the bonds is in Year 7. This is the last year that the expected YTC will be less than the expected YTM. At this time, the firm still finds an advantage to calling the bonds, rather than seeing them to maturity.

5-23 Determinants of Interest Rates. Suppose you and most other investors expect the inflation rate to be 7% next year, to fall to 5% during the following year, and then to remain at a rate of 3% thereafter. Assume that the real risk-free rate, r*, will remain at 2% and that maturity risk premiums on Treasury securities rise from zero on very short-term securities (those that mature in a few days) to a level of 0.2 percentage points for 1-year securities. Furthermore, maturity risk premiums increase by 0.2 percentage points for each year to maturity, up to a limit of 1.0 percentage point on 5-year or longer-term T-notes and T-bonds. a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities, and plot the yield curve. b. Now suppose ExxonMobil’s bonds, rated AAA, have the same maturities as the Treasury bonds. As an approximation, plot an ExxonMobil yield curve on the same graph with the Treasury bond yield curve. (Hint: Think about the default risk premium on ExxonMobil’s long-term versus short-term bonds.) c. Now plot the approximate yield curve of Long Island Lighting Company, a risky nuclear utility.

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Solution: a. Years to Maturity

Real RiskFree Rate

1 2 3 4 5 10 20

2% 2 2 2 2 2 2

Annual Expected Inflation Rate 7.0% 5.0 3.0 3.0 3.0 3.0 3.0

Inflation Premium = Average Inflation Rate1 7.00% 6.00 5.00 4.50 4.20 3.60 3.30

Maturity Risk Premiums

0.2% 0.4 0.6 0.8 1.0 1.0 1.0

Treasury Security Rate

9.20% 8.40 7.60 7.30 7.20 6.60 6.30

Notes: 1.

Average Inflation Rate for Year t = (Sum of annual rates for all years up to and including Year t)/t. For example, the average inflation rate for Year 2 = (Annual expected inflation in Year 1 + Annual expected inflation in Year 2)/2 = (7% + 5%)/2 = 6%. For Year 3, it is (7% + 5% + 3%)/3 = 15%/3 = 5%. The Treasury Security Rate is sum of Real Risk-Free Rate + Average Inflation Rate + Maturity Risk Premium. For example, the Treasury Security Rate in Year 2 = 2% + 6% + 0.4% = 8.4%. Thus, the yield curve would be as follows:

The interest rate on the ExxonMobil bonds has the same components as the Treasury securities, except that the ExxonMobil bonds have default risk, so a default risk premium must be included. Therefore, rExxon = r* + IP + MRP + DRP. For a strong company such as ExxonMobil, the default risk premium is virtually zero for short-term bonds. However, as time to maturity increases, the probability of default, although still small, is sufficient to warrant a default premium. Thus, the yield risk curve for the ExxonMobil bonds will rise above the yield curve for the Treasury securities. In the graph, the default risk premium was assumed to be 1.0 percentage point on the 20-year Exxon bonds. The return should equal 6.3% + 1% = 7.3%.

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LILCO bonds would have significantly more default risk than either Treasury securities or Exxon bonds, and the risk of default would increase over time due to possible financial deterioration. In this example, the default risk premium was assumed to be 1.0 percentage point on the 1-year LILCO bonds and 2.0 percentage points on the 20-year bonds. The 20-year return should equal 6.3% + 2% = 8.3%.

SOLUTION TO SPREADSHEET PROBLEM 5-24 Build a Model: Bond Valuation. Start with the partial model in the file Ch05 P24 Build a Model.xlsx on the textbook’s website. A 20-year, 8% semiannual coupon bond with a par value of $1,000 may be called in 5 years at a call price of $1,040. The bond sells for $1,100. (Assume that the bond has just been issued.) a. What is the bond’s yield to maturity? b. What is the bond’s current yield? c. What is the bond’s capital gain or loss yield? d. What is the bond’s yield to call? e. How would the price of the bond be affected by a change in the going market interest rate? (Hint: Conduct a sensitivity analysis of price to changes in the going market interest rate for the bond. Assume that the bond will be called if and only if the going rate of interest falls below the coupon rate. This is an oversimplification, but assume it for purposes of this problem.) f. Now assume the date is October 25, 2022. Assume further that a 12%, 10-year bond was issued on July 1, 2022, pays interest semiannually (on January 1 and July 1), and sells for $1,100. Use your spreadsheet to find the bond’s yield. Solution: The detailed solution for the problem is in the file Ch05 P24 Build a Model Solution.xlsx and is available on the instructor’s side of the textbook’s website.

MINI CASE Sam Strother and Shawna Tibbs are vice presidents of Mutual of Seattle Insurance Company and codirectors of the company’s pension fund management division. An important new client, the North-Western Municipal Alliance, has requested that Mutual of Seattle present an investment seminar to the mayors of the represented cities, and Strother and Tibbs, who will make the actual presentation, have asked you to help them by answering the following questions. a.

What are the key features of a bond? Answer: 1. Par or face value. We generally assume a $1,000 par value, but par can be anything, and often $5,000 or more is used. With registered bonds, which is what are issued today, if you bought $50,000 worth, that amount would appear on the certificate. 2.

Coupon rate. The dollar coupon is the ―rent‖ on the money borrowed, which is generally the par value of the bond. The coupon rate is the annual interest payment divided by the par value, and it is generally set at the value of r on the day the bond is issued.

Maturity. This is the number of years until the bond matures and the issuer must repay the loan (return the par value).

Issue date. This is the date the bonds were issued.

Default risk is inherent in all bonds except treasury bonds—will the issuer have the cash to make the

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promised payments? Bonds are rated from AAA to D, and the lower the rating the riskier the bond, the higher its default risk premium, and, consequently, the higher its required rate of return, r. b.

What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky?

Answer: A call provision is a provision in a bond contract that gives the issuing corporation the right to redeem the bonds under specified terms prior to the normal maturity date. The call provision generally states that the company must pay the bondholders an amount greater than the par value if they are called. The additional sum, which is called a call premium, is typically set equal to 1 year’s interest if the bonds are called during the first year, and the premium declines at a constant rate of INT/n each year thereafter. A sinking fund provision is a provision in a bond contract that requires the issuer to retire a portion of the bond issue each year. A sinking fund provision facilitates the orderly retirement of the bond issue. The call privilege is valuable to the firm but potentially detrimental to the investor, especially if the bonds were issued in a period when interest rates were cyclically high. Therefore, bonds with a call provision are riskier than those without a call provision. Accordingly, the interest rate on a new issue of callable bonds will exceed that on a new issue of noncallable bonds. Although sinking funds are designed to protect bondholders by ensuring that an issue is retired in an orderly fashion, it must be recognized that sinking funds will at times work to the detriment of bondholders. On balance, however, bonds that provide for a sinking fund are regarded as being safer than those without such a provision, so at the time they are issued sinking fund bonds have lower coupon rates than otherwise similar bonds without sinking funds. c.

How does one determine the value of any asset whose value is based on expected future cash flows determined?

Answer: The value of an asset is the present value of its expected future cash flows: N



CF3 CF t . VALUE = PV = CF 1 + CF2 + + . . . + CFN = t 1 2 3 N (1+ r ) (1+ r ) (1+ r ) (1+ r ) t = 1 (1+ r ) Following is a time line for these cash flows: 0 |

rd%

1 | CF1

2 | CF2

3 | CF3

∙∙∙

N | CFN

PV CF1 PV CF2 PV CF3 PV CFN VALUE If the cash flows have widely varying risk, or if the yield curve is not horizontal, which signifies that interest rates are expected to change over the life of the cash flows, it would be logical for each period’s cash flow to have a different discount rate. However, it is very difficult to make such adjustments; hence it is common practice to use a single discount rate for all cash flows. The discount rate is the opportunity cost of capital; that is, it is the rate of return that could be obtained on alternative investments of similar risk. For a bond, the discount rate is r d. d.

How is the value of a bond determined? What is the value of a 10-year, $1,000 par value bond with a

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10% annual coupon if its required rate of return is 10%? Answer: A bond has a specific cash flow pattern consisting of a stream of constant interest payments plus the return of par at maturity. The annual coupon payment is the cash flow: PMT = (coupon rate)  (par value) = 0.1($1,000) = $100. For a 10-year, 10% annual coupon bond, the bond’s value is found as follows: 0 |

10%

1 | 100

2 | 100

3 | 100

9 | 100

∙∙∙ |

10 | 100 1,000

90.91 82.64 75.13

42.41 38.55 385.54 1,000.00 Expressed as an equation, we have:

VB =

$100 (1+ rd )

$100

+...+

(1+ rd )

$1,000 (1+ rd )

= $90.91+ . . . + $38.55 + $385.54 = $ 1,000. The bond consists of a 10-year, 10% annuity of $100 per year plus a $1,000 lump sum payment at t = 10: PV Annuity PV Maturity Value Value of Bond

= $ 614.46 = 385.54 = $1,000.00

To find the bond’s value by using a financial calculator. Input N = 10, r d = I/YR = 10, PMT = 100, and FV = 1000, and then press PV to find the bond’s value, $1,000. Then change n from 10 to 1 and press PV to get the value of the 1-year bond, which is also $1,000. e.

What would be the value of the bond described in part d if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13% return? If rates rose to 15%? Would we now have a discount or a premium bond?

Answer: With a financial calculator, just change the value of rd = I/YR from 10% to 13%, and press the PV button to determine the value of the bond: VB(10-YR) = $837.21. Using the formulas and setting r to 13% results in the same answer: VB(10-YR) = $100 ((1 – 1/(1 + 0.13)10)/0.13) + $1,000 (1/(1 + 0.13)10) = $542.62 + $294.59 = $837.21. Use the same approaches shown above except change the rate to 15%. The resulting value of the bond is

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$749.06. In a situation like this, where the required rate of return, rd, rises above the coupon rate, the bonds’ values fall below par, so they sell at a discount. e.

What would happen to the bond’s value if inflation fell and r d declined to 7%? If rates fell to 5%? Would we now have a premium or a discount bond?

Answer: In the second situation, where rd falls to 7%, the price of the bond rises above par. To see this, change the value I/YR to 7%, and press the PV button to determine the value of the bond: VB(10-YR) = $1,210.71. We see that the 10-year bond’s value rises to $1,210.71. Using formulas provides the same result. VB(10-YR)= $100 ((1 – 1/(1 + 0.07)10)/0.07) + $1,000 (1/(1 + 0.07)10) = $702.36 + $508.35 = $1,210.71. Use the same approaches shown above except change the rate to 5%. The resulting value of the bond is $1,386.09. Thus, when the required rate of return falls below the coupon rate, the bonds’ value rises above par, or to a premium. Further, the longer the maturity, the greater the price effect of any given interest rate change. e.

What would happen to the value of the 10-year bond over time if the required rate of return remained at 15%, or if it remained at 5%? (Hint: With a financial calculator, enter PMT, I/YR, FV, and N, and then change N to see what happens to the PV as the bond approaches maturity.)

Answer: Assuming that interest rates remain at the new levels (either 5% or 15%), we could find the bond’s value as time passes, and as the maturity date approaches. If we then plotted the data, we would find the situation shown below:

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At maturity, the value of any bond must equal its par value (plus accrued interest). Therefore, if interest rates, hence the required rate of return, remain constant over time, then a bond’s value must move toward its par value as the maturity date approaches, so the value of a premium bond decreases to $1,000, and the value of a discount bond increases to $1,000 (barring default). f.

What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does the fact that a bond sells at a discount or at a premium tell you about the relationship between rd and the bond’s coupon rate?

Answer: The yield to maturity (YTM) is the discount rate which equates the present value of a bond’s cash flows to its price. In other words, it is the promised rate of return on the bond. (Note that the expected rate of return is less than the YTM if some probability of default exists.) On a timeline, we have the following situation when the bond sells for $887: 0 |

rd%

1 | 90

2 | 90

3 | 90

∙∙∙ |

9 | 90

10 | 90 1,000

PV1 PV2 PV3 PV9 PV10 PVM 887

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We want to find rd in this equation:

INT

VB = PV =

(1+ rd )

+ ... +

INT (1+ rd )

M (1+ rd )

We know that n = 10, PV = –887, PMT = 90, and FV = 1000, so we have an equation with one unknown, r d. We can solve for rd by entering the known data into a financial calculator and then pressing the I/YR = r d button. The result is a YTM of 10.91%. We can tell from the bond’s price, even before we begin the calculations, that the YTM must be above the 9% coupon rate. We know this because the bond is selling at a discount, and discount bonds always have r > coupon rate. If the bond were priced at $1,134.20, then it would be selling at a premium. In that case, it must have a YTM that is below the 9% coupon rate, because all premium bonds must have coupons which exceed the going interest rate. To determine the yield, us the same procedures as before: plug the appropriate values into a financial calculator, including the new PV of 1134.20, and then press the r = I button, which results in a price of $1,134.20 and r = YTM = 7.08%. f.

What are the total return, the current yield, and the capital gains yield for the discount bond? (Assume the bond is held to maturity and the company does not default on the bond.)

Answer: The current yield is defined as follows: Current Yield =

Annual coupon int erest payment . Current price of t he bond

The capital gains yield is defined as follows: Capit al gains yield =

Expect ed change in bond's price . Beginning- of - year price

The total expected return is the sum of the current yield and the expected capital gains yield:

Expect ed Expect ed Expect ed capit al . t ot al Ret urn = current yield + gains yield For our 9% coupon, 10-year bond selling at a price of $887 with a YTM of 10.91%, the current yield is:

Current yield =

$90 = 0.1015 = 10.15%. $887

Knowing the current yield and the total return, we can find the capital gains yield: YTM = Current yield + Capital gains yield And Capital gains yield = YTM – Current yield = 10.91% – 10.15% = 0.76%.

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The capital gains yield calculation can be checked by asking this question: ―What is the expected value of the bond 1 year from now, assuming that interest rates remain at current levels?‖ This is the same as asking, ―What is the value of a 9-year, 9% annual coupon bond if its YTM (its required rate of return) is 10.91%?‖ The answer, using the bond valuation function of a calculator, is $893.87. With this data, we can now calculate the bond’s capital gains yield as follows: Capital gains yield = (VB1 − VB0 )/VB0 = ($893.87 – $887)/$887 = 0.0077 = 0.77% This agrees with our earlier calculation (except for rounding). When the bond is selling for $1,134.20 and providing a total return of r d = YTM = 7.08%, we have this situation: Current yield = $90/$1,134.20 = 7.94% Capital gains yield= 7.08% – 7.94% = –0.86% The bond provides a current yield that exceeds the total return, but a purchaser would incur a small capital loss each year, and this loss would exactly offset the excess current yield and force the total return to equal the required rate. g.

How does the equation for valuing a bond change if semiannual payments are made? Find the value of a 10-year, semiannual payment, 10% coupon bond if nominal r d = 13%.

Answer: The majority of bonds issued in the United States have semiannual coupons and are valued using the cash flows shown below: Years Periods

0 0 |

1 | INT 2

1 2 | INT 2

2 4 | INT 2

3 | INT 2

9 18 | INT 2



19 | INT 2

10 20 | INT 2 M

PV1 PV2 PV18 PV19 PV20 PVM VBond = Sum of PVs We would use this equation to find the bond’s value: 2N

VB = 

INT / 2

t = 1 (1+ rd / 2)

M (1+ rd / 2)

The payment stream consists of an annuity of 2N payments plus a lump sum equal to the maturity value.

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To find the value of the 10-year, semiannual payment bond, semiannual interest = annual coupon/2 = $100/2 = $50 and N = 2 (years to maturity) = 2(10) = 20. To find the value of the bond with a financial calculator, enter n = 20, rd/2 = I/YR = 5, PMT = 50, FV = 1000, and then press PV to determine the value of the bond. Its value is $1,000. You could then change rd = I/YR to see what happens to the bond’s value as r changes and plot the values. The resulting the graph would look like the one we developed earlier. For example, if rd rose to 13%, we would input I/YR= 6.5 rather than 5%, and find the 10-year bond’s value to be $834.72. If rd fell to 7%, then input I/YR = 3.5 and press PV to find the bond’s new value, $1,213.19. We would find the values with a financial calculator, but they could also be found with formulas. Thus: = $50 ((1 – 1/(1 + 0.05)20)/0.065) + $1,000 (1/(1 + 0.05)20)

V10-YEAR

= $50(12.4622) + $1,000(0.37689) = $623.11 + $376.89 = $1,000.00. At a 13% required return: V10-YEAR = $50 ((1 – 1/(1 + 0.065)20)/0.065) + $1,000 (1/(1 + 0.065)20) = $834.72. At a 7% required return: V10-YEAR = $50 ((1 – 1/(1 + 0.035)20)/0.035) + $1,000 (1/(1 + 0.035)20) = $1,213.19. h.

Suppose a 10-year, 10%, semiannual coupon bond with a par value of $1,000 is currently selling for $1,135.90, producing a nominal yield to maturity of 8%. However, the bond can be called after 5 years for a price of $1,050.

What is the bond’s nominal yield to call (YTC)?

Answer: If the bond were called, bondholders would receive $1,050 at the end of Year 5. The time line would look like this: 0 |

0.5 | 50

1 | 50

1.5 | 50

2 | 50

2.5 | 50

3 | 50

3.5 | 50

4 | 50

4.5 | 50

5 | 50 1,000

PV0.5 PV1 PV4 PV4.5 PV5 PVM 1,135.90 = sum of PVs The easiest way to find the YTC on this bond is to input values into your calculator: n = 10; PV = –1135.90; PMT = 50; and FV = 1050, which is the par value plus a call premium of $50; and then press the rd = I/YR button to find I/YR = 3.765%. However, this is the 6-month rate, so we would find the nominal rate on the bond as follows:

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rNOM = 2(3.765%) = 7.5301% ≈ 7.5%. This 7.5% is the rate brokers would quote if you asked about buying the bond. You could also calculate the EAR on the bond: EAR = (1.03765)2 – 1 = 7.672%. Usually, people in the bond business just talk about nominal rates, which is OK so long as all the bonds being compared are on a semiannual payment basis. When you start making comparisons among investments with different payment patterns, though, it is important to convert to EARs. h.

If you bought this bond, do you think you would be more likely to earn the YTM or the YTC? Why?

Answer: Since the coupon rate is 10% versus YTC = rd = 7.53%, it would pay the company to call the bond, get rid of the obligation to pay $100 per year in interest, and sell replacement bonds whose interest would be only $75.30 per year. Therefore, if interest rates remain at the current level until the call date, the bond will surely be called, so investors should expect to earn 7.53%. In general, investors should expect to earn the YTC on premium bonds, but to earn the YTM on par and discount bonds. (Bond brokers publish lists of the bonds they have for sale; they quote YTM or YTC depending on whether the bond sells at a premium or a discount.) i.

Write a general expression for the yield on any debt security (r d) and define these terms: real riskfree rate of interest (r*), inflation premium (IP), default risk premium (DRP), liquidity premium (LP), and maturity risk premium (MRP).

Answer: rd = r* + IP + DRP + LP + MRP. r* is the real risk-free interest rate. It is the rate you see on a riskless security if there were no inflation. The inflation premium (IP) is a premium added to the real risk-free rate of interest to compensate for expected inflation. The default risk premium (DRP) is a premium based on the probability that the issuer will default on the loan, and it is measured by the difference between the interest rate on a U.S. Treasury bond and a corporate bond of equal maturity and marketability. A liquid asset is one that can be sold at a predictable price on short notice; a liquidity premium is added to the rate of interest on securities that are not liquid. The maturity risk premium (MRP) is a premium which reflects interest rate risk; longer-term securities have more interest rate risk (the risk of capital loss due to rising interest rates) than do shorter-term securities, and the MRP is added to reflect this risk. j.

Define the real risk-free rate (r*). What security can be used as an estimate of r*? What is the nominal risk-free rate (rRF)? What securities can be used as estimates of rRF?

Answer: The real risk-free rate, r*, is the rate that a hypothetical riskless security pays each moment if zero inflation were expected. The real risk-free rate is not constant because r* changes over time depending on economic conditions. The best approximation for r* is the yield on a short-term TIPS bond. It is generally assumed that r* is in the range of 1 to 4 percentage points, although it can be higher or lower. The nominal risk-free rate, rRF, can be approximate by the yield on a Treasury security. There is no truly riskless security, but the closest thing is a short-term U.S. Treasury bill (T-bill), which is free of most risks. The real risk-free rate, r*, is estimated by subtracting the expected rate of inflation from the rate on short-term Treasury securities. The T-bond rate is used as a proxy for the longterm risk-free rate. However, we know that all long-term bonds contain interest rate risk, so the

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T-bond rate is not really riskless. It is, however, free of default risk. k.

Describe a way to estimate the inflation premium (IP) for a t-year bond.

Answer: Treasury Inflation-Protected Securities (TIPS) are indexed to inflation. The IP for a particular length maturity can be approximated as the difference between the yield on a non-indexed Treasury security of that maturity minus the yield on a TIPS of that maturity. l.

What is a bond spread and how is it related to the default risk premium? How are bond ratings related to default risk? What factors affect a company’s bond rating?

Answer: A ―bond spread‖ is often calculated as the difference between a corporate bond’s yield and a Treasury security’s yield of the same maturity. Therefore: Spread = DRP + LP. Bonds of large, strong companies often have very small LPs. Bonds of small companies often have LPs as high as 2%. Bond ratings are based upon a company’s default risk. They are based on both qualitative and quantitative factors, some of which are listed below. 1.

Financial performance—determined by ratios such as the debt, TIE, FCC, and current ratios.

2. A. B. C. D. E.

Provisions in the bond contract: Secured vs. unsecured debt Senior vs. subordinated debt Guarantee provisions Sinking fund provisions Debt maturity

3. Other factors: A. Earnings stability B. Regulatory environment C. Potential product liability D. Accounting policy m. What is interest rate (or price) risk? Which bond has more interest rate risk: an annual payment 1year bond or a 10-year bond? Why? Answer: Interest rate risk, which is often just called price risk, is the risk that a bond will lose value as the result of an increase in interest rates. Earlier, we developed the following values for a 10%, annual coupon bond: With a financial calculator, just change the value of rd = I/YR from 10% to 13%, and press the PV button to determine the value of the bond: VB(10-YR) = $837.21. at 13% VB(10-YR)= $100 ((1 – 1/(1 + 0.07)10)/0.07) + $1,000 (1/(1 + 0.07)10) = $702.36 + $508.35 = $1,210.71. rd 5% 10

Maturity 1-Year $1,048 1,000

Change 4.8% 4.4%

Maturity 10-Year $1,386 1,000

Change 38.6% 25.1%

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956

rd 5% 10 15

10-Yr Maturity

1-Year $1,048 1,000 956

Rate

749 Maturity Change 4.8% 4.4%

1-Yr Maturity Price

Rate

10-Year $1,386 1,000 749

Change 38.6%

x Price

rd 7.0%

$1,210.71

5.0%

$1,047.62

10.0%

$1,000.00

10.0%

$1,000.00

13.0%

$837.21

15.0%

$956.52

A 5-percentage-point increase in r causes the value of the 1-year bond to decline by only 4.8%, but the 10-year bond declines in value by more than 38%. Thus, the 10-year bond has more interest rate price risk.

The graph above shows the relationship between bond values and interest rates for a 10%, annual coupon bond with different maturities. The longer the maturity, the greater the change in value for a given change in interest rates, rd. n.

What is reinvestment rate risk? Which has more reinvestment rate risk: a 1-year bond or a 10-year bond?

Answer: Investment rate risk is defined as the risk that cash flows (interest plus principal repayments) will have to be reinvested in the future at rates lower than today’s rate. To illustrate, suppose you just won the lottery and now have $500,000. You plan to invest the money and then live on the income from your investments. Suppose you buy a 1-year bond with a YTM of 10%. Your income will be $50,000 during the first year.

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Then, after 1 year, you will receive your $500,000 when the bond matures, and you will then have to reinvest this amount. If rates have fallen to 3%, then your income will fall from $50,000 to $15,000. On the other hand, had you bought 30-year bonds that yielded 10%, your income would have remained constant at $50,000 per year. Clearly, buying bonds that have short maturities carries reinvestment rate risk. Note that long maturity bonds also have reinvestment rate risk, but the risk applies only to the coupon payments, and not to the principal amount. Since the coupon payments are significantly less than the principal amount, the reinvestment rate risk on a long-term bond is significantly less than on a short-term bond. o.

How are interest rate risk and reinvestment rate risk related to the maturity risk premium?

Answer: Long-term bonds have high interest rate risk but low reinvestment rate risk. Short-term bonds have low interest rate risk but high reinvestment rate risk. Nothing is riskless! Yields on longer-term bonds usually are greater than on shorter-term bonds, so the MRP is more affected by interest rate risk than by reinvestment rate risk. p.

What is the term structure of interest rates? What is a yield curve?

Answer: The term structure of interest rates is the relationship between interest rates, or yields, and maturities of securities. When this relationship is graphed, the resulting curve is called a yield curve.

Briefly describe bankruptcy law. If this firm were to default on the bonds, would the company be immediately liquidated? Would the bondholders be assured of receiving all of their promised payments?

Answer: When a business becomes insolvent, it does not have enough cash to meet scheduled interest and principal payments. A decision must then be made whether to dissolve the firm through liquidation or to permit it to reorganize and thus stay alive. The decision to force a firm to liquidate or to permit it to reorganize depends on whether the value of

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the reorganized firm is likely to be greater than the value of the firm’s assets if they were sold off piecemeal. In a reorganization, a committee of unsecured creditors is appointed by the court to negotiate with management on the terms of a potential reorganization. The reorganization plan may call for a restructuring of the firm’s debt, in which case the interest rate may be reduced, the term to maturity lengthened, or some of the debt may be exchanged for equity. The point of restructuring is to reduce the financial charges to a level that the firm’s cash flows can support. If the firm is deemed to be too far gone to be saved, it will be liquidated and the priority of claims would be as follows: 1. Secured creditors. 2. Trustee’s costs. 3. Expenses incurred after bankruptcy was filed. 4. Wages due workers, up to a limit of $2,000 per worker. 5. Claims for unpaid contributions to employee benefit plans. 6. Unsecured claims for customer deposits up to $900 per customer. 7. Federal, state, and local taxes. 8. Unfunded pension plan liabilities. 9. General unsecured creditors. 10. Preferred stockholders, up to the par value of their stock. 11. Common stockholders, if anything is left. If the firm’s assets are worth more ―alive‖ than ―dead,‖ the company would be reorganized. Its bondholders, however, would expect to take a ―hit.‖ Thus, they would not expect to receive all their promised payments. If the firm is deemed to be too far gone to be saved, it would be liquidated.

WEB EXTENSION 5A A Closer Look at Zero Coupon Bonds, Original Discount Bonds, and Original Issue Premium Bonds

ANSWERS TO QUESTIONS (5A-1) Do all original issue discount (OID) bonds have zero coupon payments? Explain. Answer: No, not all original issue discount bonds have zero coupons. Zero coupon bonds are just one type of original issue discount bond. Any nonconvertible bond whose coupon rate is set below the going market rate at the time of its issue will sell at a discount, and its will be classified (for tax and other purposes) as an OID bond. (5A-2) What are Treasury STRIPS? Are they callable? Explain. Answer: Shortly after corporations began to issue zeros, investment bankers figured out a way to create zeros from U.S. Treasury bonds, which at the time were issued only in coupon form. In 1983, Salomon Brothers bought $1 billion of 12%, 30-year Treasuries. Each bond had 60 coupons worth $60 each, which represented the interest payments due every 6 months. Salomon then in effect clipped the coupons and placed them in 60 piles: the last pile also contained the now ―stripped‖ bond itself, which represented a promise of $1,000 in 2013. These 60 piles of U.S. Treasury promises were then placed with the trust department of a bank and used as collateral for ―zero coupon U.S. Treasury Trust Certificates,‖ which are, in essence, zero coupon Treasury bonds. Treasury zeros are, of course, safer than corporate zeros, so they are very popular with pension fund managers. In response to this demand, the Treasury has also created its own ―Strips‖ program, which allows investors to purchase zeros electronically.

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Stripped U.S. Treasury bonds (Treasury zeros) generally are not callable because the Treasury normally sells noncallable bonds. (5A-3) Do Treasury zeros face any interest rate (price) or reinvestment rate risk? Explain. Answer: Treasury zeros are not protected from interest rate (price) risk, because the principal is totally susceptible to interest rate movements. You can see this by changing interest rates and seeing what happens to the value of the zero bond. However, since Treasury zeros generally are not callable and because there are no coupon payments to reinvest, Treasury zeros are completely protected against reinvestment risk (the risk of having to invest cash flows from a bond at a lower rate because of a decline in interest rates). (5A-4) What is a premium bond? What are the pros and cons to corporations issuing them? To investors of purchasing them? Answer: Premium bonds are bonds that are issued or trade at a price above par value. The annual after-tax cash flows differ between premium and OID bonds. OID bonds have the lowest after-tax cash flows before maturity while premium bonds have the highest after-tax cash flows before maturity. Companies wishing to conserve cash over the short term will want to issue OID bonds, or at least avoid issuing premium bonds. Investors who desire high current income will prefer premium bonds while investors who want to reduce their reinvestment risk will prefer OID bonds.

SOLUTIONS TO PROBLEMS (5A-1) Zero Coupon Bonds A company has just issued 4-year zero coupon bonds with a maturity value of $1,000 and a yield to maturity of 8%. Its tax rate is 25%. What is its after-tax cost of debt? Solution: Year

$735.03

$793.83

$857.34

$925.93

$1,000.00

Accrued interest

–

$58.80

$63.51

$68.59

$74.07

Tax savings (25%)

–

$14.70

$15.88

$17.15

$18.52

$735.03

$14.70

$15.88

$17.15

−$981.48

Accrued value

Cash flow

Enter the following data into your calculator to determine the price of each bond: N = 4; I/YR = 8; PMT = 0; FV = 1000; PV = ? Solve for PV = $735.03. Accrued valuet = Accrued valuet – 1(1.08). Interest = Accrued valuet – Accrued valuet – 1. Tax savings = Interest(T). Note that in Year 4, the company must pay the maturity value of the bond; therefore, the cash flow in Year 4 is equal to –$1,000 + Tax savings. To solve for the IRR of this cash flow stream, using a financial calculator, enter the individual cash flows into the cash flow register and solve for the IRR of this cash flow stream. IRR = 6%. Alternatively, the after-tax cost of debt can be calculated as 0.08(1 – T) = 0.08 (1 – 0.25) = 5.4%.

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(5A-2) Zero Coupon Bonds An investor in the 35% tax bracket purchases a 4-year zero coupon bond with a maturity value of $1,000 and a yield to maturity of 10%. What is the investor’s after-tax return? Solution: Year

$683.01

$751.31

$826.45

$909.09

$1,000.00

Accrued interest

–

$68.30

$75.13

$82.64

$90.91

Tax expense (35%)

–

$23.91

$26.30

$28.93

$31.82

−$683.01

−$23.91

−$26.30

−$28.93

$968.18

Accrued value

Cash flow

Enter the following data into your calculator to determine the price of each bond: N = 4; I/YR = 10; PMT = 0; FV = 1000; PV = ? Solve for PV = $683.01. Accrued valuet = Accrued valuet – 1(1.10). Interest = Accrued valuet – Accrued valuet – 1. Tax expense = Interest(T). Note that in Year 4, the investor receives the maturity value of the bond; however, he must pay taxes on the interest income in Year 4. Thus, cash flow in Year 4 equals $1,000 – Taxes. To solve for the IRR of this cash flow stream, using a financial calculator, enter the individual cash flows into the cash flow register and solve for the IRR. IRR = 6.5%. Alternatively, the after-tax return can be calculated as 0.10(1 – T) = 0.10(1 – 0.35) = 6.5%. (5A-3) Stripped U.S. Treasury Bond McGwire Company’s pension fund projected that a significant number of its employees would take advantage of an early retirement program the company plans to offer in 5 years. Anticipating the need to fund these pensions, the firm bought zero coupon STRIPS maturing in 5 years. When these instruments were originally issued, they were 12% coupon, 30-year U.S. Treasury bonds. The STRIPS are currently priced to yield 10%. Their total maturity value is $6 million. What is their price today? Solution: Using a financial calculator, enter the following data: N = 5; I/YR = 10; PMT = 0; FV = 6000000; and then solve for PV = $3,725,527.94. (5A-4) Zero Coupon Bond At the beginning of the year, you purchased a 7-year, zero-coupon bond with a yield to maturity of 6.8%. The bond has a face value of $1,000. Your tax rate is 25%. What is the total tax that you will have to pay on the bond during the first year? Solution: Step 1: Find out what was paid for the bond: PV = $1,000/(1.068)7 = $630.959. Step 2: Determine the Year 1 accrued interest: The accrued interest in the first year is $630.959  0.068 = $42.905.

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Step 3: Calculate the tax on the accrued interest: Tax on the accrued interest is $42.905  0.25 = $10.73. (5A-5) Zeros and Expectations Theory A 2-year, zero coupon Treasury bond with a maturity value of $1,000 has a price of $873.4387. A 1-year, zero coupon Treasury bond with a maturity value of $1,000 has a price of $938.9671. If the pure expectations theory is correct, for what price should 1-year, zero coupon Treasury bonds sell 1 year from now? Solution: First find the yields on 1-year and 2-year zero coupon bonds, so you can find the implied rate on a 1year bond, 1 year from now. Then use this implied rate to find its price. 1-Year: Using a financial calculator, enter the following data: N = 1; PV = –938.9671; PMT = 0; FV = 1000; and then solve for I/YR = 6.5%. 2-Year: Using a financial calculator, enter the following data: N = 2; PV = –873.4387; PMT = 0; FV = 1000; and then solve for I/YR = 7.0%. Therefore, if the implied rate = X, then: (1.065)(1 + X) = (1.07)2C 1.065 + 1.065X = 1.1449 1.065X = 0.0799 X = 7.5%. Now find the price of a 1-year zero, 1 year from now: Using a financial calculator, enter the following data: N = 1; I/YR = 7.5; PMT = 0; FV = 1000; and then solve for PV = –$930.23. (5A-6) Zero Coupon Bonds and EAR Assume that the city of Tampa sold tax-exempt (muni) zero coupon bonds 5 years ago. The bonds had a 25-year maturity and a maturity value of $1,000 when they were issued, and the interest rate built into the issue was a nominal 10% with semiannual compounding. The bonds are now callable at a premium of 10% over the accrued value. If they were called today, what effective annual rate of return would be earned by an investor who bought the bonds when they were issued and who still owns them today? Solution: 0 –87.2037

50 1,000

 (1.05)10 = 142.0457  1.10 156.2503 Step 1: Using a financial calculator, we find the PV of the zeros at Time 0 by entering the following data: N = 50; I/YR = 5; PMT = 0; FV = 1000; and then solve for PV = $87.2037. Step 2: Using a financial calculator, we can find the investor’s effective annual rate of return by entering the following data:

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N = 10; PV = –87.2037; PMT = 0; FV = 156.2503; and then solve for I NOM/2 = 6.0055%. (Remember, this is a periodic semiannual rate.) EAR = (1.060055)2 – 1 = 0.1237 = 12.37%.

WEB EXTENSION 5E The Pure Expectations Theory and Estimation of Forward Rates

SOLUTIONS TO PROBLEMS (5E-1) Expectations Theory One-year Treasury securities yield 5%. The market anticipates that 1 year from now, 1-year Treasury securities will yield 6%. If the pure expectations theory is correct, what is the yield today for 2-year Treasury securities? Solution: rT1 = 5%; 1rT1 = 6%; rT2 = ? (1 + rT2)2 = (1.05)(1.06) (1 + rT2)2 = 1.113 1 + rT2 = 1.055 rT2 = 5.5%. (5E-2) Expectations Theory Interest rates on 4-year Treasury securities are currently 7%, while 5-year Treasury securities yield 7.5%. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now? Solution: Let X equal the yield on 2-year securities 4 years from now: (1.07)4(1 + X)2 = (1.075)6 (1.3108)(1 + X)2 = 1.5433

 1.5433  1+X =    1.3108  X = 8.5%.

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(5E-3) Expectations Theory and Inflation Suppose 2-year Treasury bonds yield 4.5% while 1-year bonds yield 3%. The maturity risk premium is 0% and r* is 1%. a. Using expectations theory, what is the yield on a 1-year bond 1 year from now? b. What is the expected inflation rate in Year 1? Year 2? Solution: a. (1.045)2 = (1.03)(1 + X) 1.092/1.03 = 1 + X X = 6%. b.

For riskless bonds under the expectations theory, the interest rate for a bond of any maturity is rN = r*

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+ average inflation over N years. If r* = 1%, we can solve for IPN: Year 1:

r1 = 1% + I1 = 3%; I1 = expected inflation = 3% – 1% = 2%.

Year 2:

r1 = 1% + I2 = 6%; I2 = expected inflation = 6% – 1% = 5%.

Note also that the average inflation rate is (2% + 5%)/2 = 3.5%, which, when added to r * = 1%, produces the yield on a 2-year bond, 4.5%. Therefore, all of our results are consistent. (5E-4) Expectations Theory Assume that the real risk-free rate is 2% and that the maturity risk premium is 0%. If the 1-year bond yield is 5% and a 2-year bond (of similar risk) yields 7%, then what is the 1-year interest rate expected for Year 2? What inflation rate is expected during Year 2? Comment on why the average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2. Solution: r* = 2%; MRP = 0%; r1 = 5%; r2 = 7%; X = ? X represents the 1-year rate on a bond 1 year from now (Year 2). (1.07)2 = (1.05)(1 + X) 1.1449 =1+X 1.05 X = 9%. 9% = r* + I2 9% = 2% + I2 7% = I2. The average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2 because of the inflation rate reflected in the two interest rates. The inflation rate reflected in the interest rate on any security is the average rate of inflation expected over the security’s life.

Solution and Answer Guide CHAPTER 6: RISK AND RETURN

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 138 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 141 Easy Problems 1-4 ................................................................................................................................ 141 Intermediate Problems 5–10 ................................................................................................................. 142 Challenging Problems 11–14 ................................................................................................................ 145 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 147 MINI CASE ............................................................................................................................................. 148

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ANSWERS TO END-OF-CHAPTER QUESTIONS 6-1

Define the following terms, using graphs or equations to illustrate your answers where feasible. a. Risk in general; stand-alone risk; probability distribution and its relation to risk b. Expected rate of return, ̂ c. Continuous probability distribution d. Standard deviation, σ; variance, σ2 e. Risk aversion; realized rate of return, ̅ f. Risk premium for Stock i, RPi; market risk premium, RPM g. Capital asset pricing model (CAPM) h. Expected return on a portfolio, ̂ ; market portfolio i. Correlation as a concept; correlation coefficient, ρ j. Market risk; diversifiable risk; relevant risk k. Beta coefficient, b; average stock’s beta l. Security market line (SML); SML equation m. Slope of SML and its relationship to risk aversion n. Equilibrium; Efficient Markets Hypothesis (EMH); three forms of EMH o. Fama-French three-factor model p. Behavioral finance; herding; anchoring Answer: a. Risk is the chance that some unfavorable event will occur. For instance, the risk of an asset is essentially the chance that the asset’s cash flows will be unfavorable or less than expected. Stand-alone risk is only a part of total risk and pertains to the risk an investor takes by holding only one asset. A probability distribution is a listing, chart or graph of all possible outcomes, such as expected rates of return, with a probability assigned to each outcome. When in graph form, the tighter the probability distribution, the less uncertain the outcome. b.

The expected rate of return ( r̂ ) is the expected value of a probability distribution of expected returns.

A continuous probability distribution contains an infinite number of outcomes and is graphed from  and +.

The standard deviation (σ) is a statistical measure of the variability of a set of observations. The variance (σ2) of the probability distribution is the sum of the squared deviations about the expected value adjusted for deviation.

A risk averse investor dislikes risk and requires a higher rate of return as an inducement to buy riskier securities. A realized return is the actual return an investor receives on their investment. It can be quite different than their expected return.

A risk premium is the difference between the rate of return on a risk-free asset and the expected return on Stock I, which has higher risk. The market risk premium is the difference between the expected return on the market and the riskfree rate.

CAPM is a model based upon the proposition that any stock’s required rate of return is equal to the risk-free rate of return plus a risk premium reflecting only the risk remaining after diversification.

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The expected return on a portfolio. r̂ p, is simply the weighted-average expected return of the individual stocks in the portfolio, with the weights being the fraction of total portfolio value invested in each stock. The market portfolio is a portfolio consisting of all stocks.

Correlation is the tendency of two variables to move together. A correlation coefficient (ρ) of +1.0 means that the two variables move up and down in perfect synchronization, while a coefficient of – 1.0 means the variables always move in opposite directions. A correlation coefficient of zero suggests that the two variables are not related to one another; that is, they are independent.

Market risk is that part of a security’s total risk that cannot be eliminated by diversification. It is measured by the beta coefficient. Diversifiable risk is also known as company specific risk, that part of a security’s total risk associated with random events not affecting the market as a whole. This risk can be eliminated by proper diversification. The relevant risk of a stock is its contribution to the riskiness of a well-diversified portfolio.

The beta coefficient is a measure of a stock’s market risk. A stock with a beta greater than 1 has stock returns that tend to be higher than the market when the market is up but tend to be below the market when the market is down. The opposite is true for a stock with a beta less than 1. The security market line (SML) represents in a graphical form, the relationship between the risk of an asset as measured by its beta and the required rates of return for individual securities. The SML equation is essentially the CAPM, ri = rRF + bi(RPM). It can also be written in terms of the required market return: ri = rRF + bi(rM – rRF).

m. The slope of the SML equation is (rM – rRF), the market risk premium. The slope of the SML reflects the degree of risk aversion in the economy. The greater the average investors aversion to risk, then the steeper the slope, the higher the risk premium for all stocks, and the higher the required return. n.

Equilibrium is the condition under which the expected return on a security is just equal to its required return, r̂ = r, and the market price is equal to the intrinsic value. The Efficient Markets Hypothesis (EMH) states (1) that stocks are always in equilibrium and (2) that it is impossible for an investor to consistently ―beat the market.‖ In essence, the theory holds that the price of a stock will adjust almost immediately in response to any new developments. In other words, the EMH assumes that all important information regarding a stock is reflected in the price of that stock. Financial theorists generally define three forms of market efficiency: weak form, semistrong form, and strong form. Weak-form efficiency assumes that all information contained in past price movements is fully reflected in current market prices. Thus, information about recent trends in a stock’s price is of no use in selecting a stock. Semistrong-form efficiency states that current market prices reflect all publicly available information. Therefore, the only way to gain abnormal returns on a stock is to possess inside information about the company’s stock. Strong-form efficiency assumes that all information pertaining to a stock, whether public or inside information, is reflected in current market prices. Thus, no investors would be able to earn abnormal returns in the stock market.

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The Fama-French three-factor model has one factor for the excess market return (the market return minus the risk-free rate), a second factor for size (defined as the return on a portfolio of small firms minus the return on a portfolio of big firms), and a third factor for the book-to-market effect (defined as the return on a portfolio of firms with a high book-to-market ratio minus the return on a portfolio of firms with a low book-to-market ratio).

Most people don’t behave rationally in all aspects of their personal lives, and behavioral finance assumes that investors have the same types of psychological behaviors in their financial lives as in their personal lives. Herding is the tendency of investors to follow the crowd. Anchoring bias is the human tendency to ―anchor‖ too closely on recent events when predicting future events. When combined with overconfidence, anchoring and herding can contribute to market bubbles.

6-2

The probability distribution of a less risky return is more peaked than that of a riskier return. What shape would the probability distribution have for (a) completely certain returns and (b) completely uncertain returns? Answer: a. The probability distribution for complete certainty is a vertical line. b.

6-3

The probability distribution for total uncertainty is the X axis from - to +.

Security A has an expected return of 7%, a standard deviation of returns of 35%, a correlation coefficient with the market of −0.3, and a beta coefficient of −1.5. Security B has an expected return of 12%, a standard deviation of returns of 10%, a correlation with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why? Answer: Security A is less risky if held in a diversified portfolio because of its lower beta and negative correlation with other stocks. In a single-asset portfolio, Security A would be riskier because σA > σB and CVA > CVB.

6-4

If investors’ aversion to risk increased, would the risk premium on a high-beta stock increase by more or less than that on a low-beta stock? Explain. Answer: The risk premium on a high beta stock would increase more. RPj = Risk Premium for Stock j = (rM - rRF)bj. If risk aversion increases, the slope of the SML will increase, and so will the market risk premium (r M – rRF). The product (rM – rRF)bj is the risk premium of the jth stock. If b j is low (say, 0.5), then the product will be small; RPj will increase by only half the increase in RP M. However, if bj is large (say, 2.0), then its risk premium will rise by twice the increase in RP M.

6-5

If a company’s beta were to double, would its expected return double? Answer: According to the security market line (SML) equation, an increase in beta will increase a company’s expected return by an amount equal to the market risk premium times the change in beta. For example, assume that the risk-free rate is 6 percent, and the market risk premium is 5 percent. If the company’s beta doubles from 0.8 to 1.6 its expected return increases from 10 percent to 14 percent. Therefore, in general, a company’s expected return will not double when its beta doubles.

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SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1-4 6-1

Portfolio Beta. Your investment club has only two stocks in its portfolio. $20,000 is invested in a stock with a beta of 0.7, and $35,000 is invested in a stock with a beta of 1.3. What is the portfolio’s beta? Solution: Investment

Beta

$20,000

0.7

35,000

1.3

Total $55,000 Portfolio’s beta = ($20,000/$55,000)(0.7) + ($35,000/$55,000)(1.3) = 1.08. 6-2

Required Rate of Return. AA Corporation’s stock has a beta of 0.8. The risk-free rate is 4%, and the expected return on the market is 12%. What is the required rate of return on AA’s stock? Solution: rRF = 4%; rM = 12%; b = 0.8; rs = ? rs = rRF + (rM – rRF)b = 4% + (12% – 4%)0.8 = 10.4%.

6-3

Required Rates of Return. Suppose that the risk-free rate is 5% and that the market risk premium is 7%. What is the required return on (1) the market, (2) a stock with a beta of 1.0, and (3) a stock with a beta of 1.7? Solution: rRF = 5%; RPM = 7% Required return on market: rM = 5% + 7% = 12%. Required return on stock with a beta = 1: rs = 5% + (7%)1 = 12%. Required return on stock with a beta = 1.7: rs = 5% + 7%(1.7) = 16.9%.

6-4

Fama-French Three-Factor Model. An analyst gathered daily stock returns for February 1 through March 31, calculated the Fama-French factors for each day in the sample (SMB t and HMLt), and estimated the Fama-French regression model shown in Equation 6-21. The estimated coefficients were ai = 0, bi = 1.2, ci = −0.4, and di = 1.3. On April 1, the market return was 10%, the return on the SMB portfolio (rSMB) was 3.2%, and the return on the HML portfolio (r HML) was 4.8%. Using the estimated model, what was the stock’s predicted return for April 1? Solution: Predicted return = ai + bi( r M,t) + ci( r SMB,t) + di( r HML,t) = 0.0% + 1.2(10%) + (-0.4)(3.2%) + 1.3(4.8%) = 16.96%

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INTERMEDIATE PROBLEMS 5–10 6-5

Expected Return: Discrete Distribution. A stock’s return has the following distribution: Demand for the Company’s Products Weak Below average Average Above average Strong

Probability of This Demand Occurring 0.1 0.2 0.4 0.2 0.1 1.0

Rate of Return If This Demand Occurs (%) −50% −5 16 25 60

Calculate the stock’s expected return and standard deviation. Solution:

r̂ = (0.1)(–50%) + (0.2)(–5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%) = 11.40%. σ2 = (–50% – 11.40%)2(0.1) + (–5% – 11.40%)2(0.2) + (16% – 11.40%)2(0.4) + (25% – 11.40%)2(0.2) + (60% – 11.40%)2(0.1) 2 σ = 0.071244 σ = 26.69%. 6-6

Expected Returns: Discrete Distribution. The market and Stock J have the following probability distributions: Probability

0.3

15%

20%

0.4

0.3

8 a. b.

Calculate the expected rates of return for the market and Stock J. Calculate the standard deviations for the market and Stock J.

Solution: a.

r̂ m = (0.3)(15%) + (0.4)(9%) + (0.3)(18%) = 13.5%. r̂ j = (0.3)(20%) + (0.4)(5%) + (0.3)(12%) = 11.6%.

σM = [(0.3)(15% – 13.5%)2 + (0.4)(9% – 13.5%)2 + (0.3)(18% –13.5%)2]1/2 =

14.85% = 3.85%.

σJ = [(0.3)(20% – 11.6%)2 + (0.4)(5% – 11.6%)2 + (0.3)(12% – 11.6%)2]1/2 =

38.64% = 6.22%.

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6-7

Required Rate of Return. Suppose rRF = 5%, rM = 10%, and rA = 12%. a. b.

Calculate Stock A’s beta. If Stock A’s beta were 2.0, then what would be A’s new required rate of return?

Solution: a. rA = rRF + (rM – rRF)bA 12% = 5% + (10% – 5%)bA 12% = 5% + 5%(bA) 7% = 5%(bA) bA = 1.4 b.

rA = 5% + 5%(bA) rA = 5% + 5%(2) rA = 15%

6-8

Required Rate of Return. As an equity analyst you are concerned with what will happen to the required return for Universal Toddler’s stock as market conditions change. Suppose r RF = 5%, rM = 12%, and bUT = 1.4. a. Under current conditions, what is rUT, the required rate of return on UT stock? b. Now suppose rRF (1) increases to 6% or (2) decreases to 4%. The market risk premium, RP M (i.e., the slope of the SML), remains constant. How would this affect r M and rUT? c. Now assume rRF remains at 5% but rM (1) increases to 14% or (2) falls to 11%. The market risk premium, RPM, (i.e., the slope of the SML) does not remain constant. How would these changes affect rUT? Solution: a. ri = rRF + (rM – rRF)bi = 5% + (12% – 5%)1.4 = 14.8%. b.

rRF increases to 6%: The slope of the SML is equal to the market risk premium, RP M, which does not change. From Part a, the market risk premium is 7%: rM – rRF = 12% – 5% = 7%. Using 6% for the risk-free rate and 7% for the market risk premium, the required return on the stock is: ri = rRF + (RPM)bi = 6% + (7%)1.4 = 15.8%.

rRF decreases to 4%: ri = rRF + (RPM)bi = 4% + (7%)1.4 = 13.8%.

rM increases to 14%: If the risk-free rate does not change but the required return on the market does change, then the market risk premium changes. For rRF = 5% and rM = 14%, the new market risk premium is 9%: RPM = rM – rRF = 14% – 5% = 9%. The required return on the stock is: ri = rRF + (RPM)bi = 5% + (9%)1.4 = 17.6%.

rM decreases to 11%: The new market risk premium is 6%: RPM = rM – rRF = 11% – 5% = 6%. The required return on the stock is: ri = rRF + (rM – rRF)bi = 5% + (6%)1.4 = 13.4%.

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6-9

Portfolio Beta. Your retirement fund consists of a $5,000 investment in each of 15 different common stocks. The portfolio’s beta is 1.20. Suppose you sell one of the stocks with a beta of 0.8 for $5,000 and use the proceeds to buy another stock whose beta is 1.6. Calculate your portfolio’s new beta. Solution: $70,000 $5,000 (b) + (0.8) $75,000 $75,000 1.2 = 0.9333b + 0.0533 1.1467 = 0.9333b b = 1.229

Old portfolio beta =

New portfolio beta = 0.9333(1.229) + 0.0667(1.6) = 1.25. Alternative Solutions: 1.

Old portfolio beta = 1.2 = (0.0667)b 1 + (0.0667)b2 + ... + (0.0667)b20 1.2 = (bi)(0.0667) bi = 1.2/0.0667 = 18.0. New portfolio beta = (18.0 – 0.8 + 1.6)(0.0667) = 1.253 = 1.25.

bi excluding the stock with the beta equal to 0.8 is 18.0 – 0.8 = 17.2, so the beta of the portfolio excluding this stock is b = 17.2/14 = 1.2286. The beta of the new portfolio is: 1.2286(0.9333) + 1.6(0.0667) = 1.1575 = 1.253.

6-10 Portfolio Required Return. Suppose you manage a $4 million fund that consists of four stocks with the following investments: Stock

Investment

Beta

$400,000

1.50

600,000

−0.50

1,000,000

1.25

2,000,000

0.75

If the market’s required rate of return is 14% and the risk-free rate is 6%, what is the fund’s required rate of return? Solution: Portfolio beta =

$400, 000 $600, 000 (1.50) + (–0.50) $4, 000, 000 $4, 000, 000 $1, 000, 000 $2, 000, 000 (1.25) + (0.75) $4, 000, 000 $4, 000, 000 = (0.1)(1.5) + (0.15)(–0.50) + (0.25)(1.25) + (0.5)(0.75) = 0.15 – 0.075 + 0.3125 + 0.375 = 0.7625.

rp = rRF + (rM – rRF)(bp) = 6% + (14% – 6%)(0.7625) = 12.1%. Alternative solution: First compute the return for each stock using the CAPM equation [r RF + (rM – rRF)b], and then compute the weighted average of these returns. rRF = 6% and rM – rRF = 8%.

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Stock A B C D

Investment $400,000 600,000 1,000,000 2,000,000

Total

$4,000,000

Beta 1.50 (0.50) 1.25 0.75

r = rRF + (rM – rRF)b 18% 2 16 12

Weight 0.10 0.15 0.25 0.50 1.00

rp = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%.

CHALLENGING PROBLEMS 11–14 6-11 Portfolio Beta. You have a $2 million portfolio consisting of a $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.1. You are considering selling $100,000 worth of one stock with a beta of 0.9 and using the proceeds to purchase another stock with a beta of 1.4. What will the portfolio’s new beta be after these transactions? Solution: First, calculate the beta of what remains after selling the stock: bp = 1.1 = ($100,000/$2,000,000)0.9 + ($1,900,000/$2,000,000)b R 1.1 = 0.045 + (0.95)bR bR = 1.1105. bN = (0.95)1.1105 + (0.05)1.4 = 1.125. 6-12 Required Rate of Return. Stock R has a beta of 1.5, Stock S has a beta of 0.75, the expected rate of return on an average stock is 13%, and the risk-free rate is 7%. By how much does the required return on the riskier stock exceed that on the less risky stock? Solution: We know that bR = 1.50, bS = 0.75, rM = 13%, rRF = 7%. ri = rRF + (rM – rRF)bi = 7% + (13% – 7%)bi. rR = 7% + 6%(1.50) = 16.0% rS = 7% + 6%(0.75) = 11.5 4.5% 6-13 Historical Realized Rates of Return. You are considering an investment in either individual stocks or a portfolio of stocks. The two stocks you are researching, Stock A and Stock B, have the following historical returns: Year 2019 2020 2021 2022 2

r̄ A −20.00% 42.00 20.00 −8.00 25.00

r̄ B −5.00% 15.00 −13.00 50.00 12.00

023 a.

Calculate the average rate of return for each stock during the 5-year period.

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c. d.

Suppose you had held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? Calculate the standard deviation of returns for each stock and for the portfolio. Suppose you are a risk-averse investor. Assuming Stocks A and B are your only choices, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

Solution: The answers to a, b, and c are given below:

Year

Portfolio

2019

(20.00%)

(5.00%)

(12.50%)

2020

42.00

15.00

28.50

2021

20.00

(13.00)

3.50

2022

(8.00)

50.00

21.00

2023

25.00

12.00

18.50

Mean

11.80

StdDev

25.28

24.32

16.34

A risk-averse investor would choose the portfolio over either Stock A or Stock B alone, since the portfolio offers the same expected return but with less risk. This result occurs because returns on A and B are not perfectly positively correlated (ρAB = –0.13).

6-14 Historical Returns: Expected and Required Rates of Return. You have observed the following returns over time: Year

Stock X

Stock Y

Market

2019

14%

13%

12%

2020

2021

−16

−5

−12

2022

2023

Assume that the risk-free rate is 6% and the market risk premium is 5%. a. b. c.

What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?

Solution: a. bX = 1.3471; bY = 0.6508. These can be calculated with a spreadsheet. b.

rX = 6% + (5%)1.3471 = 12.7355%. rY = 6% + (5%)0.6508 = 9.2540%.

bp = 0.8(1.3471) + 0.2(0.6508) = 1.2078. rp = 6% + (5%)1.2078 = 12.04%. Alternatively,

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rp = 0.8(12.7355%) + 0.2(9.254%) = 12.04%.

SOLUTION TO SPREADSHEET PROBLEM 6-15 Evaluating Risk and Return. Start with the partial model in the file Ch06 P15 Build a Model.xlsx on the textbook’s website. The file contains data for this problem. Goodman Corporation’s and Landry Incorporated’s stock prices and dividends, along with the Market Index, are shown here. Stock prices are reported for December 31 of each year, and dividends reflect those paid during the year. The market data are adjusted to include dividends. Goodman Corporation

Landry Incorporated

Market Index Includes Dividends

Year

Stock Price

Dividend

Stock Price

Dividend

2023

$25.88

$1.73

$73.13

$4.50

17,495.97

2022

22.13

1.59

78.45

4.35

13,178.55

2021

24.75

1.50

73.13

4.13

13,019.97

2020

16.13

1.43

85.88

3.75

9,651.05

2019

17.06

1.35

90.00

3.38

8,403.42

2018 a.

f. g.

11.44

1.28

83.63

3.00

7,058.96

Use the data given to calculate annual returns for Goodman, Landry, and the Market Index, and then calculate average annual returns for the two stocks and the index. (Hint: Remember, returns are calculated by subtracting the beginning price from the ending price to get the capital gain or loss, adding the dividend to the capital gain or loss, and then dividing the result by the beginning price. Assume that dividends are already included in the index. Also, you cannot calculate the rate of return for 2018 because you do not have 2017 data.) Calculate the standard deviations of the returns for Goodman, Landry, and the Market Index. (Hint: Use the sample standard deviation formula given in the chapter, which corresponds to the STDEV function in Excel.) Construct a scatter diagram graph that shows Goodman’s returns on the vertical axis and the Market Index’s returns on the horizontal axis. Construct a similar graph showing Landry’s stock returns on the vertical axis. Estimate Goodman’s and Landry’s betas as the slopes of regression lines with stock return on the vertical axis (y-axis) and market return on the horizontal axis (x-axis). (Hint: Use Excel’s SLOPE function.) Are these betas consistent with your graph? The risk-free rate on long-term Treasury bonds is 6.04%. Assume that the market risk premium is 5%. What is the required return on the market? Now use the SML equation to calculate the two companies’ required returns. If you formed a portfolio that consisted of 50% Goodman stock and 50% Landry stock, what would be its beta and its required return? Suppose an investor wants to include some Goodman Industries stock in his portfolio. Stocks A, B, and C are currently in the portfolio, and their betas are 0.769, 0.985, and 1.423, respectively. Calculate the new portfolio’s required return if it consists of 25% Goodman, 15% Stock A, 40% Stock B, and 20% Stock C.

Solution:

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The detailed solution for the spreadsheet problem is available in the file Ch06-P15 Build a Model Solution.xlsx on the textbook’s website.

MINI CASE Assume that you recently graduated and landed a job as a financial planner with Cicero Services, an investment advisory company. Your first client recently inherited some assets and has asked you to evaluate them. The client owns a bond portfolio with $1 million invested in zero coupon Treasury bonds that mature in 10 years. The client also has $2 million invested in the stock of Blandy, Inc., a company that produces meat-and-potatoes frozen dinners. Blandy’s slogan is ―Solid food for shaky times.‖ Unfortunately, Congress and the president are engaged in an acrimonious dispute over the budget and the debt ceiling. The outcome of the dispute, which will not be resolved until the end of the year, will have a big impact on interest rates one year from now. Your first task is to determine the risk of the client’s bond portfolio. After consulting with the economists at your firm, you have specified five possible scenarios for the resolution of the dispute at the end of the year. For each scenario, you have estimated the probability of the scenario occurring and the impact on interest rates and bond prices if the scenario occurs. Given this information, you have calculated the rate of return on 10-year zero coupon Treasury bonds for each scenario. The probabilities and returns are shown here:

Probability of Scenario

Return on a 10-Year Zero Coupon Treasury Bond During the Next Year

Worst Case

0.10

−14%

Poor Case

0.20

−4%

Most Likely

0.40

Good Case

0.20

16%

Best Case

0.10

26%

Scenario

1.00

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You have also gathered historical returns for the past 10 years for Blandy and Gourmange Corporation (a producer of gourmet specialty foods), and the stock market. Historical Stock Returns Year

Market

Blandy

Gourmange

30%

26%

47%

−54

−14

−22

−15

−14

−28

−18

−10

−23

−3

−32

−4

Average return:

8.0%

9.2%

Standard deviation:

20.1%

38.6%

Correlation with the market:

1.00

0.678

Beta:

1.00

1.30

The risk-free rate is 4% and the market risk premium is 5%. a.

What are investment returns? What is the return on an investment that costs $1,000 and is sold after 1 year for $1,060? Answer: Investment return measures the financial results of an investment. They may be expressed in either dollar terms or percentage terms. The dollar return is $1,60 – $1,000 = $60. The percentage return is $60/$1,000 = 0.06 = 6%.

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Graph the probability distribution for the bond returns based on the five scenarios. What might the graph of the probability distribution look like if there were an infinite number of scenarios (i.e., if it were a continuous distribution and not a discrete distribution)? Answer: Here is the probability distribution for the five possible outcomes:

A continuous distribution might look like this:

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Use the scenario data to calculate the expected rate of return for the 10-year zero coupon Treasury bonds during the next year. Answer: The expected rate of return, r̂ , is expressed as follows: n

r̂ =  P i r i. i =1

Here, pi is the probability of occurrence of the ith state, ri is the estimated rate of return for that state, and n is the number of states. Here is the calculation:

r̂ = 0.1(–14.0%) + 0.2(–4.0%) + 0.4(6.0%) + 0.2(16.0%) + 0.1(26.0%) = 6.0%. d.

What is stand-alone risk? Use the scenario data to calculate the standard deviation of the bond’s return for the next year. Answer: Stand-alone risk is the risk of an asset if it is held by itself and not as a part of a portfolio. Standard deviation measures the dispersion of possible outcomes, and for a single asset, the stand-alone risk is measured by standard deviation. The variance and standard deviation are calculated as follows: n

σ 2 =  p i(r i  rˆi )

i=1

σ2   2 =

 p (r  rˆ ) . 2

i=1

σ2 = [(0.1) (–0.14 – 0.06)2 + (0.2) (–0.04 – 0.06)2 + (0.4) (0.06 – 0.06)2 + (0.2) (0.16 – 0.06)2 + (0.1) (0.26 – 0.06)2] = 0.0120 σ= e.

2 =

0.0120 = 0.1095 = 10.95%.

Your client has decided that the risk of the bond portfolio is acceptable and wishes to leave it as it is. Now your client has asked you to use historical returns to estimate the standard deviation of Blandy’s stock returns. (Note: Many analysts use 4 to 5 years of monthly returns to estimate risk, and many use 52 weeks of weekly returns; some even use a year or less of daily returns. For the sake of simplicity, use Blandy’s 10 annual returns.) Answer: The formulas are shown below: T  r t r Avg = t 1 T T

 (rt  rAvg )2

Estimated σ = S =

t 1

T 1

Using Excel, the past average returns and standard deviations are:

Average return:

Market

Blandy

Gourmange

8.0%

6.4%

9.2%

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Standard deviation of returns: f.

Market

Blandy

Gourmange

20.1%

25.2%

38.6%

Your client is shocked at how much risk Blandy stock has and would like to reduce the level of risk. You suggest that the client sell 25% of the Blandy stock and create a portfolio with 75% Blandy stock and 25% in the high-risk Gourmange stock. How do you suppose the client will react to replacing some of the Blandy stock with high-risk stock? Show the client what the proposed portfolio return would have been in each of year of the sample. Then calculate the average return and standard deviation using the portfolio’s annual returns. How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation? Answer: To find historical returns on the portfolio, we first find each annual return for the portfolio using the portfolio weights and the annual stock returns: The percentage of a portfolio’s value that is invested in Stock I is denoted by the ―weight,‖ wi. Notice that the sum of all the weights must equal 1. With n stocks in the portfolio, its return each year will be:

r p = w1 r 1 + w2 r 2 + ⋯ + wn r n n

=  w i ri i 1

The portfolio return each year will be: ̅ ̅

(̅ (̅

) )

(̅ (̅

) )

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Following is a table showing the portfolio’s return in each year. It also shows the average return and standard deviation during the past 10 years.

Stock Returns Year

Blandy

Gourmange

Portfolio

26.0%

47.0%

31.3%

15.0%

–54.0%

–2.3%

–14.0%

15.0%

–6.8%

–15.0%

7.0%

–9.5%

2.0%

–28.0%

–5.5%

–18.0%

40.0%

–3.5%

42.0%

17.0%

35.8%

30.0%

–23.0%

16.8%

–32.0%

–4.0%

–25.0%

28.0%

75.0%

39.8%

Average return:

6.4%

9.2%

7.1%

Standard deviation of returns:

25.2%

38.6%

22.2%

Notice that the portfolio risk is actually less than the standard deviations of the stocks making up the portfolio. The average portfolio return during the past 10 years can be calculated as average return of the 10 yearly returns. But there is another way—the average portfolio return over a number of periods is also equal to the weighted average of the stock’s average returns: n

r Avg,p =  w r i 1

i Avg,i

This method is used below:

r Avg,p = 0.75(6.4%) + 0.25(9.2%) = 7.1% Note, however, that the only way to calculate the standard deviation of historical returns for a portfolio is to first calculate the portfolio’s annual historical returns and then calculate its standard deviation. A portfolio’s historical standard deviation is not the weighted average of the individual stocks’ standard deviations! (The only exception occurs when there is zero correlation among the portfolio’s stocks, which would be extremely rare.) g.

Explain correlation to your client. Calculate the estimated correlation between Blandy and Gourmange. Does this explain why the portfolio standard deviation was less than Blandy’s standard deviation? Answer: Loosely speaking, the correlation (ρ) coefficient measures the tendency of two variables to move together. The formula, shown below, is complicated, but it is easy to use Excel to calculate the correlation. T

 (r  r Estimated ρi,j = R =

t 1

i,t

i,Avg

)(r j,t  r j,Avg )

T T 2  2   (ri,t  ri,Avg )    (r j,t  r j,Avg )   t 1   t 1 

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Using Excel, the correlation between Blandy (B) and Gourmange (G) is: Est. ρB,G = 0.11 A correlation coefficient of +1 means that the stocks always move together; a correlation coefficient of −1 means that the stocks always move oppositely to one another. A correlation coefficient of 0 means that there is no relationship between the stocks’ movements. The correlation coefficient of 0.11 means that sometimes when Blandy is up, Gourmange is down, and vice versa. This makes the total risk of the portfolio less than the risk of holding either stock by itself. h.

Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio’s risk? Answer: The standard deviation gets smaller as more stocks are combined in the portfolio, while rp (the portfolio’s return) remains constant. Thus, by adding stocks to your portfolio, which initially started as a one-stock portfolio, risk has been reduced.

In the real world, stocks are positively correlated with one another—if the economy does well, so do stocks in general, and vice versa. Correlation coefficients between stocks generally range from +0.5 to +0.7. The average correlation between stocks is about 0.35. A single stock selected at random would on average have a standard deviation of about 35 percent. As additional stocks are added to the portfolio, the portfolio’s standard deviation decreases because the added stocks are not perfectly positively correlated. However, as more and more stocks are added, each new stock has less of a risk-reducing impact, and eventually adding additional stocks has virtually no effect on the portfolio’s risk as measured by σ. In fact, σ stabilizes at about 20 percent when 40 or more randomly selected stocks are added. Thus, by combining stocks into well-diversified portfolios, investors can eliminate almost one-half the riskiness of holding individual stocks. (Note: It is not completely costless to diversify, so even the largest institutional investors hold less than all stocks. Even index funds generally hold a smaller portfolio, which is highly correlated with an index such as the S&P 500 rather than hold all the stocks in the index.) The implication is clear: investors should hold well-diversified portfolios of stocks rather than individual stocks. (In fact, individuals can hold diversified portfolios through mutual fund investments.) By doing so, they can eliminate about half of the riskiness inherent in individual stocks.

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Should portfolio effects influence how investors think about the risk of individual stocks?

Answer: Portfolio diversification does affect investors’ views of risk. A stock’s stand-alone risk as measured by its σ or CV, may be important to an undiversified investor, but it is not relevant to a well-diversified investor. A rational, risk-averse investor is more interested in the impact that the stock has on the riskiness of his or her portfolio than on the stock’s stand-alone risk. Stand-alone risk is composed of diversifiable risk, which can be eliminated by holding the stock in a well-diversified portfolio, and the risk that remains is called market risk because it is present even when the entire market portfolio is held. i.

If you decided to hold a one-stock portfolio and consequently were exposed to more risk than diversified investors, could you expect to be compensated for all of your risk; that is, could you earn a risk premium on that part of your risk that you could have eliminated by diversifying?

Answer: If you hold a one-stock portfolio, you will be exposed to a high degree of risk, but you won’t be compensated for it. If the return were high enough to compensate you for your high risk, it would be a bargain for more rational, diversified investors. They would start buying it, and these buy orders would drive the price up and the return down. Thus, you simply could not find stocks in the market with returns high enough to compensate you for the stock’s diversifiable risk. j.

According to the Capital Asset Pricing Model, what measures the amount of risk that an individual stock contributes to a well-diversified portfolio? Define this measurement. Answer: Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall risk of the portfolio. It is measured by a stock’s beta coefficient. The beta of Stock i, denoted by bi, is calculated as:

 i   iM  M 

bi = 

A stock’s beta can also be estimated by running a regression with the stock’s returns on the y-axis and the market portfolio’s returns on the x-axis. The slope of the regression line gives the same result as the formula shown previously. k.

What is the security market line (SML)? How is beta related to a stock’s required rate of return? Answer: Here is the SML equation: ri = rRf + RPM bi. ri = rRf + (rM − rRf)bi. The SML asserts that because investing in stocks is risky, an investor must expect to get at least the risk-free rate of return plus a premium to reflect the additional risk of the stock. The premium is for a stock begins with the premium required to hold an average stock (RP M) and is scaled up or down depending on the stock’s beta.

Calculate the correlation coefficient between Blandy and the market. Use this and the previously calculated (or given) standard deviations of Blandy and the market to estimate Blandy’s beta. Does Blandy contribute more or less risk to a well-diversified portfolio than does the average stock? Use the SML to estimate Blandy’s required return. Answer: Using the formula for correlation or the Excel function, CORREL, Blandy’s correlation with the market (ρB,M) is:

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ρB,M = 0.481

 i   0.252   ρiM    (0.481) = 0.6  0.201    M

bi = 

Blandy’s beta is less than 1, so it contributes less risk than that of an average stock. Suppose the risk-free rate is 4% and the market risk premium is 5%. The required rate of return on Blandy is ri = rRF + bi (RPM) ri = 4% + 0.60(5%) = 7% m. Show how to estimate beta using regression analysis. Answer: Betas are calculated as the slope of the ―characteristic‖ line, which is the regression line showing the relationship between a given stock’s returns and the stock market’s returns. The following graph shows this regression as calculated using Excel.

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Suppose the risk-free rate goes up to 7%. What effect would higher interest rates have on the SML and on the returns required on high-risk and low-risk securities?

Answer: The SML is shifted higher, but the slope is unchanged.

Here we have plotted the SML for betas ranging from 0 to 2.0. The base case SML is based on rRF = 4% and rM = 5%. If interest rates increase by 3 percentage points, with no change in risk aversion, then the entire SML is shifted upward (parallel to the base case SML) by 3 percentage points. Now, rRF = 7%, rM = 12%, and all securities’ required returns rise by 3 percentage points. Note that the market risk premium, rM − rRF = 7%, remains at 5 percentage points.

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Suppose instead that investors’ risk aversion increased enough to cause the market risk premium to increase to 8%. (Assume the risk-free rate didn’t change.) What effect would this have on the SML and on returns of high- and low-risk securities?

Answer: When investors’ risk aversion increases, the SML is rotated upward about the y-intercept, which is rRF. Suppose rRF remains at 4%, but now rM increases to 12%, so the market risk premium increases to 8%. The required rate of return will rise sharply on high-risk (high-beta) stocks, but not much on low-beta securities.

Your client decides to invest $1.4 million in Blandy stock and $0.6 million in Gourmange stock. What are the weights for this portfolio? What is the portfolio’s beta? What is the required return for this portfolio? Answer: The portfolio’s beta is the weighted average of the stocks’ betas: bp = 0.7(bBlandy) + 0.3(bGour.) = 0.7(0.60) + 0.3(1.30) = 0.81. There are two ways to calculate the portfolio’s expected return. First, we can use the portfolio’s beta and the SML: rp = rRF + bp (RPM) = 4.0% + 0.81%(5%) = 8.1%. Second, we can find the weighted average of the stocks’ expected returns: n

rp =

wr i 1

i i

= 0.7(7.0%) + 0.3(10.5%) = 8.1%.

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Jordan Jones (JJ) and Casey Carter (CC) are portfolio managers at your firm. Each manages a welldiversified portfolio. Your boss has asked for your opinion regarding their performance in the past year. JJ’s portfolio has a beta of 0.6 and had a return of 8.5%; CC’s portfolio has a beta of 1.4 and had a return of 9.5%. Which manager had better performance? Why? Answer: To evaluate the managers, calculate the required returns on their portfolios using the SML and compare the actual returns to the required returns, as follows: Portfolio Manager JJ

Portfolio beta =

0.7

1.4

Risk-free rate =

Market risk premium =

Portfolio required return =

7.50%

11.00%

Portfolio actual return =

8.50%

9.50%

Over (Under) Performance =

1.00%

–1.50%

Notice that JJ’s portfolio had a higher return than investors required (given the risk of the portfolio) and CC’s portfolio had a lower return than expected by investors. Therefore, JJ had the better performance. q.

What does market equilibrium mean? If equilibrium does not exist, how will it be established? Answer: Market equilibrium means that marginal investors (the ones whose trades determine prices) believe that all securities are fairly priced. This means that the market price of a security must equal the security’s intrinsic value (intrinsic value reflects the size, timing, and risk of the future cash flows): Market price = Intrinsic value Market equilibrium also means that the expected return a security must equal its required return (which reflects the security’s risk).

r̂ = r If the market is not in equilibrium, then some assets will be undervalued and/or some will be overvalued. If this is the case, traders will attempt to make a profit by purchasing undervalued securities and short-selling overvalued securities. The additional demand for undervalued securities will drive up their prices and the lack of demand for overvalued securities will drive down their prices. This will continue until market prices equal intrinsic values, at which point the traders will not be able to earn profits greater than justified by the assets’ risks. r.

What is the Efficient Markets Hypothesis (EMH), and what are its three forms? What evidence supports the EMH? What evidence casts doubt on the EMH? Answer: The EMH is the hypothesis that securities are normally in equilibrium, and are ―priced fairly,‖ making it impossible to ―beat the market.‖ Weak-form efficiency says that investors cannot profit from looking at past movements in stock prices—the fact that stocks went down for the last few days is no reason to think that they will go up (or down) in the future. This form has been proven by empirical tests, even though people still employ ―technical analysis.‖

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Semistrong-form efficiency says that all publicly available information is reflected in stock prices, hence that it won’t do much good to pore over annual reports trying to find undervalued stocks. This one is (I think) largely true, but superior analysts can still obtain and process new information fast enough to gain a small advantage. Strong-form efficiency says that all information, even inside information, is embedded in stock prices. This form does not hold—insiders know more, and could take advantage of that information to make abnormal profits in the markets. Trading on the basis of insider information is illegal. Most empirical evidence supports weak-form EMH because very few trading strategies consistently earn in excess of the CAPM prediction, with two possible exceptions that earn very small excess returns: (1) short-term momentum and (2) long-term reversals. Most empirical evidence supports the semistrong-form EMH. For example, the vast majority of portfolio managers do not consistently have returns in excess of CAPM predictions. There are two possible exceptions that earn excess returns: (1) small companies and (2) companies with high book-to-market ratios. In addition, there are times when a market becomes overvalued. This is often called a bubble. Bubbles are hard to burst because trading strategies expose traders to possible big negative cash flows if the bubble is slow to burst.

Solution and Answer Guide CHAPTER 7: CORPORATE V ALUATION, S TOCK VALUATION, AND STOCK M ARKET EQUILIBRIUM

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 160 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 163 Easy Problems 1-10 .............................................................................................................................. 163 Intermediate Problems 11-21 ................................................................................................................ 167 Challenging Problems 22-24................................................................................................................. 173 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 176 MINI CASE ............................................................................................................................................. 178

ANSWERS TO END-OF-CHAPTER QUESTIONS 7-1

Define each of the following terms: a. Proxy; proxy fight; preemptive right; classified stock; founders’ shares b. Free cash flow valuation model; value of operations; nonoperating assets c. Constant growth model; horizon date and horizon value d. Multistage valuation model e. Estimated value (Pˆ0 ); market price (P0) f.

Required rate of return, rs; expected rate of return, r̂s ; actual, or realized, rate of return, rs

g. h.

Capital gains yield; dividend yield; expected total return Preferred stock

Answer: a. A proxy is a document giving one person the authority to act for another, typically the power to vote shares of common stock.

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If earnings are poor and stockholders are dissatisfied, an outside group may solicit the proxies in an effort to overthrow management and take control of the business, known as a proxy fight. The preemptive right gives the current shareholders the right to purchase any new shares issued in proportion to their current holdings. The preemptive right may or may not be required by state law. When granted, the preemptive right enables current owners to maintain their proportionate share of ownership and control of the business. It also prevents the sale of shares at low prices to new stockholders which would dilute the value of the previously issued shares. Classified stock is sometimes created by a firm to meet special needs and circumstances. Generally, when special classifications of stock are used, one type is designated Class A, another as Class B, and so on. Class A might be entitled to receive dividends before dividends can be paid on Class B stock. Class B might have the exclusive right to vote. Founders’ shares are stocks owned by the firm’s founders that have sole voting rights but restricted dividends for a specified number of years. b.

The free cash flow valuation model defines the total value of a company as the value of operations plus the value of nonoperating assets. The value of operations is the present value of all the future expected free cash flows when discounted at the weighted average cost of capital: 

Vop (at t im e 0)  

t 1

FCFt

 1 WACC

Nonoperating assets include investments in marketable securities and noncontrolling interests in the stock of other companies, and other financial securities. c.

Constant growth occurs when a firm’s earnings, dividends, and free cash flows grow at some constant long-term rate. In this situation, the constant growth model can be used to estimate the present value of the growing cash flows or dividends. For free cash flows, the present value is: Vop (constant growth) 

FCF1 WACC  gL



FCF0 (1 gL ) WACC  gL

When applied to dividends, the model is:

P̂0 

D0 (1 gL ) rs  gL



D1 rs  gL

The horizon date is the last year in a cash flow forecast. Cash flows may grow unevenly during the forecast period, but are assumed to grow at a constant rate for all periods after the horizon date. The horizon value is the value all cash flows beyond the horizon date when discounted back to the horizon date. When applied to free cash flows, the horizon value is the value of operations at the end of the explicit forecast period. It is equal to the present value of all free cash flows beyond the forecast period, discounted back to the end of the forecast period at the weighted average cost of capital. Because growth after the horizon is constant, the constant growth model can be applied at the horizon date:

HVT  Vop (at t im e T) 

FCFT  1 WACC  gL



FCFT (1 gL ) WACC  gL

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When applied to dividends, the horizon value is the intrinsic stock price at the end of the explicit forecast period. It is equal to the present value of all dividends beyond the forecast period, discounted back to the end of the forecast period at the required rate of return on stock. Because growth after the horizon is constant, the constant growth model can be applied at the horizon date:

ˆ = Horizon value for stock = P T d.

DT  1 rs  gL



DT 1 gL



rs  gL

A multistage valuation model is used when the growth rate is nonconstant for several years before becoming constant. In this case, the constant growth model is applied at the end of the forecast horizon when the growth rate has become constant. The total present value of cash flows is the present value of all cash flows in the forecast periods plus the present value of the horizon value:

FCFt

Vop,0 = 

t 1

(1  WACC)



HVT (1  WACC) T

When applied to dividends, the present value of dividends is: T

P̂0   t=1

Dt (1 + rS )

PˆT (1 + rS )T

Estimated value ( P̂0 ) is the present value of the expected future cash flows. The market price (P0) is the price at which an asset can be sold.

The required rate of return on common stock, denoted by r s, is the minimum acceptable rate of return considering both its riskiness and the returns available on other investments. The expected rate of return, denoted by r̂s , is the rate of return expected on a stock given its current price and expected future cash flows. If the stock is in equilibrium, the required rate of return will equal the expected rate of return. The realized (actual) rate of return, denoted by rs , is the rate of return that was actually realized at the end of some holding period. Although expected and required rates of return must always be positive, realized rates of return over some periods may be negative.

The capital gains yield results from changing prices and is calculated as (P1 – P0)/P0, where P0 is the beginning-of-period price and P1 is the end-of-period price. For a constant growth stock, the capital gains yield is g, the constant growth rate. The dividend yield on a stock can be defined as either the end-of-period dividend divided by the beginning-of-period price, or the ratio of the current dividend to the current price. Valuation formulas use the former definition. The expected total return, or expected rate of return, is the expected capital gains yield plus the expected dividend yield on a stock. The expected total return on a bond is the yield to maturity.

Preferred stock is a hybrid—it is similar to bonds in some respects and to common stock in other respects. Preferred dividends are similar to interest payments on bonds in that they are fixed in amount and generally must be paid before common stock dividends can be paid. If the preferred dividend is not earned, the directors can omit it without throwing the company into bankruptcy. So, although preferred stock has a fixed payment like bonds, a failure to make this payment will not lead to bankruptcy. Most preferred stocks entitle their owners to regular fixed dividend payments.

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7-2 Two investors are evaluating General Electric’s stock for possible purchase. They agree on the expected value of D1 and also on the expected future dividend growth rate. Further, they agree on the risk of the stock. However, one investor normally holds stocks for 2 years and the other normally holds stocks for 10 years. On the basis of the type of analysis done in this chapter, they should both be willing to pay the same price for General Electric’s stock. True or false? Explain. Answer: True. The value of a share of stock is the PV of its expected future dividends. If the two investors expect the same future dividend stream, and they agree on the stock’s riskiness, then they should reach similar conclusions as to the stock’s value. 7-3 A bond that pays interest forever and has no maturity date is a perpetual bond, also called a perpetuity. In what respect is a perpetual bond similar to (1) a no-growth common stock and (2) a share of preferred stock? Answer: A perpetual bond is similar to a no-growth stock and to a share of preferred stock in the following ways:

1. All three derive their values from a series of cash inflows—coupon payments from the perpetual bond, and dividends from both types of stock. 2. All three are assumed to have indefinite lives with no maturity value (M) for the perpetual bond and no capital gains yield for the stocks. 7-4

Explain how to use the free cash flow valuation model to find the price per share of common equity. Answer: The first step is to find the value of operations by discounting all expected future free cash flows at the weighted average cost of capital. The second step is to find the total corporate value by summing the value of operations, the value of nonoperating assets, and the value of growth options. The third step is to find the value of equity by subtracting the value of debt and preferred stock from the total value of the corporation. The last step is to divide the value of equity by the number of shares of common stock.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1-10 7-1

FCF Projections. Ogier Incorporated currently has $800 million in sales, which are projected to grow by 12.5% in Year 1 and by 5% in Year 2. Its operating profitability ratio (OP) is 10%, and its capital requirement ratio (CR) is 80%. a. What are the projected sales in Years 1 and 2? b. What are the projected amounts of net operating profit after taxes (NOPAT) for Years 1 and 2? c. What are the projected amounts of total net operating capital (OpCap) for Years 1 and 2? d. What is the projected FCF for Year 2? Solution: a. Sales_1 = $800(1 + 0.125) = $900 million Sales_2 = $900(1 + 0.05) = $945 million b.

NOPAT_1 = 0.10($900) = $90.00 million NOPAT_2 = 0.10($945) = $94.50 million

OpCap_1 = 0.80($900) = $720.00 million OpCap_2 = 0.80($945) = $756.00 million

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d. 7-2

$94.5 – ($756 – $720) = $58.50 million

Value of Operations: Constant FCF Growth. EMC Corporation’s current free cash flow is $400,000 and is expected to grow at a constant rate of 5%. The weighted average cost of capital is WACC = 12%. Calculate EMC’s estimated value of operations. Solution: Value of operations = Vop = PV of expected future free cash flow Vop  FCF (1 g)  WACC  g

7-3

$400,000 (1.05) = $6,000,000. 0.12  0.05

Horizon Value of Free Cash Flows. Current and projected free cash flows for Radell Global Operations are shown here. The growth rate from 2025 to 2026 is projected to remain the same for all years beyond 2026. The weighted average cost of capital is 11%. What is the horizon (continuing) value at 2026?

Actual

Projected

2023 $606.820

Free cash flow (millions of dollars)

2024 $667.500

2025 $707.547

2026 $750.000

Solution: The growth rate in FCF from 2025 to 2026 is g = ($750.000 – $707.547)/$707.547 = 0.06. HV2026 = VOp at 2026 = 7-4

FCF2026 (1 gL ) WACC  gL

$750 (1.06) = $15,900 million. 0.11 0.06

Value of Operations. JenBritt Incorporated had a free cash flow (FCF) of $80 million in 2023. The firm projects FCF of $200 million in 2024 and $500 million in 2025. FCF is expected to grow at a constant rate of 4% in 2026 and thereafter. The weighted average cost of capital is 9%. What is the current (i.e., beginning of 2024) value of operations? Solution: HV2025 = (FCF2025 (1 + gL))/(WACC – gL) = ($500(1 + 0.04))/(0.09 – 0.04) = $10,400 million. Vop =

Vop =

FCF2024

FCF2025

 1+ WACC  1+ WACC 1

$200

 1 0.09 



$500

 1 0.09 



HV2025

 1+ WACC

$10, 400

 1 0.09 

= $9,357.80 million. 7-5

Intrinsic Price per Share Based on FCFs. Blunderbluss Manufacturing’s balance sheets report $200 million in total debt, $70 million in short-term investments, and $50 million in preferred stock. Blunderbluss has 10 million shares of common stock outstanding. A financial analyst estimated that Blunderbuss’s value of operations is $800 million. What is the analyst’s estimate of the intrinsic stock price per share? Solution:

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V_op

$800

+ ST investments

$70

Total value

$870

–Total debt

$200

–Preferred stock

$50

Intrinsic value of equity

$620

Divided by # shares

Intrinsic stock price

$62.00

7-6 DPS Calculation. Thress Industries just paid a dividend of $1.50 a share (i.e., D0 = $1.50). The dividend is expected to grow 5% a year for the next 3 years and then 10% a year thereafter. What is the expected dividend per share for each of the next 5 years? Solution: D0 = $1.50; g1-3 = 5%; gn = 10%; D1 through D5 = ? D1 = D0(1 + g1) = $1.50(1.05) = $1.5750. D2 = D0(1 + g1)(1 + g2) = $1.50(1.05)2 = $1.6538. D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.50(1.05)3 = $1.7364. D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.05)3(1.10) = $1.9101. D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.50(1.05)3(1.10)2 = $2.1011. 7-7 Constant Dividend Growth Valuation. Boehm Incorporated is expected to pay a $1.50 per share dividend at the end of this year (i.e., D1 = $1.50). The dividend is expected to grow at a constant rate of 6% a year. The required rate of return on the stock, rs, is 13%. What is the estimated value per share of Boehm’s stock? Solution: D1 = $1.50; g = 6%; rs = 13%; P̂0 = ?

P̂0 =

D1 rs  g

$1.50 = $21.43. 0.13  0.06

7-8 Constant Dividend Growth Valuation. Woidtke Manufacturing’s stock currently sells for $22 a share. The stock just paid a dividend of $1.20 a share (i.e., D 0 = $1.20), and the dividend is expected to grow forever at a constant rate of 10% a year. What is the estimated required rate of return on Woidtke’s stock? (Assume the market is in equilibrium with the required return equal to the expected return.) What stock price is expected 1 year from now? Solution: P0 = $22; D0 = $1.20; g = 10%; P̂1 = ?; r̂s = ?

r̂s =

D1 P0

+g=

$1.20 (1.10) + 0.10 $22

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$1.32 + 0.10 = 16.00%. r̂s = 16.00%. $22

P̂1 = D2/(r – g) = $1.20(1.10)(1.10)/(0.16 – 0.10) = $24.20 Alternately, since this company is in a constant growth phase, the capital gains yield is equal to the dividend growth rate, so the price is also growing at the dividend growth rate:

P̂1 = P0(1 + g) = $22(1.10) = $24.20. Note that this only holds when the stock is in a constant growth phase. The price will NOT grow at the year’s dividend growth rate when the company is in a nonconstant growth situation. 7-9 Nonconstant Dividend Growth Valuation. A company currently pays a dividend of $2 per share (D 0 = $2). It is estimated that the company’s dividend will grow at a rate of 20% per year for the next 2 years and then at a constant rate of 7% thereafter. The company’s stock has a beta of 1.2, the risk-free rate is 7.5%, and the market risk premium is 4%. What is your estimate of the stock’s current price? Solution: 0

g = 20%

3→ ∞

g = 7% D2

g = 7% → ∞ →∞

Step 1: Calculate the required rate of return on the stock: rs = rRF + (rM – rRF)b = 7.5% + (4%)1.2 = 12.3%. Step 2: Calculate the expected dividends: D0 = $2.00 D1 = $2.00(1.20) = $2.40 D2 = $2.00(1.20)2 = $2.88 D3 = $2.88(1.07) = $3.08

1 g = 20%

3→ ∞

2 g = 20%

g = 7%

gL = 7% → ∞ →∞

$2.00

$2(1.2)

$2.40(1.2)

$2.88(1.07) → ∞

$2.00

$2.40

$2.88

$3.08

→∞

Step 3: Calculate the PV of the expected dividends: PVDiv = $2.40/(1.123) + $2.88/(1.123)2 = $2.14 + $2.28 = $4.42. Step 4: Calculate P̂2 :

P̂2 = D3/(rs – g) = $3.082/(0.123 – 0.07) = $58.11.

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(Note: If you carry out the calculations for D3 to more decimal places then P̂2 = $58.14 and the resulting answer is $50.53 instead of the $50.50 we report in Step 6 below.) Step 5: Calculate the PV of P̂2 : PV = $58.11/(1.123)2 = $46.08. Step 6: Sum the PVs to obtain the stock’s price:

P̂0 = $4.42 + $46.08 = $50.50. Alternatively, using a financial calculator, input the following: CF0 = 0, CF1 = 2.40, and CF2 = 60.99 (2.88 + 58.11) and then enter I/YR = 12.3 to solve for NPV = $50.50. 7-10 Preferred Stock Rate of Return. Nick’s Enchiladas has preferred stock outstanding that pays a dividend of $5 at the end of each year. The preferred stock sells for $50 a share. What is the stock’s required rate of return? (Assume the market is in equilibrium with the required return equal to the expected return.) Solution: Dps = $5.00; Vps = $50; rps = ? rps =

Dps vps

$5.00 = 10%. $50.00

INTERMEDIATE PROBLEMS 11-21 7-11 Constant FCF Growth Valuation. Brook Corporation’s free cash flow for the current year (FCF0) was $3.00 million. Its investors require a 13% rate of return on (WACC = 13%). What is the estimated value of operations if investors expect FCF to grow at a constant annual rate of (1) −5%, (2) 0%, (3) 5%, or (4) 10%? Solution: a.

$3(1 0.05) $2.85 = = $15.83. 0.13  0.05 0.18

Vop =

Vop = $3/0.13 = $23.08.

Vop =

$3 (1.05) $3.15 = = $39.38. 0.13  0.05 0.08

Vop =

$3(1.10) $3.30 = = $110.00. 0.13  0.10 0.03

7-12 Value of Operations. Kendra Enterprises has never paid a dividend. Free cash flow is projected to be $80,000 and $100,000 for the next 2 years, respectively; after the second year, FCF is expected to grow at a constant rate of 8%. The company’s weighted average cost of capital is 12%.

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a. b.

What is the terminal, or horizon, value of operations? (Hint: Find the value of all free cash flows beyond Year 2 discounted back to Year 2.) Calculate Kendra’s value of operations.

Solution: $108,000 = $2,700,000. 0.12  0.08

HV2 =

WACC = 12%, so Vops = 80,000/(1.12) + 100,000/(1.12) 2 + 2,700,000/(1.12)2 = $71,428.57 + 79,719.39 + 2,152,423.47 = $2,303,571.43

7-13 Free Cash Flow Valuation. Dozier Corporation is a fast-growing supplier of office products. Analysts project the following free cash flows (FCFs) during the next 3 years, after which FCF is expected to grow at a constant 7% rate. Dozier’s weighted average cost of capital is WACC = 13%.

Year Free cash flow (millions of dollars) a. b. c.

−$20

$30

$40

What is Dozier’s horizon value? (Hint: Find the value of all free cash flows beyond Year 3 discounted back to Year 3.) What is the current value of operations for Dozier? Suppose Dozier has $10 million in marketable securities, $100 million in debt, and 10 million shares of stock. What is the intrinsic price per share?

Solution: a.

HV3 =

$40 (1.07) = $713.33. 0.13  0.07

3→ ∞

g = 7% → ∞

g = 7%

−$20

$30

$40

→∞

($17.70) $23.49 $522.10 $527.89

Vop,3 = 713.33

$753.33 c.

Total value t = 0 = $527.89 + $10.0 = $537.89. Value of common equity = $537.89 - $100 = $437.89. Price per share =

$437.89 = $43.79. 10.0

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7-14 Declining FCF Growth Valuation. Brushy Mountain Mining Company’s coal reserves are being depleted, so its sales are falling. Also, environmental costs increase each year, so its costs are rising. As a result, the company’s free cash flows are declining at the constant rate of 4% per year. If its current free cash flow (FCF0) is $6 million and its weighted average cost of capital (WACC) is 14%, what is the estimated value of Brushy Mountain’s value of operations? Solution:

P̂0 =

D1 rs  g

D0 (1 g) rs  g

$5.76 $6 [ 1 ( 0.04)] = = $32.00. 0.14  ( 0.04)] 0.18

7-15 Constant Dividend Growth Rate, gL. Holts’s Investigative Services has stock trading at $80 per share. The stock is expected to have a year-end dividend of $4 per share (D1 = $4), and it is expected to grow at some constant rate, g, throughout time. The stock’s required rate of return is 14% (assume the market is in equilibrium with the required return equal to the expected return). What is your forecast of gL? Solution: The problem asks you to determine the constant growth rate, given the following facts: P0 = $80, D1 = $4, and rs = 14%.

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Use the constant growth rate formula to calculate gL: r̂s =

0.14 =

D1 P0

+ gL

$4 + gL $80

gL = 0.09 = 9%. 7-16 Constant Dividend Growth Valuation. Crisp Cookware’s common stock is expected to pay a dividend of $3 a share at the end of this year (D1 = $3.00); its beta is 0.8. The risk-free rate is 5.2%, and the market risk premium is 6%. The dividend is expected to grow at some constant rate g, and the stock currently sells for $40 a share. Assuming the market is in equilibrium, what does the market believe will be the stock’s price at the end of 3 years (i.e., what is P̂3 )? Solution: The problem asks you to determine the value of P̂3 , given the following facts: D1 = $3, b = 0.8, rRF = 5.2%, RPM = 6%, and P0 = $40. Proceed as follows: Step 1:

Calculate the required rate of return: rs = rRF + (rM – rRF)b = 5.2% + (6%)0.8 = 10%.

Step 2:

Use the constant growth rate formula to calculate g: r̂s =

0.10 =

D1 P0

$3 +g $40

g = 0.025 = 2.5%. Step 3:

Calculate P̂3 :

P̂3 = P0(1 + g)3 = $40(1.025)3 = $43.076 ≈ $43.08. Alternatively, you could calculate D4 and then use the constant growth rate formula to solve for P̂3 : D4 = D1(1 + g)3 = $3.00(1.025)3 = $3.2307.

P̂3 = $3.2307/(0.10 – 0.025) = $43.0756  $43.08. 7-17 Preferred Stock Rate of Return. What is the required rate of return on a preferred stock with a $50 par value, a stated annual dividend of 7% of par, and a current market price of (a) $30, (b) $40, (c) $50, and (d) $70? (Assume the market is in equilibrium with the required return equal to the expected return.)

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Solution: Vps = Dps/rps; therefore, rps = Dps/Vps. a.

rps = $3.5/$30 = 11.67%.

rps = $3.5/$40 = 8.75%.

rps = $3.5/$50 = 7.00%.

rps = $3.5/$70 = 5.00%.

7-18 Nonconstant Dividend Growth Valuation. Assume that the average firm in C&J Corporation’s industry is expected to grow at a constant rate of 6% and that its dividend yield is 7%. C&J is about as risky as the average firm in the industry and just paid a dividend (D 0) of $1. Analysts expect that the growth rate of dividends will be 50% during the first year (g 0,1 = 50%) and 25% during the second year (g1,2 = 25%). After Year 2, dividend growth will be constant at 6%. What is the required rate of return on C&J’s stock? What is the estimated intrinsic per share? Solution: D0 = $1, rS = 7% + 6% = 13%, g1 = 50%, g2 = 25%, gn = 6%. D1 = 1.50 D2 = 1.875 D3 = 1.9875 HV2 = 1.9875/(0.13 – 0.06) = 28.393

P̂0 = 1.50/1.13 + (1.875 + 28.393)/1.132 = $25.03 7-19 Nonconstant Dividend Growth Valuation. Simpkins Corporation does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of $0.50 coming 3 years from today. The dividend should grow rapidly—at a rate of 80% per year—during Years 4 and 5. After Year 5, the company should grow at a constant rate of 7% per year. If the required return on the stock is 16%, what is the value of the stock today? (Assume the market is in equilibrium with the required return equal to the expected return.) Solution: Calculate the dividend stream and place them on a time line. Also, calculate the price of the stock at the end of the nonconstant growth period, and include it, along with the dividend to be paid at t = 5, as CF 5. Then, enter the cash flows as shown on the time line into the cash flow register, enter the required rate of return as I = 15, and then find the value of the stock using the NPV calculation. Be sure to enter CF0 = 0, or else your answer will be incorrect. D0

D3(1 + g3,4)

D4(1 + g4,5)

D5(1 + g5,6)

0.5

0.5(1.8)

0.9(1.8)

1.62(1.07)

0.5

0.9

1.62

1.7334

0.50

0.9

1.62

→∞

1.7334→∞

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0 0

Horizon Value:

0.32

1.7334

0.50

(0.16 − 0.07)

0.77

↓

9.17

19.26

10.76 Follow these directions to find the current price of the stock with a financial calculator.

P̂5 = D6/(rs – g) = 1.7334/(0.16 – 0.07) = 19.26. This is the price of the stock at the end of Year 5. CF0 = 0; CF1-2 = 0; CF3 = 0.5; CF4 = 0.9; CF5 = 20.88; I = 16%. With these cash flows in the CFLO register, press NPV to get the value of the stock today: NPV = $10.76. 7-20 Preferred Stock Valuation. Several years ago, Rolen Riders issued preferred stock with a stated annual dividend of 10% of its $100 par value. Preferred stock of this type currently yields 8%. Assume dividends are paid annually. a. What is the estimated value of Rolen’s preferred stock? b. Suppose interest rate levels have risen to the point where the preferred stock now yields 12%. What would be the new estimated value of Rolen’s preferred stock? Solution: a.

Vps =

Dps rps

$10 = $125. 0.08

$10 = $83.33. 0.12

7-21 Return on Common Stock. You buy a share of The Ludwig Corporation stock for $21.40. You expect it to pay dividends of $1.07, $1.1449, and $1.2250 in Years 1, 2, and 3, respectively, and you expect to sell it at a price of $26.22 at the end of 3 years. a. Calculate the growth rate in dividends. b. Calculate the expected dividend yield. c. Assuming that the calculated growth rate is expected to continue, you can add the dividend yield to the expected growth rate to obtain the expected total rate of return. What is this stock’s expected total rate of return? (Assume the market is in equilibrium with the required return equal to the expected return.)

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Solution: a. g = $1.1449/$1.07 – 1.0 = 7%. Calculator solution: Input N = 1, PV = –1.07, PMT = 0, FV = 1.1449, I/YR = ? I = 7.00%. b.

$1.07/$21.40 = 5%.

r̂s = D1/P0 + g = $1.07/$21.40 + 7% = 5% + 7% = 12%.

CHALLENGING PROBLEMS 22-24 7-22 Constant Dividend Growth Valuation. You are analyzing Jillian’s Jewelry (JJ) stock for a possible purchase. JJ just paid a dividend of $1.50 yesterday. You expect the dividend to grow at the rate of 6% per year for the next 3 years; if you buy the stock, you plan to hold it for 3 years and then sell it. a. What dividends do you expect for JJ stock over the next 3 years? In other words, calculate D 1, D2, and D3. Note that D0 = $1.50. b. JJ stock has a required return of 13%, the rate you’ll use to discount dividends. Find the present value of the dividend stream; that is, calculate the PV of D1, D2, and D3, and then sum these PVs. c.

d. e. f.

JJ stock should trade for $27.05 3 years from now (i.e., you expect P̂3 = $27.05). Discounted at a 13% rate, what is the present value of this expected future stock price? In other words, calculate the PV of $27.05. If you plan to buy the stock, hold it for 3 years, and then sell it for $27.05, what is the most you should pay for it? Use the constant growth model to calculate the present value of this stock. Assume that gL = 6% and is constant. Is the value of this stock dependent on how long you plan to hold it? In other words, if your planned holding period were 2 years or 5 years rather than 3 years, would this affect the value of the stock today, P̂0 ? Explain your answer.

Solution: a. D1 = $1.5(1.06) = $1.59. D2 = $1.50(1.06)2 = $1.69. D3 = $1.5(1.06)3 = $1.79. b.

PV = $1.59(0.8850) + $1.69(0.7831) + $1.79(0.6930) = $3.97. Calculator solution: Input 0, 1.59, 1.69, and 1.79 into the cash flow register, input I/YR = 13, PV = ? PV = $3.97.

$27.05(0.6930) = $18.74.

Calculator solution: Input 0, 0, 0, and 27.05 into the cash flow register, I/YR = 13, PV = ? PV = $18.74. d.

$18.74 + $3.97 = $22.71 = Maximum price you should pay for the stock. (rounding differences may give you $22.72.)

P̂0 =

D0 (1 g) rs  g

D1 rs  g

$1.59 = $22.71. 0.13  0.06

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The value of the stock is not dependent upon the holding period. The value calculated in parts a through d is the value for a 3-year holding period. It is equal to the value calculated in part e except for a small rounding error. Any other holding period would produce the same value of P̂0 ; that is, P̂0 = $22.71.

7-23 Nonconstant FCF Growth Valuation. Reizenstein Technologies (RT) has just developed a solar panel capable of generating 200% more electricity than any solar panel currently on the market. As a result, RT is expected to experience a 15% annual growth rate for the next 5 years. By the end of 5 years, other firms will have developed comparable technology, and RT’s growth rate will slow to 5% per year indefinitely. RT has a 12% weighted average cost of capital. The most recent annual free cash flow (FCF0) was $1.75 million. a. Calculate RT’s expected FCFs for t = 1, t = 2, t = 3, t = 4, and t = 5. b. What is the horizon value at t = 5 (HV5)? c. What is the present value of the horizon value? d. What is the present value of the free cash flows expected at t = 1, t = 2, t = 3, t = 4, and t = 5? e. What is the value of operations at t = 0? Solution: a. FCFt

= FCF0(1 + g)t

FCF1

= $1.75(1.15)1 = $2.0125 million.

FCF2

= $1.75(1.15)2 = $2.3114 million.

FCF3

= $1.75(1.15)3 = $2.6615 million.

FCF4

= $1.75(1.15)4 = $3.0608 million.

FCF5

= $1.75(1.15)5 = $3.5199 million.

HV5 =

FCF6 WACC  gn



FCF5 (1 gn ) WACC  gn

$3.5199 (1.05) = $52.80 million. 0.12  0.05

This is the value of operations 5 years from now. c.

PV of HV5 = $52.80/(1 + WACC)5 = $52.80/(1 + 1.02)5 = $29.96. Calculator solution: N = 5, I/YR = 12, PV = ?, PMT = 0, FV = –$52.80: PV = $29.96

Total PV of FCF1 through FCF5 = $2.0125/(1 + 0.12)1 + $2.3114/(1 + 0.12)2 + $2.6615/(1 + 0.12)3 + $3.0608/(1 + 0.12)4 + $3.5199/(1 + 0.12)5 = $9.48 Calculator solution: Input 0, 2.0125, 2.3114, 2.6615, 3.0608, 3.5199 into the cash flow register, input I/YR = 12, PV = ? PV = $9.48.

The total value of operations today is the sum or the PV of the horizon value and the PVs of the free cash flows from Year 1 through 5: Vop,0 = PV FCF Years 1 through 5 + PV of HV5 = $9.48 + $29.96 = $39.44 million. Calculator solution: Input 0, 2.01, 2.31, 2.66, 3.06, 56.32 (3.52 + 52.80) into the cash flow register, input I/YR = 12, PV = ? PV = $39.44.

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7-24 Nonconstant Dividend Growth Valuation. Conroy Consulting Corporation (CCC) has a current dividend of D0 = $2.50. Shareholders require a 12% rate of return. Although the dividend has been growing at a rate of 30% per year in recent years, this growth rate is expected to last only for another 2 years (g0,1 = g1,2 = 30%). After Year 2, the growth rate will stabilize at gL = 7%. a. What is CCC’s stock worth today? b. What is the expected stock price at Year 1? c. What is the Year 1 expected (1) dividend yield, (2) capital gains yield, and (3) total return? d. What is its expected dividend yield for the second year? The expected capital gains yield? The expected total return? Solution: a. Graphical representation of the problem: Nonconstant growth 0 | D0

1 |

Normal growth 2 |

3 |

∞

(D2 + P̂2 )

D∞

PVD1 PVD2 PV P̂2 P0 D1 = D0(1 + gs) = $2.50(1.30) = $3.25. D2 = D0(1 + gs)2 = $2.50(1.30)2 = $4.225.

P̂2 =

rs  gn

D2 (1 gn ) rs  gn

$4.225 (1.07) = $90.415 0.12  0.07

ˆ ) P̂0 = PV(D1) + PV(D2) + PV (P 2 =

D1 (1 rs )



D2 (1 rs )2



ˆ P 2 (1 rs )2

$3.25 $4.225 $90.415   (1 0.12) (1 0.12)2 (1 0.12)2

= $78.3482. Calculator solution: Input 0, 3.25, 94.64 (4.225 + 90.415) into the cash flow register, input I/YR = 12, PV = ? PV = $78.3482.

HV2  D2

$90.415  $4.225 = $84.50. 1 0.12

P̂1 =

Expected dividend yield: D1/P0 = $3.25/$78.3482 = 4.148%.

1 rs

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Capital gains yield =

P̂1  P0 P0

$84.50  $78.3482 = 7.852%. $78.3482

Total return = Dividend yield + capital gains yield = 4.148% + 7.852% = 12.00%. Notice that this is the same as the stock’s required return, r s. d.

Expected dividend yield: D2/P1 = $4.225/$84.500 = 5.00%. Capital gains yield =

HV2  P1 P1

$90.415  $84.500 = 7.00%. $84.500

Total return = Dividend yield + capital gains yield = 5.00% + 7.00% = 12.00%. Notice that this is the same as the stock’s required return, rs. Notice also that Year 1 had a bigger capital gains yield because the dividend was growing faster in Year 1.

SOLUTION TO SPREADSHEET PROBLEM 7-25 Build a Model: Free Cash Flow Valuation Model. Start with the partial model in the file Ch07 P25 Build a Model.xlsx on the textbook’s website. Selected data for the Derby Corporation are shown here. Use the data to answer the following questions: a. Calculate the estimated horizon value (i.e., the value of operations at the end of the forecast period immediately after the Year 4 free cash flow). Assume growth becomes constant after Year 3. b. Calculate the present value of the horizon value, the present value of the free cash flows, and the estimated Year 0 value of operations. c. Calculate the estimated Year 0 price per share of common equity.

INPUTS (In Millions)

Year Current 0

Free cash flow Marketable securities

$40

Notes payable

$100

Long-term bonds

$300

Preferred stock

$50

WACC Number of shares of stock

Projected 1

−$20.0

$20.0

$80.0

$84.0

9.00% 40

Solution: The detailed solution for the spreadsheet problem, Ch07 P25 Build a Model Solution.xlsx, is available at the textbook’s website. 7-26 Build a Model: Value Drivers in the Free Cash Flow Valuation Model. Start with the partial model in Ch07 P26 Build a Model.xlsx on the textbook’s website. Traver-Dunlap Corporation has a 15% weighted average cost of capital (WACC). Its most recent sales were $980 million, and its total net operating capital is $970 million. The following table shows estimates of the forecasted growth rates,

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operating profitability ratios, and capital requirement ratios for the next 3 years. All of these ratios are expected to remain constant after the third year. Use this information to answer the following questions: a. Use the data to forecast sales, net operating profit after taxes (NOPAT), total net operating capital (OpCap), free cash flow (FCF), growth rate in FCF, and return on invested capital (ROIC) for the next 3 years. What is the FCF growth rate for Year 3, and how does it compare with the growth rate in sales? What is the ROIC for Year 3 and how does it compare with the 15% WACC? b. What is the value of operations at Year 3, Vop,3? What is the current value of operations, Vop,0? How does the value of operations at Year 0 compare with the total net operating working capital at Year 3, and what might explain this relationship? c. Suppose the growth rates for Years 2, 3, and thereafter can be increased to 7%. What is the new value of operations? Did it go up or down? Why did it change in this manner? d. Return the growth rates to the original values. Now suppose that the capital requirement ratio can be decreased to 60% for all 3 years and thereafter. What is the new value of operations? Did it go up or down relative to the original base case? Why did it change in this manner? e. Leave the capital requirement ratios at 60% for all 3 years and thereafter, but increase the sales growth rates for Years 2, 3, and thereafter to 7%. What is the new value of operations? Did it go up or down relative to the other scenarios? Why did it change in this manner?

Estimated Base Case Data for Traver-Dunlap Corporation Forecast Year 1

Annual sales growth rate

20%

Operating profitability (NOPAT/Sales)

12%

10%

Capital requirement (OpCap/Sales)

80%

Tax rate

35%

Solution: The detailed solution for the spreadsheet problem, Ch07 P26 Build a Model Solution.xlsx, is available at the textbook’s website.

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7-27 Build a Model: Dividend Growth Valuation Model. Start with the partial model in the file Ch07 P27 Build a Model.xlsx on the textbook’s website. Hamilton Landscaping’s dividend growth rate is expected to be 30% in the next year, drop to 15% from Year 1 to Year 2, and drop to a constant 5% for Year 2 and all subsequent years. Hamilton has just paid a dividend of $2.50, and its stock has a required return of 11%. a. What is Hamilton’s estimated stock price today? b. If you bought the stock at Year 0, what are your expected dividend yield and capital gains for the upcoming year? c. What are your expected dividend yield and capital gains for the second year (from Year 1 to Year 2)? Why aren’t these the same as for the first year? Solution: The detailed solution for the spreadsheet problem, Ch07 P27 Build a Model Solution.xlsx, is available at the textbook’s website.

MINI CASE Your employer, a midsized human resources management company, is considering expansion into related fields, including the acquisition of Temp Force Company, an employment agency that supplies word processor operators and computer programmers to businesses with temporary heavy workloads. Your employer is also considering the purchase of Biggerstaff & McDonald (B&M), a privately held company owned by two friends, each with 5 million shares of stock. B&M currently has free cash flow of $24 million, which is expected to grow at a constant rate of 5%. B&M’s financial statements report short-term investments of $100 million, debt of $200 million, and preferred stock of $50 million. B&M’s weighted average cost of capital (WACC) is 11%. Answer the following questions. a.

Briefly describe the legal rights and privileges of common stockholders. Answer: The common stockholders are the owners of a corporation, and as such, they have certain rights and privileges as described below.

Ownership implies control. Thus, a firm’s common stockholders have the right to elect its firm’s directors, who in turn elect the officers who manage the business.

Common stockholders often have the right, called the preemptive right, to purchase any additional shares sold by the firm. In some states, the preemptive right is automatically included in every corporate charter; in others, it is necessary to insert it specifically into the charter.

What is free cash flow (FCF)? What is the weighted average cost of capital? What is the free cash flow valuation model? Answer: Free cash flow (FCF) is the cash flow available for distribution to all of a company’s investors. FCF is generated by a company’s operations. The weighted average cost of capital (WACC) is the overall rate of return required by all of the company’s investors. The PV of their expected future free cash flows, discounted at the WACC, is the value of operations. This is the essence of the FCF valuation model.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach 

Vop =

 (1  WACC) t 1

FCFt

Nonoperating assets are marketable securities and ownership of noncontrolling interest in another company. The value of nonoperating assets usually is very close to figure that is reported on balance sheets. c.

Use a pie chart to illustrate the sources that comprise a hypothetical company’s total value. Using another pie chart, show the claims on a company’s value. How is equity a residual claim? Answer: Total corporate value is sum of value of operations and value of nonoperating assets. Some company’s also have growth options, but assume they are negligible for this company. Debt holders have first claim. Preferred stockholders have the next claim. Any remaining value belongs to stockholders.

Suppose the free cash flow at Time 1 is expected to grow at a constant rate of g L forever. If gL < WACC, what is a formula for the present value of expected free cash flows when discounted at the WACC?

Answer:

Vop  d.

FCF1

 WACC  gL 

If the most recent free cash flow is expected to grow at a constant rate of g L forever (and gL < WACC), what is a formula for the present value of expected free cash flows when discounted at the WACC?

Answer: FCF0 (1 gL ) Vop  WACC  gL





Use B&M’s data and the free cash flow valuation model to answer the following questions. What is its estimated value of operations?

Answer:

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Vop 

FCF0 (1 gL )

 WACC  g  L

Vop 

24 (1 0.05)

0.11 0.05 

 420

What is its estimated total corporate value? (This is the entity value.)

Answer: Total corporate value

= Vop + Short-term investments. = $420 + $100 = $520 million

What is its estimated intrinsic value of equity?

Answer: Intrinsic value of equity

= Total value − Debt − Pref. = $520 – $200 – $50 = $270 million

What is its estimated intrinsic stock price per share?

Answer: Intrinsic stock price per share

= Value of equity/Number of shares = $270/10 – $200 – $50 = $27.00

You have just learned that B&M has undertaken a major expansion that will change its expected free cash flows to −$10 million in 1 year, $20 million in 2 years, and $35 million in 3 years. After 3 years, free cash flow will grow at a rate of 5%. No new debt or preferred stock was added; the investment was financed by equity from the owners. Assume the WACC is unchanged at 11% and that there are still 10 million shares of stock outstanding. What is the company’s horizon value (i.e., its value of operations at Year 3)? What is its current value of operations (i.e., at Time 0)?

Answer:

Year FCF

…t

–$10

$20

$35

FCF3(1 + 0.05)

FCF4(1 + 0.05)

FCFt(1 + 0.05)

HV3  Vop,3 

HV3 = Vop,3 =

FCF3 (1 gL ) WACC  gL

35 (1 0.05) = $612.50 0.11 0.05

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Year

FCF

FCF1 ←↵

PV of FCF in explicit forecast

←↵

PV of HV is the PV of FCF beyond the explicit forecast

…t

FCF3(1 + gL) ←↵

FCF4(1 + gL)

FCFt(1 + gL) ←↵

FCF2 FCF3 ←↵ ←↵

←↵

0 WACC = 11% 1

–10

HV3 ←↵

gL = 5%

4 |

←↵

N 

$ –9.009 16.232 25.592 = 612.5 =

447.855 $480.67 = Value of operations f.

What is its estimated intrinsic value of equity on a price per share basis?

Answer:

Value of operations

$480.67

+ Value of nonoperating assets

100.00

Total estimated value of firm − Debt

$580.67 200.00

− Preferred stock

50.00

Estimated value of equity

$330.67

÷ Number of shares

10.00

Estimated stock price per share =

$33.07

If B&M undertakes the expansion, what percent of B&M’s value of operations at Year 0 is due to cash flows from Years 4 and beyond? (Hint: Use the horizon value at t = 3 to help answer this question.) Answer: First, calculate the present value of the horizon value. Then divide the present value of the horizon value by the Year 0 value of operations. This will show what percent of value is due to cash flows occurring 4 or more years in the future. Vop,0 = $480.67 HV3 = $612.50

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PV of HV3 = $612.50/(1 + 0.11)3 = $447.855 Percent of value due to cash flows from Year 4 and beyond: % due to long term = (PV of HV3)/Vop,0 = $447.855/$480.67 = 0.93 = 93% h.

Based on your answer to the previous question, what are two reasons why managers often emphasize short-term earnings? Answer: 1. Changes in quarterly earnings can signal changes future in cash flows. This would affect the current stock price. 2.

Managers often have bonuses tied to quarterly earnings, so they have incentive to manage earnings.

Your employer also is considering the acquisition of Hatfield Medical Supplies. You have gathered the following data regarding Hatfield, with all dollars reported in millions: (1) most recent sales of $2,000; (2) most recent total net operating capital, OpCap = $1,120; (3) most recent operating profitability ratio, OP = NOPAT/Sales = 4.5%; and (4) most recent capital requirement ratio, CR = OpCap/Sales = 56%. You estimate that the growth rate in sales from Year 0 to Year 1 will be 10%, from Year 1 to Year 2 will be 8%, from Year 2 to Year 3 will be 5%, and from Year 3 to Year 4 will be 5%. You also estimate that the long-term growth rate beyond Year 4 will be 5%. Assume the operating profitability and capital requirement ratios will not change. Use this information to forecast Hatfield's sales, net operating profit after taxes (NOPAT), OpCap, free cash flow, and return on invested capital (ROIC) for Years 1 through 4. Also estimate the annual growth in free cash flow for Years 2 through 4. The weighted average cost of capital (WACC) is 9%. How does the ROIC in Year 4 compare with the WACC? Answer: The operating items are forecast as follows: Sales1 = $2,000(1 + 0.10) = $2,200; NOPAT1 = $2,200(0.045) = $99; and OpCap1 = $2,200(0.56) = $1,232. The operating items for the other years are forecast in a similar manner. Actual Scenario: No Change Sales

$2,000

$2,200

NOPAT OpCap

Forecast

$1,120

FCF

$2,376

$2,495

$2,620

$99

$107

$112

$117.879

$1,232

$1,331

$1,397.088

$1,466.942

−$13

$8.36

$45.738

$48.025

–164%

447.1%

5.0%

8.0%

Growth in FCF ROIC

8.0%

The ROIC4 is 8% and the WACC is 9%. This means that ROIC < WACC/(1 + g L) at the horizon: 0.08 < 9%/(1 + 0.05) = 0.0857. Therefore, we expect that the value of operations at Year 4 (i.e., the horizon value at Year 4) should be less than the total net operating capital at Year 4, OpCap 4. j.

What is the horizon value at Year 4? What is the total net operating capital at Year 4? Which is larger, and what can explain the difference? What is the value of operations at Year 0? How does the

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Year 0 value of operations compare with the Year 0 total net operating capital? Answer: HV4 



  $48.025  1 0.05   $1, 260.65  WACC  gL  0.09  0.05 

FCF4 1 gL

PV of HV4  PV of FCF 

PV of FCF 

HV4



1 WACC



FCF1



$1, 260.65



1 0.09

 $893.08



FCF2



 1 WACC  1 WACC 1

$13



$8.36

 1 0.09   1 0.09  1



FCF3

 1 WACC

$45.738

 1 0.09 



FCF4

 1 WACC

$48.025

 1 0.09 

PV of FCF = $64.45 The value of operations is the sum of the PV of the horizon value plus the PVs of the FCFs: Present value of HV

$893.08

+ Present value of FCF

$64.45

Value of operations ≈

$958

Notice that the value of operations at Year 4 (i.e., the horizon value, HV 4) is $1,260.65 and that the total net operation capital at Year 4 (OpCap4 from Part i) is $1,466.94. In other words, the value of operations is less than the total net operating capital. This is because ROIC4 < WACC/(1 + gL) at the horizon: 0.08 < 9%/(1 + 0.05) = 0.0857. Also, at Year 0, the most recent total net operating capital, OpCap0 = $1,120. Note that the value of operations at Year 0 is $958, and this is less than the OpCap 0. Thus, the low ROIC relative to the WACC causes the value of operations to be less than the total net operating capital. k.

What are value drivers? What happens to the ROIC and current value of operations if expected growth increases by 1 percentage point relative to the original growth rates (including the long-term growth rate)? What can explain this? (Hint: Use Scenario Manager.) Answer: Value drivers are the inputs to the FCF valuation model that managers are able to influence: sales growth rates, operating profitability, capital requirements, and cost of capital. No Change

Improve Growth

g0,1

10%

11%

g1,2

g2,3

g3,4

4.5%

56.0%

ROIC

8.0%

Scenario

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Current value of operations

$958

$933

WACC

9.00%

WACC/(1 + WACC)

8.26%

Higher growth causes Vop,0 to fall. ROIC must be greater than WACC/(1 + WACC) for growth to add value. l.

Assume growth rates are at their original levels. What happens to the ROIC and current value of operations if the operating profitability ratio increases to 5.5%? Now assume growth rates and operating profitability ratios are at their original levels. What happens to the ROIC and current value of operations if the capital requirement ratio decreases to 51%? Assume growth rates are at their original levels. What is the impact of simultaneous improvements in operating profitability and capital requirements? What is the impact of simultaneous improvements in the growth rates, operating profitability, and capital requirements? (Hint: Use Scenario Manager.) Answer: Scenario

No Change

Improve OP

g0,1

10%

g1,2

g2,3

g3,4

4.5%

5.5%

56.0%

ROIC

8.0%

9.8%

Current value of operations

$958

$1,523

WACC

9.00%

WACC/(1 + WACC)

8.26%

The improvement in operating profitability increases the ROIC, which increases the value of operations.

Scenario g0,1 g1,2 g2,3 g3,4 gL OP CR ROIC Current value of operations WACC WACC/(1 + WACC)

No Change

Improve CR

10% 8% 5% 5% 5% 4.5% 56.0% 8.0% $958 9.00% 8.26%

10% 8% 5% 5% 5% 4.5% 51.0% 8.8% $1,191 9.00% 8.26%

The improvement in capital requirements increases the ROIC, which increases the value of operations.

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Scenario g0,1 g1,2 g2,3 g3,4 gL OP CR ROIC Current value of operations WACC WACC/(1 + WACC)

No Change

Improve OP and CR

10% 8% 5% 5% 5% 4.5% 56.0% 8.0% $958 9.00% 8.26%

10% 8% 5% 5% 5% 5.5% 51.0% 10.8% $1,756 9.00% 8.26%

The improvements in operating profitability and capital requirements increased the ROIC, so growth now adds substantial value. Scenario g0,1 g1,2 g2,3 g3,4 gL OP CR ROIC Current value of operations WACC WACC/(1 + WACC)

No Change

Improve All

10% 8% 5% 5% 5% 4.5% 56.0% 8.0% $958 9.00% 8.26%

11% 9% 6% 6% 6% 5.5% 51.0% 10.8% $2,008 9.00% 8.26%

The improvements in operating profitability increased the ROIC, so growth now adds substantial value. m. What insight does the free cash flow valuation model provide regarding possible reasons for market volatility? (Hint: Look at the value of operations for the combinations of ROIC and g L in the previous questions.) Answer: ROIC gL

8.0%

8.8%

9.8%

10.8%

$958

$1,191

$1,523

$1,756

$933

$1,247

$1,694

$2,008

Small changes in ROIC and growth cause large changes in value. Similarly, small changes in the cost of capital (WACC) cause large changes in value. As new information arrives, investors continually update their estimates of operating profitability, capital requirements, growth, risk, and interest rates. If stock prices aren’t volatile, then this means there isn’t a good flow of information. n.

Write out a formula that can be used to value any dividend-paying stock, regardless of its dividend pattern.

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Answer: The value of any stock is the present value of its expected dividend stream:

P̂0 =

D1 (1 rs )



D2 (1 rs )



D3 (1 rs )



D (1 rs )

However, some stocks have dividend growth patterns that allow them to be valued using short-cut formulas. n.

What is a constant growth stock? How are constant growth stocks valued?

Answer: A constant growth stock is one whose dividends are expected to grow at a constant rate forever. ―Constant growth‖ means that the best estimate of the future growth rate is some constant number, not that we really expect growth to be the same each and every year. Many companies have dividends that are expected to grow steadily into the foreseeable future, and such companies are valued as constant growth stocks. For a constant growth stock: D1 = D0(1 + gL), D2 = D1(1 + gL) = D0(1 + gL)2, and so on. With this regular dividend pattern, the general stock valuation model can be simplified to the following very important equation:

P̂0 =

D1 rs  gL

D0 (1 gL ) rs  gL

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This is the well-known ―Gordon,‖ or ―constant-growth‖ model for valuing stocks. Here, D1, is the next expected dividend, which is assumed to be paid 1 year from now, r s is the required rate of return on the stock, and g is the constant growth rate. n.

What happens if a company has a constant g L that exceeds its rs? Will many stocks have expected growth greater than the required rate of return in the short run (i.e., for the next few years)? In the long run (i.e., forever)?

Answer: The model is derived mathematically, and the derivation requires that r s > gL. If gL is greater than rs, the model gives a negative stock price, which is nonsensical. The model simply cannot be used unless (1) rs > gL, (2) gL is expected to be constant, and (3) gL can reasonably be expected to continue indefinitely. Stocks may have periods of nonconstant growth, where g > r s; however, this growth rate cannot be sustained indefinitely. In the long-run, gL < rs. o.

Assume that Temp Force has a beta coefficient of 1.2, that the risk-free rate (the yield on T-bonds) is 7%, and that the market risk premium is 5%. What is the required rate of return on the firm’s stock? Answer: Here we use the SML to calculate temp force’s required rate of return: rs = rRF + (rM – rRF)bTemp Force = 7% + (12% – 7%)(1.2) = 7% + (5%)(1.2) = 7% + 6% = 13%.

Assume that Temp Force is a constant growth company whose last dividend (D 0, which was paid yesterday) was $2.00 and whose dividend is expected to grow indefinitely at a 6% rate. What is the firm’s current estimated intrinsic stock price?

Answer: We could extend the time line on out forever, find the value of Temp Force’s dividends for every year on out into the future, and then the PV of each dividend, discounted at r = 13%. For example, the PV of D1 is $1.76106; the PV of D2 is $1.75973; and so forth. Note that the dividend payments increase with time, but as long as r s > gL, the present values decrease with time. If we extended the graph on out forever and then summed the PVs of the dividends, we would have the value of the stock. However, since the stock is growing at a constant rate, its value can be estimated using the constant growth model: P̂0 =

D1 rs  gL

D1 = D0 (1 + gL) = $2.00 (1.06) = $2.12 P̂0 =

D1 rs  g

$2.12 $2.12 = = $30.29. 0.13  0.06 0.07

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What is the stock’s expected value 1 year from now?

Answer: After 1 year, D1 will have been paid, so the expected dividend stream will then be D 2, D3, D4, and so on. Thus, the expected value one year from now is $32.10:

P̂1 =

D2 (rs  gL )

D2 = D1 (1 + gL) = $2.12(1.06) = 2.2472

P̂1 = p.

D2 (rs  gL )

$2.2472 $2.2472 = = $32.10. (0.13  0.06) 0.07

What is the expected dividend yield, the capital gains yield, and the total return during the first year?

Answer: The expected dividend yield in any year n is Dividend Yield =

$2.12 P̂n  1 0.13  0.06

Expected Dividend Yield at Time 0 =

D1 P̂0

$2.12 = 7% $30.29

While the expected capital gains yield is Capital Gains Yield =

Expected Capital Gains Yield at Time 0 =

ˆ P ˆ ) (P n n1 P̂n  1

$32.10  $30.29 $1.81 = = 6% $30.29 $30.29

Alternatively,

Capital Gains Yield = rs – Dividend Yield = 13% − 7% = 6% The total yield is comprised of the dividend yield and the capital gains yield.

Dividend yield =

7.0%

Capital gains yield =

6.0%

Total return =

13.0%

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Now assume that the stock is currently selling at $30.29. What is its expected rate of return? Answer: The constant growth model can be rearranged to this form:

r̂s =

D1 P0

g.

Here, the current price of the stock is known, and we solve for the expected return. For Temp Force:

r̂s = $2.12/$30.29 + 0.060 = 0.070 + 0.060 = 13%. r.

Now assume that Temp Force’s dividend is expected to experience nonconstant growth of 30% from Year 0 to Year 1, 25% from Year 1 to Year 2, and 15% from Year 2 to Year 3. After Year 3, dividends will grow at a constant rate of 6%. What is the stock’s intrinsic value under these conditions? What are the expected dividend yield and capital gains yield during the first year? What are the expected dividend yield and capital gains yield during the fourth year (from Year 3 to Year 4)? Answer: Temp Force is no longer a constant growth stock, so the constant growth model is not applicable. Note, however, that the stock is expected to become a constant growth stock in 3 years. Thus, it has a nonconstant growth period followed by constant growth. The easiest way to value such nonconstant growth stocks is to set the situation up on a time line, as shown below:

1 g = 30%

2 g = 25%

$2.00

$2(1.3) $2.6

g = 15% D2 $2.60(1.25) $3.25

3→∞ g = 6% D3 $3.25(1.15) $3.735

→∞ →∞

After forecasting dividends, the next step is to determine the horizon value and then find the present value of the horizon value and the dividends prior to the horizon. The horizon value is:

P̂3 =

2.3009 2.5452 41.8149 46.6618

3.735(1.06) 3.9618 = = $56.5971 0.13  0.06 0.13  0.06

$2.6

$3.25

$3.7350 $56.5971 $60.3321

Enter $2 and multiply by (1.30) to get D1 = $2.60; multiply that result by 1.25 to get D2 = $3.25, multiply that result by 1.15 to get D3 = $3.7375 and multiply that result by 1.06 to get D 4 = $3.9618. Then recognize that after Year 3, Temp Force becomes a constant growth stock, and at that point

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P̂3 can be found using the constant growth model. P̂3 is the present value as of t = 3 of the dividends in Year 4 and beyond. With the cash flows for D1, D2, D3, and P̂3 shown on the time line, we discount each value back to Year 0, and the sum of these four PVs is the intrinsic value of the stock today, P̂0 = $46.661 ≈ $46.66. The dividend yield and the capital gains yield are:

Dividend yield =

$2.600 = 0.0557 ≈ 5.6%. $46.66

Capital gains yield = 13.00% – 5.6% = 7.4%. During the nonconstant growth period, the dividend yields and capital gains yields are not constant, and the capital gains yield does not equal g. However, after Year 3, the stock becomes a constant growth stock, with gL = capital gains yield = 6.0% and dividend yield = 13.0% − 6.0% = 7.0%. s.

What is the market multiple method of valuation? What are its strengths and weaknesses? Answer: Analysts often use the P/E multiple (the price per share divided by the earnings per share) or the P/CF multiple (price per share divided by cash flow per share, which is the earnings per share plus the dividends per share) to value stocks. For example, estimate the average P/E ratio of comparable firms. This is the P/E multiple. Multiply this average P/E ratio by the expected earnings of the company to estimate its stock price. The entity value (V) is the market value of equity (# shares of stock multiplied by the price per share) plus the value of debt. Pick a measure, such as EBITDA, sales, customers, eyeballs, etc. Calculate the average entity ratio for a sample of comparable firms. For example, V/EBITDA, V/customers. Then find the entity value of the firm in question. For example, multiply the firm’s sales by the V/sales multiple, or multiply the firm’s number of customers by the V/customers ratio. The result is the total value of the firm. Subtract the firm’s debt to get the total value of equity. Divide by the number of shares to get the price per share. There are problems with market multiple analysis. (1) It is often hard to find comparable firms. (2) The average ratio for the sample of comparable firms often has a wide range. For example, the average P/E ratio might be 20, but the range could be from 10 to 50. How do you know whether your firm should be compared to the low, average, or high performers?

What are the advantages of the free cash flow valuation model relative to the dividend growth model? Answer: You can apply FCF model in more situations, such as privately held companies, divisions of companies, and companies that pay zero (or very low) dividends. However, the FCF model requires forecasted financial statements to estimate FCF.

What is preferred stock? Suppose a share of preferred stock pays a dividend of $2.10 and investors require a return of 7%. What is the estimated value of the preferred stock? Answer: Dps $2.10 Vps    $30.00 rps 0.07

Solution and Answer Guide CHAPTER 8: FINANCIAL OPTIONS AND APPLICATIONS IN CORPORATE FINANCE

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TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 191 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 192 Easy Problems 1–2 ................................................................................................................................ 192 Intermediate Problems 3–4 ................................................................................................................... 192 Challenging Problems 5–8 .................................................................................................................... 193 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 195 Mini Case ................................................................................................................................................. 196

ANSWERS TO END-OF-CHAPTER QUESTIONS 8-1

Define each of the following terms: a. Option; call option; put option b. Exercise value; strike price c. Black-Scholes option pricing model Answer: a. An option is a contract that gives its holder the right to buy or sell an asset at some predetermined price within a specified period of time. A call option allows the holder to buy the asset, while a put option allows the holder to sell the asset. b.

A simple measure of an option’s value is its exercise value. The exercise value is equal to the current price of the stock (underlying the option) less the striking price of the option. The strike price is the price stated in the option contract at which the security can be bought (or sold). For example, if the underlying stock sells for $50 and the striking price is $20, the exercise value of the option would be $30.

The Black-Scholes option pricing model is widely used by option traders to value options. It is derived from the concept of a riskless hedge. By buying shares of a stock and simultaneously selling call options on that stock, the investor will create a risk-free investment position. This riskless return must equal the risk-free rate or an arbitrage opportunity would exist. People would take advantage of this opportunity until the equilibrium level estimated by the Black-Scholes model was reached.

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8-2

Why do options sell at prices higher than their exercise values? Answer: The market value of an option is typically higher than its exercise value due to the speculative nature of the investment. Options allow investors to gain a high degree of personal leverage when buying securities. The option allows the investor to limit their loss but amplify their return. The exact amount this protection is worth is the options time value, which is the difference between the option’s price and its exercise value.

8-3

Describe the effect on a call option’s price that results from an increase in each of the following factors: (1) stock price, (2) strike price, (3) time to expiration, (4) risk-free rate, and (5) standard deviation of stock return. Answer: (1) An increase in stock price causes an increase in the value of a call option. (2) An increase in strike price causes a decrease in the value of a call option. (3) An increase in the time to expiration causes an increase in the value of a call option. (4) An increase in the risk-free rate causes an increase in the value of a call option. (1) An increase in the standard deviation of stock return causes an increase in the

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–2 8-1

Options A call option on the stock of Bedrock Boulders has a market price of $7. The stock sells for $30 a share, and the option has a strike price of $25 a share. What is the exercise value of the call option? What is the option’s time value? Solution: Exercise value = Current stock price – Strike price = $30 − $25 = $5. Time value = Option price – Exercise value = $7 – $5 = $2.

8-2

Options The exercise price on one of Flanagan Company’s call options is $15, its exercise value is $22, and its time value is $5. What are the option’s market value and the price of the stock? Solution: Option’s strike price = $15; Exercise value = $22; Time value = $5; V = ? P 0 = ? Time Value = Market price of option – Exercise value $5 = V – $22 V = $27. Exercise value = P0 – Strike price $22 = P0 – $15 P0 = $37.

INTERMEDIATE PROBLEMS 3–4 8-3

Black-Scholes Model Assume that you have been given the following information on Purcell Corporation’s call options:

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Inputs

Intermediate Calculations

Current stock price = $15

d1 = 0.24495

Time to maturity of option = 6 months

d2 = 0.00000

Variance of stock return = 0.12

N(d1) = 0.59675

Strike price of option = $15

N(d2) = 0.50000

Risk-free rate = 6% According to the Black-Scholes option pricing model, what is the option’s value? Solution: P = $15; X = $15; t = 0.5; rRF = 0.06; 2 = 0.12; d1 = 0.24495; d2 = 0.0000; N(d1) = 0.59675; N(d2) = 0.500000; V = ? Using the Black-Scholes option pricing model, you calculate the option’s value as: V = P[N(d1)] – Xe rRF t [N(d2)] = $15(0.59675) – $15e(-0.06)(0.5)(0.50000) = 8.95125 – $15(0.970446)(0.50) = 8.95125 - 7.27835 = 1.67295  $1.67. 8-4

Put-Call Parity The current price of a stock is $33, and the annual risk-free rate is 6%. A call option with a strike price of $32 and with 1 year until expiration has a current value of $6.56. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option? Solution: Put = V – P + X exp(-rRF t) = $6.56 – $33 + $32 e–0.06(1) = $6.56 – $33 + $30.136 = $3.696  $3.70.

CHALLENGING PROBLEMS 5–8 8-5

Black-Scholes Model Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $30, (2) strike price is $35, (3) time to expiration is 4 months, (4) annualized risk-free rate is 5%, and (5) variance of stock return is 0.25. Answer: d1 

ln(P/ X)  [rRF  ( 2 / 2 )]t  t



ln($30/ $35)  [0.05  (0.25/ 2)](0 .333333)

  0.3319.

0.5 0.33333

d2 = d1 – σ (t)0.5 = –0.3319 – 0.5(0.33333)0.5 = –0.6206. N(d1) = 0.3700 (from Excel NORMSDIST function). N(d2) = 0.2674 (from Excel NORMSDIST function). V = P[N(d1)] – Xe rRF t [N(d2)] = $30(0.3700) – $35e(-0.05)(0.33333)(0.2674) = $11.1000 – $9.2043

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= $1.8957  $1.90. 8-6

Binomial Model The current price of a stock is $20. In 1 year, the price will be either $26 or $16. The annual risk-free rate is 5%. Find the price of a call option on the stock that has a strike price of $21 and that expires in 1 year. (Hint: Use daily compounding with 365 days in a year.)

Answer: The stock’s range of payoffs in 1 year is $26 – $16 = $10. At expiration, the option will be worth $26 – $21 = $5 if the stock price is $26, and zero if the stock price $16. The range of payoffs for the stock option is $5 – 0 = $5. Equalize the range to find the number of shares of stock: Option range/Stock range = $5/$10 = 0.5. With 0.5 shares, the stock’s payoff will be either $13 or $8. The portfolio’s payoff will be $13 – $5 = $8, or $8 – 0 = $8. The present value of $8 at the daily compounded risk-free rate is: PV = $8 / (1 + (0.05/365))365 = $7.610. The option price is the current value of the stock in the portfolio minus the PV of the payoff: V = 0.5($20) – $7.610 = $2.39. 8-7

Binomial Model The current price of a stock is $15. In 6 months, the price will be either $18 or $13. The annual risk-free rate is 6%. Find the price of a call option on the stock that has a strike price of $14 and that expires in 6 months. (Hint: Use daily compounding with 365 days in a year.) Answer: The stock’s range of payoffs in 6 months is $18 – $13 = $5. At expiration, the option will be worth $18 – $14 = $4 if the stock price is $18, and zero if the stock price is $13. The range of payoffs for the stock option is $4 – 0 = $5. Equalize the range to find the number of shares of stock: Option range/Stock range = $4/$5 = 0.8. With 0.8 shares, the stock’s payoff will be either 0.8($18) = $14.40 or 0.8($13) = $10.40. The portfolio’s payoff will be $14.4 – $4 = $10.40, or $10.40 – 0 = $10.40. The present value of $10.40 at the daily compounded risk-free rate is: PV = $10.40/1 + (0.06/365))365/2 = $10.093.

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The option price is the current value of the stock in the portfolio minus the PV of the payoff: V = 0.8($15) – $10.093 = $1.907  $1.91. 8-8

Two-Period Binomial Model The current price of a stock is $30. Over the next 6 months, the price will either increase by a factor (u) of 1.2 or decrease by a factor (d) of 0.8330. The same is true for the next 6month period. The annual risk-free rate is 6%. Find the price of a call option on the stock that has a strike price of $32 and that expires in 1 year. (Hint: One year is two 6-month periods. Use daily compounding. Carry at least four decimal places when calculating πu and πd.) Answer: t = 1.0, n = 2, S = $30, X = $32, r RF = 6%, u = 1.2000, d = 0.8333 The stock prices are: Time 0

6 months

1 year 43.20 = 36(1.20000)

36.00 = 30(1.2000) 30.00

30.00 = 36(0.8333) 25.00 = 30(0.8333) 20.83 = 25(0.8333)

 0 .06  1.0    e  2   0 .8333    er RF (t / n)  d      1.2000  0.8333   u  d     0.5218 πu    (t / n ) 1.0 0.0 6( ) er RF 2 e  1.0    0 .06    1.2000  e  2   r   u  e RF (t / n)      1.2000  0.8333   u  d     0.44 8 7  and πd =  1.0 r RF (t / n) 0 .06( ) e 2 e

The option prices are: Time 0

6 months

5.8442 = 11.20(0.5218) + 0(0.4487) 3.0495 = 5.8442(0.5218) + 0(0.4487) 0 = 0(0.5218) + 0(0.4487)

1 year 11.20 = max(43.20 – 32.00,0) 0 = max(30.00 – 32.00,0) 0 = max(20.83 – 32.00,0)

The call option price is $3.0495.

SOLUTION TO SPREADSHEET PROBLEM 8-9

Build a Model: Black-Scholes Model Start with the partial model in the file Ch08 P09 Build a Model.xlsx on the textbook’s website. You have been given the following information for a call option on the stock of Puckett Industries: P = $65.00, X = $70.00, t = 0.50, r RF = 5.00%, and σ = 0.50. a. Use the Black-Scholes option pricing model to determine the value of the call option.

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Suppose there is a put option on Puckett’s stock with exactly the same inputs as the call option. What is the value of the put? Solution: The detailed solution for the problem is available in the file Ch08 P09 Build a Model Solution.xlsx at the textbook’s website. b.

8-10 Build a Model: Two-Period Binomial Model Start with the partial model in the file Ch08 P10 Build a Model.xlsx on the textbook’s website. You have been given the following information for a call option on the stock of Kelley Enterprises: P = $65.00, X = $70.00, t = 0.50, r RF = 5.00%, and σ = 0.50. a. Use the binomial option pricing model with two periods to expiration to determine the value of the call option. Note that each period is 0.25 years. b. Suppose there is a put option on Kelley’s stock with exactly the same inputs as the call option. What is the value of the put? (Hint: All you need do is change the formula for the exercise value at expiration.) Solution: The detailed solution for the problem is available in the file Ch08 P10 Build a Model Solution.xlsx at the textbook’s website.

MINI CASE Assume that you have just been hired as a financial analyst by Triple Play Inc., a midsized California company that specializes in creating high-fashion clothing. Since no one at Triple Play is familiar with the basics of financial options, you have been asked to prepare a brief report that the firm’s executives could use to gain at least a cursory understanding of the topic. To begin, you gathered some outside materials the subject and used these materials to draft a list of pertinent questions that need to be answered. In fact, one possible approach to the paper is to use a questionand-answer format. Now that the questions have been drafted, you have to develop the answers. a.

What is a financial option? What is the single most important characteristic of an option? Answer: A financial option is a contract that gives its holder the right to buy (or sell) an asset at a predetermined price within a specified period of time. An option’s most important characteristic is that it does not obligate its owner to take any action; it merely gives the owner the right to buy or sell an asset.

Options have a unique set of terminology. Define the following terms: (1) Call option; (2) Put option; (3) Strike price or exercise price; (4) Expiration date; (5) Exercise value; (6) Option price; (7) Time value; (8) Writing an option; (9) Covered option; (10) Naked option; (11) In-the-money call; (12) Out-of-the-money call; and (13) LEAPS. Answer: 1. A call option is an option to buy a specified number of shares of a security within some future period. 2.

A put option is an option to sell a specified number of shares of a security within some future period.

The strike price is the price stated in the option contract at which the security can be bought (or sold). The strike prices is also called the exercise price.

The expiration date is the last date the option can be exercised.

The exercise value is the value of a call option if it were exercised today, and it is equal to the current stock price minus the strike price. (Note: The exercise value is zero if the stock price is less than the strike price.)

The option price is the market price of the option contract.

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The time value is the difference between the option price and the exercise value.

For every new option, there is an investor who ―writes‖ the option. A writer creates the contract, sells it to another investor, and must fulfill the option contract if it is exercised. For example, the writer of a call must be prepared to sell a share of stock to the investor who owns the call.

A covered option is a call option written against stock held in an investor's portfolio.

10. A naked option is an option sold without the stock to back it up. 11. An in-the-money call is a call option whose strike price is less than the current price of the underlying stock. 12. An out-of-the-money call is a call option whose strike price exceeds the current stock price. 13. LEAPS stands for long-term equity anticipation securities. They are similar to conventional options except they are long-term options with maturities of up to 2½ years. c.

Consider Triple Play’s call option with a $25 strike price. The following table contains historical values for this option at different stock prices: Stock Price $25 30 35 40 45 50

Create a table that shows stock price (P), strike price (X), exercise value, option price (C), and the time value (which is the option’s price less its exercise value).

Answer: Price of Stock (P) $25.00 30.00 35.00 40.00 45.00 50.00 c.

Call Option Price $ 3.00 7.50 12.00 16.50 21.00 25.50

Strike Price (X) $25.00 25.00 25.00 25.00 25.00 25.00

Exercise Value Option: MAX[P – X,0] $ 0.00 5.00 10.00 15.00 20.00 25.00

Market Price of Option (C) $ 3.00 7.50 12.00 16.50 21.00 25.50

Time Value (C – X) $3.00 2.50 2.00 1.50 1.00 0.50

What happens to the time value as the stock price rises? Why?

Answer: As the table shows, the option’s time value declines as the stock price increases. This is due to the declining degree of leverage provided by options as the underlying stock prices increase, and to the greater loss potential of options at higher option prices. d.

Consider a stock with a current price of P = $27. Suppose that over the next 6 months the stock price will either go up by a factor of 1.41 or down by a factor of 0.71. Consider a call option on the stock with a strike price of $25 that expires in 6 months. The risk-free rate is 6%.

1. Using the binomial model, what are the ending values of the stock price? What are the payoffs of the call option? Answer:

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The assumptions that underlie the OPM are as follows: Strike price: X =

$25.00

Current stock price: P =

$27.00

Up factor for stock price: u = Down factor for stock price: d = Up option payoff: Cu = MAX[0,P(u)-X] = Down option payoff: Cd =MAX[0,P(d)-X] =

1.41 0.71 $13.07 $0.00

Ending ―up‖ stock price = P(u) =

$38.07

Option payoff: Cu = MAX[0,P(u)-X] =

$13.07

Ending ―down‖ stock price = P(d) = Option payoff: Cd =MAX[0,P(d)-X] =

$19.17 $0.00

Current stock price P = $27

Suppose you write one call option and buy Ns shares of stock. How many shares must you buy to create a portfolio with a riskless payoff (i.e., a hedge portfolio)? What is the payoff of the portfolio? Answer: Ns = (Cu – Cd) / P(u – d) = 0.69153 Stock price = P (u) =

$38.07 Portfolio’s stock payoff: = P(u)(Ns) =

$26.33

Subtract option's payoff: Cu =

$13.07

Portfolio’s net payoff = P(u)Ns – Cu =

$13.26

Portfolio’s stock payoff: = P(d)(Ns) = Subtract option's payoff: Cd =

$13.26 $0.00

Portfolio's net payoff = P(d)Ns – Cd =

$13.26

P = $27

Stock price = P (d) =

$19.17

What is the present value of the hedge portfolio? What is the value of the call option?

Answer: PV of payoff =

Payoff (1 + rRF/365)365*(t) VC = =

$13.2567 1.03045

$12.865

Ns (P) – Present value of riskless payoff (0.69153)($27) − $12.86

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= d.

$5.81

What is a replicating portfolio? What is arbitrage?

Answer: If you borrow an amount equal to the present value of the hedge portfolio’s riskless payoff and purchase Ns shares of stock, the portfolio’s payoffs will replicate the call option’s payoffs. The option’s value must be the same as the portfolio’s cost; otherwise, you would have an opportunity for arbitrage, which is a situation in which you have none of your own money invested, you have no risk, yet you have a positive cash flow. Arbitrage opportunities can’t exist long in a well-functioning economy, so the option’s price will be driven towards the cost of the replicating portfolio.

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In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM).

What assumptions underlie the OPM?

Answer: The assumptions that underlie the OPM are as follows:



The stock underlying the call option provides no dividends during the life of the option.



No transactions costs are involved with the sale or purchase of either the stock or the option.



The short-term, risk-free interest rate is known and is constant during the life of the option.



Security buyers may borrow any fraction of the purchase price at the short-term, risk-free rate.



Short-term selling is permitted without penalty, and sellers receive immediately the full cash proceeds at today's price for securities sold short.



The call option can be exercised only on its expiration date.



Security trading takes place in continuous time, and stock prices move randomly in continuous time.

Write out the three equations that constitute the model.

Answer: The OPM consists of the following three equations: r t

V = P[N(d1) – Xe RF [N(d2)]. d1 =

ln(P/ X)  [rRF  ( 2 / 2)]t  t

d2 = d1 –  t . Here, V = Current value of a call option with time t until expiration. P = Current price of the underlying stock. N(di) = Probability that a deviation less than di will occur in a standard normal distribution. Thus, N(d 1) and N(d2) represent areas under a standard normal distribution function. X = Strike price of the option. e  2.7183. rRF = Risk-free interest rate. t = Time until the option expires (the option period). ln(P/X) = Natural logarithm of P/X.  = Standard deviation of the rate of return on the stock. e.

According to the OPM, what is the value of a call option with the following characteristics? Stock price = $27.00 Strike price = $25.00 Time to expiration = 6 months = 0.5 years Risk-free rate = 6.0% Stock return standard deviation = 0.49

Answer:

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The input variables are: P = $27.00; X = $25.00; rRF = 6.0%; t = 6 months = 0.5 years; and  = 0.49. Now, we proceed to use the OPM: VC = $27[N(d1)] – $25e-(0.06)(0.5)[N(d2)]. d1 =

ln($27/ $25)  [(0.06  0.492 / 2)](0.5) (0.49) 0.5

= 0.4819. d2 = 0.4819 – (0.49) = 0.1355.

0.5

N(d1) = 0.6851 (From Excel NORMSDIST function). N(d2) = 0.5539. Therefore, VC = $27(0.6851) – $25e-(0.06(0.5)(0.5539) = $5.06. f.

What impact does each of the following parameters have on the value of a call option? 1. 2. 3. 4. 5.

Current stock price Strike price Option’s term to maturity Risk-free rate Variability of the stock price

Answer: 1. The value of a call option increases (decreases) as the current stock price increases (decreases).

As the strike price of the option increases (decreases), the value of the option decreases (increases).

As the expiration date of the option is lengthened, the value of the option increases. This is because the value of the option depends on the chance of a stock price increase, and the longer the option period, the higher the stock price can climb.

As the risk-free rate increases, the value of the option tends to increase as well. Since increases in the risk-free rate tend to decrease the present value of the option's strike price, they also tend to increase the current value of the option.

The greater the variance in the underlying stock price, the greater the possibility that the stock's price will exceed the strike price of the option; thus, the more valuable the option will be.

What is put-call parity? Answer: Put-call parity specifies the relationship between puts, calls, and the underlying stock price that must hold to prevent arbitrage: Put + Stock = Call + PV of strike price

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CHAPTER 9: T HE COST OF CAPITAL

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 202 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 204 Easy Problems 1-8 ................................................................................................................................ 204 Intermediate Problems 9-14 .................................................................................................................. 206 Challenging Problems 15−17 ................................................................................................................ 209 SOLUTIONS TO SPREADSHEET PROBLEM ................................................................................. 213 MINI CASE ............................................................................................................................................. 214

ANSWERS TO END-OF-CHAPTER QUESTIONS 9-1 Define each of the following terms: a. Weighted average cost of capital, WACC; after-tax cost of debt, rd(1 − T); after-tax cost of shortterm debt, rstd(1 − T) b. Cost of preferred stock, rps; cost of common equity (or cost of common stock), r s c. Target capital structure d. Flotation cost, F; cost of new external common equity, re Answer: a. The weighted average cost of capital, WACC, is the weighted average of the after-tax component costs of capital, which are debt, preferred stock, and common equity. Each weighting factor is the proportion of that type of capital in the optimal, or target, capital structure. The after-tax cost of debt, rd(1 – T), is the relevant cost to the firm of new debt financing. Since interest is deductible from taxable income, the after-tax cost of debt to the firm is less than the before-tax cost. Thus, rd(1 – T) is the appropriate component cost of debt (in the weighted average cost of capital). If a company has short-term debt with a cost of rstd, then its after-tax cost is rstd(1 – T) is the appropriate component cost of debt (in the weighted average cost of capital). b.

The cost of preferred stock, rps, is the cost to the firm of issuing new preferred stock. For perpetual preferred, it is the preferred dividend, Dps, divided by the net issuing price, Pn. Note that no tax adjustments are made when calculating the component cost of preferred stock because, unlike interest payments on debt, dividend payments on preferred stock are not tax deductible. The cost of new common equity, re, is the cost to the firm of equity obtained by selling new common stock. It is, essentially, the cost of retained earnings adjusted for flotation costs. Flotation costs are the costs that the firm incurs when it issues new securities. The amount actually available to the firm for capital investment from the sale of new securities is the sales price of the securities less flotation costs. Note that flotation costs consist of (1) direct expenses such as printing costs and brokerage commissions, (2) any price reduction due to increasing the supply of stock, and (3) any drop in price due to informational asymmetries.

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The target capital structure is the relative amount of debt, preferred stock, and common equity that the firm desires. The WACC should be based on these target weights.

There are considerable costs when a company issues a new security, including fees to an investment banker and legal fees. These costs are called flotation costs. The cost of new common equity, re, is higher than that of common equity raised internally by reinvesting earnings. Projects financed with external equity must earn a higher rate of return, since the project must cover the flotation costs.

9-2 How can the WACC be both an average cost and a marginal cost? Answer: The WACC is an average cost because it is a weighted average of the firm’s component costs of capital. However, each component cost is a marginal cost; that is, the cost of new capital. Thus, the WACC is the weighted average marginal cost of capital. 9-3 How would each of the factors in the following table affect a firm’s cost of debt, rd(1 − T), its cost of equity, rs, and its weighted average cost of capital, WACC? Indicate by a plus (+), a minus (−), or a zero (0) if the factor would increase, reduce, or have an indeterminate effect on the item in question. Assume that all other factors are held constant. Be prepared to justify your answer, but recognize that several of the parts probably have no single correct answer; these questions are designed to stimulate thought and discussion. Effect on: rd(1 − T)

WACC

a. The corporate tax rate is lowered.

_________

b. The Federal Reserve tightens credit.

_________

c. The firm uses more debt.

_________

d. The firm doubles the amount of capital it raises during the year.

_________

e. The firm expands into a risky new area.

_________

___ ______

f. Investors become more risk averse.

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Answer: Effect on: rd(1 − T)

WACC

a. The corporate tax rate is lowered.

b. The Federal Reserve tightens credit.

c. The firm uses more debt.

d. The firm doubles the amount of capital it 0 or + raises during the year.

0 or +

e. The firm expands into a risky new area.

f. Investors become more risk averse.

9-4 Distinguish between beta (i.e., market) risk, within-firm (i.e., corporate) risk, and stand-alone risk for a potential project. Of the three measures, which is theoretically the most relevant, and why? Answer: Stand-alone risk views a project’s risk in isolation, hence without regard to portfolio effects; within-firm risk, also called corporate risk, views project risk within the context of the firm’s portfolio of assets; and market risk (beta) recognizes that the firm’s stockholders hold diversified portfolios of stocks. In theory, market risk should be most relevant because of its direct effect on stock prices. 9-5 Suppose a firm estimates its overall cost of capital for the coming year to be 10%. What might be reasonable costs of capital for average-risk, high-risk, and low-risk projects? Answer: If a company’s composite WACC estimate were 10%, its managers might use 10% to evaluate averagerisk projects, 12% for high-risk projects, and 8% for low-risk projects. Unfortunately, given the data, there is no completely satisfactory way to specify exactly how much higher or lower we should go in setting risk-adjusted costs of capital.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1-8 9-1

After-Tax Cost of Debt. Calculate the after-tax cost of debt under each of the following conditions: a. rd of 13%, tax rate of 0% b. rd of 13%, tax rate of 20% c. rd of 13%, tax rate of 35% Solution: a. rd(1 − T) = 13%(1 − 0) = 13.00%..

9-2

rd(1 − T) = 13%(0.80) = 10.40%.

rd(1 − T) = 13%(0.65) = 8.45%.

After-Tax Cost of Debt. LL Incorporated’s currently outstanding 11% coupon bonds have a yield to maturity of 8.4%. LL believes it could issue new bonds at par that would provide a similar yield to maturity. If its marginal tax rate is 25%, what is LL’s after-tax cost of debt? Solution:

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rd(1 − T) = 8.4%(0.75) = 6.3%. 9-3

Cost of Preferred Stock. Duggins Veterinary Supplies can issue perpetual preferred stock at a price of $50 a share with an annual dividend of $4.50 a share. Ignoring flotation costs, what is the company’s cost of preferred stock, rps? Solution: Vps = $50; Dps = $4.50; F = 0%; rps = ? D ps

rps =

Vps (1  F)

$4.50 $50 (1  0.0)

= 9%. 9-4

Cost of Preferred Stock with Flotation Costs. Burnwood Tech plans to issue some $60 par preferred stock with a 6% dividend. A similar stock is selling on the market for $70. Burnwood must pay flotation costs of 5% of the issue price. What is the cost of the preferred stock? Solution: rps =

9-5

$3.60 $60 (0.06) = = 5.41%. $70.00 (1  0.05) $66.50

Cost of Equity: Dividend Growth. Summerdahl Resort’s common stock is currently trading at $36 a share. The stock is expected to pay a dividend of $3.00 a share at the end of the year (D 1 = $3.00), and the dividend is expected to grow at a constant rate of 5% a year. What is its cost of common equity? Solution: P0 = $36; D1 = $3.00; g = 5%; rs = ? rs =

9-6

D1 + g = ($3.00/$36.00) + 0.05 = 13.33%. P0

Cost of Equity: CAPM. Booher Book Stores has a beta of 0.8. The yield on a 3-month T-bill is 4%, and the yield on a 10-year T-bond is 6%. The market risk premium is 5.5%, and the return on an average stock in the market last year was 15%. What is the estimated cost of common equity using the CAPM? Solution: rs = rRF + bi(RPM) = 0.06 + 0.8(0.055) = 10.4%.

9-7

WACC. Shi Import-Export’s balance sheet shows $300 million in debt, $50 million in preferred stock, and $250 million in total common equity. Shi’s tax rate is 25%, rd = 6%, rps = 5.8%, and rs = 12%. If Shi has a target capital structure of 30% debt, 5% preferred stock, and 65% common stock, what is its WACC? Solution: 30% Debt; 5% Preferred Stock; 65% Equity; rd = 6%; T = 25%; rps = 5.8%; rs = 12%. WACC = (wd)(rd)(1 − T) + (wps)(rps) + (ws)(rs)

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WACC = 0.30(0.06)(1 − 0.25) + 0.05(0.058) + 0.65(0.12) = 9.44%. 9-8

WACC. David Ortiz Motors has a target capital structure of 40% debt and 60% equity. The yield to maturity on the company’s outstanding bonds is 9%, and the company’s tax rate is 25%. Ortiz’s CFO has calculated the company’s WACC as 9.9%. What is the company’s cost of equity capital? Solution: 40% Debt; 60% Equity; rd = 9%; T = 25%; WACC = 9.96%; rs = ? WACC = (wd)(rd)(1 − T) + (ws)(rs) 9.9% = (0.4)(9%)(1 − 0.25) + (0.6)rs 9.9% = 2.70% + 0.6rs 7.2% = 0.6rs rs = 12%.

INTERMEDIATE PROBLEMS 9-14 9-9

Bond Yield and After-Tax Cost of Debt. A company’s 6% coupon rate, semiannual payment, $1,000 par value bond that matures in 30 years sells at a price of $515.16. The company’s federal-plus-state tax rate is 25%. What is the firm’s after-tax component cost of debt for purposes of calculating the WACC? (Hint: Base your answer on the nominal annual rate.) Solution: Enter these values: N = 60, PV = –515.16, PMT = 30, and FV = 1000, to get I = 6% = periodic rate. The nominal rate is 6%(2) = 12%, and the after-tax component cost of debt is 12%(0.75) = 9%.

9-10 Cost of Equity. The earnings, dividends, and stock price of Shelby Inc. are expected to grow at 7% per year in the future. Shelby’s common stock sells for $23 per share, its last dividend was $2.00, and the company will pay a dividend of $2.14 at the end of the current year. a. Using the discounted cash flow approach, what is its cost of equity? b. If the firm’s beta is 1.6, the risk-free rate is 9%, and the expected return on the market is 13%, then what would be the firm’s cost of equity based on the CAPM approach? c. If the firm’s bonds earn a return of 12%, then what would be your estimate of r s using the own-bondyield-plus-judgmental-risk-premium approach? (Hint: Use a 4% risk premium.) d. On the basis of the results of parts a–c, what would be your estimate of Shelby’s cost of equity? Solution:

$2.14 D1 +g= + 7% = 9.3% + 7% = 16.3%. P0 $23

rs =

rs = rRF + (rM − rRF)b = 9% + (13% − 9%)1.6 = 9% + (4%)1.6 = 9% + 6.4% = 15.4%.

rs = Bond rate + Risk premium = 12% + 4% = 16%.

The bond-yield-plus-judgmental-risk-premium approach and the CAPM method both resulted in lower cost of equity values than the dividend growth approach. The firm's cost of equity should be estimated to be about 15.9%, which is the average of the three methods.

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9-11 Cost of Equity. Radon Homes’ current EPS is $6.50. It was $4.42 five years ago. The company pays out 40% of its earnings as dividends, and the stock sells for $36. a. Calculate the historical growth rate in earnings. (Hint: This is a 5-year growth period.) b. Calculate the next expected dividend per share, D1. (Hint: D0 = 0.4($6.50) = $2.60.) Assume that the past growth rate will continue. c. What is Radon’s cost of equity, rs? Solution: a. $6.50 = $4.42(1 + g)5 (1 + g)5 = 6.50/$4.42 = 1.471 (1 + g) = 1.471(1/5) = 1.080 g = 8%. Alternatively, with a financial calculator, input N = 5, PV = −4.42, PMT = 0, FV = 6.50, and then solve for I/YR = 8.02%  8%. b.

D1 = D0(1 + g) = $2.60(1.08) = $2.81.

rs = D1/P0 + g = $2.81/$36.00 + 8% = 15.81%.

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9-12 Calculation of gL and EPS. Spencer Supply’s stock is currently selling for $60 a share. The firm is expected to earn $5.40 per share this year and to pay a year-end dividend of $3.60. a. If investors require a 9% return, what rate of growth must be expected for Spencer? b. If Spencer reinvests earnings in projects with average returns equal to the stock’s expected rate of return, then what will be next year’s EPS? (Hint: gL = ROE × Retention ratio.) Solution: a.

rs =

D1 +g P0

0.09 =

$3.60 +g $60.00

0.09 = 0.06 + g g = 3%. b.

Current EPS

$5.400

Less: Dividends per share

3.600

Retained earnings per share

$1.800

Rate of return

 0.090

Increase in EPS

$0.162

Current EPS

5.400

Next year's EPS

$5.562

Alternatively, EPS1 = EPS0(1 + g) = $5.40(1.03) = $5.562. 9-13 The Cost of Equity and Flotation Costs. Messman Manufacturing will issue common stock to the public for $30. The expected dividend and the growth in dividends are $3.00 per share and 5%, respectively. If the flotation cost is 10% of the issue’s gross proceeds, what is the cost of external equity, r e? Solution: P0 = $30; D1 = $3.00; g = 5%; F = 10%; rs = ? rs = [D1/(1 − F) P0] + g = [$3/(1 − 0.10)($30)] + 0.05 = 16.1%. 9-14 The Cost of Debt and Flotation Costs. Suppose a company will issue new 20-year debt with a par value of $1,000 and a coupon rate of 9%, paid annually. The issue price will be $1,000. The tax rate is 25%. If the flotation cost is 2% of the issue proceeds, then what is the after-tax cost of debt? What if the flotation costs were 10% of the bond issue?

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Solution: If flotation costs are 2% of the issue price, then they total $1,000(2%) = $20. This is less than de minimis of $1,000(0.25%)(20) = $50 so the costs are amortized linearly. The annual amortized cost is $20/20 = $1 per year. The tax benefit from this amortized cost is $1(0.25) = $0.25 per year. This is the amount by which you reduce the after-tax coupon payment to calculate the after-tax cost of debt. Enter these values: N = 20, PV = $1,000(1 – 2%) = $980, PMT = −90(1 – 0.25) + $0.25 = −$67.25, and FV = −1000 to get I/YR = 6.91%. This is the after-tax component cost of debt if flotation costs are 2%. If flotation costs are 10% of the proceeds, then they total $1,000 × $100 which is greater than de minimis of $1,000(0.25%)(20) = $50 so the constant yield method is used. Enter these values: N = 20, PV = 1,000(1 − 0.10) = 900, PMT = −90, and FV = −1000, to get I/YR = 10.19%, which is the yield to maturity if you consider the after-flotation cost proceeds as the issue price. Multiply this by (1 – T) to get the after-tax component cost of debt = 10.19%(0.75) = 7.64%.

CHALLENGING PROBLEMS 15−17 9-15 WACC Estimation. On January 1, the total market value of the Tysseland Company was $60 million. During the year, the company plans to raise and invest $30 million in new projects. The firm’s present market value capital structure, shown here, is considered to be optimal. There is no short-term debt. Debt

$30,000,000

Common equity

30,000,000

Total capital

$60,000,000

New bonds will have an 8% coupon rate, and they will be sold at par. Common stock is currently selling at $30 a share. The stockholders’ required rate of return is estimated to be 12%, consisting of a dividend yield of 4% and an expected constant growth rate of 8%. (The next expected dividend is $1.20, so the dividend yield is $1.20/$30 = 4%.) The marginal tax rate is 25%. a. In order to maintain the present capital structure, how much of the new investment must be financed by common equity? b. Assuming there is sufficient cash flow for Tysseland to maintain its target capital structure without issuing additional shares of equity, what is its WACC? c. Suppose now that there is not enough internal cash flow and the firm must issue new shares of stock. Qualitatively speaking, what will happen to the WACC? No numbers are required to answer this question. Solution: a. Common equity needed: 0.5($30,000,000) = $15,000,000.

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Cost using rs: After-Tax Weight



Cost

Product

Debt:

0.50



6.0%*

3.0%

Common equity:

0.50



12.0

6.0 9.0%

WACC = 9.0% *8%(1 − T) = 8%(0.75) = 6.0%. c.

rs and the WACC will increase due to the flotation costs of new equity.

9-16 Market Value Capital Structure. Suppose the Schoof Company has this book value balance sheet: Current assets

$30,000,000

Current liabilities

$20,000,000

Notes payable

10,000,000

Long-term debt

30,000,000

Common stock (1 million shares)

1,000,000

__________

Retained earnings

39,000,000

$100,000,000

Total liabilities and equity

Fixed assets

Total assets

70,000,000

$100,000,000

The notes payable are to banks, and the interest rate on this debt is 10%, the same as the rate on new bank loans. These bank loans are not used for seasonal financing but instead are part of the company’s permanent capital structure. The long-term debt consists of 30,000 bonds, each with a par value of $1,000, an annual coupon interest rate of 6%, and a 20-year maturity. The going rate of interest on new long-term debt, rd, is 10%, and this is the present yield to maturity on the bonds. The common stock sells at a price of $60 per share. Calculate the firm’s market value capital structure. Solution: The book and market value of the notes payable are $10,000,000. The bonds have a value of V

= $60([1/0.10] − [1/(0.1*(1 + 0.10)20)]) + $1,000((1 + 0.10) −20) = $60(8.5136) + $1,000(0.1486) = $510.82 + $148.60 = $659.42.

Alternatively, using a financial calculator, input: N = 20, I/YR = 10, PMT = 60, and FV = 1000 to arrive at a PV = $659.46. The total market value of the long-term debt is 30,000($659.46) = $19,783,800. There are 1 million shares of stock outstanding, and the stock sells for $60 per share. Therefore, the market value of the equity is $60,000,000. Therefore, the market value capital structure is: Short-term debt

$10,000,000

11.14%

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Long-term debt

19,783,800

22.03

Common equity

60,000,000

66.83

$89,783,800

100.00%

9-17 WACC Estimation. The following table gives the current balance sheet for Travelers Inn Inc. (TII), a company that was formed by merging a number of regional motel chains. Travelers Inn (Millions of Dollars) Cash

$ 10

Accounts payable

$ 10

Accounts receivable

Accruals

Inventories

Short-term debt

Current assets

$ 50

Current liabilities

$ 25

Net fixed assets

Long-term debt

Preferred stock (50,000 shares)

Common equity Common stock (3,800,000 shares) Retained earnings

Total assets

$ 10 30

____

Total common equity

$ 40

$100

Total liabilities and equity

$100

The following facts also apply to TII. (1) The long-term debt consists of 29,412 bonds, each having a 20-year maturity, semiannual payments, a coupon rate of 7.6%, and a face value of $1,000. Currently, these bonds provide investors with a yield to maturity of 11.8%. If new bonds were sold, they would have an 11.8% yield to maturity. (2) TII’s perpetual preferred stock has a $100 par value, pays a quarterly dividend per share of $2, and has a yield to investors of 10%. New perpetual preferred stock would have to provide the same yield to investors, and the company would incur a 3.85% flotation cost to sell it. (3) The company has 3.8 million shares of common stock outstanding, a price per share = P0 = $20, dividend per share = D0 = $1, and earnings per share = EPS0 = $5. The return on equity (ROE) is expected to be 10%. (4) The stock has a beta of 1.6%. The T-bond rate is 6%, and RPM is estimated to be 5%. (5) TII’s financial vice president recently polled some pension fund investment managers who hold TII’s securities regarding what minimum rate of return on TII’s common would make them willing to buy the common rather than TII bonds, given that the bonds yielded 11.8%. The responses suggested a risk premium over TII bonds of 3 percentage points. (6) TII is in the 25% federal-plus-state tax bracket. Assume that you were recently hired by TII as a financial analyst and that your boss, the treasurer, has asked you to estimate the company’s WACC under the assumption that no new equity will be issued. Your cost of capital should be appropriate for use in evaluating projects that are in the same risk class as the assets TII now operates. Based on your analysis, answer the following questions. a.

What are the current market value weights for debt, preferred stock, and common stock? (Hint: Do your work in dollars, not millions of dollars. When you calculate the market values of debt and preferred stock, be sure to round the market price per bond and the market price per share of preferred to the nearest penny.) What is the after-tax cost of debt?

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c. d. e. f. g.

What is the cost of preferred stock? What is the required return on common stock using CAPM? Use the retention growth equation to estimate the expected growth rate. Then use the expected growth rate and the dividend growth model to estimate the required return on common stock. What is the required return on common stock using the own-bond-yield-plus-judgmental-riskpremium approach? Use the required return on stock from the CAPM model, and calculate the WACC.

Solution: Several steps are involved in the solution of this problem. Our solution follows: a.

In this case, A/P and accruals should be disregarded because they are not sources of financing from investors—they are not capital components. Debt: The annual yield to maturity is 11.8%, so the semiannual YTM is 11.8%/2 = 5.9%. The semiannual coupon payment is 7.6%($1,000)/2 = $38. Each bond has a market value found as follows: 40

V0 =

 (1.059)  (1.059) $38

t 1

$1, 000

Financial calculator inputs are N = 40, I/YR = 5.9, PMT = −39, PV = ?, FV = −1000. Solve for PV = $680.0037. Round to $680. There are 29,412 bonds, so the total market value of the bonds is $680(29,412) = $20,000,160. Preferred Stock: The preferred stock has a value of: Pps =

$2(4) = $80. 0.10

There are 50,000 shares of preferred outstanding, so the total market value of the preferred is Total market value of preferred = 50,000($80) = $4,000,000. Common Stock: There are 3,800,000 shares of common stock, so the market value of the common stock is: Total market value of common stock = 3,800,000($20) = $76,000,000. Therefore, here is the firm's market value capital structure, which we assume to be optimal: Long-term debt:

$20,000,160

20%

Preferred stock:

4,000,000

Common equity:

80,000,000

$100,000,000

100%

We would round these weights to 20% debt, 4% preferred, and 76% common equity.

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What is the after-tax cost of debt? rd(1 − T) = 11.8%(1 − 0.25) = 8.85%.

What is the cost of preferred stock? Annual dividend on new preferred = 10%($100) = $10. Therefore, rps = $10/[$100(1 − 0.0385)] = $10.4%.

What is the required return on common stock using CAPM? rRF = T-bond rate = 6% RPM = 5% beta = 1.6 rs = 6% + 1.6(5.0) = 14.00%.

Use the retention growth equation to estimate the expected growth rate. Then use the expected growth rate and the dividend growth model to estimate the required return on common stock. Payout ratio = DPS/EPS = $1/$5 =20%. g = ROE(1 – Payout ratio) = 10%(1 – 20%) = 8%. rs =

$1(1  0.08) D0 (1  g)  0.08 = 0.134 = 13.4% g = P0 $20

What is the required return on common stock using the own-bond-yield-plus-judgmental-riskpremium approach? rs = rd + Judgmental risk premium = 11.8% + 3% = 14.8%.

Use the required return on stock from the CAPM model and calculate the WACC. WACC = rd(1 − T)wd + rpswps + rsws = 8.85%(0.20) + 10.4%(0.04) + 14%(0.76) = 12.826%.

SOLUTIONS TO SPREADSHEET PROBLEM 9-18 Build a Model: WACC. Start with the partial model in the file Ch09 P18 Build a Model.xlsx on the textbook’s website. The stock of Gao Computing sells for $50, and last year’s dividend was $3.13. Security analysts are projecting that the common dividend will grow at a rate of 7% a year. A flotation cost of 10% would be required to issue new common stock. Gao’s preferred stock sells for $32.61, pays a dividend of $3.30 per share, and new preferred stock could be sold with a flotation cost of 8%. The firm has outstanding bonds with 20 years to maturity, a 12% annual coupon rate, semiannual payments, and $1,000 par value. The bonds are trading at $1,171.59. The tax rate is 25%. The market risk premium is 6%, the risk-free rate is 6.5%, and Gao’s beta is 1.2. In its cost-of-capital calculations, Gao uses a target capital structure with 45% debt, 5% preferred stock, and 50% common equity. a. Calculate the cost of each capital component—in other words, the after-tax cost of debt, the cost of preferred stock (including flotation costs), and the cost of equity (ignoring flotation costs). Use both the CAPM method and the dividend growth approach to find the cost of equity. b. Calculate the cost of new stock using the dividend growth approach.

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Assuming that GAO will not issue new equity and will continue to use the same target capital structure, what is the company’s WACC?

Solution: The detailed solution for the problem is available in the file Ch09 P18 Build a Model Solution.xlsx at the textbook’s website.

MINI CASE During the last few years, Jana Industries has been too constrained by the high cost of capital to make many capital investments. Recently, though, capital costs have been declining, and the company has decided to look seriously at a major expansion program proposed by the marketing department. Assume that you are an assistant to Leigh Jones, the financial vice president. Your first task is to estimate Jana’s cost of capital. Jones has provided you with the following data, which she believes may be relevant to your task:    

The firm's tax rate is 25%. The current price of Jana’s 12% coupon, semiannual payment, and noncallable bonds with 15 years remaining to maturity is $1,153.72. There are 70,000 bonds. Jana does not use short-term interestbearing debt on a permanent basis. New bonds would be privately placed with no flotation cost. The current price of the firm’s 10%, $100 par value, quarterly dividend, perpetual preferred stock is $116.95. There are 200,000 outstanding shares. Jana would incur flotation costs equal to 5% of the proceeds on a new issue. Jana’s common stock is currently selling at $50 per share. There are 3 million outstanding common shares. Its last dividend (D0) was $3.12, and dividends are expected to grow at a constant rate of 5.8% in the foreseeable future. Jana’s beta is 1.2, the yield on T-bonds is 5.6%, and the market risk premium is estimated to be 6%. For the own-bond-yield-plus-judgmental-risk-premium approach, the firm uses a 3.2% judgmental risk premium.

To help you structure the task, Leigh Jones has asked you to answer the following questions: a.

What sources of capital should be included when you estimate Jana’s weighted average cost of capital (WACC)?

Answer: The WACC is used primarily for making long-term capital investment decisions, i.e., for capital budgeting. Thus, the WACC should include the types of capital used to pay for long-term assets, and this is typically long-term debt, preferred stock (if used), and common stock. Short-term sources of capital consist of (1) spontaneous, noninterest-bearing liabilities such as accounts payable and accruals and (2) short-term interest-bearing debt, such as notes payable. If the firm uses short-term interest-bearing debt to acquire fixed assets rather than just to finance working capital needs, then the WACC should include a short-term debt component. Noninterest-bearing debt is generally not included in the cost of capital estimate because these funds are netted out when determining investment needs, that is, net rather than gross working capital is included in capital expenditures. a.

Should the component costs be figured on a before-tax or an after-tax basis?

Answer: Stockholders are concerned primarily with those corporate cash flows that are available for their use, namely, those cash flows available to pay dividends or for reinvestment. Since dividends are paid from and reinvestment is made with after-tax dollars, all cash flow and rate of return calculations should be done on an after-tax basis. a.

Should the costs be historical (embedded) costs or new (marginal) costs?

Answer: In financial management, the cost of capital is used primarily to make decisions which involve raising new capital. Thus, the relevant component costs are today's marginal costs rather than historical costs.

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What is the market interest rate on Jana’s debt, and what is the component cost of this debt for WACC purposes? Answer: Jana’s 12% bond with 15 years to maturity is currently selling for $1,153.72. Enter N = 30, PV = –1153.72, PMT = 60, and FV = 1000, and then press the I/YR button to find r d/2 = 5.0%. Since this is a semiannual rate, multiply by 2 to find the annual rate, r d = 10%, the pre-tax cost of debt. Since interest is tax deductible, Uncle Sam, in effect, pays part of the cost, and Jana’s relevant component cost of debt is the after-tax cost: rd(1 – T) = 10.0%(1 – 0.25) = 10.0%(0.75) = 7.5%.

What is the firm's cost of preferred stock?

Answer: Since the preferred issue is perpetual, its cost is estimated as follows: rps =

D ps Pps (1  F)

$10 0.1 ($100) = = 0.090 = 9.0%. $116.95(1  0.05) $111.10

Note (1) that flotation costs for preferred are significant, so they are included here; (2) that since preferred dividends are not deductible to the issuer, there is no need for a tax adjustment; and (3) that we could have estimated the effective annual cost of the preferred, but as in the case of debt, the nominal cost is generally used. c.

Jana’s preferred stock is riskier to investors than its debt, yet the preferred stock's yield to investors is lower than the yield to maturity on the debt. Does this suggest that you have made a mistake? (Hint: Think about taxes.)

Answer: Corporate investors own most preferred stock, because 50% of preferred dividends received by corporations are nontaxable. Therefore, preferred often has a lower before-tax yield than the before-tax yield on debt issued by the same company. Note, though, that the after-tax yield to a corporate investor, and the after-tax cost to the issuer, are higher on preferred stock than on debt. d.

What are the two primary ways companies raise common equity?

Answer: A firm can raise common equity in two ways: (1) by reinvesting (retaining) earnings and (2) by issuing new common stock. d.

Why is there a cost associated with reinvested earnings?

Answer: Management may either pay out earnings in the form of dividends or else retain earnings for reinvestment in the business. If part of the earnings is retained, an opportunity cost is incurred: Stockholders could have received those earnings as dividends and then invested that money in stocks, bonds, real estate, and so on. d.

Jana doesn’t plan to issue new shares of common stock. Using the CAPM approach, what is Jana’s estimated cost of equity?

Answer: rs = 0.056 + (0.06)1.2 = 12.8%. e.

What is the estimated cost of equity using the dividend growth approach?

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Answer: 

rs =

$3.12 (1.058) D (1  g) D1  0.058 = 12.4%. = 0 g = $50 P0 P0

Suppose the firm has historically earned 15% on equity (ROE) and has paid out 62% of earnings, and suppose investors expect similar values to obtain in the future. How could you use this information to estimate the future dividend growth rate, and what growth rate would you get? Is this consistent with the 5.8% growth rate given earlier?

Answer: Another method for estimating the growth rate is to use the retention growth model: g = (1 – Payout ratio)ROE In this case g = (1 − 0.62)0.15 = 5.7%. This is consistent with the 5.8% rate given earlier. e.

Could the dividend growth approach be applied if the growth rate was not constant? How?

Answer: Yes, you could use the dividend growth approach using nonconstant growth. You would find the PV of the dividends during the nonconstant growth period and add this value to the PV of the series of inflows when growth is assumed to become constant. f.

What is the cost of equity based on the own-yield-plus-judgmental-risk-premium method? Answer: rs = Company’s own bond yield + judgmental risk premium. The YTM of the company’s bonds is 10%. The assumed judgmental risk premium is 3.2%, thus rs = 0.10 + 0.032 = 13.2%.

What is your final estimate for the cost of equity, rs? Answer: The final estimate for the cost of equity would simply be the average of the values found using the above three methods.

CAPM

12.8%

Dividend growth

12.4

Bond yield + RP

13.2

Average

12.8%

Jana’s target capital structure is 30% long-term debt, 10% preferred stock, and 60% common equity. How does this compare with the current market value capital structure? Answer: Market value of debt = (Number of bonds)(Price per bond) = 70,000($1,153.72) = $80,760,400 ≈ $80.76 million. Market value of preferred stock = (Number of shares)(Price per share) = 200,000($116.95) = $23,390,000 = $23.39 million. Market value of common stock = (Number of shares)(Price per share)

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= (3 million)($50.00) = $150 million. Total market value = $80.76 + $23.39 + $150 = $254.15 million. Market weights: Debt = $80.76/$254.15 = 31.78% Preferred stock = $23.39/$254.15 = 9.2% Common stock = $150/$254.15 = 59.02% The current market value weights are very close to the target weights. i.

Use Jana’s target weights to calculate the weighted average cost of capital (WACC). Answer: WACC = wdrd(1 – T) + wpsrps + ws(rs) = 0.3(0.10)(1 – 0.25) + 0.1(0.09) + 0.6(0.128) = 0.1083 = 10.83%.

What factors influence a company’s WACC? Answer: There are factors that the firm cannot control and those that they can control that influence WACC. Factors the Firm Cannot Control: Stock and Bond Markets The Market Risk Premium Market Environment Tax Rates Factors the Firm Can Control: Capital Structure Policy Dividend Policy Investment Policy

Should the company use the overall WACC as the hurdle rate for each of its divisions? Answer: No. The composite WACC reflects the risk of an average project undertaken by the firm. Therefore, the WACC only represents the ―hurdle rate‖ for a typical project with average risk. Different projects have different risks. The project’s WACC should be adjusted to reflect the project’s risk.

What procedures can be used to estimate the risk-adjusted cost of capital for a particular division? What approaches are used to measure a division’s beta? Answer: The following procedures can be used to determine a division’s risk-adjusted cost of capital: (1)

Subjective adjustments to the firm’s composite WACC.

(2)

Attempt to estimate what the cost of capital would be if the division were a stand-alone firm. This requires estimating the division’s beta.

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The following approaches can be used to measure a division’s beta: (1)

Pure play approach. Find several publicly traded companies exclusively in the project’s business. Then, use the average of their betas as a proxy for the project’s beta. (It’s hard to find such companies.)

(2)

Accounting beta approach. Run a regression between the project’s ROA and the S&P index ROA. Accounting betas are correlated (0.5 – 0.6) with market betas. However, you normally can’t get data on new project ROAs before the capital budgeting decision has been made.

m. Jana is interested in establishing a new division that will focus primarily on developing new onlinebased projects. In trying to determine the cost of capital for this new division, you discover that specialized firms involved in similar projects have, on average, the following characteristics: Their capital structure is 10% debt and 90% common equity; their cost of debt is typically 12%; and they have a beta of 1.7. Given this information, what would your estimate be for the division’s cost of capital? Answer: rs DIV. = rRF + (rM – rRF)bDIV. = 5.6% + (6%)1.7 = 15.8%. WACCDIV. = wdrd(1 – T) + wsrs = 0.1(12%)(1 – 0.25) + 0.9(15.8%) = 15.12%. The division’s WACC = 15.12% vs. the corporate WACC = 10.38%. The division’s market risk is greater than the firm’s average projects. Typical projects within this division would be accepted if their returns are above 15.12%. n.

What are three types of project risk? How can each type of risk be considered when thinking about the new division’s cost of capital? Answer: The three types of project risk are: 1. Stand-Alone Risk 2. Corporate Risk 3. Market Risk Market risk is theoretically best in most situations. However, creditors, customers, suppliers, and employees are more affected by corporate risk. Therefore, corporate risk is also relevant. Stand-alone risk is the easiest type of risk to measure. Taking on a project with a high degree of either stand-alone or corporate risk will not necessarily affect the firm’s market risk. However, if the project has highly uncertain returns, and if those returns are highly correlated with returns on the firm’s other assets and with most other assets in the economy, the project will have a high degree of all types of risk.

Explain in words why new common stock that is raised externally has a higher percentage cost than equity that is raised internally by reinvesting earnings. Answer: The company is raising money in order to make an investment. The money has a cost, and this cost is based primarily on the investors’ required rate of return, considering risk and alternative investment opportunities. So, the new investment must provide a return at least equal to the investors’ opportunity cost. If the company raises capital by selling stock, the company doesn’t receive all of the money that investors contribute. For example, if investors put up $100,000, and if they expect a 15% return on that $100,000, then $15,000 of profits must be generated. But if flotation costs are 20% ($20,000), then the

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company will receive only $80,000 of the $100,000 investors contribute. That $80,000 must then produce a $15,000 profit, or a $15/$80 = 18.75% rate of return versus a 15% return on equity raised as retained earnings. p.

What four common mistakes in estimating the WACC should Jana avoid? Answer: 1. Don’t use the coupon rate on a firm’s existing debt as the pre-tax cost of debt. Use the current cost of debt. 2.

When estimating the risk premium for the CAPM approach, don’t subtract the current long-term Tbond rate from the historical average return on stocks. For example, the historical average return on stocks has been about 12.7%. If inflation has driven the current risk-free rate up to 10%, it would be wrong to conclude that the current market risk premium is 12.7% – 10% = 2.7%. In all likelihood, inflation would also have driven up the expected return on the market. Therefore, the historical return on the market would not be a good estimate of the current expected return on the market.

Don’t use book weights to estimate the weights for the capital structure. Use the target capital structure to determine the weights for the WACC. If you don’t have the target weights, then use market value rather than book value to obtain the weights. Use the book value of debt only as a last resort.

Always remember that capital components are sources of funding that come from investors. If it’s not a source of funding from an investor, then it’s not a capital component.

Solution and Answer Guide CHAPTER 10: T HE BASICS OF CAPITAL BUDGETING: EVALUATING CASH F LOWS

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 219 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 222 Easy Problems 1-7 ................................................................................................................................ 222 Intermediate Problems 8–18 ................................................................................................................. 224 Challenging Problems 19–24 ................................................................................................................ 237 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 244 MINI CASE ............................................................................................................................................. 245

ANSWERS TO END-OF-CHAPTER QUESTIONS 10-1 Define each of the following terms: a. Capital budgeting; payback period; discounted payback period b. Independent projects; mutually exclusive projects c. Net present value (NPV) method; internal rate of return (IRR) method; profitability index (PI) d. Modified internal rate of return (MIRR) method

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e. f. g. h.

NPV profile; crossover rate Nonnormal cash flow projects; normal cash flow projects; multiple IRRs Reinvestment rate assumption Replacement chain; economic life; capital rationing; equivalent annual annuity (EAA)

Answer: a. Capital budgeting is the whole process of analyzing projects and deciding whether they should be included in the capital budget. This process is of fundamental importance to the success or failure of the firm as the fixed asset investment decisions chart the course of a company for many years into the future. The payback, or payback period, is the number of years it takes a firm to recover its project investment. Payback may be calculated with either raw cash flows (regular payback) or discounted cash flows (discounted payback). In either case, payback does not capture a project’s entire cash flow stream and is thus not the preferred evaluation method. Note, however, that the payback does measure a project’s liquidity, and hence many firms use it as a risk measure.

Mutually exclusive projects cannot be performed at the same time. We can choose either Project 1 or Project 2, or we can reject both, but we cannot accept both projects. Independent projects can be accepted or rejected individually.

The net present value (NPV) and internal rate of return (IRR) techniques are discounted cash flow evaluation techniques because they explicitly recognize the time value of money. NPV is the present value of the project’s expected future cash flows (both inflows and outflows), discounted at the appropriate cost of capital. NPV is a direct measure of the value of the project to shareholders. The internal rate of return (IRR) is the discount rate that equates the present value of the expected future cash inflows and outflows. IRR measures the rate of return on a project, but it assumes that all cash flows can be reinvested at the IRR rate. The profitability index is the ratio of the present value of future cash flows to the project’s initial cost. It shows the relative profitability of any project. A profitability index greater than 1 is equivalent to a positive NPV project.

The modified internal rate of return (MIRR) assumes that cash flows from all projects are reinvested at the cost of capital as opposed to the project’s own IRR. This makes the modified internal rate of return a better indicator of a project’s true profitability.

An NPV profile is the plot of a project’s NPV versus its cost of capital. The crossover rate is the cost of capital at which the NPV profiles for two projects intersect, indicating that at that point their NPVs are equal.

Capital projects with nonnormal cash flows have a large cash outflow either sometime during or at the end of their lives. A common problem encountered when evaluating projects with nonnormal cash flows is multiple IRRs. A project has normal cash flows if one or more cash outflows (costs) are followed by a series of cash inflows.

The mathematics of the NPV method imply that project cash flows are reinvested at the cost of capital while the IRR method assumes reinvestment at the IRR. Since project cash flows can be replaced by new external capital that costs r, the proper reinvestment rate assumption is the cost of capital, and thus the best capital budget decision rule is NPV.

A replacement chain is a method of comparing mutually exclusive projects that have unequal lives. Each project is replicated such that they will both terminate in a common year. If projects with lives

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of 3 years and 5 years are being evaluated, the 3-year project would be replicated five times and the 5-year project replicated three times; thus, both projects would terminate in 15 years. Not all projects maximize their NPV if operated over their engineering lives and therefore it may be best to terminate a project prior to its potential life. The economic life is the number of years a project should be operated to maximize its NPV, and is often less than the maximum potential life. Capital rationing occurs when a firm’s management limits its capital expenditures to an amount less than would be required to fund the optimal capital budget. The equivalent annual annuity method is an alternative method of comparing mutually exclusive projects that have unequal lives. This method converts the annual cash flows under the alternative investments into a constant cash flow stream whose NPV is equal to the NPV of the initial stream. 10-2 What types of projects require the least detailed and the most detailed analyses in the capital budgeting process? Answer: Projects requiring greater investments or that have greater risk should be given detailed analysis of the capital budgeting process. 10-3 Explain why the NPV of a relatively long-term project, defined as one for which a high percentage of its cash flows are expected in the distant future, is more sensitive to changes in the cost of capital than is the NPV of a short-term project. Answer: The NPV is obtained by discounting future cash flows, and the discounting process actually compounds the interest rate over time. Thus, an increase in the discount rate has a much greater impact on a cash flow in Year 5 than on a cash flow in Year 1. 10-4 When two mutually exclusive projects are being compared, explain why the short-term project might be ranked higher under the NPV criterion if the cost of capital is high, whereas the long-term project might be deemed better if the cost of capital is low. Would changes in the cost of capital ever cause a change in the IRR ranking of two such projects? Why or why not? Answer: This question is related to Question 10-3 and the same rationale applies. With regard to the second part of the question, the answer is no; the IRR rankings are constant and independent of the firm’s cost of capital. 10-5 Suppose a firm is considering two mutually exclusive projects. One has a life of 6 years and the other a life of 10 years. Would the failure to employ some type of replacement chain analysis bias an NPV analysis against one of the projects? Explain. Answer: Generally, the failure to employ common-life analysis in such situations will bias the NPV against the shorter project because it ―gets no credit‖ for profits beyond its initial life, even though it could possibly be ―renewed‖ and thus provide additional NPV.

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SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1-7 10-1 NPV A project has an initial cost of $40,000, expected net cash inflows of $9,000 per year for 7 years, and a cost of capital of 11%. What is the project’s NPV? (Hint: Begin by constructing a time line.) Solution: NPV = –$40,000 + $9,000[(1/I) – (1/(I × (1 + I)N)] = –$40,000 + $9,000[(1/0.11) – (1/(0.11 × (1 + 0.11)7)] = $2,409.77. Financial calculator solution: Input CF0 = –40000, CF1-7 = 9000, I/YR = 11, and then solve for NPV = $2,409.77. 10-2 IRR Refer to Problem 10-1. What is the project’s IRR? Solution: Financial calculator solution: Input CF0 = –40000, CF1-7 = 9000, and then solve for IRR = 12.84%. 10-3 MIRR Refer to Problem 10-1. What is the project’s MIRR? Solution: MIRR: PV Costs = $40,000. FV Inflows: PV 0 12% |

40,000

1 | 9,000

2 | 9,000

3 | 9,000

4 | 9,000

5 | 9,000

6 | 9,000

MIRR= 11.93%

FV 7 | 9,000.00 9,900.00 11,088.90 12,308.68 13,662.63 15,165.52 16,833.73 88,049.46

Financial calculator: Obtain the FVA by inputting N = 7, I/YR = 11, PV = 0, PMT = 9000, and then solve for FV = $88,049.5. The MIRR can be obtained by inputting N = 7, PV = –40000, PMT = 0, FV = 88049.5, and then solving for I/YR = 11.93%. 10-4 Profitability Index Refer to Problem 10-1. What is the project’s PI? Solution: PV = $9,000[(1/I) – (1/(I × (1 + I)N)] = $9,000[(1/0.11) – (1/(0.11 × (1 + 0.11)7)] = $42,410. Financial calculator: Find present value of future cash flows by inputting N = 7, I/YR = 11, PMT = –9000, FV = 0, then solve for PV = $42,409.77. PI = PV of future cash flows/Initial cost

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= $42,409.77/$40,000 = 1.06. 10-5 Payback Refer to Problem 10-1. What is the project’s payback period? Solution: Since the cash flows are a constant $9,000, calculate the payback period as: $40,000/$9,000 = 4.44, so the payback is about 4 years. 10-6 Discounted Payback Refer to Problem 10-1. What is the project’s discounted payback period? Solution: The project’s discounted payback period is calculated as follows: Discounted CF (@11%)

Cumulative Discounted CF –40,000.00

9,000

8,108.11

(31,891.89)

9,000

7,304.60

(24,587.29)

9,000

6,580.72

(18,006.57)

9,000

5,928.58

(12,077.99)

9,000

5,341.06

(6,736.93)

9,000

4,811.77

(1,925.16)

9,000

4,334.93

2,409.77

Year 0

Annual CF –40,000

1 2

The discounted payback period is 6 +

$1,925.16 years, or 6.44 years. $4, 334.93

10-7 NPV Your division is considering two investment projects, each of which requires an up-front expenditure of $15 million. You estimate that the investments will produce the following net cash flows: Year 1 2 3 a. b.

Project A $ 5,000,000 10,000,000 20,000,000

Project B $20,000,000 10,000,000 6,000,000

What are the two projects’ net present values, assuming the cost of capital is 5%? 10%? 15%? What are the two projects’ IRRs at these same costs of capital?

Solution: a. Project A: Using a financial calculator, enter the following: CF0 = CF1 = CF2 = CF3 =

–15000000 5000000 10000000 20000000

I/YR = 10; NPV = $12,836,213. Change I/YR = 10 to I/YR = 5; NPV = $16,108,952. Change I/YR = 5 to I/YR = 15; NPV = $10,059,587. Project B: Using a financial calculator, enter the following: CF0 = CF1 = CF2 = CF3 =

–15000000 20000000 10000000 6000000

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I/YR = 10; NPV = $15,954,170. Change I/YR = 10 to I/YR = 5; NPV = $18,300,939. Change I/YR = 5 to I/YR = 15; NPV = $13,897,838. b.

Using the data for Project A, enter the cash flows into a financial calculator and solve for IRRA = 43.97%. The IRR is independent of the WACC, so IRR doesn’t change when the WACC changes. Using the data for Project B, enter the cash flows into a financial calculator and solve for IRR B = 82.03%. Again, the IRR is independent of the WACC, so IRR doesn’t change when the WACC changes.

INTERMEDIATE PROBLEMS 8–18 10-8 NPVs, IRRs, and MIRRs for Independent Projects Edelman Engineering is considering including two pieces of equipment, a truck and an overhead pulley system, in this year’s capital budget. The projects are independent. The cash outlay for the truck is $17,100, and that for the pulley system is $22,430. The firm’s cost of capital is 14%. After-tax cash flows, including depreciation, are as follows: Year 1 2 3 4 5

Truck $5,100 5,100 5,100 5,100 5,100

Pulley $7,500 7,500 7,500 7,500 7,500

Calculate the IRR, the NPV, and the MIRR for each project, and indicate the correct accept/reject decision for each. Solution: Truck: NPV = –$17,100 + $5,100(PVIFA14%,5) = –$17,100 + $5,100(3.4331) = –$17,100 + $17,509 = $409. (Accept) Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 14, and then solve for NPV = $409. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 14.99% ≈ 15%. MIRR: PV Costs = $17,100. FV Inflows: PV 0 |

1 14% | 5,100

2 | 5,100

3 | 5,100

17,100

4 | 5,100

FV 5 | 5,100 5,814 6,628 7,556 8,614 33,712

MIRR = 14.54% (Accept)

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Financial calculator: Obtain the FVA by inputting N = 5, I/YR = 14, PV = 0, PMT = 5100, and then solve for FV = $33,712. The MIRR can be obtained by inputting N = 5, PV = –17100, PMT = 0, FV = 33712, and then solving for I/YR = 14.54%. Pulley: NPV = –$22,430 + $7,500(3.4331) = –$22,430 + $25,748 = $3,318. (Accept) Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 14, and then solve for NPV = $3,318. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 20%. MIRR: PV Costs = $22,430. FV Inflows: PV 0 |

1 14% | 7,500

2 | 7,500

3 | 7,500

4 | 7,500

22,430

FV 5 | 7,500 8,550 9,747 11,112 12,667 49,576

MIRR = 17.19% (Accept) Financial calculator: Obtain the FVA by inputting N = 5, I/YR = 14, PV = 0, PMT = 7500, and then solve for FV = $49,576. The MIRR can be obtained by inputting N = 5, PV = –22430, PMT = 0, FV = 49576, and then solving for I/YR = 17.19%. 10-9 NPVs and IRRs for Mutually Exclusive Projects Davis Industries must choose between a gas-powered and an electric-powered forklift truck for moving materials in its factory. Because both forklifts perform the same function, the firm will choose only one. (They are mutually exclusive investments.) The electric-powered truck will cost more, but it will be less expensive to operate; it will cost $22,000, whereas the gas-powered truck will cost $17,500. The cost of capital that applies to both investments is 12%. The life for both types of truck is estimated to be 6 years, during which time the net cash flows for the electric-powered truck will be $6,290 per year, and those for the gas-powered truck will be $5,000 per year. Annual net cash flows include depreciation expenses. Calculate the NPV and IRR for each type of truck and decide which to recommend. Solution: Electric-powered: NPVE = –$22,000 + $6,290[(1/i) – (1/(i × (1 + i)n)] = –$22,000 + $6,290[(1/0.12) – (1/(0.12 × (1 + 0.12)6)] = –$22,000 + $6,290(4.1114) = –$22,000 + $25,861 = $3,861. Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 12, and then solve for NPV = $3,861. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 18%.

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Gas-powered: NPVG = –$17,500 + $5,000[(1/i) – (1/(i × (1 + i)n)] = –$17,500 + $5,000[(1/0.12) – (1/(0.12 × (1 + 0.12)6)] = –$17,500 + $5,000(4.1114) = –$17,500 + $20,557 = $3,057. Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 12, and then solve for NPV = $3,057. Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 17.97% ≈ 18%. The firm should purchase the electric-powered forklift because it has a higher NPV than the gas-powered forklift. The company gets a high rate of return (18% > r = 12%) on a larger investment. 10-10 Capital Budgeting Methods Project S has a cost of $10,000 and is expected to produce benefits (cash flows) of $3,000 per year for 5 years. Project L costs $25,000 and is expected to produce cash flows of $7,400 per year for 5 years. Calculate the two projects’ NPVs, IRRs, MIRRs, and PIs, assuming a cost of capital of 12%. Which project would be selected, assuming they are mutually exclusive, using each ranking method? Which should actually be selected? Solution: Financial calculator solution, NPV: Project S Inputs

5 N

3000

I/YR

PMT

7400

= –10,814.33

Output

NPVS = $10,814.33 – $10,000 = $814.33. Project L Inputs

5 N

12 I/YR

PMT

= –26,675.34

Output

NPVL = $26,675.34 – $25,000 = $1,675.34. Financial calculator solution, IRR: Input CF0 = –10000, CF1 = 3000, Nj = 5, IRRS = ? IRRS = 15.24%. Input CF0 = –25000, CF1 = 7400, Nj = 5, IRRL = ? IRRL = 14.67%. Financial calculator solution, MIRR: Project S Inputs

5 N

Output

3000

I/YR

PMT

FV = –19,058.54

PV costsS = $10,000.

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FV inflowsS = $19,058.54. Inputs

5 N

–10000

19058.54

PMT

I/YR

Output

= 13.77

MIRRS = 13.77%. Project L Inputs

Output

7400

I/YR

PMT

FV –47,011.07

PV costsL = $25,000. FV inflowsL = $47,011.07. Inputs

5 N

–25000

47011.07

PMT

I/YR

Output

= 13.46

MIRRL = 13.46%. PIS =

$10,814.33 $26,675.34 = 1.081. PIL = = 1.067. $10,000 $25,000

Thus, NPVL > NPVS, IRRS > IRRL, MIRRS > MIRRL, and PIS > PIL. The scale difference between Projects S and L results in the IRR, MIRR, and PI favoring S over L. However, NPV favors Project L; thus, L adds more value to the firm so L should be chosen. 10-11 MIRR and NPV Your company is considering two mutually exclusive projects, X and Y, whose costs and cash flows are shown here: Year

−$5,000

1,000

4,500

1,500

2,000

1,000

4,000

500

The projects are equally risky, and their cost of capital is 12%. You must make a recommendation, and you must base it on the modified IRR (MIRR). Which project has the higher MIRR? Solution: Because both projects are the same size you can just calculate each project’s MIRR and choose the project with the higher MIRR. (Remember, MIRR gives conflicting results from NPV when there are scale differences between the projects.)

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Project X:

0 1 | 12% | –5,000 1,000

5,000

2 | 1,500

3 | 2,000

4 | 4,000.00 2,240.00 1,881.60 1,404.93 9,526.53

17.49% = MIRRX

$5,000 = $9,529/(1 + MIRRX)4. Project Y:

0 1 | 12% | –5,000 4,500

5,000

2 | 1,500

3 | 1,000

4 | 500.00 1,120.00 1,881.60 6,322.18 9,823.78

18.39% = MIRRY

$1,000 = $1,636.37/(1 + MIRRY)4. Thus, since MIRRY > MIRRX, Project Y should be chosen. Alternative step: You could calculate NPVs, see that Project X has the higher NPV, and just calculate MIRRX. NPVX = $1,054.28 and NPVY = $1,243.19. 10-12 NPV and IRR Analysis After discovering a new gold vein in the Colorado mountains, CTC Mining Corporation must decide whether to go ahead and develop the deposit. The most cost-effective method of mining gold is sulfuric acid extraction, a process that could result in environmental damage. Before proceeding with the extraction, CTC must spend $900,000 for new mining equipment and pay $165,000 for its installation. The mined gold will net the firm an estimated $350,000 each year for the 5-year life of the vein. CTC’s cost of capital is 14%. For the purposes of this problem, assume that the cash inflows occur at the end of the year. a. What are the project’s NPV and IRR? b. Should this project be undertaken if environmental impacts were not a consideration? c. How should environmental effects be considered when evaluating this or any other project? How might these concepts affect the decision in part b? Solution: a. Purchase price Installation Initial outlay

$ 900,000 165,000 $1,065,000

CF0 = –1065000; CF1-5 = 350000; I/YR = 14; NPV = ? NPV = $136,578; IRR = 19.22%. b.

Ignoring environmental concerns, the project should be undertaken because its NPV is positive and its IRR is greater than the firm’s cost of capital.

Environmental effects could be added by estimating penalties or any other cash outflows that might be imposed on the firm to help return the land to its previous state (if possible). These outflows

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could be so large as to cause the project to have a negative NPV—in which case, the project should not be undertaken. 10-13 NPV and IRR Analysis Cummings Products is considering two mutually exclusive investments whose expected net cash flows are as follows: Expected Net Cash Flows Year 0 1 2 3 4 5 6 7 a. b. c. d. e.

Project A −$400 −528 −219 −150 1,100 820 990 −325

Project B −$650 210 210 210 210 210 210 210

Construct NPV profiles for Projects A and B. What is each project’s IRR? If each project’s cost of capital were 10%, which project, if either, should be selected? If the cost of capital were 17%, what would be the proper choice? What is each project’s MIRR at the cost of capital of 10%? At 17%? (Hint: Consider Period 7 as the end of Project B’s life.) What is the crossover rate, and what is its significance?

Solution: a.

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NPVA

NPVB

0.0%

$1,288

$820

10.0

$479

$372

12.0

$366

$308

14.8

$228

$229

18.0

$94

$150

20.7

$94

25.8

−$150

30.0

−$245

−$62

IRRA = 20.7%; IRRB = 25.8%.

At r = 10%, Project A has the greater NPV, specifically $478.83 as compared to Project B’s NPV of $372.37. Thus, Project A would be selected. At r = 17%, Project B has an NPV of $173.70 which is higher than Project A’s NPV of $133.76. Thus, choose Project B if r = 17%.

Here is the MIRR for Project A when r = 10%:

PV costs = $400 + $528/(1.10)1 + $219/(1.10)2 + $150/(1.10)3 + $325/(1.10)7 = $1,340.47 TV inflows = $1,100(1.10)3 + $820(1.10)2 + $990(1.10)1 = $3,545.30. Now, MIRR is that discount rate which forces the PV of $3,545.30 in 7 years to equal $1,340.47: $1,340.47 = $3,545.30/(1 + MIRR)7 MIRRA = 14.91%. Here is the MIRR for Project B when r = 10%: PV costs = 600. TV of inflows: Financial calculator settings are N = 7, I/YR = 10, PV = 0, PMT = 210, and solve for FV = –1992.3059. Similarly, $650 = $1,992.31/(1 + MIRR)7 MIRRB = 17.35%. At r = 17%, MIRRA = 18.76%. MIRRB = 21.03%. e.

To find the crossover rate, construct a Project ∆ which is the difference in the two projects’ cash flows:

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Year

Project ∆ = CFA – CFB

$250

−738

−429

−360

890

610

780

−535

IRR∆ = Crossover rate = 14.76%. Projects A and B are mutually exclusive, thus, only one of the projects can be chosen. As long as the cost of capital is greater than the crossover rate, both the NPV and IRR methods will lead to the same project selection. However, if the cost of capital is less than the crossover rate the two methods lead to different project selections—a conflict exists. When a conflict exists the NPV method must be used. Because of the sign changes and the size of the cash flows, Project ∆ has multiple IRRs. Thus, the IRR function for some calculators will not work (it will work, however, on a BAII Plus). The HP can be ―tricked‖ into giving the roots by selecting an initial guess near one of the roots. After you have keyed Project Delta’s cash flows into the CFj register of an HP-10B, you will see an ―Error-Soln‖ message. Now enter 10  STO  IRR/YR and the 14.76% IRR is found. Then enter 100  STO  IRR/YR to obtain IRR = 246.02%. Similarly, Excel can also be used. 10-14 Timing Differences The Ewert Exploration Company is considering two mutually exclusive plans for extracting oil on property for which it has mineral rights. Both plans call for the expenditure of $10 million to drill development wells. Under Plan A, all the oil will be extracted in 1 year, producing a cash flow at t = 1 of $12 million; under Plan B, cash flows will be $1.75 million per year for 20 years. a. What are the annual incremental cash flows that will be available to Ewert Exploration if it undertakes Plan B rather than Plan A? (Hint: Subtract Plan A’s flows from B’s.) b. If the company accepts Plan A and then invests the extra cash generated at the end of Year 1, what rate of return (reinvestment rate) would cause the cash flows from reinvestment to equal the cash flows from Plan B? c. Suppose a firm’s cost of capital is 10%. Is it logical to assume that the firm would take on all available independent projects (of average risk) with returns greater than 10%? Further, if all available projects with returns greater than 10% have been taken, would this mean that cash flows from past investments would have an opportunity cost of only 10% because all that the firm could do with these cash flows would be to replace money that has a cost of 10%? Finally, does this imply that the cost of capital is the correct rate to assume for the reinvestment of a project’s cash flows? d. Construct NPV profiles for Plans A and B, identify each project’s IRR, and indicate the crossover rate. Solution: a. Incremental Cash Year 0($10,000,000) 11,750,000 2-201,750,0000

Plan B ($10,000,000) 12,000,000 0

Flow (B – A) $ 0 (10,250,000) 1,750,000

Plan A

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If the firm goes with Plan B, it will forgo $10,250,000 in Year 1, but will receive $1,750,000 per year in Years 2–20. b.

If the firm could invest the incremental $10,250,000 at a return of 16.07%, it would receive cash flows of $1,750,000. If we set up an amortization schedule, we would find that payments of $1,750,000 per year for 19 years would amortize a loan of $10,250,000 at 16.0665%.

Financial calculator solution: Inputs

19 N

I/YR

Output

–10250000

1750000

PMT

= 16.0665

Yes, assuming (1) equal risk among projects, and (2) that the cost of capital is a constant and does not vary with the amount of capital raised.

See graph. If the cost of capital is less than 16.07%, then Plan B should be accepted; if r > 16.07%, then Plan A is preferred. NPV (Millions of Dollars) 25

B 20

Crossover Rate = 16.07%

A IRRB = 16.7% IRRA = 20%

Cost of Capital (%)

10-15 Scale Differences The Pinkerton Publishing Company is considering two mutually exclusive expansion plans. Plan A calls for the expenditure of $50 million on a large-scale, integrated plant that will provide an expected cash flow stream of $8 million per year for 20 years. Plan B calls for the expenditure of $15 million to build a somewhat less efficient, more labor-intensive plant that has an expected cash flow stream of $3.4 million per year for 20 years. The firm’s cost of capital is 10%. a. Calculate each project’s NPV and IRR. b. Set up a Project ∆ by showing the cash flows that will exist if the firm goes with the large plant rather than the smaller plant. What are the NPV and the IRR for this Project ∆? c. Graph the NPV profiles for Plan A, Plan B, and Project ∆. Solution: a. Financial calculator solution:

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Plan A Inputs

I/YR

8000000

PMT

3400000

PMT

8000000

PMT

–15000000

3400000

PMT

PV = –68,108,510

Output

NPVA = $68,108,510 – $50,000,000 = $18,108,510. Plan B Inputs

I/YR

PV = –28,946,117

Output

NPVB = $28,946,117 – $15,000,000 = $13,946,117. Plan A Inputs

–50000000

20 N

I/YR

Output

= 15.03

IRRA = 15.03%. Plan B Inputs

20 N

I/YR

Output

= 22.26

IRRB = 22.26%. b.

If the company takes Plan A rather than B, its cash flows will be (in millions of dollars): Cash Flows Year 0 1 2 – – – 20

Cash Flows From A ($50) 8 8 – – – 8

Project ∆ From B ($15.0) 3.4 3.4 – – – 3.4

Cash Flows ($35.0) 4.6 4.6 – – – 4.6

So, Project ∆ has a ―cost‖ of $35,000,000 and ―inflows‖ of $4,600,000 per year for 20 years.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Inputs

Output

I/YR

4600000

PMT

4600000

PMT

PV –39,162,393

NPV = $39,162,393 – $35,000,000 = $4,162,393. Inputs

–35000000

Output

I/YR

11.71

IRR = 11.71%. Since IRR∆ > r, we should accept ∆. This means we should accept the larger project (Project A). In addition, when dealing with mutually exclusive projects, we use the NPV method for choosing the best project.

c. NPV (Millions of Dollars) 125

A Crossover Rate = 11.7%

100

IRRA = 15.03%

IRRB = 22.26% 25

Cost of Capital (%) -25



IRR = 11.7%

-50

10-16 Unequal Lives Shao Airlines is considering the purchase of two alternative planes. Plane A has an expected life of 5 years, will cost $100 million, and will produce net cash flows of $30 million per year. Plane B has a life of 10 years, will cost $132 million, and will produce net cash flows of $25 million per year. Shao plans to serve the route for only 10 years. Inflation in operating costs, airplane costs, and fares are expected to be zero, and the company’s cost of capital is 12%. By how much would the value of the company increase if it accepted the better project (plane)? What is the equivalent annual annuity for each plane? Solution: Plane A: Expected life = 5 years; Cost = $100 million; NCF = $30 million; COC = 12%.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Plane B:

Expected life = 10 years; Cost = $132 million; NCF = $25 million; COC = 12%.

0 1 A: | 12% | –100 30

2 | 30

3 | 30

4 | 30

5 | 30 –100 –70

6 | 30

7 | 30

8 | 30

9 | 30

10 | 30

Enter these values into the cash flow register: CF0 = –100; CF1-4 = 30; CF5 = –70; CF6-10 = 30. Then enter I/YR = 12, and press the NPV key to get NPV A = $12.764 million. 0 1 B: | 12% | –132 25

2 | 25

3 | 25

4 | 25

5 | 25

6 | 25

7 | 25

8 | 25

9 | 25

10 | 25

Enter these cash flows into the cash flow register, along with the interest rate, and press the NPV key to get NPVB = $9.256 million. Project A is the better project and will increase the company’s value by $12.764 million. The EAA of plane A is found by first finding the PV: N = 5, I/YR = 12, PMT = 30, FV = 0; solve for PV = $108.143. The NPV is $108.143 − $100 = $8.143 million. We convert this to an equivalent annual annuity by inputting: N = 5, I/YR = 12, PV = –8.143, FV = 0, and solve for PMT = EAA = $2.259 million. For plane B, we already found the NPV of $9.256 million. We convert this to an equivalent annual annuity by inputting: N = 10, I/YR = 12, PV = –9.256, FV = 0, and solve for PMT = EAA = $1.638 million. 10-17 Unequal Lives The Perez Company has the opportunity to invest in one of two mutually exclusive machines that will produce a product it will need for the foreseeable future. Machine A costs $10 million but realizes after-tax inflows of $4 million per year for 4 years. After 4 years, the machine must be replaced. Machine B costs $15 million and realizes after-tax inflows of $3.5 million per year for 8 years, after which it must be replaced. Assume that machine prices are not expected to rise because inflation will be offset by cheaper components used in the machines. The cost of capital is 10%. By how much would the value of the company increase if it accepted the better machine? What is the equivalent annual annuity for each machine? Solution: 01 2 A: | 10% | –10 4

3 | 4

4 | 4

5 | 4 –10 –6

6 | 4

7 | 4

8 | 4

| 4

Machine A’s simple NPV is calculated as follows: Enter CF0 = –10 and CF1-4 = 4. Then enter I/YR = 10, and press the NPV key to get NPVA = $2.679 million. However, this does not consider the fact that the project can be repeated again. Enter these values into the cash flow register: CF0 = –10; CF1-3 = 4; CF4 = –6; CF5-8 = 4. Then enter I/YR = 10, and press the NPV key to get Extended NPV A = $4.5096 ≈ $4.51 million.

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0 1 B: | 10% | -15 3.5

2 | 3.5

3 | 3.5

4 | 3.5

5 | 3.5

6 | 3.5

7 | 3.5

8 | 3.5

For Machine B’s NPV, enter these cash flows into the cash flow register, along with the interest rate, and press the NPV key to get NPVB = $3.672 ≈ $3.67 million. Machine A is the better project and will increase the company’s value by $4.51 million. The EAA of Machine A is found by first finding the PV: N = 4, I/YR = 10, PMT = 4, FV = 0; solve for PV = $12.679. The NPV is $12.679 − $10 = $2.679 million. We convert this to an equivalent annual annuity by inputting: N = 4, I/YR = 10, PV = –2.679, FV = 0, and solve for PMT = EAAA = 0.845 ≈ $0.85 million. For Machine B, we already found the NPV of $3.672 million. We convert this to an equivalent annual annuity by inputting: N = 8, I/YR = 10, PV = –3.672, FV = 0, and solve for PMT = EAAB = 0.688 ≈ $0.69 million. Again, the EAA method demonstrates that Machine A is the better project since EAAA > EAAB. 10-18 Unequal Lives Filkins Fabric Company is considering the replacement of its old, fully depreciated knitting machine. Two new models are available: Machine 190-3, which has a cost of $190,000, a 3-year expected life, and after-tax cash flows (labor savings and depreciation) of $87,000 per year; and Machine 360-6, which has a cost of $360,000, a 6-year life, and after-tax cash flows of $98,300 per year. Knitting machine prices are not expected to rise because inflation will be offset by cheaper components (microprocessors) used in the machines. Assume that Filkins’s cost of capital is 14%. Should the firm replace its old knitting machine? If so, which new machine should it use? By how much would the value of the company increase if it accepted the better machine? What is the equivalent annual annuity for each machine? Solution: Cash flow time line for Machine 190-3: 0 1 14% | | –190,000 87,000

2 | 87,000

3 | 87,000

Using a financial calculator, input the following data: CF0 = –190000; CF1-3 = 87000; I/YR = 14; and solve for NPV190-3 = $11,982 (for 3 years). Extended NPV190-3 = $11,982 + $11,982/(1.14)3 = $20,070. EAA190-3:

Using a financial calculator, input the following data: N = 3; I/YR = 14; PV = –11982; and FV = 0. Solve for PMT = EAA = $5,161.

Cash flow time line for Machine 360-6: 0 1 2 14% | | | –360,000 98,300 98,300

3 | 98,300

4 | 98,300

5 | 98,300

6 | 98,300

Using a financial calculator, input the following data: CF0 = –360000; CF1-6 = 98300; I/YR = 14; and solve for NPV360-6 = $22,256 (for 6 years). EAA360-6: Using a financial calculator, input the following data: N = 6; I/YR = 14; PV = –22256; and FV = 0. Solve for PMT = EAA = $5,723. Both new machines have positive NPVs; hence, the old machine should be replaced. Further, since its NPV is greater with the replacement chain approach and its EAA is higher than Model 190-3, choose Model 360-6.

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CHALLENGING PROBLEMS 19–24 10-19 Multiple Rates of Return The Ulmer Uranium Company is deciding whether or not to open a strip mine whose net cost is $4.4 million. Net cash inflows are expected to be $27.7 million, all coming at the end of Year 1. The land must be returned to its natural state at a cost of $25 million, payable at the end of Year 2. a. Plot the project’s NPV profile. b. Should the project be accepted if r = 8%? If r = 14%? Explain your reasoning. c. Can you think of some other capital budgeting situations in which negative cash flows during or at the end of the project’s life might lead to multiple IRRs? d. What is the project’s MIRR at r = 8%? At r = 14%? Does the MIRR method lead to the same accept–reject decision as the NPV method? Solution: a. The project’s expected cash flows are as follows (in millions of dollars): Time 0 1 2

Net Cash Flow ($ 4.4) 27.7 (25.0)

We can construct the following NPV profile: NPV (Millions of Dollars) Maximum NPV at 80.5%

Discount Rate (%) 10

-1

80.5

IRR1 = 9.2%

420

IRR2 = 420%

-2

-3

-4

NPV approaches -$4.4 as the cost of capital approaches 

-4.4

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Discount Rate 0% 9 10 50 100 200 300 400 410 420 430

NPV ($1,700,000) (29,156) 120,661 2,955,556 3,200,000 2,055,556 962,500 140,000 70,204 2,367 (63,581)

The table above was constructed using a financial calculator with the following inputs: CF 0 = –4400000, CF1 = 27700000, CF2 = –25000000, and I/YR = discount rate to solve for the NPV. b.

If r = 8%, reject the project since NPV < 0 as shown in the project’s NPV profile. But if r = 14%, accept the project because NPV > 0 as shown in the project’s NPV profile.

Other possible projects with multiple rates of return could be nuclear power plants where disposal of radioactive wastes is required at the end of the project’s life, or leveraged leases where the borrowed funds are repaid at the end of the lease life

Here is the MIRR for the project when r = 8%:

PV costs = $4,400,000 + $25,000,000/(1.08) 2 = $25,833,470.51. TV inflows = $27,700,000(1.08)1 = $29,916,000.00. Now, MIRR is the discount rate that forces the PV of the TV of $29,916,000 over 2 years to equal $25,833,470.51: $25,833,470.51 = $29,916,000(PVIFr,2). Inputs

2 N

Output

–25833470.51

29916000

PMT

I/YR = 7.61

MIRR = 7.61%. At r = 14%, MIRR for the project is calculated as follows: PV costs = $4,400,000 + $25,000,000/(1.14) 2 = $23,636,688.21. TV inflows = $27,700,000(1.14)1 = $31,578,000.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Now, MIRR is that discount rate which forces the PV of the TV of $31,578,000 over 2 years to equal $23,636,688.21: $23,636,688.21 = $31,578,000(PVIFr,2). Inputs

2 N

–23636688.21

31578000

PMT

I/YR

Output

= 15.58

MIRR = 15.58%. Yes. The MIRR method leads to the same conclusion as the NPV method. Reject the project if r = 8%, which is greater than the corresponding MIRR of 7.61%, and accept the project if r = 14%, which is less than the corresponding MIRR of 15.58%. 10-20 Present Value of Costs The Aubey Coffee Company is evaluating the within-plant distribution system for its new roasting, grinding, and packing plant. The two alternatives are (1) a conveyor system with a high initial cost but low annual operating costs and (2) several forklift trucks, which cost less but have considerably higher operating costs. The decision to construct the plant has already been made, and the choice here will have no effect on the overall revenues of the project. The cost of capital for the plant is 8%, and the projects’ expected net costs are listed in the following table: Expected Net Cost

a. b.

Year

Conveyor

Forklift

−$500,000

−$200,000

−120,000

−160,000

−120,000

−160,000

−120,000

−160,000

−120,000

−160,000

−20,000

−160,000

What is the IRR of each alternative? What is the present value of the costs of each alternative? Which method should be chosen?

Solution: a. The IRRs of the two alternatives are undefined. To calculate an IRR, the cash flow stream must include both cash inflows and outflows. b.

The PV of costs for the conveyor system is ($911,067), while the PV of costs for the forklift system is ($838,834). Thus, the forklift system is expected to be ($838,834) – ($911,067) = -$72,233 less costly than the conveyor system, and hence the forklift trucks should be used. Financial calculator solution: Input: CF0 = –500000, CF1 = –120000, Nj = 4, CF2 = –20000, I/YR = 8, NPVC = ? NPVC = –911,067. Input: CF0 = –200000, CF1 = –160000, Nj = 5, I/YR = 8, NPVF = ? NPVF = –838,834. 10-21 Payback, NPV, and MIRR Your division is considering two investment projects, each of which requires an up-front expenditure of $25 million. You estimate that the cost of capital is 10% and that the investments will produce the following after-tax cash flows (in millions of dollars):

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Year 1 2 3 4 a. b. c. d. e. f. g.

Project A 5 10 15 20

Project B 20 10 8 6

What is the regular payback period for each of the projects? What is the discounted payback period for each of the projects? Calculate the NPV and IRR of the two projects. If the two projects are independent and the cost of capital is 10%, which project or projects should the firm undertake? If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake? If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake? What is the crossover rate? If the cost of capital is 10%, what is the modified IRR (MIRR) of each project?

Solution: a. Payback A (cash flows in thousands): Period 0 1 2 3 4

Annual Cash Flows ($25,000) 5,000 10,000 15,000 20,000

Cumulative ($25,000) (20,000) (10,000) 5,000 25,000

PaybackA = 2 + $10,000/$15,000 = 2.67 years. Payback B (cash flows in thousands): Period 0 1 2 3 4

Annual Cash Flows ($25,000) 20,000 10,000 8,000 6,000

Cumulative ($25,000) (5,000) 5,000 13,000 19,000

PaybackB = 1 + $5,000/$10,000 = 1.50 years. b. Discounted Payback A (cash flows in thousands): Period 0 1 2 3 4

Annual Cash Flows ($25,000) 5,000 10,000 15,000 20,000

Discounted @10% Cash Flows ($25,000.00) 4,545.45 8,264.46 11,269.72 13,660.27

Cumulative ($25,000.00) (20,454.55) (12,190.09) (920.37) 12,739.90

Discounted PaybackA = 3 + $920.37/$13,660.27 = 3.07 years. Discounted Payback B (cash flows in thousands):

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Annual Cash Flows ($25,000) 20,000 10,000 8,000 6,000

Period 0 1 2 3 4

Discounted @10% Cash Flows ($25,000.00) 18,181.82 8,264.46 6,010.52 4,098.08

Cumulative ($25,000.00) (6,818.18) 1,446.28 7,456.80 11,554.88

Discounted PaybackB = 1 + $6,818.18/$8,264.46 = 1.825 years. c. NPVA = $12,739,908; IRRA = 27.27%. NPVB = $11,554,880; IRRB = 36.15%. Both projects have positive NPVs, so both projects should be undertaken. d. At a discount rate of 5%, NPVA = $18,243,813. At a discount rate of 5%, NPVB = $14,964,829. At a discount rate of 5%, Project A has the higher NPV; consequently, it should be accepted. e. At a discount rate of 15%, NPVA = $8,207,071. At a discount rate of 15%, NPVB = $8,643,390. At a discount rate of 15%, Project B has the higher NPV; consequently, it should be accepted. f. Year 0 1 2 3 4

Project ∆ = CFA – CFB $ 0 (15) 0 7 14

IRR∆ = Crossover rate = 13.5254% ≈ 13.53%. g.

Use 3 steps to calculate MIRRA @ r = 10%: Step 1:

Calculate the NPV of the uneven cash inflow stream, so its FV can then be calculated. With a financial calculator, enter the cash inflow stream into the cash flow registers being sure to enter 0 for CF0, then enter I/YR = 10, and solve for NPV = $37,739,908.

Step 2:

Calculate the FV of the cash inflow stream as follows:

Enter N = 4, I/YR = 10, PV = -37739908, and PMT = 0 to solve for FV = $55,255,000. Step 3:

Calculate MIRRA as follows:

Enter N = 4, PV = –25000000, PMT = 0, and FV = 55255000 to solve for I/YR = 21.93%. Use 3 steps to calculate MIRRB @ r = 10%: Step 1:

Step 2:

Calculate the FV of the cash flow stream as follows:

Enter N = 4, I/YR = 10, PV = –36554880, and PMT = 0 to solve for FV = $53,520,000.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Step 3:

Calculate MIRRB as follows:

Enter N = 4, PV = –25000000, PMT = 0, and FV = 53520000 to solve for I/YR = 20.96%. According to the MIRR approach, if the 2 projects were mutually exclusive, Project A would be chosen because it has the higher MIRR. This is consistent with the NPV approach. 10-22 Economic Life The Scampini Supplies Company recently purchased a new delivery truck. The new truck cost $22,500, and it is expected to generate net after-tax operating cash flows, including depreciation, of $6,250 per year. The truck has a 5-year expected life. The expected salvage values after tax adjustments for the truck are given here. The company’s cost of capital is 10%. Year

a. b.

Annual Operating Cash Flow

Salvage Value

−$22,500

$22,500

6,250

17,500

6,250

14,000

6,250

11,000

6,250

5,000

6,250

Should the firm operate the truck until the end of its 5-year physical life? If not, then what is its optimal economic life? Would the introduction of salvage values, in addition to operating cash flows, ever reduce the expected NPV and/or IRR of a project?

Solution: a. NPV of termination after Year t: NPV0 = –$22,500 + $22,500 = 0. Using a financial calculator, input the following: CF0 = -22500, CF1 = 23750, and I/YR = 10 to solve for NPV1 = –$909.09 ≈ –$909. Using a financial calculator, input the following: CF0 = -22500, CF1 = 6250, CF2 = 20250, and I/YR = 10 to solve for NPV2 = –$82.64 ≈ –$83. Using a financial calculator, input the following: CF0 = –22500, CF1 = 6250, Nj = 2, CF3 = 17250, and I/YR = 10 to solve for NPV3 = $1,307.29 ≈ $1,307. Using a financial calculator, input the following: CF0 = –22500, CF1 = 6250, Nj = 3, CF4 = 11250, and I/YR = 10 to solve for NPV4 = $726.73 ≈ $727. Using a financial calculator, input the following: CF0 = –22500, CF1 = 6250, Nj = 5, and I/YR = 10 to solve for NPV5 = $1,192.42 ≈ $1,192. The firm should operate the truck for 3 years, NPV3 = $1,307. b.

No. Salvage possibilities could only raise NPV and IRR. The value of the firm is maximized by terminating the project after Year 3.

10-23 IRR and Realized Rate of Return Your project manager presents to you two mutually exclusive projects, A and B. They have the same initial investment and the WACCC is 10%. The cash flows are below.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

a. b.

Year

Project A

Project B

–$1,000

1,205

2,741

Calculate the IRR for each project. Your intern says that since they have the same investment and the same IRR, you should be indifferent between them. He says ―Why should I care which way I earn 23% on an investment of $1,000? Either way, I invest the same amount and earn the same return, right?‖ Explain to your intern why this isn’t correct. (Hint: Calculate the NPV and MIRR for each project to help you explain.) Use the WACC for the financing rate and reinvestment rate in the MIRR calculation.

Solution: a. Using a financial calculator, input the following: CF0 = –1000, CF1 = 1205, CF2 = 10, CF3 = 10, CF4 = 10, CF5 = 10, and IRR to solve for IRRA = 22.95%. Do the same for IRRB = 22.95%. The IRRs of the two projects are the same. b.

Using a financial calculator, input the following: CF0 = –1000, CF1 = 1205, CF2 = 10, CF3 = 10, CF4 = 10, CF5 = 10, and I/YR = 10 to solve for NPVA = $124.27. NPVB = $733.64.

To find MIRRA, using a financial calculator, enter all of the inflows in the cash flow register, find their NPV, and then find their FV as of the end of the project: CF 0 = 0, CF1 = 1205, CF2 = 10, CF3 = 10, CF4 = 10, CF5 = 10, and I/YR = 10 to solve for PV of inflows = $1124.27. Then, find this FV as of Year 5: 1124.27(1.1)5 = 1,810.65. This is the future value of all of the inflows. MIRRA = (1810.65/1000)1/5 – 1 = 12.61%. MIRRB = 22.80%. Although the two projects are the same size and have the same rate of return, Project B gets to earn this high IRR for a longer time and is six times as valuable. The final large cash flow for B stays in the project for a full 5 years earning the IRR. The large cash flow for A occurs in the first year and only gets to earn that high IRR for 1 year. You'd rather earn a high rate of return for a long time than for a short time. The MIRR addresses this by assuming that once the cash flow is paid out, it only earns the WACC and not the IRR. That's because once it is paid out, it is no longer invested in the project and is typically reinvested in the firm's operations at a rate closer to the WACC. 10-24 PI, IRR, and Margin for Error PI and IRR can be interpreted as measuring a project’s ―bang for the buck‖ as well as its ―margin for error.‖ Consider Projects A and B, below. The WACC is 10%. Year 0 1 2 3 4 a. b.

Project A –$1,000 500 500 500 500

Project B –$1,000 3,339 3,339 3,339 3,339

Calculate the NPV, IRR, and PI for each project. What can you conclude about the two projects? Suppose the outflow at Year 0 is correct but the inflows in Years 1–4 are 10% smaller than originally forecast. What can you conclude about the two projects now? Why did this happen?

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Solution: a. IRR: Using a financial calculator, input the following: CF0 = –1000, CF1 = 500, F1 = 4 and IRR to solve for IRRA = 34.9%. Do the same for IRRB = 12.7%. NPV: Using a financial calculator, input the following: CF0 = –1000, CF1 = 500, F1 = 4 and I/YR = 10 to solve for NPVA = $584.93. NPVB = $584.18. The NPVs are almost exactly the same. PI: Using a financial calculator, input the following: CF0 = 0, CF1 = 500, F1 = 4 and I/YR = 10 to solve for NPV of inflows = $1584.93. PIA = PV of inflows/Initial investment = 1584.93/1000 = 1.585. PI B = 1.058. Note that PIA is much greater than 1.0 and IRRA is much greater than the WACC. PIB is close to 1.0 and IRRB is close to the WACC. So, Project A has a bigger bang for the buck and a larger margin for error. b.

If the cash flows decrease by 10%, then for Project A, the cash flows in Years 1–4 will be $450 = 500(1 – .10) per year. The cash flows for Project B in Years 1–4 will be $3,005.1 = 3339(1 – 0.10) per year.

NPV: Using a financial calculator, input the following: CF0 = –1000, CF1 = 450, F1 = 4 and I/YR = 10 to solve for NPVA after reduction = $426.44. NPVB after reduction = NPVB = –$474.24 and is negative. The project with the bigger margin for error, Project A, can sustain a small reduction in cash flows and still be profitable. The project with the small margin for error, Project B, has a negative NPV and is unprofitable after a small reduction in cash flows.

SOLUTION TO SPREADSHEET PROBLEM 10-25 Build a Model: Capital Budgeting Tools Start with the partial model in the file Ch10 P25 Build a Model.xlsx on the textbook’s website. Gardial Fisheries is considering two mutually exclusive investments. The projects’ expected net cash flows are as follows: Expected Net Cash Flows

a. b. c. d. e.

Year

Project A

Project B

−$375

−$575

−300

190

−200

190

−100

190

600

190

600

190

926

190

−200

190

If each project’s cost of capital is 12%, which project should be selected? If the cost of capital is 18%, what project is the proper choice? Construct NPV profiles for Projects A and B. What is each project’s IRR? What is the crossover rate, and what is its significance? What is each project’s MIRR at a cost of capital of 12%? At r = 18%?

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

f. g. h.

What is the regular payback period for these two projects? At a cost of capital of 12%, what is the discounted payback period for these two projects? What is the profitability index for each project if the cost of capital is 12%?

Solution: The detailed solution for the problem is available in the file Solution for Ch10 P25 Build a Model.xlsx at the textbook’s Web site.

MINI CASE You have just graduated from the MBA program of a large university, and one of your favorite courses was Today’s Entrepreneurs. In fact, you enjoyed it so much you have decided you want to ―be your own boss.‖ While you were in the master’s program, your grandfather died and left you $1 million to do with as you please. You are not an inventor and you do not have a trade skill that you can market; however, you have decided that you would like to purchase at least one established franchise in the fast-foods area, maybe two (if profitable). The problem is that you have never been one to stay with any project for too long, so you figure that your time frame is 3 years. After 3 years, you will go on to something else. You have narrowed your selection down to two choices; (1) Franchise L, Lisa’s Soups, Salads & Stuff, and (2) Franchise S, Sam’s Fabulous Fried Chicken. The net cash flows that follow include the price you would receive for selling the franchise in Year 3 and the forecast of how each franchise will do over the 3-year period. Franchise L’s cash flows will start off slowly but will increase rather quickly as people become more health-conscious, while Franchise S’s cash flows will start off high but will trail off as other chicken competitors enter the marketplace and as people become more health-conscious and avoid fried foods. Franchise L serves breakfast and lunch, while Franchise S serves only dinner, so it is possible for you to invest in both franchises. You see these franchises as perfect complements to one another: You could attract both the lunch and dinner crowds and the health-conscious and not-so-health-conscious crowds without the franchises directly competing against one another. Here are the net cash flows (in thousands of dollars): Year 0 1 2 3

Expected Net Cash Flows Franchise L – $100 10 60 80

Franchise S – $100 70 50 20

Depreciation, salvage values, net working capital requirements, and tax effects are all included in these cash flows. You also have made subjective risk assessments of each franchise and concluded that both franchises have risk characteristics that require a return of 10%. You must now determine whether one or both of the franchises should be accepted. a.

What is capital budgeting?

Answer: Capital budgeting is the process of analyzing additions to fixed assets. Capital budgeting is important because, more than anything else, fixed asset investment decisions chart a company’s course for the future. Conceptually, the capital budgeting process is identical to the decision process used by individuals making investment decisions. These steps are involved: 1.

Estimate the cash flows—interest and maturity value or dividends in the case of bonds and stocks, operating cash flows in the case of capital projects.

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Assess the risk of the cash flows.

Determine the appropriate discount rate, based on the riskiness of the cash flows and the general level of interest rates. This is called the project cost of capital in capital budgeting.

Evaluate the cash flows.

What is the difference between independent and mutually exclusive projects?

Answer: Projects are independent if the cash flows of one are not affected by the acceptance of the other. Conversely, two projects are mutually exclusive if acceptance of one impacts adversely the cash flows of the other; that is, at most one of two or more such projects may be accepted. Put another way, when projects are mutually exclusive it means that they do the same job. For example, a forklift truck versus a conveyor system to move materials, or a bridge versus a ferry boat. c.

Define the term ―net present value (NPV).‖ What is each franchise’s NPV?

Answer: The net present value (NPV) is simply the sum of the present values of a project’s cash flows: N

NPV =

CFt

 (1 r ) . t 0

Franchise L’s NPV is $18.79: 0 10% | (100.00) 9.09 49.59 60.11 18.79 = NPVL

1 | 10

2 | 60

3 | 80

NPVs are easy to determine using a calculator with an NPV function. Enter the cash flows sequentially, with outflows entered as negatives; enter the cost of capital; and then press the NPV button to obtain the franchise’s NPV, $18.78 (note the penny rounding difference). The NPV of Franchise S is NPV S = $19.98. c.

What is the rationale behind the NPV method? According to NPV, which franchise or franchises should be accepted if they are independent? Mutually exclusive?

Answer: The rationale behind the NPV method is straightforward: if a project has NPV = $0, then the project generates exactly enough cash flows (1) to recover the cost of the investment and (2) to enable investors to earn their required rates of return (the opportunity cost of capital). If NPV = $0, then in a financial (but not an accounting) sense, the project breaks even. If the NPV is positive, then more than enough cash flow is generated, and conversely if NPV is negative. Consider Franchise L’s cash inflows, which total $150. They are sufficient (1) to return the $100 initial investment, (2) to provide investors with their 10% aggregate opportunity cost of capital, and (3) to still have $18.79 left over on a present value basis. This $18.79 excess PV belongs to the shareholders—the debtholders’ claims are fixed, so the shareholders’ wealth will be increased by $18.79 if Franchise L is accepted. Similarly, shareholders gain $19.98 in value if Franchise S is accepted.

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If Franchises L and S are independent, then both should be accepted, because they both add to shareholders’ wealth, hence to the stock price. If the franchises are mutually exclusive, then Franchise S should be chosen over L, because S adds more to the value of the firm. c.

Would the NPVs change if the cost of capital changed?

Answer: The NPV of a project is dependent on the cost of capital used. Thus, if the cost of capital changed, the NPV of each franchise would change. NPV declines as r increases, and NPV rises as r decreases. d.

Define the term ―internal rate of return (IRR).‖ What is each franchise’s IRR?

Answer: The internal rate of return (IRR) is the discount rate that forces the NPV of a project to equal zero: 0 | CF0 PVCF1 PVCF2 PVCF3 0

IRR

1 | CF1

2 | CF2

3 | CF3

= SUM OF PVs = NPV.

Expressed as an equation, we have: N

IRR:

CFt

 (1 IRR) = $0 = NPV. t 0

Note that the IRR equation is the same as the NPV equation, except that to find the IRR the equation is solved for the particular discount rate, IRR, which forces the project’s NPV to equal zero (the IRR) rather than using the cost of capital (r) in the denominator and finding NPV. Thus, the two approaches differ in only one respect: In the NPV method, a discount rate is specified (the project’s cost of capital) and the equation is solved for NPV, while in the IRR method, the NPV is specified to equal zero and the discount rate (IRR) that forces this equality is found.

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Franchise S’s IRR is 18.1%: 0 1 2 23.56% | | | –100.00 70 50 56.65 32.75 10.60 $ 0.00 if IRRL = 23.65% is used as the discount rate.

3 | 20

Therefore, IRRS ≈ 18.1%. Franchise L’s IRR is 18.1%: 0 1 2 3 18.1% | | | | –100.00 10 60 80 8.47 43.02 48.57 $ 0.06 ≈ $0 if IRRL = 18.13% is used as the discount rate. Therefore, IRRL ≈ 18.1%. A financial calculator is extremely helpful when calculating IRRs. The cash flows are entered sequentially, and then the IRR button is pressed. For Franchise S, IRR S ≈ 23.6%. Note that with many calculators, you can enter the cash flows into the cash flow register, also enter r = I/YR, and then calculate both NPV and IRR by pressing the appropriate buttons. d.

How is the IRR on a project related to the YTM on a bond? For example, suppose the initial cost of a project is $100 and it has cash flows of $40 at Years 1, 2, and 3. What is its IRR? Use the Excel RATE function as though the project were a bond.

Answer: The IRR is the discount rate that forces the PV of a project’s expected future cash flows to equal the initial cash flow. This is analogous to a bond’s yield because a bond’s yield is the discount rate that forces the present value of a bonds coupons and maturity value to equal the price of the bond. Using the RATE function: IRR = RATE(3,40,–100) = 9.7% The time line solution is: 0 1 2 3 9.7% | | | | –100.00 40 40 40 36.5 33.2 30.3 $ 0.0 ≈ $0 if IRRL = 9.7% is used as the discount rate. Therefore, IRRL ≈ 9.7%. d.

What is the logic behind the IRR method? According to IRR, which franchises should be accepted if they are independent? Mutually exclusive?

Answer: IRR measures a project’s profitability in the rate of return sense: If a project’s IRR equals its cost of capital, then its cash flows are just sufficient to provide investors with their required rates of return. An IRR greater than r implies an economic profit, which accrues to the firm’s shareholders, while an IRR less than r indicates an economic loss, or a project that will not earn enough to cover its cost of capital.

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Projects’ IRRs are compared to their costs of capital, or hurdle rates. Since Franchises L and S both have a hurdle rate of 10%, and since both have IRRs greater than that hurdle rate, both should be accepted if they are independent. However, if they are mutually exclusive, Franchise S would be selected, because it has the higher IRR. d.

Would the franchises’ IRRs change if the cost of capital changed?

Answer: IRRs are independent of the cost of capital. Therefore, neither IRRS nor IRRL would change if r changed. However, the acceptability of the franchises could change—L would be rejected if r were above 18.1%, and S would also be rejected if r were above 23.6%. e.

Draw NPV profiles for Franchises L and S. At what discount rate do the profiles cross?

Answer: The NPV profiles are plotted in the following figure.

Note the following points: 1.

The Y-intercepts for the projects are the projects’ NPV when r = 0%. These are $50 for L and $40 for S.

The X-intercepts are the projects’ IRRs. These are 18.1% for L and 23.6% for S.

NPV profiles are curves rather than straight lines. The profiles approach the projects’ costs (–$100) as r approaches infinity.

The figure on the previous pages shows that the crossover rate is 8.68%. You can calculate the crossover rate by two methods. First, subtracting the cash flows of Franchise S from those of Franchise

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L and then calculating the IRR of these differences. Second, you could also subtract Franchise L’s cash flow from Franchise S and find the IRR of the differences. The result is 8.68%.

Look at your NPV profile graph without referring to the actual NPVs and IRRs. Which franchise or franchises should be accepted if they are independent? Mutually exclusive? Explain. Are your answers correct at any cost of capital less than 23.6%?

Answer: The NPV profiles show that the IRR and NPV criteria lead to the same accept/reject decision for any independent project. Consider Franchise L. It intersects the X-axis at its IRR, 18.1%. According to the IRR rule, L is acceptable if r is less than 18.1%. Also, at any r less than 18.1%, L’s NPV profile will be above the X-axis, so its NPV will be greater than $0. Thus, for any independent project, NPV and IRR lead to the same accept/reject decision. Now assume that L and S are mutually exclusive. In this case, a conflict might arise. First, note that IRRS = 23.6% > 18.1% = IRRL. Therefore, regardless of the size of r, Franchise S would be ranked higher by the IRR criterion. However, the NPV profiles show that NPV L > NPVS if r is less than 8.7%. Therefore, for any r below the 8.7% crossover rate, say r = 7%, the NPV rule says choose L, but the IRR rule says choose S. Thus, if r is less than the crossover rate, a ranking conflict occurs. f.

What is the underlying cause of ranking conflicts between NPV and IRR?

Answer: For normal projects’ NPV profiles to cross, one project must have both a higher vertical axis intercept and a steeper slope than the other. A project’s vertical axis intercept typically depends on (1) the size of the project and (2) the size and timing pattern of the cash flows—large projects, and ones with large distant cash flows, would generally be expected to have relatively high vertical axis intercepts. The slope of the NPV profile depends entirely on the timing pattern of the cash flows—long-term projects have steeper NPV profiles than short-term ones. Thus, we conclude that NPV profiles can cross in two situations: (1) when mutually exclusive projects differ in scale (or size) and (2) when the projects’ cash flows differ in terms of the timing pattern of their cash flows (as for Franchises L and S). g.

Define the term ―modified IRR (MIRR).‖ Find the MIRRs for Franchises L and S.

Answer: MIRR is the discount rate that equates the present value of the terminal value of the inflows, compounded at the cost of capital, to the present value of the costs. Use the Excel function MIRR: A 1 2 3 4 5 6 7

2 60

3 80

r = 10% Year 0 (100)

1 10

MIRR = MIRR(A4:D4,B4,B4) MIRR = 16.50%

Alternatively, here is the setup for calculating Franchise L’s modified IRR:

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0 | r = 10% (100.00)

PV of Costs =

PV of TV $100 =

1 | 10

(1 MIRR)3

3 | 80.00 66.00 12.10 TV of Inflows = 158.10

MIRR = ?

= 100.00

$158.10

2 | 60

. N

 CIF (1 r)

N- t

PV costs =

TV (1 MIRR)N

COFt

 (1 r ) = t  1(1 MIRR)N t 0

After you calculate the TV, enter N = 3, PV = –100, PMT = 0, FV = 158.1, and then press I/YR to get the answer, MIRRL = 16.5%. We could calculate MIRRS similarly: MIRRS = 16.9%. Thus, Franchise S is ranked higher than L. This result is consistent with the NPV decision. h.

What does the profitability index (PI) measure? What are the PIs for Franchises S and L?

Answer: The PI is equal to the present value of all future cash flows divided by the initial cost. It measures the ―bang for the buck.‖ PIS = $119.98/$100 = 1.1998. PIL = $118.78/$100 = 1.1878. i.

What is the payback period? Find the paybacks for Franchises L and S.

Answer: The payback period is the expected number of years required to recover a project’s cost. We calculate the payback by developing the cumulative cash flows, as shown below for Franchise L (in thousands of dollars): Project L’s Expected NCF Annual Cumulative ($100) ($100) 10 (90) 60 (30) 80 50

Year 0 1 2 3 0 | –100

r = 10%

1 | 10 –90

2 | 60 –30

3 | 80 +50

Payback is between t = 2 and t = 3

Franchise L’s $100 investment will not be recovered by the end of Year 2 but it will be more than recovered by the end of Year 3. Thus, the recovery period is between 2 and 3 years. If we assume that the cash flows occur evenly over the year, then the investment is recovered will be recovered at about 0.4 of the year: $30/$80 = 0.375 ≈ 0.4 into Year 3. Therefore, Payback L = 2.4 years. Using similar calculations, PaybackS is 1.6 years.

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What is the rationale for the payback method? According to the payback criterion, which franchise or franchises should be accepted if the firm’s maximum acceptable payback is 2 years, and if Franchises L and S are independent? If they are mutually exclusive?

Answer: Payback represents a type of ―break-even‖ analysis: The payback period tells us when the project will break even in a cash flow sense. With a required payback of 2 years, Franchise S is acceptable, but Franchise L is not. If projects are independent and payback is part of management’s decision process, a company would accept all projects with paybacks greater than the required payback and reject those with paybacks less than the required payback. If projects were independent, management would accept all project having a payback of 2 years or less. Management would reject the remaining projects having a payback greater than 2 years. In this example, management would accept project L and reject franchise S. If projects were mutually exclusive, management would accept the project with the shortest payback, which is franchise L. Whether the two projects are independent or mutually exclusive makes no difference in this case. i.

What is the difference between the regular and discounted payback periods?

Answer: Discounted payback is similar to payback except that discounted cash flows are used. Setup for Franchise L’s discounted payback, assuming a 10% cost of capital:

Year 0 1 2 3

Cash Flows ($100) 10 60 80

Expected Net Cash Flows Discounted Cumulative Cash Flows Cash Flows ($100.00) ($100.00) 9.09 (90.91) 49.59 (41.32) 60.11 18.79

Discounted PaybackL = 2 + ($41.32/$60.11) = 2.69 = 2.7 years. This is longer than the regular payback for Franchise L, which is 2.4 years. Using a similar approach, the discounted payback for Franchise S is 1.6 years. i.

What is the main disadvantage of discounted payback? Is the payback method of any real usefulness in capital budgeting decisions?

Answer: Regular payback has three critical deficiencies: (1) It ignores the time value of money, (2) it ignores the cash flows that occur after the payback period, and (3) it does not provide a specific acceptance rule. Discounted payback does consider the time value of money, but it still fails to consider cash flows after the payback period and it does not provide a specific acceptance rule. Therefore, it still has basic flaws. In spite of these deficiencies, many firms today still calculate the discounted payback and give some weight to it when making capital budgeting decisions. However, payback is not generally used as the primary decision tool. Rather, it is used as a rough measure of a project’s liquidity and riskiness. j.

As a separate project (Project P), you are considering sponsoring a pavilion at the upcoming World’s Fair. The pavilion would cost $800,000, and it is expected to result in $5 million of incremental cash inflows during its single year of operation. However, it would then take another year, and $5 million

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of costs to demolish the site and return it to its original condition. Thus, Project P’s expected net cash flows look like this (in millions of dollars): Year 0 1 2

Net Cash Flows −$0.8 5.0 −5.0

The project is estimated to be of average risk, so its cost of capital is 10%. j.

What are normal and nonnormal cash flows?

Answer: Normal cash flows begin with a negative cash flow (or a series of negative cash flows), switch to positive cash flows, and then remain positive. They have only one change in sign. (Note: Normal cash flows can also start with positive cash flows, switch to negative cash flows, and then remain negative.) Nonnormal cash flows have more than one sign change. For example, they may start with negative cash flows, switch to positive, and then switch back to negative. Projects with normal cash flows have outflows, or costs, in the first year (or years) followed by a series of inflows. Projects with nonnormal cash flows have one or more outflows after the inflow stream has begun. Here are some examples:

Normal

Nonnormal

0 – – – – – +

Inflow (+) Or Outflow (–) in Year 1 2 3 4 + + + + – + + + – – + + + + +

+ + +

+ – –

+ + –

5 + + + – – –

What is Project P’s NPV? What is its IRR? Its MIRR?

Answer: Here is the time line for the cash flows, and the NPV: 0 1 10% | | –800,000 5,000,000

2 | –5,000,000

NPVP = –$386,776.86. We can find the NPV by entering the cash flows into the cash flow register, entering I/YR = 10, and then pressing the NPV button. However, calculating the IRR presents a problem. With the cash flows in the register, press the IRR button. An HP-10B financial calculator will give the message ―error-soln.‖ This means that Project P has multiple IRRs. An HP-17B will ask for a guess. If you guess 10%, the calculator will produce IRR = 25%. If you guess a high number, such as 200%, it will produce the second IRR, 400%1. The MIRR of Project P = 5.6%, and is found by computing the discount rate that equates the terminal value ($5.5 million) to the present value of cost ($4.93 million). j.

Draw Project P’s NPV profile. Does Project P have normal or nonnormal cash flows? Should this project be accepted?

Looking at the figure below, if you guess an IRR to the left of the peak NPV rate, the lower IRR will appear. If you guess IRR > peak NPV rate, the higher IRR will appear.

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Answer: You could put the cash flows in your calculator and then enter a series of r values, get an NPV for each, and then plot the points to construct the NPV profile. We used a spreadsheet program to automate the process and then to draw the profile. Note that the profile crosses the X-axis twice, at 25% and at 400%, signifying two IRRs. Which IRR is correct? In one sense, they both are—both cause the project’s NPV to equal zero. However, in another sense, both are wrong—neither has any economic or financial significance. Project P has nonnormal cash flows; that is, it has more than one change of signs in the cash flows. Without this nonnormal cash flow pattern, we would not have multiple IRRs. Since Project P’s NPV is negative, the project should be rejected, even though both IRRs (25% and 400%) are greater than the project’s 10% cost of capital. The MIRR of 5.6% also supports the decision that the project should be rejected.

What is the main disadvantage of discounted payback? Is the payback method of any real usefulness in capital budgeting decisions?

Answer: A major disadvantage of payback and discounted payback is that they ignore cash flows beyond the payback period. Longer term expected cash flows probably have more uncertainty than short term cash flows. This means that projects with longer payback and longer discounted payback are exposed to more risk than projects with shorter paybacks. Therefore, payback is a crude measure of risk due to longer-term cash flows. k.

In an unrelated analysis, you can choose between the following two mutually exclusive projects, Project T (which lasts for 2 years) and Project F (which lasts for 4 years):

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Expected Net Cash Flows Project T Project F – $100,000 – $100,000 60,000 33,500 60,000 33,500 — 33,500 — 33,500

Year 0 1 2 3 4

The projects provide a necessary service, so whichever one is selected is expected to be repeated into the foreseeable future. Both projects have a 10% cost of capital. k.

What is each project’s initial NPV without replication?

Answer: The NPVs, found with a financial calculator, are calculated as follows: Input the following: CF0 = –100000, CF1 = 60000, NJ = 2, and I/YR = 10 to solve for NPVT = $4,132.23 ≈ $4,132. Input the following: CF0 = –100000, CF1 = 33500, NJ = 4, and I/YR = 10 to solve for NPVF = $6,190.49 ≈ $6,190. However, if we make our decision based on the initial NPVs, we would be biasing the decision against the shorter project. Since the projects are expected to be replicated, if we initially choose Project T, it would be repeated after 2 years. However, the initial NPVs do not reflect the replication cash flows. k.

What is each project’s equivalent annual annuity?

Answer: We begin with the NPVs found in the previous step. We then find the annuity payment stream that has the same present value as follows: For Project T, input the following: N = 2, I/YR = 10, PV = –4,132.23, FV = 0, and solve for PMT = EAA = $2,380.95. For Project F, input the following: N = 4, I/YR = 10, PV = –6,190.49, FV = 0, and solve for PMT = EAA = $1,952.92. Project T is preferred because it has a higher EAA. k.

Apply the replacement chain approach to determine the projects’ extended NPVs. Which project should be chosen?

Answer: The simple replacement chain approach assumes that the projects will be replicated out to a common life. Since Project T has a 2-year life and F has a 4-year life, the shortest common life is 4 years.

Project F’s common-life NPV is its initial NPV: Common-Life NPVF = $6,190. However, Project T would be replicated in Year 2, and if we assume that the replicated project’s cash flows are identical to the first set of cash flows, then the replicated NPV is also $4,132, but it arrives in Year 2. We can put Project T’s cash flow situation on a time line:

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0 | 4,132 3,415 7,547

10%

1 |

2 | 4,132

3 |

4 |

Here we see that T’s common-life NPV is NPVT = $7,547. Thus, when compared over a 4-year common life, Project T has the higher NPV; hence, it should be chosen. Project T would have the higher NPV over any common life. k.

Now assume that the cost to replicate Project T in 2 years will increase to $105,000 due to inflation. How should the analysis be handled now, and which project should be chosen?

Answer: If the cost of Project T is expected to increase, the replication project is not identical to the original, and the EAA approach cannot be used. In this situation, we would put the cash flows on a time line as follows: 0 1 r = 10% | | –100,000 60,000

2 | 60,000 –105,000 –45,000

3 | 60,000

4 | 60,000

Common-Life NPVT = $3,415. With this change, the common-life NPV of Project T is less than that for Project F, and hence Project F should be chosen. l.

You are also considering another project which has a physical life of 3 years—that is, the machinery will be totally worn out after 3 years. However, if the project were terminated prior to the end of 3 years, the machinery would have a positive salvage value. Here are the project’s estimated cash flows: Initial Investment and Operating Cash Flows – $5,000 2,100 2,000 1,750

Year 0 1 2 3

End-of-Year Net Salvage Value $5,000 3,100 2,000 0

Using the 10% cost of capital, what is the project’s NPV if it is operated for the full 3 years? Would the NPV change if the company planned to terminate the project at the end of Year 2? At the end of Year 1? What is the project’s optimal (economic) life? Answer: Here are the time lines for the three alternative lives: No termination: 0 | –5,000

10%

1 | 2,100

2 | 2,000

3 | 1,750 0 1,750

NPV for 3 years= –$123.22

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Terminate after 2 years: 0 | –5,000

10%

0 | –5,000

10%

1 | 2,100

2 | 2,000 2,000 4,000

NPV = $214.88.

Terminate after 1 year: 1 | 2,100 3,100 5,200

NPV = –$272.73. We see (1) that the project is acceptable only if operated for 2 years, and (2) that a project’s engineering life does not always equal its economic life.

Solution and Answer Guide CHAPTER 11: CASH F LOW ESTIMATION AND RISK ANALYSIS

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 257 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 261 Easy Problems 1–4 ................................................................................................................................ 261 Intermediate Problems 5–10 ................................................................................................................. 263 Challenging Problems 11–17 ................................................................................................................ 270 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 285 MINI CASE ............................................................................................................................................. 286

ANSWERS TO END-OF-CHAPTER QUESTIONS 11-1 Define each of the following terms: a. Project cash flow; accounting income b. Incremental cash flow; sunk cost; opportunity cost; externality; cannibalization; expansion project; replacement project c. Cash flow due to changes in net operating working capital; salvage value d. Stand-alone risk; corporate (within-firm) risk; market (beta) risk e. Sensitivity analysis; scenario analysis; Monte Carlo simulation analysis f. Risk-adjusted discount rate; project cost of capital g. Decision tree; staged decision tree; decision node; branch

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h. i.

Real options; managerial options; strategic options; embedded options Investment timing option; growth option; abandonment option; flexibility option

Answer: a. Project cash flow, which is the relevant cash flow for project analysis, represents the actual flow of cash, which includes investments in capital and working capital, but does not include interest expenses or noncash charges like depreciation (except to the extent that depreciation affects taxes). In other words, project cash flow is the free cash flow generated by the project. Accounting income, on the other hand, reports accounting data as defined by generally accepted accounting principles (GAAP). b.

Incremental cash flows are those cash flows that arise solely from the asset that is being evaluated. For example, assume an existing machine generates revenues of $1,000 per year and expenses of $600 per year. A machine being considered as a replacement would generate revenues of $1,000 per year and expenses of $400 per year. On an incremental basis, the new machine would not increase revenues at all, but would decrease expenses by $200 per year. Thus, the annual incremental cash flow is a before-tax savings of $200. A sunk cost is one that has already occurred and is not affected by the capital project decision. Sunk costs are not relevant to capital budgeting decisions. Within the context of this chapter, an opportunity cost is a cash flow that a firm must forgo to accept a project. For example, if the project requires the use of a building that could otherwise be sold, the market value of the building is an opportunity cost of the project. An externality is something that is external to the project but occurs because of the project. Cannibalization occurs when a project’s product reduces the company’s sales of similar products. An expansion project is one in which new sales are generated. A replacement project is one in which an existing machine is replaced with a more efficient one—new sales might not be created, but cash flows improve because of the more efficient machine.

Net operating working capital changes are the increases in current operating assets resulting from accepting a project less the resulting increases in current operating liabilities, or accruals and accounts payable. A net operating working capital change must be financed just as a firm must finance its increases in fixed assets. Salvage value is the market value of an asset after its useful life. Salvage values and their tax effects must be included in project cash flow estimation.

Stand-alone risk is the risk a project would have if it was held in isolation. Corporate (within-firm) risk is the risk that a project contributes to a company after taking into consideration the cash flows of the company’s other projects; because projects are not perfectly correlated, corporate risk usually will be less than stand-alone risk. Market (beta) risk is the risk that a company contributes to a well-diversified portfolio.

Sensitivity analysis indicates exactly how much NPV or other output variables such as IRR or MIRR will change in response to a given change in an input variable, other things held constant. Sensitivity analysis is sometimes called ―what if‖ analysis because it answers this type of question.

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Scenario analysis is a shorter version of simulation analysis that uses only a few outcomes. Often the outcomes considered are optimistic, pessimistic and most likely. Monte Carlo simulation analysis is a risk analysis technique in which a computer is used to simulate probable future events and thus to estimate the profitability and risk of a project. e.

A risk-adjusted discount rate incorporates the risk of the project’s cash flows. The cost of capital to the firm reflects the average risk of the firm’s existing projects. Thus, new projects that are riskier than existing projects should have a higher risk-adjusted discount rate. Conversely, projects with less risk should have a lower risk-adjusted discount rate. This adjustment process also applies to a firm’s divisions. Risk differences are difficult to quantify, thus risk adjustments are often subjective in nature. A project’s cost of capital is its risk-adjusted discount rate for that project.

A decision tree is a way of structuring a set of sequential decisions that depend on the outcomes at specific points in time. A staged decision tree analysis divides the analysis into different phases. At each phase a decision is made either to proceed or to stop the project. These decisions are represented on the decision trees by circles and are called decision nodes. Each path that depends on a decision is called a branch.

Real options occur when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life. They are referred to as real options because they deal with real as opposed to financial assets. They are also called managerial options because they give opportunities to managers to respond to changing market conditions. Sometimes they are called strategic options because they often deal with strategic issues. Finally, they are also called embedded options because they are a part of another project.

Investment timing options give companies the option to delay a project rather than implement it immediately. This option to wait allows a company to reduce the uncertainty of market conditions before it decides to implement the project. Capacity options allow a company to change the capacity of their output in response to changing market conditions. This includes the option to contract or expand production. Growth options allow a company to expand if market demand is higher than expected. This includes the opportunity to expand into different geographic markets and the opportunity to introduce complementary or second-generation products. It also includes the option to abandon a project if market conditions deteriorate too much. A flexibility option permits a company to alter operations depending on how conditions change during the life of the project.

11-2 Cash flows, rather than accounting profits, are used in project analysis. What is the basis for this emphasis on cash flows as opposed to net income? Answer: Only cash can be spent or reinvested, and since accounting profits do not represent cash, they are of less fundamental importance than cash flows for investment analysis. Recall that in the stock valuation chapters we focused on dividends and free cash flows, which represent cash flows, rather than on earnings per share, which represent accounting profits. 11-3 Why is it true, in general, that a failure to adjust expected cash flows for expected inflation biases the calculated NPV downward?

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Answer: Since the cost of capital includes a premium for expected inflation, failure to adjust cash flows means that the denominator, but not the numerator, rises with inflation, and this lowers the calculated NPV. 11-4 Explain why sunk costs should not be included in a capital budgeting analysis but opportunity costs and externalities should be included. Answer: Capital budgeting analysis should only include those cash flows which will be affected by the decision. Sunk costs are unrecoverable and cannot be changed, so they have no bearing on the capital budgeting decision. Opportunity costs represent the cash flows the firm gives up by investing in this project rather than its next best alternative, and externalities are the cash flows (both positive and negative) to other projects that result from the firm taking on this project. These cash flows occur only because the firm took on the capital budgeting project; therefore, they must be included in the analysis. 11-5 Explain how net operating working capital is recovered at the end of a project’s life and why it is included in a capital budgeting analysis. Answer: When a firm takes on a new capital budgeting project, it typically must increase its investment in receivables and inventories, over and above the increase in payables and accruals, thus increasing its net operating working capital. Since this increase must be financed, it is included as an outflow in Year 0 of the analysis. At the end of the project’s life, inventories are depleted and receivables are collected. Thus, there is a decrease in NOWC, which is treated as an inflow. 11-6 How do simulation analysis and scenario analysis differ in the way they treat very bad and very good outcomes? What does this imply about using each technique to evaluate project risk? Answer: Scenario analysis analyzes a limited number of outcomes. Although the base-case scenario may be the most likely, or expected outcome, the bad and good scenarios are frequently worst-case and best-case scenarios, that is, when everything goes bad together, or everything goes right together. It is unlikely that everything will go wrong all at once, or everything will go right all at once and so scenario analysis can tend to overestimate the riskiness of a project. Simulation analysis, on the other hand, allows the variables being simulated to either vary together or independently, as the modeler sees fit. With enough runs of the simulation, this procedure should provide a reasonably accurate description of the possible outcomes. Note, however, that if the project is big and its failure could threaten the viability of the firm, then evaluating a worst-case scenario may very well be important! A simulation may only identify that worst-case outcome infrequently and with a scenario analysis you can specify the worst case and see if it drags the company down. 11-7 Why are interest charges not deducted when a project’s cash flows are calculated for use in a capital budgeting analysis? Answer: The costs associated with financing are reflected in the weighted average cost of capital. To include interest expense in the capital budgeting analysis would ―double count‖ the cost of debt financing. 11-8 Most firms generate cash inflows every day, not just once at the end of the year. In capital budgeting, should we recognize this fact by estimating daily project cash flows and then using them in the analysis? If we do not, will this bias our results? If it does, would the NPV be biased up or down? Explain.

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Daily cash flows would be theoretically best, but they would be costly to estimate and probably no more accurate than annual estimates because we simply cannot forecast accurately at a daily level. Therefore, in most cases we simply assume that all cash flows occur at the end of the year. However, for some projects, it might be useful to assume that cash flows occur at mid-year, or even quarterly or monthly. There is no clear upward or downward bias on NPV since both revenues and costs are being recognized at the end of the year. Unless revenues and costs are distributed radically different throughout the year, there should be no bias. 11-9 What are some differences in the analysis for a replacement project versus that for a new expansion project? Answer: In replacement projects, the benefits are generally cost savings, although the new machinery may also permit additional output. The data for replacement analysis are generally easier to obtain than for new products, but the analysis itself is somewhat more complicated because almost all of the cash flows are incremental, found by subtracting the new cost numbers from the old numbers. Similarly, differences in depreciation and any other factor that affects cash flows must also be determined. 11-10 Distinguish among beta (or market) risk, within-firm (or corporate) risk, and stand-alone risk for a project being considered for inclusion in a firm’s capital budget. Answer: Stand-alone risk is the project’s risk if it is held as a lone asset. It disregards the fact that it is but one asset within the firm’s portfolio of assets and that the firm is but one stock in a typical investor’s portfolio of stocks. Stand-alone risk is measured by the variability of the project’s expected returns. Corporate, or within-firm, risk is the project’s risk to the corporation, giving consideration to the fact that the project represents only one in the firm’s portfolio of assets, hence some of its risk will be eliminated by diversification within the firm. Corporate risk is measured by the project’s impact on uncertainty about the firm’s future earnings. Market, or beta, risk is the riskiness of the project as seen by welldiversified stockholders who recognize that the project is only one of the firm’s assets and that the firm’s stock is but one small part of their total portfolios. Market risk is measured by the project’s effect on the firm’s beta coefficient. 11-11 In theory, market risk should be the only ―relevant‖ risk. However, companies focus as much on standalone risk as on market risk. What are the reasons for the focus on stand-alone risk? Answer: It is often difficult to quantify market risk. On the other hand, we can usually get a good idea of a project’s stand-alone risk, and that risk is normally correlated with market risk: The higher the stand-alone risk, the higher the market risk is likely to be. Therefore, firms tend to focus on stand-alone risk, then deal with corporate and market risk by making subjective, judgmental modifications to the calculated stand-alone risk.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–4 11-1 Investment Outlay Talbot Industries is considering launching a new product. The new manufacturing equipment will cost $17 million, and production and sales will require an initial $5 million investment in net operating working capital. The company’s tax rate is 25%. a. What is the initial investment outlay? b. The company spent and expensed $150,000 on research related to the new product last year. What is the initial investment outlay?

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Rather than build a new manufacturing facility, the company plans to install the equipment in a building it owns but is not now using. The building could be sold for $1.5 million after taxes and real estate commissions. What is the initial investment outlay?

Solution: a. Equipment NWC Investment Initial investment outlay

$ 17,000,000 5,000,000 $22,000,000

No, last year’s $150,000 expenditure is considered a sunk cost and does not represent an incremental cash flow. Hence, it should not be included in the analysis: Initial outlay = $22,000,000 − $0 = $22,000,000.

The potential sale of the building represents an opportunity cost of conducting the project in that building. Therefore, the possible after-tax sale price must be charged against the project as a cost: Initial outlay = $22,000,000 + $1,500,000 = $23,500,000.

11-2 Project Cash Flow The financial staff of Cairn Communications has identified the following information for the first year of the roll-out of its new proposed service: Projected sales

$18 million

Operating costs (not including depreciation)

$9 million

Depreciation

$4 million

Interest expense

$3 million

The company faces a 25% tax rate. What is the project’s cash flow for the first year (t = 1)? Solution: Project Recurring Cash Flows: t = 1 Sales revenues $18,000,000 Operating costs 9,000,000 Depreciation 4,000,000Operating income before taxes $ 5,000,000 Taxes (25%) 1,250,000 Operating income after taxes $ 3,750,000 Add back depreciation 4,000,000 Project recurring cash flow $ 7,750,000 11-3 Net Salvage Value Allen Air Lines must liquidate some equipment that is being replaced. The equipment originally cost $12 million, of which 75% has been depreciated. The used equipment can be sold today for $4 million and Allen faces a 25% tax rate. What is the equipment’s after-tax net salvage value? Solution: Equipment's original cost Depreciation (75%) Book value

$12,000,000 9,000,000 $ 3,000,000

Gain on sale = $4,000,000 – $3,000,000 = $1,000,000. Tax on gain = $1,000,000(0.25) = $250,000. AT net salvage value = $4,000,000 - $250,000 = $3,750,000. 11-4 Replacement Analysis Although the Chen Company’s milling machine is old, it is still in relatively good working order and would last for another 10 years. It is inefficient compared to modern standards, though, and so the company is considering replacing it. The new milling machine, at a cost of $110,000

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delivered and installed, would also last for 10 years and would produce after-tax cash flows (labor savings and depreciation tax savings) of $19,000 per year. It would have zero salvage value at the end of its life. The project cost of capital is 10%, and its marginal tax rate is 25%. Should Chen buy the new machine? Solution: Cash outflow = $110,000. Increase in annual after-tax cash flows: CF = $19,000. Place the cash flows on a time line: 0 1 10% | | –110,000 19,000

2 | 19,000

•••

10 | 19,000

With a financial calculator, input the appropriate cash flows into the cash flow register, input I/YR = 10, and then solve for NPV = $6,746.78. Thus, Chen should purchase the new machine.

INTERMEDIATE PROBLEMS 5–10 11-5 Depreciation Methods Wendy’s boss wants to use straight-line depreciation for the new expansion project because he said it will give higher net income in earlier years and give him a larger bonus. The project will last 4 years and requires $1,700,000 of equipment. The company could use either straightline or the 3-year MACRS accelerated method. Under straight-line depreciation, the cost of the equipment would be depreciated evenly over its 4-year life. (Ignore the half-year convention for the straight-line method.) The applicable MACRS depreciation rates are 33.33%, 44.45%, 14.81%, and 7.41%, as discussed in Appendix 13A. The project cost of capital is 10%, and its tax rate is 25%. a. What would the depreciation expense be each year under each method? b. Which depreciation method would produce the higher NPV, and how much higher would it be? c. Why might Wendy’s boss prefer straight-line depreciation? Solution: a. The MACRS rates are 33.33%, 44.45%, 14.81%, and 7.41%. The first MACRS depreciation expense is 33.33%($1,700,000) = $566,610. The others are calculated similarly. The applicable depreciation values are as follows for the two scenarios: Scenario 1 Scenario 2 Year (Straight Line) (MACRS) 1 $425,000 $566,610 2 425,000 755,650 3 425,000 251,770 4 425,000 125,970 b.

To find the difference in net present values under these two methods, we must determine the difference in incremental cash flows each method provides. The depreciation expenses cannot simply be subtracted from each other, as there are tax ramifications due to depreciation expense. The full depreciation expense is subtracted from Revenues to get operating income, and then taxes due are computed. Then, depreciation is added to after-tax operating income to obtain the project recurring cash flow. Therefore, if the tax rate is 25%, only 75% of the depreciation expense is actually subtracted out during the after-tax operating income calculation and the full depreciation expense is added back to calculate operating income. So, there is a tax benefit associated with the depreciation expense that amounts to 25% of the depreciation expense. Therefore, the differences between depreciation expenses under each scenario should be computed and multiplied by 0.25 to determine the benefit provided by the depreciation expense.

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Year 1 2 3 4

Depreciation Expense Difference (2 – 1) $141,610 330,650 –173,230 –299,030

Depreciation Expense Diff.  0.25 (MACRS) $35,402.5 82,662.5 –43,307.5 –74,757.5

Now to find the difference in NPV to be generated under these scenarios, just enter the cash flows that represent the benefit from depreciation expense and solve for net present value based upon a cost of capital of 10%. CF0 = 0; CF1 = 35402.5; CF2 = 82662.5; CF3 = –43307.5; CF4 = –74757.5; and I/YR = 10. Solve for NPV = $16,902.26. So, all else equal the use of the accelerated depreciation method will result in a higher NPV (by $16,902.26) than would the use of a straight-line depreciation method. c.

If Wendy’s boss has a bonus plan that depends on net income instead of cash flow, then he will make a larger bonus in the first 2 years of the project if they use straight- line depreciation, and a smaller bonus in the last 2 years. This is despite the fact that accelerated depreciation is better economically for the firm. The fault lies in the bonus plan. Paying a manager a bonus based on net income can lead to decisions that are not in the best interest of the company’s shareholders, like this one.

11-6 New-Project Analysis The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer’s base price is $920,000, and it would cost another $20,000 to install it. The machine falls into the MACRS 3-year class, and it would be sold after 3 years for $500,000. The MACRS rates for the first three years are 0.3333, 0.4445, and 0.1481. The machine would require an increase in net working capital (inventory) of $15,500. The sprayer would not change revenues, but it is expected to save the firm $304,000 per year in before-tax operating costs, mainly labor. Campbell’s marginal tax rate is 25%. a. What is the Year-0 cash flow? b. What are the project recurring cash flows in Years 1, 2, and 3? c. What is the additional Year-3 cash flow (i.e., the after-tax salvage and the return of working capital)? d. If the project’s cost of capital is 12%, what is the NPV? Solution: a. The net initial cash flow is:

Machine price Installation cost NWC required

−$920,000 −$20,000 −$15,500

Year 0 CF

−$955,500

The project recurring cash flows are:

First, calculate deprecation basis, annual depreciation expenses, and the annual tax savings due to depreciation. The tax rate is 25%. Basis:

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Machine cost

920,000

Installation expense

20,000

Depreciation basis

940,000

Depreciation tax savings: Year 1

Year 2

Year 3

Year 4

Depreciation rates

33.330%

44.450%

14.810%

7.410%

Depreciation expense

$313,302.00

$417,830.00

$139,214.00

$69,654.00

Depreciation tax savings

$78,325.50

$104,457.50

$34,803.50

Second, calculate the after-tax operating savings. Year 1

Year 2

Year 3

Before-tax operating savings

304,000

Tax on operating savings

76,000

After-tax operating savings

228,000

Third, calculate the total annual project recurring cash flows. Total annual after-tax operating CF

Year 1

Year 2

Year 3

After-tax operating savings

$228,000.0

Depreciation tax savings

$78,325.5

$104,457.5

$34,803.5

Project recurring cash flow

$306,325.5

$332,457.5

$262,803.5

The additional Year-3 cash flows are: First, find the remaining book value: Salvage value calculation

Additional Year-3 CF

Depreciation basis

$940,000.0

Total depreciation expense in Years 1 through 3

$870,346.0

Remaining book value

$69,654.0

Second, calculate the tax on the salvage value: Salvage value

$500,000.0

Remaining book value

$69,654.0

Salvage minus remaining book value

$430,346.0

Tax on gain

$107,586.5

Third, calculate the Year-3 additional cash flow: Salvage value

$500,000.0

Tax on salvage gain

$107,586.5

NWC recovery

$15,500.0

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Salvage value

$500,000.0

Additional Year-3 CF

$407,913.5

The cost of capital is 12%. The total annual cash flows are: Year 0

Year 1

Year 2

Year 3

$306,325.5

$332,457.5

$262,803.5

–$955,500.0

Year 0 CF Net operating CF Additional Year-3 CF

$407,913.5 –$955,500.0

Total CF

$306,325.5

$332,457.5

$670,717.0

The NPV is $60,441.11. 11-7 New-Project Analysis The president of MorChuck Enterprises has asked you to evaluate the proposed acquisition of a new chromatograph for the firm’s R&D department. The equipment’s basic price is $70,000, and it would cost another $15,000 to modify it for special use by your firm. The chromatograph, which falls into the MACRS 3-year class, would be sold after 3 years for $30,000. The MACRS rates for the first three years are 0.3333, 0.4445, and 0.1481. Use of the equipment would require an increase in net working capital (spare parts inventory) of $4,000. The machine would have no effect on revenues, but it is expected to save the firm $25,000 per year in before-tax operating costs, mainly labor. The firm’s marginal federal-plus-state tax rate is 25%. a. What is the Year-0 cash flow? b. What are the project recurring cash flows in Years 1, 2, and 3? c. What is the additional (nonoperating) cash flow in Year 3? d. If the project’s cost of capital is 10%, should the chromatograph be purchased? Solution: a. The net cost is $89,000:

Basic price

$70,000.00

Modifications

$15,000.00

NWC increase

$4,000.00

Time 0 CF

$89,000.00

The project recurring cash flows follow: Depreciation basis

$85,000.000 1

Depreciation expenses

$28,330.500

$37,782.500

$12,588.500

Depreciation tax shield

$7,082.625

$9,445.625

$3,147.125

Pre-tax cost savings

$25,000.000

After-tax savings

$18,750.000

Project recurring cash flow

$25,832.625

$28,195.625

$21,897.125

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Notes:

The after-tax cost savings is $25,000(1 – T) = $25,000(0.75) = $18,750.

The depreciation expense in each year is the depreciable basis, $85,000, times the MACRS allowance percentage of 0.3333, 0.4445, and 0.1481 for Years 1, 2, and 3, respectively. Depreciation expenses in Years 1, 2, and 3 are $28,330.5, $37,782.5, and $12,588.5. The depreciation shield is calculated as the tax rate (25%) times the depreciation expense in each year.

The additional end-of-project cash flow is $24,519:

Beginning Book Value

$85,000.00

$56,669.50

$18,887.00

Depreciation

$28,330.50

$37,782.50

$12,588.50

Ending Book Value

$56,669.50

$18,887.00

$6,298.50

Salvage value

$30,000.000

Book value

$6,298.500

Taxable profit

$23,701.500

Tax

−$5,925.375

A-T Salvage value

$24,074.625

Recover NWC

$4,000.000

Additional CF Year 3

$28,074.625

The project has an NPV of −$4,669.11. Thus, it should not be accepted. Year Time 0 CF

$25,832.625

$28,195.625

$21,897.125

–$89,000.00

Project recurring cash flow Additional CF Year 3

$28,074.625

Total CF

–$89,000.00

NPV

–$4,669.11

$25,832.625

$28,195.625

$49,971.750

11-8 Inflation Adjustments The Rodriguez Company is considering an average-risk investment in a mineral water spring project that has an initial after-tax cost of $170,000. The project will produce 1,000 cases of mineral water per year indefinitely, starting at Year 1. The Year-1 sales price will be $138 per case, and the Year-1 cost per case will be $105. The firm is taxed at a rate of 25%. Both prices and costs are expected to rise after Year 1 at a rate of 6% per year due to inflation. The firm uses only equity, and it has a cost of capital of 15%. Assume that cash flows consist only of after-tax profits because the spring has an indefinite life and will not be depreciated. a. What is the present value of future cash flows? (Hint: The project is a growing perpetuity, so you must use the constant growth formula to find its NPV.) What is the NPV?

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Suppose that the company had forgotten to include future inflation. What would they have incorrectly calculated as the project's NPV?

Solution: a.

Year 1 sales = Year 1 costs =

1,000($138) = $138,000 1,000($105) = 105,000

Sales revenues at Year 1 Costs at Year 1

$138,000.00 $105,000.00

Pre-tax CF at Year 1 Tax (25%) Year 1 after-tax CF

$33,000.00 $8,250.00 $24,750.00

PV of future CFs Initial after-tax cost NPV

$275,000.00 $170,000.00 $105,000.00

Using the Year-1 price and the constant growth formula, the present value of all of the future cash flows is: PV0 =

CF1 $24,750 = = $275,000 r – g .15 – .06

NPV = 275,000 – 170,000 = 105,000.

If the inflation is not incorporated: PV0 =

CF1 $24,750 = = $165,000 r .15

NPV = 165,000 – 170,000 = −$5,000. 11-9 Replacement Analysis The Gilbert Instrument Corporation is considering replacing the wood steamer it currently uses to shape guitar sides. The steamer has 6 years of remaining life. If kept, the steamer will have depreciation expenses of $650 for 5 years and $325 for the sixth year. Its current book value is $3,575, and it can be sold on an Internet auction site for $4,150 at this time. If the old steamer is not replaced, it can be sold for $800 at the end of its useful life. Gilbert is considering purchasing the Side Steamer 3000, a higher-end steamer, which costs $12,000 and has an estimated useful life of 6 years with an estimated salvage value of $1,500. This steamer falls into the MACRS 5-year class, so the applicable depreciation rates are 20.00%, 32.00%, 19.20%, 11.52%, 11.52%, and 5.76%. The new steamer is faster and allows for an output expansion, so sales would rise by $2,000 per year; the new machine’s much greater efficiency would reduce operating expenses by $1,900 per year. To support the greater sales, the new machine would require that inventories increase by $2,900, but accounts payable would simultaneously increase by $700. Gilbert’s marginal federal-plusstate tax rate is 25%, and the project cost of capital is 15%. Should it replace the old steamer? Solution: First determine the net cash flow at t = 0: CF0 Calculation Purchase Price Sale of old machine Tax on sale (25%)

–$12,000.00 $4,150.00 –$143.75

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Net working capital

–$2,200.00

Total investment

–$10,193.75

The market value is $4,150 – $3,575 = $575 above the book value. Thus, there is a $575 recapture of depreciation, and Gilbert would have to pay 0.25($575) = $143.75 in taxes. b The change in net working capital is a $2,900 increase in current assets minus a $700 increase in current liabilities, which totals to $2,200. Annual after-tax revenue increases Sales increase

$2,000.00

Reduced expenses

$1,900.00

Total

$3,900.00

Taxes

$975.00

After-tax revenue increase Year

$2,925.00

New depreciation

$2,400.00

$3,840.00

$2,304.00

$1,382.40

$691.20

Old depreciation

$650.00

$325.00

$1,750.00

$3,190.00

$1,654.00

$732.40

$366.20

$437.50

$797.50

$413.50

$183.10

$91.55

Change in depreciation Incremental Depr. Tax savings

Recover NWC

$2,200.00

Sell replacement machine

$1,500.00

Tax on sale of replacement machine (is fully depreciated)

–$375.00

Opportunity cost of not selling old machine

–$800.00

Taxes not paid on sale of old machine (would be fully depreciated)

$200.00

Total CFs NPV

–$10,193.75

$3,362.50

$3,722.50

$3,338.50

$3,108.10

$5,741.55

$3,544.60

11-10 Replacement Analysis St. Johns River Shipyard’s welding machine is 15 years old, fully depreciated, and has no salvage value. However, even though it is old, it is still functional as originally designed and can be used for quite a while longer. A new welder will cost $182,500 and have an estimated life of 8 years with no salvage value. The new welder will be much more efficient, however, and this enhanced

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efficiency will increase earnings before depreciation from $27,000 to $74,000 per year. The new machine will be depreciated over its 5-year MACRS recovery period, so the applicable depreciation rates are 20.00%, 32.00%, 19.20%, 11.52%, 11.52%, and 5.76%. The applicable corporate tax rate is 25%, and the project cost of capital is 12%. What is the NPV if the firm replaces the old welder with the new one? Solution: 1. Net investment at t = 0: Cost of new machine Net investment outlay (CF0)

$182,500 $182,500

The after-tax earnings are ($74,000 − $27,000) (1 – T) = $47,000(0.75) = $35,250

The after-tax cash flow due to the tax shelter of depreciations is: Depreciation tax shield = T(Dep)

For example, depreciation in Year-1 is: Year-1 depreciation = 20%($182,500) = $36,500. The tax shield is in Year-1 is: Tax shield in Year-1: 25%($36,500) = $9,125.

Year

Initial investment

$182,500

Depreciation

Increase in EBITDA after tax

Increase in depreciation tax shield

Total CF –$182,500

$36,500

$35,250

$9,125

$44,375

$58,400

$35,250

$14,600

$49,850

$35,040

$35,250

$8,760

$44,010

$21,024

$35,250

$5,256

$40,506

$21,024

$35,250

$5,256

$40,506

$10,512

$35,250

$2,628

$37,878

$35,250

The NPV of the total CFs using a 12% cost of capital is $26,285.

CHALLENGING PROBLEMS 11–17 11-11 Scenario Analysis Shao Industries is considering a proposed project for its capital budget. The company estimates the project’s NPV is $12 million. This estimate assumes that the economy and market conditions will be average over the next few years. The company’s CFO, however, forecasts there is only a 50% chance that the economy will be average. Recognizing this uncertainty, she has also performed the following scenario analysis:

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Economic Scenario

Probability of Outcome

NPV

Recession

0.05

−$70 million

Below average

0.20

−25 million

Average

0.50

12 million

Above average

0.20

20 million

Boom

0.05

30 million

What are the project’s expected NPV, standard deviation, and coefficient of variation? Solution: E(NPV) = 0.05(–$70) + 0.20(–$25) + 0.50($12) + 0.20($20) + 0.05($30) = –$3.5 + –$5.0 + $6.0 + $4.0 + $1.5 = $3.0 million. = [0.05(–$70 – $3)2 + 0.20(–$25 – $3)2 + 0.50($12 – $3)2 + 0.20($20 – $3)2 + 0.05($30 - $3)2]0.5 = $23.622 million.

σNPV

$23.622 = 7.874. $3.0 11-12 New-Project Analysis Madison Manufacturing is considering a new machine that costs $350,000 and would reduce pre-tax manufacturing costs by $110,000 annually. Madison would use the 3-year MACRS method to depreciate the machine, and management thinks the machine would have a value of $33,000 at the end of its 5-year operating life. The applicable depreciation rates are 33.33%, 44.45%, 14.81%, and 7.41%. Working capital would increase by $35,000 initially, but it would be recovered at the end of the project’s 5-year life. Madison’s marginal tax rate is 25%, and a 10% cost of capital is appropriate for the project. a. Calculate the project’s NPV, IRR, MIRR, and payback. b. Assume management is unsure about the $110,000 cost savings—this figure could deviate by as much as plus or minus 20%. What would the NPV be under each of these extremes? c. Suppose the CFO wants you to do a scenario analysis with different values for the cost savings, the machine’s salvage value, and the working capital (WC) requirement. She asks you to use the following probabilities and values in the scenario analysis:

CVNPV

Scenario Worst case Base case Best case

Probability 0.35 0.35 0.30

Cost Savings $ 88,000 110,000 132,000

Salvage Value $28,000 33,000 38,000

WC $40,000 35,000 30,000

Calculate the project’s expected NPV, its standard deviation, and its coefficient of variation. Would you recommend that the project be accepted? Solution: a. First, set up a depreciation schedule. Inputs: Life of project = 5 years Depreciation basis = $350,000.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Depreciation rate

33.33%

44.45%

14.81%

7.41%

The depreciation for Year-1 is: Depreciation for Year 1 = (Depreciation basis)(Depreciation rate) = $350,000(0.3333) = $116,655. The book value at Year-1 is: Book value at Year 1 = $350,000 – $116,655 = $233,345

= Book value at Year 0 – Year 1 depreciation

Then beginning basis for a year is equal to the ending basis for the previous year. 0

Depreciation rate

33.33%

44.45%

14.81%

7.41%

Depreciation Ending Book Value

$116,655 $233,345

$155,575 $77,770

$51,835 $25,935

$25,935 $0

$0 $0

Second, use the depreciation schedule and the other information to estimate the annual cash flows as shown next. 0

Cost savings

$110,000

Depreciation

$116,655

$155,575

$51,835

$25,935

Op. Inc. before taxes

–$6,655

–$45,575

$58,165

$84,065

$110,000

Taxes

–$1,664

–$11,394

$14,541

$21,016

$27,500

A-T operating income

–$4,991

–$34,181

$43,624

$63,049

$82,500

Add depreciation

$116,655

$155,575

$51,835

$25,935

Operating CF

$111,664

$121,394

$95,459

$88,984

$82,500

$111,664

$121,394

$95,459

$88,984

$82,500

Machine cost

–$350,000

Net working capital

–$35,000

Return of NWC

$35,000

Sale of machine

$33,000

Tax on sale

-$8,250

Total CF

–$385,000

$111,664

$121,394

$95,459

$88,984

$142,250

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

NPV

$37,661

IRR

13.72%

MIRR

12.07%

Cumulative CF Payback b.

–$385,000

–$273,336

–$151,943

–$56,484

$32,500

$174,750

3.63

If savings increase by 20%, then savings will be (1.2)($110,000) = $132,000. If savings decrease by 20%, then savings will be (0.8)($110,000) = $88,000. (1) Savings increase by 20%: 0

Cost savings

$132,000

Depreciation

$116,655

$155,575

$51,835

$25,935

Op. Inc. before taxes

$15,345

–$23,575

$80,165

$106,065

$132,000

Taxes

$3,836

–$5,894

$20,041

$26,516

$33,000

A-T operating income

$11,509

–$17,681

$60,124

$79,549

$99,000

Add depreciation

$116,655

$155,575

$51,835

$25,935

Operating CF

$128,164

$137,894

$111,959

$105,484

$99,000

$111,664

$121,394

$95,459

$88,984

$82,500

Machine cost

–$350,000

Net working capital

–$35,000

Return of NWC

$35,000

Sale of machine

$33,000

Tax on sale

–$8,250

Total CF NPV

–$385,000

$128,164

$137,894

$111,959

$105,484

$158,750

$100,209

(2) Savings decrease by 20%: 0 Machine cost

–$350,000

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Net working capital

–$35,000

Cost savings

$88,000

Depreciation

$116,655

$155,575

$51,835

$25,935

Op. Inc. before taxes

–$28,655

–$67,575

$36,165

$62,065

$88,000

Taxes

–$7,164

–$16,894

$9,041

$15,516

$22,000

A-T operating income

–$21,491

–$50,681

$27,124

$46,549

$66,000

Add depreciation

$116,655

$155,575

$51,835

$25,935

Operating CF

$95,164

$104,894

$78,959

$72,484

$66,000

$111,664

$121,394

$95,459

$88,984

$82,500

Return of NWC

$35,000

Sale of machine

$33,000

Tax on sale

–$8,250

Total CF

–$385,000

$95,164

$104,894

$78,959

$72,484

$125,750

NPV –$24,887

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Worst-case scenario: 0

Cost savings Depreciation

$88,000 $116,655

$88,000 $155,575

$88,000 $51,835

$88,000 $25,935

$88,000 $0

Op. Inc. before taxes Taxes

–$28,655 –$7,164

–$67,575 –$16,894

$36,165 $9,041

$62,065 $15,516

$88,000 $22,000

–$21,491

–$50,681

$27,124

$46,549

$66,000

$116,655 $95,164 $111,664

$155,575 $104,894 $121,394

$51,835 $78,959 $95,459

$25,935 $72,484 $88,984

$0 $66,000 $82,500 $40,000 $28,000 −$7,000

$95,164

$104,894

$78,959

$72,484

$127,000

Machine cost Net working capital

–$350,000 –$40,000

A-T operating income Add depreciation Operating CF Return of NWC Sale of machine Tax on sale Total CF

–$390,000

NPV

–$29,111

IRR

7.08%

MIRR

8.31%

Cumulative CF Payback

–$390,000

–$294,836

–$189,943

–$110,984

–$38,500

$88,500

4.30

Base-case scenario: This was worked out in Part a. NPV = $37,035.13.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Best-case scenario: 0

Cost savings

$132,000

Depreciation

$116,655

$155,575

$51,835

$25,935

Op. Inc. before taxes

$15,345

–$23,575

$80,165

$106,065

$132,000

Taxes

$3,836

–$5,894

$20,041

$26,516

$33,000

A-T operating income

$11,509

–$17,681

$60,124

$79,549

$99,000

Add depreciation

$116,655

$155,575

$51,835

$25,935

Operating CF

$128,164

$137,894

$111,959

$105,484

$99,000

$111,664

$121,394

$95,459

$88,984

$82,500

Machine cost

−$350,000

Net working capital

–$30,000

Return of NWC

$30,000

Sale of machine

$38,000

Tax on sale

–$9,500 –$380,000

Total CF NPV

$104,432

IRR

20.18%

MIRR

15.47%

Cumulative CF Payback

–$380,000

$128,164

$137,894

–$251,836

$111,959

–$113,943

$105,484

–$1,984

$157,500

$103,500

$261,000

3.02

Scenario probabilities

NPV

Prob.

Prob x NPV

Dev. Squared

Prob(Dev. Squared)

35%

Worst

–$29,111

35%

–$10,189

4,023,775,752

1,408,321,513

35%

Base

$37,661

35%

$13,181

11,146,193

3,901,168

30%

Best

$104,432

30%

$31,330

4,915,471,209

1,474,641,363

$34,322 Expected NPV

$34,322

sigma NPV

$53,730

$2,886,864,043

1.57 E[NPV] = Sum of NPV x Prob. = sum in 5th column of preceding table = $34,322. NPV = Square root of sum of squared deviations in last column of preceding table. = ($2,886,864,043)½

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= $53,730. CV = Standard deviation/Expected value = $53,730/$34,322 = 1.57. 11-13 Replacement Analysis The Everly Equipment Company’s flange-lipping machine was purchased 5 years ago for $55,000. It had an expected life of 10 years when it was bought, and its remaining depreciation is $5,500 per year for each year of its remaining life. As older flange-lippers are robust and useful machines, this one can be sold for $20,000 at the end of its useful life. A new high-efficiency, digital-controlled flange-lipper can be purchased for $120,000, including installation costs. During its 5-year life, it will reduce cash operating expenses by $30,000 per year, although it will not affect sales. The new equipment will have zero salvage value.. MACRS depreciation will be used, and the machine will be depreciated over its 3-year class life rather than its 5-year economic life, so the applicable depreciation rates are 33.33%, 44.45%, 14.81%, and 7.41% (There will be no depreciation in its fifth year since it will already be fully depreciated.) The old machine can be sold today for $35,000. The firm’s tax rate is 25%, and the appropriate cost of capital is 16%. a. If the new flange-lipper is purchased, what is the amount of the initial cash flow at Year 0? (Hint: You need to calculate the book value of the old machine so you can calculate its after-tax salvage value.) b. What are the incremental cash flows that will occur at the end of Years 1 through 5? (Hint: Be sure to also include the annual depreciation tax savings and the after-tax opportunity cost of not selling the old machine at Year 5!) c. What is the NPV of this project? Should Everly replace the flange-lipper? Solution: a. Old depreciation = $5,500 per year. Book value = $55,000 – 5($5,500) = $27,500. Gain = $35,000 – $27,500 = $7,500. Tax on book gain = $7,500(0.25) = $1,875. Price SV (old machine) Tax effect Initial outlay

($55,000) 35,000 (1,875) ($ 86,875)

b. MACRS Rate

14.81%

7.41%

$5,500

$1,375

MACRS Rate

33.33%

44.45%

14.81%

7.41%

0.00%

New depreciation

$39,996

$53,340

$17,772

$8,892

New tax shield

$9,999

$13,335

$4,443

$2,223

Old depreciation Old tax shield Basis

33.33%

44.45%

$5,500

0.00%

$120,000

The total cash flows are:

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After tax savings

$22,500

Depreciation tax shield new

$9,999

$13,335

$4,443

$2,223

Depreciation tax shield old

–$1,375

–$1,375 –$15,000

Opportunity cost of not selling old machine (after-tax) Total CF c.

–$86,875

$31,124

$34,460

$25,568

$23,348

$6,125

NPV –$2,243.15

11-14 Replacement Analysis DeYoung Entertainment Enterprises is considering replacing the latex molding machine it uses to fabricate rubber chickens with a newer, more efficient model. The current machine has a book value of $450,000 and is being depreciated by $90,000 per year over its remaining useful life of 5 years. The current machine would be worn out and worthless in 5 years, but DeYoung can sell it now to a Halloween mask manufacturer for $135,000. If DeYoung doesn’t replace the current machine, it will have no salvage value at the end of its useful life. The new machine has a purchase price of $775,000, an estimated useful life and MACRS class life of 5 years, and an estimated salvage value of $105,000. The applicable depreciation rates are 20.00%, 32.00%, 19.20%, 11.52%, 11.52%, and 5.76%. Being highly efficient, it is expected to economize on electric power usage, labor, and repair costs, and, most importantly, to reduce the number of defective chickens. In total, an annual savings of $185,000 will be realized if the new machine is installed. The company’s marginal tax rate is 25%, and the project cost of capital is 12%. a. What is the after-tax initial cash flow if the new machine is purchased and the old one is replaced? b. What is the incremental depreciation tax shield each year (i.e., the change taxes due to the change in depreciation expenses) if the replacement is made? (Hint: First calculate the annual depreciation expense for the new machine and compare it to the depreciation on the old machine.) c. What is the after-tax salvage value at Year 5? d. What are the total incremental project cash flows in Years 0 through 5? What is the NPV? Solution: a. New machine cost

–$775,000

Salvage of old machine

$135,000

Book value

$450,000

Loss on sale of old machine

–$315,000

Tax effect of salvage = 0.25(Loss) = Total

$78,750 –$561,250

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

b. 0

Old depreciation

$90,000

Old tax shield: Depr. x T

$22,500

MACRS depreciation rate

20.000%

32.000%

19.200%

11.520%

New depreciation

$155,000

$248,000

$148,800

$89,280

New tax shield: Depr. x T

$38,750

$62,000

$37,200

$22,320

Incremental depreciation

$65,000

$158,000

$58,800

–$720

Incremental depreciation tax shield

$16,250

$39,500

$14,700

–$180

Basis

$775,000

c. Year 5 Salvage of new machine

$105,000

Book value

$44,640

Pre-tax profit from salvage

$60,360

Tax on salvage

$15,090

After-tax CF due to salvage

$89,910

d. 0

annual pre-tax savings

$185,000

annual after-tax savings

$138,750

Incremental depreciation tax shield

$16,250

$39,500

$14,700

−$180

Initial cash flow

−$561,250

After-tax CF due to salvage Total project CF

$89,910 −$561,250

$155,000

$178,250

$153,450

$138,570

$228,480

NPV = $46,175

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11-15 Risky Cash Flows The Bartram-Pulley Company (BPC) must decide between two mutually exclusive investment projects. Each project costs $6,750 and has an expected life of 3 years. Annual cash flows from each project begin 1 year after the initial investment is made and have the following probability distributions: Project A Probability

Project B

Cash Flows

Probability

Cash Flows

0.2

$6,000

0.2

0.6

6,750

0.6

6,750

0.2

7,500

0.2

18,000

BPC has decided to evaluate the riskier project at a 12% rate and the less risky project at a 10% rate. a. What are the expected values of the annual cash flows from each project? What is the coefficient of variation (CV) for each project? (Hint: σB = $5,798 and CVB = 0.76.) b. What is the risk-adjusted NPV of each project? c. If it were known that Project B is negatively correlated with other cash flows of the firm, whereas Project A is positively correlated, how would this affect the decision? If Project B’s cash flows were negatively correlated with gross domestic product (GDP), would that influence your assessment of its risk? Solution: a. Expected annual cash flows: Project A: Probability



Cash Flow

0.2



$6,000

$1,200

0.6



6,750

4,050

0.2



7,500

1,500

Expected annual cash flow

$6,750

Project B Probability



Cash Flow

0.2



0.6



6,750

4,050

0.2



18,000

3,600

Expected annual cash flow

$7,650

Coefficient of variation: CV = Standard deviation/Expected value = σCF/Expected CF Project A: σA =

( $750)2 (0.2)  ($0)2 (0.6)  ($750)2 (0.2)  $474.34.

Project B:

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

σB = ( $7,650)2 (0.2)  (  $900)2 (0.6)  ($10, 350)2 (0.2) = $5,797.84. CVA = $474.34/$6,750 = 0.0703. CVB = $5,797.84/$7,650 = 0.7579. b.

Project B is the riskier project because it has the greater variability in its probable cash flows, whether measured by the standard deviation or the coefficient of variation. Hence, Project B is evaluated at the 12% cost of capital, while Project A requires only a 10% cost of capital.

Project A: With a financial calculator, input the appropriate cash flows into the cash flow register, input I/YR = 10, and then solve for NPV = $10,036.25. Project B: With a financial calculator, input the appropriate cash flows into the cash flow register, input I = 12, and then solve for NPV = $11,624.01. Project B has the higher NPV; therefore, the firm should accept Project B. c.

The portfolio effects from Project B would tend to make it less risky than otherwise. This would tend to reinforce the decision to accept Project B. Again, if Project B were negatively correlated with the GDP (Project B is profitable when the economy is down), then it is less risky and Project B’s acceptance is reinforced.

11-16 Simulation Singleton Supplies Corporation (SSC) manufactures medical products for hospitals, clinics, and nursing homes. SSC may introduce a new type of X-ray scanner designed to identify certain types of cancers in their early stages. There are a number of uncertainties about the proposed project, but the following data are believed to be reasonably accurate:

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Probability

Developmental Costs

Random Numbers

0.3

$2,000,000

00–29

0.4

4,000,000

30–69

0.3

6,000,000

70–99

Probability

Project Life (Years)

Random Numbers

0.2

00–19

0.6

20–79

0.2

80–99

Probability

Sales in Units

Random Numbers

0.2

100

00–19

0.6

200

20–79

0.2

300

80–99

Probability

Sales Price

Random Numbers

0.1

$13,000

00–09

0.8

13,500

10–89

0.1

14,000

90–99

Probability

Cost per Unit (Excluding Developmental Costs)

Random Numbers

0.3

$5,000

00–29

0.4

6,000

30–69

0.3

7,000

70–99

SSC uses a cost of capital of 15% to analyze average-risk projects such as this one. The firm is in the 25% federal-plus-state income tax bracket. a. b.

What is the project’s NPV? Could you estimate σNPV without either simulation or a complex statistical analysis?? What is the IRR of the expected cash flows for the X-ray scanner project? Base your answer on the expected values of the variables. (Hint: You’ll need to calculate the expected value of each variable. To make your calculations easier, note that because these distributions are symmetric, the expected value is also equal to the middle value.) Also, assume the after-tax ―profits‖ figure that you develop is equal to annual cash flows. All facilities are leased, so depreciation may be disregarded. Can you determine the value of σIRR short of actual simulation or complex statistical analysis Show the process by which a computer would perform a simulation analysis for this project. Assume the computer has generated the random numbers used in parts (1) and (2). (1) Use the random numbers 17 and 44 to determine the project’s life and development costs; these will be the same for all sample years. (2) Use 16, 58, and 1 as random numbers to determine the unit sales, sales price per unit, and cost per unit in the first year, respectively. Calculate the net income. Repeat this for Year 2 by using the random values 79, 83, and 86 to determine the unit sales, sales price per unit, and cost per unit in the second year. Repeat this for Year 3 (and any subsequent years) by using the random values 19, 62, and 37 to determine the unit sales, sales price per unit, and cost per unit in the third year, respectively. (3) What is the NPV for this sample?

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Solution: a. First, note that with symmetric probability distributions, the middle value of each distribution is the expected value. Therefore, Expected Net Income Sales (units) Sales price Sales in dollars Costs (200 x $6,000) Earnings before taxes Taxes (25%) Net income

200 $13,500 $2,700,000 1,200,000 $1,500,000 375,000 $1,125,000

Expected annual cash flow based on assumptions = Net income = $1,125,000. Expected life of project = 8 years. Expected initial cost = $4,000,000. Solve this equation for IRR: ∑

(

)

Using a financial calculator, input the following: CF0 = −4000000, CF1 = 1125000, and Nj = 8, to solve for IRR = 22.62%. Assuming complete independence between the distributions, and normality, it would be possible to derive σIRR statistically. Alternatively, we could employ simulation to develop a distribution of IRRs, hence σIRR. There is no easy way to get σIRR. b.

Using a financial calculator, input the following: CF0 = −4000000, CF1 = 1125000, Nj = 8, and I/YR = 15 to solve for NPV = $1,048,236.70. Again, there is no easy way to estimate σNPV.

(1) a.

Calculate developmental costs. The 44 random number value, coming between 30 and 70, indicates that the costs for this run are $4 million. (2) a. Estimate unit sales. The 16 indicates sales of 100 units.

Calculate the project life. The 17, being less than 20, indicates that a 3-year life should be used.

Estimate the sales price. The 58 indicates a sales price of $13,500.

Estimate the cost per unit. The 1 indicates a cost of $5,000.

Now estimate the after-tax cash flow for Year 1. It is [100($13,500 – $5,000)](1 – 0.25) = $637,500 = CF1.

Repeat the process for Year 2. Sales will be 200 with a random number of 79; the price will be $13,500 with a random number of 83; and the cost will be $7,000 with a random number of 86: [200($13,500 – $7,000)](0.75) = $975,000 = CF2. Repeat the process for Year 3. Sales will be 100 units with a random number of 19; the price will be $13,500 with a random number of 62; and the cost will be $5,000 with a random number of 37:

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[100($13,500 – $6,000)](0.75) = $562,500 = CF3. (3) The time line is: Year 0 −$4,000,000

Year 1 $637,500

Year 2 $975,000

Year 3 $562,500

Using a 15% cost of capital, the NPV is −$2,338,559. The results of this run are very bad because the project’s life is so short. Had the life turned out (by chance) to be 13 years, the longest possible life, the NPV would have been positive for most runs. 11-17 Decision Tree The Yoran Yacht Company (YYC), a prominent sailboat builder in Newport, may design a new 30-foot sailboat based on the ―winged‖ keels first introduced on the 12-meter yachts that raced for the America’s Cup. First, YYC would have to invest $10,000 at t = 0 for the design and model tank testing of the new boat. YYC’s managers believe there is a 60% probability that this phase will be successful and the project will continue. If Stage 1 is not successful, the project will be abandoned with zero salvage value. The next stage, if undertaken, would consist of making the molds and producing two prototype boats. This would cost $500,000 at t = 1. If the boats test well, YYC would go into production. If they do not, the molds and prototypes could be sold for $100,000. The managers estimate the probability is 80% that the boats will pass testing and that Stage 3 will be undertaken. Stage 3 consists of converting an unused production line to produce the new design. This would cost $1 million at t = 2. If the economy is strong at this point, the net value of sales would be $3 million; if the economy is weak, the net value would be $1.5 million. Both net values occur at t = 3, and each state of the economy has a probability of 0.5. YYC’s corporate cost of capital is 12%. a. Assume this project has average risk. Construct a decision tree and determine the project’s expected NPV. b. Find the project’s standard deviation of NPV and coefficient of variation of NPV. If YYC’s average project had a CV of between 1.0 and 2.0, would this project be of high, low, or average stand-alone risk? Solution: a. The resulting decision tree is:

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t=0

t=1

NPV P 0.24

t=2 t=3 $3,000,000

($1,000,000)

P = 0.5

P = 0.80

1,500,000

($500,000)

0.24

NPV Product $881,718 $211,612

(185,952)

(44,628)

P = 0.5

P = 0.60 100,000 ($10,000)

0.12

(376,709)

(45,205)

P = 0.20

0.40

P = 0.40

(10,000)

1.00

(4,000)

Exp. NPV = $117,779

The NPV of the top path is:

$3,000,000 (1.12)



$1,000,000 (1.12)



$500,000 (1.12)1

 $10,000  $881,718.

Using a financial calculator, input the following: CF0 = –10000, CF1 = –500000, CF2 = –1000000, CF3 = 3000000, and I/YR = 12 to solve for NPV = $881,718.29  $881,718. The other NPVs were determined in the same manner. If the project is of average risk, it should be accepted because the expected NPV of the total project is positive. b.

σ2NPV = 0.24($881,718 – $117,779)2 + 0.24(–$185,952 – $117,779)2 + 0.12(–$376,709 – $117,779)2 + 0.4(–$10,000 – $117,779)2 = 198,078,470,853.

σNPV = $445,060. $445,060 = 3.78. $117, 779 Since the CV is 3.78 for this project, while the firm’s average project has a CV of 1.0 to 2.0, this project is of high risk.

CVNPV =

SOLUTION TO SPREADSHEET PROBLEM 11-18 Build a Model: Issues in Capital Budgeting Start with the partial model in the file Ch11 P18 Build a Model.xlsx on the textbook’s website. Webmasters.com has developed a powerful new server that would be used for corporations’ Internet activities. It would cost $10 million at Year 0 to buy the equipment necessary to manufacture the server. The project would require net working capital at the beginning of each year in an amount equal to 10% of the year’s projected sales; for example, NWC0 = 10%(Sales1). The servers would sell for $24,000 per unit, and Webmasters believes that variable costs would amount to

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$18,000 per unit. After Year 1, the sales price and variable costs will increase at the inflation rate of 3%. The company’s nonvariable costs would be $1 million at Year 1 and would increase with inflation. The server project would have a life of 4 years. If the project is undertaken, it must be continued for the entire 4 years. Also, the project’s returns are expected to be highly correlated with returns on the firm’s other assets. The firm believes it could sell 1,000 units per year. The equipment would be depreciated over a 5-year period, using MACRS rates. The estimated market value of the equipment at the end of the project’s 4-year life is $500,000. Webmasters.com’s federal-plus-state tax rate is 25%. Its cost of capital is 10% for average-risk projects, defined as projects with a coefficient of variation of NPV between 0.8 and 1.2. Low-risk projects are evaluated with an 8% project cost of capital and high-risk projects at 13%. a. Develop a spreadsheet model, and use it to find the project’s NPV, IRR, and payback. b. Now conduct a sensitivity analysis to determine the sensitivity of NPV to changes in the sales price, variable costs per unit, and number of units sold. Set these variables’ values at 10% and 20% above and below their base-case values. Include a graph in your analysis. c. Now conduct a scenario analysis. Assume that there is a 25% probability that best-case conditions, with each of the variables discussed in Part b being 20% better than its base-case value, will occur. There is a 25% probability of worst-case conditions, with the variables 20% worse than base, and a 50% probability of base-case conditions. d. If the project appears to be more or less risky than an average project, find its risk-adjusted NPV, IRR, and payback. e. On the basis of information in the problem, would you recommend the project should be accepted? Solution: The detailed solution for the problem is available in the file Ch 11 P18 Build a Model Solution.xlsx at the textbook’s website.

MINI CASE Shrieves Casting Company is considering adding a new line to its product mix, and the capital budgeting analysis is being conducted by Sidney Johnson, a recently graduated MBA. The production line would be set up in unused space in the main plant. The machinery’s invoice price would be approximately $200,000, another $10,000 in shipping charges would be required, and it would cost an additional $30,000 to install the equipment. The machinery has an economic life of 4 years, and Shrieves has obtained a special tax ruling that places the equipment in the MACRS 3-year class. The machinery is expected to have a salvage value of $25,000 after 4 years of use. The new line would generate incremental sales of 1,000 units per year for 4 years at an incremental cost of $100 per unit in the first year, excluding depreciation. Each unit can be sold for $200 in the first year. The sales price and cost are both expected to increase by 3% per year due to inflation. Further, to handle the new line, the firm’s net working capital would have to increase by an amount equal to 12% of sales revenues. The firm’s tax rate is 25%, and its overall weighted average cost of capital, which is the risk-adjusted cost of capital for an average project (r), is 10%. a.

Define ―incremental cash flow.‖

Answer: This is the firm’s cash flow with the project minus the firm’s cash flow without the project. a.

Should you subtract interest expense or dividends when calculating project cash flow?

Answer: The cash flow statement should not include interest expense or dividends. The return required by the investors furnishing the capital is already accounted for when we apply the 10% cost of capital discount rate; hence, including financing flows would be ―double counting.‖ Put another way, if we deducted capital costs in the

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table, and thus reduced the bottom-line cash flows, and then discounted those CFs by the cost of capital, we would, in effect, be subtracting capital costs twice. a.

Suppose the firm had spent $100,000 last year to rehabilitate the production line site. Should this cost be included in the analysis? Explain.

Answer: The $100,000 cost to rehabilitate the production line site was incurred last year, and presumably also expensed for tax purposes. Since, it is a sunk cost, it should not be included in the analysis. a.

Now assume the plant space could be leased out to another firm at $25,000 per year. Should this be included in the analysis? If so, how?

Answer: If the plant space could be leased out to another firm, then if Shrieves accepts this project, it would forgo the opportunity to receive $25,000 in annual cash flows. This represents an opportunity cost to the project, and it should be included in the analysis. Note that the opportunity cost cash flow must be net of taxes, so it would be a $25,000(1 – T) = $25,000(0.6) = $15,000 annual outflow. a.

Finally, assume that the new product line is expected to decrease sales of the firm’s other lines by $50,000 per year. Should this be considered in the analysis? If so, how?

Answer: If a project affects the cash flows of another project, this is an ―externality‖ that must be considered in the analysis. If the firm's sales would be reduced by $50,000, then the net cash flow loss would be a cost to the project. Note that this annual loss would not be the full $50,000, because Shrieves would save on cash operating costs if its sales dropped. Note also that externalities can be positive as well as negative. b.

Disregard the assumptions in part a. What is the depreciable basis? What are the annual depreciation expenses?

Answer: The asset’s depreciable basis includes shipping and installation costs. Thus, the asset’s depreciable basis = $200,000 + $10,000 + $30,000 = $240,000. Get the depreciation rates from Table 11A-2 in the book. Note that because of the half-year convention, a 3-year project is depreciated over four calendar years: Basis

Depr. Rate

Depr. = Basis(Rate)

Remaining book value

Year 1

0.3333

$79,992

$160,008

Year 2

0.4445

$106,680

$53,328

Year 3

0.1481

$35,544

$17,784

Year 4

0.0741

$17,784

$240,000

Calculate the annual sales revenues and costs (other than depreciation). Why is it important to include inflation when estimating cash flows?

Answer: With an inflation rate of 3%, the annual revenues and costs are:

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Year 1

Year 2

Year 3

Year 4

Units

1,000

Unit price

$200

$206

$212

$219

Unit cost

$100

$103

$106

$109

Sales

$200,000

$206,000

$212,180

$218,545

Costs

$100,000

$103,000

$106,090

$109,273

The cost of capital is a nominal cost; i.e., it includes a premium for inflation. In other words, it is larger than the real cost of capital. Similarly, nominal cash flows (those that are inflated) are larger than real cash flows. If you discount the low, real cash flows with the high, nominal rate, then the resulting NPV is too low. Therefore, you should always discount nominal cash flows with a nominal rate, and real cash flows with a real rate. In theory, you could do the analysis either way and obtain the correct answer. However, there is no accurate way to convert a nominal cost of capital to a real cost. Therefore, you should inflate cash flows and then discount at the nominal cost of capital. d.

Calculate annual net operating profit after sales (NOPAT). Then calculate the project recurring cash flows.

Answer:

Year 1

Year 2

Year 3

Year 4

Sales

$200,000

$206,000

$212,180.0

$218,545.4

Costs

$100,000

$103,000

$106,090.0

$109,272.7

Depreciation

$79,992

$106,680

$35,544.0

$17,784.0

EBIT

$20,008

–$3,680

$70,546.0

$91,488.7

Taxes (25%)

$5,002

–$920

$17,636.5

$22,872.2

NOPAT

$15,006

–$2,760

$52,909.5

$68,616.5

NOPAT

Depreciation

Op. CF = NOPAT + Depr.

Year 1

$15,006.00

$79,992.00

$94,998.00

Year 2

–$2,760.00

$106,680.00

$103,920.00

Year 3

$52,909.50

$35,544.00

$88,453.50

Year 4

$68,616.53

$17,784.00

$86,400.53

Estimate the required net operating working capital (NOWC) for each year and the cash flow due to investments in NOWC.

Answer: The project requires a level of net working capital in the amount equal to 12% of the next year’s sales. Any increase in NWC is a negative cash flow, and any decrease is a positive cash flow. This project has a 4-year operating life, so any NWC expenditures will be recovered in Year 4. (That is, accounts receivables are received and inventories are drawn down.) Following are the cash flows due to investment in NOWC.

Sales Year 0

NWC (% of sales) $24,000

CF due to investment in NOWC) –$24,000

Year 1

$200,000

$24,720

–$720

Year 2

$206,000

$25,462

–$742

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Year 3

$212,180

$26,225

–$763

Year 4

$218,545

$26,225

Calculate the after-tax salvage cash flow.

Answer: When the project is terminated at the end of Year 4, the equipment can be sold for $25,000. But, since it has been depreciated to a $0 book value, taxes must be paid on the full salvage value. For this project, the after-tax salvage cash flow is: (1) Salvage value (2) Book value (3) Gain or loss: (1) − (2) (4)Tax on gain or loss (5) After-tax salvage CF: (1) − (4) g.

$25,000 $0 $25,000 $6,250 $18,750

Calculate the net cash flows for each year. Based on these cash flows and the average project cost of capital, what are the project’s NPV, IRR, MIRR, PI, payback, and discounted payback? Do these indicators suggest that the project should be undertaken?

Answer: The net cash flows are: Year 0

Year 1

Year 2

Year 3

Year 4

$94,998

$103,920

$88,453.5

$86,400.5

–$720

–$742

–$763.0

$26,225.0

–$240,000

Initial CF Op. CF

–$24,000

NOWC CF Salvage CF

$18,750.0 –$264,000

Project CF

$94,278

$103,178

$87,690.5

NPV =

$62,593

IRR =

20.1%

MIRR =

16.0%

PI =

1.24

Payback =

2.8

Discounted payback

3.3

$131,375.5

What does the term ―risk‖ mean in the context of capital budgeting; to what extent can risk be quantified; and, when risk is quantified, is the quantification based primarily on statistical analysis of historical data or on subjective, judgmental estimates?

Answer: Risk throughout finance relates to uncertainty about future events, and in capital budgeting, this means the future profitability of a project. For certain types of projects, it is possible to look back at historical data and to statistically analyze the riskiness of the investment. This is often true when the investment involves an expansion decision; for example, if Sears were opening a new store, if Citibank were opening a new branch, or if GM were expanding its Chevrolet plant, then past experience could be a useful guide to future risk. Similarly, a company that is considering going into a new business might be able to look at historical data on existing firms in that industry to get an idea about the riskiness of its proposed investment. However, there are times when it is impossible to obtain historical data regarding proposed investments; for example, if GM were

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considering the development of an electric auto, not much relevant historical data for assessing the riskiness of the project would be available. Rather, GM would have to rely primarily on the judgment of its executives, and they, in turn would have to rely on their experience in developing, manufacturing, and marketing new products. We will try to quantify risk analysis, but you must recognize at the outset that some of the data used in the analysis will necessarily be based on subjective judgments rather than on hard statistical observations. i.

What are the three types of risk that are relevant in capital budgeting?

How is each of these risk types measured, and how do they relate to one another?

Answer: Here are the three types of project risk:



Stand-alone risk is the project’s total risk if it were operated independently. Stand-alone risk ignores both the firm’s diversification among projects and investors’ diversification among firms. Stand-alone risk is measured either by the project’s standard deviation of NPV (σNPV) or its coefficient of variation of NPV (CVNPV). Note that other profitability measures, such as IRR and MIRR, can also be used to obtain stand-alone risk estimates.



Within-firm risk is the total riskiness of the project giving consideration to the firm’s other projects, that is, to diversification within the firm. It is the contribution of the project to the firm’s total risk, and it is a function of (a) the project’s standard deviation of NPV and (b) the correlation of the projects’ returns with those of the rest of the firm. Within-firm risk is often called corporate risk, and it is measured by the project’s corporate beta, which is the slope of the regression line formed by plotting returns on the project versus returns on the firm.



Market risk is the riskiness of the project to a well-diversified investor; hence, it considers the diversification inherent in stockholders’ portfolios. It is measured by the project’s market beta, which is the slope of the regression line formed by plotting returns on the project versus returns on the market.

How is each type of risk used in the capital budgeting process?

Answer: Because management’s primary goal is shareholder wealth maximization, the most relevant risk for capital projects is market risk. However, creditors, customers, suppliers, and employees are all affected by a firm’s total risk. Since these parties influence the firm’s profitability, a project’s within-firm risk should not be completely ignored. Unfortunately, by far the easiest type of risk to measure is a project’s stand-alone risk. Thus, firms often focus on this type of risk when making capital budgeting decisions. However, this focus does not necessarily lead to poor decisions, because most projects that a firm undertakes are in its core business. In this situation, a project’s stand-alone risk is likely to be highly correlated with its within-firm risk, which in turn is likely to be highly correlated with its market risk. j.

What is sensitivity analysis?

Answer: Sensitivity analysis measures the effect of changes in a particular variable, say revenues, on a project’s NPV. To perform a sensitivity analysis, all variables are fixed at their expected values except one. This one variable is then changed, often by specified percentages, and the resulting effect on NPV is noted. (One could allow more than one variable to change, but this then merges sensitivity analysis into scenario analysis.)

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Perform a sensitivity analysis on the cost per unit, unit sales, and salvage value. Assume each of these variables can vary from its base-case (i.e., expected, value) by plus or minus 10%, 20%, and 30%. Include a sensitivity diagram and discuss the results.

Answer: The sensitivity data are given here in tabular form: NPV for deviations in inputs Cost per unit Units Sold

Deviation from Base Case –30% –15% 0% 15% 30%

$136,927 $99,760 $62,593 $25,426 –$11,742

–$9,363 $26,615 $62,593 $98,571 $134,548

Salvage $58,751 $60,672 $62,593 $64,514 $66,435

We generated the data with a spreadsheet model in the file Ch11 Mini Case.xlsx. The following is a graph showing the sensitivities of the project to these inputs.

Sensitivity Analysis NPV ($) 140,000

[SERIES NAME]

120,000 100,000 80,000 [SERIES NAME]

60,000 40,000

20,000 0 -20,000 -30%

-20%

-10%

10%

20%

30%

Deviation from Base-Case Value

A. The sensitivity lines intersect at 0% change and the base-case NPV, $62,593. Since all other variables are set at their base-case, or expected, values, the zero-change situation is the base case and gives the base-case NPV, $62,593.

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B. The plots for unit sales is steep and upward sloping, indicating that higher-variable values lead to higher NPVs. The salvage value line is also upward sloping, but only slightly, indicating that the salvage value has a relatively small impact on NPVs. Conversely, the plot for cost per unit is downward sloping (and steeper than the line for units sold), because a higher cost per unit leads to a lower NPV. C. Steeper sensitivity lines indicate greater risk. Thus, in comparing two projects, the one with the steeper sensitivity lines is considered to be the riskier project. j.

What is the primary weakness of sensitivity analysis? What is its primary usefulness?

Answer: The two primary disadvantages of sensitivity analysis are (1) that it does not reflect the effects of diversification and (2) that it does not incorporate any information about the possible magnitudes of the forecast errors. Thus, a sensitivity analysis might indicate that a project’s NPV is highly sensitive to the sales forecast; hence, that the project is quite risky, but if the project’s sales, hence its revenues, are fixed by a long-term contract, then sales variations may actually contribute little to the project’s risk. It also ignores any relationships between variables, such as unit sales and sales price. Therefore, in many situations, sensitivity analysis is not a particularly good risk indicator. However, sensitivity analysis does identify those variables that potentially have the greatest impact on profitability, and this helps management focus its attention on those variables that are probably most important. k.

Assume that Sidney Johnson is confident of her estimates of all the variables that affect the project’s cash flows except unit sales and sales price. If product acceptance is poor, unit sales would be only 800 units a year and the unit price would only be $160; a strong consumer response would produce sales of 1,200 units and a unit price of $240. Sidney believes that there is a 25% chance of poor acceptance, a 25% chance of excellent acceptance, and a 50% chance of average acceptance (the base case).

What is scenario analysis?

Answer: Scenario analysis examines several possible situations, usually worst case, most likely case, and best case. It provides a range of possible outcomes. k.

What is the worst-case NPV? The best-case NPV?

Answer: The worst case NPV is –$63,399. The best case NPV is $227,595. See the file Ch11 Mini Case.xls for calculations. k.

Use the worst-, base-, and best-case NPVs and probabilities of occurrence to find the project’s expected NPV, as well as the NPV’s standard deviation and coefficient of variation.

Answer: We used a spreadsheet model to develop the scenarios, which are summarized below: Scenario Best Case Base Case Worst Case

Prob. 25% 50% 25%

Unit Sales 1,200 1,000 800

Unit Price NPV $240 $227,595 $200 $62,593 $160 –$63,399 Expected NPV = $72,345 Standard Deviation = 103,343 Coefficient of Variation = Std Dev/Expected NPV = 1.43

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Are there problems with scenario analysis? Define simulation analysis and discuss its principal advantages and disadvantages.

Answer: Scenario analysis examines several possible scenarios, usually worst case, most likely case, and best case. Thus, it usually considers only three possible outcomes. Obviously, the world is much more complex, and most projects have an almost infinite number of possible outcomes. Simulation analysis is a type of scenario analysis that uses randomly generated inputs rather than specific values. Here the uncertain cash flow variables (such as unit sales) are entered as continuous probability distribution parameters rather than as point values. Then, the computer uses a random number generator to select values for the uncertain variables on the basis of their designated distributions. Once all of the variable values have been selected, they are combined and an NPV is calculated. The process is repeated many times, say 1,000 times, with new values selected from the distributions for each run. The end result is a probability distribution of NPV based on a sample of 1,000 values. Simulation can provide the distribution as well as summary statistics such as expected NPV and σNPV. Simulation provides the decision maker with a better idea of the profitability of a project than scenario analysis does because it incorporates many more possible outcomes. Although simulation analysis is technically refined, its usefulness is limited because managers are often unable to accurately specify the variables’ probability distributions. Further, the correlations among the uncertain variables must be specified, along with the correlations over time. If managers are unable to do this with much confidence, then the results of simulation analyses are of limited value. Recognize also that neither sensitivity, scenario, nor simulation analysis provides a decision rule—they may indicate that a project is relatively risky, but they do not indicate whether the project’s expected return is sufficient to compensate for its risk. Finally, remember that sensitivity, scenario, and simulation analyses all focus on stand-alone risk, which is not the most relevant risk in capital budgeting analysis. m. 1.

Assume the company’s average project has a coefficient of variation in the range of 0.2 to 0.4. Would the new line be classified as high risk, average risk, or low risk? What type of risk is being measured here?

Answer: The project has a CV of 1.15, which is above the average range of 0.2 to 0.4, so it falls into the high-risk category. The CV measures a project’s stand-alone risk; it is merely a measure of the variability of returns (as measured by NPV) about the expected return. m. 2.

Shrieves typically adds or subtracts 3 percentage points to the overall cost of capital to adjust for risk. Should the new line be accepted?

Answer: Since the project is judged to have above-average risk, its differential risk-adjusted, or project, cost of capital would be 13%. At this discount rate, its NPV would be $41,584, so it would still be acceptable. If it were a low-risk project, its cost of capital would be 7%, its NPV would be $86,037, and it would be an even more profitable project on a risk-adjusted basis. m. 3.

Are there any subjective risk factors that should be considered before the final decision is made?

Answer: A numerical analysis such as this one may not capture all of the risk factors inherent in the project. If the project has a potential for bringing on harmful lawsuits, then it might be riskier than first assessed. Also, if the project’s assets can be re-deployed within the firm or can be easily sold, then, as a result of ―abandonment possibilities,‖ the project may be less risky than the analysis indicates. n.

What is a real option? What are some types of real options?

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Answer: Real options exist when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life in response to changing market conditions. Some types of real options are listed below: 1.

Investment timing options

Growth options a. Expansion of existing product line b. New products c. New geographic markets

Abandonment options a. Contraction b. Temporary suspension c. Complete abandonment

Flexibility options a. Inputs b. Outputs c. Both

Solution and Answer Guide CHAPTER 12: CORPORATE VALUATION AND FINANCIAL P LANNING

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 294 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 297 Easy Problems 1–3 ................................................................................................................................ 297 Intermediate Problems 4–6 ................................................................................................................... 299 Challenging Problems 7–9 .................................................................................................................... 302 SOLUTION TO SPREADSHEET PROBLEMS ................................................................................. 309 MINI CASE ............................................................................................................................................. 311

ANSWERS TO END-OF-CHAPTER QUESTIONS 12-1 Define each of the following terms: a. Operating plan; financial plan b. Spontaneous liabilities; profit margin; payout ratio c. Additional funds needed (AFN); AFN equation; capital intensity ratio; self-supporting growth rate d. Forecasted financial statement approach using percentage of sales e. Excess capacity; lumpy assets; economies of scale f. Full capacity sales; target fixed assets to sales ratio; required level of fixed assets Answer:

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

The operating plan provides detailed implementation guidance designed to accomplish corporate objectives. It details who is responsible for what particular function, and when specific tasks are to be accomplished. The financial plan details the financial aspects of the corporation’s operating plan.

Spontaneous liabilities are the first source of expansion capital as these accounts increase automatically through normal business operations. Examples of spontaneous liabilities include accounts payable, accrued wages, and accrued taxes. No interest is normally paid on these spontaneous liabilities; however, their amounts are limited due to credit terms, contracts with workers, and tax laws. Therefore, spontaneous liabilities are used to the extent possible, but there is little flexibility in their usage. Note that notes payable, although a current liability account, is not a spontaneous liability since an increase in notes payable requires a specific action between the firm and a creditor. A firm’s profit margin is calculated as net income divided by sales. The higher a firm’s profit margin, the larger the firm’s net income available to support increases in its assets. Consequently, the firm’s need for external financing will be lower. A firm’s payout ratio is calculated as dividends per share divided by earnings per share. The less of its income a company distributes as dividends, the larger its addition to retained earnings. Therefore, the firm’s need for external financing will be lower.

Additional funds needed (AFN) are those funds required from external sources to increase the firm’s assets to support a sales increase. A sales increase will normally require an increase in assets. However, some of this increase is usually offset by a spontaneous increase in liabilities as well as by earnings retained in the firm. Those funds that are required but not generated internally must be obtained from external sources. Although most firms’ forecasts of capital requirements are made by developing forecasted financial statements, the AFN formula is sometimes used as an approximation of financial requirements. It is written as follows: Additional funds

(A0*/S0)S

Increase in

–

increase

needed

AFN

Required asset

spontaneous

–

(L0*/S0)S

retained earnings

liab.

–

MS1(1 – Payout rate)

Capital intensity is the dollar amount of assets required to produce a dollar of sales. The capital intensity ratio is calculated as operating assets divided by sales, and if a company has only operating assets, then it is also the reciprocal of the total assets turnover ratio. The sustainable growth rate is the maximum growth rate the firm could achieve without having to raise any external capital. A firm’s self-supporting growth rate can be calculated as follows: Self-supporting g =

M(1  POR)(S0 ) A 0 *  L 0 *  M(1  POR)(S0 )

The forecasted financial statement approach using percentage of sales develops a complete set of financial statements that can be used to calculate projected EPS, free cash flow, various other financial ratios, and a projected stock price. This approach first forecasts sales, the required assets, the funds that will be spontaneously generated, and then net income, dividends, and retained earnings.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

A firm has excess capacity when its sales can grow before it must add fixed assets such as plant and equipment. Lumpy assets are those assets that cannot be acquired smoothly, but require large, discrete additions. For example, an electric utility that is operating at full capacity cannot add a small amount of generating capacity, at least not economically. When economies of scale occur, the ratios are likely to change over time as the size of the firm increases. For example, retailers often need to maintain base stocks of different inventory items, even if current sales are quite low. As sales expand, inventories may then grow less rapidly than sales, so the ratio of inventory to sales declines.

Full capacity sales are calculated as actual sales divided by the percentage of capacity at which fixed assets were operated. The target fixed assets to sales ratio is calculated as actual fixed assets divided by full capacity sales. The required level of sales is calculated as the target fixed assets to sales ratio multiplied by the projected sales level.

12-2 Some liability and net worth items increase spontaneously with increases in sales. Put a check () by the following listed items that typically increase spontaneously: Accounts payable

__________

Long-term bonds

__________

Notes payable to banks

__________

Common stock

__________

Accrued wages

__________

Retained earnings

__________

Accrued taxes

__________

Answer: Accounts payable, accrued wages, and accrued taxes increase spontaneously. Retained earnings may or may not increase, depending on profitability and dividend payout policy. 12-3 The following equation is sometimes used to forecast financial requirements: AFN = (A0*/S0)(∆S) − (L0*/S0)(∆S) − MS1(1 − POR) What key assumption do we make when using this equation? Under what conditions might this assumption not hold true? Answer: The equation gives good forecasts of financial requirements if the ratios A0*/S and L0*/S, the profit margin, and payout ratio are stable. This equation assumes that ratios are constant. This would not occur if there were economies of scale, excess capacity, or when lumpy assets are required. Otherwise, the forecasted financial statement method should be used. 12-4 Name five key factors that affect a firm’s external financing requirements. Answer: The five key factors that impact a firm’s external financing requirements are sales growth, capital intensity, spontaneous liabilities to sales ratio, profit margin, and payout ratio. 12-5 What is meant by the term ―self-supporting growth rate‖? How is this rate related to the AFN equation, and how can that equation be used to calculate the self-supporting growth rate? Answer:

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The self-supporting growth rate is the maximum rate a firm can achieve without having to raise external capital. The self-supporting growth rate is calculated using the AFN equation, setting AFN equal to zero, replacing the term ΔS with the term g × S0, and replacing the term S1 with S0 × (1 + g). Once the AFN equation is rewritten with these modifications, you can now solve for g. This ―g‖ obtained is the firm’s self-supporting growth rate. 12-6 Suppose a firm makes the following policy changes listed. If a change means that external, nonspontaneous financial requirements (AFN) will increase, indicate this by a (+); indicate a decrease by a (−); and indicate no effect or an indeterminate effect by a (0). Think in terms of the immediate effect on funds requirements. a. The dividend payout ratio is increased. __________ b. The firm decides to pay all suppliers on delivery rather than after a 30-day delay in order to take advantage of discounts for rapid payment. __________ c. The firm begins to offer credit to its customers, whereas previously all sales had been on a cash basis. __________ d. The firm’s profit margin is eroded by increased competition, although sales hold steady. __________ e. The firm sells its manufacturing plants for cash to a contractor and simultaneously signs an outsourcing contract to purchase from that contractor goods that the firm formerly produced. __________ f. The firm negotiates a new contract with its union that lowers its labor costs without affecting its output. __________ Answer: a. +. b.

+. It reduces spontaneous funds; however, it may eventually increase retained earnings.

–.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–3 12-1 AFN Equation. Broussard Skateboard’s sales are expected to increase by 15% from $8 million in 2023 to $9.2 million in 2024. Its operating assets were $5 million at the end of 2023. Broussard is already at full capacity, so its operating assets must grow at the same rate as projected sales. At the end of 2023, current liabilities were $1.4 million, consisting of $450,000 of accounts payable, $500,000 of notes payable, and $450,000 of accruals. The after-tax profit margin is forecasted to be 6%, and the forecasted payout ratio is 40%. Use the AFN equation to forecast Broussard’s additional funds needed for the coming year.

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Solution: AFN = (A0*/S0)∆S – (L0*/S0)∆S – (PM)(S1)(1 – payout rate)

 $5,000,000   $900,000  =  $1,200,000 –   $1,200,000 – 0.06($9,200,000)(1 – 0.4) $8,000,000    $8,000,000  = (0.625)($1,200,000) – (0.1125)($1,200,000) – ($552,000)(0.6) = $750,000 – $135,000 – $331,200 = $283,800. 12-2 Projected Operating Assets. Berman & Jaccor Corporation’s current sales and partial balance sheet are shown here. Sales are expected to grow by 10% next year. Assuming no change in operations from this year to next year, what are the projected total operating assets? This year Sales

$1,000

Balance Sheet: Assets Cash

$100

Short-term investments

$80

Accounts receivable

$200

Inventories

$200

Total current assets

$580

Net fixed assets

$500

Total assets

$1,080

Solution: Cash/Sales = $100/$1,000 = 10.0% AR/Sales = $200/$1,000 = 20.0% Inventories/Sales = $200/$1,000 = 20.0% Net fixed assets = $580/$1,000 = 50.0% Projected sales = (1 + 0.1)($1,000) = $1,100 Projections: Cash = 10.0% × $1,100 = $110 Accounts receivable = 20.0% × $1,100 = $220 Inventories = 20.0% × $1,100 = $220 Net fixed assets = 50.0% × $1,100 = $550 Total operating assets = $1,100 12-3 Projected Spontaneous Liabilities. Smiley Corporation's current sales and partial balance sheet are shown here. Sales are expected to grow by 10% next year. Assuming no change in operations from this year to next year, what are the projected spontaneous liabilities? This year

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

This year Sales

$10,000

Balance Sheet: Liabilities Accounts payable

$1,500

Notes payable

$2,000

Accruals

$1,200

Total current liabilities

$4,700

Long-term bonds

$2,000

Total liabilities

$6,700

Common stock

$1,000

Retained earnings

$3,000

Total common equity

$4,000

Total liabilities & equity

$10,700

Solution: AP/Sales = $1,500/$10,000 = 15% Accruals/Sales = $1,200/$10,000 = 12% Projections Sales = (1 + 0.10)($10,000) = $11,000 Accounts payable = 15%($11,000) = $1,650 Accruals = 12%($11,000) = $1,320 Total spontaneous liabilities = $2,970

INTERMEDIATE PROBLEMS 4–6 12-4 Self-Supporting Growth Rate. Maggie’s Muffins Bakery generated $5 million in sales during 2023, and its year-end operating assets were $2.5 million. Also, at year-end 2023, current liabilities were $1 million, consisting of $300,000 of notes payable, $500,000 of accounts payable, and $200,000 of accruals. Looking ahead to 2024, the company estimates that its operating assets must increase at the same rate as sales, its spontaneous liabilities will increase at the same rate as sales, its profit margin will be 7%, and its payout ratio will be 80%. How large a sales increase can the company achieve without having to raise funds externally—that is, what is its self-supporting growth rate? Solution: S0 = $5,000,000; A0* = $2,500,000; CL = $700,000; NP = $300,000; AP = $500,000; Accruals = $200,000; M = 7%; payout ratio = 80%; A0*/S0 = 0.50; L0* = (AP + Accruals)/S0 = ($500,000 + $200,000)/$5,000,000 = 0.14. AFN = (A0*/S0)∆S – (L0*/S0)∆S – (M)(S1)(1 – payout rate) = (0.50)∆S – (0.14) ∆S – (0.07)(S1)(1 – 0.8) = (0.50)∆S – (0.14)∆S – (0.014)S1 = (0.36)∆S – (0.014)S1

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= 0.36(S1 – S0) – (0.014)S1 = 0.36(S1 – $5,000,000) – (0.014)S1 = 0.36S1 – $1,800,000 – 0.014S1 $1,800,000 = 0.346S1 S1 = $5,202,312 Sales can increase by $5,202,312 – $5,000,000 = $202,312 without additional funds being needed. 12-5 Long-Term Financing Needed. At year-end 2023, Wallace Landscaping’s total assets, all of which are used in operations, were $2.17 million, and its accounts payable were $560,000. Sales, which in 2023 were $3.5 million, are expected to increase by 35% in 2024. Total assets and accounts payable are proportional to sales, and that relationship will be maintained. Wallace typically uses no current liabilities other than accounts payable. Common stock amounted to $625,000 in 2023, and retained earnings were $395,000. Wallace has arranged to sell $195,000 of new common stock in 2024 to meet some of its financing needs. The remainder of its financing needs will be met by issuing new long-term debt at the end of 2024. (Because the debt is added at the end of the year, there will be no additional interest expense due to the new debt.) Its net profit margin on sales is 5%, and 45% of earnings will be paid out as dividends. a. What were Wallace’s total long-term debt and total liabilities in 2023? b. How much new long-term debt financing will be needed in 2024? (Hint: AFN − New stock = New long-term debt.) Solution: a.

Total liab.

Accounts

Long-term

Common

Retained

debt stock earnings and equity payable $2,170,000 = $560,000 + Long-term debt + $625,000 + $395,000

Long-term debt

= $590,000.

Total liabilities = Accounts payable + Long-term debt = $560,000 + $590,000 = $1,150,000. b.

Assets/Sales (A0*/S0) = $2,170,000/$3,500,000 = 62%. L0*/Sales = $560,000/$3,500,000 = 16%. 2022 Sales = (1.35)($3,500,000) = $4,725,000. AFN = (A0*/S0)(∆S) – (L0*/S0)(∆S) – (M)(S1)(1 – payout) – New common stock = (0.62)($1,225,000) – (0.16)($1,225,000) – (0.05)($4,725,000)(0.55) – $195,000 = $759,500 – $196,000 – $129,937.50 – $195,000 = $238,562.50 Alternatively, using the forecasted financial statement method: 2023

Forecast basis is % of 2023 Sales

Additions

2024

(New Financing and ΔRE)

Sales

$3.500,000

$4,725,000

Total assets

$2,170,000

0.62

$2,929,500

Current liabilities

$ 560,000

0.16

$ 756,000

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

2023

Preliminary long-term debt

Forecast basis is % of 2023 Sales

Additions

2024

(New Financing and ΔRE)

590,000

Total liabilities

$1,150,000

$1,346,000

Common stock

625,000

195,000*

820,000

Retained earnings

395,000

129,937**

524,937

Total common equity

$1,020,000

$1,344,937

Preliminary total liabilities and equity

$2,170,000

$2,690,937

AFN = Total assets – Preliminary total liabilities & equity = S2,929,500 – 2,690,937 = $238,563 AFN = Additional required long-term debt = $238,563 *Given in problem that firm will sell new common stock = $195,000. **PM = 5%; Payout = 45%; NI2019 = $3,500,000 × 1.35 × 0.05 = $236,250. Addition to RE = NI × (1 – Payout) = $236,250 × 0.33 = $129,937. 12-6 Additional Funds Needed. The Booth Company’s sales are forecasted to double from $1,000 in 2023 to $2,000 in 2024. Here is the December 31, 2023, balance sheet: Cash Accounts receivable Inventories Net fixed assets

$ 100 200 200 500

Total assets

$1,000

Accounts payable Notes payable Accruals Long-term debt Common stock Retained earnings Total liabilities and equity

50 150 50 400 100 250 $1,000

Booth’s fixed assets were used to only 50% of capacity during 2023, but its current assets were at their proper levels in relation to sales. All assets except fixed assets must increase at the same rate as sales, and fixed assets would also have to increase at the same rate if the current excess capacity did not exist. Booth’s after-tax profit margin is forecasted to be 5% and its payout ratio to be 60%. What is Booth’s additional funds needed (AFN) for the coming year? (Hint: Forecast next year’s financial statements. Forecast fixed assets taking into account the current year’s capacity level and assuming you’d use up this excess capacity before adding fixed assets.) Solution: Cash Accounts receivable Inventories Net fixed assets* Total assets

$ 100.00 200.00 200.00 500.00 $1,000.00

   

2.0 2.0 2.0 1.0

= = = =

$ 200.00 400.00 400.00 500.00 $1,500.00

Accounts payable Accruals Notes payable Long-term debt Common stock Retained earnings**

$ 50.00 50.00 150.00 400.00 100.00 250.00

  + + + +

2 2 0 0 0 40

= = = = = =

$ 100.00 100.00 150.00 400.00 100.00 290.00

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Total liabilities and equity

$1,000.00 AFN =

$1,140.00 $ 360.00

*Capacity sales = Sales/0.5 = $1,000/0.5 = $2,000 with respect to existing fixed assets. Target FA/S ratio = $500/$2,000 = 0.25. Target FA = 0.25($2,000) = $500 = Required FA. Since the firm currently has $500 of fixed assets, no new fixed assets will be required. Note: If sales were expected to grow only to $1,500 instead of $2,000, then the target FA would be only 0.25 × $1,500 = $375, which is less than the current amount of FA. In this case, you would project FA at $500 (and NOT $375) since that is how much FA is there now. You would not reduce fixed assets. **Addition to RE = (M)(S1)(1 – Payout ratio) = 0.05($2,000)(0.4) = $40.

CHALLENGING PROBLEMS 7–9 12-7 Forecasted Statements and Ratios. Upton Computers makes bulk purchases of small computers, stocks them in conveniently located warehouses, ships them to its chain of retail stores, and has a staff to advise customers and help them set up their new computers. Upton’s balance sheet as of December 31, 2023, is shown here (millions of dollars): Balance Sheets Cash

3.5

Accounts payable

Receivables

26.0

Notes payable

18.0

Inventories

58.0

Line of credit

Total current assets Net fixed assets

Total assets

$ 87.5 35.0

$122.5

Accruals Total current liabilities

9.0

8.5 $ 35.5

Mortgage loan

6.0

Common stock

15.0

Retained earnings

66.0

Total liabilities and equity

$122.5

Sales for 2023 were $350 million, and net income for the year was $10.5 million, so the firm’s profit margin was 3.0%. Upton paid dividends of $4.2 million to common stockholders, so its payout ratio was 40%. Its tax rate was 25%, and it operated at full capacity. Assume that all assets/sales ratios, (spontaneous liabilities)/sales ratios, the profit margin, and the payout ratio remain constant in 2024. a. b.

If sales are projected to increase by $70 million, or 20%, during 2024, use the AFN equation to determine Upton’s projected external capital requirements. Using the AFN equation, determine Upton’s self-supporting growth rate. That is, what is the maximum growth rate the firm can achieve without having to employ nonspontaneous external funds? Use the forecasted financial statement method to forecast Upton’s balance sheet for December 31, 2024. Assume that all additional external capital is raised as a line of credit at the end of the year. (Because the debt is added at the end of the year, there will be no additional interest expense due to

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

the new debt.) Assume Upton’s profit margin and dividend payout ratio will be the same in 2024 as they were in 2023. What is the amount of the line of credit reported on the 2024 forecasted balance sheets? (Hint: You don’t need to forecast the income statements because the line of credit is taken out on the last day of the year and you are given the projected sales, profit margin, and dividend payout ratio; these figures allow you to calculate the 2024 addition to retained earnings for the balance sheet without actually constructing a full income statement.) Solution: a. AFN = (A0*/S0)(S) – (L0*/S0)(S) – (M)(S1)(1 – payout) $122.5 $17.5 $10.5 = ($70) – ($70) – ($420)(0.6) = $13.44 million. $350 $350 $350 b.

Self-supporting g =

M(1  POR)(S 0) A 0 *  L 0 *  M(1 POR)(S 0) =

0.03(1  0.4)(350) 122.5 17.5  0.03(1 0.4)(350)

= 6.38%

c. Upton Computers Pro Forma Balance Sheet December 31, 2023 (Millions of Dollars) Forecast Basis: Percent of Forecasted Sales $ 3.5

0.0100  Sales

Receivables

26.0

0.0743  Sales

Inventories

58.0

0.1657  Sales

Total current assets Net fixed assets

$ 87.5 35.0

0.100  Sales

Total assets

$122.5

Accounts payable

$ 9.0

0.0257  Sales

18.0 0.0 8.5

0.0243  Sales

Cash

Notes payable Line of credit Accruals Total current liabilities Mortgage loan Common stock Retained earnings Total liab. and equity

$ 35.5 6.0 15.0 66.0 $122.5

Forecasted sales = $420 million Profit margin = M = $10.5/$350 = 3%. Payout ratio = $4.2/$10.5 = 40%. NI = Forecasted sales  Profit margin = $350  1.2  0.03 = $12.6. Dividends = NI(Payout ratio) = $12.6(40%) = $5.04. Addition to RE = NI – DIV = $12.6 – $5.04 = $7.56.

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The additional investment in assets is equal to the change in total assets because there are not shortterm investments: Additional investments in assets = $147.0 − $122.5 = $24.5 The additional funding from the increase in spontaneous liabilities and from the reinvested earnings is: Additional funding = [($10.8 + $10.2) – ($9.0 + $8.5)] + $7.56 = $3.5 + $7.56 = $11.06 Financing surplus (deficit) = Additional funding – Additional assets = $11.06 − $24.5 = −$13.44 Because this is negative, it is a financing deficit. This means the LOC should be $13.44.

Upton Computers Pro Forma Balance Sheet December 31, 2024 (Millions of Dollars)

2023

Forecast Basis: Percent of Forecasted Sales

$ 3.5

0.0100

Receivables

26.0

0.0743

31.20

Inventories

58.0

0.1657

69.60

$105.00

42.00

$147.00

Cash

Total current assets

$ 87.5

Net fixed assets

35.0

Total assets

$122.5

0.100

Additions

2024 Pro Forma $

Financing

4.20

2024 Pro Forma After Financing $

4.20

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

2023

Forecast Basis: Percent of Forecasted Sales

Accounts payable

$ 9.0

0.0257

Notes payable

Additions

2024 Pro Forma

2024 Pro Forma After Financing

Financing

$ 10.80

18.0

18.00

Line of credit

0.0

0.00

Accruals

8.5

+13.44

10.20

$ 35.5

$ 39.00

$ 52.44

Mortgage loan

6.0

6.00

Common stock

15.0

15.00

Retained earnings

66.0

73.56

$133.56

$147.00

Total current liabilities

Total liab. and equity

0.0243

+13.44

7.56

$122.5 Deficit =

$ 13.44

12-8 Financing Deficit. Stevens Textile Corporation’s 2023 financial statements are shown here. Stevens grew rapidly in 2023 and financed the growth with notes payable and long-term bonds. Balance Sheet as of December 31, 2023 (Thousands of Dollars) Cash

$ 1,080

Accounts payable

$ 4,320

Receivables

6,480

Accruals

Inventories

9,000

Line of credit

Total current assets

$16,560

Notes payable

2,100

Net fixed assets

12,600

Total current liabilities

Total assets

$29,160

2,880

$ 9,300

Mortgage bonds

3,500

Common stock

3,500

Retained earnings

12,860

Total liabilities and equity

$29,160

Income Statement for December 31, 2023 (Thousands of Dollars) Sales

$36,000

Operating costs

34,000

Earnings before interest and taxes Interest Pre-tax earnings

$ 2,000 160 $ 1,840

Taxes (25%)

460

Net income

$ 1,380

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Dividends Addition to retained earnings

552 $

828

Stevens expects sales to grow by 15% in the next year but will finance the growth with a line of credit, not notes payable or long-term bonds. Use the forecasted financial statement method to forecast a balance sheet and income statement for December 31, 2024. The interest rate on all debt is 10%, and cash earns no interest income. The line of credit is added at the end of the year, which means that you should base the forecasted interest expense on the balance of debt at the beginning of the year. Use the forecasted income statement to determine the addition to retained earnings. Assume that the company was operating at full capacity in 2023, that it cannot sell off any of its fixed assets, and that assets, spontaneous liabilities, and operating costs are expected to increase by the same percentage as sales. a. b. c. d. e. f. g. h.

What is the projected value for earnings before interest and taxes? What is the projected value for pre-tax earnings? What is the projected net income? What is the projected addition to retained earnings? What is the projected value of total current assets? What is the projected value of total assets? What is the projected sum of accounts payable, accruals, and notes payable? What is the forecasted line of credit?

Solution: The first column shows the financial statement accounts and the method used for projections. Projected sales are equal to the actual sales that grow at the specified growth rate. Projected operating costs are equal to a percentage of the projected sales, with the percentage equal to the ratio of actual operating costs to sales in the actual year. Projected cash, receivables, inventories, and fixed assets are determined in the same manner as projected operating costs. Projected interest is equal to the product of the interest rate and the total debt in the actual year because the LOC is added at the end of the projected year. Income Statements (Thousands of Dollars)

Actual

Projected

Sales = $36,000(1.15)

$36,000

$41,400

Op. costs = ($34,000/$36,000)($41,400)

34,000

39,100

Earnings before interest and taxes

$2,000

$2,300

160

560

1,840

$1,740

460

435

$1,380

$1,305

Dividends = 40%(Net income)

552

522

Addition to retained earnings

$828

$783

Balance Sheet Assets (Thousands of Dollars)

Actual

Projected

Cash= ($1,080/$36,000)($41,400)

$1,080

$1,242

Interest = 10%($2,100 + $3,500) Pre-tax earnings Taxes = 25%(Pre-tax earnings) Net income

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Receivables= ($6,480/$36,000)($41,400)

6,480

7,452

Inventories= ($9,000/$36,000)($41,400)

9,000

10,350

Total current assets

$16,560

$19,044

Net fixed assets = ($12,600/$36,000)($41,400)

12,600

14,490

Total assets

$29,160

$33,534

Balance Sheet Liabilities and Equity

Actual

Projected

Accounts payable = ($4,320/$36,000)($41,400)

$4,320

$4,968

Accruals= ($2,880/$36,000)($41,400)

2,880

3,312

Line of credit (see calculation below)

2,511

Notes payable = carry over

2,100

Total current liabilities

$9,300

$12,891

Long-term bonds = carry over

$3,500

Common stock = carry over

$3,500

Retained earnings REActual + Add. to REProj.

$12,860

$13,643

Total liabilities and equity

$29,160

$33,534

LOC = TA – (AP + Accr. + Notes pay. + LT bonds + com. stk + RE) a.

What is the projected value for earnings before interest and taxes? $2,300.

What is the projected value for pre-tax earnings? $1,740.

What is the projected net income? $1,305.

What is the projected addition to retained earnings? $783.

What is the projected value of total current assets? $19,044.

What is the projected value of total assets? $33,534.

What is the projected sum of accounts payable, accruals, and notes payable? $10,380

What is the forecasted line of credit? $2,511.

$2,511

12-9 Financing Deficit. Garlington Technologies Inc.’s 2023 financial statements are shown here. Suppose that in 2024 sales increase to $4.4 million and that 2024 dividends will increase to $200,000. Forecast the financial statements using the forecasted financial statement method. Assume the firm operated at full capacity in 2023. The long-term bonds have an interest rate of 12%. New financing will be with a line of credit. Assume it will be added at the end of the year. Cash does not earn any interest income.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Income Statement for December 31, 2023 Sales

$4,000,000

Operating costs

3,200,000

EBIT

$ 800,000

Interest

120,000

Pre-tax earnings

$680,000

Taxes (25%)

170,000

Net income

$ 510,000

Dividends

$ 190,000

Balance Sheet as of December 31, 2023 Cash

$ 160,000

Accounts payable

Receivables

360,000

Line of credit

Inventories

720,000

Accruals

200,000

Total CA

$1,240,000

Total CL

$ 560,000

Fixed assets

4,000,000

Long-term bonds

$1,000,000

Common stock

$1,100,000

$2,580,000

Total L&E

$5,240,000

Total assets

$5,240,000

360,000

Solution: Income Statements for December 31 in Current and Projected Years Current year

Current % of Sales

Next year

Sales

$4,000,000

Given

$4,400,000

Operating costs

$3,200,000

80%× Proj. Sales

$3,520,000

EBIT

$800,000

$880,000

Interest

$120,000

Pre-tax earnings

$680,000

$760,000

Taxes (25%)

$170,000

$190,000

Net income

$510,000

$570,000

Dividends

$190,000

$200,000

Addn. to RE

$320,000

$370,000

12% × LT bonds

$120,000

Balance Sheet as of December 31 in Current and Projected Years Assets

Current year

Cash

$160,000

Current % of Sales 4%

Next year $176,000

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Receivables

360,000

396,000

Inventories

720,000

18%

792,000

Total CA

$1,240,000

Fixed assets

4,000,000

Total assets

$5,240,000

$1,364,000 100%

4,400,000 $5,764,000

Balance Sheet as of December 31 in Current and Projected Years

Liab. & Equity

Current year

Accounts payable

$360,000

Line of credit

Current % of Sales or Other Method

Next year

$396,000

TA – AP –Accr. – LT bonds – stk – RE

98,000

220,000

Accruals

200,000

Total CL

$560,000

LT bonds

$1,000,000

Carry over

$1,000,000

Common stock

1,100,000

Carry over

$1,100,000

2,580,000

Current RE + Add. To RE

$2,950,000

Total L&E

$5,240,000

$714,000

$5,764,000

The required LOC is $98,000 as shown above.

SOLUTION TO SPREADSHEET PROBLEMS 12-10 Build a Model: Forecasting Financial Statements. Start with the partial model in the file Ch12 P10 Build a Model.xlsx on the textbook’s website, which contains the 2023 financial statements of Zieber Corporation. Forecast Zieber's 2024 income statement and balance sheets. Use the following assumptions: (1) Sales grow by 6%. (2) The ratios of expenses to sales, depreciation to fixed assets, cash to sales, accounts receivable to sales, and inventories to sales will be the same in 2024 as in 2023. (3) Zieber will not issue any new stock or new long-term bonds. (4) The interest rate is 11% for long-term debt, and the interest expense on long-term debt is based on the average balance during the year. (5) No interest is earned on cash. (6) Regular dividends grow at an 8% rate. (7) The tax rate is 25%. Calculate the additional funds needed (AFN). If new financing is required, assume it will be raised by drawing on a line of credit with an interest rate of 12%. Assume that any draw on the line of credit will be made on the last day of the year, so there will be no additional interest expense for the new line of credit. If surplus funds are available, pay a special dividend. a.

What are the forecasted levels of the line of credit and special dividends? (Hints: Create a column showing the ratios for the current year; then create a new column showing the ratios used in the forecast. Also, create a preliminary forecast that doesn't include any new line of credit or special dividends. Identify the financing deficit or surplus in this preliminary forecast and then add a new column that shows the final forecast that includes any new line of credit or special dividend.)

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Now assume that the growth in sales is only 3%. What are the forecasted levels of the line of credit and special dividends?

Solution: The detailed solution is available in the file Ch12 P10 Build a Model Solution.xlsx at the textbook’s website. 12-11 Build a Model: Forecasting and Valuation. Start with the partial model in the file Ch12 P11 Build a Model.xlsx on the textbook’s website, which contains Henley Corporation’s most recent financial statements. Use the following ratios and other selected information for the current and projected years to answer the questions that follow. Actual

Projected

12/31/

2023

2024

2025

2026

2027

15%

10%

Sales growth rate Costs/Sales

72%

Depreciation/(Net PPE)

Cash/Sales

(Accounts receivable)/Sales

(Inventories)/Sales

(Net PPE)/Sales

(Accounts payable)/Sales

Accruals/Sales

Tax rate

Weighted average cost of capital (WACC)

0.5

a. b.

1 0.5

Forecast the parts of the income statement and balance sheet that are necessary for calculating free cash flow. Calculate free cash flow for each projected year. Also calculate the growth rates in free cash flow each year to ensure that there is constant growth (that is, the same as the constant growth rate in sales) by the end of the forecast period. Calculate the return on invested capital (ROIC = NOPAT/[Total net operating capital]) and the growth rate in free cash flow. What is the ROIC in the last year of the forecast? What is the longterm constant growth rate in free cash flow (gL is the growth rate in FCF in the last forecast period because all ratios are constant)? Do you think that Hensley's value would increase if it could add growth without reducing its ROIC? (Hint: Growth will add value if the ROIC > WACC/[1+WACC]). Do you think that the company will have a value of operations greater than its total net operating capital? (Hint: Is ROIC > WACC/[1 + gL]?) Calculate the current value of operations. (Hint: First calculate the horizon value at the end of the forecast period, which is equal to the value of operations at the end of the forecast period. Assume that the annual growth rate beyond the horizon is equal to the growth rate at the horizon.) How does the current value of operations compare with the current amount of total net operating capital? Calculate the intrinsic price per share of common equity as of December 31, 2023.

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Solution: The detailed solution for is available in the file Ch12 P11 Build a Model Solution.xlsx at the textbook’s website.

MINI CASE Hatfield Medical Supply’s stock price had been lagging behind its industry averages, so its board of directors brought in a new CEO, Jaiden Lee. Lee had brought in Ashley Novak, a finance MBA who had been working for a consulting company, to replace the old CFO, and Lee asked Ashley to develop the financial planning section of the strategic plan. In her previous job, Novak’s primary task had been to help clients develop financial forecasts, and that was one reason Lee hired her. Novak began by comparing Hatfield’s financial ratios to the industry averages. If any ratio was substandard, she discussed it with the responsible manager to see what could be done to improve the situation. The following data show Hatfield’s latest financial statements plus some ratios and other data that Novak plans to use in her analysis. Hatfield Medical Supply (Millions of Dollars, Except per Share Data) Balance Sheet, 12/31/2023

Income Statement, Year Ending 2023

Cash

$ 90

Sales

$9,000.9

Accounts receivable

1,260

Op costs (excl. depr.)

8,100.9

Inventories

1,440

Depreciation

360.0

Total CA

$2,790

EBIT

$540.0

Net fixed assets

3,600

Interest

144.0

Total assets

$6,390

Pre-tax earnings

$396.0

Taxes (25%)

99.0

Net income

$ 297.0

Accts. pay. & accruals Line of credit

$1,620 0

Total CL

$1,620

Additional Information

Long-term debt

1,800

Dividends

$100

Total liabilities

$3,420

Additions to RE

$197

Common stock

2,100

Common shares

Retained earnings

870

EPS

$5.94

Total common equity.

$2,970

DPS

$2.00

Total liab. & equity

$6,390

Ending stock price

$41.00

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Hatfield Medical Supply: Selected Additional Data (Millions of Dollars), December 31 Hatfield

Ind.

Hatfield

Ind.

(Op. costs)/Sales

90%

88%

Profit margin (M)

3.30%

5.60%

Depr./FA

10%

12%

Return on assets (ROA)

4.6%

9.5%

Cash/Sales

Return on equity (ROE)

10.0%

15.1%

Receivables/Sales

14%

11%

Sales/Assets

1.41

1.69

Inventories/Sales

16%

15%

Asset/Equity

2.15

1.59

Fixed assets/Sales

40%

32%

Debt/TA

28.2%

16.9%

(Acc. pay. & accr.)/Sales

18%

12%

(Total liabilities)/(Total assets)

53.5%

37.3%

Tax rate

25%

Times interest earned

3.8

11.7

Target WACC

10%

11%

P/E ratio

6.9

16.0

Interest rate on debt

OP ratio: NOPAT/Sales

4.5%

6.1%

CR ratio: (Total op. capital)/Sales

53.0%

47.0%

ROIC

8.5%

13.0%

Using Hatfield’s data and its industry averages, how well run would you say Hatfield appears to be in comparison with other firms in its industry? What are its primary strengths and weaknesses? Be specific in your answer, and point to various ratios that support your position. Also, use the DuPont equation (see Chapter 3) as one part of your analysis. Answer: Hatfield has lower operating profitability as shown by operating profitability ratio (OP): 4.5% vs. 6.1%. Hatfield utilizes operating capital less efficiently, as shown by capital requirement ratio (CR): 53% vs. 47%. As a consequence, Hatfield has a lower ROIC: 8.5% vs. 13%. In fact, Hatfield’s ROIC is less than its 10% WACC. The debt/TA ratio and the TL/TA ratio indicate that Hatfield has more leverage than its industry competitors. The combination of higher interest payments and lower operating profitability causes Hatfield’s times interest earned ratio to be much lower than the industry average. ROEHatfield = Profit margin = 3.30% = 10.0%.

× ×

Asset turnover 1.41

× (Equity multiplier) × 2.15

ROEIndustry = Profit margin

Asset turnover

× (Equity multiplier)

1.69

= =

5.60% 15.1

1.59

From the DuPont equation, you can see that Hatfield’s profitability and asset management ratios are lower than the industry average and its leverage is higher than the industry average. The combined effect results in a much lower return on equity for the firm relative to the industry average. b.

Use the AFN equation and the Selected Additional Data to estimate Hatfield’s required new external capital for 2024 if the sales growth rate is 11.1%. Assume that the firm’s 2023 ratios will remain the same in 2024. (Hint: Hatfield was operating at full capacity in 2023.)

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Answer: Data for AFN Equation Growth rate in sales (g)

11.1%

Sales (S0)

$9,001

Required assets (A0*)

$6,390

Spontaneous liabilities (L0*)

$1,620

Forecasted sales (S1)

$10,000

Increase in sales (∆S = gS0)

$999

Profit margin (M)

3.30%

Assets/Sales (A0*/S0)

71.0%

Payout ratio (POR)

33.7%

Spont. Liab./Sales (L0*/S0)

18.0%

Here is the AFN equation: AFN = (A0*/S0)∆S – (L0*/S0)∆S – M(S1)(1 – Payout) = (0.71)($999) – (0.18)($999) – (0.033)($10,000)(1 − 0.337) = $709.29 – $179.82 – $218.79 = $310.68 million. c.

Define the term capital intensity. Explain how a decline in capital intensity would affect the AFN, other things held constant. Would economies of scale combined with rapid growth affect capital intensity, other things held constant? Also, explain how changes in each of the following would affect AFN, holding other things constant: the growth rate, the amount of accounts payable, the profit margin, and the payout ratio. Answer: The capital intensity ratio is the amount of assets required per dollar of sales, A0*/S0, and it has a major effect on capital requirements. A decline in the capital intensity ratio would lower the need for external capital as this would mean a smaller amount of assets would be required per dollar of sales. Economies of scale combined with rapid growth would mean that it is likely that the capital intensity ratio would change over time as the size of the firm increased. Rapidly growing companies require large increases in assets and a corresponding large amount of external financing, other things held constant. Accounts payable are spontaneous liabilities that come about due to normal day-to-day business operations. Firms don’t have a lot of control over the level of spontaneous liabilities as they’re a function of industry norm and tax laws. The higher the firm’s level of accounts payable (spontaneous liabilities), the smaller the amount of external financing, other things held constant. The higher the profit margin, the larger the net income available to support increases in assets; hence, the less the need for external financing, other things held constant. The less of its income a company distributes as dividends, the larger its addition to retained earnings; hence, the smaller the need for external capital— other things held constant.

Define the term self-supporting growth rate. What is Hatfield’s self-supporting growth rate? Would the self-supporting growth rate be affected by a change in the capital intensity ratio or the other factors mentioned in the previous question? Other things held constant, would the calculated capital intensity ratio change over time if the company were growing and were also subject to economies of scale and/or lumpy assets?

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Answer: The self-supporting growth rate is the maximum growth rate the firm could achieve if it had no access to external capital. From the data given, Hatfield’s self-supporting growth rate is calculated as: Self-supporting g = [M(1 – POR)(S0)]/[A0* – L0* – M(1 – POR)(S0)] M=

3.30%

POR =

33.7%

1-POR =

66.3%

S0 =

$9,001

A0* =

$6,390

L0* =

$1,620

Self-supporting g = [M(1 – POR)(S0)]/[A0* – L0* – M(1 – POR)(S0)] = [(0.033)(0.663)($9001)]/[$6,390 – $1,620 – 0.033(0.663)($9001)] = $196.93/$4,573.07 = 0.0431 = 4.3%. The higher the firm’s capital intensity ratio, the lower the firm’s self-supporting growth rate because the firm would require more assets per dollar of sales. The higher the firm’s profit margin and the lower its payout ratio, the higher the firm’s self-supporting growth rate. The calculated capital intensity ratio will change over time if the firm company is expanding and if economies of scale and lumpy assets exist. When economies occur, the capital intensity ratio will change over time as the size of the firm increases. In many industries, technological considerations dictate that if a firm is to be competitive, it must add fixed assets in large, discrete units. These assets are referred to as lumpy assets. When this occurs, the firm’s capital intensity ratio will change. So, at the point where the assets must increase in a large amount, the capital intensity ratio will be high, so required external financing will be high. As sales increase but assets don’t need to increase, the capital intensity ratio will fall—until sales reach the point where large increases in assets are required again.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Use these assumptions to answer the following questions: (1) Operating ratios remain unchanged. (2) Sales will grow by 11.1%, 8%, 5%, and 5% for the next 4 years. (3) The target weighted average cost of capital (WACC) is 10%. This is the No Change scenario because operations remain unchanged.

Actual Inputs

2023

Sales growth rate:

2024

2025

2026

2027

11.1%

(Op. costs)/Sales:

90.00%

90.0%

90%

Depr./FA

10.00%

10%

Cash/Sales:

1.00%

(Acct. rec.)/Sales

14.00%

14%

Inv./Sales:

16.00%

16%

FA/Sales:

40.00%

40%

(AP & accr.)/Sales:

18.00%

18%

Tax rate:

25.00%

25%

10%

Rate on all debt Div. growth rate:

5.00%

Target WACC

Forecast

For each of the next 4 years, forecast the following items: sales, cash, accounts receivable, inventories, net fixed assets, accounts payable and accruals, operating costs (excluding depreciation), depreciation, and earnings before interest and taxes (EBIT).

Answer: Forecast sales as: Salest = Salest-1(1 + gt). For example, Sales2024 = $9,00.9(1 + 0.111) = $10,000. Forecast other items as a percent of sales (or as percent of fixed assets for depreciation). For example, Inventories2024 = $10,000(0.16) = $1,600.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Actual

Forecast

2023

2024

2025

2026

2027

Net sales

$9,000.9

$10,000

$10,800

$11,340

$11,907

Op. costs (excl. depr.)

$8,100.9

$9,000

$9,720

$10,206

$10,716

Depreciation

$360.0

$400

$432

$454

$476

EBIT

$540.0

$600

$648

$680

$714

Cash

$90.0

$100

$108

$113

$119

Accounts receivable

$1,260.0

$1,400

$1,512

$1,588

$1,667

Inventories

$1,440.0

$1,600

$1,728

$1,814

$1,905

Net fixed assets

$3,600.0

$4,000

$4,320

$4,536

$4,763

Accts. pay. & accruals

$1,620.0

$1,800

$1,944

$2,041

$2,143

Using the previously forecasted items, calculate for each of the next 4 years the net operating profit after taxes (NOPAT), net operating working capital, total operating capital, free cash flow (FCF), annual growth rate in FCF, and return on invested capital. What does the forecasted free cash flow in the first year imply about the need for external financing? Compare the forecasted ROIC with the WACC. What does this imply about how well the company is performing?

Answer: NOPAT = EBIT(1-T) NOWC = (Cash + accounts receivable + inventories) − (Accounts payable & accruals) Total operating capital = NOWC + Net fixed assets FCF = NOPAT − Change in total operating capital ROIC = NOPAT/(Total operating capital) Scenario:

Actual

No Change

2023

2024

2025

2026

2027

NOPAT

$405

$450

$486

$510

$536

NOWC

$1,170

$1,300

$1,404

$1,474

$1,548

Total op. capital

$4,770

$5,300

$5,724

$6,010

$6,311

–$80

$62

$224

$235

261.5%

5.0%

FCF

Forecast

Growth in FCF ROIC

8.5%

ROIC – WACC

–1.5%

Forecasted ROIC is less than the WACC: 8.5% < 10% The company is not adding value to its investors. e.

Assume that FCF will continue to grow at the growth rate for the last year in the forecast horizon (Hint: gL = 5%). What is the horizon value at 2027? What is the present value of the horizon value? What is the present value of the forecasted FCF? (Hint: Use the free cash flows for 2024 through 2027). What is the current value of operations? Using information from the 2023 financial statements, what is the current estimated intrinsic stock price?

Answer:

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

With no rounding in intermediate steps, FCF2027 = $235.305. ( (

) )

(

)

(

)

Scenario: No Change

Present value of HV

$3,375.05

+ Present value of FCF

307.60

Value of operations =

$3,682.64

+ ST investments

Estimated total intrinsic value

$3,682.645

− All debt

1,800.000

− Preferred stock

0.000

Estimated intrinsic value of equity

$1,882.645

÷ Number of shares

Estimated intrinsic stock price =

$37.65

The estimated intrinsic stock value of $37.65 is less than the actual market price of $41. The market price indicates that the market expected the operating performance to improve; if operating performance doesn’t improve, the market price is likely to drop. But keep in mind that stocks prices are very volatile, so a difference of 8.2% ($37.65/$41 – 1 = −8.2%) is not especially large. f.

Continue with the same assumptions for the No Change scenario from the previous question, but now forecast the balance sheet and income statements for 2024 (but not for the following 3 years) using the following preliminary financial policy. (1) Regular dividends will grow by 10%. (2) No additional long-term debt or common stock will be issued. (3) The interest rate on all debt is 8%. (4) Interest expense for long-term debt is based on the average balance during the year. (5) If the operating results and the preliminary financing plan cause a financing deficit, eliminate the deficit by drawing on a line of credit. The line of credit would be tapped on the last day of the year, so it would create no additional interest expenses for that year. (6) If there is a financing surplus, eliminate it by paying a special dividend. After forecasting the 2024 financial statements, answer the following questions.

How much will Hatfield need to draw on the line of credit?

Answer: Forecast the items on the income statement. Costs are a percent of sales and depreciation is a percent of Net PP&E. Forecast interest expense on the long-term debt as the product of the interest rate and the average balance on the long-term debt (i.e., the average of the beginning value and the ending value). Pay a regular dividend. Leave the special dividend blank for now. Income Statement

2023

Input

Basis for 2024 Forecast

Sales

$9,000.9

110%

× 2023 Sales

$10,000

Op. costs (excl. depr.)

8,100.9

90%

× 2024 Sales

9,000

360.0

10%

× 2024 Net fixed assets

Depreciation

2024

400

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

EBIT

540

Less: Interest on LTD Interest on LOC Pretax earnings

144.0

× Avg bonds

× Beginning LOC

0 $

99.0

Net income (NI)

297.0

Regular common divs.

100.0

Special dividends $

600 144

396.0

Taxes (25%)

Addition to RE

25%

110%

456

× Pretax earnings

114

× 2023 regular common div.

0.0

Left blank for now

197.0

Net income – reg. div.

342

110 ?

232

Use the sales forecast to project items on the balance sheet that are proportional to sales. The forecast for sales is $10,000. Forecast the operating items as a percentage of sales. The preliminary financial policy specifies no change in the long-term debt or common stock. The preliminary estimate of retained earnings is based on the increase by the addition to retained earnings from the forecasted income statement. Leave the line of credit blank for now. Assets

2023

Input

× 2024 Sales

Accts. rec.

1,260

14%

× 2024 Sales

1,400

Inventories

1,440

16%

× 2024 Sales

1,600

Total CA

$2,790

Net fixed assets

3,600

Total assets

$6,390

Cash

Basis for Forecast

2024 $

100

$3,100 40%

× 2024 Sales

4,000 $7,100

Now forecast preliminary estimates of liabilities and equity assuming no draw yet on the line of credit. Liabilities and equity

2023

Input

Basis for Forecast

Accts. pay. & accruals

$1,620

18%

× 2024 Sales

Line of credit

Add LOC if fin. deficit

$1,800 ?

Total CL

$1,620

$1,800

Long-term debt

1,800

Total liabilities

$3,420

Common stock

$2,100

No Change

$2,100

Retained earnings

$ 870

Old RE + Add. to RE

1,102

Total common equity

$2,970

$3,202

Total liabs. & equity

$6,390

$6,802

No Change

1,800 $3,600

Based on the preliminary forecast, compare total liabilities & equity to total assets.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Check: Preliminary TL & Equ. – Preliminary TA = $6,802 − $7,100 = −$298 In this example, the difference is negative (−$298), which means the preliminary value for TL & Equity is too small. Therefore, Hatfield will need to obtain additional financing by drawing on its line of credit. (If the difference had been positive, Hatfield would have paid a special dividend.) There is a deficit, so update the balance sheets by adding $298 to the line of credit. Because the LOC is added at the end of the year, there is no additional interest, which means that there is no need to update the income statement. If the LOC were instead added earlier in the year, there would be additional interest, which would cause lower net income, which would cause a lower addition to retained earnings, which would cause a bigger financial deficit. This is called financing feedback. See Ch12 Tool Kit.xls and look at the worksheet CFO Model for a simple way to resolve financing feedback and for an extension of the 1year forecasted financial statements to multiple years. After drawing on its line of credit, the balance sheets are shown next. Assets Cash Accts. rec. Inventories Total CA Net fixed assets

2024 $ 100 1,400 1,600 $3,100 4,000

Total assets

$7,100

Liabilities and equity Accts. pay. & accruals Line of credit Total CL Long-term debt Total liabilities Common stock Retained earnings Total common equity Total liabs. & equity

2024 $ 1,800 298 $ 2,098 1,800 $ 3,898 2,100 1,102 $ 3,202 $ 7,100

Sometimes it is easier to present your results to others without making them watch you work your way through a full set of financial statements. Instead, you can provide a summary. Start with the additions to operating assets, subtract the increase in spontaneous liabilities (accounts payable and accruals), subtract any new external financing from long-term debt or common stock, subtract the previous line of credit because the preliminary financial plan does not call for any LOC, and subtract the amount of reinvested net income (the amount that is not paid out in common dividends). The result is the financing deficit (if it is negative) or the financing surplus (if it is positive). If there is a deficit, draw on the LOC. If there is a surplus, pay a special dividend. Using this approach, this simplified presentation of surplus/deficit identification is shown next. Start with the increase in spontaneous liabilities. Alternative Approach to Identify Surplus or Deficit (1) Increase in spontaneous liabilities (accounts payable and accruals) (2) + Increase in long-term debt and common stock (3) − Previous LOC (4) + Net income minus regular common dividends (5) Increase in financing (6) − Increase in total assets (7) Amount of deficit or surplus financing: (8) If deficit in financing (negative), draw on line of credit (9) If surplus in financing (positive), pay special dividend

$180 $0 $0 $232 $412 $710 −$298 $298 $0

This approach shows that there is a deficit of $298, which agrees with the previous projections shown in the complete financial statements. But the projection here is in a condensed style, which makes it better for presentations. Of course, you should have the full analysis available in case someone wants to see it.

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What are some alternative ways than those in the preliminary financial policy that Hatfield might choose to eliminate the financing deficit?

Answer: Here are some alternative ways to eliminate the deficit: Cut dividends. Add long-term debt. Issue common stock. Cut back on growth in the operating plan. Improve the operating plan. g.

Repeat the analysis performed in the previous question, but now assume that Hatfield is able to improve the following inputs: (1) Reduce operating costs (excluding depreciation) to sales to 89.4% at a cost of $40 million. (2) Reduce inventories/sales to 14% at a cost of $10 million. (3) Reduce net fixed assets/sales to 38% at a cost of $20 million. This is the Improve scenario.

(1)

Should Hatfield implement the improvement plan? How much value would it add to the company?

(2)

How much can Hatfield pay as a special dividend in the Improve Scenario? What else might Hatfield do with the financing surplus?

Should Hatfield implement the improvement plan? How much value would it add to the company?

Answer: To answer this question, project the financial statement using the improved inputs, shown in red. Scenario: Improve Balance Sheets Assets Cash Accts. rec. Inventories Total CA Net fixed assets Total assets

2023 $90 $1,260 $1,440 $2,790 $3,600 $6,390

Input 1% 14% 14%

Basis for 2024 Forecast × 2024 Sales × 2024 Sales × 2024 Sales

38%

× 2024 Sales

2023 $1,620 $0 $1,620 $1,800 $3,420 $2,100 $870 $2,970

Input 18%

Basis for 2024 Forecast × 2024 Sales Draw on LOC if fin. def.

2024 $100 $1,400 $1,400 $2,900 $3,800 $6,700

Scenario: Improve Liabilities and equity Accts. pay. & accrls. Line of credit Total CL Long-term debt Total liabilities Common stock Retained earnings Total com. equity

Carry over from prev. year Carry over from prev. year Old RE + Add. to RE

2024 $1,800 0 $1,800 $1,800 $3,600 2,100 1,000 $3,100

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Total liabs. & eq.

$6,390

$6,700

Scenario: Improve Income Statement

2023

Input

Basis for 2024 Forecast

2024

Sales

$9,000.9

1.111

× 2023 Sales

$10,000

Op. costs (excl. depr.)

8,100.9

89.4%

× 2024 Sales

8,940

Depreciation

360.0

10.00%

× 2024 Net FA

380

EBIT

$540.0

$680

Less: Interest on LTD

144.0

8.00%

× Avg bonds

144

Interest on LOC

0.0

8.00%

× Beginning LOC

Pretax earnings

$396.0

$ 536

Taxes (25%)

99.0

25.00%

× Pretax earnings

134

Net income

$297.0

Regular common dividends

$100.0

Special dividends

$0.0

$162

Addition to RE

$197.0

$130

$402 110%

× 2023 Dividends

$110

Improve

No Change

Net Change in Value

Value of operations

$5,662

$3,683

$1,980

Cost of Improvement

–$70

Total value

$5,592

–$70 $3,683

$1,910

The plan adds a net value of $1,910, so it should be adopted. g.

How much can Hatfield pay as a special dividend in the Improve scenario? What else might Hatfield do with the financing surplus?

Answer: Hatfield can pay a special dividend of $162. Instead, Hatfield could: (1) Repurchase stock. (2) Repay some of their debt if the debt level exceeds their optimum level as described in Chapter 15. (3) Use some of it to buy short-term securities as a safety measure to help the company if their results fall in the future due to a worsening economy or changes in demand for their products. (4) Pay part of it as bonuses to employees. (5) Pay all or part of the costs for employees to continue their education. (6) Make a donation to Habitat for Humanity to sponsor some homes. (7) Take the senior executives and their spouses on a "retreat" at a luxurious location with great scuba diving and stay for 2 weeks. Just kidding. Unless they invite my wife and me, too.

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Solution and Answer Guide CHAPTER 13: CORPORATE GOVERNANCE

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 322 MINI CASE ............................................................................................................................................. 324

ANSWERS TO END-OF-CHAPTER QUESTIONS 13-1 Define each of the following terms: a. Agent; principal; agency relationship b. Agency cost c. Basic types of agency conflicts d. Managerial entrenchment; nonpecuniary benefits e. Greenmail; poison pills; restricted voting rights f. Stock option; ESOP Answer: a. An agency relationship arises whenever one or more individuals, the principals, hire another individual, the agent, to perform some service and then delegate decision-making authority to that agent. Primary agency relationships exist between (1) stockholders and managers and (2) between debtholders and stockholders. b.

Agency costs include all costs borne by shareholders to encourage managers to maximize a firm’s stock price rather than act in their own self-interests. The three major categories of agency costs are (1) expenditures to monitor managerial actions, such as audit costs; (2) expenditures to structure the organization in a way that will limit undesirable managerial behavior, such as appointing outside investors to the board of directors; and (3) opportunity costs that are incurred when shareholderimposed restrictions, such as requirements for stockholder votes on certain issues, limit the ability of managers to take timely actions that would enhance shareholder wealth.

An agency problem arises whenever a manager of a firm owns less than 100% of the firm’s common stock, creating a potential conflict of interest called an agency conflict. The fact that the manager will neither gain all the benefits of the wealth created by his or her efforts nor bear all of the costs of perquisite consumption will increase the incentive to take actions that are not in the best interests of the nonmanager shareholders. In addition to conflicts between stockholders and managers, there can also be conflicts between stockholders (through managers) and creditors. Creditors have a claim on part of the firm’s earnings stream for payment of interest and principal on debt, and they have a claim on the firm’s assets in the event of bankruptcy. However, stockholders have control (through managers) of decisions that affect the riskiness of the firm.

Managerial entrenchment occurs when a company has such a weak board of directors and has such strong anti-takeover provisions in its corporate charter that senior managers feel there is very little chance that they will be removed.

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Nonpecuniary benefits are perks that are not actual cash payments, such as lavish offices, memberships at country clubs, corporate jets, and excessively large staffs. e.

Targeted share repurchases, also known as greenmail, occur when a company buys back stock from a potential acquiror at a higher than fair-market price. In return, the potential acquiror agrees not to attempt to take over the company. Shareholder rights provisions, also known as poison pills, allow existing shareholders in a company to purchase additional shares of stock at lower than market value if a potential acquiror purchases a controlling stake in the company. A restricted voting rights provision automatically deprives a shareholder of voting rights if the shareholder owns more than a specified amount of stock.

A stock option allows its owner to purchase a share of stock at a fixed price, called the strike price, no matter what the actual price of the stock is. Stock options always have an expiration date, after which they cannot be exercised. A restricted stock grant allows an employee to buy shares of stock at a large discount from the current stock price, but the employee is restricted from selling the stock for a specified number of years. An employee stock ownership plan, often called an ESOP, is a type of retirement plan in which employees own stock in the company.

13-2 What is the possible agency conflict between inside owner/managers and outside shareholders? Answer: Owner/managers benefit from higher wealth due to ownership, but they also benefit from the perks they consume, such as lavish offices, vacations, golf club memberships, etc. If the owner/manager is the only manager, then the owner/manager bears full cost of the perks. But if the owner/manager only owns part of the company, the owner/manager reaps all the benefits of the perks but the cost is shared by the outside shareholders. Potential investors know this might happen, so they pay less for a minority interest in a company. 13-3 What are some possible agency conflicts between borrowers and lenders? Answer: After the loan is originated, borrowers might make decisions that are harmful to the lender. For example, borrowers might invest in risky projects. From the borrower’s point of view, risky projects are like options. If the project pays off big, most of the benefits accrue to the borrowers (the creditors just get the principal back). If the project fails by a little or by a lot, the borrower doesn’t get anything. So, borrowers have an incentive to take on riskier projects. Borrowers also might take on additional debt. Lenders anticipate this, and charge a higher interest rate. 13-4 What are some actions an entrenched management might take that would harm shareholders? Answer: Entrenched managers consume too many perquisites, such as lavish offices, excessive staffs, country club memberships, and corporate jets. They also invest in projects or acquisitions that make the firm larger, even if they don’t make the firm more valuable. 13-5 How is it possible for an employee stock option to be valuable even if the firm’s stock price fails to meet shareholders’ expectations? Answer:

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Stock options in compensation plans usually are issued with a strike price equal to the current stock price. As long as the stock price increases, the option will become valuable, even if the stock price doesn’t increase as much as investors expect.

MINI CASE Suppose you decide (like Steve Jobs and Mark Zuckerberg did) to start a company. Your product is a software platform that integrates a wide range of media devices, including laptop computers, desktop computers, digital video recorders, and cell phones. Your initial market is the student body at your university. Once you have established your company and set up procedures for operating it, you plan to expand to other colleges in the area, and eventually to go nationwide. At some point, hopefully sooner rather than later, you plan to go public with an IPO and then to buy a yacht and take off for the South Pacific to indulge in your passion for underwater photography. With these issues in mind, you need to answer for yourself, and potential investors, the following questions. a.

Briefly describe the election process for boards of directors. Answer: For most companies, every seat on the board comes up for election each year. Ballots are provided to shareholders with only the company’s nominees listed. The only way to vote for a different candidate it to do it with a write-in vote. In most situations, all shareholders have 1 vote for each share owned. However, sometimes different share classes have different voting rights. For example, Class A shares might have 1 vote per share but Class B shares might have 10 votes per share. When a company goes public, the founders will often keep the class of shares with superior voting rights and sell a class of shares with inferior voting rights in the IPO to the public. Noncumulative voting means that a shareholder can cast 1 vote per candidate. If there are 10 board members being elected, a shareholder can cast 1 vote for each candidate. Cumulative voting means that a shareholder can cast 10 votes for a single candidate and none for the other candidates.

How diverse are boards of directors? How is this changing? Answer: White men make up a larger percentage of the average board of directors than their percentage of the total population. Women and other ethnic groups make up a smaller percentage of the average board of directors than their percentage of the total population. Panel A: All Directors: Ethnicity

Number

Percent

Black

564

10.6%

Latino

243

4.6

Asian

286

5.4

0.1

1098

20.6%

4,222

79.4

5,320

100.0%

Gender

Number

Percent

Men

3,724

70%

Women

1,596

30%

Two or more Non-white subtotal White Total

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Total

5,320

100%

Board composition is becoming more representative of the general population. But it will take more years of new directors before boards represent the general population. Panel B: New Directors: Ethnicity

Number

Percent

Black

140

31%

Other non-white

214

47%

242

456

100%

Gender

Percent

Men

260

57%

Women

196

456

100%

Non-white subtotal White Total

Total c.

What is an agency relationship? When you first begin operations, assuming you are the only employee and only your money is invested in the business, would any agency conflicts exist? Explain your answer. Answer: An agency relationship arises whenever one or more individuals, called principals, (1) hires another individual or organization, called an agent, to perform some service and (2) then delegates decision-making authority to that agent. No agency problem would exist. A potential agency problem arises whenever the manager of a firm owns less than 100% of the firm’s common stock, or the firm borrows. Since you are the only employee and only your money is invested in the business, you own 100% of the firm. As a single proprietor, presumably you will operate the business so as to maximize your own welfare, with welfare measured in the form of increased personal wealth, more leisure, or perquisites.

If you expanded and hired additional people to help you, might that give rise to agency problems? Answer: By expanding the business and hiring additional employees, this might give rise to agency problems. An agency relationship could exist between you and your employees if you, the principal, hired the employees to perform some service and delegated some decision-making authority to them.

Suppose you need additional capital to expand, and you sell some stock to outside investors. If you maintain enough stock to control the company, what type of agency conflict might occur? Answer: As the owner/manager you benefit from your increased wealth due to the company, but you also benefit from perquisites, such as more leisure, luxurious offices, executive assistants, expense accounts, limousines, corporate jets, and a generous retirement plan. However, if the owner/manager incorporates the business and then sells some of the stock to outsiders, a potential conflict of interest immediately arises. Notice that the value of the perquisites still accrues to the owner/manager, but the cost of the perquisites is now partially born by the outsiders. This might even induce the owner/manager to increase consumption of perquisites.

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Suppose your company raises funds from outside lenders. What type of agency costs might occur? How might lenders mitigate the agency costs? Answer: An agency conflict occurs between the borrow and the lender because the borrower makes decisions after the loan is made that affect the lender’s welfare. For example, the borrower could invest in risky projects or take on additional debt. Anticipating such behavior, creditors might charge a higher-than-normal interest rate to compensate for the possible risk. This high interest rate is an agency cost. Creditors can protect themselves by (1) having the loan secured and (2) placing restrictive covenants in debt agreements.

Suppose your company is very successful, and you cash out most of your stock and turn the company over to an elected board of directors. Neither you nor any other stockholders own a controlling interest (this is the situation at most public companies). List six potential managerial behaviors that can harm a firm’s value. Answer: Managers might: 1. Expend too little time and effort. 2. Consume too many nonpecuniary benefits. 3. Avoid difficult decisions (e.g., close plant) out of loyalty to friends in company. 4. Reject risky positive NPV projects to avoid looking bad if project fails; take on risky negative NPV projects to try and hit a home run. 5. Avoid returning capital to investors by making excess investments in marketable securities or by paying too much for acquisitions. 6. Massage information releases or manage earnings to avoid revealing bad news.

What is corporate governance? List five corporate governance provisions that are internal to a firm and under its control. Answer: Corporate governance is the set of laws, rules, and procedures that influence a company’s operations and the decisions made by its managers. The provisions under a firm’s control are: (1) monitoring and discipline by the board of directors; (2) charter provisions and bylaws that affect the likelihood of hostile takeovers; (3) compensation plans; (4) capital structure choices; and (5) accounting control systems.

What characteristics of the board of directors usually lead to effective corporate governance? Answer: (1) The CEO is not also the chairman of the board and does not have undue influence over the nominating committee; (2) the board has a majority of true outsiders who bring some type of business expertise to the board (and the board is not an interlocked board); (3) the board is not too large; and (4) board members are compensated appropriately (not too high, and some compensation is linked to company’s performance).

List three provisions in the corporate charter that affect takeovers. Answer: These include targeted share repurchases (i.e., greenmail), shareholder rights provisions (i.e., poison pills), and restricted voting rights plans.

Briefly describe the use of stock options in a compensation plan. What are some potential problems with stock options as a form of compensation? Answer: Gives the owner of the option the right to buy a share of the company’s stock at a specified price (called the strike price) even if the actual stock price is higher. Owners of stock options usually can’t exercise the option for several years (called the vesting period) and They can’t exercise the option after a certain number of years (called the expiration, or maturity, date).

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A manager can underperform the market or peer group, yet still reap rewards from options as long as the stock price increases to above the exercise cost. Options sometimes encourage managers to falsify financial statements or take excessive risks. l.

What is block ownership? How does it affect corporate governance? Answer: Block ownership occurs when an outside investor owns a large amount (i.e., block) of a company’s shares. Large institutional investors, such as CalPERS or TIAA-CREF, often own large blocks. Blockholders often monitor managers and take an active role, leading to better corporate governance.

m. Briefly explain how regulatory agencies and legal systems affect corporate governance. Answer: Companies in countries with strong protection for investors tend to have better access to financial markets, a lower cost of equity, increased in market liquidity, and less noise in stock prices.

Solution and Answer Guide CHAPTER 14: DISTRIBUTIONS TO SHAREHOLDERS : DIVIDENDS AND REPURCHASES

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 327 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 330 Easy Problems 1–5 ................................................................................................................................ 330 Intermediate Problems 6–9 ................................................................................................................... 332 Challenging Problems 10–12 ................................................................................................................ 333 SPREADSHEET PROBLEM ................................................................................................................ 337 MINI CASE ............................................................................................................................................. 337

ANSWERS TO END-OF-CHAPTER QUESTIONS 14-1 Define each of the following terms: a. Optimal distribution policy b. Dividend irrelevance theory; bird-in-the-hand theory; tax effect theory c. Signaling hypothesis; clientele effect d. Residual distribution model; extra dividend e. Declaration date; holder-of-record date; ex-dividend date; payment date f. Dividend reinvestment plan (DRIP) g. Stock split; stock dividend; stock repurchase Answer: a. The optimal distribution policy is one that strikes a balance between dividend yield and capital gains so that the firm’s stock price is maximized.

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The dividend irrelevance theory holds that dividend policy has no effect on either the price of a firm’s stock or its cost of capital. The principal proponents of this view are Merton Miller and Franco Modigliani (MM). They prove their position in a theoretical sense, but only under strict assumptions, some of which are clearly not true in the real world. The ―bird-in-the-hand‖ theory assumes that investors value a dollar of dividends more highly than a dollar of expected capital gains because the dividend yield component, D1/P0, is less risky than the g component in the total expected return equation r S = D1/P0 + g. The tax effect theory proposes that investors prefer capital gains over dividends because capital gains taxes can be deferred into the future, but taxes on dividends must be paid as the dividends are received.

The signaling hypothesis holds that investors regard dividend changes as ―signals‖ of management forecasts. Thus, when dividends are raised, this is viewed by investors as recognition by management of future earnings increases. Therefore, if a firm’s stock price increases with a dividend increase, the reason may not be investor preference for dividends, but expectations of higher future earnings. Conversely, a dividend reduction may signal that management is forecasting poor earnings in the future. The clientele effect is the attraction of companies with specific dividend policies to those investors whose needs are best served by those policies. Thus, companies with high dividends will have a clientele of investors with low marginal tax rates and strong desires for current income. Similarly, companies with low dividends will attract a clientele with little need for current income, and who often have high marginal tax rates.

The residual distribution model states that firms should make distributions only when more earnings are available than needed to support the optimal capital budget. An extra dividend is a dividend paid, in addition to the regular dividend, when earnings permit. Firms with volatile earnings may have a low regular dividend that can be maintained even in lowprofit (or high capital investment) years, and then supplement it with an extra dividend when excess funds are available.

The declaration date is the date on which a firm’s directors issue a statement declaring a dividend. If a company lists the stockholder as an owner on the holder-of-record date, then the stockholder receives the dividend. The ex-dividend date is the date when the right to the dividend leaves the stock. This date was established by stockbrokers to avoid confusion and is 1 business day prior to the holder of record date. If the stock sale is made prior to the ex-dividend date, the dividend is paid to the buyer. If the stock is bought on or after the ex-dividend date, the dividend is paid to the seller. The date on which a firm actually mails dividend checks is known as the payment date.

Dividend reinvestment plans (DRIPs) allow stockholders to automatically purchase shares of common stock of the paying corporation in lieu of receiving cash dividends. There are two types of plans—one involves only stock that is already outstanding, while the other involves newly issued stock. In the first type, the dividends of all participants are pooled and the stock is purchased on the open market. Participants benefit from lower transaction costs. In the second type, the company issues new shares to the participants. Thus, the company issues stock in lieu of the cash dividend.

In a stock split, current shareholders are given some number (or fraction) of shares for each stock owned. Thus, in a 3-for-1 split, each shareholder would receive three new shares in exchange for each old share, thereby tripling the number of shares outstanding. Stock splits usually occur when the stock price is outside of the optimal trading range.

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Stock dividends also increase the number of shares outstanding, but at a slower rate than splits. In a stock dividend, current shareholders receive additional shares on some proportional basis. Thus, a holder of 100 shares would receive 5 additional shares at no cost if a 5% stock dividend was declared. Stock repurchases occur when a firm repurchases its own stock. These shares of stock are then referred to as treasury stock. The higher EPS on the now decreased number of shares outstanding will cause the price of the stock to rise and, thus, capital gains are substituted for cash dividends. 14-2 How would each of the following changes tend to affect aggregate payout ratios (that is, the average for all corporations), other things held constant? Explain your answers. a. An increase in the personal income tax rate b. A liberalization of depreciation for federal income tax purposes—that is, faster tax write-offs c. A rise in interest rates d. An increase in corporate profits e. A decline in investment opportunities f. Permission for corporations to deduct dividends for tax purposes as they now do interest charges g. A change in the Tax Code so that both realized and unrealized capital gains in any year were taxed at the same rate as dividends Answer: a. From the stockholders’ point of view, an increase in the personal income tax rate would make it more desirable for a firm to retain and reinvest earnings. Consequently, an increase in personal tax rates should lower the aggregate payout ratio. b.

If the depreciation allowances were raised, cash flows would increase. With higher cash flows, payout ratios would tend to increase. On the other hand, the change in tax-allowed depreciation charges would increase rates of return on investment, other things being equal, and this might stimulate investment, and consequently reduce payout ratios. On balance, it is likely that aggregate payout ratios would rise, and this has in fact been the case.

If interest rates were to increase, the increase would make retained earnings a relatively attractive way of financing new investment. Consequently, the payout ratio might be expected to decline. On the other hand, higher interest rates would cause r d, rs, and firm’s MCCs to rise—that would mean that fewer projects would qualify for capital budgeting and the residual would increase (other things constant), hence the payout ratio might increase.

A permanent increase in profits would probably lead to an increase in dividends, but not necessarily to an increase in the payout ratio. If the aggregate profit increase were a cyclical increase that could be expected to be followed by a decline, then the payout ratio might fall, because firms do not generally raise dividends in response to a short-run profit increase.

If investment opportunities for firms declined while cash inflows remained relatively constant, an increase would be expected in the payout ratio.

Dividends are currently paid out of after-tax dollars, and interest charges from before-tax dollars. Permission for firms to deduct dividends as they do interest charges would make dividends less costly to pay than before and would thus tend to increase the payout ratio.

This change would make capital gains less attractive and would lead to an increase in the payout ratio.

14-3 What is the difference between a stock dividend and a stock split? As a stockholder, would you prefer to see your company declare a 100% stock dividend or a 2-for-1 split? Assume that either action is feasible. Answer:

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The difference is largely one of accounting. In the case of a split, the firm simply increases the number of shares and simultaneously reduces the par or stated value per share. In the case of a stock dividend, there must be a transfer from retained earnings to capital stock. For most firms, a 100% stock dividend and a 2-for-1 split accomplish exactly the same thing; hence, investors may choose either one. 14-4 One position expressed in the financial literature is that firms set their dividends as a residual after using income to support new investments. Explain what a residual policy implies (assuming that all distributions are in the form of dividends), illustrating your answer with a table showing how different investment opportunities could lead to different dividend payout ratios. Answer: The residual distribution policy is based on the premise that, since new common stock is more costly than retained earnings, a firm should use all the retained earnings it can to satisfy its common equity requirement. Thus, the distribution under this policy is a function of the firm’s investment opportunities. 14-5 Indicate whether the following statements are true or false. If the statement is false, explain why. a. If a firm repurchases its stock in the open market, the shareholders who tender the stock are subject to capital gains taxes. b. If you own 100 shares in a company’s stock and the company’s stock splits 2-for-1, then you will own 200 shares in the company following the split. c. Some dividend reinvestment plans increase the amount of equity capital available to the firm. d. The Tax Code encourages companies to pay a large percentage of their net income in the form of dividends. e. A company that has established a clientele of investors who prefer large dividends is unlikely to adopt a residual dividend policy. f. If a firm follows a residual dividend policy then, holding all else constant, its dividend payout will tend to rise whenever the firm’s investment opportunities improve. Answer: a. True. When investors sell their stock, they are subject to capital gains taxes. b.

True. If a company’s stock splits 2-for-1, and you own 100 shares, then after the split you will own 200 shares.

True. Dividend reinvestment plans that involve newly issued stock will increase the amount of equity capital available to the firm.

False. The Tax Code, through the tax deductibility of interest, encourages firms to use debt and thus pay interest to investors rather than dividends, which are not tax deductible. In addition, due to a lower capital gains tax rate than the highest personal tax rate, the Tax Code encourages investors in high tax brackets to prefer firms who retain earnings rather than those that pay large dividends.

True. If a company’s clientele prefers large dividends, the firm is unlikely to adopt a residual dividend policy. A residual dividend policy could mean low or zero dividends in some years, which would upset the company’s developed clientele.

False. If a firm follows a residual dividend policy, all else constant, its dividend payout will tend to decline whenever the firm’s investment opportunities improve.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–5 14-1 Residual Distribution Model. Puckett Products is planning for $5 million in capital expenditures next year. Puckett’s target capital structure consists of 60% debt and 40% equity. If net income next year is $3

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million and Puckett follows a residual distribution policy with all distributions as dividends, what will be its dividend payout ratio? Solution: The company’s capital structure is 60% debt and 40% equity; its capital budget is $5,000,000; and its net income is $3,000,000. Equity retained for capital budget = 0.4($5,000,000) = $2,000,000. NI: Additions: Earnings Remaining:

$3,000,000 2,000,000 $1,000,000

Payout = $1,000,000 = 33.33%. $3,000,000 14-2 Residual Distribution Policy. Petersen Company has a capital budget of $1.2 million. The company wants to maintain a target capital structure that is 60% debt and 40% equity. The company forecasts that its net income this year will be $600,000. If the company follows a residual distribution model and pays all distributions as dividends, what will be its payout ratio? Solution: The company requires 0.40($1,200,000) = $480,000 of equity financing. If the company follows a residual dividend policy it will retain $480,000 for its capital budget and pay out the $120,000 ―residual‖ to its shareholders as a dividend. The payout ratio would therefore be $120,000/$600,000 = 0.20 = 20%. 14-3 Dividend Payout. The Wei Corporation expects next year’s net income to be $15 million. The firm is currently financed with 40% debt. Wei has $12 million of profitable investment opportunities, and it wishes to maintain its existing debt ratio. According to the residual distribution model (assuming all payments are in the form of dividends), how large should Wei’s dividend payout ratio be next year? Solution: Equity financing = $12,000,000(0.60) = $7,200,000. Dividends = Net income − Equity financing = $15,000,000 − $7,200,000 = $7,800,000. Dividend payout ratio = Dividends/Net income = $7,800,000/$15,000,000 = 52%. 14-4 Stock Repurchase. A firm has 10 million shares outstanding with a market price of $20 per share. The firm has $25 million in extra cash (short-term investments) that it plans to use in a stock repurchase; the firm has no other financial investments or any debt. What is the firm's value of operations, and how many shares will remain after the repurchase? Solution: Vop = (n0 P) − Extra cash = (10,000,000 × $20) − $25,000,000 = $175,000,000. n = Vop / P = $175,000,000/$20 = 8,750,000. 14-5 Stock Split. JPix management is considering a stock split. JPix currently sells for $120 per share and a 3for-2 stock split is contemplated. What will be the company’s stock price following the stock split, assuming that the split has no effect on the total market value of JPix’s equity? Solution: P0 = $120; Split = 3-for-2

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P0 New = $120 = $80. 32

INTERMEDIATE PROBLEMS 6–9 14-6 External Equity Financing. Gardial GreenLights, a manufacturer of energy-efficient lighting solutions, has had such success with its new products that it is planning to substantially expand its manufacturing capacity with a $15 million investment in new machinery. Gardial plans to maintain its current 30% debt-to-total-assets ratio for its capital structure and to maintain its dividend policy in which at the end of each year it distributes 55% of the year’s net income. This year’s net income was $8 million. How much external equity must Gardial seek now to expand as planned? Solution: Retained earnings = Net income (1 – Payout ratio) = $8,000,000(0.45) = $3,600,000. External equity needed: Total equity required = (New investment)(1 – Debt ratio) = $15,000,000(0.70) = $10,500,000. New external equity needed = $10,500,000 – $3,600,000 = $6,900,000. 14-7 Stock Split. Suppose you own 2,000 common shares of Laurence Incorporated. The EPS is $10.00, the DPS is $3.00, and the stock sells for $80 per share. Laurence announces a 2-for-1 split. Immediately after the split, how many shares will you have, what will the adjusted EPS and DPS be, and what would you expect the stock price to be? Solution: Number of shares = 2,000(2) = 4,000. EPS = $10.00/2 = $5.00. DPS = $3.00/2 = $1.50. Price = $40.00. 14-8 Stock Split. Fauver Enterprises declared a 3-for-1 stock split last year, and this year its dividend is $1.50 per share. This total dividend payout represents a 6% increase over last year’s pre-split total dividend payout. What was last year’s dividend per share? Solution: DPS after split = $1.50. Equivalent pre-split dividend = $1.50(3/1) = $4.50. New equivalent dividend = Last year’s dividend(1.06) $4.50 = Last year’s dividend(1.06) Last year’s dividend = $4.50/1.06 = $4.25. 14-9 Residual Distribution Policy. Dreebyshaw Industries must set its investment and dividend policies for the coming year. It has three independent projects from which to choose, each of which requires a $3 million investment. These projects have different levels of risk, and therefore different costs of capital. Their projected internal rates of return (IRRs) and costs of capital are as follows: Project A: Cost of capital = 17%; IRR = 20%

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Project B: Cost of capital = 13%; IRR = 10% Project C: Cost of capital = 7%; IRR = 9% Dreebyshaw intends to maintain its 35% debt and 65% common equity capital structure, and its net income is expected to be $4,750,000. If Dreebyshaw maintains its residual dividend policy (with all distributions in the form of dividends), what will its payout ratio be? Solution: Capital budget should be $6 million since the company will accept all independent projects whose IRR exceeds the project’s cost of capital. We know that 65% of the $6 million should be equity. Therefore, the company should pay dividends of: Dividends = Net income – needed equity = $4,750,000 – $3,900,000 = $850,000. Payout ratio = $850,000/$4,750,000 = 0.1789 = 17.89%.

CHALLENGING PROBLEMS 10–12 14-10 Alternative Dividend Policies. Boehm Corporation has had stable earnings growth of 8% a year for the past 10 years, and in 2023 Boehm paid dividends of $4 million on net income of $10 million. However, net income is expected to grow by 28% in 2024, and Boehm plans to invest $7.5 million in a plant expansion. This one-time unusual earnings growth won’t be maintained, though, and after 2024 Boehm will return to its previous 8% earnings growth rate. Its target debt ratio is 34%. Boehm has 1 million shares of stock. a. What are Boehm's 2023 payout ratio and dividends per share? What is Boehm's 2024 projected net income? b. Calculate Boehm’s dividends per share for 2024 under each of the following policies: (1) Its 2024 dividend payment is set to force dividends to grow at the long-run growth rate in earnings. (2) It continues the 2023 dividend payout ratio. (3) It uses a pure residual policy with all distributions in the form of dividends (34% of the $7.5 million investment is financed with debt). (4) It employs a regular-dividend-plus-extras policy, with the regular dividend being based on the long-run growth rate and the extra dividend being set according to the residual policy. What is the regular dividend per share? What is the residual dividend per share? c.

Which of the preceding policies would you recommend? Restrict your choices to the ones listed, but justify your answer.

Solution: a. 2023 Payout ratio = 2023 dividends / 2023 net income = $4,000,000/$10,000,000 = 40% 2023 dividends per share = $4,000,000/1,000,000 = $4. 2024 projected net income = (2023 net income)(1 + g2023) = $10,000,000(1 + 0.28) = $12,800,000. b.

(1) 2024 DPS = (2023 Dividends)(1 + LT g)/(# shares) = ($4,000,000)(1 + 0.08) /1,000,000 = $4.32. (2) 2024 DPS = (Net income × 2023 Payout ratio)/Number of shares

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= (12,800,000)(40%)/1,000,000 = $5.12. (3)

Percentage of project financed with debt = PctDebt = 34% Percentage of project financed with net income = 1 – PctDebt PctNI = 1 – 0.34 = 0.66 = 66% Net income spent on project: = (Project cost)(PctNI) = $7,500,000(0.66) = $4,950,000 2024 DPS = (2024 Net income – Net income spent on project)/(# shares) =($12,800,000 – $4,950,000)/(1,000,000) = $7.85 All of the equity financing is done with reinvested retained earnings as long as they are available.

(4) As calculated in Step 1, the regular DPS is $4.32. In Step 3, the residual DPS is $7.85. The extra DPS is: Extra DPS = $7.85 – $4.32 = $3.53. An even better use of the surplus funds might be a stock repurchase. c.

Policy 4, based on the regular dividend with an extra, seems most logical. Implemented properly, it would lead to the correct capital budget and the correct financing of that budget, and it would give correct signals to investors.

14-11 Residual Distribution Model. Kendra Brown is analyzing the capital requirements for Reynold Corporation for next year. Kendra forecasts that Reynold will need $15 million to fund all of its positive-NPV projects and her job is to determine how to raise the money. Reynold’s net income is $11 million, and it has paid a $2 dividend per share (DPS) for the past several years (1 million shares of common stock are outstanding); its shareholders expect the dividend to remain constant for the next several years. The company’s target capital structure is 30% debt and 70% equity. a. Suppose Reynold follows the residual model and makes all distributions as dividends. How much retained earnings will it need to fund its capital budget? b. If Reynold follows the residual model with all distributions in the form of dividends, what will be its dividend per share and payout ratio for the upcoming year? c. If Reynold maintains its current $2 DPS for next year, how much reinvested earnings will be available for the firm’s capital budget? d. Can Reynold maintain its current capital structure, maintain its current dividend per share, and maintain a $15 million capital budget without having to raise new common stock? Why or why not? e. Suppose management is firmly opposed to cutting the dividend; that is, it wishes to maintain the $2 dividend for the next year. Suppose also that the company is committed to funding all profitable projects and is willing to issue more debt (along with the available reinvested earnings) to help finance the company’s capital budget. Assume the resulting change in capital structure has a minimal impact on the company’s composite cost of capital, so that the capital budget remains at $15 million. What portion of this year’s capital budget would have to be financed with debt? f. Suppose once again that management wants to maintain the $2 DPS. In addition, the company wants to maintain its target capital structure (30% debt, 70% equity) and its $15 million capital budget. What is the minimum dollar amount of new common stock the company would have to issue in order to meet all of its objectives? g. Now consider the case in which management wants to maintain the $2 DPS and its target capital structure but also wants to avoid issuing new common stock. The company is willing to cut its

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capital budget in order to meet its other objectives. Assuming the company’s projects are divisible, what will be the company’s capital budget for the next year? If a firm follows the residual distribution policy, what actions can it take when its forecasted retained earnings are less than the retained earnings required to fund its capital budget?

Solution: a. Capital budget = $15,000,000; Capital structure = 70% equity, 30% debt. Retained earnings needed = $15,000,000(0.7) = $10,500,000. b.

According to the residual dividend model, only $500,000 is available for dividends: NI – Retained earnings needed for cap. projects = Residual dividend. $11,000,000 – $10,500,000 = $500,000. DPS = $500,000/1,000,000 = $0.50. Payout ratio = $500,000/$11,000,000 = 4.55%.

Retained earnings available = $11,000,000 – $2.00 (1,000,000) = $11,000,000 – $2,000,000 = $9,000,000.

No. If the company maintains its $2.00 DPS, only $9 million of retained earnings will be available for capital projects. However, if the firm is to maintain its current capital structure, $10.5 million of equity is required. This would necessitate the company having to issue $1.5 million of new common stock.

Capital budget = $15 million; Dividends = $2 million; NI = $11 million. Capital structure = ? RE available = $11,000,000 – $2,000,000 = $9,000,000.

Percentage of cap. budget financed with RE =

$9,000,000 = 60%. $15,000,000

Percentage of cap. budget financed with debt =

$6,000,000 = 40%. $15,000,000

Dividends = $2 million; Capital budget = $15 million; 70% equity, 30% debt; NI = $11 million. Equity needed = $15,000,000(0.7) = $10,500,000. RE available = $11,000,000 – $2.00(1,000,000) = $11,000,000 – $2,000,000 = $9,000,000. External (new) equity needed = $10,500,000 – $9,000,000 = $1,500,000.

Dividends = $2 million; NI = $11 million; Capital structure = 70% equity, 30% debt. RE available = $11,000,000 – $2,000,000 = $9,000,000.

We’re forcing the RE available = Required equity to find the new capital budget. Required equity = Capital budget (target equity ratio) $9,000,000 = Capital budget(0.7)

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Capital budget = $12,857,143. Therefore, if Reynolds cuts its capital budget from $15 million to $12.86 million, it can maintain its $2.00 DPS, its current capital structure, and still follow the residual dividend policy. h.

The firm can do one of four things: (1) Cut dividends. (2) Change capital structure, that is, use more debt. (3) Cut its capital budget. (4) Issue new common stock. Realize that each of these actions is not without consequences to the company’s cost of capital, stock price, or both.

14-12 Stock Repurchase. Bayani Bakery’s most recent FCF was $48 million; the FCF is expected to grow at a constant rate of 6%. The firm’s WACC is 12%, and it has 15 million shares of common stock outstanding. The firm has $30 million in short-term investments, which it plans to liquidate and distribute to common shareholders via a stock repurchase; the firm has no other nonoperating assets. It has $368 million in debt and $60 million in preferred stock. a. What is the value of operations? b. Immediately prior to the repurchase, what is the intrinsic value of equity? c. Immediately prior to the repurchase, what is the intrinsic stock price? d. How many shares will be repurchased? How many shares will remain after the repurchase? e. Immediately after the repurchase, what is the intrinsic value of equity? The intrinsic stock price? Solution: Prior to Repurchase

After Repurchase

Value of operations = (FCF(1 + g))/(WACC – g) = + Value of nonoperating assets

$848,000,000.0 30,000,000.0

$848,000,000.0 0.0

Total intrinsic value of firm

$878,000,000.0

$848,000,000.0

− Debt

368,000,000.0

− Preferred stock

60,000,000.0

Intrinsic value of equity

$450,000,000.0

$420,000,000.0

÷ Number of shares

15,000,000

14,000,000

Intrinsic stock price

$30.00

# shares repurchased = (Cash used in repurchase)/Price =

1,000,000

$848 million.

$450 million.

$30.

1 million; 14 million.

$420 million; $30.

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SPREADSHEET PROBLEM 14-13 Build a Model: Distributions as Dividends or Repurchases. Start with the partial model in the file Ch14 P13 Build a Model.xlsx on the textbook’s website. J. Clark Inc. (JCI), a manufacturer and distributor of sports equipment, has grown until it has become a stable, mature company. Now JCI is planning its first distribution to shareholders. (See the file for the most recent year’s financial statements and projections for the next year, 2024; JCI’s fiscal year ends on June 30.) JCI plans to liquidate and distribute $500 million of its short-term securities on July 1, 2024, the first day of the next fiscal year, but it has not yet decided whether to distribute with dividends or with stock repurchases. a. Assume first that JCI distributes the $500 million as dividends. Fill in the missing values in the file’s balance sheet column for July 1, 2024, which is labeled ―Distribute as Dividends.‖ (Hint: Be sure that the balance sheets balance after you fill in the missing items.) Assume that JCI did not have to establish an account for dividends payable prior to the distribution. b. Now assume that JCI distributes the $500 million through stock repurchases. Fill in the missing values in the file’s balance sheet column for July 1, 2024, which is labeled ―Distribute as Repurchase.‖ (Hint: Be sure that the balance sheets balance after you fill in the missing items.) c. Calculate JCI’s projected free cash flow; the tax rate is 25%. d. What is JCI’s current intrinsic stock price (the price on 6/30/2023)? What is the projected intrinsic stock price for 6/30/2024? e. What is the projected intrinsic stock price on 7/1/2024 if JCI distributes the cash as dividends? f. What is the projected intrinsic stock price on 7/1/2024 if JCI distributes the cash through stock repurchases? How many shares will remain outstanding after the repurchase? Solution: The detailed solution for the problem is available in the file Ch14 P13 Build a Model Solution.xlsx on the textbook’s website.

MINI CASE Integrated Waveguide Technologies (IWT) is a 6-year-old company founded by Hunt Jackson and David Smithfield to exploit metamaterial plasmonic technology to develop and manufacture miniature microwave frequency directional transmitters and receivers for use in mobile Internet and communications applications. The technology, although highly advanced, is relatively inexpensive to implement, and their patented manufacturing techniques require little capital as compared to many electronics fabrication ventures. Because of the low capital requirement, Jackson and Smithfield have been able to avoid issuing new stock and thus own all of the shares. Because of the explosion in demand for its mobile Internet applications, IWT must now access outside equity capital to fund its growth, and Jackson and Smithfield have decided to take the company public. Until now, Jackson and Smithfield have paid themselves reasonable salaries but routinely reinvested all after-tax earnings in the firm, so dividend policy has not been an issue. However, before talking with potential outside investors, they must decide on a dividend policy. Your new boss at the consulting firm Flick and Associates, which has been retained to help IWT prepare for its public offering, has asked you to make a presentation to Jackson and Smithfield in which you review the theory of dividend policy and discuss the following issues. a.

What is meant by the term ―distribution policy‖? How has the mix of dividend payouts and stock repurchases changed over time?

Answer: Distribution policy is defined as the firm’s policy with regard to (1) the level of distributions, (2) the form of distributions (dividends or stock repurchases), and (3) the stability of distributions.

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The percentage of cash distributions relative to net income was around 27% until the early 2000s. It exceeded 90% since 2012. Since 1998, repurchases have exceeded dividends. As of 9/30/2022, the average dividend yield was 1.37% and the repurchase yield was 2.57%, for a total yield of 3.94%. The percentage of companies paying a dividend has changed over time. The percentage of NYSE, AMEX, and NASDAQ firms paying a dividend was 66.5% in 1978 but fell to 20.8% in 1999. One possible reason is that there were many IPOs in this period, most of which didn’t pay a dividend. In the 12-month ending 3/31/2022, S&P 500 companies paid $524.9 billion dividends and repurchased $984.6 billion of stock. This was the biggest ever amount of repurchases in a 12-month period. a. 2. The terms ―irrelevance,‖ ―dividend preference‖ (or ―bird in the hand‖), and ―tax effect‖ have been used to describe three major theories regarding the way dividend payouts affect a firm’s value. Explain these terms, and briefly describe each theory.

Answer: Dividend irrelevance refers to the theory that investors are indifferent between dividends and capital gains, making dividend policy irrelevant with regard to its effect on the value of the firm. Dividend preference, or ―bird in the hand,‖ refers to the theory that a dollar of dividends in the hand is preferred by investors to a dollar retained in the business, in which case dividend policy would affect a firm’s value. The dividend irrelevance theory was proposed by MM, but they had to make some very restrictive assumptions to ―prove‖ it (zero taxes, no flotation or transactions costs). MM argued that paying out a dollar per share of dividends reduces the growth rate in earnings and dividends, because new stock will have to be sold to replace the capital paid out as dividends. Under their assumptions, $1 of dividends will reduce the stock price by exactly $1. Therefore, according to MM, stockholders should be indifferent between dividends and capital gains. The dividend preference, or ―bird-in-the-hand‖ theory, is identified with Myron Gordon and John Lintner, who argued that investors perceive a dollar of dividends in the hand to be less risky than a dollar of potential future capital gains in the bush; hence, stockholders prefer a dollar of actual dividends to a dollar of retained earnings. In addition, high payouts mitigate agency costs by depriving managers of cash to waste and by causing companies to go to the external capital markets more often (which leads to greater scrutiny and less misuse of resources by managers). If the bird-in-the-hand theory is true, then investors would regard a firm with a high payout ratio as being less risky than one with a low payout ratio, all other things equal; hence, firms with high payout ratios would have higher values than those with low payout ratios. MM opposed the Gordon-Lintner theory, arguing that a firm’s risk is dependent only on the riskiness of its cash flows from assets and its capital structure, not by how its earnings are distributed to investors. The tax effect theory recognizes that there are two tax-related reasons for believing that investors might prefer a low dividend payout to a high payout: (1) taxes are not paid on capital gains until the stock is sold. (2) If a stock is held by someone until he or she dies, no capital gains tax is due at all—the beneficiaries who receive the stock can use the stock’s value on the death day as their cost basis and thus escape the capital gains tax. a. 3. payouts?

What do the three theories indicate regarding the actions management should take with respect to dividend

Answer: If the dividend irrelevance theory is correct, then dividend payout is of no consequence, and the firm may pursue any dividend payout. If the bird-in-the-hand theory is correct, the firm should set a high payout if it is to maximize its stock price. If the tax effect theory is correct, the firm should set a low payout if it is to maximize its stock price. Therefore, the theories are in total conflict with one another. a. 4. What results have empirical studies of the dividend theories produced? How does all this affect what we can tell managers about dividend payouts?

Answer: Unfortunately, empirical tests of the theories have been mixed (because firms don’t differ just with respect to payout).

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Some evidence shows that high payout firms have higher required stock return, which supports the tax effect theory. Research shows that in countries with relatively low dividend tax penalties: (1) more companies pay dividends and (2) dividend payments are larger. In countries with relatively high dividend tax penalties, more companies repurchase stock. This evidence doesn’t directly support the tax effect hypothesis, but it does show that taxes affect payout policies. In 2010 and 2012, there was fear of tax increases on dividends. When comparing late 2010 and 2012 (periods with great uncertainty regarding future tax rates on dividends) with late 2009 and 2011, many companies changed their policies and paid additional special dividends of over $7 billion. Also, 176 companies moved up payment dates from the beginning of the next year to late in 2010 and 2012 to avoid potential increases in tax rates, leading to over $12 billion in sooner-than-normal regular dividend payments. Interestingly, companies with higher insider ownership were more likely to pay special dividends or accelerate payment dates. This evidence doesn’t directly support the tax effect hypothesis, but it does show that taxes affect payout policies. However, other research shows that high-payout firms in countries with poor investor protection (where agency costs are most severe) are valued less than low-payout firms, which supports the dividend preference theory. b.

Discuss the effects on distribution policy consistent with: (1) the signaling hypothesis (also called the information content hypothesis) and (2) the clientele effect.

Answer: 1. It has long been recognized that the announcement of a dividend increase often results in an increase in the stock price, while an announcement of a dividend cut typically causes the stock price to fall. One could argue that this observation supports the premise that investors prefer dividends to capital gains. However, MM argued that dividend announcements are signals through which management conveys information to investors. Information asymmetries exist—managers know more about their firms’ prospects than do investors. Further, managers tend to raise dividends only when they believe that future earnings can comfortably support a higher dividend level, and they cut dividends only as a last resort. Therefore, (1) a larger-than-normal dividend increase ―signals‖ that management believes the future is bright; (2) a smaller-than-expected increase, or a dividend cut, is a negative signal; and (3) if dividends are increased by a ―normal‖ amount, this is a neutral signal. 2.

Different groups, or clienteles, of stockholders prefer different dividend payout policies. For example, many retirees, pension funds, and university endowment funds are in a low (or zero) tax bracket, and they have a need for current cash income. Therefore, this group of stockholders might prefer high-payout stocks. These investors could, of course, sell some of their stock, but this would be inconvenient, transactions costs would be incurred, and the sale might have to be made in a down market. Conversely, investors in their peak earnings years who are in high tax brackets and who have no need for current cash income should prefer low-payout stocks.

Clienteles do exist, but the real question is whether there are more members of one clientele than another, which would affect what a change in its dividend policy would do to the demand for the firm’s stock. There are also costs (taxes and brokerage) to stockholders who would be forced to switch from one stock to another if a firm changes its policy. Therefore, we cannot say whether a policy change to appeal to one particular clientele or another would lower or raise a firm’s cost of equity. MM argued that one clientele is as good as another, so in their view the existence of clienteles does not imply that one dividend policy is better than another. Still, no one has offered convincing proof that firms can disregard clientele effects. We know that stockholder shifts will occur if policy is changed, and since such shifts result in transaction costs and capital gains taxes, policy changes should not be taken lightly. Further, dividend policy should be changed slowly, rather than abruptly, in order to give stockholders time to adjust. c. 1. Assume that IWT has completed its IPO and has a $112.5 million capital budget planned for the coming year. You have determined its present capital structure (80% equity and 20% debt) is optimal, and its net income is forecasted at $140 million. Use the residual distribution approach to determine IWT’s total dollar distribution. Assume for now that the distribution is in the form of a dividend. IWT has 100 million shares of stock outstanding. What is the forecasted dividend payout ratio?

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach What is the forecasted dividend per share? What would happen to the payout ratio and DPS if net income were forecasted to decrease to $90 million? To increase to $160 million?

Answer: We make the following points: a.

Given the optimal capital budget and the target capital structure, we must now determine the amount of equity needed to finance the projects. Of the $112.5 million required for the capital budget, 0.8($112.5) = $90 million must be raised as equity and 0.2($112.5) = $22.5 million must be raised as debt if we are to maintain the optimal capital structure:

If a residual exists—that is, if net income exceeds the amount of equity the company needs—then it should distribute the residual amount out as either dividends or stock repurchases. For now, we assume all payouts are in the form of dividends. Since $140 million of earnings is available, and only $90 million is needed, the residual is $140 – $90 = $50 million, so this is the amount which should be paid out as dividends. Thus, the payout ratio would be $50/$140 = 0.357 = 35.7%. DPS would be $50/100 = $0.50.

If only $90 million of earnings were available, the residual is $90 – $90 = $0, so nothing should be paid out as dividends. Thus, the payout ratio would be zero, as would be the DPS.

If $160 million of earnings were available, the residual is $160 – $90 = $70 million, so this is the amount which should be paid out as dividends. Thus, the payout ratio would be $70/$160 = 0.438 = 43.8%. The DPS would be $70/100 = $0.70. c. 2. In general terms, how would a change in investment opportunities affect the payout ratio under the residual payment policy?

Answer: A change in investment opportunities would lead to an increase (if investment opportunities were good) or a decrease (if investment opportunities were not good) in the amount of equity needed, hence, in the residual dividend payout. c. 3. effects.)

What are the advantages and disadvantages of the residual policy? (Hint: Don’t neglect signaling and clientele

Answer: The primary advantage of the residual policy is that under it the firm makes maximum use of lower cost retained earnings, thus minimizing flotation costs and hence the cost of capital. Also, whatever negative signals are associated with stock issues would be avoided. However, if it were applied exactly, the residual model would result in dividend payments that fluctuated significantly from year to year as capital requirements and internal cash flows fluctuated. This would (1) send investors conflicting signals over time regarding the firm’s future prospects, and (2) since no specific clientele would be attracted to the firm; it would be an ―orphan.‖ These signaling and clientele effects would lead to a higher required return on equity which would more than offset the effects of lower flotation costs. Because of these factors, few if any publicly owned firms follow the residual model on a year-to-year basis. Even though the residual approach is not used to set the annual dividend, it is used when firms establish their long-run dividend policy. If ―normalized‖ cost of capital and investment opportunity conditions suggest that in a ―normal‖ year the company should pay out about 60% of its earnings, this fact will be noted and used to help determine the long-run policy. d.

Describe the procedures a company follows when it make a distribution through dividend payments.

Answer: November 16, 2023: December 13, 2023:

Declaration date Dividend goes with stock (owner on this day will get dividend)

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December 14, 2023:

Ex-dividend date (purchaser on or after this date doesn't get dividend)

December 15, 2023:

Holder-of-record date

January 5, 2024:

Payment date

d. 2. What is a stock repurchase? Describe the procedures a company follows when it make a distribution through a stock repurchase.

Answer: A firm may distribute cash to stockholders by repurchasing its own stock rather than paying out cash dividends. Stock repurchases can be used (1) somewhat routinely as an alternative to regular dividends, (2) to dispose of excess (nonrecurring) cash that came from asset sales or from temporarily high earnings, and (3) in connection with a capital structure change in which debt is sold and the proceeds are used to buy back and retire shares. A company announces intent to purchase a dollar amount of its own stock during a specific period. The announcement is not binding; in fact, companies often don’t actually complete the repurchase. Three methods are used for a repurchase: (1) Open market (usually through trustee) with stock purchases spread over a period of time; (2) tender offer, where company buys directly from shareholders who wish to tender their stock to the company; or (3) targeted stock repurchase in which the company buys from a large blockholder. e.

Discuss the advantages and disadvantages of a firm repurchasing its own shares.

A repurchase announcement may be viewed as a positive signal that management believes the shares are undervalued.

Stockholders have a choice—if they want cash, they can tender their shares, receive the cash, and pay the taxes, or they can keep their shares and avoid taxes. On the other hand, one must accept a cash dividend and pay taxes on it.

If the company raises the dividend to dispose of excess cash, this higher dividend must be maintained to avoid adverse stock price reactions. A stock repurchase, on the other hand, does not obligate management to future repurchases.

Repurchased stock, called treasury stock, can be used later in mergers, when employees exercise stock options, when convertible bonds are converted, and when warrants are exercised. Treasury stock can also be resold in the open market if the firm needs cash. Repurchases can remove a large block of stock that is ―overhanging‖ the market and keeping the price per share down.

Repurchases can be varied from year to year without giving off adverse signals, while dividends may not.

Repurchases can be used to produce large-scale changes in capital structure.

Disadvantages of repurchases: 1.

A repurchase could lower the stock’s price if it is taken as a signal that the firm has relatively few good investment opportunities. On the other hand, though, a repurchase can signal stockholders that managers are not engaged in ―empire building,‖ where they invest funds in low-return projects.

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If the IRS establishes that the repurchase was primarily to avoid taxes on dividends, then penalties could be imposed. Such actions have been brought against closely held firms, but to our knowledge charges have never been brought against publicly held firms.

Selling shareholders may not be fully informed about the repurchase; hence, they may make an uninformed decision and may later sue the company. To avoid this, firms generally announce repurchase programs in advance.

The firm may bid the stock price up and end up paying too high a price for the shares. In this situation, the selling shareholders would gain at the expense of the remaining shareholders. This could occur if a tender offer were made and the price was set too high, or if the repurchase was made in the open market and buying pressure drove the price above its equilibrium level. f. 1. Suppose IWT has decided to distribute $50 million, which it presently is holding in very liquid short-term investments. IWT’s value of operations is estimated to be about $1,937.5 million; it has $387.5 million in debt and zero preferred stock. As mentioned previously, IWT has 100 million shares of stock outstanding. Assume that IWT has not yet made the distribution. What is IWT’s intrinsic value of equity? What is its intrinsic stock price per share?

Answer: Value of operations

$1,937.50

+ Value of nonoperating assets

50.00

Total intrinsic value of firm

$1,987.50

− Debt

387.50

Intrinsic value of equity

$1,600.00

÷ Number of shares

100.00

Intrinsic price per share

$16.00

f. 2. Now suppose that IWT has just made the $50 million distribution in the form of dividends. What is IWT’s intrinsic value of equity? What is its intrinsic stock price per share?

Answer: Before

After Dividend

Value of operations

$1,937.50

+ Value of nonoperating assets

50.00

0.00

Total intrinsic value of firm

$1,987.50

$1,937.50

− Debt

387.50

Intrinsic value of equity

$1,600.00

$1,550.00

÷ Number of shares

100.00

Intrinsic price per share

$16.00

$15.50

Dividend per share

$0.50

f. 3. Suppose instead that IWT has just made the $50 million distribution in the form of a stock repurchase. Now what is IWT’s intrinsic value of equity? How many shares did IWT repurchase? How many shares remained outstanding after the repurchase? What is its intrinsic stock price per share after the repurchase?

Answer: nPost = nPrior − (CashRep/PPrior) nPost = 100 − ($50/$16) nPost = 100 − 3.125 = 96.875

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Before

After Repurchase

Value of operations

$1,937.50

+ Value of nonoperating assets

50.00

0.00

Total intrinsic value of firm

$1,987.50

$1,937.50

− Debt

387.50

Intrinsic value of equity

$1,600.00

$1,550.00

÷ Number of shares

100.00

96.875

Intrinsic price per share

$16.00

Number of shares repurchased g.

3.125

Describe the series of steps that most firms take in setting dividend policy.

Answer: Firms establish dividend policy within the framework of their overall financial plans. The steps in setting dividend policy are listed below: 1. The firm forecasts its annual capital budgets and its annual sales, along with its working capital needs, for a relatively long-term planning horizon, often 5 years.

The target capital structure, presumably the one which minimizes the WACC while retaining sufficient reserve borrowing capacity to provide ―financing flexibility,‖ will also be established.

With its capital structure and investment requirements in mind, the firm can estimate the approximate amount of debt and equity financing required during each year over the planning horizon.

A long-term target payout ratio is then determined, based on the residual model concept. Because of flotation costs and potential negative signaling, the firm will not want to issue common stock unless this is absolutely necessary. At the same time, due to the clientele effect, the firm will move cautiously from its past dividend policy, if a new policy appears to be warranted, and it will move toward any new policy gradually rather than in one giant step.

An actual dollar dividend, say $2 per year, will be decided upon. The size of this dividend will reflect (1) the long-run target payout ratio and (2) the probability that the dividend, once set, will have to be lowered, or, worse yet, omitted. If there is a great deal of uncertainty about cash flows and capital needs, then a relatively low initial dollar dividend will be set, for this will minimize the probability that the firm will have to either reduce the dividend or sell new common stock. The firm will run its corporate planning model so that management can see what is likely to happen with different initial dividends and projected growth rates under different economic scenarios.

What are stock splits and stock dividends? What are the advantages and disadvantages of each?

Answer: When it uses a stock dividend, a firm issues new shares in lieu of paying a cash dividend. For example, in a 5% stock dividend, the holder of 100 shares would receive an additional 5 shares. In a stock split, the number of shares outstanding is increased (or decreased in a reverse split) in an action unrelated to a dividend payment. For example, in a 2-for-1 split, the number of shares outstanding is doubled. A 100% stock dividend and a 2-for-1 stock split would produce the same effect, but there would be differences in the accounting treatments of the two actions. Both stock dividends and stock splits increase the number of shares outstanding and, in effect, cut the pie into more, but smaller, pieces. If the dividend or split does not occur at the same time as some other event that would alter perceptions about future cash flows, such as an announcement of higher earnings, then one would expect the price of the stock to adjust such that each investor’s wealth remains unchanged.

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For example, a 2-for-1 split of a stock selling for $50 would result in the stock price being cut in half, to $25. It is hard to come up with a convincing rationale for small stock dividends, like 5% or 10%. No economic value is being created or distributed, yet stockholders have to bear the administrative costs of the distribution. Further, it is inconvenient to own an odd number of shares, which may result after a small stock dividend. Thus, most companies today avoid small stock dividends. On the other hand, there is a good reason for stock splits or large stock dividends. Specifically, there is a widespread belief that an optimal price range exists for stocks. The argument goes as follows: if a stock sells for about $20–$80, then it can be purchased in round lots, hence at reduced commissions, by most investors. A higher price would put round lots out of the price range of many small investors, while a stock price lower than about $20 would convey the image of a stock that is doing poorly. Thus, most firms try to keep their stock prices within the $20 to $80 range. If the company prospers, it will split its stock occasionally to hold the price down. (Also, companies that are doing poorly occasionally use reverse splits to raise their price.) Many companies do operate outside the $20 to $80 range, but most stay within it. Another factor that may influence stock splits and dividends is the belief that they signal management’s belief that the future is bright. If a firm’s management would be inclined to split the stock or pay a stock dividend only if it anticipated improvements in earnings and dividends, then a split/dividend action could provide a positive signal and thus boost the stock price. However, if earnings and cash dividends did not subsequently rise, the price of the stock would fall back to its old level, or even lower, because managers would lose credibility. Interestingly, one of the most astute investors of the 20th century, Warren Buffett, chairman of Berkshire-Hathaway, has never split his firm’s stock. Berkshire currently (March 2020) sells for over $310,895 per share, and its performance over the years has been absolutely spectacular. It may be that Berkshire’s market value would be higher if it had a 425-to-1 stock split, or it may be that the conventional wisdom is wrong. i.

What is a dividend reinvestment plan (DRIP), and how does it work?

Answer: Under a dividend reinvestment plan (DRIP), shareholders have the option of automatically reinvesting their dividends in shares of the firm’s common stock. In an open-market purchase plan, a trustee pools all the dividends to be reinvested and then buys shares on the open market. Shareholders use the DRIP for three reasons: (1) brokerage costs are reduced by the volume purchases, (2) the DRIP is a convenient way to invest excess funds, and (3) the company generally pays all administrative costs associated with the operation. In a new stock plan, the firm issues new stock to the DRIP members in lieu of cash dividends. No fees are charged, and many companies even offer the stock at a 5% discount from the market price on the dividend date on the grounds that the firm avoids flotation costs that would otherwise be incurred. Only firms that need new equity capital use new stock plans, while firms with no need for new stock use an open-market purchase plan.

Solution and Answer Guide CHAPTER 15: CAPITAL S TRUCTURE DECISIONS

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 345 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 347 Easy Problems 1–9 ................................................................................................................................ 347 Intermediate Problems 10–11 ............................................................................................................... 348

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Challenging Problems 12–15 ................................................................................................................ 351 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 354 MINI CASE ............................................................................................................................................. 355 SOLUTIONS TO WEB EXTENSION PROBLEMS .......................................................................... 366 SOLUTION TO WEB EXTENSION SPREADSHEET PROBLEM ................................................ 369

ANSWERS TO END-OF-CHAPTER QUESTIONS 15-1 Define each of the following terms: a. Capital structure; business risk; financial risk b. Operating leverage; financial leverage; break-even point c. Reserve borrowing capacity Answer: a. Capital structure is the manner in which a firm’s assets are financed; that is, the right-hand side of the balance sheet. Capital structure is normally expressed as the percentage of each type of capital used by the firm–debt, preferred stock, and common equity. Business risk is the risk inherent in the operations of the firm, prior to the financing decision. Thus, business risk is the uncertainty inherent in a total risk sense, future operating income, or earnings before interest and taxes (EBIT). Business risk is caused by many factors. Two of the most important are sales variability and operating leverage. Financial risk is the risk added by the use of debt financing. Debt financing increases the variability of earnings before taxes (but after interest); thus, along with business risk, it contributes to the uncertainty of net income and earnings per share. Business risk plus financial risk equals total corporate risk. b.

Operating leverage is the extent to which fixed costs are used in a firm’s operations. If a high percentage of a firm’s total costs are fixed costs, then the firm is said to have a high degree of operating leverage. Operating leverage is a measure of one element of business risk, but does not include the second major element, sales variability. Financial leverage is the extent to which fixedincome securities (debt and preferred stock) are used in a firm’s capital structure. If a high percentage of a firm’s capital structure is in the form of debt and preferred stock, then the firm is said to have a high degree of financial leverage. The break-even point is that level of unit sales at which costs equal revenues. Break-even analysis may be performed with or without the inclusion of financial costs. If financial costs are not included, break-even occurs when EBIT equals zero. If financial costs are included, break-even occurs when EBT equals zero.

Reserve borrowing capacity exists when a firm uses less debt under ―normal‖ conditions than called for by the trade-off theory. This allows the firm some flexibility to use debt in the future when additional capital is needed.

15-2 What term refers to the uncertainty inherent in projections of future ROIC? Answer: Business risk refers to the uncertainty inherent in projections of future ROIC = ROE U. 15-3 Firms with relatively high nonfinancial fixed costs are said to have a high degree of what? Answer: Firms with relatively high nonfinancial fixed costs are said to have a high degree of operating leverage.

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15-4 ―One type of leverage affects both EBIT and EPS. The other type affects only EPS.‖ Explain this statement. Answer: Operating leverage affects EBIT and, through EBIT, EPS. Financial leverage has no effect on EBIT–it only affects EPS, given EBIT. 15-5 Why is the following statement true? ―Other things being the same, firms with relatively stable sales are able to carry relatively high debt ratios.‖ Answer: If sales tend to fluctuate widely, then cash flows and the ability to service fixed charges will also vary. Such a firm is said to have high business risk. Consequently, there is a relatively large risk that the firm will be unable to meet its fixed charges, and interest payments are fixed charges. As a result, firms in unstable industries tend to use less debt than those whose sales are subject to only moderate fluctuations. 15-6 Why do public utility companies usually have capital structures that are different from those of retail firms? Answer: Public utilities place greater emphasis on long-term debt because they have more stable sales and profits as well as more fixed assets. Also, utilities have fixed assets which can be pledged as collateral. Further, trade firms use retained earnings to a greater extent, probably because these firms are generally smaller and, hence, have less access to capital markets. Public utilities have lower retained earnings because they have high dividend payout ratios and a set of stockholders who want dividends. 15-7 Why is EBIT generally considered to be independent of financial leverage? Why might EBIT be influenced by financial leverage at high debt levels? Answer: EBIT depends on sales and operating costs. Interest is deducted from EBIT. At high debt levels, firms lose business, employees worry, and operations are not continuous because of financing difficulties. Thus, financial leverage can influence sales and costs, and hence EBIT, if excessive leverage is used. 15-8 If a firm went from zero debt to successively higher levels of debt, why would you expect its stock price to first rise, then hit a peak, and then begin to decline? Answer: The tax benefits from debt increase linearly, which causes a continuous increase in the firm’s value and stock price. However, financial distress costs get higher and higher as more and more debt is employed, and these costs eventually offset and begin to outweigh the benefits of debt. 15-9 Your firm’s CEO has just learned about options and how your firm’s equity can be viewed as an option. Why might he want to increase the riskiness of the firm, and why might the bondholders be unhappy about this? Answer: If equity is viewed as an option on the total value of the firm with a strike price equal to the face value of debt, then the equity value should be affected by risk in the same way that an option is affected by risk. An option is worth more if the underlying asset is riskier, so a manager wanting to maximize the option value of the firm might want to switch investment decisions to make the firm more risky. Of course, bondholders will not like this, since the increase in equity value comes at their expense. They will write covenants into the bonds specifying how the proceeds can be used, and if management still manages to engage in this ―bait-and-switch‖ tactic, the firm will find it difficult to raise capital through bond issues in the future.

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SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–9 15-1

Break-Even Quantity Shapland Inc. has fixed operating costs of $500,000 and variable costs of $50 per unit. If it sells the product for $75 per unit, what is the break-even quantity? Solution: QBE = F/(P – V) = $500,000/($75 – $50) = 20,000.

15-2

Unlevered Beta Counts Accounting’s beta is 1.2 and its tax rate is 25%. If it is financed with 21% debt, what is its unlevered beta? Solution: If wd = 0.21, then ws = 1 – 0.21 = 0.79. So, D/S = wd/we = 0.21/0.79. bU = b/[1 + (1 – T)(D/S)] = 1.2/[1 + (1 – 0.25)(0.21/0.79)] = 1.0.

15-3

Premium for Financial Risk Ethier Enterprise has an unlevered beta of 1.0. Ethier is financed with 50% debt and has a levered beta of 1.6. If the risk-free rate is 5.5% and the market risk premium is 6%, how much is the additional premium that Ethier’s shareholders require to be compensated for financial risk? Solution: If the company had no debt, its required return would be: rs,U = rRF + bU RPM = 5.5% + 1.0(6%) = 11.5%. With debt, the required return is: rs,L = rRF + bL RPM = 5.5% + 1.6(6%) = 15.1%. Therefore, the extra premium required for financial risk is 15.1% – 11.5% = 3.6%.

15-4

MM Model With Zero Taxes Quillpen Company is unlevered and has a value of $40 billion. An otherwise identical but levered firm finances 25% of its capital structure with debt. Under the MM zerotax model, what is the value of the levered firm? Solution: With zero debt, the MM model is: V L = VU: VL = VU = $40 billion.

15-5

MM Model With Corporate Taxes Walkrun Inc. is unlevered and has a value of $400 billion. An otherwise identical but levered firm finances 25% of its capital structure with debt at an 8% interest rate. No growth is expected. Assume the corporate tax rate is 25%. Use the MM model with corporate taxes to determine the value of the levered firm. Solution: VL = VU + TD = $400 + 0.25($100) = $425 billion.

15-6

Miller Model With Corporate and Personal Taxes Cruz Corporation has $100 billion of debt outstanding. An otherwise identical firm has no debt and has a market value of $500 billion. Under the Miller model, what is Cruz's value if the federal-plus-state corporate tax rate is 28%, the effective personal tax rate on stock is 17%, and the personal tax rate on debt is 29%? Solution:

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 (1 Tc )(1 Ts )  VL = V U +  1  D (1 Td )    (1 0.28)(1 0.17)  = $500 +  1  100 (1 0.29)  

= $500 + (1 − 0.8417)($100) = $515.83 million. 15-7

Value of Equity After Recapitalization Nichols Corporation’s value of operations is equal to $500 million after a recapitalization (the firm had no debt before the recap). It raised $200 million in new debt and used this to buy back stock. Nichols had no short-term investments before or after the recap. After the recap, wd = 40%. What is S (the value of equity after the recap)? Solution: SPost = (1 – wd)(VopNew) = (1 – 0.4)($500) = $300 million.

15-8

Stock Price after Recapitalization Lee Manufacturing’s value of operations is equal to $900 million after a recapitalization. (The firm had no debt before the recap.) Lee raised $300 million in new debt and used this to buy back stock. Lee had no short-term investments before or after the recap. After the recap, wd = 1/3. The firm had 30 million shares before the recap. What is P (the stock price after the recap)? Solution: PPost = (VopNew – Dold)/nprior = ($900 – 0)/30 = $30 Note: This is the price after issuing the new debt but before undertaking the repurchase. This is the easiest way to work it. Also, SPost = (1 – wd)(VopNew) = (1 – 1/3)($900) = $600 million. This gives the ending equity value, which isn’t asked for in this problem.

15-9

Shares Remaining After Recapitalization Dye Trucking raised $150 million in new debt and used this to buy back stock. After the recap, Dye’s stock price is $7.50. If Dye had 60 million shares of stock before the recap, how many shares does it have after the recap? Solution: nPost = Original shares – shares repurchased = nPrior – (Dollar value of shares repurchased/Repurchase Price) = 60 – ($150/$7.5) = 60 – 20 = 40 million. Note that the formula nPost = nPrior [(VOpNew – DNew)/(VOpNew – DOld)] can be used if you note that VOpNew = $60 × $7.50 = $450 and DOld = $0 so that nPost = 60[($450 – $150)/($450 – 0)] = 40 million shares.

INTERMEDIATE PROBLEMS 10–11 15-10

Break-Even Point Schweser Satellites Inc. produces satellite earth stations that sell for $100,000 each. The firm’s fixed costs, F, are $2 million; 50 earth stations are produced and sold each year; profits total $500,000; and the firm’s assets (all equity financed) are $5 million. The firm estimates that it can change its production process, adding $4 million to assets and $500,000 to fixed operating costs. This change will reduce variable costs per unit by $10,000 and increase output by 20 units. However, the sales price

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on all units must be lowered to $95,000 to permit sales of the additional output. The firm has tax loss carryforwards that render its tax rate zero, its cost of equity is 16%, and it uses no debt. a. What is the incremental profit? To get a rough idea of the project’s profitability, what is the project’s expected rate of return for the next year (defined as the incremental profit divided by the investment)? Should the firm make the investment? Why or why not? b. Would the firm’s break-even point increase or decrease if it made the change?

Solution: a. Here are the steps involved: (1) Determine the variable cost per unit at present, V: Profit = P(Q) – FC – V(Q) $500,000 = ($100,000)(50) – $2,000,000 – V(50) 50(V) = $2,500,000 V = $50,000. (2) Determine the new profit level if the change is made: New profit

= P2(Q2) – FC2 – V2(Q2) = $95,000(70) – $2,500,000 – ($50,000 – $10,000)(70) = $1,350,000.

(3) Determine the incremental profit: Profit = $1,350,000 – $500,000 = $850,000. (4) Estimate the approximate rate of return on new investment: Return = Profit/Investment = $850,000/$4,000,000 = 21.25%. Since the return exceeds the 16% cost of equity, this analysis suggests that the firm should go ahead with the change. b.

15-11

The change would increase the breakeven point: Old:

QBE =

$2,000,000 F = = 40 units. PV $100,000  $50,000

New:

QBE =

$2,500,000 = 45.45 units. $95,000  $40,000

Capital Structure Analysis The Rivoli Company has no debt outstanding, and its financial position is given by the following data: Expected EBIT Growth rate in EBIT, gL

Cost of equity, rs

10%

Shares outstanding, n0 Tax rate, T (federal-plus-state) a.

$600,000

200,000 25%

What is Rivoli's intrinsic value of operations (i.e., its unlevered value)? What is its intrinsic stock price? Its earnings per share?

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Rivoli is considering selling bonds and simultaneously repurchasing some of its stock. If it moves to a capital structure with 30% debt based on market values, its cost of equity, r s, will increase to 12% to reflect the increased risk. Bonds can be sold at a cost, r d, of 7%. Based on the new capital structure, what is the new weighted average cost of capital? What is the levered value of the firm? What is the amount of debt?

Based on the new capital structure, what is the new stock price? What is the remaining number of shares? What is the new earnings per share?

Solution: a. Original value of the firm (D = $0): Original free cash flow: FCF = NOPAT = EBIT(1 – T) since no growth = $600,000(1 – 0.25) = $450,000 Original cost of capital: WACC = wd rd(1-T) + wsrs = 0 + (1.0)(10%) = 10%. Original intrinsic value of operations is: Vop =

FCF (EBIT)(1 T) ($600,000)(1 0.25) = $4,500,000.   WACC WACC 0.10

Original intrinsic stock price = Vop/n0 = $4,500,000/200,000 = $22.50 Original EPS = NI/n0 = (EBIT – Interest)(1 – T)/n0 = [($600,000 – $0)(0.75)]/200,000 = $2.25 b.

Using its target capital structure of 30% debt: With financial leverage (wd = 30%): WACC = wd rd(1-T) + wcers = (0.3)(7%)(1 – 0.25) + (0.7)(12%) = 9.975%. Leverage doesn’t change FCF, so the value of a levered firm is the value of operations based on the new WACC: Vop =

FCF (EBIT)(1 T) ($600,000)(1 0.25)   = $4,511,278 WACC WACC 0.09975

D = wd Vop = 0.30($4,511,278.195) = $1,353,383 c.

The stock price after the debt is issued but before shares are purchased, P Prior: PPrior = (Vop + ST investments – Debt)/nPrior = (Vop + New Debt – (Old debt + New Debt)/nPrior = (Vop – Old debt)/nPrior = ($4,511,278.195 – $0)/200,000 =$22.5564 The stock price after the repurchase, PPost, is equal to PPrior. = $22.56 The number of shares that are repurchased is nRepurchase: nRepurchase = (D – D0)/PPost = ($1,353,383.459 - $0)/$22.5564 = 59,999.98  60,000. Note that rounded figures will give different number of shares. $1,353,383/$22.56 = 59,990.

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The number of remaining shares, n, is: n = 200,000 – 60,000 = 140,000.

New EPS with financial leverage: EPS = [($600,000 – 0.07($1,353,383.459))(1 – 0.25)]/140,000 = [($600,000 – $94,736.8421)(0.75)]/140,000 = $378,947.3684/140,000 = $2.7068 ≈ $2.71.

CHALLENGING PROBLEMS 12–15 15-12

Capital Structure Analysis Pettit Printing Company (PPC) has a total market value of $100 million, consisting of 1 million shares selling for $50 per share and $50 million of 10% perpetual bonds now selling at par. The company’s EBIT is $13.24 million, and its tax rate is 15%. Pettit can change its capital structure by either increasing its debt to 70% (based on market values) or decreasing it to 30%. If it decides to increase its use of leverage, it must call its old bonds and issue new ones with a 12% coupon. If it decides to decrease its leverage, it will call its old bonds and replace them with new 8% coupon bonds. The company will sell or repurchase stock at the new equilibrium price to complete the capital structure change. PPC expects no growth in its EBIT, so gL is zero. Its current cost of equity, rs, is 14%. If it increases leverage, rs will be 16%. If it decreases leverage, rs will be 13%. What is the firm’s WACC and total corporate value under each capital structure? Solution: a. Present situation (50% debt): WACC = wd rd(1 – T) + wcers = (0.5)(10%)(1 – 0.15) + (0.5)(14%) = 11.25%. V=

FCF (EBIT)(1 T) ($13.24)(1 0.15)   = $100 million. WACC WACC 0.1125

70 percent debt: WACC = wd rd(1 – T) + wcers = (0.7)(12%)(1 – 0.15) + (0.3)(16%) = 11.94%. V=

FCF (EBIT)(1 T) ($13.24)(1 0.15)   = $94.255 million. WACC WACC 0.1194

30 percent debt: WACC = wd rd(1 – T) + wcers = (0.3)(8%)(1 – 0.15) + (0.7)(13%) = 11.14%. V= 15-13

FCF (EBIT)(1 T) ($13.24)(1 0.15)   = $101.023 million. WACC WACC 0.1114

Optimal Capital Structure With Hamada Beckman Engineering and Associates (BEA) is considering a change in its capital structure. BEA currently has $20 million in debt carrying a rate of 8%, and its stock price is $40 per share with 2 million shares outstanding. BEA is a zero-growth firm and pays out all of its earnings as dividends. The firm’s EBIT is $16 million, and it faces a 25% federal-plus-state tax rate. The market risk premium is 4%, and the risk-free rate is 6%. BEA is considering increasing its debt

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level to a capital structure with 40% debt, based on market values, and repurchasing shares with the extra money that it borrows. BEA will have to retire the old debt in order to issue new debt, and the rate on the new debt will be 9%. BEA has a beta of 1.0. a. What is BEA’s unlevered beta? Use market value D/S (which is the same as wd/ws) when unlevering. b. What are BEA’s new beta and cost of equity if it has 40% debt? c. What are BEA’s WACC and total value of the firm with 40% debt? Solution: a. BEA’s unlevered beta: bU = b/(1+(1 – T)(D/S)) = 1.0/(1+(1 – 0.25)(20/80)) = 0.8421. b.

BEA’s new beta at 40% debt: b = bU (1 + (1 – T)(D/S)). bL = 0.8421 (1 + (1 - 0.25)(40%/60%)) = 1.2632. Cost of Equity at 40% debt: rS = 6 + 1.2632(4) = 11.0528%

BEA’s WACC at 40% debt: WACC = wd rd(1 – T) + wcers = (0.4)(9%)(1 – 0.25) + (0.6)(11.0528%) = 9.3317%. Total Value of the firm with 40% debt: V=

15-14

FCF (EBIT)(1 T) ($16)(1 0.25) = $128.60 million.   WACC WACC 0.093317

WACC and Optimal Capital Structure F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows: Market Debt-toValue Ratio (wd)

Market Equity-toValue Ratio (ws)

Market Debt-toEquity Ratio (D/S)

Before-Tax Cost of Debt (rd)

0.0

1.0

0.00

6.0%

0.10

0.90

0.1111

6.4

0.20

0.80

0.2500

7.0

0.30

0.70

0.4286

8.2

0.40

0.60

0.6667

10.0

F. Pierce uses the CAPM to estimate its cost of common equity, rs and at the time of the analysis the risk-free rate is 5%, the market risk premium is 6%, and the company’s tax rate is 25%. F. Pierce estimates that its beta now (which is ―unlevered‖ because it currently has no debt) is 0.8. Based on this information, what is the firm’s optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure? Solution: Tax rate = 25% rRF = 5.0%

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rM – rRF = 6.0%

bU = 0.8

From data given in the problem and table, we can develop the following table:

D/S

rd(1 – T)

Levered betaa

rsb

WACCc

0.00

1.00

0.00

6.0%

4.50%

0.800

9.800%

9.80%

0.1

0.9

0.111

6.4%

4.80%

0.867

10.200%

9.66%

0.2

0.8

0.250

7.0%

5.25%

0.950

10.700%

9.61%

0.3

0.7

0.429

8.2%

6.15%

1.057

11.343%

9.79%

0.4

0.6

0.667

10.0%

7.50%

1.200

12.200%

10.32%

Notes: a These beta estimates were calculated using the Hamada equation: b = bU[1 + (1 – T)(D/S)]. b These rs estimates were calculated using the CAPM, rs = rRF + (rM – rRF)b. c These WACC estimates were calculated with the following equation: WACC = wd(rd)(1 – T) + (ws)(rs). The firm’s optimal capital structure is that capital structure which minimizes the firm’s WACC. The WACC is minimized at a capital structure consisting of 20% debt and 80% equity. At that capital structure, the firm’s WACC is 9.61%. 15-15

Equity Viewed as an Option A. Fethe Inc. is a custom manufacturer of guitars, mandolins, and other stringed instruments and is located near Knoxville, Tennessee. Fethe’s current value of operations, which is also its value of debt plus equity, is estimated to be $100 million. Fethe has $50 million face value, zero coupon debt that is due in 10 years. The risk-free rate is 6%, and the standard deviation of returns for companies similar to Fethe is 50%. Fethe’s owners view their equity investment as an option, and they would like to know the value of their investment. a. Using the Black-Scholes option pricing model, how much is Fethe’s equity worth? b. How much is the debt worth today? What is its yield? c. How would the equity value and the yield on the debt change if Fethe’s managers could use risk management techniques to reduce its volatility to 30%? Can you explain this? Solution: a. The inputs to the Black and Scholes option pricing model are: P = 100 X = 50 rRF = 6%  = 50% t = 10 years. The formula for the value of an option is: V = P[N(d 1)]  Xe RF [N(d 2 )] -r t

The first step is to use the inputs to calculate d1 and d2. Given these inputs, their values are calculated as: 2

d1 =

ln(P/X)  [rRF   / 2]t 

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ln(100/50)  [0.06  0.52 /2]10 0.5 10

= 1.60843 d2 = d1 -  t = 1.60843 − 0.5 10 = 0.2729 The next step is to calculate N(d1) and N(d2). Using Excel’s NORMSDIST function, their values are: N(d1) = 0.94613 N(d2) = 0.51089 Using the values of P, X, rRF, t, N(d1), and N(d2) gives the value of the call option equal to: -r t

V = P[N(d 1)]  Xe RF [N(d2 )] V = $100 [N[1.6083)] – $50e0.06(10) [N(0.2729)] V = $100[0.94613] – $50e0.06(10) [0.51089] = $80.594 million b.

Therefore, the debt must be worth $100 − $80.594 = $19.406 million. Its yield is: 1

 $50 10 Yield =    1  0.0993  9.93% .  $19.406  c.

At a volatility of 30%, d1 = 1.83744, N(d1) = 0.99693, d2 = 0.88876, and N(d2) = 0.81293. This gives an option value of $73.3854 million. The debt value is then 100 – 74.3854 = $25.6146 million. Its yield is 6.92%. The value of the stock goes down because Fethe has less of a chance of a ―home run.‖ The value of the debt goes up (and the yield goes down) because it becomes less risky.

SOLUTION TO SPREADSHEET PROBLEM 15-16

Build a Model: WACC and Optimal Capital Structure Start with the partial model in the file Ch15 P16 Build a Model.xlsx on the textbook’s website. Reacher Technology has consulted with investment bankers and determined the interest rate it would pay for different capital structures, as shown in the following table. Data for the risk-free rate, the market risk premium, an estimate of Reacher’s unlevered beta, and the tax rate are also shown. Reacher expects zero growth. Based on this information, what is the firm's optimal capital structure, and what is the weighted average cost of capital at the optimal structure?

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Percent Financed With Debt (wd)

Before-Tax Cost Debt (rd)

Input Data

6.0%

Risk-free rate

4.5%

6.1%

Market risk premium

5.5%

10%

6.3%

Unlevered beta

1.1

15%

6.7%

Tax rate

25.0%

20%

10.0%

30%

12.5%

35%

15.5%

40%

18.0%

Solution: The detailed solution for the problem is available in the file Ch15 P16 Build a Model Solutions.xlsx on the textbook’s website. 15-17

Build a Model: Equity Viewed as an Option Higgs Bassoon Corporation is a custom manufacturer of bassoons and other wind instruments. Its current value of operations, which is also its value of debt plus equity, is estimated to be $200 million. Higgs has zero coupon debt outstanding that matures in 3 years with $110 million face value. The risk-free rate is 5%, and the standard deviation of returns for similar companies is 60%. The owners of Higgs Bassoon view their equity investment as an option and would like to know its value. Start with the partial model in the file Ch15 P17 Build a Model.xlsx on the textbook’s website, and answer the following questions: a. Using the Black-Scholes option pricing model, how much is the equity worth? b. How much is the debt worth today? What is its yield? c. How would the equity value change if the company used risk management techniques to reduce its volatility to 45%? Can you explain this? d. Graph the yield to maturity on debt versus the face value of debt for values of the face value from $10 to $160 million. e. Graph the values of debt and equity for volatilities from 0.10 to 0.90 when the face value of the debt is $110 million. Solution: The detailed solution for the problem is available in the file Ch15 P17 Build a Model Solution.xlsx on the textbook’s website.

MINI CASE Assume you have just been hired as a business manager of PizzaPalace, a regional pizza restaurant chain. The company’s EBIT was $120 million last year and is not expected to grow. PizzaPalace is in the 25% state-plusfederal tax bracket, the risk-free rate is 6%, and the market risk premium is 6%. The firm is currently financed with all equity and it has 10 million shares outstanding. When you took your corporate finance course, your instructor stated that most firms’ owners would be financially better off if the firms used some debt. When you suggested this to your new boss, he encouraged you to pursue the idea. If the company were to recapitalize, debt would be issued, and the funds received would be used to repurchase stock. As a first step, assume that you obtained from the firm’s investment banker the following estimated costs of debt for the firm at different capital structures: But before proceeding, your boss had some questions for you.

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Data from problem statement: EBIT last year = $120 million Growth rate = g = 0% Tax rate = T = 25% Risk free rate = rRF = 6% Market risk premium = RPM Current capital structure = wd = 0% and ws = 100%

Using the free cash flow valuation model, what are the only avenues by which capital structure can affect value? Answer: The basic definitions are: (1) V = Value of Firm (2) FCF = Free Cash Flow (3) WACC = Weighted Average Cost of Capital (4) rs and rd are costs of stock and debt (5) ws and wd are percentages of the firm that are financed with stock and debt. ∑

(

)

The impact of capital structure on value depends upon the effect of debt on WACC and/or FCF. As we write this in 2022, the corporate tax rate is a flat 21%. Interest expense deductions are limited to 30% of EBIT in any single year. Any excess may be carried forward indefinitely. The reduction in the corporate tax rate and the limitations on interest expense deductibility should cause firms to reduce debt. b.

What is business risk? What factors influence a firm’s business risk?

Answer: Business risk is uncertainty about EBIT. Factors that influence business risk include: uncertainty about demand (unit sales); uncertainty about output prices; uncertainty about input costs; product and other types of liability; degree of operating leverage (DOL). b.

What is operating leverage, and how does it affect a firm’s business risk? Show the operating break-even point if a company has fixed costs of $200, a sales price of $15, and variables costs of $10.

Answer: Operating leverage is the change in EBIT caused by a change in quantity sold. The higher the proportion of fixed costs within a firm’s overall cost structure, the greater the operating leverage. Higher operating leverage leads to more business risk, because a small sales decline causes a larger EBIT decline. Q is quantity sold, F is fixed cost, V is variable cost, TC is total cost, and P is price per unit.

Operating Break-even = QBE

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QBE = F/(P – V) If, F = $200, P = $15, and V = $10: QBE = $200/($15 – $10) = 40 c.

Explain the difference between financial risk and business risk. Answer: Business risk increases the uncertainty in future EBIT. It depends on business factors such as competition, operating leverage, etc. Financial risk is the additional business risk concentrated on common stockholders when financial leverage is used. It depends on the amount of debt and preferred stock financing.

To illustrate the effects of financial leverage for PizzaPalace’s management, consider two hypothetical firms: Firm U (which uses no debt financing) and Firm L (which uses $4,000 of 8% interest rate debt). Both firms have $20,000 in net operating capital, a 25% tax rate, and an expected EBIT of $2,400.

Construct partial income statements, which start with EBIT, for the two firms.

Answer: Partial Income Statements:

EBIT Interest EBT Taxes NI d.

Firm U $2,400 $0 $2,400 $600 $1,800

Firm L $2,400 $320 $2,080 $520 $1,560

Calculate NOPAT, ROIC, and ROE for both firms.

Answer: EBIT = NOPAT = EBIT(1 − T) = Operating capital = ROIC = NOPAT/Op. Cap. = Equity = Net income = ROE = NI/Equity = d.

Firm U $2,400 $1,800 $20,000 9.0% $20,000 $1,800 9.0%

Firm L $2,400 $1,800 $20,000 9.0% $16,000 $1,560 9.8%

What does this example illustrate about the impact of financial leverage on ROE?

Answer: 1. ROIC wasn’t affected by financial leverage. 2. ROE went up, increasing the expected return to shareholders. 3. ROEL was greater than ROEU. d.

Why did leverage increase ROE in this example?

Answer: 1. More total dollars paid to L’s investors: a. U: NI = $1,800. b. L: NI + Int = $1,560 + $320 = $1,880. 2. Lower taxes paid by L:

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a. U: $600 b. L: $520. Less equity tied up in L: a. U: $20,000 b. L: $16,000

What happens to ROE for Firm U and Firm L if EBIT falls to $1,600? What happens if EBIT falls to $1,200? What is the after-tax cost of debt? What does this imply about the impact of leverage on risk and return? Answer: x EBIT Interest EBT Taxes NI

Firm U $1,600 $0 $1,600 $400 $1,200

Firm L $1,600 $320 $1,280 $320 $960

ROIC ROE

6.0% 6.0%

EBIT Interest EBT Taxes NI

Firm U $1,200 $0 $1,200 $300 $900

Firm L $1,200 $320 $880 $220 $660

ROIC ROE

4.5% 4.5%

4.5% 4.1%

Leverage only adds value if ROIC is greater than the after-tax cost of debt.

ROIC rd(1 – T)

EBIT $2,400 9.0% 6.0%

EBIT $1,600 6.0% 6.0%

EBIT $1,200 4.5% 6.0%

ROE

9.8%

6.0%

4.1%

What does capital structure theory attempt to do? What lessons can be learned from capital structure theory? Be sure to address the MM models and the Miller model. Answer: MM theory begins with the assumption of zero taxes. MM prove, under a very restrictive set of assumptions, that a firm’s value is unaffected by its financing mix: V L = V U. Therefore, capital structure is irrelevant. Any increase in roe resulting from financial leverage is exactly offset by the increase in risk (i.e., rs), so WACC is constant. MM theory later includes corporate taxes. Corporate tax laws favor debt financing over equity financing. With corporate taxes, the benefits of financial leverage exceed the risks because more EBIT goes to investors and less to taxes when leverage is used. MM shows that: VL = VU + TD.

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If T = 25%, then every dollar of debt adds 25 cents of extra value to firm. Notice that this is less than extra value added by debt prior to the TCJA because the previous federal-plus-state tax rate was about 40%. Miller later included personal taxes into the model, resulting in: 

VL = V U +  1   

 1 Tc  1 Ts   D  1 Td  

where Ts is the personal tax rate on income from stocks. Personal taxes lessen the advantage of corporate debt. Corporate taxes favor debt financing since corporations can deduct interest expenses, but personal taxes favor equity financing, since no gain is reported until stock is sold, and long-term gains are taxed at a lower rate. Miller’s conclusions with personal taxes are that the use of debt financing remains advantageous, but benefits are less than under only corporate taxes. Firms should still use 100% debt. Note: However, Miller argued that in equilibrium, the tax rates of marginal investors would adjust until there was no advantage to debt. MM theory ignores bankruptcy (financial distress) costs, which increase as more leverage is used. At low leverage levels, tax benefits outweigh bankruptcy costs. At high levels, bankruptcy costs outweigh tax benefits. An optimal capital structure exists that balances these costs and benefits. This is the trade-off theory. MM assumed that investors and managers have the same information. But managers often have better information. Thus, they would sell stock if stock is overvalued, and sell bonds if stock is undervalued. Investors understand this, so view new stock sales as a negative signal. This is signaling theory. The pecking order theory states that firms use internally generated funds first, because there are no flotation costs or negative signals. If more funds are needed, firms then issue debt because it has lower flotation costs than equity and not negative signals. If more funds are needed, firms then issue equity. One agency problem is that managers can use corporate funds for nonvalue maximizing purposes. The use of financial leverage bonds ―free cash flow,‖ and forces discipline on managers to avoid perks and nonvalue-adding acquisitions. A second agency problem is the potential for ―underinvestment‖. Debt increases risk of financial distress. Therefore, managers may avoid risky projects even if they have positive NPVs. Firms with many investment opportunities should maintain reserve borrowing capacity, especially if they have problems with asymmetric information (which would cause equity issues to be costly). The market timing theory states that managers try to ―time the market‖ when issuing securities. They issue equity when the market is ―high‖ and after big stock price run-ups. They issue debt when the stock market is ―low‖ and when interest rates are ―low.‖ They issue short-term debt when the term structure is upward sloping and long-term debt when it is relatively flat. g.

What does the empirical evidence say about capital structure theory? What are the implications for managers? Answer: Tax benefits are important. At the optimal capital structure, $1 debt adds about $0.10 to $0.20 to value on average. For the average firm financed with 25% to 30% debt, this adds about 3% to 6% to the total value. However, these results were based on periods prior to the TCJA and may now overstate the value added by debt. Bankruptcies are costly– costs can be up to 10% to 20% of firm value. Firms have targets, but don’t make quick corrections when stock price changes cause their debt ratios to change. The average speed of adjustment from the current capital structure to the target capital structure is about 30% per year. The speed is about 50% per year for firms with high cash flow. The speed is about 70% for firms with high cash flow

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that are above target. The lost value from being above target is bigger than lost value from being below target. When a company is above the target, distress costs rise very rapidly. Sometimes companies will deliberately increase debt to above target to take advantage of unexpected investment opportunity. After big stock price run-ups, the debt ratio falls, but firms tend to issue equity instead of debt. This is inconsistent with the trade-off model, inconsistent with the pecking order theory, but is consistent with the windows of opportunity hypothesis. Many firms, especially those with growth options and asymmetric information problems, tend to maintain excess borrowing capacity. Managers should take advantage of tax benefits by issuing debt, especially if the firm has a high effective tax rate, stable sales, and less operating leverage than the typical firm in its industry. Managers should avoid financial distress costs by maintaining excess borrowing capacity, especially if the firm has volatile sales, high operating leverage, many potential investment opportunities, or special purpose assets (instead of general purpose assets that make good collateral). If a manager has asymmetric information regarding the firm’s future prospects, then the manager should avoid issuing equity if actual prospects are better than the market perceives. Managers should always consider the impact of capital structure choices on lenders’ and rating agencies’ attitudes. h.

With the above points in mind, now consider the optimal capital structure for PizzaPalace.

For each capital structure under consideration, calculate the levered beta, the cost of equity, and the WACC.

Answer: MM theory implies that beta changes with leverage. bu is the beta of a firm when it has no debt (the unlevered beta). Hamada’s equation provides the beta of a levered firm: bL = bU [1 + (1 – T)(D/S)]. For example, to find the cost of equity for wd = 20%, we first use Hamada’s equation to find beta: b = bU [1 + (1 – T)(D/S)] = 1.0 [1 + (1 – 0.25) (20%/80%)] = 1.188 Then, use CAPM to find the cost of equity: rs = rRF + b (RPM) = 6% + 1.188 (6%) = 13.13% Next, the WACC for wd = 20% is: WACC = wd (1 – T) rd + ws rs WACC = 0.2 (1 – 0.25) (8%) + 0.8 (13.13%) WACC = 11.7% Then repeat this for all capital structures under consideration.

wd 0% 20% 30% 40% 50%

rd 0.0% 8.0% 8.5% 10.0% 12.0%

ws 100% 80% 70% 60% 50%

b 1.00 1.188 1.32 1.50 1.75

rs 12.00% 13.13% 13.93% 15.00% 16.50%

WACC 12.00% 11.70% 11.66% 12.00% 12.75%

The WACC is minimized at 11.66% for wd = 30%. h.

Now calculate the corporate value for each capital structure.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Answer: For example, suppose that we use wd = 20% to illustrate the calculations: FCF = NOPAT – Investments in operating capital = EBIT(1 − T) – Investments in operating capital = $120(1 – 0.25) – $0 = $90. Vop = FCF(1 + g)/(WACC-g) = $90(1 + 0)/(0.1170 − 0) = $769.23 million

Repeating this for all capital structures results in the following table:

wd 0% 20%

WACC 12.00% 11.70%

Vop $750.00 $769.23

30%

11.66%

$771.70

40% 50%

12.00% 12.75%

$750.00 $705.88

Describe the recapitalization process and apply it to PizzaPalace. Calculate the resulting value of the debt that will be issued, the resulting market value of equity, the price per share, the number of shares repurchased, and the remaining shares. Considering only the capital structures under analysis, what is PizzaPalace’s optimal capital structure? Answer: PizzaPalace will issue debt and use the proceeds to repurchase shares of stock. The situation before the recap is: Vop + ST Inv. VTotal − Debt S ÷n P

$750.00 0 $750.00 0 $750.00 10.00 $75.00

S −Cash distr. Wealth

$750.00 0 $750.00

The stock price is $75 and the total wealth of shareholders is $750 million. Now consider the situation if the firm moves to a capital structure with wd = 20% by issuing $153.85 million in debt but has not yet repurchased equity. The firm’s value of operations increases because its WACC decreases. The firm also temporarily has $153.85 million in short-term investments.

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Vop + ST Inv. VTotal − Debt S ÷n P

Before Debt $750.00 + 0 $750.00 −0.00 $750.00 ÷10.00 $75.00

S −Cash distr. Wealth

$750.00 0 $750.00

After Debt, Before Rep. $769.23 + 153.85 $923.08 −153.85 $769.23 ÷10.00 $76.92 $769.23 0 $769.23

Notice that the stock price increases and the wealth of shareholders increases. The repurchase itself will not change the stock price. If investors thought that the repurchase would increase the stock price, they would all purchase stock the day before, which would drive up its price. If investors thought that the repurchase would decrease the stock price, they would all sell short the stock the day before, which would drive down the stock price. The number of shares repurchased is: Number of shares repurchased = (D – D0)/P = ($153.85 – 0)/$76.92 = 2.0 The number of remaining shares after the repurchase is: Number of shares remaining n = n0 – no. of shares repurchased n = 10 – 2 =8

Vop + ST Inv. VTotal − Debt S ÷n P

Before Debt $750.00 + 0 $750.00 −0.00 $750.00 ÷10.00 $75.00

S +Cash distr. Wealth

$750.00 0 $750.00

After Debt, Before Rep.

After Rep.

$769.23 + 153.85 $923.08 −153.85 $769.23 ÷10.00 $76.92

$769.23 + 0.00 $769.23 −153.85 $615.38 ÷8.00 $76.92

$769.23 0 $769.23

$615.38 153.85 $769.23

Notice that the value of the equity declines as more debt is issued because the cash raised from issuing debt is used to repurchase stock. But the total wealth of shareholders is the value of stock after the recap plus the cash received in repurchase, and this total is not changed by the repurchase. There are some shortcuts we can take to find the values of S, P, and n after the repurchase:

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S = (1 – wd) Vop

 VopNew  D New    VopNew  D Old 

nPost

= nPrior 

PPost

VopNew  D Old n Pr ior

We apply these relationships for each possible capital structure:

wd 0% 20%

WACC 12.00% 11.70%

Vop $750.00 $769.23

D $0.00 $153.85

S $750.00 $615.38

n 10.0 8.0

P $75.00 $76.92

30%

11.66%

$771.70

$231.51

$540.19

7.0

$77.17

40% 50%

12.00% 12.75%

$750.00 $705.88

$300.00 $352.94

$450.00 $352.94

6.0 5.0

$75.00 $70.59

The optimal capital structure is for wd = 30%. This gives the highest corporate value, the lowest WACC, and the highest stock price per share. But notice that wd = 20% is very similar to the optimal solution; in other words, the optimal range is fairly wide. This is typical for most companies. j.

Liu Industries is a highly levered firm. Suppose there is a large probability that Liu will default on its debt. The value of Liu’s operations is $4 million. The firm’s debt consists of 1-year, zero coupon bonds with a face value of $2 million. Liu’s volatility, σ, is 0.60, and the risk-free rate rRF is 6%. Because Liu's debt is risky, its equity is like a call option and can be valued with the Black-Scholes Option Pricing Model (OPM). (See Chapter 7 for details of the OPM.)

What are the values of Liu’s stock and debt? What is the yield on the debt?

Answer: Liu’s equity can be considered as a call option on the total value of l with an exercise price of $2 million, and an expiration date in one year. If the value of Liu’s operations is less than $2 million in a year, then Liu’s management will not be able to make its required payment on the debt, and the firm will be bankrupt. The debtholders will take over the firm and the equity holders will receive nothing. If Liu’s value is greater than $2 million in one year, then management will repay the debt and the stockholders will keep the company. This option can be valued with the Black-Scholes Option Pricing Model: d1 = [ln(P/X) + (r + 0.52)T]/[T0.5] d2 = d1 – T0.5 V = P[N(d1)] – Xe-RTN(d2) And n() is the cumulative normal distribution function, from either Appendix A in the back of the text, or the NORMSDIST() function in Excel.

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in this case,

P = $4 X = $2  = 0.60 T = 1.0 r = 0.06

and calculating, d1 = 1.552 d2 = 0.9552 N(d1) = 0.9491 N(d2) = 0.8303 V = $2.1964 million. This leaves debt value of $4 million – $2.1964 million = $1.8036 million. The yield on this debt is calculated as Price = (Face Value)/(1 + Yield)N Solving for Yield: Yield = [Face Value/Price]1/N – 1.0 = [2.0/1.8036] – 1.0 = 10.89% In this case, the value of the debt must be $1.8036 million, and it is yielding 10.89%. The value of the equity is $2.1964 million. j.

What are the values of Liu’s stock and debt for volatilities of 0.40 and 0.80? What are yields on the debt?

Answer: Using the same procedure as in the previous question (j. 2.), the Mini Case model shows the results for the table below. In addition to the answers for volatilities of 0.40 and 0.80, the table below also shows other values.

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Value of Stock and Debt for Different Volatilities Volatility (σ) 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 j.

Equity 2.12 2.12 2.12 2.12 2.13 2.14 2.16 2.17 2.20 2.22 2.25 2.28 2.31 2.34 2.38 2.41

Debt 1.88 1.88 1.88 1.88 1.87 1.86 1.84 1.83 1.80 1.78 1.75 1.72 1.69 1.66 1.62 1.59

Debt Yield 6.18% 6.20% 6.27% 6.48% 6.89% 7.53% 8.41% 9.54% 10.89% 12.46% 14.24% 16.23% 18.40% 20.77% 23.33% 26.08%

What incentives might the manager of Liu have if she understands the relationship between equity value and volatility? What might debtholders do in response?

Answer: The value of the equity increases as the volatility increases—and the value of the debt decreases as well. A manager who knows this may choose to invest the proceeds from borrowing in assets that are riskier than usual. This is called ―bait and switch.‖ This action decreases the value of the debt, because now its claim is riskier. It increases the value of equity because the worse the stockholders can do is default on the bonds, but the best they can do is potentially unlimited. Bondholders who face this possibility will write covenants into their bond contracts limiting management’s ability to invest in assets other than originally planned. If this isn’t possible, then bondholders will demand a higher rate of return in order to compensate them for the possibility that management will switch investments. k.

How do companies manage the maturity structure of their debt? Answer: Factors that influence the decision to issue long-term bonds rather than short-term debt: Maturity matching: Finance long-term assets with long-term debt Finance short-term assets with short-term debt. Information asymmetries: Firms with better future opportunities than investors expect may not want to reveal details because that might attract competitors. But keeping details secret means that investors will charge higher interest rate because they don’t know enough about the company’s actual prospects. This means that if the company issues long-term debt it will have a higher interest rate than is commensurate with its actual prospects. Therefore, this type of firm will issue short-term debt (even though its rate is too high) but refinance later at appropriate rate when company’s prospects are revealed.

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SOLUTIONS TO WEB EXTENSION PROBLEMS WEB EXTENSION 15-B BOND REFUNDING (15B-1) Refunding Analysis Jan Volk, financial manager of Green Sea Transport (GST), has been asked by her boss to review GST’s outstanding debt issues for possible bond refunding. Five years ago, GST issued $40,000,000 of 11%, 25-year debt. The issue, with semiannual coupons, is currently callable at a premium of 11%, or $110 for each $1,000 par value bond. Flotation costs on this issue were 6%, or $2,400,000. Volk believes that GST could issue 20-year debt today with a coupon rate of 8%. The firm has placed many issues in the capital markets during the last 10 years, and its debt flotation costs are currently estimated to be 4% of the issue’s value. GST’s federal-plus-state tax rate is 25%. Help Volk conduct the refunding analysis by answering the following questions: a. What is the total dollar call premium required to call the old issue? Is it tax deductible? What is the net after-tax cost of the call? b. What is the dollar flotation cost on the new issue? Is it immediately tax deductible? What is the after-tax flotation cost? c. What amounts of old-issue flotation costs have not been expensed? Can these deferred costs be expensed immediately if the old issue is refunded? What is the value of the tax savings? d. What is the net after-tax cash outlay required to refund the old issue? e. What is the semiannual tax savings that arises from amortizing the flotation costs on the new issue? What is the forgone semiannual tax savings on the old-issue flotation costs? f. What is the semiannual after-tax interest savings that would result from the refunding? g. Thus far, Volk has identified two future cash flows: (1) the net of new-issue flotation cost tax savings and old-issue flotation cost tax savings that are lost if refunding occurs and (2) after-tax interest savings. What is the sum of these two semiannual cash flows? What is the appropriate discount rate to apply to these future cash flows? What is their present value? h. What is the NPV of refunding? Should GST refund now or wait until later? Solution: a. Since the call premium is 11%, the total premium is 0.11($40,000,000) = $4,400,000. However, this is a tax-deductible expense, so the relevant after-tax cost is $4,400,000(1 – T) = $4,400,000(0.75) = $3,300,000. b.

The dollar flotation cost on the new issue is 0.04($40,000,000) = $1,600,000. This cost is not immediately tax deductible, and hence the after-tax cost is also $1,600,000. (Note that the flotation cost can be amortized and expensed over the life of the issue. The value of this tax savings will be calculated in part e.)

The flotation costs on the old issue were 0.06($40,000,000) = $2,400,000. These costs were deferred and are being amortized over the 25-year life of the issue, and hence $2,400,000/25 = $96,000 are being expensed each year, or $48,000 each 6 months. Since the bonds were issued 5 years ago, (5/25)($2,400,000) = $480,000 of the flotation costs have already been expensed, and (20/25)($2,400,000) = $1,920,000 remain unexpensed. If the issue is refunded, the unexpensed portion of the flotation costs can be immediately expensed, and this would result in a tax savings of T($1,920,000) = 0.25($1,920,000) = $480,000.

The net after-tax initial cash outlay is shown below: Old issue call premium from part a: New issue flotation cost from part b: Tax savings on old issue flotation costs from part c:

$3,300,000 1,600,000 (480,000)

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Net cash outlay

$4,420,000

The new issue flotation costs of $1,600,000 would be amortized over the 20-year life of the issue. Thus, $1,600,000/20 = $80,000 would be expensed each year, or $40,000 each 6 months. The tax savings from this tax deduction is (0.25)$40,000 = $10,000 per semiannual period. By refunding the old issue and immediately expensing the remaining old issue flotation costs, the firm forgoes the opportunity to continue to expense the old flotation costs over time. Specifically, $2,400,000/25 = $96,000 each year, or $48,000 semiannually. The value of each $48,000 deduction forgone is 0.25($48,000) = $12,000.

The interest on the old issue is 0.11($40,000,000) = $4,400,000 annually, or $2,200,000 semiannually. Since interest payments are tax deductible, the after-tax semiannual amount is 0.75($2,200,000) = $1,650,000. The new issue carries an 8% coupon rate. Therefore, the annual interest would be 0.08($40,000,000) = $3,200,000, or $1,600,000 semiannually. The after-tax cost is thus 0.75($1,600,000) = $1,200,000. Thus, the after-tax net interest savings if refunding takes place would be $1,650,000 − $1,200,000 = $450,000 semiannually.

Semiannual Flotation Cost Tax Effects: Semiannual tax savings on new flotation: Tax benefits lost on old flotation: Net amortization tax effects

$10,000 (12,000) ($ 2,000)

Semiannual after-tax Interest Savings Due to Refunding: Semiannual after-tax interest on old bond: Semiannual after-tax interest on new bond: Net semiannual after-tax interest savings

$1,650,000 (1,200,000) $ 450,000

Semiannual cash flow = $450,000 – $2,000 = $448,000 The cash flows are based on contractual obligations, and hence have about the same amount of risk as the firm's debt. Further, the cash flows are already net of taxes. Thus, the appropriate interest rate is GST's after-tax cost of debt. (The source of the cash to fund the net investment outlay also influences the discount rate, but most firms use debt to finance this outlay, and, in this case, the discount rate should be the after-tax cost of debt.) Finally, since we are valuing future flows, the appropriate debt cost is today’s cost, or the cost of the new issue, and not the cost of debt floated 5 years ago. Thus, the appropriate discount rate is 0.75(8%) = 6% annually, or 3% per semiannual period. Using a financial calculator, input N = 40, I = 3, PMT = –448000, FV = 0, PV = ? PV = $10,355,418. h.

PV of net benefits from part g: Initial cash flow from part d: Refunding NPV =

$10,355,418 −$4,420,000 $5,935,418

The decision to refund now rather than wait till later is much more difficult than finding the NPV of refunding now. If interest rates were expected to fall, and hence GST would be able to issue debt in the future below today’s 8% rate, then it might pay to wait. However, interest rate movements are very difficult, if not impossible, to forecast, and hence most financial managers would probably take the ―bird-in-the-hand‖ and refund now with such a large NPV. Note, though, that if the NPV had been quite small, say $1,000, management would have undoubtedly waited, hoping that interest rates would fall further, and the cost of waiting ($1,000) would not have been high enough to worry about.

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(15B-2) Refunding Analysis Mullet Technologies is considering whether or not to refund a $75 million, 12% coupon, 30-year bond issue that was sold 5 years ago. It is amortizing $5 million of flotation costs on the 12% bonds over the issue’s 30year life. Mullet’s investment banks have indicated that the company could sell a new 25-year issue at an interest rate of 10% in today’s market. Neither they nor Mullet’s management anticipate that interest rates will fall below 10% any time soon, but there is a chance that rates will increase. A call premium of 12% would be required to retire the old bonds, and flotation costs on the new issue would amount to $5 million. Mullet’s marginal federal-plus-state tax rate is 25%. The new bonds would be issued 1 month before the old bonds are called, with the proceeds being invested in shortterm government securities returning 6% annually during the interim period. a. Conduct a complete bond refunding analysis. What is the bond refunding’s NPV? b. What factors would influence Mullet’s decision to refund now rather than later? Solution: a. Investment outlay required to refund the issue (all figures after-tax): Call premium on the old bond Flotation costs on new issue Immediate tax savings on old flotation expense Extra interest paid on old issue Interest earned on short-term investment Total after-tax initial outlay

−$6,750,000 −$5,000,000 $1,041,667 −$562,500 $281,250 −$10,989,583

Annual tax savings from new-issue flotation Annual lost tax savings from old-issue flotation Net flotation cost tax savings Interest on old bond Interest on new bond Net interest savings Total annual CF

$50,000 −$41,667 $8,333

$6,750,000 −$5,625,000 $1,125,000

= Net flotation cost tax savings + Net interest savings = $8,333 + $1,125,000 = $1,133,333

After-tax interest rate = 10%(1 − 0.25) = 7.5% Using a financial calculator, N = 25, I = 7.5, PMT = −$1,133,333, and solve for PV = $12,633,202. Without rounding in intermediate steps, PV = $12,633,205. NPV = after-tax initial CF + PV future CF = −$10,989,583 + $12,633,205 = $1,643,622. b.

The company should consider what interest rates might be next year. If there is a high probability that rates will drop below the current rate, it may be more advantageous to refund later versus now. If there is a high probability that rates will increase, the firm should act now to refund the old issue. Also, the company should consider how much ill will is created with investors if the issue is called. If Mullet is highly dependent on a small group of investors, it would want to avoid future difficulty in obtaining financing. However, bond issues are callable after a certain time and investors expect them to be called if rates drop considerably.

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SOLUTION TO WEB EXTENSION SPREADSHEET PROBLEM (15B-3) Build a Model: Bond Refunding Start with the partial model in the file Ch15 Web15A P03 Build a Model.xlsx on the textbook’s website. Schumann Shoe Manufacturer is considering whether or not to refund a $70 million, 10% coupon, 30-year bond issue that was sold 8 years ago. It is amortizing $4.5 million of flotation costs on the 10% bonds over the issue's 30-year life. Schumann's investment bankers have indicated that the company could sell a new 22-year issue at an interest rate of 8 percent in today's market. Neither they nor Schumann's management anticipate that interest rates will fall below 6% any time soon, but there is a chance that interest rates will increase. A call premium of 10% would be required to retire the old bonds, and flotation costs on the new issue would amount to $5 million. Schumann’s marginal federal-plus-state tax rate is 25%. The new bonds would be issued 1 month before the old bonds are called, with the proceeds being invested in short-term government securities returning 5% annually during the interim period. a. Conduct a complete bond refunding analysis. What is the bond refunding’s NPV? b. At what interest rate on the new debt is the NPV of the refunding no longer positive? Solution: The detailed solution for the spreadsheet problem, Solution for Ch15 Web15B P03 Build a Model.xlsx, is available on the textbook’s website.

Solution and Answer Guide CHAPTER 16: SUPPLY CHAINS AND WORKING CAPITAL M ANAGEMENT

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 369 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 373 Easy Problems 1–5 ................................................................................................................................ 373 Intermediate Problems 7–12 ................................................................................................................. 375 Challenging Problems 13–17 ................................................................................................................ 379 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 383 MINI CASE ............................................................................................................................................. 384

ANSWERS TO END-OF-CHAPTER QUESTIONS 16-1 Define each of the following terms: a. Working capital; net working capital; net operating working capital b. Current asset usage policies: relaxed policy, restricted policy, and moderate policy c. Permanent operating current assets; temporary operating current assets d. Current asset financing policies: maturity matching, aggressive, and conservative

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Inventory conversion period; average collection period; payables deferral period; cash conversion cycle f. Cash budget; target cash balance g. Transactions balance; compensating balance; precautionary balance h. Trade (cash) discounts i. Credit policy; credit period; credit standards; collection policy; cash discounts j. Account receivable; days sales outstanding; aging schedule k. Accruals; trade credit l. Stretching accounts payable; free trade credit; costly trade credit m. Promissory note; line of credit; revolving credit agreement n. Commercial paper; secured loan Answer: a. Working capital is a firm’s investment in short-term assets—cash, marketable securities, inventory, and accounts receivable. Net working capital is current assets minus current liabilities. Net operating working capital is operating current assets minus operating current liabilities. b.

A relaxed current asset policy refers to a policy under which relatively large amounts of cash, marketable securities, and inventories are carried and under which sales are stimulated by a liberal credit policy, resulting in a high level of receivables. A restricted policy refers to a policy under which holdings of cash, securities, inventories, and receivables are minimized. A moderate current asset investment policy lies between the relaxed and restricted policies.

Permanent current operating assets are the current operating assets needed even at the low point of the business cycle. For a growing firm in a growing economy, permanent current assets tend to increase over time. Temporary current operating assets are the current operating assets required above the permanent level when the economy is strong and/or seasonal sales are high.

Current assets consist of permanent current assets and temporary current assets. These current assets can be financed with short-term debt, long-term debt, or a mixture. A maturity matching financing policy matches asset and liability maturities—permanent current assets are financed with long-term capital and temporary current assets are financed with short-term debt. This is also referred to as a ―self-liquidating‖ approach because the short-term debt is paid off as the temporary current assets decline. With an aggressive current asset financing policy, some of the permanent current assets are financed with long-term capital but the remainder is financed with short-term debt. With a conservative current asset financing policy, all permanent current assets and some temporary current assets are financed with long-term capital; the remainder of temporary current assets is financed with short-term debt. This policy leads to periods when the company has too much permanent financing and must invest the excess in short-term securities.

The inventory conversion period is the average length of time it takes to convert materials into finished goods and then to sell them. It is calculated by dividing total inventory by daily cost of goods sold. The average collection period is the average length of time required to convert a firm’s receivables into cash. It is calculated by dividing accounts receivable by sales per day.

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The payables deferral period is the average length of time between a firm’s purchase of materials and labor and the payment of cash for them. It is calculated by dividing accounts payable by credit purchases per day (COGS/365). The cash conversion cycle is the length of time between the firm's actual cash expenditures on productive resources (materials and labor) and its own cash receipts from the sale of products (that is, the length of time between paying for labor and materials and collecting on receivables.) Thus, the cash conversion cycle equals the length of time the firm has funds tied up in current assets. f.

A cash budget is a schedule showing cash flows (receipts, disbursements, and cash balances) for a firm over a specified period. The target cash balance is the desired cash balance that a firm plans to maintain in order to conduct business.

Transactions balance (routine) is the cash balance associated with payments and collections; the balance necessary for day-to-day operations. A compensating balance is an amount that a firm must maintain in its checking account to compensate the bank for services rendered or for granting a loan. A precautionary balance is a cash balance held in reserve for random, unforeseen fluctuations in cash inflows and outflows.

Trade discounts, which are also called cash discounts, are price reductions that suppliers offer customers for early payment of bills.

Credit policy defines the policies and procedures for granting and collecting credit. There are four elements of credit policy, or credit policy variables. These are credit period, credit standards, collection policy, and discounts. The credit period is the length of time for which credit is extended. If the credit period is lengthened, sales will generally increase, as will accounts receivable. This will increase the financing needs and possibly increase bad debt losses. A shortening of the credit period will have the opposite effect. Credit standards determine the minimum financial strength required to become a credit, versus cash, customer. The optimal credit standards equate the incremental costs of credit to the incremental profits on increased sales. The collection policy is the procedure for collecting accounts receivable. A change in collection policy will affect sales, days sales outstanding, bad debt losses, and the percentage of customers taking discounts. Cash discounts are often used to encourage early payment and to attract customers by effectively lowering prices. Credit terms are usually stated in the following form: 2/10, net 30. This means a 2% discount will apply if the account is paid within 10 days, otherwise the account must be paid within 30 days.

An account receivable is created when a good is shipped or a service is performed, and payment for that good is not made on a cash basis, but on a credit basis. Days sales outstanding (DSO) is a measure of the average length of time it takes a firm’s customers to pay off their credit purchases. An aging schedule breaks down accounts receivable according to how long they have been outstanding. This gives the firm a more complete breakdown of their accounts receivable than that provided by days sales outstanding.

Accruals are continually recurring short-term liabilities, especially accrued wages and accrued taxes.

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Trade credit is debt arising from credit sales and recorded as an account receivable by the seller and as an account payable by the buyer. l.

Stretching accounts payable is the practice of deliberately paying accounts payable late. Free trade credit is credit received during the discount period. Credit taken in excess of free trade credit, whose cost is equal to the discount lost, is termed costly trade credit.

m. A promissory note is a document specifying the terms and conditions of a loan, including the amount, interest rate, and repayment schedule. A line of credit is an arrangement in which a bank agrees to lend up to a specified maximum amount of funds during a designated period. A revolving credit agreement is a formal, committed line of credit extended by a bank or other lending institution. n.

Commercial paper is unsecured, short-term promissory notes of large firms, usually issued in denominations of $100,000 or more and having an interest rate somewhat below the prime rate. A secured loan is backed by collateral, often inventories or receivables.

16-2 What are the two principal reasons for holding cash? Can a firm estimate its target cash balance by summing the cash held to satisfy each of the two reasons? Answer: The two principal reasons for holding cash are for transactions and compensating balances. The target cash balance is not equal to the sum of the holdings for each reason because the same money can often partially satisfy both motives. 16-3 Is it true that, when one firm sells to another on credit, the seller records the transaction as an account receivable while the buyer records it as an account payable and that, disregarding discounts, the receivable typically exceeds the payable by the amount of profit on the sale? Answer: False. Both accounts will record the same transaction amount. 16-4 What are the four elements of a firm’s credit policy? To what extent can firms set their own credit policies as opposed to accepting policies that are dictated by its competitors? Answer: The four elements in a firm’s credit policy are (1) credit standards, (2) credit period, (3) discount policy, and (4) collection policy. The firm is not required to accept the credit policies employed by its competition, but the optimal credit policy cannot be determined without considering competitors’ credit policies. A firm’s credit policy has an important influence on its volume of sales, and thus on its profitability. 16-5 What are the advantages of matching the maturities of assets and liabilities? What are the disadvantages? Answer: If an asset’s life and returns can be positively determined, the maturity of the asset can be matched to the maturity of the liability incurred to finance the asset. This matching will ensure that funds are borrowed only for the time they are required to finance the asset and that adequate funds will have been generated from the asset by the time the financing must be repaid. A basic fallacy is involved in the above discussion, however. Borrowing to finance receivables or inventories may be on a short-term basis because these turn over 8 to 12 times a year. But as a firm’s

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sales grow, its investment in receivables and inventories grow, even though they turn over. Hence, longer-term financing should be used to finance the permanent components of receivables and inventory investments. 16-6 From the standpoint of the borrower, is long-term or short-term credit riskier? Explain. Would it ever make sense to borrow on a short-term basis if short-term rates were above long-term rates? Answer: From the standpoint of the borrower, short-term credit is riskier because short-term interest rates fluctuate more than long-term rates, and the firm may be unable to repay the debt. If the lender will not extend the loan, the firm could be forced into bankruptcy. A firm might borrow short term if it thought that interest rates were going to fall and, therefore, that the long-term rate would go even lower. A firm might also borrow short term if it were only going to need the money for a short while and the higher interest would be offset by lower administration costs and no prepayment penalty. Thus, firms do consider factors other than interest rates when deciding on the maturity of their debt. 16-7 Discuss this statement: ―Firms can control their accruals within fairly wide limits.‖ Answer: This statement is false. A firm cannot ordinarily control its accruals since payrolls and the timing of wage payments are set by economic forces and by industry custom, while tax payment dates are established by law. 16-8 Is it true that most firms are able to obtain some free trade credit and that additional trade credit is often available, but at a cost? Explain. Answer: Yes. If a firm is able to buy on credit at all, if the credit terms include a discount for early payment, and if the firm pays during the discount period, it has obtained ―free‖ trade credit. However, taking additional trade credit by paying after the discount period can be quite costly. 16-9 What kinds of firms use commercial paper? Answer: Commercial paper refers to promissory notes of large, strong corporations. These notes have maturities that generally vary from 1 day to 9 months, and the return is usually 1½ to 3½ percentage points below the stated prime rate, and up to ½ of a percentage point above the T-bill rate. Most commercial paper outstanding is issued by financial institutions.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–5 16-1 Inventory Management. Williams & Sons last year reported sales of $12 million, cost of goods sold (COGS) of $10 million, and an inventory turnover ratio of 2. The company is now adopting a new inventory system. If the new system is able to reduce the firm’s inventory level and increase the firm’s inventory turnover ratio to 5 while maintaining the same level of sales and COGS, how much cash will be freed up? Solution: COGS = $10,000,000; Inventory turnover = COGS/Inventory = 2. Inventory = COGS/(Inventory turnover) = $10,000,000 = $5,000,000. 2

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If Turnover = 5, how much cash is freed up? Inventory = COGS/(Inventory turnover) =

$10,000,000 = $2,000,000. 5

Cash freed = $5,000,000 – $2,000,000 = $3,000,000. 16-2 Receivables Investment. Medwig Corporation has a DSO of 17 days. The company averages $3,500 in sales each day (all customers take credit). What is the company’s average accounts receivable? Solution: DSO = 17; Sales/Day = $3,500; A/R = ? A/ R S/ 365 17 = A/R $3,500

DSO =

A/R = DSO(Sales per day) = 17  $3,500 = $59,500. 16-3 Cost of Trade Credit. What are the nominal and effective costs of trade credit under the credit terms of 3/15, net 30? Solution: Nominal cost of trade credit =

3 365  97 30  15

= 0.0309  24.33 = 0.7526 = 75.26%. Effective cost of trade credit = (1.0309)24.33 – 1.0 = 1.0984 = 109.84%. 16-4 Financing Operating Current Assets. Cycling Biking Corporation (CBC) sells unicycles and bicycles. It has fixed assets of $200 million and permanent current assets of $30 million. Its business is cyclical and requires and it requires a total of $40 million in current assets at the height of its cycle in June but only requires a total of $30 million in current assets at the bottom of its cycle in January. CBC has a total of $230 million in financing by permanent total equity, long-term nonspontaneous debt, and spontaneous liabilities. How much additional short-term financing will it need in January? In June? Hint: Draw a graph. Solution: Inputs Fixed assets Permanent current assets Total current assets at top of seasonal cycle in June Total current assets at bottom of seasonal cycle in January Total permanent financing already in place

$200 $30 $40 $30 $230a

Total assets that are required in January and July: Fixed assets Permanent current assets Additional seasonal current assets Total assets required

January $200 $30 $0 $230

July $200 $30 $10 $240

Required additional financing via debt:

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Total assets Total permanent financing already in place Required additional financing via debt

January $230 $230 0

July $240 $230 $10

Note: Sum of permanent total equity, long-term nonspontaneous debt, and spontaneous liabilities.

16-5 Cost of Trade Credit. A large retailer obtains merchandise under the credit terms of 1/15, net 45, but routinely takes 60 days to pay its bills. (Because the retailer is an important customer, suppliers allow the firm to stretch its credit terms.) What is the retailer’s effective cost of trade credit? Solution: Effective cost of trade credit = (1 + 1/99)8.11 – 1.0 = 0.0849 = 8.49%. 16-6 Accounts Payable. A chain of appliance stores, APP Corporation, purchases inventory with a net price of $500,000 each day. The company purchases the inventory under the credit terms of 2/15, net 40. APP always takes the discount but takes the full 15 days to pay its bills. What is the average accounts payable for APP? Solution: Net purchase price of inventory = $500,000/day. Credit terms = 2/15, net 40. $500,000  15 = $7,500,000.

INTERMEDIATE PROBLEMS 7–12 16-7 Receivables Investment. Snider Industries sells on terms of 2/10, net 45. Total sales for the year are $1,500,000. Thirty percent of customers pay on the 10th day and take discounts; the other 70% pay, on average, 50 days after their purchases. a. What is the days sales outstanding? b. What is the average amount of receivables? c. What would the new days sales outstanding and average receivables be if Snider toughened its collection policy with the result that all nondiscount customers paid on the 45th day? Solution: a. The days sales outstanding are: DSO = 0.3(10) + 0.7(50) = 38 days. b.

Since total sales for the year are $1,500,000, per day sales will be: $1,500,000/365 = $4,109.59 sales per day. Thus, the average amount of receivables is: Average receivables = $4,109.59(38) = $156,164.

New DSO = 0.3(10) + 0.7(45) = 34.5 days. $1,500,000/365 = $4,109.59 sales per day. New Average receivables = $4,109.59(34.5) = $141,781.

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Sales may also decline as a result of the tighter credit. This would further reduce receivables. Also, some customers may now take discounts further reducing receivables. 16-8 Cost of Trade Credit. Captain Whitman Ship Supplies offers terms of 3/15, net 45. a. If a purchaser takes the discount and pays on the 15th day, what is the nominal cost of trade credit? b. Now suppose a purchaser actually pays on the 20th day but still takes the discount. What is the actual nominal cost of the trade credit? Solution: a. Nominal cost of trade credit = Cost per period 𝗑 (Number of periods per year) Nominal cost of trade credit = ( =( b.

Actual Nominal cost of trade credit =

)(

–

3 100 – 3

–

)

365

) (45 – 15) = 0.3763 = 37.63%

3 365 = 45.15%.  97 45  20

16-9 Cost of Trade Credit. Grunewald Industries sells on terms of 2/10, net 40. Gross sales last year were $4,562,500 and accounts receivable averaged $437,500. Half of Grunewald’s customers paid on the 10th day and took discounts. What are the nominal and effective costs of trade credit to Grunewald’s nondiscount customers? (Hint: Calculate daily sales based on a 365-day year, calculate the average receivables for discount customers, and then find the DSO for the nondiscount customers.) Solution: Sales per day =

$4,562,500 = $12,500. 365

Discount sales per day = 0.5($12,500) = $6,250. A/R attributable to discount customers = $6,250(10) = $62,500. A/R attributable to nondiscount customers: Total A/R Discount customers’ A/R Nondiscount customers’ A/R

$437,500 - 62,500 $375,000

Nondiscount sales per day = (1 – 0.5)($12,500) = $6,250.

A/ R $375,000 Days sales out st anding nondiscount cust omers  Sales per day  $6,250  60 days. Alternatively, DSO = $437,500/$12,500 = 35 days. Substituting the DSO for nondiscount of 35 days into the equation for the nondiscount customers 35 = 0.5(10) + 0.5(DSONondiscount) DSONondiscount = 30/0.5 = 60 days.

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Nondiscount customers are supposed to pay within 40 days, but they are actually paying, on average, in 60 days. Cost of trade credit to nondiscount customers equals the rate of return to the firm: Nominal rate =

2 365 = 0.0204(7.3) = 14.90%.  98 60  10

Effective cost = (1 + 2/98)365/50 – 1 = 15.89%. 16-10 Effective Cost of Trade Credit. The D.J. Masson Corporation needs to raise $500,000 for 1 year to supply working capital to a new store. Masson buys from its suppliers on terms of 3/10, net 90, and it currently pays on the 10th day and takes discounts. However, it could forgo the discounts, pay on the 90th day, and thereby obtain the needed $500,000 in the form of costly trade credit. What is the effective annual interest rate of this trade credit? Solution: Accounts payable:

 3   365     = (0.03093)(4.5625) = 14.11%.  97   80 

Nominal cost = 

EAR cost = (1.03093)4.5625 – 1.0 = 14.91%. 16-11 Cash Conversion Cycle. Negus Enterprises has an inventory conversion period of 50 days, an average collection period of 35 days, and a payables deferral period of 25 days. Assume that cost of goods sold is 80% of sales. a. What is the length of the firm’s cash conversion cycle? b. If annual sales are $4,380,000 and all sales are on credit, what is the firm’s investment in accounts receivable? c. How many times per year does Negus Enterprises turn over its inventory? Solution: a. Cash

Invent ory Average Payables conversion = conversion  collect ion  def erral cycle period period period = 50 + 35 – 25 = 60 days.

Average sales per day = $4,380,000/365 = $12,000 Investment in receivables = $12,000  35 = $420,000.

COGS = 0.80 × Sales = 0.80 × $4,380,000 = $3,504,000. Inv. conversion period =

Inv. COGS/ 365

50 =

Inv. $3,504,000/365

Inv. = $480,000. Inventory turnover = COGS/Inventory = $3,504,000/$480,000 = 7.3×.

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16-12 Working Capital Cash Flow Cycle. Strickler Technology is considering changes in its working capital policies to improve its cash flow cycle. Strickler’s sales last year were $3,250,000 (all on credit), and its net profit margin was 7%. Its inventory turnover was 6.0 times during the year, and its DSO was 41 days. Its annual cost of goods sold was $1,800,000. The firm had fixed assets totaling $535,000. Strickler’s payables deferral period is 45 days. a. Calculate Strickler’s cash conversion cycle. b. Assuming Strickler holds negligible amounts of cash and marketable securities, calculate its total assets turnover and ROA. c. Suppose Strickler’s managers believe the annual inventory turnover can be raised to 9 times without affecting sale or profit margins. What would Strickler’s cash conversion cycle, total assets turnover, and ROA have been if the inventory turnover had been 9 for the year? Solution: a. First, express inventory turnover in terms of COGS and inventory. Inventory turnover = COGS/Inventory. This implies: Inventory = COGS/(Inventory turnover) = $1,800,000/6 = $300,000. Inventory conversion period = Inv/(COGS/365) = $300,000/($1,800,000/365) = 60.8333 Average collection period = DSO = 41.0 days. Payables deferral period = PDP = 45.0 days.

Cash Invent ory Average Payables conversion = conversion  collect ion  def erral cycle period period period = 60.8 + 41 – 45 = 56.8 days. b.

Inventory = $300,000 (as calculated in part a). DSO = Receivables/(Daily sales) Receivables = DSO(Daily sales) = 41($3,250,000/365) = $365,068.49 Total assets = Inventory + Receivables + Fixed assets = $300,000 + $365,068.49 + $535,000 = $300,000 + $365,068.49 + $535,000 = $1,200,068.49 Total assets turnover = Sales/Total assets = $3,250,000/$1,200,068.49 = 2.7082. ROA = Profit margin  Total assets turnover = 0.07  2.7082 = 0.1896 = 18.96%.

Inventory turnover = COGS/Inv. Inventory = COGS/(Inventory turnover) = $1,800,000/9 = $200,000 Inventory conversion period = Inventory/(Daily COGS) = $200,000/($1,800,000/365)

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= 40.56 days. Cash conversion cycle = 40.6 + 41 – 45 = 36.6 days. Note: The receivables balance was calculated in part b and does not change; the inventory was calculated in part c. Total assets = Inventory + Receivables + Fixed assets = $200,000 + $365,068.49 + $535,000 = $1,100,068.49 Total assets turnover = Sales/TA = $3,250,000/$1,100,068.49 = 2.9544. ROA = Profit margin  Total assets turnover ROA = 0.07  2.9544 = 0.2068 = 20.68%.

CHALLENGING PROBLEMS 13–17 16-13 Current Asset Usage Policy. Payne Products had $1.6 million in sales revenues in the most recent year and expects sales growth to be 25% this year. Payne would like to determine the effect of various current assets policies on its financial performance. Payne has $1 million of fixed assets and intends to keep its debt ratio at its historical level of 40%. Payne’s debt interest rate is currently 8%. You are to evaluate three different current asset policies: (1) a restricted policy in which current assets are 45% of projected sales, (2) a moderate policy with 50% of sales tied up in current assets, and (3) a relaxed policy requiring current assets of 60% of sales. Earnings before interest and taxes are expected to be 12% of sales. Payne’s tax rate is 25%. a. What is the expected return on equity under each current asset level? b. In this problem, we have assumed that the level of expected sales is independent of current asset policy. Is this a valid assumption? Why or why not? c. How would the overall risk of the firm vary under each policy? Solution: a. Current year sales are expected to be $1,600,000 × (1.25) = $2,000,000. Return on equity may be computed as follows: Restricted

Moderate

Relaxed

(% of sales × Sales)

$900,000

$1,000,000

$1,200,000

Fixed assets

1,000,000

Total assets

$1,900,000

$2,000,000

$2,200,000

Debt (40% of assets)

$760,000

$800,000

$880,000

Equity

1,140,000

1,200,000

1,320,000

Total liability and equity

$1,900,000

$2,000,000

$2,200,000

$240,000

Current assets

EBIT (12% of sales) Interest (8%)

60,800

64,000

70,400

Pre-tax earnings

$179,200

$176,000

$169,600

Taxes (25%)

44,800

44,000

42,400

Net income

$134,400

$132,000

$127,200

Return on equity

11.79%

11.00%

9.64%

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No, this assumption would probably not be valid in a real-world situation. A firm’s current asset policies, particularly with regard to accounts receivable, such as discounts, collection period, and collection policy, may have a significant effect on sales. The exact nature of this function may be difficult to quantify, however, and determining an ―optimal‖ current asset level may not be possible in actuality.

As the answers to part a indicate, the tighter policy leads to a higher expected return. However, as the current asset level is decreased, presumably some of this reduction comes from accounts receivable. This can be accomplished only through higher discounts, a shorter collection period, and/or tougher collection policies. As outlined above, this would in turn have some effect on sales, possibly lowering profits. More restrictive receivable policies might involve some additional costs (collection, and so forth) but would also probably reduce bad debt expenses. Lower current assets would also imply lower liquid assets; thus, the firm’s ability to handle contingencies would be impaired. Higher risk of inadequate liquidity would increase the firm’s risk of insolvency and thus increase its chance of failing to meet fixed charges. Also, lower inventories might mean lost sales and/or expensive production stoppages. Attempting to attach numerical values to these potential losses and probabilities would be extremely difficult.

16-14 Cash Budgeting. Dorothy Koehl recently leased space in the Southside Mall and opened a new business, Koehl’s Doll Shop. Business has been good, but Koehl frequently runs out of cash. This has necessitated late payment on certain orders, which is beginning to cause a problem with suppliers. Koehl plans to borrow from the bank to have cash ready as needed, but first she needs a forecast of how much she should borrow. Accordingly, she has asked you to prepare a cash budget for the critical period around Christmas, when needs will be especially high. Sales are made on a cash basis only. Koehl’s purchases must be paid for during the following month. Koehl pays herself a salary of $4,800 per month, and the rent is $2,000 per month. In addition, she must make a tax payment of $12,000 in December. The current cash on hand (on December 1) is $400, but Koehl has agreed to maintain an average bank balance of $6,000—this is her target cash balance. (Disregard the amount in the cash register, which is insignificant because Koehl keeps only a small amount on hand in order to lessen the chances of robbery.) The estimated sales and purchases for December, January, and February are shown below. Purchases during November amounted to $140,000.

a. b.

Sales

Purchases

December

$160,000

$40,000

January

40,000

February

60,000

40,000

Prepare a cash budget for December, January, and February. For each month, report the amount that must be borrowed or the amount of the surplus. Suppose that Koehl starts selling on a credit basis on December 1, giving customers 30 days to pay. All customers accept these terms, and all other facts in the problem are unchanged. What would the company’s loan requirements be at the end of December in this case? (Hint: The calculations required to answer this part are minimal.)

Solution: a. Collections and Purchases: December $160,000

January $40,000

February $60,000

Purchases

40,000

Payments for purchases Salaries

140,000* 4,800

40,000 4,800

Sales (Collections) (A)

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Rent Taxes Total payments (B)

2,000 12,000 $158,800

2,000 --$46,800

Cash at start of forecast Net cash flow (A) – (B) Cumulative cash balance Target cash balance Surplus cash or loans needed

--($ 6,800) ($ 5,200) 6,000

--$13,200 $ 8,000 6,000

400 1,200 1,600 6,000

($ 4,400)

($ 11,200)

$ 2,000

*November purchases = $140,000. b.

If the company began selling on credit on December 1, then it would have zero receipts during December, down from $160,000. Thus, it would have to borrow an additional $160,000, so its loans outstanding by December 31 would be $164,400. The loan requirements would build gradually during the month. We could trace the effects of the changed credit policy on out into January and February, but here it would probably be best to simply construct a new cash budget.

16-15 Cash Discounts. Suppose a firm makes purchases of $3.65 million per year under terms of 2/10, net 30, and takes discounts. a. What is the average amount of accounts payable net of discounts? (Assume the $3.65 million of purchases is net of discounts—that is, gross purchases are $3,724,489.80, discounts are $74,489.80, and net purchases are $3.65 million.) b. Is there a cost of the trade credit the firm uses? c. If the firm did not take discounts but did pay on the due date, what would be its average payables and the nominal and effective costs of this non-free trade credit? d. What would be the firm’s nominal and effective costs of not taking discounts if it could stretch its payments to 40 days? Solution: a.

$3,650,000 Average account s =  10 days = $10,000  10 = $100,000. 365 days payable

There is no cost of trade credit at this point. The firm is using ―free‖ trade credit.

Average payables $3,650,000 =  30 = $10,000  30 = $300,000. (net of discount ) 365

Nominal cost = (2/98)(365/20) = 37.24%, or $74,489.80/($300,000 – $100,000) = 37.24%. Effective cost = (1 + 2/98)365/20 – 1 = 0.4459 = 44.59%. d.

Nominal rate =

2 365 × = 24.83%. 98 40  10

Effective cost = (1 + 2/98)365/30 – 1 = 0.2786 = 27.86%. 16-16 Trade Credit. The Thompson Corporation projects an increase in sales from $1.5 million to $2 million, but it needs an additional $300,000 of current assets to support this expansion. Thompson can finance the expansion by no longer taking discounts, thus increasing accounts payable. Thompson purchases under terms of 2/10, net 30, but it can delay payment for an additional 35 days—paying in 65 days and thus becoming 35 days past due—without a penalty because its suppliers currently have excess capacity. What is the effective, or equivalent, annual cost of the trade credit? Solution:

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Trade Credit Terms: 2/10, net 30. But the firm plans delaying payments 35 additional days, which is the equivalent of 2/10, net 65. Discount percent

Nominal cost =

100 

Discount percent

365 Days credit Discount  is outstanding period

2 365 2 365 × = × = 0.0204 (6.6364) = 13.54% . 100  2 65  10 98 55

Effective cost = (1 + 2/98)365/55 – 1 = 14.35%. 16-17 Bank Financing. The Raattama Corporation had sales of $3.5 million last year, and it earned a 5% return (after taxes) on sales. Recently, the company has fallen behind in its accounts payable. Although its terms of purchase are net 30 days, its accounts payable represents 60 days’ purchases. The company’s treasurer is seeking to increase bank borrowing in order to become current in meeting its trade obligations (that is, to have 30 days’ payables outstanding). The company’s balance sheet is as follows (in thousands of dollars):

a. b.

Cash Accounts receivable Inventory Current assets Land and buildings Equipment

$ 100 300 1,400 $1,800 600 600

Total assets

$3,000

Accounts payable Bank loans Accruals Current liabilities Mortgage on real estate Common stock, $0.10 par Retained earnings Total liabilities and equity

$ 600 700 200 $1,500 700 300 500 $3,000

How much bank financing is needed to eliminate the past-due accounts payable? Assume that the bank will lend the firm the amount calculated in part a. The terms of the loan offered are 8%, simple interest, and the bank uses a 360-day year for the interest calculation. What is the interest charge for 1 month? (Assume there are 30 days in a month.) Now ignore part b and assume that the bank will lend the firm the amount calculated in part a. The terms of the loan are 7.5%, add-on interest, to be repaid in 12 monthly installments. (1) What is the total loan amount? (2) What are the monthly installments? (3) What is the APR of the loan? (4) What is the effective rate of the loan? Would you, as a bank loan officer, make this loan? Why or why not?

Solution: a.

   Days payables Purchases  Size of bank loan =    outstanding  30  Days payables outstanding     = ($600,000/60)(60 – 30) = $10,000(30) = $300,000. Alternatively, one could simply recognize that accounts payable must be cut to half of its existing level, because 30 days is half of 60 days.

Simple interest rate per day = Nominal rate/Days in year = 0.08/360 = 0.000222222. Interest charge for month = Rate per day × Loan amount × Days in month

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= 0.000222222 × $300,000 × 30 = $2,000. c.

(1) Add-on interest = $300,000 × 0.075 = $22,500. Total loan amount = $300,000 + $22,500 = $322,500. (2) Monthly installments = $322,500/12 = $26,875. (3) Enter the following inputs into your calculator: N = 12; PV = 300000; PMT = –26875; FV = 0; and solve for I/YR. I/YR = 1.130552026%. Remember, this is a monthly rate, so APR is: APR = 12 × 1.130552026% = 13.57%. (4) Effective rate of the loan = (1.01130552026)12 – 1 = 14.44%.

Given the limited information, the decision must be based on the rule-of-thumb comparisons, such as the following: 1. Debt ratio = ($1,500,000 + $700,000)/$3,000,000 = 73%. Raattama’s debt ratio is 73%, as compared to a typical debt ratio of 50%. The firm appears to be undercapitalized. 2. Current ratio = $1,800,000/$1,500,000 = 1.20. The current ratio appears to be low, but current assets could cover current liabilities if all accounts receivable can be collected and if the inventory can be liquidated at its book value. 3. Quick ratio = $400,000/$1,500,000 = 0.27. The quick ratio indicates that current assets, excluding inventory, are only sufficient to cover 27% of current liabilities, which is very bad. The company appears to be carrying excess inventory and financing extensively with debt. Bank borrowings are already high and the liquidity situation is poor. On the basis of these observations, the loan should be denied, and the treasurer should be advised to seek permanent capital, especially equity capital.

SOLUTION TO SPREADSHEET PROBLEM 16-18 Build a Model: Cash Budgeting. Start with the partial model in the file Ch16 P18 Build a Model.xlsx on the textbook’s website. Rusty Spears, CEO of Rusty’s Renovations, a custom building and repair company, is preparing documentation for a line of credit request from his commercial banker. Among the required documents is a detailed sales forecast for parts of 2024 and 2025:

May 2024 June July August September October November

Sales $60,000 100,000 130,000 120,000 100,000 80,000 60,000

Labor and Raw Materials $75,000 90,000 95,000 70,000 60,000 50,000 20,000

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December January 2025

40,000 30,000

20,000 NA

Estimates obtained from the credit and collection department are as follows: collections within the month of sale, 15%; collections during the month following the sale, 65%; collections the second month following the sale, 20%. Payments for labor and raw materials are typically made during the month following the one in which these costs were incurred. Total costs for labor and raw materials are estimated for each month, as shown in the table. General and administrative salaries will amount to approximately $15,000 a month; lease payments under long-term lease contracts will be $5,000 a month; depreciation charges will be $7,500 a month; miscellaneous expenses will be $2,000 a month; income tax payments of $25,000 will be due in both September and December; and a progress payment of $80,000 on a new office suite must be paid in October. Cash on hand on July 1 will amount to $60,000, and a minimum cash balance of $40,000 will be maintained throughout the cash budget period. a. Prepare a monthly cash budget for the last 6 months of 2024. b. Prepare an estimate of the required financing (or excess funds)—that is, the amount of money Rusty’s Renovations will need to borrow (or will have available to invest)—for each month during that period. c. Assume that receipts from sales come in uniformly during the month (i.e., cash receipts come in at the rate of 1/30 each day) but that all outflows are paid on the 5th of the month. Will this have an effect on the cash budget—in other words, would the cash budget you have prepared be valid under these assumptions? If not, what can be done to make a valid estimate of peak financing requirements? No calculations are required, although calculations can be used to illustrate the effects. d. Rusty’s Renovations produces on a seasonal basis, just ahead of sales. Without making any calculations, discuss how the company’s current ratio and debt ratio would vary during the year assuming all financial requirements were met by short-term bank loans. Could changes in these ratios affect the firm’s ability to obtain bank credit? Why or why not? e. If its customers began to pay late, this would slow down collections and thus increase the required loan amount. Also, if sales dropped off, this would have an effect on the required loan amount. Perform a sensitivity analysis that shows the effects of these two factors on the maximum loan requirement. Solution: The detailed solution for the spreadsheet problem, Ch16 P18 Build a Model Solution.xlsx, is available on the textbook’s website.

MINI CASE Karen Johnson, CFO for Raucous Roasters (RR), a specialty coffee manufacturer, is rethinking her company’s working capital policy in light of a recent scare she faced when RR’s corporate banker, citing a nationwide credit crunch, balked at renewing RR’s line of credit. Had the line of credit not been renewed, RR would not have been able to make payroll, potentially forcing the company out of business. Although the line of credit was ultimately renewed, the scare has forced Johnson to examine carefully each component of RR’s working capital to make sure it is needed, with the goal of determining whether the line of credit can be eliminated entirely. In addition to (possibly) freeing RR from the need for a line of credit, Johnson is well aware that reducing working capital will improve free cash flow. Historically, RR has done little to examine working capital, mainly because of poor communication among business functions. In the past, the production manager resisted Johnson’s efforts to question his holdings of raw materials, the marketing manager resisted questions about finished goods, the sales staff resisted questions about credit policy (which affects accounts receivable), and the treasurer did not want to talk about the cash and securities balances. However, with the recent credit scare, this resistance became unacceptable and Johnson has undertaken a company-wide examination of cash, marketable securities, inventory, and accounts receivable levels.

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Johnson also knows that decisions about working capital cannot be made in a vacuum. For example, if inventories could be lowered without adversely affecting operations, then less capital would be required, and free cash flow would increase. However, lower raw materials inventories might lead to production slowdowns and higher costs, and lower finished goods inventories might lead to stockouts and loss of sales. So, before inventories are changed, it will be necessary to study operating as well as financial effects. The situation is the same with regard to cash and receivables. Johnson has begun her investigation by collecting the ratios shown here. (The partial cash budget shown after the ratios is used later in this mini case.)

Industry

Current

1.75

2.25

Quick

0.92

1.16

Total liabilities/assets

58.76%

50.00%

Turnover of cash and securities

16.67

22.22

Days sales outstanding (365-day basis)

45.63

32.00

Inventory turnover

10.80

20.00

Fixed assets turnover

7.75

13.22

Total assets turnover

2.60

3.00

Profit margin on sales

2.07%

3.50%

Return on equity (ROE)

10.45%

21.00%

Payables deferral period

30.00

33.00

Johnson plans to use the preceding ratios as the starting point for discussions with RR’s operating team. Based on the data, does RR seem to be following a relaxed, moderate, or restricted current asset usage policy? Answer: A company with a relaxed current asset usage policy would carry relatively large amounts of current assets relative to sales. It would be guarding against the possibility of running out of stock, running short of cash, and losing sales to customers who need some credit. We can see that RR has relatively low cash and inventory turnover ratios. For example, inventory turnover = 10.80 versus 20.00 for an average firm in its industry. Thus, RR is carrying a lot of inventory per dollar of sales, which would meet the definition of a relaxed policy. Similarly, RR’s DSO is relatively high. Since DSO is calculated as receivables/sales per day, a high DSO indicates a lot of receivables per dollar of sales. Thus, RR seems to have a relaxed working capital policy, and a lot of current assets.

How can one distinguish between a relaxed but rational working capital policy and a situation in which a firm simply has excessive current assets because it is inefficient? Does RR’s working capital policy seem appropriate? Answer: RR may choose to hold large amounts of inventory to avoid the costs of ―running short,‖ and to cater to customers who expect to receive their coffee immediately. RR may also choose to hold high amounts of receivables to maintain good relationships with its customers. However, if RR is holding large stocks of inventory and receivables to better serve customers, it should be able to offset the costs of carrying that working capital with high prices or higher sales, and its ROE should be no lower than that of firms with other working capital policies. It is clear from the data in the table that RR is not as profitable as the average firm in its industry. This suggests that it simply has excessive working capital, and that it should take steps to reduce its working capital.

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Calculate the firm’s cash conversion cycle given annual sales are $660,000 and cost of goods represent 90% of sales. Assume a 365-day year. Answer: A firm’s cash conversion cycle is calculated as:

Cash Payables Invent ory Average conversion + collect ion – def erral = conversion period cycle period period We need to determine the RR’s inventory conversion period from the data given. We know that its inventory turnover ratio (COGS/Inventory) is 10.8. So its level of inventories is calculated as $594,000/10.8 = $55,000. We also know that the firm’s COGS is 0.90 × $660,000 = $594,000. Its inventory conversion period can now be calculated as: Inventory conversion period = Inventory/(COGS/365) = $55,000/($594,000/365) = 33.8. RR’s average collection period is equal to its DSO. Its DSO is given as 45.6 days. We are given that its payables deferral period is 30 days, so now we have all the individual components to calculate RR’s cash conversion cycle. Cash conversion cycle = 33.8 days + 45.6 days – 30 days = 49.4 days. Thus, RR’s cash conversion cycle is approximately 49 days. d.

Is there any reason to think that RR may be holding too much inventory? Answer: As pointed out in part a, RR’s inventory turnover (10.8) is considerably lower than the average firm’s turnover (20.00). This indicates that the firm is carrying excessive inventory per dollar of sales.

If RR reduces its inventory without adversely affecting sales, what effect should this have on free cash flow: (1) in the short run and (2) in the long run? Answer: A one-time reduction in inventory causes an identical one-time increase in free cash flows. However, if sales grow and inventory improvement processes are maintained, then future FCF each year will be greater than it otherwise would have been. An improvement in a working capital process is a gift that keeps on giving.

Johnson knows that RR sells on the same credit terms as other firms in its industry. Use the ratios presented earlier to explain whether RR’s customers pay more or less promptly than those of its competitors. If there are differences, does that suggest RR should tighten or loosen its credit policy? What four variables make up a firm’s credit policy, and in what direction should each be changed by RR? Answer: RR’s DSO is 45.63 days as compared with 32 days for the average firm in its industry. This suggests that RR’s customers are paying less promptly than those of its competitors. Because the firm’s DSO is higher than the industry average, the firm should tighten its credit policy in an attempt to lower its DSO. The four variables that make up a firm’s credit policy are (1) discount amount and period, (2) credit period, (3) credit standards, and (4) collection policy. Cash discounts generally produce two benefits: (1) They attract new customers who view discounts as a price reduction, thus sales would increase, and (2) they cause a reduction in the days sales outstanding (DSO) since some established customers will pay more promptly to take advantage of the discount; thus. the level of receivables held would decline. Discounts

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might encourage customers now paying late to pay more promptly. Of course, these benefits are offset to some degree by the dollar cost of the discounts. The effect on bad debt expense is indeterminate. If the firm tightened its credit policy, it is unclear what the firm would do with its cash discount policy. The firm could decrease the discount period and keep discounts unchanged. Credit period is the length of time allowed all ―qualified‖ customers to pay for their purchases. The shorter a firm’s credit period, the shorter the firm’s days sales outstanding, and the lower the level of receivables held. A shorter credit period might also tend to decrease sales, especially when a competitor’s credit period is longer than the firm’s own credit period. The effect of the credit period on bad debt expense is indeterminate. In order to qualify for credit in the first place, customers must meet the firm’s credit standards. These dictate the minimum acceptable financial position required of customers to receive credit. Also, a firm may impose differing credit limits depending on the customer’s financial strength. Tight credit standards would tend to decrease sales (fewer customers would qualify for credit), decrease the level of receivables held, and would cause a decrease in the amount of bad debt expenses. The level of receivables held would decrease due to the lower level of sales and also the probability that customers now qualifying for credit would take less time to pay. Bad debt expenses should decrease due to raising customers’ minimum acceptable financial positions. Finally, collection policy refers to the procedures that the firm follows to collect past-due accounts. These can range from a simple letter or phone call to turning the account over to a collection agency. A tight collection policy would decrease the level of receivables held, as customers would decrease the length of time they took to pay their bills. A tight collection policy would also cause a decrease in the amount of bad debt losses the firm incurred. A tightening of credit policy would tend to decrease sales, decrease the level of receivables held, and decrease the amount of bad debt expenses. g.

Does RR face any risks if it tightens its credit policy? Answer: A tighter credit policy may discourage sales. Some customers may choose to go elsewhere if they are pressured to pay their bills sooner.

If the company reduces its DSO without seriously affecting sales, what effect would this have on its free cash flow (1) in the short run and (2) in the long run? Answer: Similar to the situation with inventory, a one-time reduction in DSO causes an identical one-time increase in free cash flows. If sales grow and DSO remains at its new level, then future FCF each year will be greater than it otherwise would have been.

What is the impact of higher levels of accruals, such as accrued wages or accrued taxes? Is it likely that RR could make changes to accruals?

Answer: Higher levels of accruals increase free cash flow. No, RR could not make greater use of its accruals. Accruals arise because (1) workers are paid after they have actually provided their services, and (2) taxes are paid after the profits have been earned. Thus, accruals represent cash owed either to workers or to the IRS. The cost of accruals is generally considered to be zero, since no explicit interest must be paid on these items. The amount of accruals is generally limited by the amount of wages paid and the firm’s profitability, as well as by industry conventions regarding when wage payments are made and IRS regulations regarding tax payments. (Increasingly, Congress is putting businesses on a pay-as-you-go, or even pay-ahead-of-time basis through the use of estimated taxes.) A firm cannot ordinarily control its accruals. Firms use all the accruals they can, but they have little control over the levels of these accounts.

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Assume that RR purchases $200,000 (net of discounts) of materials on terms of 1/10, net 30, but that it can get away with paying on the 40th day if it chooses not to take discounts. How much free trade credit can the company get from its equipment supplier, how much costly trade credit can it get, and what is the nominal annual interest rate of the costly credit? Should RR take discounts? Answer: If RR’s net purchases are $200,000 annually, then, with a 1% discount, its gross purchases are $200,000/0.99 = $202,020. Net daily purchases from this supplier are $200,000/365 = $547.94. If the discount is taken, then RR must pay this supplier at the end of Day 10 for purchases made on Day 1, on Day 11 for purchases made on Day 2, and so on. Thus, in a steady state, RR will on average have 10 days’ worth of purchases in payables, so, Payables = 10($547.94) = $5,479. If the discount is not taken, then RR will wait 40 days before paying, so Payables = 40($547.94) = $21,918. Therefore: Trade credit if discounts are not taken: Trade credit if discounts are taken: Difference:

$21,918 = total trade credit – 5,479 = free trade credit $16,439 = costly trade credit

To obtain $16,439 of costly trade credit, RR must give up 0.01($202,020) = $2,020 in lost discounts annually. Since the forgone discounts pay for $16,439 of credit, the nominal annual interest rate is 12.29%.

$2,020 = 0.1229 = 12.29%. $16,439

Here is a formula that can be used to find the nominal annual interest rate of costly trade credit: Discount % 365 days Nominal cost × . = of trade credit 1  Discount % Days taken  Discount period

In this situation, Nominal cost of trade credit =

1 365 = 0.0101 x 12.1667 = 0.1229 = 12.29% × 99 40  10

Note (1) that the formula gives the same nominal annual interest rate as was calculated earlier, (2) that the first term is the periodic cost of the credit (RR spends $1 to get the use of $99), and (3) that the second term is the number of ―savings periods‖ per year (RR delays payment for 40 – 10 = 30 days), and there are 365/30 = 12.1667 30-day periods in a year. Therefore, we could calculate the exact effective annual interest rate as: effective rate = (1.0101) 12.1667 – 1 = 13.01%. If RR can obtain financing from its bank (or from other sources) at an interest rate of less than 13.01%, it should borrow the funds and take discounts. k.

Cash doesn’t earn interest, so why would a company have a positive target cash balance? Answer: 1. Transactions balances. A company must have some cash to pay current bills. 2. Precautionary balances (i.e., ―Safety stock‖) to handle unexpected needs. These balances can be low if a company has credit line or other holdings of short-term securities.

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3. 4. l.

It is essential that a firm have sufficient cash to take trade discounts. Compensating balances. Some banks require compensating balances for loans and/or services provided.

What might RR do to reduce its target cash balance without harming operations? Answer: 1. Synchronize cash inflows and outflows. 2. Use float. 3. Use lockboxes. 4. Insist on wire transfers or automatic debit from customers. 5. Increase forecast accuracy to reduce the need for a cash ―safety stock.‖ 6. Hold marketable securities instead of a cash ―safety stock.‖ 7. Negotiate a line of credit (also reduces need for a ―safety stock‖).

m. RR tries to match the maturity of its assets and liabilities. Describe how RR could adopt either a more aggressive or more conservative financing policy. Answer: There are three alternative current asset financing policies: aggressive, moderate, and relaxed. A moderate financing policy matches asset and liability maturities. (Of course, exact maturity matching is not possible because of (1) the uncertainty of asset lives and (2) some common equity must be used and common equity has no maturity.) With this strategy, the firm minimizes its risk that it will be unable to pay off maturing obligations. An aggressive financing policy occurs when the firm finances all of its fixed assets with longterm capital, but part of its permanent current operating assets with short-term, nonspontaneous credit. There are degrees of aggressiveness. In fact, a firm could choose to finance all of its permanent current operating assets and part of its fixed assets with short-term credit; this would be a highly aggressive position, and one that would subject the firm to the dangers of rising interest rates as well as to loan renewal problems. A conservative financing policy occurs when the firm finances all of its permanent current operating asset requirements and some of its seasonal demands with permanent capital. This position is a very safe one. Therefore, an aggressive financing policy uses the greatest amount of short-term debt, while the conservative policy uses the least. The maturity matching policy falls between these two policies. n.

What are the advantages and disadvantages of using short-term debt as a source of financing? Answer: Although using short-term credit is generally riskier than using long-term credit, short-term credit does have some significant advantages. A short-term loan can be obtained much faster than long-term credit. Lenders insist on a more thorough financial examination before extending long-term credit. If a firm’s needs for funds are seasonal or cyclical, it may not want to commit to long-term debt because: (1) flotation costs are generally high for long-term debt but trivial for short-term debt. (2) Prepayment penalties with long-term debt can be expensive; short-term debt provides flexibility. (3) Long-term loan agreements contain provisions that constrain a firm’s future actions, while short-term credit agreements are less onerous. (4) The yield curve is normally upward sloping, indicating that interest rates are generally lower on short-term than on long-term debt. Even though short-term debt is often less expensive than long-term debt, short-term debt subjects the firm to more risk than long-term financing. The reasons for this are: (1) if a firm uses long-term debt, its interest costs will be relatively stable over time; however, if the firm uses short-term debt, its interest expense will fluctuate widely. (2) If a firm borrows heavily on a short-term basis, it may find itself unable to repay this debt, and it may be in such a weak financial position that the lender will not extend the loan, which could force the firm into bankruptcy.

Would it be feasible for RR to finance with commercial paper? Answer:

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It would not be feasible for RR to finance with commercial paper. Commercial paper is unsecured, shortterm debt issued by large, financially strong firms and sold primarily to other business firms, to insurance companies, to pension funds, to money market mutual funds, and to banks. Maturities are generally 270 days (9 months) or less, because SEC registration is required on maturities beyond 270 days. There is a very active, liquid market for commercial paper, and, since there is virtually no default risk, commercial paper rates are generally less than the stated prime rate, and not much more than the T-bill rate. Note, though, that issuers of commercial paper are required to have back-up lines of bank credit that can be used to pay off the paper if need be when it matures. These backup credit lines have a cost, and this cost must be added to the interest rate on the paper to determine its effective cost. Since only large, well-known, financially strong companies can issue commercial paper, it would be impossible for RR to tap this market. p.

In an attempt to better understand RR’s cash position, Johnson developed a cash budget for the first 2 months of the year. She has the figures for the other months, but they are not shown. After looking at the cash budget, answer the following questions. RR’S CASH BUDGET FOR JANUARY AND FEBRUARY November

December

January

February

March

April

$71,218

$68,212.00

$65,213.00

$52,475.00

$42,909

$30,524

Sales (1)

Sales (Gross)

Collections: (2) During Month of Sale (0.2)(0.98)(Month’s Sales) 12,781.75 (3) During First Month After Sale 0.7(Previous Month’s Sales) 47,748.40 (4) During Second Month After Sale 0.1(Sales 2 Months Ago) 7,121.80 (5) Total Collections (Lines 2 + 3 + 4) $67,651.95 Purchases: (6) 0.85(Forecasted Sales 2 Months From Now)

4 5,649.10 6,821.20 $62,755.40

$44,603.75

$36,472.65

$25,945.40

44,603.75

36,472.65 6,690.56 2,500.00

5,470.90 2,500.00

$53,794.31

$44,443.55

Net Cash Flows (12) Cash at Beginning of Forecast $ 3,000.00 (13) Net Cash Flow: Collections – Payments $13,857.64 (14) Cumulative NCF (Prior mos. + this mos. NCF) 16,857.64

$18,311.85 35,169.49

Cash Surplus (or Loan Requirement) (15) Target Cash Balance (16) Surplus Cash or Loan Needed

1,500.00 $33,669.49

Payments (7) Payments for Purchases (8) Wages and Salaries (9) Rent (10) Taxes (11) Total Payments

10,285.10

1,500.00 $15,357.64

What does the cash budget show regarding the target cash level?

Answer: The forecasted cash balances are higher than the target, indicating that RR could invest this excess cash in short-term securities.

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Should depreciation expense be explicitly included in the cash budget? Why or why not?

Answer: No, depreciation expense is a noncash charge and should not appear explicitly in the cash budget that focuses on the actual cash flowing into and out of a firm. However, a firm’s depreciation expense does impact its tax liability, and hence depreciation affects RR’s quarterly tax payments. p.

What are some other potential cash inflows besides collections?

Answer: 1. Proceeds from fixed asset sales. 2. Proceeds from stock and bond sales. 3. Interest earned. 4. Court settlements. p.

How can interest earned or paid on short-term securities or loans be incorporated in the cash budget?

Answer: 1. Interest earned: Add line in the collections section. 2. Interest paid: Add line in the payments section. 3. Found as interest rate × surplus/loan line of cash budget for preceding month. 4. Note: Interest on any other debt would need to be incorporated as well. p.

In her preliminary cash budget, Johnson has assumed that all sales are collected and thus that RR has no bad debts. Is this realistic? If not, how would bad debts be dealt with in a cash budgeting sense? (Hint: Bad debts will affect collections but not purchases.)

Answer: It is not realistic to assume zero bad debts. When credit is granted, bad debts should be expected. Collections in each month would be lowered by the percentage of bad debts. Payments would be unchanged, so the result would be that loan balances would be larger and cash surplus balances would be smaller by the difference in the collection amounts.

Solution and Answer Guide CHAPTER 17: MULTINATIONAL FINANCIAL MANAGEMENT

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 392 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 395 Easy Problems 1–4 ................................................................................................................................ 395 Intermediate Problems 5–8 ................................................................................................................... 395 Challenging Problems 9–14 .................................................................................................................. 396 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 400 MINI CASE ............................................................................................................................................. 401

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ANSWERS TO END-OF-CHAPTER QUESTIONS 17-1 Define each of the following terms: a. Multinational corporation b. Exchange rate; fixed exchange rate system; floating exchange rate c. Trade deficit; devaluation; revaluation d. Exchange rate risk; convertible currency; pegged exchange rate e. Interest rate parity; purchasing power parity f. Spot rate; forward exchange rate; discount on foreign currency forward rate; premium on foreign currency forward rate g. Repatriation of earnings; political risk h. Eurodollar; Eurobond; international bond; foreign bond i. The euro Answer: a. A multinational corporation is one that operates in two or more countries. b.

The exchange rate specifies the number of units of a given currency that can be purchased for one unit of another currency. The fixed exchange rate system was in effect from the end of World War II until August 1971. Under the system, the U.S. dollar was linked to gold at the rate of $35 per ounce, and other currencies were then tied to the dollar. Under the floating exchange rate system, which is currently in effect, the forces of supply and demand are allowed to determine currency prices with little government intervention.

A country has a trade deficit balance when it imports more goods from abroad than it exports. Devaluation is the lowering, by governmental action, of the price of its currency relative to another currency. For example, in 1967 the British pound was devalued from $2.80 per pound to $2.50 per pound. Revaluation, the opposite of devaluation, occurs when the relative price of a currency is increased.

Exchange rate risk refers to the fluctuation in exchange rates between currencies over time. A convertible currency is one which can be traded in the currency markets and can be redeemed at current market rates. When an exchange rate is pegged, the rate is fixed against a major currency such as the U.S. dollar. Consequently, the values of the pegged currencies move together over time.

Interest rate parity holds that investors should expect to earn the same return in all countries after adjusting for risk. Purchasing power parity, sometimes referred to as the ―law of one price,‖ implies that the level of exchange rates adjusts so that identical goods cost the same in different countries.

The spot rate is the exchange rate that applies to ―on the spot‖ trades, or, more precisely, exchanges that occur two days following the day of trade. In other words, the spot rate is for current exchanges. The forward exchange rate is the prevailing exchange rate for exchange (delivery) at some agreedupon future date, usually 30, 90, or 180 days from the day the transaction is negotiated. Forward exchange rates are analogous to future prices on commodity exchanges.

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The forward rate is selling at discount when the foreign currency indirect spot rate is less than the forward rate; i.e., the foreign currency is expected to depreciate (based on forward rates) with respect to the home currency. Conversely, the forward rate is selling at a premium when the foreign currency indirect spot rate is greater than the forward rate; i.e., the foreign currency is expected to appreciate (based on forward rates) with respect to the home currency. g.

Repatriation of earnings is the cash flow, usually in the form of dividends or royalties, from the foreign branch or subsidiary to the parent company. These cash flows must be converted to the currency of the parent, and thus are subject to future exchange rate changes. A foreign government may restrict the amount of cash that may be repatriated. Political risk refers to the possibility of expropriation and to the unanticipated restriction of cash flows to the parent by a foreign government.

A Eurodollar is a U.S. dollar on deposit in a foreign bank, or a foreign branch of a U.S. bank. Eurodollars are used to conduct transactions throughout Europe and the rest of the world. An international bond is any bond sold outside of the country of the borrower. There are two types of international bonds: Eurobonds and foreign bonds. A Eurobond is any bond sold in some country other than the one in whose currency the bond is denominated. Thus, a U.S. firm selling dollar bonds in Switzerland is selling Eurobonds. A foreign bond is a bond sold by a foreign borrower but denominated in the currency of the country in which the issue is sold. Thus, a U.S. firm selling bonds denominated in Swiss francs in Switzerland is selling foreign bonds.

The euro is a currency used by the nations in the European Monetary Union who signed the Treaty of Maastricht.

17-2 Under the fixed exchange rate system, what was the currency against which all other currency values were defined? Why? Answer: The U.S. dollar. The primary reason for using the dollar was that it provided a relatively stable benchmark, and it was accepted universally for transaction purposes. 17-3 Exchange rates fluctuate under both the fixed exchange rate and floating exchange rate systems. What, then, is the difference between the two systems? Answer: Under the fixed exchange rate system, the fluctuations were limited to +1% and –1%. Under the floating exchange rate system, there are no agreed-upon limits. 17-4 If the Swiss franc depreciates against the U.S. dollar, can a dollar buy more or fewer Swiss francs as a result? Answer: A dollar will buy more Swiss francs. 17-5 If the United States imports more goods from abroad than it exports, then foreigners will tend to have a surplus of U.S. dollars. What will this do to the value of the dollar with respect to foreign currencies? What is the corresponding effect on foreign investments in the United States? Answer:

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There will be an excess supply of dollars in the foreign exchange markets, and thus, will tend to drive down the value of the dollar. Foreign investments in the United States will increase. 17-6 Why do U.S. corporations build manufacturing plants abroad when they could build them at home? Answer: Taking into account differential labor costs abroad, transportation, tax advantages, and so forth, U.S. corporations can maximize long-run profits. There are also nonprofit behavioral and strategic considerations, such as maximizing market share and enhancing the prestige of corporate officers. 17-7 Should firms require higher rates of return on foreign projects than on identical projects located at home? Explain. Answer: The foreign project’s cash flows have to be converted to U.S. dollars, since the shareholders of the U.S. corporation (assuming they are mainly U.S. residents) are interested in dollar returns. This subjects them to exchange rate risk, and therefore requires an additional risk premium. There is also a risk premium for political risk (mainly the risk of expropriation). However, foreign investments also help diversify cash flows, so the net effect on the required rate of return is ambiguous. 17-8 What is a Eurodollar? If a French citizen deposits $10,000 in Chase Bank in New York, have Eurodollars been created? What if the deposit is made in Barclays Bank in London? Chase’s Paris branch? Does the existence of the Eurodollar market make the Federal Reserve’s job of controlling U.S. interest rates easier or more difficult? Explain. Answer: A Eurodollar is a dollar deposit in a foreign bank, normally a European bank. The foreign bank need not be owned by foreigners—it only has to be located in a foreign country. For example, a Citibank subsidiary in Paris accepts Eurodollar deposits. The Frenchman’s deposit at Chase Manhattan Bank in New York is not a Eurodollar deposit. However, if he transfers his deposit to a bank in London or Paris, it would be. The existence of the Eurodollar market makes the Federal Reserve’s job of controlling U.S. interest rates more difficult. Eurodollars are outside the direct control of the U.S. monetary authorities. Because of this, interest rates in the U.S. cannot be insulated from those in other parts of the world. Thus, any domestic policies the Federal Reserve might take toward interest rates would be affected by the Eurodollar market. 17-9 Does interest rate parity imply that interest rates are the same in all countries? Answer: No, interest rate parity implies that an investment in the United States with the same risk as a similar investment in a foreign country should have the same return. Using direct quotes for the spot rate and forward rate, interest rate parity is expressed as: Forw ard rat e 1 rh  . Spot rat e 1 rf Interest rate parity shows why a particular currency might be at a forward premium or discount. A currency is at a forward premium whenever domestic interest rates are higher than foreign interest rates. Discounts prevail if domestic interest rates are lower than foreign interest rates. If these conditions do not hold, then arbitrage will soon force interest rates back to parity. 17-10 Why might purchasing power parity fail to hold? Answer: Purchasing power parity assumes there are neither transaction costs nor regulations that limit the ability to buy and sell goods across different countries. In many cases, these assumptions are incorrect, which explains why PPP is often violated. An additional complication, when empirically testing to see whether PPP holds, is that

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products in different countries are rarely identical. Frequently, there are real or perceived differences in quality, which can lead to price differences in different countries.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–4 17-1 Cross Rates At today’s spot exchange rates 1 U.S. dollar can be exchanged for 9 Mexican pesos or for 111.23 Japanese yen. You have pesos that you would like to exchange for yen. What is the cross rate between the yen and the peso; that is, how many yen would you receive for every peso exchanged? Solution: $1 = 9 Mexican pesos; $1 = 111.23 Japanese yen; Cross exchange rate, yen/peso = ? Cross Rate = (yen per dollar)/(pesos per dollar) = 111.23/9 = 12.3589 yen per peso. 17-2 Interest Rate Parity The nominal yield on 6-month T-bills is 7%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 5.5%. In the spot exchange market, 1 yen equals $0.009. If interest rate parity holds, what is the 6-month forward exchange rate? Solution: rNom, 6-month T-bills = 7%; rNom of similar default-free 6-month Japanese bonds = 5.5%; Spot exchange rate, e0: 1 Yen = $0.009; 6-month forward exchange rate = ft = ?

(1  rh ) ft (1  rh )   ft = e0 e 0 (1  rf ) (1  rf ) ft = $0.009{[1 + (7%/2)]/[1 + (5.5%/2)]} = $0.009(1.035/1.0275) = $0.0097 17-3 Purchasing Power Parity A computer costs $500 in the United States. The same model costs €550 in France. If purchasing power parity holds, what is the spot exchange rate between the euro and the dollar? Solution: U.S. computer = $500; French computer = 550 euros; Spot rate between euro and dollar = ? Ph = Pf(e0)  e0 = Ph/Pf e0 = $500/€550 = $0.9091 per euro 17-4 Exchange Rate If euros sell for $1.50 (U.S.) per euro, what should dollars sell for in euros per dollar? Solution: Dollars should sell for 1/1.50, or 0.6667 euros per dollar.

INTERMEDIATE PROBLEMS 5–8 17-5 Currency Appreciation Suppose that the exchange rate is 0.60 dollars per Swiss franc. If the franc appreciates 10% against the dollar, how many francs would a dollar buy tomorrow?

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Solution: The current exchange rate is 0.60 dollars per Swiss franc. A 10% appreciation will make it 0.66 dollars per Swiss franc. To find Swiss francs per dollar, divide 1 by the exchange rate: 1/0.66 = 1.5152 Swiss francs per dollar. 17-6 Cross Rates Suppose the exchange rate between U.S. dollars and the Swiss franc is SFr1.6 = $1 and the exchange rate between the dollar and the British pound is £1 = $1.50. What then is the cross rate between francs and pounds? Solution: Cross rate

= Swiss francs/dollars  dollars/pounds = Swiss francs per pounds = 1.6  1.5 = 2.4 Swiss francs per pound.

17-7 Interest Rate Parity Assume that interest rate parity holds. In both the spot market and the 90-day forward market, 1 Japanese yen equals 0.0086 dollar. In Japan, 90-day risk-free securities yield 4.6%. What is the yield on 90-day risk-free securities in the United States? Solution: Spot rate = 1 yen = $0.0086; ft = 1 yen = $0.0087; rNom of 90-day Japanese risk-free securities = 4.6%; rNom of 90-day U.S. risk-free securities = ?

ft Spot rat e



(1 rh ) (1 rf )

rf = 4.6%/4 = 1.15%; rh = ? (0.0087/0.0086) =

(1 rh ) 1.0115

1 + rh = 1.0115(0.0087/0.0086) rh = 0.0232616. rNom = 2.32616%  4 = 9.30%. 17-8 Purchasing Power Parity In the spot market, 7.8 pesos can be exchanged for 1 U.S. dollar. A pair of headphones costs $15 in the United States. If purchasing power parity holds, what should be the price of the same headphones in Mexico? Solution: $1 = 7.8 pesos; headphones = $15.00; price of headphones in Mexico = ? Price of headphones in Mexico = $15(7.8) = $117

CHALLENGING PROBLEMS 9–14 17-9 Exchange Gains and Losses Your Boston-headquartered manufacturing company, Wruck Enterprises, obtained a 50-million-peso loan from a Mexico City bank last month to fund the expansion of your Monterrey, Mexico, plant. The exchange rate was 10 U.S. cents per peso when you took out the loan, but since then the exchange rate has dropped to 9 U.S. cents per peso. Has Wruck Enterprises made a gain or a loss due to the exchange rate change, and how much? Note that your shareholders live in the United States. Solution: The U.S. dollar liability of the corporation falls from (0.10 dollars per peso)(50,000,000 pesos) = $5,000,000 to (0.09 dollars per peso)(50,000,000 pesos) = $4,500,000, corresponding to a gain of

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500,000 U.S. dollars for the corporation. However, the real economic situation might be somewhat different. For example, the loan is presumably a long-term loan. The exchange rate will surely change again before the loan is paid. What really matters, in an economic sense, is the expected present value of future interest and principal payments denominated in U.S. dollars. There are also possible gains and losses on inventory and other assets of the firm. A discussion of these issues quickly takes us outside the scope of this textbook. 17-10

Results of Exchange Rate Changes In 1983, the Japanese yen–U.S. dollar exchange rate (USD/JPY) was 245 yen per dollar, and the dollar cost of a compact Japanese-manufactured car was $8,000. Suppose that now the exchange rate is 80 yen per dollar. Assume there has been no inflation in the yen cost of an automobile so that all price changes are due to exchange rate changes. What would the dollar price of the car be now, assuming the car’s price changes only with exchange rates? Solution: The 1983 cost in yen was (245 yen per dollar)(8,000 dollars) = 1,960,000 yen. At an exchange rate of 80 yen per dollar, this is (1,960,000 yen)/(80 yen per dollar) = $24,500.

17-11

Spot and Forward Rates Boisjoly Watch Imports has agreed to purchase 15,000 Swiss watches for 1 million francs at today’s spot rate. The firm’s financial manager, James Desreumaux, has noted the following current spot and forward rates: U.S. Dollar/Swiss Franc

Swiss Franc/U.S. Dollar

Spot

1.6590

0.6028

30-day forward

1.6540

0.6046

90-day forward

1.6460

0.6075

180-day forward

1.6400

0.6098

On the same day, Desreumaux agrees to purchase 15,000 more watches in 3 months at the same price of 1 million Swiss francs. a. What is the cost of the watches in U.S. dollars, if purchased at today’s spot rate? b. What is the cost in dollars of the second 15,000 batch if payment is made in 90 days and the spot rate at that time equals today’s 90-day forward rate? c. If the exchange rate is 0.50 Swiss francs per dollar in 90 days, how much will Desreumaux have to pay (in dollars) for the watches? Solution: a. (1,000,000 Swiss francs)/(0.6028 Swiss francs per dollar) = $1,658,925. b.

(1,000,000 Swiss francs)/(0.6075 Swiss francs per dollar) = $1,646,091.

If the exchange rate is 0.500 Swiss francs per dollar when payment is due in 3 months, the SFr. 1,000,000 will cost: (1,000,000 Swiss francs)/(0.500 Swiss francs per dollar) = $2,000,000, which is more than the spot price today and more than purchasing a forward contract for 90 days.

17-12

Interest Rate Parity Assume that interest rate parity holds and that 90-day risk-free securities yield 5% in the United States and 5.3% in Germany. In the spot market, 1 euro equals $1.40. What is the 90-day forward rate? Is the 90-day forward rate trading at a premium or a discount relative to the spot rate? Solution: rNom of 90-day U.S. risk-free securities = 5%; of 90-day German risk-free securities = 5.3%; spot rate = 1 euro = $0.80; ft selling at premium or discount = ?

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ft Spot rat e



(1 rh ) (1 rf )

rh = 5%/4 = 1.25%; rf = 5.3%/4 = 1.325%; spot rate = $1.40 ft 1.0125 = 1.01325 $1.40 ft = 0.9993. $1.40 ft = $1.3990. The forward rate is selling at a discount, since a euro buys fewer dollars in the forward market than it does in the spot. In other words, in the spot market $1 would buy 1/1.40 = 0.7143 euros, but at the forward rate $1 would buy 1/1.3990 = 0.7148 euros; therefore, the forward currency is said to be selling at a discount. 17-13

Foreign Investment Analysis Chapman Inc. is a U.S. company with a Mexican subsidiary, V. Gomez Corporation. Gomez is expected to pay to Chapman 50 pesos in dividends in 1 year after all foreign and U.S. taxes have been subtracted. The exchange rate in 1 year is expected to be 0.10 dollars per peso. After this, the peso is expected to depreciate against the dollar at a rate of 4% a year forever due to the different inflation rates in the United States and Mexico. The peso-denominated dividend is expected to grow at a rate of 8% a year indefinitely. Chapman owns 10 million shares of V. Gomez. What is the present value of the dividend stream, in dollars, assuming V. Gomez’s cost of equity is 13%? Solution: First, convert the pesos to dollars: D1 = (30 pesos)(0.10 dollars per peso) = 3 pesos. Second, find the growth rate in dollar denominated pesos. If the peso is depreciating 4% a year with respect to the dollar, then the exchange rate at t = 2 will be (0.10 dollars per peso)(1 – 0.04) = 0.096 dollars per peso. This is a growth rate of (0.096 – 0.10)/0.10 = −0.04 = −4%. In other words, the exchange rate is ―growing‖ at the rate it is depreciating. Therefore, the total growth rate in dollar denominated dividends is: g = (1 + 0.08)(1 − 0.04) – 1 = 3.68%. P0 = =

D1 rs  g $3 (0.13  0.0368)

= $32.1888. Total equity 17-14

= $32.1888  10 million shares = $321.888 million ≈ $322 million.

Foreign Capital Budgeting The South Korean multinational manufacturing firm, Nam Sung Industries, is debating whether to invest in a 2-year project in the United States. The project’s expected dollar cash flows consist of an initial investment of $1 million with cash inflows of $700,000 in Year 1 and $600,000 in Year 2. The risk-adjusted cost of capital for this project is 13%. The current exchange rate is 1,050 won per U.S. dollar. Risk-free interest rates in the United States and S. Korea are: U.S. S. Korea

1-Year 4.0% 3.0%

2-Year 4.25% 3.25%

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a. b.

If this project were instead undertaken by a similar U.S.-based company with the same risk-adjusted cost of capital, what would be the net present value and rate of return generated by this project? What is the expected forward exchange rate 1 year from now and 2 years from now? (Hint: Take the perspective of the Korean company when identifying home and foreign currencies and direct quotes of exchange rates.) If Nam Sung undertakes the project, what is the net present value and rate of return of the project for Nam Sung?

Solution: a. If a U.S.-based company undertakes the project, the rate of return for the project is a simple calculation, as is the net present value. NPV = −$1,000,000 + $700,000/1.13 + $600,000/(1.13) 2 = $89,357. Rate of return: Enter into your financial calculator or Excel cash flow register CF0 = −1,000,000, CF1 = 700,000, CF2 = 600,000, and calculate IRR = 20.0%. b.

This analysis is from the perspective of a South Korean investor, so South Korea is the home country and the United States is the foreign country. The interest rate parity relationship uses direct quotes for exchange rates; direct quotes are number of units of home currency per unit of foreign currency. Therefore, a direct quote from a Korean perspective is the number of won per dollar.

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According to interest rate parity, the following condition holds:

 1 rKorea  Forw ard exchange rat e =    1 r Spot exchange rat e US  

For the 1-year forward rate:

Forw ard exchange rat e 1.03 = 1050 1.04 Forw ard exchange rat e 1050 Forward exchange rate

= 0.990381 = 1,039.90 won per U.S. $.

The 2-year exchange rate is calculated as:

Forw ard exchange rat e  1.0325  =   1050  1.0425 

2-year forward exchange rate = 1029.95 won per U.S. dollar. c.

First, we must adjust the cash flows to reflect Nam Sung’s home currency. The expected won cash flows are Year 0: (−1,000,000 dollars)(1,050 won per dollar) = −1,050.00 million won. Year 1: (700,000 dollars)(1039.90 won per dollar) = 727.93 million won. Year 2: (600,000 dollars)(1029.95 won per dollar) = 617.97 million won. Using the won-denominated cash flows, the appropriate NPV and rate of return can be found. NPV = −1,050 + 727.93/1.13 + 617.97/1.13 2 = 78.15 million Won. Rate of return: Enter into your financial calculator or Excel cash flow register CF0 = −1,050, CF1 = 727.93, CF2 = 617.97, and calculate IRR = 18.85%.

SOLUTION TO SPREADSHEET PROBLEM 17-15

Build a Model: Multinational Financial Management Start with the partial model in the file Ch17 P15 Build a Model.xlsx on the textbook’s website. Mark Collins, luthier and businessman, builds and sells custom-made acoustic and electric stringed instruments. Although located in Maryville, Tennessee, he purchases raw materials from around the globe. For example, he constructs his top-of-the line acoustic guitar with onboard electronics, the MC-28, from rosewood and mahogany imported from a distributor in Mexico, spruce harvested in and imported from Canada, and ebony and the electronics imported from a Japanese distributor. He obtains other parts in the United States. When broken down on a per-guitar basis, the component and finishing costs are as follows: Rosewood and mahogany: 2,750 Mexican pesos Spruce: 200 Canadian dollars Ebony and electronics: 12,400 Japanese yen Other parts plus woodworking labor: $600

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Collins sells some of this model in the United States, but the majority of the units are sold in England, where he has developed a loyal following and the guitars have become something of a cult symbol. There, his guitars fetch £1,600, excluding shipping. Mark is concerned about the effect of exchange rates on his materials costs and profit. You will find Figures 17-2 and 17-3 useful for this problem. a. How much, in dollars, does it cost for Collins to produce his MC-28? What is the dollar sale price of the MC-28 sold in England? b. What is the dollar profit that Collins makes on the sale of the MC-28? What is the percentage profit? c. If the U.S. dollar were to depreciate by 10% against all foreign currencies, what would be the dollar profit for the MC-28? d. If the U.S. dollar were to depreciate by 10% only against the pound and remain constant relative to all other foreign currencies, what would be the dollar and percentage profits for the MC-28? e. The rate of return on 90-day U.S. Treasury securities is 3.9%, and the rate of return on 90-day U.K. risk-free securities is 5.0%. Using the spot exchange information from Table 17-1, estimate the 90day forward exchange rate. f. Assuming that purchasing power parity (PPP) holds, what would be the sale price of the MC-28 if it were sold in France rather than in England? (Hint: Assume England is the home country.) Solution: The detailed solution for the spreadsheet problem, Ch 17 P15 Build a Model Solution.xlsx, is available on the textbook’s website.

MINI CASE With the growth in demand for exotic foods, Possum Inc.’s CEO Michael Munger is considering expanding the geographic footprint of its line of dried and smoked low-fat opossum, ostrich, and venison jerky snack packs. Historically, jerky products have performed well in the southern United States, but there are indications of a growing demand for these unusual delicacies in Europe. Munger recognizes that the expansion carries some risk. Europeans may not be as accepting of opossum jerky as initial research suggests, so the expansion will proceed in steps. The first step will be to set up sales subsidiaries in France and Sweden (the two countries with the highest indicated demand), and the second is to set up a production plant in France with the ultimate goal of product distribution throughout Europe. Possum Inc.’s CFO, Kevin Uram, although enthusiastic about the plan, is nonetheless concerned about how an international expansion and the additional risk that entails will affect the firm's financial management process. He has asked you, the firm’s most recently hired financial analyst, to develop a 1-hour tutorial package that explains the basics of multinational financial management. The tutorial will be presented at the next board of directors’ meeting. To get you started, Uram has supplied you with the following list of questions. a.

What is a multinational corporation? Why do firms expand into other countries? Answer: Use the examples given here when discussing why firms ―go international.‖ 1.

To seek new markets. Coca-Cola and McDonald’s have expanded around the world to seek new markets. Likewise, Sony, Toshiba, and other Japanese consumer electronics manufacturers have aggressively pushed into the United States.

To seek raw materials. U.S. oil companies have searched around the world for years for new sources of oil. It is not surprising that a large company like Chevron has oil production facilities not only in the continental United States and Alaska, but also in the North Sea, Nigeria, Angola, and Australia. Currently, the company is trying to get a foothold in the Soviet Union.

To seek new technology. No one country has the lead in all technologies, so many companies are going global to ensure access to new technologies. For example, in the last several years, there have

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been four joint ventures between Japanese and American chip manufacturers for the sole purpose of exchanging technology.

To gain production efficiencies.

To avoid political and regulatory hurdles. The most prominent example here is the move by Toyota, Honda, Mazda, and Mitsubishi to produce cars and trucks in the United States to avoid import quotas.

To diversify. By establishing worldwide production facilities and markets, firms can cushion the impact of adverse economic trends in any single country.

What are nine major factors which distinguish multinational financial management from financial management as practiced by a purely domestic firm? Answer: 1. Different currency denominations. Cash flows in various parts of multinational corporate systems will be denominated in different currencies. Hence, an analysis of exchange rates, and the effect of fluctuating currency values, must be included in all financial analyses. 2.

Language differences. The ability to communicate is critical in all business matters, and U.S. business men and women have been notoriously poor in learning other languages. In effect, it is easier for foreign firms to invade our markets than for us to invade theirs. It is interesting to note, though, that English has become the international business language. Many business school programs in Europe, for example, Nijenrode in the Netherlands, are conducted in English rather than in the host country’s language. Also, some multinational companies, such as ABB, a large Swedish firm headquartered in Zurich, have adopted English as the language of corporate communication. Although English is now spoken by most international businesspeople, knowledge of other languages remains critical to the success of multinational firms.

Cultural differences. Different countries, and even different regions in a single country, have unique cultural heritages that shape values and influence the role of business in the society. Such differences affect consumption patterns, defining the appropriate firm goals, attitudes toward risk taking, dealings with employees, and so on. For example, most Japanese workers view their jobs as a lifetime commitment, while many American workers view theirs as temporary until something better comes along. To give another illustration, consider PepsiCo’s move into the Japanese market by its Frito-Lay subsidiary. At first, Frito-Lay marketed popular American products such as Ruffles potato chips and Doritos corn chips. These products did poorly, and the Japanese venture almost failed, but it was saved when the company began producing a chip with soy sauce and seaweed flavoring.

Economic systems. At one extreme are countries with free markets (i.e., unfettered capitalism); at the other are countries with command (or planned) economies. For example, Singapore, Hong Kong, and Denmark place the least restrictions on business activities, whereas North Korea and Cuba place the most. However, most countries are a mixture. For example, the United States is very much in the freemarket spectrum while Belarus is towards the other end.

Legal systems. Some countries, such as the United States and the United Kingdom, base their legal systems on common law, which emphasizes prior court decisions and usually provides stronger protection for investors and property owners. In contrast, civil law legal systems, such as in France, rely on detailed laws and regulations enacted by the government. Different legal systems complicate matters ranging from the simple recording of business transactions to the role played by the judiciary in resolving conflicts. Such differences can even make procedures that are required in one part of the company illegal in another part.

Taxation. Differences in countries’ tax laws can cause strikingly different after-tax cash flows for identical transactions.

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Government intervention. The terms under which companies compete, the actions that must be taken or avoided, the ability to curtail unprofitable operations, and the terms of trade on various transactions often are determined not in the marketplace but by direct negotiation with host governments.

Political risk. A foreign government might place constraints on the transfer of corporate resources or even expropriate assets within its boundaries. Also, corrupt government officials might expect gifts or bribes.

Terrorism and crime. Terrorist groups and criminals might threaten a company’s property or the safety of its employees. This includes extortion and kidnapping. In fact, some terrorist groups finance substantial portions of their budgets through kidnap and ransom.

Consider the following illustrative exchange rate quotes.

Currencies Euros Swedish krona c.

U.S. Dollars Required to Buy One Unit of Foreign Currency 1.2500 

Units of Foreign Currency Required to Buy One U.S. Dollar  7.0000

What is a direct quotation? What is the direct quote for euros?

Answer: From a U.S. perspective, the quotes in the first column are called direct quotes because there are a number of units of a foreign currency that can be purchased by 1 unit of the home currency. The direct quote for the euro is EUR/USD = 1.25. The financial press would report this as ―the euro is trading at $1.25.‖ c.

What is an indirect quotation? What is the indirect quotation for kronor (the plural of krona is kronor).

Answer: Indirect quotations are the number of units of foreign currency that can be purchased with one unit of home currency (the home currency is the U.S. dollar in this example). The indirect quote for the krona is USD/SEK = 7. c.

The euro and British pound usually are quoted as direct quotes. Most other currencies are quoted as indirect quotes. How would you calculate the indirect quote for a euro? How would you calculate the direct quote for a krona?

Answer: Indirect quotations are the reciprocal of the direct quotation, and direct quotations are the reciprocal of the indirect quotation. The indirect quote for the euro is USD/EUR = 1/1.25 = 0.80. The direct quote for the krona is SEK/USD = 1/7 = 0.1429. c.

What is a cross rate? Calculate the two cross rates between euros and kronor.

Answer: The exchange rate between any two currencies that does not involve U.S. dollars is a cross rate. Use the exchange rates versus the dollar, so use the direct for the dollars per euro and the indirect for kronor per dollar. Here is the cross rate for kronor per euro:

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Kronor Dollars  Dollar Euros = 7  1.2500 = 8.750 kronor per euro.

Cross rate =

Euros per krona cross rate c.

= 1/(8.750 kronor per euro) = 0.1143 euros per krona.

Assume Possum Inc. can produce a package of jerky and ship it to France for $1.75. If the firm wants a 50% markup on the product, what should the jerky sell for in France?

Answer: To achieve the markup, the price in dollars must be ($1.75)(1.50) = $2.625. The reported quote is the direct quote for dollars per euro. Therefore, the calculation using the direct quote is: [ * c.

][

Now assume that Possum Inc. begins producing the same package of jerky in France. The product costs 2 euros to produce and ship to Sweden, where it can be sold for 20 kronor. What is the dollar profit on the sale?

Answer: Using the unrounded cross rate of 8.50 kronor per euro, we get: (2.0 euros)(8.750 kronor/euro) = 17.50 kronor The profit on the sale in Sweden is 20 – 17.50 = 2.50 kronor. Now, there are 0.1481 dollar per krona, so the dollar profit is (2.5 kronor)/(7 kronor per dollar) = $0.36. c.

What is exchange rate risk?

Answer: The volatility inherent in a floating exchange rate system increases the uncertainty of cash flows that must be translated from one currency into another. This increase in uncertainty is exchange rate risk. d.

Briefly describe the current international monetary system. How does the current system differ from the system that was in place prior to August 1971? Answer: By 1914, governments of most developed countries were issuing paper currencies that could be redeemed for gold from the government’s treasury, so the monetary system was called the gold standard. For example, gold was worth $20.67 an ounce in the United States and £4.24 in the United Kingdom (£ is the symbol for British pounds). The gold standard requires considerable international cooperation regarding (1) the prices at which gold can be redeemed in local currencies and (2) the free flow of gold and trade from one country to another. However, World War I and subsequent depressions caused many governments to cease cooperation, which essentially ended the gold standard. The International Monetary Fund was created in 1944 to promote international trade and prosperity by stabilizing exchange rates, by reducing restrictions on currency exchanges, and by providing short-term financial help to countries with financial crises. The IMF has over 180 member nations. From 1946 to 1971, the world operated on a fixed exchange rate system. The value of the U.S. dollar was linked to gold at the fixed price of $35 per ounce, and the values of other currencies were then tied to the dollar. For example, in 1964, the British pound was fixed at $2.80 for 1 pound, with a 1% permissible fluctuation around this rate. Thus, the British government had to regularly intervene in the foreign

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exchange market to keep the pound in the range of $2.77 to $2.83. When the pound fell, the Bank of England had to buy pounds, offering either foreign currencies or gold in exchange. Conversely, if the pound reached the top of the range, the Bank of England would sell pounds. The official exchange rates were occasionally ―reset‖ to reflect changing economic conditions. The current international monetary system for about 30 industrialized nations is a free floating rate system. In this system, currency exchange rates are allowed to fluctuate in response to market conditions with a minimum of governmental intervention. Changes in currency demand can be due to trade deficits (i.e., one nation imports more from another nation than it exports, causing there to be higher relative demand for the currency of the bigger exporter). It can also be due to capital movements. For example, if interest rates are relatively high in one country, then investors might seek to purchase that country’s securities, which increases demand for that country’s currency. The IMF classifies about 40 more countries as floating because they have a little more government intervention than free floating currencies. Many countries use an exchange rate that is ―pegged,‖ or fixed, with respect to another currency. Examples of pegged currencies pegged to the U.S. dollar are those of Belize, Barbados, and Saudi Arabia. Denmark pegs to the euro. Some countries have managed currency that behaves like a pegged currency, but the country hasn’t reported it as such. This category includes Singapore, Costa Rica, Burundi, and about 15 other countries. A few countries, including China, are in the IMF category of ―Other Managed Arrangements‖ because the currency policy doesn’t fit into any other IMF category. For example, China has a currency that is pegged to basket of currencies; however, China doesn’t tell what currencies are in basket. Sometimes China lets the exchange rate float, sometimes it manages the currency more actively. Some countries belong to a monetary union and have no individual currency but instead agree to use a common currency. The largest is the European Monetary Union (EMU). Nineteen EMU countries (as of summer 2017) use the euro. The European Central Bank controls the monetary policy of the EMU nations using the euro. When a currency increases in value relative to another currency, it is said to appreciate. Under the fixed exchange rate system, strong currencies had to be revalued occasionally, which changed the tie to other currencies to a new, higher rate. Conversely, a currency that loses value is said to depreciate, and such currencies had to be devalued under the old fixed rate system. e.

What is a freely convertible currency? What problems arise when a multinational company operates in a country whose currency is not convertible? Answer: A freely convertible currency is traded in the international currency markets with no government restrictions. It is also called a fully convertible currency and a hard currency. Countries with free floating exchange systems also have fully convertible currencies. In addition, several other floating rate currencies are fully convertible, such as the New Zealand dollar and the Israeli new shekel. A partially convertible currency is one that trades in international FOREX markets but that has significant government-imposed restrictions. Restrictions include: (1) limiting FOREX trading in country to small group of currencies; (2) limits on the amounts of its currency that may be converted to foreign currencies for purposes of investing abroad; and (3) limits on amounts foreigners may invest inside the country. Most currencies fall into this category, including India and China. A nonconvertible currency is one that is not traded in international FOREX markets due to government restrictions. It is also called a soft currency or a blocked currency. Cuba and North Korea have nonconvertible currencies. When a country’s currency is not fully convertible, it is difficult for multinational companies to conduct business in that country, because there is no easy way to return profits earned to the company’s home country. Often, in this situation, it is necessary to engage in some kind of barter arrangement to promote investment.

What is the difference between spot rates and forward rates? When is the foreign currency forward rate selling at a premium to the spot rate? At a discount?

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Answer: Spot rates are the rates paid to buy currency for immediate delivery (actually, 2 days after the date of the trade). Forward rates are the rates paid to buy currency for delivery at some agreed-upon date in the future (say, 90 days). If a dollar buys more of the foreign currency in the spot market than in the forward market, then the foreign currency is appreciating. Therefore, the forward foreign currency is selling at a premium. For example, suppose the spot rate = 110 yen per dollar and the forward rate = 100 yen per dollar. This means that the dollar buys fewer yen in the future. Therefore, the yen is appreciating. In other words, the yen is selling for a premium in the forward market. If a dollar buys less of the foreign currency in the spot market than in the forward market, then the foreign currency is depreciating and the forward foreign currency is selling at a discount. Firms use currency forward markets to hedge against adverse exchange rate fluctuations that might occur before a transaction is completed. To illustrate, suppose a U.S. importer buys German appliances for sale in the United States. The terms are net 90, so the importer must pay in Euros in 90 days. The dollar could weaken against the euro over the period, and hence force the importer to use more dollars to buy the merchandise. To guard against this possibility, the importer could buy euros for delivery in 90 days, thus locking in the current forward rate. g.

What is interest rate parity? Currently, you can exchange 1 euro for 1.25 dollars in the 180-day forward market, and the risk-free rate on 180-day securities is 6% in the United States and 4% in France. Does interest rate parity hold? If not, which securities offer the highest expected return? Answer: Interest rate parity holds that investors should expect to earn the same return in all countries after adjusting for risk. What is the implied forward rate, given the spot rate of $1.2500? Spot rate = 1 euro = $1.2500; rh = 6%/2 = 3.00%; rf = 4%/2 = 2.00%.

ft 1  rh  Spot rate 1  rf

ft 1.03  1.2500 1.02 ft  $1.2623. If interest rate parity held, then ft = $1.2623; however, ft = $1.2700, so parity doesn’t hold. The French securities offer the highest return as calculated below:

Assume you convert $1,000 to euros in the spot market. In the spot market, spot rate = 0.8000 euros per dollar. Convert $1,000  0.8000 euros/dollar = 800 euros.

Invest 800 euros in the 180-day French security which offers a semi-annual return of 4%/2 = 2%. So, in 180 days you will receive 800  1.02 = 816 euros.

Agree today to exchange the 800 euros 180 days from now at a 180-day forward exchange rate of ft = 1.2700 dollars per euro. Your dollar return after 180 days = 800 euros × 1.2700 dollars per euro = $1,036.32.

The investment’s expected 180-day return = $36.32/$1,000 = 0.03632 = 3.632%, or a nominal return of 2  3.632% = 7.26%.

What is purchasing power parity? If a package of jerky costs $2 in the United States and purchasing power parity holds, what should be the price of the jerky package in France? Answer: Purchasing power parity, sometimes referred to as the law of one price (LOP), implies that the level of exchange rates adjusts so that identical goods cost the same amount in different countries.

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Purchasing power parity: Ph = Pf(spot rate) Spot rate = Ph/Pf $1.2500 = $2.00/Pf Pf = $2.00/$1.2500 = 1.60 euros. i.

What effect does relative inflation have on interest rates and exchange rates? Answer: To illustrate, consider the situation between Japan and the United States. Japan has generally had a lower inflation rate than the United States, so Japanese interest rates have been lower than U.S. interest rates. This might tempt treasurers of U.S. multinational firms to borrow in Japan rather than in the United States. However, a foreign currency will, on average, depreciate (or appreciate) at a percentage rate approximately equal to the amount by which its inflation rate exceeds (or is less than) our own. Thus, the dollar has generally weakened against the yen over time, so it would take more and more dollars to pay back interest denominated in yen.

Briefly discuss the international capital markets. Answer: Individuals buy securities issued by foreign governments and firms, and U.S. firms issue securities abroad. These transactions take place in the international capital markets. Here is a brief description of the major international capital markets:

A Eurodollar is a U.S. dollar deposited in a bank outside the United States. The major difference between a ―regular‖ dollar and a Eurodollar is its location. This places Eurodollars outside the direct control of U.S. monetary authorities, so regulations such as fractional reserves and FDIC insurance premiums do not apply. Eurodollars are borrowed by U.S. and foreign individuals, corporations, and governments which need dollars for various purposes. Since the borrower must pay back the lender in dollars, Eurodollar transactions are not used to convert currencies, but rather represent another source of dollar borrowing. Interest rates on Eurodollars are tied to the London Interbank Offer Rate (LIBOR), which is the rate of interest offered by the largest and strongest London banks on Eurodollar deposits. LIBOR rates are generally 0.5 to 1.0 percentage points higher than the rate on comparable deposits offered by domestic banks in the United States. The Eurodollar market deals mostly with short maturities, generally less than 1 year, although loans of up to 5 years have occurred.

International bonds, which are any bond sold outside the country of the borrower, fall into two categories. Foreign bonds are bonds sold by a foreign borrower, but denominated in the currency of the country in which they are sold. Thus, when Bell Canada sells bonds in the United States denominated in U.S. dollars, the firm is selling foreign bonds. In general, foreign bonds have to meet all the regulations of the country in which they are issued. Eurobonds are bonds sold in some country other than the one in whose currency the bond is denominated. For example, when Mercedes-Benz (a German company) sell bonds denominated in German marks in Switzerland, these bonds are Eurobonds. In general, countries do not apply as stringent requirements on bonds denominated in a foreign currency as they do bonds denominated in the home currency. Further, most Eurobonds are issued in bearer form, so buyers have anonymity, both for tax and other purposes. For these reasons, investors are usually willing to accept somewhat lower yields on Eurobonds than on foreign bonds or ―regular‖ bonds. Thus, U.S. firms can often sell Eurobonds denominated in dollars at lower cost than similar domestic issues.

To what extent do average capital structures vary across different countries? Answer:

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There is some evidence that average capital structures vary among the large industrial countries. One problem, however, when interpreting these numbers is that different countries often use very different accounting conventions, which makes it difficult to compare capital structures. A recent study attempts to control for differences in accounting practices. This study suggests that differences in accounting practices can explain much of the cross-country variation in capital structures. After adjusting for these accounting differences, capital structures are more similar across different countries than a previous study had suggested. l.

Briefly describe a company’s risk exposure if it invests in an international project. Answer: 1. Exchange Rate Risk Due to Changes in Exchange Rates Exchange rate risk can be mitigated for short-term cash flows by using forward contracts, but longer-term cash flows still have exchange risk. 2.

Political Risk Due to the Host Country The host country may impose curbs on currency conversion, making it difficult to move money into or out of the host country. The host country may restrict product prices charged by the subsidiary. The host country may restrict repatriation of earnings to the parent company. The host country may expropriate the subsidiary’s assets. Government officials in the host country may be corrupt and require bribes.

Taxation Risk Prior to 2018, repatriated earnings (less foreign taxes) were subject to U.S. taxes. U.S. corporate tax rates were higher than rates in most countries, making repatriation very costly. The United States occasionally had grace periods with lower tax rates on repatriated earnings, but grace periods were brief and unpredictable. The 2017 Tax Cuts and Jobs Act imposed a one-time tax on foreign earnings accumulated since 1986 even if they were left overseas. The rate is15.5% on accumulated earnings held in cash and cash equivalents, and 8% on the remainder of accumulated earnings. The tax is to be paid over an 8-year period according to the Act’s schedule. However, the Act eliminated taxes on future foreign earnings even if they are left abroad.

m. Describe the process for evaluating a foreign project. Now consider the following project. A U.S. company has the opportunity to lease a manufacturing facility in Japan for 2 years. The company must spend ¥1 billion initially to refurbish the plant. The expected net cash flows from the plant for the next 2 years, in millions, are: CF1 = ¥500 and CF2 = ¥800. A similar project in the United States would have a risk adjusted cost of capital of 10%. In the United States, a 1-year government bond pays 2% interest, and a 2-year bond pays 2.8%. In Japan, a 1-year bond pays 0.05%, and a 2-year bond pays 0.26%. What is the project’s NPV? Answer: The same general principles that apply to domestic capital budgeting also apply to foreign capital budgeting. The first step is to estimate the future expected exchange rates using the multi-year interest rate parity equation:  1 rh  Expected t-year forward exchange rate = (Spot exchange rate)    1 rf 

where the exchange rates are expressed in direct quotations. The indirect spot exchange rate is 110 yen per dollar, so the direct rate is 1/110 = 0.009091 dollars per yen. The expected forward rates are:

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Expected forward rate ($/¥)

Maturity (in years)

Spot rate ($/¥)

2.0%

0.05%

0.009091

0.009268

2.8%

0.26%

0.009091

0.009557

The current dollar cost of the project is £1,000(0.009091 $/¥) = $9.09 million. The Year 1 cash flow in dollars is ¥500 (0.009268$/¥) = $4.63 million. The complete time line and NPV are shown below. Year 0

Cash flows in yen

– ¥1,000

¥500

¥800

Expected exchange rates

0.009091

0.009268

0.009557

–$9.09

$4.63

$7.65

Cash flows in dollars Project’s cost of capital =

10%

NPV =

$1.44

Briefly discuss special factors associated with the following areas of multinational working capital management:

Cash management

Answer: Although multinational and domestic firms have the same objectives for cash management and use similar procedures, the multinational firm faces a more complex task. Since the distances involved are much greater, multinational firms tend to rely more on lockbox systems and wire transfers. Also, since multinational firms have access to more financial markets than do domestic firms, multinational companies are more likely to have global concentration banks, say in Tokyo, New York, London, and Zurich, and excess funds are transferred around the world to take advantage of the best rates available. Short-term borrowings are handled in the same way, with many more opportunities available to the firm. However, whenever the borrowing or lending takes place in a currency other than dollars, it is necessary to consider the possibility of adverse exchange rate movements. n.

Credit management

Answer: Granting credit is riskier for a multinational firm than for a domestic corporation because, in addition to the normal risk of default, the credit granting corporation must also worry about exchange rate fluctuations between the time the credit is given and the time the payment must be made. In addition to being riskier, credit is more important for international business, because much of the commerce on which lesserdeveloped countries depend could not occur if the seller did not grant credit. Many companies buy export credit risk insurance when granting credit to foreign customers. n.

Inventory management

Answer: As with other aspects of financial management, inventory management in a multinational setting is similar to, but more complex, than that in a purely domestic firm. For example, where should ExxonMobil store its inventories of crude oil and refined products, and how much should be stored at each location? The answer depends on many factors, including shipping times, carrying costs, import quotas and taxes, differential

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taxes on inventories, and expected exchange rate movements. These factors greatly complicate inventory decisions within multinational firms.

Solution and Answer Guide BRIGHAM /EHRHARDT FINANCIAL M ANAGEMENT: THEORY & PRACTICE; CHAPTER 18: PUBLIC AND PRIVATE FINANCING: INITIAL OFFERINGS , SEASONED OFFERINGS , AND INVESTMENT BANKS

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 410 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 413 Easy Problems 1–2 ................................................................................................................................ 413 Intermediate Problems 3–5 ................................................................................................................... 414 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 417 MINI CASE ............................................................................................................................................. 417

ANSWERS TO END-OF-CHAPTER QUESTIONS 18-1 Define each of the following terms: a. Going public; new issue market; initial public offering (IPO) b. Public offering; private placement c. Venture capitalists; roadshow; spread d. Securities and Exchange Commission (SEC); registration statement; shelf registration; margin requirement; insiders e. Prospectus; ―red herring‖ prospectus f. Best efforts arrangement; underwritten arrangement g. Project financing; securitization Answer: a. A closely held corporation goes public when it sells stock to the general public. Going public increases the liquidity of the stock, establishes a market value, facilitates raising new equity, and allows the original owners to diversify. However, going public increases business costs, requires disclosure of operating data, and reduces the control of the original owners. The new issue market is the market for stock of companies that go public, and the issue is called an initial public offering (IPO). b.

A public offering is an offer of new common stock to the general public; in other words, an offer in which the existing shareholders are not given any preemptive right to purchase the new shares. A private placement is the sale of stock to only one or a few investors, usually institutional investors. The advantages of private placements are lower flotation costs and greater speed, since the shares issued are not subject to SEC registration.

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A venture capitalist is the manager of a venture capital fund. The fund raises most of its capital from institutional investors and invests in start-up companies in exchange for equity. The venture capitalist gets a seat on these start-up companies’ boards of directors. Before an IPO, the senior management team and the investment banker make presentations to potential investors. They make presentations in 10 to 20 cities, with three to five presentations per day, over a 2-week period; this is called a roadshow. The spread is the difference between the price at which an underwriter sells the stock in an IPO and the proceeds that the underwriter passes on to the issuing firm. In other words, it is the fee collected by the underwriter, and it usually is seven percent of the offering price.

The Securities and Exchange Commission (SEC) is a government agency that regulates the sales of new securities and the operations of securities exchanges. The SEC, along with other government agencies and self-regulation, helps ensure stable markets, sound brokerage firms, and the absence of stock manipulation. Registration of securities is required of companies by the SEC before the securities can be offered to the public. The registration statement is used to summarize various financial and legal information about the company. Frequently, companies will file a master registration statement and then update it with a short-form statement just before an offering. This procedure is termed shelf registration because companies put new securities ―on the shelf‖ and then later sell them when the market is right. Blue sky laws are laws that prevent the sale of securities that have little or no asset backing. In other words, it refers to companies selling nothing but blue sky. The margin is the percentage of a stock’s price that an investor has borrowed in order to purchase the stock. The SEC sets margin requirements, which is the maximum percentage of debt that can be used to purchase a stock. The SEC also controls trading by corporate insiders, who are the officers, directors, and major stockholders of the firm.

A prospectus summarizes information about a new security issue and the issuing company. A ―red herring,‖ or preliminary prospectus, may be distributed to potential buyers prior to approval of the registration statement by the SEC. After the registration has become effective, the securities, accompanied by the prospectus, may be offered for sale.

A best efforts arrangement versus an underwritten sale refers to two methods of selling new stock issues. In a best efforts sale, the investment banker is only committed to making every effort to sell the stock at the offering price. In this case, the issuing firm bears the risk that the new issue will not be fully subscribed. If the issue is underwritten, the investment banker agrees to buy the entire issue at a set price, and then resells the stock at the offering price. Thus, the risk of selling the issue rests with the investment banker.

Project financings are arrangements used to finance mainly large capital projects such as energy explorations, oil tankers, refineries, utility power plants, and so on. Usually, one or more firms (sponsors) will provide the equity capital required by the project, while the rest of the project’s capital is supplied by lenders and lessors. The most important aspect of project financing is that the lenders and lessors do not have recourse against the sponsors; they must be repaid from the project’s cash flows and the equity cushion provided by the sponsors. Securitization is the process whereby financial instruments that were previously thinly traded are converted to a form that creates greater liquidity. Securitization also applies to the situation where specific assets are pledged as collateral for securities, and hence asset-backed securities are created. One example of the former is junk bonds; an example of the latter is mortgage-backed securities.

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18-2 Many companies that go public with an IPO don’t actually need additional cash to continue growing their operations. Why might such a firm decide to go public? Answer: An IPO increases liquidity and allows founders to harvest their wealth, permits founders to diversify their wealth, establishes a value for the firm (which is helpful for tax purposes if the owner dies and is helpful when selling the company to another company), increases visibility, increases credibility, and often opens potential markets. 18-3 The SEC attempts to protect investors who are purchasing newly issued securities by making sure that the information put out by a company and its investment banks is correct and is not misleading. However, the SEC does not provide an opinion about the real value of the securities; hence, an investor might pay too much for some new stock and consequently lose heavily. Do you think the SEC should, as a part of every new stock or bond offering, render an opinion to investors on the proper value of the securities being offered? Explain. Answer: No. The real value of a security is determined by the equilibrium forces of an efficient market. Assuming that the information provided on newly issued securities is accurate, the market will establish the value of a security regardless of the opinions rendered by the SEC, or, for that matter, opinions offered by any advisory service or analyst. 18-4 How do you think each of the following items would affect a company’s ability to attract new capital and the flotation costs involved in doing so? a. A decision of a privately held company to go public b. The increasing institutionalization of the ―buy side‖ of the stock and bond markets c. The trend toward financial conglomerates as opposed to stand-alone investment banking houses d. Elimination of the preemptive right e. The introduction in 1981 of shelf registration of securities Answer: a. Going public would tend to make attracting capital easier and to decrease flotation costs. b.

The increasing institutionalization of the ―buy side‖ of the stock and bond markets should increase a firm’s ability to attract capital and should reduce flotation costs.

Financial conglomerates can offer a variety of financial services and types of investments, so it seems a company’s ability to attract capital would increase and flotation costs would decrease.

Elimination of the preemptive right would likely not affect a large company, where percentage ownership is not as important. Indeed, the trend today seems to be for companies to eliminate the preemptive right.

The introduction of shelf registration tended to speed up SEC review time and lower the costs of floating each new issue. Thus, the company’s ability to attract new capital was increased.

18-5 Before entering a formal agreement, investment banks carefully investigate the companies whose securities they underwrite; this is especially true of the issues of firms going public for the first time. Because the banks do not themselves plan to hold the securities but intend to sell them to others as soon as possible, why are they so concerned about making careful investigations? Answer: Investment bankers must investigate the firms whose securities they sell, simply because, if an issue is overvalued and suffers marked price declines after the issue, the banker will find it increasingly difficult to dispose of the new issue. In other words, reputation is highly important in the investment banking industry.

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SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–2 18-1 Profit or Loss on New Stock Issue. Dreebyshaw Inc. needed to raise $14 million in an IPO and chose Security Brokers Inc. to underwrite the offering. The agreement stated that Security Brokers would sell 3 million shares to the public and provide $14 million in net proceeds to Dreebyshaw. The out-of-pocket expenses incurred by Security Brokers in the design and distribution of the issue were $300,000. What profit or loss did Security Brokers incur if the issue were sold to the public at the following average price? a. $5 per share b. $6 per share c. $4 per share Solution: a. $5 per share Gross proceeds = (3,000,000)($5) = $15,000,000. Net profit = $15,000,000 – $14,000,000 – $300,000 = $700,000. b.

$6 per share Gross proceeds = (3,000,000)($6) = $18,000,000. Net profit = $18,000,000 – $14,000,000 – $300,000 = $3,700,000.

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$4 per share Gross proceeds = (3,000,000)($4) = $12,000,000. Net profit = $12,000,000 – $14,000,000 – $300,000 = −$2,300,000.

18-2 Underwriting and Flotation Expenses. The Fryberry Company, whose stock price is now $25, needs to raise $20 million in common stock. Underwriters have informed the firm’s management that they must price the new issue to the public at $22 per share because of signaling effects. The underwriters’ compensation will be 5% of the issue price, so Fryberry will net $20.90 per share. The firm will also incur expenses in the amount of $150,000. How many shares must the firm sell to net $20 million after underwriting and flotation expenses? Solution: Net proceeds per share = $22(1 – 0.05) = $20.90. Number of shares to be sold = ($20,000,000 + $150,000)/$20.90 = 964,115 shares.

INTERMEDIATE PROBLEMS 3–5 18-3 Pricing Stock Issues. Benjamin Garcia’s start-up business is succeeding, but he needs $200,000 in additional funding to fund continued growth. Benjamin and an angel investor agree the business is worth $800,000 and the angel has agreed to invest the $200,000 that is needed. Benjamin presently owns all 40,000 shares in his business. What is a fair price per share and how many additional shares must Benjamin sell to the angel? Because the stock will be sold directly to an investor, there is no spread; the other flotation costs are insignificant. Solution: POffer = VPre-issue/(F nNew + nExisting) = $800,000/( 0(nNew) + 40,000) = $20. NNew = Investment/Price = $200,000/$20 = 10,000. Alternatively, notice that after the investment, the angel will have contributed a percentage of the company’s total value equal to 20% = $200,000/($200,000 + $800,000). Therefore, the angel will want to own 20% of the outstanding shares. Therefore, the angel must receive 10,000 new shares to have a 20% stake: 10,000/(10,000 + 40,000) = 20%. If the angel pays a total of $200,000 for 10,000 shares, the shares must be priced at $20 per share. 18-4 New Stock Issue. Bynum and Crumpton, a small jewelry manufacturer, has been successful and has enjoyed a positive growth trend. Now B&C is planning to go public with an issue of common stock, and it faces the problem of setting an appropriate price for the stock. The company and its investment banks believe that the proper procedure is to conduct a valuation and select several similar firms with publicly traded common stock and to make relevant comparisons. Several jewelry manufacturers are reasonably similar to B&C with respect to product mix, asset composition, and debt/equity proportions. Of these companies, Abercrombe Jewelers and Gunter Fashions are most similar. When analyzing the following data, assume that the most recent year has been reasonably ―normal‖ in the sense that it was neither especially good nor especially bad in terms of sales, earnings, and free cash flows. Abercrombe is listed on the AMEX and Gunter on the NYSE, while B&C will be traded in the NASDAQ market.

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Company Data

Abercrombe

Gunter

B&C

Shares outstanding

5 million

10 million

500,000

Price per share

$35.00

$47.00

Earnings per share

$2.20

$3.13

$2.60

Free cash flow per share

$1.63

$2.54

$2.00

Book value per share

$16.00

$20.00

$18.00

Total assets

$115 million

$250 million

$11 million

Total debt

$35 million

$50 million

$2 million

B&C is a closely held corporation with 500,000 shares outstanding. Free cash flows have been low and, in some years, negative due to B&C’s recent high sales growth rates, but as its expansion phase comes to an end, B&C’s free cash flows should increase. B&C anticipates the following free cash flows over the next 5 years: Year

FCF

$1,000,000

$1,050,000

$1,208,000

$1,329,000

$1,462,000

After Year 5, free cash flow growth will be stable at 7% per year. Currently, B&C has no nonoperating assets, and its WACC is 12%. Using the free cash flow valuation model (see Chapters 7 and 12), estimate the (1) horizon value, (2) intrinsic value of operations, (3) intrinsic value of equity, and (4) intrinsic per share price. Calculate debt to total assets, P/E, market to book, P/FCF, and ROE for Abercrombe, Gunter, and B&C. For calculations that require a price for B&C, use the per share price you obtained with the corporate valuation model in part a. Using Abercrombe’s and Gunter’s P/E, Market/Book, and Price/FCF ratios, calculate the range of prices for B&C’s stock that would be consistent with these ratios. For example, if you multiply B&C’s earnings per share by Abercrombe’s P/E ratio you get a price. What range of prices do you get? How does this compare with the price you get using the corporate valuation model?

Solution: a. Company Data

Abercrombe

Gunter

B&C

Shares outstanding

5 million

10 million

500,000

Price per share

$35.00

$47.00

Earnings per share

$2.20

$3.13

$2.60

Free cash flow per share

$1.63

$2.54

$2.00

Book value per share

$16.00

$20.00

$18.00

Total assets

$115 million

$250 million

$11 million

Total debt

$35 million

$50 million

$2 million

Year

FCF

$1,000,000

$1,050,000

$1,208,000

$1,329,000

$1,462,000

Growth rate at horizon = 7%, WACC = 12% The horizon value at the end of Year 5 is 1, 462,000(1.07) = 31,286,800. 0.12  0.07

Year

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FCF

$1,000,000

$1,050,000

$1,208,000

$1,329,000

$1,000,000

$1,050,000

$1,208,000

$1,329,000

$1,462,000 31,286,800 32,748,800

The present value of the horizon value (at Year 5) and the free cash flows in Years 1 through 5 is $22,016,893 and this is the value of operations for the company. Value of operations + Non-operating assets – Debt Value of equity

$22,016,893 0 2,000,000 $20,016,893

Per share value of equity = $20,016,893/500,000 = $40.03 b. Abercrombe

Gunter

B&C

D/A

30.43%

20.00%

18.18%

P/E

15.91

15.02

15.40

Market/Book

2.19

2.35

2.22

ROE

13.8%

15.7%

14.4%

P/FCF

21.47

18.50

20.02

Notes: Market/Book = market price per share divided by book value of equity per share. ROE can be calculated from per-share information as earnings per share divided by book value per share. c.

The implied prices are obtained by multiplying B&C’s measure (earnings per share, or book value per share or FCF per share) by the corresponding ratio (also called a ―multiple‖) for each of the two comparison companies:

Ratio

B&C Measure

Implied B&G Price per Share

2.60

$41.36

Abercrombe P/E

15.91

Gunter P/E

15.02

2.60

$39.04

Abercrombe Market/Book

2.19

18.00

$39.38

Gunter Market/Book

2.35

18.00

$42.30

Abercrombe P/FCF

21.47

2.00

$42.94

Gunter P/FCF

18.50

2.00

$37.01

The range of implied prices from multiple’s methods is from $37.01 to $42.94. These are comparable to the $40.03 price estimated by the free cash flow valuation model. 18-5 Pricing Stock Issues in an IPO. Dode Industries has hired the investment banking firm of Eric, Schwartz, & Mann (ESM) to help it go public. Dode and ESM agree that Zang’s current value of equity is $60 million. Dode currently has 4 million shares outstanding and will issue 1 million new shares. ESM charges a 7% spread. What is the correctly valued offer price, rounded to the nearest penny? How much cash will Dode raise net of the spread (use the rounded offer price)? Solution: POffer = VPre-issue/(F nNew + nExisting) = $60,000,000/((0.07)(1,000,000) + 4,000,000) = $14.742 ≈ $14.74

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Amount raised = POffer(1-F)(nNew) = $14.74(1 – 0.07)(1,000,000) = $13,708,200

SOLUTION TO SPREADSHEET PROBLEM 18-6 Build a Model: IPO Terms. Start with the partial model in the file Ch18 P06 Build a Model.xlsx on the textbook’s website. Lingadalli Corporation (LC) is considering an IPO. LC has 12 million shares of common stock owned by its founder and early investors. LC has no preferred stock, debt, or short-term investments. Based on its free cash flow projection, LC's intrinsic value of operations is $210 million. LC wants to raise $30 million (net of flotation costs) in net proceeds. The investment bank charges a 7% underwriting spread. All other costs associated with the IPO are small enough to be neglected in this analysis, and all shares sold in the IPO will be newly issued shares. Answer the following questions. a. What is the intrinsic stock price per share before the IPO? b. Given the target net proceeds, what amount of gross proceeds are required? c. What is the projected total value of LC immediately after the IPO? Based on the total amount paid by the shareholders purchasing new shares in the IPO, what percentage of the total post-IPO value do you think the new shareholders require to justify their stock purchases? d. How many new shares must be sold in the IPO to provide the percentage of ownership required by the new shareholders? How many total shares will be outstanding after the IPO? e. Based on number of new shares sold in the IPO and the total amount paid by the new shareholders, what is the offer price? f. Based on total value of the company after the IPO and the total number of outstanding shares after the IPO, what is the intrinsic price per share after the IPO? g. Compare the pre-IPO price, the offer price, and the post-IPO price. Explain why they are similar or different. (No calculations are required.) Solution: The detailed solution for the spreadsheet problem, Solution for Ch18 P06 Build a Model.xlsx, is available on the textbook’s website.

MINI CASE Randy’s, a family-owned restaurant chain operating in Alabama, has grown to the point that expansion throughout the entire Southeast is feasible. The proposed expansion would require the firm to raise about $18.6 million in new capital. Because Randy’s currently has a debt ratio of 50% and because family members already have all their personal wealth invested in the company, the family would like to sell common stock to the public to raise the $18.3 million. However, the family wants to retain voting control. You have been asked to brief family members on the issues involved by answering the following questions. a.

What agencies regulate securities markets? Answer: The main agency that regulates the securities market is the Securities and Exchange Commission. Some of the responsibilities of the SEC include (1) the regulation of all national stock exchanges; (2) the regulation of companies whose securities are listed on an exchange and that must file annual reports with the SEC; (3) prohibiting manipulation by pools or wash sales; (4) control over trading by corporate insiders; and (5) control over the proxy statement and how it is used to solicit votes. The Federal Reserve Board controls flow of credit into security transactions through margin requirements. States also have some control over the issuance of new securities within their boundaries.

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The securities industry itself realizes the importance of stable markets; therefore, the various exchanges work closely with the SEC to police transactions and to maintain the integrity and credibility of the system. b.

How are start-up firms usually financed? Answer: The first financing comes from the founders. The first external financing comes from angels, who are wealthy individuals. The next external financing comes from a venture capital fund. The fund raises capital from institutional investors, usually around $70 to $80 million. The managers of the fund are called venture capitalists. The fund invests in 10 to 12 companies, and the venture capitalist sits on their boards.

Differentiate between a private placement and a public offering. Answer: In a private placement, stock is sold directly to one or a small group of investors rather than being distributed to the public at large. A private placement has the advantage of lower flotation costs; however, since the stock would be bought by a small number of outsiders, it would not be actively traded, and a liquid market would not exist. Further, since it would not have gone through the SEC registration process, the holders would be unable to sell it except to a restricted set of ―sophisticated‖ investors. Further, it might be difficult to find investors willing to invest large sums in the company and yet be minority stockholders. Thus, many of the advantages listed above would not be obtained. For these reasons, a public placement makes more sense in Randy’s situation.

Why would a company consider going public? What are some advantages and disadvantages? Answer: A firm is said to be ―going public‖ when it sells stock to the public for the first time. A company’s first stock offering to the public is called an ―initial public offering (IPO).‖ Thus, Randy’s will go public if it goes through with its planned IPO. There are several advantages and disadvantages to going public: Advantages to going public:    

Going public will allow the family members to diversify their assets and reduce the riskiness of their personal portfolios. It will increase the liquidity of the firm’s stock, allowing the family stockholders to sell some stock if they need to raise cash. It will make it easier for the firm to raise funds. The firm would have a difficult time trying to sell stock privately to an investor who was not a family member. Outside investors would be more willing to purchase the stock of a publicly held corporation which must file financial reports with the sec. Going public will establish a value for the firm.

Disadvantages to going public:  

 

The firm will have to file financial reports with the SEC and perhaps with state officials. There is a cost involved in preparing these reports. The firm will have to disclose operating data to the public. Many small firms do not like having to do this, because such information is available to competitors. Also, some of the firm’s officers, directors, and major stockholders will have to disclose their stock holdings, making it easy for others to estimate their net worth. Managers of publicly owned corporations have a more difficult time engaging in deals which benefit them personally, such as paying themselves high salaries, hiring family members, and enjoying notstrictly-necessary, but tax-deductible, fringe benefits. If the company is very small, its stock may not be traded actively and the market price may not reflect the stock’s true value.

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The advantages of public ownership would be recognized by key employees, who would most likely be granted stock options, which would certainly be more valuable if the stock were publicly traded. e.

What are the steps of an initial public offering? Answer: Select an investment banker; file the S-1 registration document with the SEC; choose a price range for the preliminary, or ―red herring,‖ prospectus; go on a roadshow; set final price on final prospectus.

What criteria are important in choosing an investment banker? Answer: (1) Reputation and experience in the industry; (2) existing mix of institutional and retail (i.e., individual) clients; (3) support in the post-IPO secondary market, especially the reputation of the analyst who will cover the stock.

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Would a company that goes public use a negotiated deal or a competitive bid? Answer: The firm would almost certainly use a negotiated deal. The competitive bid process for setting investment bankers’ fees is feasible only for large, well-established firms on large issues, and even here the use of bids is rare for equity issues. This is because the process of making a bid is costly (mainly for the research necessary to establish the price, but also because of the need for SEC registration), and investment bankers simply would not incur these costs unless they were assured of getting the deal or the issue was so large that a huge fee awaited the winner.

Would the sale be on an underwritten or best efforts basis? Answer: Most stock offerings are done on an underwritten basis, but the price is not set until the investment banker has checked investors for interest in the stock and has received oral assurances of commitments at a price that will virtually guarantee the success of the offering barring a major stock market collapse. So, there is little effective difference between a best efforts and an underwritten deal.

The estimated pre-IPO value of equity in the company is about $63 million and there are 4 million shares of existing shares of stock held by family members. The investment bank will charge a 7% spread, which is the difference between the price the new investor pays and the proceeds to the company. To net $18.6 million, what is the value of stock that must be sold? What is the total postIPO value of equity? What percentage of this equity will the new investors require? How many shares will the new investors require? What is the estimated offer price per share? Answer: To net $18.6 million, the value of stock the company must issue $18.6/(1 – 0.07) = $20 million. The value of equity after the IPO is equal to the value before plus the net proceeds: Post-IPO equity = $63 + $20(1 – 0.07) = $81.6 million. The new owners are investing $20 million, so they require a share of the equity that is equal to their investment: Percent required by investors = $20/$81.6 = 24.51%. The new investors require 24.51% of the shares after the IPO: nNew = [(% to new)(nExisting)]/(1 – % to new) = [0.2451)(4)]/(1 – 0.2451) = 1.30 million. The estimated offer price is the total amount purchased by the new investors divided by the number of new shares: POffer = $20/1.3 = $15.38

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What is a roadshow? What is book building? Answer: The senior management team, the investment banker, and the lawyer make presentations to potential institutional investors. They usually visit 10 to 20 cities, and make three to five presentations in each city. Management can’t say anything that is not in the registration statement, because the SEC imposes a ―quiet period‖ from the time it makes the registration effective until 25 days after the stock begins trading. The purpose is to prevent select investors from getting information that is not available to other investors. During the roadshow, the investment bankers ask the investors to indicate how many shares they plan on buying. The banker records this in its book. The banker hopes for oversubscription. Based on demand, the banker sets the final offer price on the evening before the stock is issued.

Describe the typical first-day return of an IPO and the long-term returns to IPO investors. Answer: First-day returns average 14.1%, with many stocks having much higher returns. The investment banker has an incentive to set a low price, both to make its brokerage customers happy and to make it easy to sell the issue, whereas the firm would like to set as high a price as possible. Returns over the 2-year period following the IPO are generally lower than for comparable firms, indicating that the offering price is too low, but that the first-day run-up is too high.

What are the direct and indirect costs of an IPO? Answer: The underwriter usually charges a 7% fee, based on the offer price. In addition, there are direct costs to lawyers, accountants, printers, etc. That can easily total $400,000. Indirect costs include the money left on the table, which is equal to the difference between the offer price and end-of-first-day price, multiplied by the number of shares. Also, much of management’s time and attention is consumed by the IPO in the months preceding the IPO.

m. What are equity carve-outs? Answer: Equity carve-outs are a special type of IPO in which a public company creates a new public company from one of its subsidiaries by issuing public stock in the subsidiary. The parent usually retains a controlling interest. n.

Describe some ways that companies use to raise funds from the capital markets other than by an IPO. Answer: In seasoned equity offers, publicly traded companies issue additional stock. Companies can issue securities using shelf registration (SEC rule 451), in which securities are registered but not all of the issue is sold at once. Instead, the company sells a percentage of the issue each time it needs to raise capital. Companies can use private placements. Some companies raise capital by securitizing their assets, such as credit card receivables.

What are some other investment banking activities? How did these increase investment banks’ risk? Answer: The repeal of Glass-Stegall in 1999 blurred the lines between traditional investment banks and other financial institutions. Modern investment banking companies engage in underwriting debt and equity offerings (the same as traditional investment banks), mergers, and acquisitions; finding potential acquisition targets; advising M&A clients; securitization; asset management for clients and on their own behalf; and trading operations.

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Traditional investment banks were primarily fee-generating organizations, but investment banks in 2007 were highly levered, often with ST borrowings (such as commercial paper). They also had large positions in risky assets, including mortgage-backed securities and credit default swaps. As a consequence, many from 2007 ―failed‖ and were sold (Bear Stearns; Merrill Lynch), liquidated (Lehman Brothers), or converted into bank to get TARP (Goldman Sachs). p.

What is meant by ―going private‖? What are some advantages and disadvantages? What roles do private equity funds play? Answer: Going private is the reverse of going public. Typically, the managers of a firm team up with a small group of outside investors who furnish most of the equity capital and purchase all the publicly held shares of the company. The firm’s senior management usually retains or is given shares in the newly private company. The outside investors typically use a large amount of debt financing, up to 90%, to complete the purchase. Such a transaction is called a ―leveraged buyout (LBO).‖ Going private gives the managers greater incentives and more flexibility in running the company. It also removes the burden of SEC filings, stockholder relations, annual reports, analyst meetings, and so on. The major disadvantage of going private is that it limits significantly the availability of new capital. Since the stock is not publicly traded, a new stock issue would not be practical, and, since such firms are normally leveraged to the hilt, it is tough to find additional debt financing. For this reason, it is common for firms that have recently gone private to sell off some assets to quickly reduce the debt burden to more conventional levels to give added financial flexibility. After several years of operating the business as a private firm, the owners typically go public again. At this time, the firm is presumably operating at its peak, and it will command top dollar compared to when it went private. In this way, the equity investors of the private firm are able to recover their investment and, hopefully, make a tidy profit. So far LBOs have, on average, been extremely profitable—since the 1970s, when LBO firms such as Kohlberg Kravis Roberts (KKR) began operating, their annual rates of return are reported to have averaged over 50% annually. However, Wall Street is becoming increasingly concerned about the use of debt, and in the beginning of the 1990s, the number of new LBOs had fallen dramatically and some old ones had major financial difficulties. A private equity (PE) funds is a limited liability partnership created to own and manage investments in nontraded equity. PE funds typically raise capital from investors and then take public companies private or invest directly in private companies. The managers of the PE fund make changes to improve the private companies with the objective to make them more valuable. After the making the company more valuable, the PE funds often reap a profit by selling the more highly valued company to private investors or by taking the company public.

What is project financing? Answer: Project financings are arrangements used to finance mainly large capital projects such as energy explorations, oil tankers, refineries, utility power plants, and so on. Usually, one or more firms (sponsors) will provide the equity capital required by the project, while the rest of the project’s capital is supplied by lenders and lessors. The most important aspect of project financing is that the lenders and lessors do not have recourse against the sponsors; they must be repaid from the project’s cash flows and the equity cushion provided by the sponsors.

Solution and Answer Guide BRIGHAM /EHRHARDT FINANCIAL M ANAGEMENT: THEORY & PRACTICE; CHAPTER 19: LEASE FINANCING

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ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 423 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 425 Easy Problems 1–3 ................................................................................................................................ 425 Intermediate Problems 4–6 ................................................................................................................... 426 Challenging Problem 7 ......................................................................................................................... 429 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 431 MINI CASE ............................................................................................................................................. 431

ANSWERS TO END-OF-CHAPTER QUESTIONS 19-1 Define each of the following terms: a. Lessee; lessor b. Operating lease; finance lease; sale-and-leaseback; combination lease c. Off-balance sheet financing; capitalizing d. Guideline lease e. Residual value f. Lessee’s analysis; lessor’s analysis g. Net advantage to leasing (NAL) Answer: a. The lessee is the party leasing the property. The party receiving the payments from the lease (that is, the owner of the property) is the lessor. b.

An operating lease, sometimes called a service lease, provides for both financing and maintenance. Generally, the operating lease contract is written for a period considerably shorter than the expected life of the leased equipment and it contains a cancelation clause. A finance lease does not provide for maintenance service, is not cancelable, and is fully amortized; that is, the lease covers the entire expected life of the equipment. In a sale-and-leaseback arrangement, the firm owning the property sells it to another firm, often a financial institution, while simultaneously entering into an agreement to lease the property back from the firm. A sale-and-leaseback can be thought of as a type of financial lease. A combination lease combines some aspects of both operating and finance leases. For example, a finance lease that contains a cancelation clause—normally associated with operating leases—is a combination lease.

Off-balance sheet financing refers to the fact that for many years neither leased assets nor the liabilities under lease contracts appeared on the lessees’ balance sheets. To correct this problem, the Financial Accounting Standards Board issued FASB Statement 13. Capitalizing means incorporating the lease provisions into the balance sheet by reporting the leased asset under fixed assets and reporting the present value of future lease payments as debt. ASU 201602 further corrected the problem by requiring operating leases be capitalized as well.

A guideline lease is a lease that meets all the IRS requirements for a genuine lease. A guideline lease is often called a tax-oriented lease. If a lease meets the IRS guidelines, the IRS allows the lessor to deduct the asset’s depreciation and allows the lessee to deduct the lease payments.

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The residual value is the market value of the leased property at the expiration of the lease. The estimate of the residual value is one of the key elements in lease analysis.

The lessee’s analysis involves determining whether leasing an asset is less costly than buying the asset. The lessee will compare the present value cost of leasing the asset with the present value cost of purchasing the asset (assuming the funds to purchase the asset are obtained through a loan). If the present value cost of the lease is less than the present value cost of purchasing, the asset should be leased. The lessee can also analyze the lease using the IRR approach. The IRR of the incremental cash flows of leasing versus purchasing represents the after-tax cost rate implied in the lease contract. If this rate is lower than the after-tax cost of debt, there is an advantage to leasing. Finally, the lessee might evaluate the lease using the equivalent loan method, which involves comparing the net savings at Time 0 if the asset is leased with the present value of the incremental costs of leasing over the term of the lease. If the Time 0 savings is greater than the present value of the incremental costs, there is an advantage to leasing. The lessor’s analysis involves determining the rate of return on the proposed lease. If the rate of return (or IRR) of the lease cash flows exceeds the lessor’s opportunity cost of capital, the lease is a good investment. This is equivalent to analyzing whether the NPV of the lease is positive.

The net advantage to leasing (NAL) gives the dollar value of the lease to the lessee. It is, in a sense, the NPV of leasing versus owning.

19-2 Distinguish between operating leases and finance leases. Would you be more likely to find an operating lease employed for a fleet of trucks or for a manufacturing plant? Answer: An operating lease is usually cancelable and includes maintenance. Operating leases are, frequently, for a period significantly shorter than the economic life of the asset, so the lessor often does not recover his full investment during the period of the basic lease. A finance lease, on the other hand, is fully amortized and generally does not include maintenance provisions. An operating lease would probably be used for a fleet of trucks, while a finance lease would be used for a manufacturing plant. 19-3 Are lessees more likely to be in higher or lower income tax brackets than lessors? Answer: You would expect to find that lessees, in general, are in relatively low income tax brackets, while lessors tend to be in high tax brackets. The reason for this is that owning tends to provide tax shelters in the early years of a project’s life. These tax shelters are more valuable to taxpayers in high brackets. However, current tax laws have reduced the depreciation benefits of owning, so tax rate differentials are less important now than in the past. 19-4 In our Anderson Company example, we assumed that the lease could not be canceled. What effect would a cancelation clause have on the lessee’s analysis? On the lessor’s analysis? Answer: A cancelation clause would reduce the risk to the lessee since the firm would be allowed to terminate the lease at any point. Since the lease is less risky than a standard finance lease, and less risky than straight debt, which cannot usually be prepaid without a prepayment charge, the discount rate on the cost of leasing might be adjusted to reflect lower risk. (Note that this requires increasing the discount rate since cash outflows are being discounted.) The effect on the lessor is just the opposite—risk is increased. (Note that this would also require an increase in the lessor’s discount rate.)

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SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–3 19-1 Cost of Tax-Oriented Lease. Bird Wing Bedding can lease an asset for 4 years with payments of $20,000 due at the beginning of the year. The firm can borrow at a 6% rate and pays a 25% federal-plusstate tax rate. The lease qualifies as a tax-oriented lease. What is the cost of leasing? Solution: Inputs Annual lease payment

$20,000

Lease term

Interest rate =

Tax rate

25%

After-tax lease payment = (Lease pmt)(1 – T)

$15,000

After-tax cost of debt = Int. rate (1 – T)

4.50%

The cost of leasing is equal to the present value of the after-tax lease payments discounted at the after-tax cost of debt. To find the cost of leasing with a financial calculator, set it to Begin mode because the payments are at the beginning of the year. Then enter N = 4, I/YR = 4.5, PMT = 15,000, and FV = 0. Solve for PV = −$56,234. In Excel, you can use the PV function or the NPV function. With the PV function, the formula is: =PV(0.045,3,15000,1)-15000. As it should be, the result is −$56,234. 19-2 Cost of Borrowing: Tax-Oriented Lease. Comey Products has decided to acquire some new equipment with a $200,000 purchase price. The equipment will last 4 years and is in the MACRS 3-year class. (The depreciation rates for Year 1 through Year 4 are equal to 0.3333, 0.4445, 0.1481, and 0.0741.) The firm can borrow at a 9% rate and pays a 25% federal-plus-state tax rate. Comey is considering leasing the property but wishes to know the cost of borrowing that it should use when comparing purchasing to leasing and has hired you to answer this question. What is the correct answer to Comey’s question? (Hint: Use the shortcut method in Section 19-5a to find the aftertax cost of the loan payments.) Solution: Purchase price = $200,000 Tax rate = 25% Cost of debt = 9% Depreciation rates

Year 0

Year 1

Year 2

Year 3

Year 4

0.3333

0.4445

0.1481

0.0741

Depreciation expense = Depr. Rate (Purchase price)

$66,660

$88,900

$29,620

$14,820

Depreciation tax shield = Depr.(Tax rate)

$16,665

$22,225

$7,405

$3,705

Intermediate calculations

PV of after-tax loan pmts = purchase price

−$200,000

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After-tax cost of debt = (Cost of debt)(1 – T)

6.75%

After-tax cash flows

−$200,000

NPV at after-tax cost of debt

−$155,945

$16,665

$22,225

$7,405

$3,705

19-3 Non-Tax-Oriented Lease: Net Advantage to Leasing. Dunbar Corporation can purchase an asset for $30,000; the asset will be worthless after 14 years. Alternatively, it could lease the asset for 14 years with an annual lease payment of $3,653 paid at the end of each year. The firm’s cost of debt is 9%. The IRS classifies the lease as a non-tax-oriented lease. What is the net advantage to leasing? Solution: The initial lease liability is the present value of the lease payments discounted at the cost of debt. Set N = 14, I/YR = 9%%, PMT = $3,653, FV = 0, and solve for PV = $28,442.81. NAL for finance lease = Purchase price − Initial lease liability = $30,000 − $28,442.8 = $1,557.2

INTERMEDIATE PROBLEMS 4–6 19-4 Financial Statement Reporting for an Operating Lease. Harmeling Paint Ball (HPB) Corporation needs a new air compressor that costs $80,000. HPB will need it for only 3 years even though the compressor's economic life is long enough so that the lease is an operating lease. The firm can lease the compressor for 3 years with $15,000 lease payments at the end of each year. HPB’s cost of debt is 12%. Answer the following questions. (Hint: See Figure 19-1.) a. What is the initial lease liability that must be reported on the balance sheet? b. What is the initial right-of-use asset? c. What will HPB report as the Year-1 lease expense? d. What is the Year-1 imputed interest expense? e. What lease liability must be reported at Year 1? f. What right-of-use asset must be reported at Year 1? Solution: a. The initial lease liability is equal to the present value of the lease payments when discounted at the cost of debt. Set N = 3, I/YR = 12, PMT = 15000, FV = 0, and solve for PV = $36,027.47 b.

The initial right-of-use asset is equal to the initial lease liability: $36,027.47

The Year-1 lease expense is equal to the lease payment: $15,000.

The Year-1 imputed interest is: Year-1 imputed interest = (Cost of debt)(Initial lease liability) = 12%($36,027.47) = $4,323.30

The Year-1 lease liability is: Year-1 lease liability = Initial lease liability + Imputed interest – Payment = $36,027.47 + $4,323.30 – $15,000 = $25,350.77

The Year-1 right-of-use asset is equal to the Year-1 lease liability: $25,350.77.

19-5 Financial Statement Reporting for a Finance Lease. Reynolds Construction (RC) needs a piece of equipment that costs $100,000. The equipment has an economic life of 2 years and no residual value. The equipment will not require maintenance because its useful life is so short. RC can borrow the full cost of the equipment at an interest rate of 8% with payments due at the end of the year. Alternatively,

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RC can lease the equipment for $55,000 with payments due at the end of the year. Assume RC chooses the lease, which is a finance lease for financial reporting purposes. Answer the following questions. (Hint: See Figure 19-1.) a. What is the initial lease liability that must be reported on the balance sheet? b. What is the initial right-of-use asset? c. What will RC report as an interest expense at Year 1? d. What will RC report as an amortization expense at Year 1? e. What will RC report as the lease liability at Year 1? f. What will RC report as the right-of-use asset at Year 1? Solution: a. The initial lease liability is equal to the present value of the lease payments when discounted at the cost of debt. Set N = 2, I/YR = 8, PMT = 55,000, FV = 0, and solve for PV = $98,079.56. b.

The initial right-of-use asset is equal to the initial lease liability: $98,079.56.

The Year-1 reported interest expense is equal to cost of debt multiplied by the initial lease liability: 8%($98,079.56.) = $7,846.36.

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The Year-1 amortization expense is Year-1 amortization expense = (Initial lease liability)/(Term of lease) = ($98,079.56)/2 = $49,039.78

The Year-1 lease liability is: Year-1 lease liability = Initial lease liability + Interest expense – Payment = $98,079.56 + $7,846.36 – $55,000 = $50,925.92 ≈ $50,925.93 with no rounding in intermediate steps

The Year-1 right-of-use asset is: Year-1 right-of-use asset = Initial lease liability – Amortization expense = $98,079.56 – $49,039.78 = $49,039.78

19-6 Lease Versus Buy. Big Sky Mining Company must install $1.5 million of new machinery in its Nevada mine. It can obtain a bank loan for 100% of the purchase price, or it can lease the machinery. Assume that the following facts apply. (1) The machinery falls into the MACRS 3-year class. (2) Under either the lease or the purchase, Big Sky must pay for insurance, property taxes, and maintenance. (3) The firm’s tax rate is 25%. (4) The loan would have an interest rate of 15%. It would be nonamortizing, with only interest paid at the end of each year for 4 years and the principal repaid at Year 4. (5) The lease terms call for $400,000 payments at the end of each of the next 4 years. (6) Big Sky Mining has no use for the machine beyond the expiration of the lease, and the machine has an estimated residual value of $250,000 at the end of the fourth year. a. What is the cost of owning? b. What is the cost of leasing? c. What is the NAL of the lease? Solution: a. Cost of Owning: First, calculate the annual depreciation. 0

Depreciation Schedule

33.33%

44.45%

14.81%

7.41%

Depreciation

$499,950

$666,750

$222,150

$111,150

$1,000,050

$333,300

$111,150

Book Value

$1,500,000

Second, calculate the after-tax cash flows. The after-tax present value of the loan payments is equal to the amount borrowed, so it is the value in the shown at Year 0. The annual depreciation tax savings are equal to the tax rate multiplied by the depreciation shown in the previous table. The tax on the residual value is equal to the residual value multiplied by the tax rate.

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Cost of Owning After tax loan payments = purchase price =

$124,988

$166,688

$55,538

$27,788

–$1,500,000

Depreciation tax savings Residual value

$250,000

Tax on residual value

–$62,500

Net cash flow

–$1,500,000

$124,988

$166,688

$55,538

$215,288

The after-tax cost of debt is rd(1 – T) = 15%(1 – 0.25) = 11.25%. The NPV of the after-tax cash flows when discounted at 11.25% is −$1,072,090.25. b.

Cost of Leasing: The after-tax lease payments are equal to (Lease payment)(1 – T) = $400,000(1 – 0.25) = $300,000. Cost of leasing

After-tax lease payment

–$300,000

Net cash flow

–$300,000

The PV of the after-tax lease payments when discounted at 11.25% is −$925,787.40. c.

Cost Comparison Net advantage to leasing (NAL) = PV of leasing – PV of owning = −$925,787.40 – (−$1,072,090.25) = $146,302.85.

CHALLENGING PROBLEM 7 19-7 Lease Versus Buy. Sadik Industries must install $1 million of new machinery in its Texas plant. It can obtain a 6-year bank loan for 100% of the cost at a 14% interest rate with equal payments at the end of each year. Sadik’s tax rate is 25%. The equipment falls in the MACRS 3-year class. (The depreciation rates for Year 1 through Year 4 are equal to 0.3333, 0.4445, 0.1481, and 0.0741.) Alternatively, a Texas investment banking firm that represents a group of investors can arrange a guideline lease calling for payments of $320,000 at the end of each year for 3 years. Under the proposed lease terms, the Sadik must pay for insurance, property taxes, and maintenance. Sadik must use the equipment if it is to continue in business, so it will almost certainly want to acquire the property at the end of the lease. If it does, then under the lease terms, it can purchase the machinery at its fair market value at Year 3. The best estimate of this market value is $200,000, but it could be much higher or lower under certain circumstances. If purchased at Year 3, the used equipment would fall into the MACRS 3-year class. Sadik would actually be able to make the purchase on the last day of the year (i.e., slightly before Year 3), so Sadik would get to take the first depreciation expense at Year 3 (the remaining depreciation expenses would be from Year 4 through Year 6). On the time line, Sadik would show the cost of purchasing the used equipment at Year 3 and its depreciation expenses starting at Year 3. To assist management in making the proper lease-versus-buy decision, you are asked to answer the following questions. a. What is the cost of owning? b. What is the cost of leasing? c. What is the net advantage to leasing? d. Consider the $200,000 estimated residual value. How high could the residual value get before the net advantage of leasing falls to zero?

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Solution: a. First, calculate the annual depreciation. Year

Depreciation rate

33.33%

44.45%

14.81%

7.41%

0.00%

Depreciation expense

$333,300

$444,500

$148,100

$74,100

$666,700

$222,200

$74,100

Book value

$1,000,000

After-tax cost of debt = 14% × (1 – T) = 14% × (1 – 0.25) = 10.5%. Depreciation tax savings = T(Depreciation). Year

$83,325

$111,125

$37,025

$18,525

$83,325

$111,125

$37,025

$18,525

–$1,000,000

Purchase price Tax savings due to depreciation Net cash flow of owning

–$1,000,000

PV of owning @ after-tax cost of debt

–$793,716.27

First, calculate the depreciation after the purchase is made on the last day of Year 3. Because the purchase was in Year 3, that is when depreciation starts. In other words, the end of the lease is on the last day of Year 3, which is t = 2.99. Year

Depreciation rate

33.33%

44.45%

14.81%

7.41%

Depreciation basis

$200,000

Depreciation

$66,660

$88,900

$29,620

$14,820

Book value after depreciation expense

$133,340

$44,440

$14,820

Now calculate the cost of owning. The after-tax lease payment is equal to (Lease payment)(1 – T) = $320,000(1 – 0.25) = $240,000. The tax saving dues to depreciation are equal to the depreciation expense multiplied by the tax rate. 0 After-tax lease payment

–$240,000

Purchase of machine at residual

–$200,000

Tax savings due to depreciation expense

$16,665

$22,225

$7,405

$3,705

–$423,335

$22,225

$7,405

$3,705

Net cash flow of leasing PV of leasing @ after-tax cost of debt

–$240,000

–$706,073.42

Net advantage to leasing = PV of leasing – PV of owning = −$706,073.42 − (−$793,716.27 ) = $87,642.85. Because the NAL is positive, the company should choose the lease.

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Note that the maintenance expense is excluded from the analysis since the firm will have to bear the cost whether it buys or leases the machinery. Because the firm is keeping the machine for at least 6 years (either because it buys the machine at Year 0 or leases and buys at Year 3), there are no different tax effects due to the ultimate sale of the machine beyond Year 6—the machine will be fully depreciated then whether the firm buys or leases. d.

Using Goal Seek, we find that the purchase price can go up to $353,163 before the NAL becomes negative.

SOLUTION TO SPREADSHEET PROBLEM 19-8 Build a Model: Lessee’s Analysis. Start with the partial model in the file Ch19 P08 Build a Model.xlsx on the textbook’s website. As part of its overall plant modernization and cost reduction program, Western Fabrics’ management has decided to install a new automated weaving loom. In the capital budgeting analysis of this equipment, the IRR of the project was found to be 20% versus the project’s required return of 12%. The loom has an invoice price of $250,000, including delivery and installation charges. The funds needed could be borrowed from the bank through a 4-year amortized loan at a 10% interest rate, with payments to be made at the end of each year. In the event the loom is purchased, the manufacturer will contract to maintain and service it for a fee of $20,000 per year paid at the end of each year. The loom falls in the MACRS 5-year class, and Western’s marginal federal-plus-state tax rate is 25%. Aubey Automation Inc., maker of the loom, has offered to lease the loom to Western for $70,000 upon delivery and installation (at t = 0) plus four additional annual lease payments of $70,000 to be made at the end of Years 1 to 4. (Note that there are five lease payments in total.) The lease agreement includes maintenance and servicing. The loom has an expected life of 8 years, at which time its expected salvage value is zero; however, after 4 years its market value is expected to equal its book value of $42,500. Western plans to build an entirely new plant in 4 years, so it has no interest in either leasing or owning the proposed loom for more than that period. a. Should the loom be leased or purchased? b. The salvage value is clearly the most uncertain cash flow in the analysis. What effect would a salvage value risk adjustment have on the analysis? (Assume that the appropriate salvage value pretax discount rate is 15%.) c. Assuming that the after-tax cost of debt should be used to discount all anticipated cash flows, at what lease payment would the firm be indifferent to either leasing or buying? Solution: The detailed solution for the spreadsheet problem, Ch19 P08 Build a Model Solution.xlsx, is available on the textbook’s website.

MINI CASE Lewis Securities Inc. has decided to acquire a new market data and quotation system for its Richmond home office. The system receives current market prices and other information from several online data services, then either displays the information on a screen or stores it for later retrieval by the firm’s brokers. The system also permits customers to call up current quotes on terminals in the lobby. The equipment costs $1,000,000 and, if it were purchased, Lewis could obtain a term loan for the full purchase price at a 10% interest rate. Although the equipment has a 6-year useful life, it is classified as a special-purpose computer and therefore falls into the MACRS 3-year class. If the system were purchased, a 4-year maintenance contract could be obtained at a cost of $20,000 per year, payable at the beginning of each year. The equipment would be sold after 4 years, and the best estimate of its residual value at that time is $200,000. However, because real-time display system technology is changing rapidly, the actual residual value is uncertain.

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As an alternative to the borrow-and-buy plan, the equipment manufacturer informed Lewis that Consolidated Leasing would be willing to write a 4-year guideline lease on the equipment, including maintenance, for payments of $260,000 at the beginning of each year. Lewis’s marginal federal-plus-state tax rate is 40%. You have been asked to analyze the lease-versus-purchase decision and, in the process, to answer the following questions. a.

Who are the two parties to a lease transaction?

Answer: The two parties are the lessee, who uses the asset, and the lessor, who owns the asset. a.

What are the four primary types of leases, and what are their characteristics?

Answer: The four primary types of leases are operating, finance, sale-and-leaseback, and combination. An operating lease, sometimes called a service lease, provides for both financing and maintenance. Generally, the operating lease contract is written for a period considerably shorter than the expected life of the leased equipment. It usually contains a cancelation clause. A finance lease does not provide for maintenance service, is not cancelable, and is fully amortized; that is, the lease covers the entire expected life of the equipment. In a sale-and-leaseback arrangement, the firm owning the property sells it to another firm, often a financial institution, while simultaneously entering into an agreement to lease the property back from the firm. A sale-and-leaseback can be thought of as a type of finance lease. A combination lease combines some aspects of both operating and finance leases. For example, a finance lease that contains a cancelation clause—normally associated with operating leases—is a combination lease. In a leveraged lease, the lessor borrows a portion of the funds needed to buy the equipment to be leased. 3. How are leases classified for tax purposes? Answer: A tax-oriented lease (also called a guideline lease) is a lease that meets all of the IRS requirements for a genuine lease. If a lease meets the IRS guidelines, the IRS allows the lessor to deduct the asset’s depreciation and allows the lessee to deduct the lease payments. If a lease does not meet the requirements for a tax-oriented lease, then it is a non-tax-oriented lease and the attributes of ownership (the tax shield of depreciation and maintenance) go to the lessee.

What effect does leasing have on a firm’s balance sheet?

Answer: Virtually all leases longer than a year must be capitalized, which means that the present value of the lease payments when discounted by the cost of debt is reported as a ―lease liability‖ and as a ―right-of-use‖ asset on the balance sheets. a.

What effect does leasing have on a firm’s capital structure?

Answer: Leasing is a substitute for debt financing, so leasing increases a firm’s financial leverage. One dollar of lease financing displaces one dollar of debt financing. For example, suppose a firm has a target capital structure of 50% debt and 50% equity. If 50% of its assets are leased, then the remainder must be financed with equity. b.

What is the present value of owning the equipment? (Hint: Set up a time line that shows the net cash flows over the period t = 0 to t = 4, and then find the PV of these net cash flows, or the PV cost of owning.)

Answer: To develop the cost of owning, we begin by constructing the depreciation schedule: depreciable basis = $1,000,000.

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MACRS Rate 0.3333 0.4445 0.1481 0.0741 1.0000

Year 1 2 3 4

Depreciation Expense $ 333,300 444,500 148,100 74,100 $1,000,000

End-of-Year Book Value $666,700 222,200 74,100 0

Step 1: Calculate net after-tax cash flows of purchase and loan payments. Year

Equipment cost

–1,000,000

Loan proceeds and repay.

1,000,000

4 –1,000,000

–100,000

25,000

–75,000

–1,075,000

Depreciation rate

0.3333

0.4445

0.1481

0.0741

Depreciation expense

333,300

444,500

148,100

74,100

Depreciation shield

83,325

111,125

37,025

18,525

–20,000

5,000

–15,000

Interest expense Tax savings from interest Principal repayment Total after-tax net purchase and loan cash flows

Step 2: Calculate the depreciation tax shield. Year

Step 3: Calculate the after-tax maintenance costs. Year Maintenance Tax savings on maintenance After-tax maintenance

Step 4: Calculate the after-tax residual value. Year

Residual value

200,000

Tax on residual value

–50,000

Net residual cash flow

150,000

Step 5: Calculate the total after-tax cash flows. The interest rate is 25% and the pre-tax cost of debt is 10%. The after-tax cost of debt = 10%(1 − 0.25) = 7.5%. Calculate the NPV of the total net present value of owning using the after-tax cost of debt.

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Year

–75,000

–1,075,000

83,325

111,125

37,025

18,525

–15,000

Net cash flow from owning

–15,000

–6,675

21,125

–52,975

PV ownership cost @ 7.5

–$724,341

Total after-tax net purchase and loan cash flows

0 0

Depreciation tax shield After-tax maintenance

Net residual cash flow

150,0000 –906,475

Depreciation is a tax-deductible expense, so it produces a tax savings of T(depreciation). For example, the savings in Year 1 is 0.25($333,300) = $83,325. Each maintenance expense is $20,000, but it is tax deductible, so it provides a tax shield of 0.25($20,000) = $5,000. The ending book value is $0, so taxes must be paid on the full $200,000 salvage (residual) value. b.

What is the discount rate for the cash flows of owning?

Answer: The proper discount rate depends on (1) the risk of the cash flow stream and (2) the general level of interest rates. The loan payments and the maintenance costs are fixed by contract; hence, are not at all risky. The depreciation deductions are also ―locked in,‖ but the tax rate could change. Thus, depreciation cash flows (tax savings) are not totally certain, but they are relatively certain. Only the residual value is highly uncertain. On balance, and in relation to cash flows associated with such activities as capital budgeting, we conclude that the cash flows in the time line are relatively safe, so they should be discounted at a relatively low rate. In fact, they have about the same degree of riskiness as the firm’s debt cash flows (which also have some tax rate risk, and which are also contractual in nature). Therefore, we conclude that leasing has about the same impact on the firm’s financial risk as debt financing, so the appropriate discount rate is Lewis’s cost of debt. (Note: The larger the residual value in relation to the other flows, the less justifiable is this statement.) Further, since the cash flows are stated on an after-tax basis, the rate should be the after-tax cost of debt. Lewis’s before-tax debt cost is 10%, and since the firm is in the 25% tax bracket, its after-tax cost is 10.0%(1 – 0.25) = 7.5%. Therefore, use 7.5% as the discount rate. c.

What is Lewis’s present value of leasing the equipment? (Hint: Construct a time line.) Answer: Each lease payment is $260,000, but this is deductible for taxes. The tax savings from the lease are 25%($260,000) = $65,000. If Lewis leased the equipment, its only cash flows would be the after-tax lease payments: Year Lease payment Tax savings from lease Net cash flow PV of leasing @ 7.5%

0 –260,000 65,000 –195,000 –702,103

1 –260,000 65,000 –195,000

2 –260,000 65,000 –195,000

3 –260,000 65,000 –195,000

What is the net advantage to leasing (NAL)? Does your analysis indicate that Lewis should buy or lease the equipment? Explain. Answer: The net advantage to leasing (NAL) is equal to the PV of leasing minus the PV of owning: NAL = PV of leasing − PV of owning

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= −$702,103 − (−$724,341) = $22,238. The NAL is positive, which indicates that the PV cost of owning is greater. Therefore, leasing is less expensive than borrowing and buying, so Lewis should lease the equipment rather than purchase it. e.

Now assume that the equipment’s residual value could be as low as $0 or as high as $400,000, but $200,000 is the expected value. Because the residual value is riskier than the other cash flows, this differential risk should be incorporated into the analysis. Describe how this could be accomplished. (No calculations are necessary but explain how you would modify the analysis if calculations were required.) What effect would the residual value’s increased uncertainty have on Lewis’s lease-versuspurchase decision? Answer: First, note that the residual value in a lease analysis will be shown either in the ―cost of owning section‖ or in the ―cost of leasing‖ section, depending on whether or not the company plans to continue using the leased asset at the expiration of the basic lease. If the lessee plans to continue using the equipment, then it will have to be purchased when the lease expires, and in this case the residual value appears as a cost in the leasing cost section. However, if the lessee plans not to continue using the equipment, then the residual value will not be shown in the leasing section—rather, it will be shown as an inflow in the cost of owning section. In Lewis’s case, the asset will not be needed at the expiration of the lease, so the residual is shown as an inflow in the owning section. In this situation, we account for increased residual risk by increasing the rate used to discount the residual value cash flow, resulting in a lower present value of the residual cash flow. This leads to a higher cost of owning, so the greater the risk of the residual value, the higher the cost of owning, and the more attractive leasing becomes. Note, though, that the situation would be different if Lewis planned to lease and then exercise a fair market value purchase option in order to continue using the equipment. Then the residual would be shown as a cost in the leasing section, and its higher risk would be reflected by discounting it at a lower rate. In that situation, the riskiness of the residual would penalize rather than help the lease. In the case at hand, the lessor, not the lessee, will own the asset at the end of the lease, so the lessor bears the residual value risk. In effect, the lease transaction passes the risk associated with the residual value from the lessee/user to the lessor. Of course, the lessor recognizes this, and as a result, assets with highly uncertain residual values will carry higher lease payments than assets with relatively certain residual values. However, the most successful leasing companies have developed expertise in renovating and disposing of used equipment, and this gives them an advantage over most lessees in reducing residual value risks. Further, leasing companies usually deal with a wide array of assets, so residual value estimates that are too high on one asset may be offset by estimates that are too low on another. See this chapter’s Mini Case Excel file for a numerical example.

The lessee compares the present value of owning the equipment with the present value of leasing it. Now put yourself in the lessor’s shoes. In a few sentences, how should you analyze the decision to write or not to write the lease? Answer: The lessor should view ―writing‖ the lease as an investment, so the lessor should compare the return on the lease with returns available on alternative investments of similar risk. Because lease payments are identical each period, analyzing a lease is analogous to analyzing a bond.

Assume that the lease payments were actually $280,000 per year, that Consolidated Leasing is also in the 25% tax bracket, and that it also forecasts a $200,000 residual value. Also, to furnish the maintenance support, it would have to purchase a maintenance contract from the manufacturer at the same $20,000 annual cost, again paid in advance. Consolidated Leasing can obtain an expected 10% pre-tax return on investments of similar risk. What are its NPV and IRR of leasing under these conditions?

Answer:

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The lessor must invest $1,000,000 to buy the equipment, but then it expects to receive tax benefits and lease payments over the life of the lease. Note that the depreciation expenses calculated earlier also apply to the lessor, so we have this cash flow stream: Year

−$1,000,000

$83,325

$111,125

$37,025

$18,525

−$20,000

$5,000

Lease payment

$280,000

Tax on lease payment

Equipment cost Depreciation shield Maintenance Tax savings on maintenance

−$70,000

Residual value

$200,000

Tax on residual value

−$50,000)

−$805,000)

$278,325

$306,125

$232,025

$168,525

Net cash flow

NPV @ 7.5% = $31,770. IRR = 9.40%. The NPV is positive, so the lessor should write the lease. g.

What do you think the lessor’s NPV would be if the lease payments were set at $260,000 per year? (Hint: The lessor’s cash flows would be a ―mirror image‖ of the lessee’s cash flows.)

Answer: With lease payments of $260,000, the lessor’s cash flows would be the ―mirror image‖ of the lessee’s NAL—the same dollars, but with signs reversed. Therefore, the lessor’s NPV would be –$22,238, the negative of the lessee’s NAL. To verify this, note that a $20,000 reduction in each lease payment would reduce the lessor’s inflows by $20,000(0.75) = $15,000 at the beginning of each year. The PV of this annuity is $54,008 so the lessor’s NPV would be $31,770 – $54,008 = -$22,238, which is identical except for rounding differences. h.

Lewis’s management has been considering moving to a new downtown location, and they are concerned that these plans may come to fruition prior to the equipment lease’s expiration. If the move occurs, then Lewis would buy or lease an entirely new set of equipment, and so management would like to include a cancelation clause in the lease contract. What effect would such a clause have on the riskiness of the lease from Lewis’s standpoint? From the lessor’s standpoint? If you were the lessor, would you insist on changing any of the other lease terms if a cancelation clause were added? Should the cancelation clause contain provisions similar to call premiums or any restrictive covenants and/or penalties of the type contained in bond indentures? Explain your answer. Answer: A cancelation clause would lower the risk of the lease to Lewis, the lessee, because then it would not be obligated to make the lease payments for the entire term of the lease. If the situation changed so that Lewis either no longer needed the equipment or else wanted to change to a more technologically advanced product, then it could terminate the lease. However, a cancelation clause would make the contract riskier for the lessor. Now the lessor bears not only the final residual value risk, but also the uncertainty of when the contract will be terminated. To account for the additional risk, the lessor would undoubtedly increase the annual lease payment. Additionally, the lessor might include clauses that would prohibit cancelation for some period and/or impose a penalty fee for early cancellation. The decision as to whether or not to include a cancelation clause would depend on who was in a better position to bear the residual value risk, the lessee or the lessor. Often lessors have more expertise at disposing of used equipment than lessees, and thus they are willing to include cancelation clauses without major increases in the required lease payments.

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What are some other issues in lease analysis? Answer: Higher residual values make leasing less attractive to the lessee. Lease financing often is more available or a ―better‖ deal than debt financing. The lease analysis presented here is applicable to real estate leases and auto leases. An investment tax credit (when available) makes owning more attractive to the potential lessee. On the other hand, the tax credit makes the lessor’s value higher, so the lessor might be willing to ―share‖ this with the lessee. Tax rate differentials between the lessee and the lessor are often the primary reason why a lease adds value to both the lessee and the lessor. Numerical analyses often indicate that owning is less costly than leasing. However, leasing is popular because it has other benefits, including the following: 1. 2.

Provision of maintenance services. Risk reduction for the lessee. a. The lessee will know the project life. b. Eliminates negative consequences due to unexpected declines in the residual value. c. Reduces operating risk. Portfolio risk reduction enables lessor to better bear these risks.

Solution and Answer Guide BRIGHAM /EHRHARDT FINANCIAL M ANAGEMENT: THEORY & PRACTICE; CHAPTER 21: DYNAMIC CAPITAL S TRUCTURES AND CORPORATE VALUATION

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 437 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 439 Easy Problems 1–5 ................................................................................................................................ 439 Intermediate Problems 6–8 ................................................................................................................... 441 Challenging Problems 9–11 .................................................................................................................. 443 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 446 MINI CASE ............................................................................................................................................. 446 Web Extension 21A ................................................................................................................................. 454

ANSWERS TO END-OF-CHAPTER QUESTIONS 21-1 Define each of the following terms: a. Interest tax shield; value of tax shield b. Adjusted present value (APV) model c. Compressed adjusted present value (CAPV) model d. Free cash flow to equity model Answer:

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An interest tax shield is the amount of cash flow that is sheltered from taxation due to the tax deductibility of interest. It is equal to rd(D)(T). The value of the tax shield is the present value of the future tax savings from the deductibility of interest payments. The value of the tax shield depends on the rate (rTS) used to discount future annual tax shields. In the MM model with taxes, rTS = rd. Because MM assume zero growth, the value of the tax shield is T(D). If growth is constant, then the value of the tax shield is r dTD(1 + gL)/(rTS − gL). where rd is the interest rate on the debt and rTS is the discount rate for the tax shield.

The adjusted present value (APV) model discounts projected free cash flows at the unlevered cost of equity and discounts interest tax shields at rTS.

The compressed adjusted present value (CAPV) model discounts projected free cash flows at the unlevered cost of equity and it also discounts interest tax shields at the unlevered cost of equity to determine the value of operations. It is called the compressed APV because the FCF and tax shields are discounted at the same rate.

The free cash flow to equity model, also called the residual dividend model, first calculates FCFE, which is the free cash flow payable to shareholders. FCFE is free cash flow less interest expense plus the interest tax shield. It then discounts the FCFEs at the levered cost of equity to arrive at the value of equity in operations. You add in the value of nonoperating assets and you get the value of the equity. To get the value of operations, you then add in the value of the debt.

21-2 Modigliani and Miller assumed that firms do not grow. How does positive growth change their conclusions about the value of the levered firm and its cost of capital? Answer: The value of a growing tax shield is greater than the value of a constant tax shield. This means that for a given initial level of debt a growing firm will have more value from the debt tax shield than a nongrowing firm. Thus, for a given face value of debt, D, and unlevered value of equity, U, a growing firm will have a smaller wd, a larger levered cost of equity, rsL, and a larger WACC. So, the MM model will underestimate the value of the levered firm and its cost of equity and WACC. 21-3 The APV model uses the unlevered cost of equity, rsU, to discount cash flows while the corporate valuation model uses the WACC. Explain why the two models use different discount rates. Answer: The corporate valuation model takes the value of the debt tax shield into account by incorporating the tax rate in the WACC by multiplying the required return on debt by (1 – T). It assumes a constant capital structure and so using this corrected, aggregate discount rate values the entire firm. The APV model, on the other hand, allows for a nonconstant capital structure. Because the capital structure is potentially changing, the contribution of the debt tax shield to value changes from year to year, and so a constant WACC won’t capture these differences. Rather, the APV calculates separately the value of the tax shield and the value of the unlevered operations and uses the unlevered cost of equity, r sU, as this discount rate. 21-4 The APV and corporate valuation models are entity valuation models while the FCFE model is an equity valuation model. Explain the difference between an entity valuation model and an equity valuation model. Answer: An entity valuation model values the cash flows (FCFs) that are available for distribution all of the firm’s investors. These investors are stockholders, bondholders, and preferred stockholders. Because the cash flows are available to all the investors, their present value is the value of all of the investor’s claims. So, the present value is the sum of the values of stock, debt, and preferred stock. An equity valuation model such as the FCFE model uses cash flows that area available for distribution only to the equity holders;

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the cash flows due to the bondholders have been subtracted. Because these cash flows are only for the equity holders, their present value is the value of equity. 21-5 Suppose you want to value a company and you expect that its capital structure (weights on debt and equity) will remain constant. Which valuation model (corporate valuation model, FCFE, or APV) should you use and why? How is this answer different if the capital structure is expected to change dramatically? Answer: If the market value capital structure will remain constant then, in principle, the FCFE, corporate valuation, and APV models should give the same answers, provided all your projected financial statements are consistent in each year with the constant market value capital structure. In practice, it is difficult to project financial statements, especially debt levels, that are consistent with the constant market value capital structure so the FCFE model is difficult to implement. The corporate valuation model should be used in this case because it only requires projecting the operating items of the financial statements and doesn’t require projecting debt levels. If the capital structure is expected to change dramatically, then the corporate valuation model isn’t applicable (since it assumes a constant capital structure) and so the APV model must be used. The FCFE model can’t be used in this case since it also assumes a constant market value capital structure. 21-6 The APV model, the MM model, and the Hamada equation have different formulas for calculating the unlevered cost of equity, rsU. Why is that and which formula should you use? Answer: The Modigliani-Miller (with taxes), Hamada, and APV models make different assumptions about three items: 1) the discount rate to use for the interest tax shields, 2) whether the company grows or not, and 3) whether or not debt is risky. Since the calculation of r sU depends on which model you use, the appropriateness of that calculation depends on how well the assumptions of the model you use match the details of the company you are analyzing. The MM model and the Hamada equation assume that debt is riskless, the company does not grow, and the appropriate discount rate for the interest tax shield is the required return on debt, rd. In addition, the Hamada equation assumes that the beta of debt is zero. For real companies, none of these assumptions are realistic. The APV model, on the other hand, allows for risky debt, allows a company to grow, and discounts the interest tax shield at the unlevered cost of equity, rsU. Clearly, corporate debt is risky and clearly, many companies grow. The text shows why r sU is a more reasonable discount rate for the interest tax shields. So, the APV model’s assumptions are more consistent with real companies so its formula for unlevering should be used in most cases.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–5 21-1 MM Model With Zero Taxes. An unlevered firm has a value of $500 million. An otherwise identical but levered firm has $50 million in debt. Under the MM zero-tax model, what is the value of the levered firm? Solution: The VU = $500 million. With zero taxes, the MM model shows that V L = VU. Therefore, VL = VU = $500 million.

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21-2 MM Model With Corporate Taxes. An unlevered firm has a value of $800 million. An otherwise identical but levered firm has $60 million in debt at a 5% interest rate, which is its pre-tax cost of debt. Its unlevered cost of equity is 11%. No growth is expected. Assuming the federal-plus-state corporate tax rate is 25%, use the MM model with corporate taxes to determine the value of the levered firm. Solution: VL = VU + TD = $800 + 0.25($60) = $815 million. 21-3 Compressed APV Model With Constant Growth. An unlevered firm has a value of $800 million. An otherwise identical but levered firm has $60 million in debt at a 5% interest rate, which is its pre-tax cost of debt. Its unlevered cost of equity is 11%. After Year 1, free cash flows and tax savings are expected to grow at a constant rate of 3%. Assuming the corporate tax rate is 25%, use the compressed adjusted present value model to determine the value of the levered firm. (Hint: The interest expense at Year 1 is based on the current level of debt.) Solution:  r (D)(Tc )  VL = V U +  d   (rsU  g) 

 0.05(60)(0.25)  = $800 +    (0.11 0.03)  = $800 + $9.375 = $809.375 million. 21-4 Calculation of FCFE. A company has the following information: Earnings before interest and taxes

$80.00

Interest expense

$8.00

Tax rate

25%

Net change in debt

$12.00

Investment in total capital

$9.00

What is its free cash flow to equity? Solution: Method 1: FCF = EBIT(1  T)  Investment in total net operating capital = $80(1  0.25)  $9 = $51 A-T interest expense

= Interest(1  T) = $8(1  0.25) = $6

Principal payments + Newly issued debt

= Net change in debt = $12 FCFE = FCF  After-tax interest expense  Principal payments + Newly issued debt = $51  $6 + $12 = $57 Method 2: Interest tax savings

= Interest(T) = $8(0.25) = $2

FCFE = FCF  Interest expense + Interest tax savings + Net change in debt = $51  $8 + $2 + $12 = $57

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Method 3: Net income

= (EBIT  Interest)(1  T) = ($80  $8)(1  0.25) = $54

FCFE = Net income  Investment in operating capital + Net change in debt = $54  $9 + $12 = $57 21-5 FCFE Valuation. A company’s most recent free cash flow to equity was $100 and is expected to grow at 5% thereafter. The company’s cost of equity is 10%. Its WACC is 8.72%. What is its current intrinsic value? Solution: VEquity = [FCFE (1 + gL)]/(rSL  gL) = [$100 (1 + 0.05)]/(0.10  0.05) = $2,100

INTERMEDIATE PROBLEMS 6–8 21-6 Business and Financial Risk—MM Model. Air Tampa has just been incorporated, and its board of directors is grappling with the question of optimal capital structure. The company plans to offer commuter air services between Tampa and smaller surrounding cities. Air Tampa believes it would have the same business risk as Jaxair, which is an airline that has been around for a few years and that has had zero growth. Jaxair’s marketdetermined beta is 2.1, and it has a current market value debt ratio (total debt to total assets) of 50% and a federal-plus-state tax rate of 25%. Air Tampa expects to have investment tax credits when it begins business, which reduces its federal-plus-state tax rate to 20%. Air Tampa’s owners expect that the total book and market value of the firm’s stock, if it uses zero debt, would be $10 million. Air Tampa’s CFO believes that the MM and Hamada formulas for the value of a levered firm and the levered firm’s cost of capital should be used because zero growth is expected. a. Estimate the beta of an unlevered firm in the commuter airline business based on Jaxair’s marketdetermined beta. b. Now assume that rd = rRF = 10% and that the market risk premium RP M = 5%. Find the required rate of return on equity for an unlevered commuter airline. c. Air Tampa is considering three capital structures: (1) $2 million debt, (2) $4 million debt, and (3) $6 million debt. Estimate Air Tampa’s levered required return on stock (rsL) for these debt levels. d. Suppose Air Tampa’s investment tax credits expire, causing it to have a 25% federal-plus-state tax rate. Calculate Air Tampa’s rsL at $6 million debt using the new tax rate. Compare this with your corresponding answer to part c. (Hint: The increase in the tax rate causes VU to drop to $9.375 million.) Solution: a. bL = bU[1 + (1 − T)(D/S)] so bU = bL/[1 + (1T)(D/S). bU =

bL 1 (1 T)(D/ S)

2.1 2.1 = = 1.2. 1 (1 0.25)(0.5/ 0.5) 1.75

rsU = rRF + (rM – rRF)bU = 10% + (5%)1.2 = 10% + 6% = 16%.

$2 million debt: VL = VU + TD = $10 + 0.20($2) = $10.4 million. rsL = rsU + (rsU − rRF)(1 − T)(D/S) = 16% + (16% − 10%)(1 − 0.20)($2/$8.4) = 17.1429% ≈ 17.14%.

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$4 million debt: VL = $10 + 0.20($4) = $10.8 million. rsL = 16% + (6%)(0.8)($4/$6.8) = 18.8235% ≈ 18.82%. $6 million debt: VL = $10 + 0.20($6) = $11.2 million. rsL = 16% + 6% (0.8)($6/$5.2) = 21.5385% ≈ 21.54%. d.

$6 million debt and tax rate %: VL = VU + TD = $9.375 + 0.25($6) = $10.875 million. S = VL – D = $10.875 – $6 = $4.875 million rsL = rsU + (rsU − rRF)(1 − T)(D/S) = 16% + (16% − 10%)(1 − 0.25)($6/$4.875) = 21.5385% ≈ 21.54%. Note that the levered cost of equity in part d is the same as in part c, even though the tax rates differ. It is possible to show that the levered beta can be expressed as:   EBIT bL = b U   EBIT  (rsUD)  This expression does not have the tax rate, T. Thus, the levered beta will not change if EBIT remains constant and the only change is to the tax rate. Intuitively, this is because changes in the tax rate change the unlevered value of the firm as well as the tax shield provided by interest payments. The changes offset one another and do not affect the levered beta. Keep in mind that this is true only for the MM assumptions of zero growth and no personal taxes.

21-7 MM With Corporate Taxes. Companies U and L are identical in every respect except that U is unlevered while L has $10 million of 5% bonds outstanding. Assume: (1) All of the MM assumptions are met, including zero growth. (2) Both firms are subject to a 25% federal-plus-state corporate tax rate. (3) EBIT is $2 million. (4) The unlevered cost of equity is 10%. a. What value would MM now estimate for each firm? (Hint: Use Proposition I.) b. What is rs for Firm U? For Firm L? c. d.

Find SL, and then show that SL + D = VL results in the same value as obtained in part a. What is the WACC for Firm U? For Firm L?

Solution: a.

VU =

EBIT(1 T) $2(1 0.25) = = $15 million. rsU 0.10

VL = VU + TD = $15 + (0.25)$10 = $17.5 million. b.

rsU = 0.10 = 10.0%. rsL = rsU + (rsU − rd)(1 − T)(D/S) = 10% + (10% − 5%)(0.75)($10/$7.5) = 10% + 5% = 15.0%.

SL =

(EBIT  rdD)(1 T) rsL

[$2  0.05($10)]0.75 = $7.5 million. 0.15

VL = SL + D = $7.5 + $10 = $17.5 million.

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WACCU = rsU = 10.00%. WACCL = (D/V)(rd)(1 − T) + (S/V)rs = ($10/$17.5)(5%)(0.75) + ($7.5/$17.5)15% = 8.57%.

21-8 Levering the Required Return on Equity With Hamada, MM, and APV. Nodebt, Inc., has zero debt (wd = 0). It is considering restructuring to increase its percentage of debt to wd = 40%. Its beta is 0.8; the risk-free rate is 6%; the market risk premium is 7%; and, if it restructures, the required return on its debt will be 9%. Nodebt’s tax rate is 25%. a. Using the Hamada equation, calculate Nodebt’s required return on equity after the recapitalization. b. Using the MM model with corporate taxes (Equation 21-16), calculate Nodebt’s required return on equity. c. Using the APV model, calculate Nodebt’s required return on equity. d. Explain why these three answers are different. Solution: a. Hamada: New beta = 0.8(1 + (1 – 0.25)(0.40/0.60) = 1.20. New rsL = 6% + 1.20(7%) = 14.40% b.

MM with corporate taxes: Old rsU = 6% + 0.80(7%) = 11.60% New rsL = 11.6% + (11.6% – 9%)(1 – 25%)(0.40/0.60) = 12.90%

APV: based on old rsU = 11.6% from part b, New rsL = 11.6% + (11.6% − 9%)(0.40/0.60) = 13.33%

They are different because the three models have different assumptions. The Hamada and the MM with taxes models assume debt is riskless, growth is zero, and the tax shield is discounted at the required return on debt. In addition, the Hamada model assumes the return on debt is equal to the risk-free rate. The APV model, on the other hand, allows for nonzero growth, risky debt, and assumes the tax shield is discounted at the unlevered required return. These three different sets of assumptions give rise to different relationships between the unlevered and levered costs of equity.

CHALLENGING PROBLEMS 9–11 21-9 Compressed Adjusted Present Value. Schwarzentraub Corporation’s expected free cash flow for the year is $500,000; in the future, free cash flow is expected to grow at a rate of 8%. The company currently has no debt, and its cost of equity is 13%. Its tax rate is 25%. Suppose the firm issues $5 million of debt at a rate of 7%. Use the compressed adjusted present value approach to answer the following questions. a. Find VU. b. Find VL and rsL. Use the APV model that allows for growth. c. Start with the value of the unlevered firm, VU, from part a. Use the MM model (with taxes but with zero growth) to calculate VL and rsL. (Hint: These answers will differ from those in part b due to differences in growth assumptions.) Solution: a. VU = $500,000/(rsU – g) = $500,000/(0.13 − 0.08) = $10,000,000. b.

Using the adjusted present value model (APV), the value of value of the levered firm equal to the value of the unlevered firm plus the value of the tax shield. The value of the tax shield is equal to the present value of the growing annual tax shields. The debt at t = 0 is: D0 = $5,000,000.

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The tax shield at year 1 is: TS1 = (Interest expense at year 1)(T) = rd(D0)(T) = (0.07)($5,000,000)(0.25) = $87,500 The present value of a tax shield that is growing at a constant rate is: TS1 VTax shield = rTS  gL

 $87,500   = $1,750,000  0.05 

=

VL = VU + VTax shield = $10,000,000 + $1,750,000 = $11,750,000 Because the firm issued debt, the levered cost of equity changed. The first step to determine the levered cost of equity is to determine the value of the stock price, S, after the firm issues the debt. S = VL − Debt = $11,750,000 – $5,000,000 = $6,750,000. Substituting the values of debt, stock, the required return on stock, and the growth rate into equation 21-19, the required return on the levered stock is:

 5,000,000  rsL  0.13  (0.13  0.07)   = 17.44%  6,750,000  c.

Under MM, VL = VU + TD = $10 million + (0.25)(5 million) = $11.25 million. S = $11.25 – 5 = $6.25 million. rsL = 0.13 + (0.13 − 0.07)(1 − 0.25)(5/6.25) = 16.60%

21-10 Compressed APV With Nonconstant Growth. Sheldon Corporation projects the following free cash flows (FCFs) and interest expenses for the next 3 years, after which FCF and interest expenses are expected to grow at a constant 7% rate. Sheldon’s unlevered cost of equity is 13%; its tax rate is 25% Year

a. b. c. d. e.

Free cash flow ($ millions)

$20.0

$30.0

$40.0

Interest expense ($ millions)

$12.8

$14.4

$16.0

What is Sheldon’s unlevered horizon value of operations at Year 3? What is the current unlevered value of operations? What is the horizon value of the tax shield at Year 3? What is the current value of the tax shield? What is the current total value of the company?

Solution:

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$40 (1.07) = $713.33. 0.13  0.07

HVU,3 =

Free cash flow valuation: 0 rSU = 13% 1



 20 30 40 g = 7%   $ 17.70  HVU,3 = 713.33  23.49  753.33 522.10  $563.29 c.

TS = (Interest expense)(T) TS1 = $12.8(0.25) = $3.2 TS2 = $14.4(0.25) = $3.6 TS3 = $16.0(0.25) = $4.0

Tax shield valuation: HVTS,3 = d.

$ 4 (1.07) = $71.33 0.13 – 0.07

Value of tax shield: 0 rSU = 13% 1

    3.2 3.6 4.00 g = 7% 2.83  HV = 71.33 2

2.82 

U,3

75.33 52.21  $57.86 e.

Total valuet=0 = $563.29 + $57.86 = $621.15.

21-11 Unlevering and Then Levering the Required Return on Equity With Hamada, MM, and APV. Somedebt, Inc., has a little debt (wd = 20%) with required return 7%. It is considering restructuring to increase its percentage of debt to wd = 40%. Its beta is 0.8; the risk-free rate is 6%; the market risk premium is 7%; and, if it restructures, the required return on its debt will be 9%. Somedebt’s tax rate is 25%. a. Using the Hamada equation, calculate Somedebt’s unlevered required return and its required return on equity after the recapitalization. b. Using the MM model with corporate taxes (Equation 21-16), calculate Somedebt’s unlevered required return and its required return on equity after the recapitalization. (Hint: You will have to use algebra to solve Equation 21-16 for rsU or use goal seek in Excel to find rsU.) c. Using the APV model, calculate Somedebt’s unlevered required return and its required return on equity after the recapitalization. d. Explain why these six answers are different. Solution: a. Hamada: bU = 0.8/(1 + (1 – 0.25)(0.20/0.80)) = 0.6737 rsU (Hamada) = 6% + 0.6737(7%) = 10.72% New beta = 0.6737(1 + (1 – 0.25)(0.40/0.60) = 1.0105

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New rsL (Hamada) = 6% + 1.0105(7%) = 13.07% b.

MM with corporate taxes: old rsL = 6% + 0.8(7%) = 11.6% rsU = [11.6%(0.80) + 7%(1 – 0.25)(0.20)]/[0.80 + (1 – 0.25)0.20] = 10.87% New rsL = 10.87% + (10.87% – 9%)(1 – 25%)(0.40/0.60) = 11.81%

APV: old rsL = 6% + 0.8(7%) = 11.6% (already calculated in part b) rsU = 11.6%(0.80) + 7%(0.20) = 10.68% New rsL = 10.68% + (10.68% − 9%)(0.40/0.60) = 11.80%

They are different because the three models have different assumptions. The Hamada and the MM with taxes models assume debt is riskless, growth is zero, and the tax shield is discounted at the required return on debt. In addition, the Hamada model assumes the return on debt is equal to the risk-free rate. The APV model, on the other hand, allows for nonzero growth, risky debt, and assumes the tax shield is discounted at the unlevered required return. Since the assumptions are different, even unlevering to find rsU gives different answers for each of the three models. Relevering also gives different answers because of the different assumptions.

SOLUTION TO SPREADSHEET PROBLEM 21-12 Build a Model: Compressed Adjusted Present Value Model. Start with the partial model in the file Ch21 P12 Build a Model.xlsx on the textbook’s website. Kasperov Corporation has an unlevered cost of equity of 12% and is taxed at a 25% rate. The 4-year forecasts of free cash flow and interest expenses are shown in the following table; free cash flow and interest expenses are expected to grow at a 5% rate after Year 4. Using the compressed APV model, answer the following questions.

a. b. c. d. e.

INPUTS (In Millions)

Projected

Year:

Free cash flow

$200

$280

$320

$340

Interest expense

$100

$120

$140

Calculate the estimated horizon value of unlevered operations at Year 4 (i.e., immediately after the Year-4 free cash flow). Calculate the current value of unlevered operations. Calculate the estimated horizon value of the tax shield at Year 4 (i.e., immediately after the Year-4 free cash flow). Calculate the current value of the tax shield. Calculate the current total value.

Solution: The detailed solution for the problem is available in the file Ch21 P12 Build a Model Solution.xlsx on the textbook’s website.

MINI CASE David Lyons, CEO of Lyons Solar Technologies, is concerned about his firm’s level of debt financing. The company uses short-term debt to finance its temporary working capital needs, but it does not use any permanent (long-term) debt. Other solar technology companies have debt, and Mr. Lyons wonders why they use debt and what its effects are on stock prices. To gain some insights into the matter, he poses the following questions to you, his recently hired assistant:

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Who were Modigliani and Miller (MM), and what assumptions are embedded in the MM and Miller models? Answer: Modigliani and Miller (MM) published their first paper on capital structure (which assumed zero taxes) in 1958, and they added corporate taxes in their 1963 paper. Modigliani won the Nobel Prize in Economics in part because of this work, and most subsequent work on capital structure theory stems from MM. Here are their assumptions:     



Firms’ business risk can be measured by σEBIT, and firms with the same degree of risk can be grouped into homogeneous business risk classes. All investors have identical (homogeneous) expectations about all firms’ future earnings. There are no transactions (brokerage) costs, either to individuals or to firms. All debt is riskless, and both individuals and corporations can borrow unlimited amounts of money at the same risk-free rate. All cash flows are perpetuities. This implies that firms and individuals issue perpetual debt, and also that firms pay out all earnings as dividends, hence have zero growth. Additionally, this implies that expected EBIT is constant over time, although realized EBIT may turn out to be higher or lower than was expected. In their first paper (1958), MM also assumed that there are no corporate or personal taxes.

These assumptions—all of them—were necessary in order for MM to use the arbitrage argument to develop and prove their equations. If the assumptions are unrealistic, then the results of the model are not guaranteed to hold in the real world. b.

Assume that firms U and L are in the same risk class and that both have EBIT = $560,000. Firm U uses no debt financing, and its cost of equity is rsU = 14%. Firm L has $1 million of debt outstanding at a cost of rd = 8%. There are no taxes. Assume that the MM assumptions hold.

Find v, s, rs, and WACC for Firms U and L. Answer: First, we find Vu and VL: VU =

EBIT $560, 000 = = $4,000,000. rsU 0.14 VL = VU = $4,000,000.

To find rsL, it is necessary first to find the market values of Firm L’s debt and equity. The value of its debt is stated to be $1,000,000. Therefore, we can find s as follows: D + SL = V L SL = VL − D = $4,000,00 − $1,000,000 = $3,000,000. Now we can find L’s cost of equity, rsL: rsL = rsU + (rsU – rd)(D/S) = 14% + (14% – 8%)($1,000,000/$3,000,000) = 14% + 2% = 16%. We know from Proposition I that the WACC must be WACC = r sU = 14.0% for all firms in this risk class, regardless of leverage, but this can be verified using the WACC formula:

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WACC = wdrd + wsrs = (D/V)rd + (S/V)rs = ($1,000,000/$4,000,000)(8.0%) + ($3,000,000/$4,000,000)(16%) = 2% + 12% = 14%.

Graph (a) the relationships between capital costs and leverage as measured by D/V and (b) the relationship between V and D.

Answer: Figure 1 plots capital costs against leverage as measured by the debt/value ratio. Note that, under the MM notax assumption, rd is a constant 8%, but rs increases with leverage. Further, the increase in rs is exactly sufficient to keep the WACC constant; the more debt the firm adds to its capital structure, the riskier the equity and thus the higher its cost. Figure 2 plots the firm’s value against leverage (debt). With zero taxes, MM argue that value is unaffected by leverage, and thus the plot is a horizontal line. (Note that we should not really extend the graphs to D/V = 100% or D = $4 million, because at this amount of leverage the debtholders become the firm’s owners, and thus a discontinuity exists.)

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Now assume that Firms L and U are both subject to a 25% corporate tax rate. Using the data given in part b, repeat the analysis called for in parts b(1) and b(2) under the MM model with taxes. Answer: With corporate taxes added, the MM propositions become: Proposition I: VL = VU + TD. Proposition II: rsL = rsU + (rsU – rd)(1 − T)(D/S). There are two very important differences between these propositions and the zero-tax propositions: (1) when corporate taxes are added, VL does not equal VU; rather, V L increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm. (2) r sL increases less rapidly when corporate taxes are considered. This is seen by noting that the Proposition II slope coefficient changes from (rsU – rd) to (rsU – rd)(1 – t), so at any positive T, the slope coefficient is smaller. Note also that with corporate taxes considered, VU changes to VU =

EBIT(1 T) $560,000(0.75) = = $3,000,000 versus $4,000,000. rsU 0.14

This represents a 25% decline in value, and it is logical, because the 25% tax rate takes away 25% of the after-tax income and hence 25% of the firm’s value. Looking at VL, we see that: VL = VU + TD = $3,000,000 + 0.25($1,000,000) VL = $3,000,000 + $250,000 = $3,250,000 versus $3,000,000 for V U. Thus, the use of $1,000,000 of debt financing increases firm value by T(D) = $250,000 over its leveragefree value. To determine the cost of equity, first it is necessary to determine the value of equity (SL): SL = VL – D = $3,250,000 − $1,000,000 = $2,250,000 Using the values for debt and equity, the cost of equity is: rsL = rsU + (rsU − rd)(1 − T)(D/S) = 14% + (14.0% − 8.0%)(0.75)($1,000,000/$2,250,000) = 14% + 2% = 16%. Firm L’s WACC is 11.8%: WACCL = (D/V)rd(1 − T) + (S/V)rs = ($1,000,000/$3,250,000)(8%)(0.75) + ($2,250,000/$3,250,000)(16%) = 1.8462% + 11.0769% = 12.9231%. The WACC is lower for the levered firm than for the unlevered firm when corporate taxes are considered.

The following figure plots the capital costs at different D/V ratios under the MM model with corporate taxes. Here, the WACC declines continuously as the firm uses more and more debt, whereas the WACC was constant in the without-tax model. This result occurs because of the tax deductibility of debt financing (interest payments), which impacts the graph in two ways: (1) the cost of debt is lowered by (1 − T), and (2) the cost of equity increases at a slower rate when corporate taxes are considered because of the (1 − T) term in Proposition II. The combined effect produces the downward-sloping WACC curve.

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The following figure shows that, when corporate taxes are considered, the firm’s value increases continuously as more and more debt is used.

Suppose that Firms U and L have the same input values as in part c except for debt of $980,000. Also, both firms have total net operating capital of $2,000,000 and both firms are expected to grow at a constant rate of 7%. (Assume that the EBIT in part c is expected at t = 1.) Use the compressed adjusted present value (APV) model to estimate the value of U and L. Also estimate the levered cost of equity and the weighted average cost of capital. Answer: If a firm is growing, the assumptions that MM made are violated. The extension to the MM model shows how growth affects the value of the debt tax shield and the cost of capital. The first difference in this situation is that the appropriate discount rate for the debt tax shield is the unlevered cost of equity, not the cost of debt. The second difference is that a growing debt tax shield is more valuable than a constant debt tax shield. First, calculate expected free cash flow: NOPAT = EBIT × (1 − T) = $560,000 × (1 – 0.25) = $420,000

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Investment in Net Operating Assets = g × Total net operating capital = 7%($2,000,000) = $140,000 Free Cash Flow = NOPAT – Investment in Net Operating Assets = $420,000 − $140,000 = $280,000. (Note that this is an expected value for the coming year since EBIT is an expected value for the coming year.) Next, note that WACC

= unlevered cost of equity if there is no debt. Therefore, WACC = rsU = 14%

The value of unlevered firm = Expected FCF/(WACC – g) VU = 280,000/(0.14 – 0.07) = $4,000,000 This is greater than the value of an unlevered firm in part C because the firm is growing. If there is $980,000 in debt then: Interest = rd (Debt) = 8%($980,000) = $78,400 The tax saving due to interest = T(Interest) = 0.25($78,400) = $19,600 The value of the growing tax savings = (Tax savings)/(rsU – g) = $19,600/(0.14 – 0.07) =$280,000. More directly the value of the (growing) debt tax shield is: Value of tax shield = rdTD/(rsU – g) = 0.08(0.25)(980,000)/(0.14 – 0.07) = $280,000 Therefore, the value of the firm is: VL = $4,000,000 + $280,000 = $4,280,000. The value of the equity is the value of the firm less the value of the Debt: S = $4,280,000 − $980,000 = $3,300,000. To calculate the new levered cost of equity: rsL = rsU + (rsU – rd)(D/S) = 14% + (14% − 8%)(980,000/3,300,000) = 15.782% And the new levered WACC: WACCL = (D/V)rd(1 − T) + (S/V)rs = (980,000/4,280,000)(8%)(1 − 0.25) + ($3,300,000/4,280,000)(0.15782) = 13.54%. Just like with MM with taxes, the cost of equity increases with D/V, and the WACC declines. But since rsL doesn’t have the (1 − T) factor in it for a growing firm, rsL is greater than MM would predict for a given D/V, and WACC is greater than MM would predict. e.

Suppose the expected free cash flow for Year 1 is $250,000 but it is expected to grow faster than 7% during the next 3 years: FCF2 = $290,000 and FCF3 = $320,000, after which it will grow at a constant rate of 7%. The expected interest expense at Year 1 is $128,000, but it is expected to grow over the next couple of years before the capital structure becomes constant: Interest expense at Year 2 will be $152,000, at Year 3 it will be $192,000, and it will grow at 7% thereafter. What is the estimated

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horizon unlevered value of operations (i.e., the value at Year 3 immediately after the FCF at Year 3)? What is the current unlevered value of operations? What is the horizon value of the tax shield at Year 3? What is the current value of the tax shield? What is the current total value? The tax rate and unlevered cost of equity remain at 25% and 14%, respectively. Answer: The unlevered horizon value of operations can be found by applying the constant growth formula: HVU,3 = [FCF3(1 + gL)]/(rsU – gL) = [$320(1.07)]/(0.14 – 0.07) = $4,891.43. The unlevered value of operations is the present value of the free cash flows and the horizon value. In Excel, the formula is: = NPV(Rate,value1,value2….) = NPV(0.14,250,290,320 + 4891.43) = $3,960.01. The unlevered value of operations, Vop,U, is $3,960.01. The tax shields are found by multiplying the interest expenses by the tax rate: Interest expense Tax rate Tax savings

$120.00

$152.00

$192.00

×25%

$32

$38

$48

The horizon value of the tax shield can be found by applying the constant growth formula: HVTS,3 = [TS3(1 + gL)]/(rsU – gL) = [$48(1.07)]/(0.14 – 0.07) = $733.71. The unlevered value of operations is the present value of the free cash flows and the horizon value. In Excel, the formula is: VU = NPV(Rate,value1,value2….) = NPV(0.14,32,38,48 + 733.71) = $584.94. The value of operations is the sum of the unlevered value of operations and the value of the tax shield: Vop = VU + VTS = $3,960.01 + $584.94 = $4,544.95. f.

Suppose Solar Technologies has no debt, its beta is 1.2, the risk-free rate is 4%, and the market risk premium is 6%. The tax rate is 25%. Lyons is considering restructuring to increase debt to a weight of 40%. If he does so, the debt he must issue will have an 8% rate of return. Lyons wants to know how this restructuring will impact Solar Tech’s required return on equity. He knows that there are three different models for this: Modigliani Miller with corporate taxes, Hamada, and the APV model. What do these three models say about Solar Tech’s required return on equity after the restructuring? Why are they different and which one should Lyons use? Answer: Since the company has no debt, its current beta is also its unlevered beta, and the CAPM estimate of the cost of equity is also the unlevered cost of equity, rsU. rsU = 4% + 1.2(6%) = 11.2% MM with taxes: rsL = rsU + (rsU – rd)(1 – T)(wd/ws) = 11.2% + (11.2% – 8%)(1 – 0.25)(0.40/0.60) = 12.8%

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Hamada: b = bU[1 + (1 – T)(wd/ws) = 1.2(1 + (1 – 0.25)(0.40/0.60) = 1.80 rsL = rf + b(RPM) = 4% + 1.80(6%) = 14.8% APV: rsL = rsU + (rsU – rd)(wd/ws) = 11.2% + (11.2% – 8%)(0.40/0.60) = 13.33% g.

How would your answer to part f be different if the information is the same but Solar Tech currently has 10% debt that has a rate of return of 7%? Answer: Since the company currently has debt, its beta is not its unlevered beta and its required return on equity is not its unlevered required return. We must first unlever the return using the assumed model, the existing rate on debt, and the existing capital structure, and then re-lever using the new capital structure and new rate on debt. Note that since each model unlevers and re-levers differently, they will give different answers for the unlevered cost of equity and for the new levered cost of equity. This is why it is important to choose a model whose assumptions are consistent with the company’s details! MM with corporate taxes: The current levered cost of equity is: rsL = 4% + 1.2(6%) = 11.20%. The unlevered cost of equity is: rsU = [rsLws + rd(1 – T)wd]/[ws + (1 – T)wd] = [11.2%(90%) + 7%(1 – 0.25)10%]/[90% + (1 – 0.25)10%] = 10.88% Re-lever: rsL = rsU + (rsU – rd)(1 – T)(wd/ws) = 10.88% + (10.88% – 8%)(1 – 0.25)(0.40/0.60) = 12.32% Hamada: Unlever: bU = b/(1 + (1 – T)(wd/ws)) = 1.2/(1 + (1 – 0.25)(0.10/0.90) = 1.1077 rsU = 4% + 1.1077(6%) = 10.65% Re-lever: b = bU[1 + (1 – T)(wd/ws) = 1.1077(1 + (1 – 0.25)(0.40/0.60)) = 1.6615 rsL = 4% + 1.6615(6%) = 13.97%

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APV: Unlever: rsU = rsws + rdwd rs = from above, 11.20% rsU = 11.20%(0.90) + 7%(0.10) = 10.78% Re-lever: rsL = rsU + (rsU – rd)(wd/ws) = 10.78% + (10.78% – 8%)(0.40.0.60) = 12.63%

WEB EXTENSION 21A (21A-1) Valuation with Change in Capital Structure Sandburg Corporation estimates that it will generate free cash flows of $2.5 million, $2.9 million, $3.4 million, and $3.57 million at Years 1 through 4, respectively, after which the free cash flows will grow at a constant 5% rate. Sandburg’s beta is 1.1, the risk-free rate is 4.4%, and the market risk premium is 6%. Sandburg currently has a target capital structure of 10% debt and 90% equity. It has debt of $13 million at an 8% interest rate. Sandburg has 1.5 million shares outstanding. The combined federalplus-state corporate tax rate is 25%. Sandburg is considering changing its capital structure to be 30% financed with debt. Sandburg will not immediately increase the percentage debt financing but will gradually increase it until the capital structure at Year 4 is financed by 30% debt. The higher capital structure will make Sandburg riskier, so the average interest rate on all its debt will increase to 8.5%. Assume that debt will be added at the end of the year, so interest expenses will be based on the previous year-end debt. Sandburg will have Year1 debt of $25 million and Year-2 debt of $38 million. a. What is Sandburg’s cost of equity before the change in capital structure? What is its WACC? Its Year-4 horizon value? Its value of operations? What is its debt at Year 0 based on its pre-change capital structure? What is its pre-change value of equity? Its pre-change stock price? b. What is Sandburg’s unlevered cost of equity? (Hint: Calculate this using the pre-change information.) After Sandburg completes its change in capital structure, what are its levered cost of equity and WACC at Year 4? Its value of operations at Year 4? c. What is Sandburg’s debt at Year 4? At Year 3? (Hint: See Section 17A-2, Step 3.) d. What are the annual interest expenses and tax shields? e. What are the annual sums of the free cash flows and interest tax shields? Using the compressed APV, what is the Year 0 value of levered operations? What is the Year-0 value of equity? The stock price? Solution: Current b = 1.4; rRF = 5%; RPM = 6%; current wd = 30%; T = 25%; rd = 8%, FCF1 = $2.5 million, FCF2 = $2.9 million, FCF3 = $3.4 million, and FCF4 = 3.57 million; FCF4 grows at gL = 5% forever. Interest payments at Years 1 through 3 are $1.5 million each year; Year 3 debt = $30.6 million; the Year 4 interest payment will grow at the long-term rate of 5%. Purchaser will assume $10.19 million in old debt. The first step is to determine the Year 4 tax payment: a.

Determine the Year 4 interest payment and tax shield:

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Year 4 interest payment

= (Year 3 debt level)(interest rate on debt) = $30.6(0.085) = $2.601 million.

TS4 = (Year 4 interest)(tax rate) = ($2.601 million)(0.40) = $1.04 million. r sU = 11.78% as calculated in Problem 21-2. b.

Determine the unlevered value of operations and the value of the tax shield tax shield: The unlevered horizon value and the unlevered value of operations is the same as in Problem 2: = FCF4(1 + g)/(rsU – g) = 3.57(1.05)/(0.1178 – 0.05) = $55.29 million

Unlevered horizon value

Unlevered Vops

2.5 2.9 3.4 3.57  55.29    2 3 1.1178 (1.1178) (1.1178) (1.1178)4

= $44.69 The tax shield horizon value is = HVTS4 = TS5/(rsU – g) = TS4(1 + g)/(rsU – g) = 1.04(1.05)/(0.1178 – 0.05) = $16.11 million Value of tax shields

0.600 0.600 0.600 1.04  16.11    2 3 1.1178 (1.1178) (1.1178) (1.1178)4

= $12.43 million c.

Determine the intrinsic value per share: The new value of operations is: Value of operations

= unlevered Vops + value of tax shields = 44.69 + 12.43 = 57.12 million

= Vops – Debt = 57.12 million – 10.82 million = $46.30 million or $46.30 per share since there are 1 million shares outstanding. Equity value to Hastings

21A-2

Valuation With Change in Capital Structure Langston Lyrics Corporation is a publicly traded company; its beta is 1.30, the risk-free rate is 6%, and the market risk premium is 5.5%. Langston’s tax rate is 25%. It has a 15% target debt ratio (i.e., 15% of its financing comes from debt) at a 9% cost of debt. Langston is considering increasing its capital structure to 35% debt financing. Because the additional leverage makes Langston riskier, the rate on all debt will be 9.5%. Langston will generate the free cash flows and will have the debt (all in millions of dollars) shown here. Answer the following questions.: Year

FCF Debt a.

$5.00

$1.30

$1.50

$1.75

$2.00

$2.12

$8.00

$11.00

$13.00

What is Langston’s pre-change cost of equity? Its unlevered cost of equity?

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b. c. d. e.

After the new capital structure has been fully implemented by Year 5, what is Langston’s Year-5 cost of equity? Its Year-5 WACC? After the new capital structure has been implemented, what is Langston’s value of operations at Year 5? Its debt at Year 5? Its debt at Year 4? What are Langston’s annual tax shields based on the new capital structure? What is Langston’s unlevered value of operations at Year 5? At Year 0? What is Langston’s tax shield value at Year 5? At Year 0? What is Langston’s total value at Year 0?

Solution: a. The appropriate discount rate reflects the risk of the cash flows. Thus, it is Langston’s unlevered cost of equity that should be used to discount the free cash flows and tax shields in Years 1–5 and at the horizon. The horizon value should be calculated using Langston’s tax shields at the stable target capital structure, which are provided for Year 5. Since Langston’s beta = 1.3, its current cost of equity, rsL = 6% + 1.3(5.5%) = 13.15%. Since its percentage of debt is 25% and the rate on its debt is 9%, its unlevered cost of equity is

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rsU = wdrd + wsrsL = 0.15(9%) + 0.85 (13.15%) = 12.53% b.

At the horizon when the new capital structure has been implemented: rsL = rsU + (rsU – rd)(D/S) = 12.53% + (12.53% – 9.5%)(0.35/0.65) = 14.16% WACC = wdrd(1 – T) + wsrs = 0.35(9.5%)(1 – 0.25) + 0.65(14.16%) = 11.70%

At the horizon when the new capital structure has been implemented: HV5 = FCF5(1 + g)/(WACC – g) = 2.12(1.06)/(0.1170 – 0.06) = $39.425 million ≈ $39.451 million if there is no rounding in intermediate steps D5 = HV5(wd) = $39.451(0.35) = $13.808 million. D4 = D5/(1 + g) = $13.808/(1.06) = $13.026 million.

Interest5 = Debt4 (9.5%) = $13.026 (9.5%) = 1.2375 TS5 = Interest5(Tax rate) = 1.2375(0.25%) = 0.3094 (You must use the post-merger tax rate) In the other years, the tax shield is equal to the interest expense multiplied by the tax rate: Year Debt Interest Tax shield

0 $4.00

1 $6.00 $0.3800 $0.0950

2 $9.00 $0.5700 $0.1425

3 $11.00 $0.8550 $0.2138

4 $13.0261 $1.0450 $0.2613

5 $13.8077 $1.2375 $0.3094

The unlevered horizon value is: HVUL5 = FCF5(1 + g)/(rsU – g) = 2.12(1.06)/(0.1253 – 0.06) = $34.413 million ≈ $34.427 if there is no rounding in intermediate steps The unlevered value of operations, assuming no rounding in intermediate steps, is:

1.3 1.5 1.75 2.0 2.12  34.427 = $25.071 million     1.1253 (1.1253)2 (1.1253)3 (1.1253)4 (1.1253)5

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The tax shield horizon value is: HVTS5 = TS6/(rsU – g) = TS5(1 + g)/(rsU – g) = 0.3094(1.06)/(0.1253 – 0.06) = $5.0224 million ≈ $5.024 million if there is no rounding in intermediate steps The value of the tax shields, assuming no rounding in intermediate steps, is:

0.0950 0.1425 0.2138 0.2613 0.3094  5.024 = $3.466 million     1.1253 (1.1253)2 (1.1253)3 (1.1253)4 (1.1253)5 The value of operations is the sum of the interest tax shields and the unlevered value = 3.466 + 25.071 = $28.537 million. Note that the total horizon value based on the CAPV method is the sum of the horizon values for the tax shield and the free cash flows: HV based on CAPV

= HV FCF + HV Tax shield = $34.427 + $5.024 = $39.451 million

This is the same horizon value we found in part c.

Solution and Answer Guide Brigham/Ehrhardt, Financial Management: Theory and Practice; Chapter 23: Enterprise Risk Management

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 458 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 460 Easy Problems 1–2 ................................................................................................................................ 460 Intermediate Problems 3–4 ................................................................................................................... 461 Challenging Problem 5 ......................................................................................................................... 462 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 463 MINI CASE ............................................................................................................................................. 464

ANSWERS TO END-OF-CHAPTER QUESTIONS 23-1 Define each of the following terms: a. Derivatives b. Enterprise risk management c. Financial futures; forward contract d. Hedging; natural hedge; long hedge; short hedge; perfect hedge; symmetric hedge; asymmetric hedge

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e. f.

Swap; structured note Commodity futures

Answer: a. A derivative is an indirect claim security that derives its value, in whole or in part, by the market price (or interest rate) of some other security (or market). Derivatives include options, interest rate futures, exchange rate futures, commodity futures, and swaps. b.

According to COSO, enterprise risk management ―is a process, effected by an entity’s board of directors, management and other personnel, applied in strategy setting and across the enterprise, designed to identify potential events that may affect the entity, and manage risk to be within its risk appetite, to provide reasonable assurance regarding the achievement of entity objectives.‖

Financial futures provide for the purchase or sale of a financial asset at some time in the future, but at a price established today. Financial futures exist for Treasury bills, Treasury notes and bonds, CDs, Eurodollar deposits, foreign currencies, and stock indexes. While physical delivery of the underlying asset is virtually never taken, under forward contracts goods are actually delivered.

A hedge is a transaction that lowers a firm’s risk of damage due to fluctuating stock prices, interest rates, and exchange rates. A natural hedge is a transaction between two counterparties where both parties’ risks are reduced. The two basic types of hedges are long hedges, in which futures contracts are bought in anticipation of (or to guard against) price increases, and short hedges, in which futures contracts are sold to guard against price declines. A perfect hedge occurs when the gain or loss on the hedged transaction exactly offsets the loss or gain on the unhedged position. A symmetric hedge is one that protects against both upward and downward price changes. Futures contracts are frequently used for symmetric hedges. An asymmetric hedge protects against one direction price change more than the other. This type of hedge looks like insurance, hedging against a loss but not compromising a gain. Options are frequently used for asymmetric hedges.

A swap is an exchange of cash payment obligations, which usually occurs because the parties involved prefer someone else’s payment pattern or type. A structured note is a debt obligation derived from another debt obligation, and permits a partitioning of risks to give investors what they want.

Commodity futures are futures contracts that involve the sale or purchase of various commodities, including grains, oilseeds, livestock, meats, fiber, metals, and wood.

23-2 Give two reasons why stockholders might be indifferent between owning the stock of a firm with volatile cash flows and that of a firm with stable cash flows. Answer: If the elimination of volatile cash flows through risk management techniques does not significantly change a firm’s expected future cash flows and WACC, investors will be indifferent to holding a company with volatile cash flows versus a company with stable cash flows. Note that investors can reduce volatility themselves: (1) through portfolio diversification, or (2) through their own use of derivatives. 23-3 List six reasons why risk management might increase the value of a firm.

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Answer: The six reasons why risk management might increase the value of a firm is that it allows corporations to (1) increase their use of debt; (2) maintain their capital budget over time; (3) avoid costs associated with financial distress; (4) utilize their comparative advantages in hedging relative to the hedging ability of individual investors; (5) reduce both the risks and costs of borrowing by using swaps; and (6) reduce the higher taxes that result from fluctuating earnings. 23-4 Discuss some of the techniques available to reduce risk exposures. Answer: There are several ways to reduce a firm’s risk exposure. First, a firm can transfer its risk to an insurance company, which requires periodic premium payments established by the insurance company based on its perception of the firm’s risk exposure. Second, the firm can transfer risk-producing functions to a third party. For example, contracting with a trucking company can in effect, pass the firm’s risks from transportation to the trucking company. Third, the firm can purchase derivatives contracts to reduce input and financial risks. Fourth, the firm can take specific actions to reduce the probability of occurrence of adverse events. This includes replacing old electrical wiring or using fire-resistant materials in areas with the greatest fire potential. Fifth, the firm can take actions to reduce the magnitude of the loss associated with adverse events, such as installing an automatic sprinkler system to suppress potential fires. Finally, the firm can totally avoid the activity that gives rise to the risk. 23-5 Explain how the futures markets can be used to reduce interest rate risk and input price risk. Answer: The futures market can be used to guard against interest rate and input price risk through the use of hedging. If the firm were concerned that interest rates will rise, it would use a short hedge, or sell financial futures contracts. If interest rates do rise, losses on the issue due to the higher interest rates would be offset by gains realized from repurchase of the futures at maturity—because of the increase in interest rates, the value of the futures would be less than at the time of issue. If the firm were concerned that the price of an input will rise, it would use a long hedge, or buy commodity futures. At the future’s maturity date, the firm will be able to purchase the input at the original contract price, even if market prices have risen in the interim. 23-6 How can swaps be used to reduce the risks associated with debt contracts? Answer: Swaps allow firms to reduce their financial risk by exchanging their debt for another party’s debt, usually because the parties prefer the other’s debt contract terms. There are several ways in which swaps reduce risk. Currency swaps, where firms exchange debt obligations denominated in different currencies, can eliminate the exchange rate risk created when currency must first be converted to another currency before making scheduled debt payments. Interest rate swaps, where counterparties trade fixed-rate debt for floating rate debt, can reduce risk for both parties based on their individual views concerning future interest rates.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–2 23-1 Swaps Zhao Automotive issues fixed-rate debt at a rate of 7.00%. Zhao agrees to an interest rate swap in which it pays LIBOR to Lee

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Financial and Lee pays 6.8% to Zhao. What is Zhao’s resulting net payment? Solution: If Zhao issues fixed rate debt and then swaps, its net cash flows will be: −7% + 6.8% − LIBOR = −(LIBOR + 0.2%). 23-2 Futures A Treasury bond futures contract has a settlement price of 89'08. What is the implied annual yield? Solution: The price of the hypothetical bond is $1,000(89 + 8.0/32)/100 = $892.50. Using a financial calculator, we can solve for rd as follows: N = 40; PV = −892.50; PMT = 30; FV = 1000; solve for I/YR = 3.504. The annual value of r d is 3.504%  2  7.01%.

INTERMEDIATE PROBLEMS 3–4 23-3 Futures What is the implied interest rate on a Treasury bond ($100,000) futures contract that settled at 100'160? If interest rates increased by 1%, what would be the contract’s new value? Solution: Futures contract settled at 100 16.0/32% of $100,000 contract value, so PV = 1.005  $1,000 = $1,005  100 bonds = $100,500. Using a financial calculator, we can solve for rd as follows: N = 40; PV = −1005; PMT = 30; FV = 1000; solve for I/Y = 2.9784% rd = 2.9784%  2 = 5.9569%  5.96%. If interest rates increase to 6.9569%, then we would solve for PV as follows: N = 40; I = 6.9569/2 = 3.47845; PMT = 30; FV = 1000; solve for PV = $897.4842  100 = $89,748.42. If there is no rounding in intermediate steps, the contract’s value is $89,748.54. Thus, the contract’s value has decreased from $100,500 to $89,748.42. 23-4 Swaps Carter Enterprises can issue floating-rate debt at LIBOR + 2% or fixed-rate debt at 10%. Brence Manufacturing can issue floating-rate debt at LIBOR + 3.1% or fixed-rate debt at 11%. Suppose Carter issues floating-rate debt and Brence issues fixed-rate debt. They are considering a swap in which Carter makes a fixed-rate payment of 7.95% to Brence and Brence makes a payment of LIBOR to Carter. What are the net payments of Carter and Brence if they engage in the swap? Would Carter be better off if it issued fixed-rate debt or if it issued floating-rate debt and engaged in the swap? Would Brence be better off if it issued floating-rate debt or if it issued fixed-rate debt and engaged in the swap? Explain your answers. Solution: If Carter issues floating rate debt and then swaps, its net cash flows will be: −(LIBOR + 2%) – 7.95% + LIBOR = −9.95%. This is less than the 10% rate at which it could directly issue fixed rate debt, so the swap is good for Carter. If Brence issues fixed rate debt and then swaps, its net cash flows will be: −11% + 7.95% − LIBOR = −(LIBOR + 3.05%). This is less than the rate at which it could directly issue floating rate debt (LIBOR + 3.05%), so the swap is good for Brence.

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CHALLENGING PROBLEM 5 23-5 Hedging The Zinn Company plans to issue $10,000,000 of 20-year bonds in June to help finance a new research and development laboratory. The bonds will pay interest semiannually. It is now November, and the current cost of debt to the high-risk biotech company is 11%. However, the firm’s financial manager is concerned that interest rates will climb even higher in coming months. The following data are available: Futures Prices: Treasury Bonds—$100,000; Pts. 32nds of 100% Delivery Month (1)

Open (2)

High (3)

Low (4)

Settle (5)

Change (6)

Open Interest (7)

Dec

94'280

95'130

94'220

95'050

+0'070

591,944

Mar

96'030

95'130

95'250

+0'080

120,353

J une a.

9 5'030

9 5'170

9 5'030

9 5'170

+ 0'080

1 3,597

What is the implied yield on the June futures contract? How many futures contracts will be needed to hedge potential losses in bond proceeds (based on current market conditions) due to waiting (round up to the nearest integer)? What is the total value of the hedge position? Assume that interest rates in general increase by 200 basis points. Suppose the bond’s terms don’t change and that the coupon rate is still 11%. How much would Zinn receive from the bond issue given the new market rates? How much less is this than the original target for proceeds? Assume that Zinn had entered the hedge found in part a. What is the new price of the hedge position? What is the gain on the hedge? What is the net effect of the loss of proceeds and the gain on the hedge?

Solution: a. The percent price of the underlying bond is: 95/100 + (17/32)/(100)) = 0.9553125. Therefore, the price on the underlying bond is $1,000(0.9553125) = $955.3125 The inputs to calculate the implied yield are: N = 40, PV = −955.3125, PMT = 30, and FV = 1000. Solving shows that the implied yield semiannual yield 3.1996%. The annual yield is 3.1996%(2) = 6.3992%. Because the underlying bond has a price of $955.3125 and there are 100 bonds in a contract, the total value of a contract is $95,531.25. This means the firm must sell 10,000,000/$95,531.25 = 104.678 ≈ 105 contracts to cover the planned $10,000,000 June bond issue. The total value of the hedge position is 105($95,531.25) = $10,030,781.25. Should interest rates rise by June, Zinn Company will be able to repurchase the futures contracts at a lower cost, which will help offset their loss from financing at the higher interest rate. Thus, the firm has hedged against rising interest rates. b.

The firm would now pay 13% on the bonds. With an 11% coupon rate, the bond issue proceeds are found by inputting N = 40; I = 13/2 = 6.5, PMT = −0.11/2  10,000,000 = −550000; FV = −10000000 and solving for PV = $8,585,447.31. The firm would lose proceeds of $10,000,000 − $8,585,447.31 = $1,414,552.69 on the bond issue due to the change in market rates.

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However, the firm will make money on its futures contracts. The implied semiannual market yield before the change was 3.1996. If market interest rates increased by 200 basis points, that would add 2% to the annual market rate and 1% to the semiannual market rate. The implied semiannual yield on the underlying bond would be 1% + 3.1996 = 4.1996. At this new rate, the value of each underlying bond in the futures contract will drop to $769.45817, found by inputting N = 40; I = 4.1996 ; PMT = −30; FV = −1000; and solving for PV = $769.45817. The value of all of the futures contracts in the hedge position will be $76,945.817(105) = $8,079,310.785. However, the value of the short futures position began at $10,030,781.25. Since Zinn Company sold the futures contracts for $10,030,781.25, and will, in effect, buy them back at $8,079,310.785, the firm would make a $10,030,781.25 − $8,079,310.785 = $1,951,470.465 profit on the transaction ignoring transaction costs. Thus, the firm gained $1,951,470.465 on its futures position, but lost $1,414,552.69 on its underlying bond issue. On net, it gained $1,951,470.465 − $1,414,552.69 = $536,917.775. In a perfect hedge, the gains on futures contracts exactly offset losses due to rising interest rates. For a perfect hedge to exist, the underlying asset must be identical to the futures asset. Using the Zinn Company example, a futures contract must have existed on Zinn’s own debt (it existed on Treasury bonds) for the company to have an opportunity to create a perfect hedge. In reality, it is virtually impossible to create a perfect hedge, since in most cases the underlying asset is not identical to the futures asset.

SOLUTION TO SPREADSHEET PROBLEM 23-6 Build a Model: Hedging Start with the partial model in the file Ch23 P06 Build a Model.xlsx on the textbook’s website. Use the following information and data. F. Pierce Products Inc. is financing a new manufacturing facility with the issue in March of $20,000,000 of 20-year bonds with semiannual interest payments. It is now October, and if Pierce were to issue the bonds now, the yield would be 10% because of Pierce’s high risk. Pierce’s CFO is concerned that interest rates will climb even higher in coming months and is considering hedging the bond issue. The following data are available: Futures Prices: Treasury Bonds—$100,000; Pts. 32nds of 100% Delivery Month (1)

Open (2)

High (3)

Low (4)

Settle (5)

Change (6)

Open Interest (7)

Dec

93'280

94'130

93'220

94'050

+0'060

723,946

Mar

95'030

94'130

94'250

+0'070

97,254

Create a hedge with the futures contract for Pierce’s planned March debt offering of $20 million using the March Treasury Bond futures contract. What is the implied yield on the bond underlying the futures contract? Suppose that interest rates fall by 300 basis points. What are the dollar savings from issuing the debt at the new interest rate? What is the dollar change in value of the futures position? What is the total dollar value change of the hedged position? Create a graph showing the effectiveness of the hedge if the change in interest rates, in basis points, is −300, −200, −100, 0, 100, 200, or 300. Show the dollar cost (or savings) from issuing the debt at

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

the new interest rates, the dollar change in value of the futures position, and the total dollar value change. Solution: The detailed solution for the spreadsheet problem, Ch23 P06 Build a Model Solution.xls, is available on the textbook’s website.

MINI CASE Assume that you have just been hired as a financial analyst by Tennessee Sunshine Inc. (TS), a mid-sized Tennessee company that specializes in creating exotic sauces from imported fruits and vegetables. The firm’s CEO, Bill Stooksbury, recently returned from an industry corporate executive conference in San Francisco, and one of the sessions he attended was on the pressing need for companies to institute corporate risk management programs. Because no one at Tennessee Sunshine is familiar with the basics of enterprise risk management, Stooksbury has asked you to prepare a brief report that the firm’s executives could use to gain at least a cursory understanding of the topics. To begin, you gathered some outside materials on derivatives and risk management and used these materials to draft a list of pertinent questions that need to be answered. In fact, one possible approach to the paper is to use a question-and-answer format. Now that the questions have been drafted, you have to develop the answers. a.

Why might stockholders be indifferent to whether or not a firm reduces the volatility of its cash flows? Answer: If volatility in cash flows is not caused by systematic risk, then stockholders can eliminate the risk of volatile cash flows by diversifying their portfolios. Also, if a company decided to hedge away the risk associated with the volatility of its cash flows, the company would have to pass on the costs of hedging to the investors. Sophisticated investors can hedge risks themselves and thus they are indifferent as to who actually does the hedging.

What are six reasons risk management might increase the value of a corporation? Answer: There are no studies proving that risk management either does or does not add value. However, there are six reasons why risk management might increase the value of a firm. Risk management allows corporations to (1) increase their use of debt; (2) maintain their capital budget over time; (3) avoid costs associated with financial distress; (4) utilize their comparative advantages in hedging relative to the hedging ability of individual investors; (5) reduce both the risks and costs of borrowing by using swaps; and (6) reduce the higher taxes that result from fluctuating earnings.

What is COSO? How does COSO define enterprise risk management? Answer: The Committee of Sponsoring Organizations of the Treadway Commission is a group of private accounting firms that put together a framework for internal control systems to prevent accounting fraud. They extended this framework to include enterprise risk management (ERM) and define ERM as ―a process, effected by an entity’s board of directors, management and other personnel, applied in strategy setting and across the enterprise, designed to identify potential events that may affect the entity, and manage risk to be within its risk appetite, to provide reasonable assurance regarding the achievement of entity objectives.‖ (We added italics for emphasis.) . Here are some key points. ERM is an ongoing process, not something a company does once and then is finished. ERM requires involvement from the board, to executives, to managers, and to workers. It is broad

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and includes strategic choices as well as operating tactics. It is applied at all levels in the organization, from the corporate level all the way to the individual operating units. Its steps include risk identification risk, risk assessment, and risk responses. The company must explicitly articulate its tolerance for risk, which is called its risk appetite. There must be a reliable and timely reporting and monitoring system. d.

Describe the eight components of the COSO ERM framework. Answer: The COSO ERM framework has eight components. 1. 2. 3. 4. 5.

6. 7. 8. e.

Internal environment. This includes the company’s mission, culture, and risk appetite. Objective setting. Explicit objectives must be set at all levels in organization. Risky event identification. An event is something that affects the achievement of an objective. Risky event assessment. How likely is the event and how bad could it be? Risky event responses. These include prevention and should correspond with the previously identified risk appetite. Responses should consider the portfolio of risky events and not just each event in isolation. Control activities. These are ways to ensure that people apply the previously identified responses. Control activities include handbooks, guidelines, policies, etc. Information & Communication. A successful ERM system requires reliable and timely information regarding risk events and responses. Monitoring.

Describe some of the risk events within the following major categories of risk: (1) strategy and reputation, (2) control and compliance, (3) hazards, (4) human resources, (5) operations, (6) technology, and (7) financial management. Answer: 1. Strategy and reputation. A company’s strategic choices simultaneously influence and respond to its competitors’ actions; corporate social responsibilities; the public’s perception of its activities; and its reputation among suppliers, peers, and customers. 2. Control and compliance. This category includes risk events related to regulatory requirements, litigation risks, intellectual property rights, reporting accuracy, and internal control systems 3. Hazards. These include fires, floods, riots, acts of terrorism, and other natural or humanmade disasters. 4. Human resources. These addresses risk events related to employees, including recruiting, succession planning, employee health, and employee safety. 5. Operations. Risk events include supply chain disruptions, equipment failures, product recalls, and changes in customer demand. 6. Technology. These include risk events related to innovations, technological failures, and IT reliability and security 7. Financial management. This category includes risk events related to (1) foreign exchange risk, (2) commodity price risk, (3) interest rate risk, (4) project selection risk (including major capital expenditures, mergers, and acquisitions), (5) liquidity risk (the risk of not having access to financing when needed), (6) customer credit risk, and (7) portfolio risk (the risk that a portfolio of financial assets will decrease in value).

What are some actions that companies can take to minimize or reduce risk exposures? Answer: There are several actions that companies can take to minimize or reduce their risk exposure. First, companies can transfer risk to an insurance company by paying periodic premiums. Second, companies can transfer functions that produce risk to third parties, such as eliminating risks associated with transportation by contracting with a trucking company. Third, purchase derivatives contracts to reduce input and financial risk. Fourth, companies can take actions to reduce the probability of occurrence of an adverse event, such

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

as replacing old wiring to reduce the possibility of fire. Fifth, actions can be taken to reduce the magnitude of the loss associated with adverse events, such as installing automatic sprinkler systems. Finally, companies can simply avoid the activities that give rise to risk. g.

What are forward contracts? How can they be used to manage foreign exchange risk? Answer: A forward contract is an agreement between two parties. One party agrees to sell a specified item at a specified price on a specified date, and the other party agrees to purchase the item under the same terms. If a company knows it is going to have a future cash flow denominated in a different currency, it can use a forward contract to lock in a price. For example, suppose a U.S. retailer is going to import ¥1 million of electronic games from Japan and the current exchange rate is 70 yen per dollar. The company might be able to take a position in a forward contract to buy one million yen at 70 yen per dollar. This locks in the dollar cost of the purchase. Banks often act as the counterparty in forward contracts.

Describe how commodity futures markets can be used to reduce input price risk. Answer: Futures markets involve contracts that call for the purchase or sale of a financial (or real) asset at some future date, but at a price which is fixed today. Futures are similar to forwards, except futures require daily marking-to-market, futures cover many more types of assets (agriculture, livestock, metals, indexes, currencies, interest rates, energy), and futures are standardized contracts that trade on exchanges, such as CBO. Thus, these markets provide the opportunity to reduce financial risk exposure. Essentially, the purchase of a commodity futures contract will allow a firm to make a future purchase of the input material at today's price, even if the market price on the good has risen substantially in the interim.

It is January, and Tennessee Sunshine is considering issuing $5 million in bonds in June to raise capital for an expansion. Currently, the firm can issue 20-year bonds with a 7% coupon (with interest paid semiannually), but interest rates are on the rise and Stooksbury is concerned that longterm interest rates might rise by as much as 1% before June. You looked online and found that June T-bond futures are trading at 111'250. What are the risks of not hedging, and how might TS hedge this exposure? In your analysis, consider what would happen if interest rates all increased by 1%. Answer: If TS waits until June to issue its bonds, and if interest rates rise, then TS will have to pay a higher interest rate on its debt. How much does that cost TS? One way to calculate the cost is to see how much the 20-year 7% semiannual bonds that it intended to issue would be worth at the new discount rate of 8%. Input N = 40, I/YR = 8/2, PMT = −5,000,000(7%/2) = 175,000, FV = −5,000,000 and solve for PV = $4,505,181. Since they were going to be worth $5 million if they were issued immediately, then this represents a loss (i.e., a cost of not hedgind) equal to: $5,000,000 − $4,505,181 = $494,819. The percentage cost of not hedging is: $494,819/$5,000,000 = 0.0990 = 9.90% TS can hedge this risk by selling T-bond futures contracts. The T-bond futures contracts are trading at 111 + 25.0/32 percent of par, which is $111,781 for a $100,000 contract value.This is $1,117.81 per bond.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

To hedge $5,000,000, TS need to sell (i.e., take a short position): $5,000,000/($111,781 per contract) = 44.7 futures contracts. Because trading is for whole contracts, TS will need 45 (which is 44.7 rounded to the nearest integer) Tbond futures contracts to hedge the bond position. T-bond futures contracts prices are based on a hypothetical bond with 20 years to maturity, a 6% annual coupon rate, and semiannual payments. Given an implicit bond price of $1,117.81 for each $1,000 face value bond, the implied yield can be caluclated with a financial calculator using these inputs: N = 40; PMT = 30; FV = 1000; PV = −1117.81. The resulting value of I/Y is 2.5284%. This is a semi-annual rate, which is an annual rate of about: 2(2.5284%) ≈ 5.057%. If interest rates increase by 1%, then the new yield on this underlying bond will be: 5.057% + 1% = 6.057%. The 6-month rate is: 6.057%/2 = 3.0285%. The corresponding price at this yield is found by inputting N = 40, I/YR = 3.0285, PMT = −30, FV = −1000 and solving for PV = 993.44. The value of each futures contract at this higher interest rate will be: ($993.44 per bond)(100 bonds) = $99,344. This represents a decrease for each contract of: $111,781 – $99,344 = $12,437. Because TS took a short position in futures contracts, the decrease of $12,437 of the futures contract is a $12,437 profit to TS. The total profit from the futures contracts is: 45($12,437) = $559,665. TS will lose $494,819 on the bonds it issues but gain $559,665 on its futures contracts. The net hedging gain is $559,665 − $494,819 = $64,846. In percentage terms, the gain from the hedge compared to the value $5,000,000 is: $64,846/$5,000,000 = 1.29%. Thus, TS will end up just a little bit better off if interest rates increase by 1%. Note that if interest rates were to decrease instead, then TS would gain on the prices of the bonds it issues but would lose on its futures contracts. See the Excel Mini Case file for the complete set of calcvulations j.

What is a swap? Suppose two firms have different credit ratings. Firm Hi can borrow fixed at 11% and floating at LIBOR + 1%. Firm Lo can borrow fixed at 11.4% and floating at LIBOR + 1.5%. Describe a floating versus fixed interest rate swap between firms Hi and Lo in which Lo also makes a ―side payment‖ of 45 basis points to Firm L. Answer:

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Hi wants fixed rate, but it will issue floating and ―swap‖ with Lo. Lo wants floating rate, but it will issue fixed and swap with Hi. Lo also makes ―side payment‖ of 0.45% to Hi. See the table below for details of the calculations. Transaction

CF to lender

−(LIBOR + 1%)

−11.40%

CF Hi to Lo

−11.40%

11.40%

CF Lo to Hi

+(LIBOR + 1%)

-(LIBOR + 1%)

CF Lo to Hi

0.45%

−0.45%

−10.95%

−(LIBOR+1.45%)

Net CF

Solution and Answer Guide BRIGHAM /EHRHARDT, FINANCIAL M ANAGEMENT: T HEORY AND PRACTICE; CHAPTER 24: BANKRUPTCY, REORGANIZATION , AND LIQUIDATION

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 468 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 471 Easy Problem 1 ..................................................................................................................................... 471 Intermediate Problem 2 ......................................................................................................................... 472 Challenging Problems 3–4 .................................................................................................................... 475 SOLUTION TO SPREADSHEET PROBLEM ................................................................................... 480 MINI CASE ............................................................................................................................................. 481

ANSWERS TO END-OF-CHAPTER QUESTIONS 24-1 Define each of the following terms: a. Informal restructuring; reorganization in bankruptcy b. Assignment; liquidation in bankruptcy; fairness; feasibility c. Absolute priority doctrine; relative priority doctrine d. Bankruptcy Reform Act of 1978; Chapter 11; Chapter 7 e. Priority of claims in liquidation f. Extension; composition; workout; cramdown; prepackaged bankruptcy; holdout Answer: a. Informal debt restructuring is the agreement between the creditors and troubled firm to change the existing debt terms. An extension postpones the required payment date, while a composition is a reduction in creditor claims. Extension provides payment in full, though delayed. Conversely, composition involves a reduced cash settlement. Restructuring often involves both extension and

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

composition. A reorganization in bankruptcy is a court-approved attempt to keep a company alive by changing its capital structure. A reorganization must adhere to the standards of fairness and feasibility. b.

Assignment is an informal procedure for liquidating debts which transfers title to a debtor's assets to a third person, known as an assignee or trustee. Assignment normally yields creditors a larger amount than they would receive in a formal bankruptcy. However, an assignment does not automatically result in a full and legal discharge of all the debtor’s liabilities, nor does it protect the creditors against fraud. Liquidation is the sale of the assets of a firm and the distribution of the proceeds to the creditors and owners in a specific priority. The decision whether to reorganize or liquidate should be based on the value of the firm if it is rehabilitated versus the value of the assets if they are sold off individually. The procedure that promises higher returns to the creditors and owners would be adopted. The standard of fairness states that claims must be recognized in the order of their legal and contractual priority. In simpler terms, the reorganization must be fair to all parties. The standard of feasibility states that there must be a reasonably high probability of successful rehabilitation and profitable future operations.

The absolute priority doctrine states that claims must be paid in strict accordance with the priority of each claim, regardless of the consequence to other claimants. The relative priority doctrine is more flexible and gives a more balanced consideration to all claimants than does the absolute priority doctrine.

The Bankruptcy Reform Act of 1978 was enacted to speed up and streamline bankruptcy proceedings. This law represents a shift to a relative priority doctrine of creditors’ claims. Chapter 11 of the Bankruptcy Act is the business reorganization chapter. Under this chapter, a case is started when a firm’s management or its creditors file a petition with the bankruptcy court. A committee of unsecured creditors is then appointed by the court to negotiate with the firm’s management. Existing management may stay in office unless a trustee is appointed by the court. If no fair and feasible reorganization can be worked out, the firm will be liquidated under the procedures spelled out in Chapter 7 of the act. Chapter 7 of the Federal Bankruptcy Reform Act accomplishes three important tasks during a liquidation: (1) it provides safeguards against fraud by the debtor, (2) it provides for an equitable distribution of the debtor’s assets among the creditors, and (3) it allows insolvent debtors to discharge all their obligations and to start new businesses unhampered by a burden of prior debt.

The priority of claims in liquidation is established in Chapter 7 of the Bankruptcy Act to provide an equitable distribution of the debtor’s assets among the creditors.

Extension and composition are both characteristics of debt restructuring. In an extension, creditors postpone the dates of required interest or principal payments, or both. In a composition, creditors voluntarily reduce their fixed claims on the debtor by accepting a lower principal amount, reducing the interest rate on the debt, accepting equity in place of debt, or some combination of these changes. Workouts are voluntary reorganization plans arranged between creditors and generally sound companies experiencing temporary financial difficulties. Workouts typically require some restructuring of the old firm’s debt. Cramdowns are bankruptcy court-mandated reorganization plans that are binding on all parties. Prepackaged bankruptcy is a new type of reorganization that combines the advantages of informal workouts and formal Chapter 11 reorganization. A holdout is a problematic characteristic of informal reorganizations where all of the involved parties do not agree to the voluntary plan. Holdouts are usually made by creditors in an effort to receive full payment on claims.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

24-2 Why do creditors usually accept a plan for financial rehabilitation rather than demand liquidation of the business? Answer: The rehabilitation plan may be accepted because of the following:    

Expenses of liquidation may consume a large proportion of the assets. The going-concern value of a firm is always substantially greater than its liquidating value. Hence, to preserve the life of the firm is to preserve a substantial portion of its value. They may retain a stable customer for the future. On balance, the creditors will accept a plan for financial rehabilitation because it appears that the funds they will receive will be much larger under this procedure.

24-3 Would it be a sound rule to liquidate whenever the liquidation value is above the value of the corporation as a going concern? Discuss. Answer: Not necessarily. The going-concern value of a firm is a function of its outlook—it might be improved by changing the management or otherwise improving operations. The firm may be temporarily distressed. 24-4 Why do liquidations usually result in losses for the creditors or the owners, or both? Would partial liquidation or liquidation over a period limit their losses? Explain. Answer: Liquidations usually result in losses for the following reasons:   

Assets typically have characteristics that make their value in existing uses greater than when resold. The organizational value of a company is lost when liquidation takes place. Because the claims of numerous parties must be adjudicated, considerable administrative, accounting, and legal costs may be incurred.

Partial liquidation over a period would have the following results:  

Probably would not decrease losses. Failure to institute the necessary operating and management changes might cause losses to continue and might cause further deterioration in the value of the company. It is often said that a swift major ―surgery‖ for a business firm is preferred to an extended illness.

24-5 Are liquidations likely to be more common for public utility, railroad, or industrial corporations? Why or why not? Answer: Because public utilities and railroads often involve essential services, reorganizations and mergers rather than liquidations are likely to take place. This is less true for industrial companies.

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SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEM 1 24-1 Liquidation. Southwestern Wear Inc. has the following balance sheet: Current assets

$1,875,000

Accounts payable

Fixed assets

1,875,000

Notes payable

750,000

Subordinated debentures

750,000

Total debt

$1,875,000

Common equity

1,875,000

Total liabilities & equity

$3,750,000

Total assets

$3,750,000

375,000

The trustee’s costs total $281,250, and the firm has no accrued taxes or wages. The debentures are subordinated only to the notes payable. If the firm goes bankrupt and liquidates, how much will each class of investors receive if a total of $2.5 million is received from sale of the assets? Solution: Distribution of proceeds on liquidation: 1.

Proceeds from sale of assets

$2,500,000

First mortgage, paid from sale of assets

Fees and expenses of administration of bankruptcy

Wages due workers earned within 3 months prior to filing of bankruptcy petition

Taxes

Unfunded pension liabilities

281,250

Available to general creditors

$2,218,750

0 281,250 0

Distribution to general creditors:

Claims of General Creditors

Claim

Application of 100% Distribution

After Subordination Adjustment

Percentage of Original Claims Received

(1)

(2)

(3)

(4)

Accounts payable

375,000

100

Notes payable

$ 750,000

100%

Subordinated debentures

750,000

100

$1,875,000

The remaining $2,218,750 – $1,875,000 = $343,750 will go to the common stockholders. They will receive only $343,750/$1,875,000 = 18.33% of the amount of equity on the balance sheet.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

INTERMEDIATE PROBLEM 2 24-2 Reorganization. Verbrugge Publishing Company is experiencing financial difficulties and has agreed on a reorganization plan with its creditors. Each share of noncallable preferred stock will be exchanged for a package consisting of one share of new preferred stock with a par value of $35 and a coupon of $2.40 per share plus one subordinated debenture having a par value of $75 and an 8% interest rate. (This subordinated debenture is like a perpetual bond that has a par value of $75.) Verbrugge will retire its current callable preferred stock using the cash generated from reducing its current assets. Verbrugge’s balance sheets (shown after the next paragraph) currently show that liabilities and equity include 1,000,000 shares of noncallable preferred stock; each share has a $110 par value and pays a dividend of $6. The balance sheet also shows 200,000 shares of callable preferred stock; each share pays a dividend of $10 and is callable at $100 per share. The tax rate is 25%. Verbrugge’s most recent balance sheet and income statement are shown next (in millions of dollars): Balance Sheets Assets:

Liabilities and Equity:

Current assets

$300

Current liabilities

Net fixed assets

200

Advance payments by customers

Noncallable preferred stock, $6 coupon, $110 par value (1,000,000 shares)

110

Callable preferred stock, $10 coupon, no par, $100 call price (200,000 shares)

200

Common stock, $2 par value (5,000,000 shares)

Retained earnings

Total assets

$500

Total liabilities & equity

$ 40

$500

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Income Statement Net sales

$540

Operating expense

516

Net operating income

$ 24

Other income

EBT

$ 28

Taxes (25%)

Net income

$ 21

Dividends on $6 preferred

Dividends on $10 preferred

Income available to common stockholders a. b. c.

$ 13

Assume that the reorganization takes place. Construct the projected balance. Show the new preferred stock at its par value. What is the value for total assets? For debt? For preferred stock? Construct the projected income statement. What is the income available to common shareholders in the proposed recapitalization? What were the total cash flows received by the noncallable preferred stockholders prior to the reorganization? What were the total cash flows to the original noncallable preferred stockholders after the reorganization? What was the net income to common stockholders before the reorganization? After the reorganization? Required pre-tax earnings are defined as the amount that is just large enough to meet fixed charges (debenture interest and/or preferred dividends). What are the required pre-tax earnings before and after the recapitalization? How is the debt ratio (i.e., liabilities/total assets) affected by the reorganization? Suppose you treated preferred stock as debt and calculated the resulting debt ratios. How are these ratios affected? If you were a holder of Verbrugge’s common stock, would you vote in favor of the reorganization? Why or why not?

Solution: a. After the reorganization, Verbrugge will have the pro forma balance sheet here. Items with dollar values are shown in millions of dollars: Current assetsa

$100

Current liabilities

Net fixed assets

$200

Advance payments by customers Subordinated debentures

Total assets

$300

$40 b

$80 $75

$2.40 preferred stock, $35 par value (1,000,000 shares)c

$35

Common stock, $2, par value (5,000,000 shares)

$10

Retained earnings

$60

Total claims

$300

Notes: a

This is equal to the previous current assets of $300 minus the $200 used to retire the callable preferred stock.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach b

This is equal to: (1 million bonds)($75 par value) = $75 million.

This is equal to 1 is equal to: (1 million shares)($35 par value) = $35.

The pro forma income statement (in millions of dollars) follows: Net sales

$540.0

Operating expense

$516.0

Net operating income

$24.0

Other income

$4.0

EBIT

$28.0

Interest

$6.0

Pre-tax earnings

$22.0

Taxes (25%)

$5.5

Net income

$16.5

Dividends on $2.4 preferred

$2.4

Income available to common stockholders

$14.1

Notes: a

0.08($75 million par value) = $6.

$2.40(1 million shares) = $240.

Cash flows to noncallable preferred stockholders: Before: Preferred dividends. $6 million After: Interest + preferred dividends. $6 + $2.4 = $8.4 million Net income to common stockholders: Before: $13 million After: $14.1 million

The pre-tax earnings required before the recapitalization are ($6 + $2)/(1 – 0.25) = $8/0.75 = $10.67 million. We divide the preferred dividends by (1 – T) since $10.67 million pre-tax must be earned to provide the $8 million needed after-tax. After recapitalization, the firm requires $2.4 million/0.75 = $3.2 million to cover the preferred dividend payment, and $6 million to cover the interest expense for a total of $9.2 million. Since interest expense is tax deductible, only $6 million in pre-tax earnings are required to cover the interest expense. Thus, required earnings will decrease by $10.67 million – $9.2 million = $1.47 million if the reorganization takes place.

The debt ratio before reorganization is: (Current liabilities + Advanced payments)/(TA) = ($40 + $80) million/$500 million = 0.24 = 24%. After reorganization, the debt ratio is ($40 + $80 + $75)/$300 = 0.65 = 65%. If preferred stock is treated as debt, the ratio was (Current liabilities + Advanced payments + All dividends)/(TA) = ($40 + $80 + $110 + $200)/$500 = 0.86 = 86%. After reorganization, the debt ratio is ($40 + $80 + $75 + $35)/$300 = 0.7667 = 76.67%. This ratio actually declines.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

CHALLENGING PROBLEMS 3–4 24-3 Liquidation. At the time it defaulted on its interest payments and filed for bankruptcy, the McDaniel Mining Company had the balance sheet shown here (in thousands of dollars). The court, after trying unsuccessfully to reorganize the firm, decided that the only recourse was liquidation under Chapter 7. Sale of the fixed assets, which were pledged as collateral to the mortgage bondholders, brought in $400,000, while the current assets were sold for another $200,000. Thus, the total proceeds from the liquidation sale were $600,000. The trustee’s costs amounted to $50,000; no single worker was due more than the maximum allowable wages per worker; and there were no unfunded pension plan liabilities. Balance Sheet (Thousands of Dollars) Current assets

$ 400

Net fixed assets

600

Accounts payable

Accrued taxes

Accrued wages

Notes payable

180

Total current liabilities First-mortgage bonds

$ 300

300

Second-mortgage bondsa

200

Debentures

200

Subordinated debentures

Total assets

100

Common stock

_____

Retained earnings

(150)

$1,000

Total liabilities & equity

$1,000

Notes: a

All fixed assets are pledged as collateral to the mortgage bonds.

Subordinated to notes payable only.

a. b. c. d. e.

How much will McDaniel’s shareholders receive from the liquidation? How much will the first mortgage bondholders receive from collateralized assets? Will they receive their full claim? If not, how much is their remaining claim? How much will the second mortgage bondholders receive from collateralized assets? Will they receive their full claim? If not, how much is their remaining claim? Who are the other priority claimants (in addition to the mortgage bondholders)? How much will they receive from the liquidation? How much remains for distribution to the remaining general creditors? Who are the remaining general creditors? How much is each creditor’s claims? What is the total of their remaining claims? How much will each receive from the distribution before subordination adjustment? How much will each receive after subordination? How much in total will the second mortgage holders receive (include the amount received from collateral)?

Solution: a. Creditor claims total $1,100,000 while the trustee has an additional $50,000 in claims, yet the liquidation produced only $600,000 in proceeds. Since the proceeds are insufficient to satisfy the creditor and trustee claims, the shareholders receive nothing. b.

The mortgage bondholders have priority claim against the proceeds from the sale of pledged property. Thus, the $400,000 from the fixed assets must first be distributed to the first and second mortgage bondholders. The first mortgage holders receive their full claim of $300,000. There is $100,000

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

remaining collateral. c.

The second mortgage holders receive the remaining $100,000 of collateral. This constitutes the total $400,000, so none of the proceeds from the sale of pledged assets are available for distribution to general creditors. Additionally, the second mortgage holders have $100,000 in unsatisfied claims, which become general creditor claims.

The priority claimants are the mortgage bondholders, trustee, workers, and government. The remaining claimants are general creditors. There is $200,000 available after the $400,000 distribution to the mortgage bondholders. This is distributed to the remaining priority claimants as follows: Remaining primary claimants

Amount

Trustee’s expenses

$ 50,000

Workers’ wages due

30,000

Governments’ taxes due

40,000

Total

$120,000

There is $80,000 still available for distribution to general creditors: $200,000 − $120,000 = $80,000. e.

Of the total $600,000 received from the liquidation, $520,000 has been distributed to priority claimants. This leaves $80,000 to distribute to the general creditors. But the general creditor claims total $630,000: Account

Claim

Accounts payable

$ 50,000

Notes payable

180,000

Second mortgage bonds

100,000

Debentures

200,000

Subordinated debentures

100,000

Total

$630,000

Note that the second mortgage holders’ unsatisfied claim of $100,000 is included. Each claimant, before subordination adjustment, would receive $80,000/$630,000 = 0.12698413 of his or her claim. Therefore, the general creditors would receive: Account

Amount

Accounts payable

$6,349.21

Notes payable

$22,857.14

Second mortgage bonds

$12,698.41

Debentures

$25,396.83

Subordinated debentures

$12,698.41

Total received

$80,000.00

Finally, the subordination adjustment must be made. The subordinated debentures are subordinate to notes payable. Therefore, the subordinate debenture holders must relinquish all claims until the note payable holders are fully satisfied. The notes payable holders are short of being fully satisfied: $180,000 − $22,860 = $157,140. Therefore, the full $12,698.41 initially allocated to the subordinated debenture holders must be

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relinquished to the notes payable holders. Therefore, the notes payable holders receive: $22,857.14 + $12,698.41 = $35,555.55 for the notes payable holders and nothing (of the general creditor portion) for the subordinate debenture holders. 24-4 Liquidation. The following balance sheet represents Boles Electronics Corporation’s position at the time it filed for bankruptcy (in thousands of dollars): Cash

Accounts payable

Receivables

100

Notes payable

500

Inventories

890

Wages payable

150

______

Taxes payable

Total current assets

$ 1,000

Total current liabilities

Net plant and property

4,000

Mortgage bonds

2,000

Net equipment

5,000

Subordinated debentures

2,500

Preferred stock

1,500

______

Common stock

1,700

$10,000

Total liabilities & equity

Total assets

$ 1,600

$ 2,300

$10,000

The mortgage bonds are secured by the plant but not by the equipment. The subordinated debentures are subordinated to notes payable. The firm was unable to reorganize under Chapter 11; therefore, it was liquidated under Chapter 7. The mortgage bonds are secured by the plant but not by the equipment. The subordinated debentures are subordinated to notes payable. The firm was unable to reorganize under Chapter 11; therefore, it was liquidated under Chapter 7. The trustee, whose legal and administrative fees amounted to $200,000, sold the noncash assets and received the following proceeds (in thousands of dollars):

Asset

Proceeds

Plant

$1,600

Equipment

1,300

Receivables

Inventories

240

Total Proceeds

3,190

No single wage earner had claims exceeding the maximum allowable wages per worker, and there were no unfunded pension plan liabilities. a.

What is the total amount available for distribution to all claimants? (Hint: Did the company have any cash at the time it declared bankruptcy?) What is the total of creditor and trustee claims? Will the preferred and common stockholders receive any distributions? Determine the dollar distribution to each creditor and to the trustee. What percentage of each claim is satisfied?

Solution: a. The total amount available for distribution is: $3,190,000 proceeds from sale plus $10,000 cash = $3,200,000.

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Asset

Proceeds (Thousands)

Plant

$1,600

Equipment

1,300

Receivables

Inventories

240

Total Proceeds

$3,190

Cash

Total available for distribution

$3,200

The total creditor and trustee claims are $6,800,000 + $200,000 = $7,000,000. No, the preferred and common stockholders will receive nothing. This is because the higher priority claims far exceed the available funds, leaving nothing for the stockholders. b.

The following tables show the steps to determine the percentage of each creditor’s claim that is paid. First, identify all claims and all distributions. Priority Distribution

Remaining Claim

Claimant

Claim

Accounts payable

$1,600

Notes payable

$500

Wages payable

$150

Taxes payable

$50

Mortgage bonds*

$2,000

$1,600

$400

Subordinated debentures

$2,500

Trustee

$200

Total

$7,000

$2,000

$5,000

Note: All values in the table shown in thousands of dollars. *Mortgage bonds are secured by the physical plant and receive the proceeds from the sale of the plant. If these proceeds are insufficient to fully cover the mortgage, the remaining amount of unpaid mortgage is grouped with general creditors. The next step is to determine the ratio of remaining claims to remaining proceeds. Priority distributions were $2,000, so that leaves $3,200 – $2,000 = $1,200 for general claimants. The percentage of claims satisfied (before subordination) is $1,200/$5,000 = 0.24 = 24%. Apply this percentage to the remaining general claims to determine the remaining creditor distributions before subordination. Third, the holders of notes payable get paid prior to the subordinated debentures. If there is any left from the pre-subordination claim by the subordinated debtholder, then that is paid to them. In this case, the claim by holders of notes payable is $500 and they are paid $120 before subordination, leaving an unfilled claim of $500 – $120 = $380. The subordinated debtholder would have received $600 before subordination, but they must lose $380 to the notes payable. The net result is that the notes payable receive $500 and the subordinated debentures receive $600 – $380 = $220. These results are shown in the following table.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Claimant

Remaining General Claims

Remaining Creditor Distributions Before Subordination Are Equal to 24% of Claim

Remaining Creditor Distributions After Subordination

Accounts payable

$1,600

$384

$500

$120

$500

Mortgage bonds

$400

$96

Subordinated debentures

$2,500

$600

$220

$5,000

$1,200

Notes payable Wages payable Taxes payable

Trustee Total

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The following table sums the priority distributions and the remaining general creditor distributions after subordination to determine total distributions and the percentage of each claimants claim that is paid. Claimant

Claim

Paid

Percentage of Claim Paid

Accounts payable

$1,600

$384

24.0%

Notes payable

$500

100.0%

Wages payable

$150

100.0%

Taxes payable

$50

100.0%

Mortgage bonds

$2,000

$1,696

84.8%

Subordinated debentures

$2,500

$220

8.8%

Trustee

$200

100.0%

Total

$7,000

$3,200

45.7%

Claimant

Priority Distribution

Accounts payable

Creditor Distribution

Subordination Adjustment

Adjustment Percentage

$ 384

24%

Notes payable

120

500

100

Wages payable

$ 150

150

100

Taxes payable

100

Mortgage bonds

1,600

1,696

600

220

200

100

$2,000

$3,200

Subordinated debentures Trustee



Funds remaining after the priority distribution = $3,200 – $2,000 = $1,200.



General creditor claims total $1,600 + $500 + $400 + $2,500 = $5,000.



After the general creditor distribution, notes payable is $500 – $120 = $380 short. Therefore, subordinated debentures must give up $380, leaving $600 – $380 = $220.

SOLUTION TO SPREADSHEET PROBLEM 24-5 Liquidation. Start with the partial model in the file Ch24 P05 Build a Model.xlsx on the textbook’s website. Duchon Amalgamated had the following balance sheet at the time it defaulted on its interest payments and filed for liquidation under Chapter 7. Sale of the fixed assets, which were pledged as collateral to the mortgage bondholders, brought in $900 million, while the current assets were sold for another $401 million. Thus, the total proceeds from the liquidation sales were $1,300 million. The trustee’s costs amounted to $1 million; no single worker was due more than the maximum allowable wages per worker; and there were no unfunded pension plan liabilities. Determine the amount available for distribution to shareholders and all claimants. Duchon Amalgamated’s Balance Sheets (Millions of Dollars)

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Current assets

$ 700

Accounts payable

$ 80

Net fixed assets

1,300

Accrued taxes

Accrued wages

Notes payable

400

Total current liabilities First-mortgage bonds

$ 630

Second-mortgage bonds

700 a

Debentures Subordinated debentures

Total assets

300 500

200

Common stock

100

_____

Retained earnings

(430)

$2,000

Total claims

$2,000

Notes: a

All fixed assets are pledged as collateral to the mortgage bonds.

Subordinated to notes payable only.

Solution: The detailed solution for the spreadsheet problem, Ch24 P05 Build a Model Solution.xlsx, is available on the textbook’s website.

MINI CASE Kimberly MacKenzie, president of Kim’s Clothes Inc.—a medium-sized manufacturer of women's casual clothing—is worried. Her firm has been selling clothes to Russ Brothers Department Store for more than 10 years, and she has never experienced any problems in collecting payment for the merchandise sold. Currently, Russ Brothers owes Kim’s Clothes $65,000 for spring sportswear that was delivered to the store just 2 weeks ago. Kim’s concern from reading an article in yesterday’s Wall Street Journal that indicated that Russ Brothers was having serious financial problems. Moreover, the article stated that Russ Brothers’ management was considering filing for reorganization, or even liquidation, with a federal bankruptcy court.

Kim’s immediate concern was whether her firm will collect its receivables if Russ Brothers goes bankrupt. In pondering the situation, Kim has also realized that she knows nothing about the process that firms go through when they encounter severe financial distress. To learn more about bankruptcy, reorganization, and liquidation, Kim has asked Ron Mitchell, the firm’s chief financial officer, to prepare a briefing on the subject for the entire board of directors. In turn, Ron has asked you, a newly hired financial analyst, to do the groundwork for the briefing by answering the following questions:

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

a. 1. What are the major causes of business failure? Answer: The major causes of business failure consist of economic factors, such as industry weakness and poor location, and financial factors, such as too much debt and insufficient capital. However, most business failures occur because a number of factors combine to make the business unsustainable.

a. 2. Do business failures occur evenly over time? Answer: A fairly large number of businesses fail each year, but the number in any 1 year has never been a large percentage of the total business population. The failure rate of businesses, however, has tended to fluctuate with the state of the economy.

a. 3. Which size of firm, large or small, is more prone to business failure? Why? Answer: Bankruptcy is more frequent among smaller firms. While bankruptcy does occur in large firms, they tend to get more help from external sources to avoid it, given their greater impact on the economy and, in the case of large financial institutions, the financial world. The federal government’s bailouts of Chrysler and Lockheed are good examples of this external assistance.

b. What key issues must managers face in the financial distress process? Answer: As a manager begins to face financial distress, he or she must begin to consider the following key issues:     

Is this a temporary cash flow problem (technical insolvency), or is it a permanent problem caused by asset values having fallen below debt obligations (insolvency in bankruptcy)? Who should bear the losses if this is a permanent problem? Would the firm be more valuable if it continued to operate or if it were liquidated and sold off in pieces? Should the firm file for bankruptcy, or should it try to use informal procedures? Who should control the firm during liquidation or reorganization?

Obviously, answers to these questions are needed to chart the course of the firm while under financial distress.

c. What informal remedies are available to firms in financial distress? In answering this question, define the following terms: (1) workout, (2) restructuring, (3) extension, (4) composition, (5) assignment, and (6) assignee (trustee). Answer: When faced with financial distress, it is often desirable for firms to pursue informal reorganizations or liquidations with creditors, given the costs associated with legal bankruptcy. Creditors generally prefer informal reorganization plans when dealing with economically sound companies whose financial difficulties appear to be temporary. These voluntary informal plans, commonly called workouts, tend to involve some type of restructuring, where current debt terms are revised to facilitate the firm's ability to make payments. Such restructurings typically involve extension and/or composition. In an extension, creditors postpone the dates of required interest or principal payments, or both. Creditors tend to prefer extensions when developing reorganization plans because they promise eventual payment in full. In a composition, creditors voluntarily reduce their fixed claims on the debtor by either accepting a lower principal amount or accepting equity in place of debt. This can be a desirable alternative if bankruptcy becomes a real possibility, since composition can help the creditor and debtor avoid the many costs associated with legal bankruptcy. Informal liquidations can also be used if it is decided that the firm is worth more by selling it off in

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pieces. Assignment is an informal procedure for liquidating a firm. It calls for title to the debtor's assets to be transferred to a third party, known as the assignee or trustee. The assignee is required to liquidate the firm's assets either through a private sale or a public auction, and then to distribute the proceeds among the firm’s creditors on a pro rata basis.

d. Briefly describe U.S. bankruptcy law, including the following terms: (1) Chapter 11, (2) Chapter 7, (3) trustee, (4) voluntary bankruptcy, and (5) involuntary bankruptcy. Answer: U.S. bankruptcy laws were first enacted in 1898 to ensure that businesses worth more as ongoing concerns were not shut down by individual creditors desiring liquidation and full payment. The Bankruptcy Reform Act of 1978 revised these laws to streamline and expedite bankruptcy proceedings. Current bankruptcy law consists of eight chapters, the most important of which are Chapter 7, which details the procedures to be followed when liquidating a company, and Chapter 11, the business reorganization chapter. When a petition for bankruptcy is filed in federal court, the petition can be either voluntary or involuntary. A voluntary petition is filed by the distressed firm’s management; an involuntary petition is filed by its creditors. The court will appoint a committee of unsecured creditors to negotiate a reorganization, which may include restructuring. A trustee will be appointed if current management is incompetent or fraud is suspected; otherwise, the existing management will retain control. If no fair and feasible reorganization can be worked out, then the firm will be liquidated under Chapter 7 procedures.

e. What are the major differences between an informal reorganization and reorganization in bankruptcy? In answering this question, be sure to discuss the following items: (1) common pool problem, (2) holdout problem, (3) automatic stay, (4) cramdown, and (5) fraudulent conveyance. Answer: There are many differences between voluntary reorganizations and reorganizations in bankruptcy. Voluntary reorganizations are far less costly and relatively simple to create as compared to reorganizations in bankruptcy. As a result, voluntary reorganizations typically allow creditors to recover more money, and sooner, than they would under legal bankruptcy. However, reorganizations in bankruptcy have their advantages. First, they avoid holdout problems that can arise with voluntary reorganizations (which occur when all creditors do not agree to the voluntary plan). Second, because of the automatic stay provision, bankruptcy avoids the common pool problem, where efforts to foreclose on the firm by one creditor cause the remaining creditors to initiate foreclosure as well. Automatic stay, which is granted to all firms in bankruptcy, limits creditors’ abilities to foreclose unilaterally on the firm to collect their claims. Third, under bankruptcy, interest and principal payments may be delayed without penalty until a reorganization plan is approved. Fourth, bankruptcy permits the firm to issue debtor in possession (dip) financing to enhance the ability of the firm to borrow funds for short-term liquidity purposes. Finally, bankruptcy gives the debtor exclusive right to submit a proposed reorganization plan for agreement from the parties affected. While bankruptcy gives the firm a chance to work out its problems without the threat of creditor foreclosure, it does not give the debtor free reign over the firm’s assets. First, bankruptcy law gives creditors the right to petition the bankruptcy court to block almost any action the firm might take while in bankruptcy. Second, fraudulent conveyance statutes, which are part of debtor-creditor law in most states, protect creditors from unjustified transfers of property by a firm in financial distress. In bankruptcy, it is much easier to gain acceptance of a reorganization plan, because the bankruptcy court will lump the creditors into classes. Each class is considered to have accepted a reorganization plan if a majority of the creditors in the class (holding at least two-thirds of the amount of debt) vote for the plan, and the plan will be approved by the court if it is deemed to be ―fair and equitable‖ to the dissenting parties. This procedure, in which the court mandates a reorganization plan in spite of dissent, is called a cramdown.

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f. What is a prepackaged bankruptcy? Why have prepackaged bankruptcies become more popular in recent years? Answer: Prepackaged bankruptcy is a relatively new type of reorganization which is a hybrid—combining the advantages of both the informal reorganization and formal Chapter 11 reorganization. The debtor obtains agreement from all, or almost all, creditors to a reorganization plan prior to filing for bankruptcy. The plan is then filed along with, or shortly after filing, the bankruptcy petition. This method can avoid the holdout problems of voluntary reorganizations, preserve creditors' claims, and provide favorable tax treatment.

g. Briefly describe the priority of claims in a Chapter 7 liquidation. Answer: Chapter 7 of the federal bankruptcy reform act provides for an equitable distribution of the debtor’s assets among the creditors. The distribution of assets is governed by the following priority of claims:           

Secured creditors (who are entitled to the proceeds of the sale of specific property pledged for a lien or a mortgage). Trustee’s costs to administer and operate the bankrupt firm. Expenses incurred after an involuntary case has begun but before a trustee has been appointed. Wages due workers if earned within 3 months prior to filing of the petition in bankruptcy. Claims for unpaid contributions to employee benefit plans that should have been paid within 6 months prior to filing. Unsecured claims for customer deposits. Taxes due to federal, state, county, and any other government agency. Unfunded pension plan liabilities. General, or unsecured, creditors. Preferred stockholders. Common stockholders.

h. Assume that Russ Brothers did indeed fail, and that it had the following balance sheet when it was liquidated (in millions of dollars): Current assets

$40.0

Net fixed assets

5.0

Accounts payable

$10.0

Notes payable (to banks)

5.0

Accrued wages

0.3

Federal taxes

0.5

State and local taxes

0.2

Current liabilities

$16.0

First-mortgage bonds

3.0

Second-mortgage bonds Subordinated debentures Total long-term debt

0.5 a

4.0 $ 7.5

Preferred stock

1.0

Common stock

13.0

Paid-in capital

2.0

Retained earnings

5.5

Total equity

$21.5

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Total assets

$45.0

Total claims

$45.0

Note: a

The debentures are subordinated to the notes payable.

The liquidation sale resulted in the following proceeds: From sale of current assets

$14,000,000

From sale of fixed assets

2,500,000

Total receipts

$16,500,000

For simplicity, assume there were no trustee’s fees or any other claims against the liquidation proceeds. Also, assume that the mortgage bonds are secured by the entire amount of fixed assets. What would each claimant receive from the liquidation distribution? Answer: The following table shows the liquidation distribution (millions of dollars): Distribution to Priority Claimants (Millions) Proceeds from the sale of assets

$16.5

Less: 1. 1st mortgage (paid from sale of fixed assets)

$2.5

2. Accrued wages

$0.3

3. Taxes due to federal, state, and local governments

$0.7

Funds available for distribution to general creditors

$13.0

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Distribution to General Creditors Amount of Claim

Pro Rata Distribution1

Distribution After Subordination

Percentage of Original Claim Received

1st mortgage

$0.5

$0.325

94%

2nd mortgage

$0.5

$0.325

65%

Notes payable

$5.0

$3.250

$5.000

100%

$10.0

$6.500

65%

$4.0

$2.600

$0.850

21%

$20.0

$13.000

General Creditor Claims

Accts. payable Subord. deben. Total

Notes: 1. 2.

$13 million is available for distribution to general creditors; however, there is $20 million in general creditor claims, so the pro rata distribution will be $13/$20 = 0.65, or 65 cents on the dollar. The debentures are subordinated to the notes payable. The amount of the unsatisfied notes payable is $5.0 – $3.25 = $1.75 million. $1.75 million is reallocated from the subordinated debentures to notes payable.

Solution and Answer Guide BRIGHAM /EHRHARDT, FINANCIAL M ANAGEMENT: T HEORY AND PRACTICE; CHAPTER 25: PORTFOLIO T HEORY AND ASSET PRICING MODELS

TABLE OF CONTENTS ANSWERS TO END-OF-CHAPTER QUESTIONS........................................................................... 486 SOLUTIONS TO END-OF-CHAPTER PROBLEMS ........................................................................ 488 Easy Problems 1–2 ................................................................................................................................ 488 Intermediate Problems 3–4 ................................................................................................................... 488 Challenging Problems 5–6 .................................................................................................................... 489 SOLUTION TO SPREADSHEET PROBLEM .................................................................................... 493 MINI CASE ............................................................................................................................................. 494

ANSWERS TO END-OF-CHAPTER QUESTIONS 25-1 Define the following terms, using graphs or equations to illustrate your answers wherever feasible: a. Portfolio; feasible set; efficient portfolio; efficient frontier b. Indifference curve; optimal portfolio c. Capital Asset Pricing Model (CAPM); Capital Market Line (CML) d. Characteristic line; beta coefficient, b e. Arbitrage Pricing Theory (APT)

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Answer:

a. A portfolio is made up of a group of individual assets held in combination. An asset that would be relatively risky if held in isolation may have little, or even no risk if held in a welldiversified portfolio. The feasible, or attainable, set represents all portfolios that can be constructed from a given set of stocks. This set is only efficient for part of its combinations. An efficient portfolio is that portfolio which provides the highest expected return for any degree of risk. Alternatively, the efficient portfolio is that which provides the lowest degree of risk for any expected return. The efficient frontier is the set of efficient portfolios out of the full set of potential portfolios. On a graph, the efficient frontier constitutes the boundary line of the set of potential portfolios. b.

An indifference curve is the risk/return trade-off function for a particular investor and reflects that investor’s attitude toward risk. The indifference curve specifies an investor's required rate of return for a given level of risk. The greater the slope of the indifference curve, the greater is the investor's risk aversion. The optimal portfolio for an investor is the point at which the efficient set of portfolios—the efficient frontier—is just tangent to the investor’s indifference curve. This point marks the highest level of satisfaction an investor can attain given the set of potential portfolios.

The Capital Asset Pricing Model (CAPM) is a general equilibrium market model developed to analyze the relationship between risk and required rates of return on assets when they are held in well-diversified portfolios. The SML is part of the CAPM. The Capital Market Line (CML) specifies the efficient set of portfolios an investor can attain by combining a risk-free asset and the risky market portfolio M. The CML states that the expected return on any efficient portfolio is equal to the riskless rate plus a risk premium, and thus describes a linear relationship between expected return and risk.

The characteristic line for a particular stock is obtained by regressing the historical returns on that stock against the historical returns on the general stock market. The slope of the characteristic line is the stock’s beta, which measures the amount by which the stock’s expected return increases for a given increase in the expected return on the market. The beta coefficient (b) is a measure of a stock’s market risk. It measures the stock’s volatility relative to an average stock, which has a beta of 1.0.

Arbitrage Pricing Theory (APT) is an approach to measuring the equilibrium risk/return relationship for a given stock as a function of multiple factors, rather than the single factor (the market return) used by the CAPM. The APT is based on complex mathematical and statistical theory, but can account for several factors (such as GNP and the level of inflation) in determining the required return for a particular stock.

25-2 Security A has an expected rate of return of 6%, a standard deviation of returns of 30%, a correlation coefficient with the market of −0.25, and a beta coefficient of −0.5. Security B has an expected return of 11%, a standard deviation of returns of 10%, a correlation with the market of 0.75, and a beta coefficient of 0.5. Which security is riskier? Why? Answer: Security A is less risky if held in a diversified portfolio because of its lower beta and negative correlation with other stocks. In a single-asset portfolio, Security A would be riskier because σA > σB and CVA > CVB.

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

SOLUTIONS TO END-OF-CHAPTER PROBLEMS EASY PROBLEMS 1–2 25-1 Beta. The standard deviation of stock returns for Stock A is 40%. The standard deviation of the market return is 20%. If the correlation between Stock A and the market is 0.70, then what is Stock A’s beta? Solution: bi = ρiM (σi / σM) = 0.70(0.40/0.20) = 1.4. 25-2 APT. An analyst has modeled the stock of Crisp Trucking using a two-factor APT model. The risk-free rate is 6%, the expected return on the first factor (r 1) is 12%, and the expected return on the second factor (r2) is 8%. If bi1 = 0.7 and bi2 = 0.9, what is Crisp’s required return? Solution: ri = rRF + (r1  rRF)bi1 + (r2  rRF)bij = 0.06 + (0.12 – 0.06)(0.7) + (0.08 – 0.06)(0.9) = 0.12 = 12%.

INTERMEDIATE PROBLEMS 3–4 25-3 Two-Asset Portfolio. Stock A has an expected return of 12% and a standard deviation of 40%. Stock B has an expected return of 18% and a standard deviation of 60%. The correlation coefficient between Stocks A and B is 0.2. What are the expected return and standard deviation of a portfolio invested 30% in Stock A and 70% in Stock B? Solution: r̂P = wA r̂ A + (1  wA) r̂ B = 0.30(12%) + 0.70(18%) = 16.20% w 2A 2A  (1 w A )2 2B  2w A (1 w A )AB AB

σp = =

(0.32 )(0.4 2 )  (0.72 )(0.62 )  2(0.3)(0.7)(0.2)(0.4)(0.6)

0.0144  0.1764  0.02016 =

0.21096 = 0.459 = 45.9%

25-4 SML and CML Comparison. The beta coefficient of an asset can be expressed as a function of the asset’s correlation with the market as follows: a. Substitute this expression for beta into the Security Market Line (SML), Equation 25-10. This results in an alternative form of the SML. b. Compare your answer to part a with the Capital Market Line (CML), Equation 25-6. What similarities do you observe? What conclusions can you draw? Solution: a.

ri  rRF  (rM  rRF )b i  rRF  (rM  rRF )

 r̂  r  CML: r̂p  rRF   M RF  p .    M  

iMi M

r r  SML: ri  rRF   M RF  riMi .    M  

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

With some arranging, the similarities between the CML and SML are obvious. When in this form, both have the same market price of risk, or slope, (rM – rRF)/σM. The measure of risk in the CML is σp. Since the CML applies only to efficient portfolios, σp not only represents the portfolio's total risk, but also its market risk. However, the SML applies to all portfolios and individual securities. Thus, the appropriate risk measure is not σi, the total risk, but the market risk, which in this form of the SML is r iMσi, and is less than for all assets except those which are perfectly positively correlated with the market, and hence have r iM = +1.0.

CHALLENGING PROBLEMS 5–6 25-5 Characteristic Line and Security Market Line. You are given the following set of data: Historical Rates of Return Year

NYSE

Stock X

−26.5%

−14.0%

37.2

23.0

23.8

17.5

−7.2

2.0

6.6

8.1

20.5

19.4

7 a. b. c.

30.6

18.2

Use a spreadsheet (or a calculator with a linear regression function) to determine Stock X’s beta coefficient. Determine the arithmetic average rates of return for Stock X and the NYSE over the period given. Calculate the standard deviations of returns for both Stock X and the NYSE. Assume that the situation during Years 1 to 7 is expected to prevail in the future (i.e., r̂X = rX,Average , r̂M = rM,Average , and both σX and bX in the future will equal their past values). Also

d. e.

assume that Stock X is in equilibrium—that is, it plots on the Security Market Line. What is the riskfree rate? Plot the Security Market Line. Suppose you hold a large, well-diversified portfolio and are considering adding to that portfolio either Stock X or another stock, Stock Y, which has the same beta as Stock X but a higher standard deviation of returns. Stocks X and Y have the same expected returns: r̂x = r̂Y = 10.6%. Which stock should you choose?

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Brigham/Ehrhardt Financial Management: Theory & Practice--Ehrhardt/Brigham Corporate Finance: A Focused Approach

Solution: a. A plot of the approximate regression line is shown in the following figure: 30

rX (%)

25 20 15 10 5

0 -30

-20

-10

-5 -10 -15 -20

Using Excel, the regression equation estimates are: Beta = 0.56; Intercept = 0.037; R 2 = 0.96. b.

The arithmetic average return for Stock X is calculated as follows: rAvg 

( 14.0  23.0  ...  18.2)  10.6%. 7

The arithmetic average rate of return on the market portfolio, determined similarly, is 12.1%. For Stock X, the estimated standard deviation is 13.1%:

X 

( 14.0  10.6)2  (23.0  10.6)2  ...  (18.2  10.6)2  13.1%. 71

The standard deviation of returns for the market portfolio is similarly determined to be 22.6%. The results are summarized below: Z

Stock X

Average return, r Avg

Standard deviation, σ

Market Portfolio

10.6%

12.1%

13.1

22.6

Several points should be noted: (1) σM over this particular period is higher than the historic average σM of about 15%, indicating that the stock market was relatively volatile during this period; (2) Stock X, with X = 13.1%, has much less total risk than an average stock, with Avg = 22.6%; and (3) this example demonstrates that it is possible for a very low-risk single stock to have less risk than a portfolio of average stocks, since σX < σM.

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Since Stock X is in equilibrium and plots on the Security Market Line (SML). Given the further assumption that ˆrX  ˆrX and r̂M  rM , then this equation must hold:

rX  rRF  (r  rRF )b X . This equation can be solved for the risk-free rate, rRF, which is the only unknown:

10.6  rRF  (12.1 rRF )0.56 10.6  rRF  6.8  0.56rRF 0.44rRF  10.6  6.8 rRF  3.8 / 0.44  8.6%. d.

The SML is plotted below. Data on the risk-free security (bRF = 0, rRF = 8.6%) and Security X (bX = 0.56, rX = 10.6%) provide the two points through which the SML can be drawn. r M provides a third point.

In theory, you would be indifferent between the two stocks. Since they have the same beta, their relevant risks are identical, and in equilibrium they should provide the same returns. The two stocks would be represented by a single point on the SML. Stock Y, with the higher standard deviation, has more diversifiable risk, but this risk will be eliminated in a well-diversified portfolio, so the market will compensate the investor only for bearing market or relevant risk. In practice, it is possible that Stock Y would have a slightly higher required return, but this premium for diversifiable risk would be small.

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25-6 Characteristic Line. You are given the following set of data: Historical Rates of Return Year

a. b. c.

NYSE

Stock Y

4.0%

3.0%

14.3

18.2

19.0

9.1

−14.7

−6.0

−26.5

−15.3

37.2

33.1

23.8

6.1

−7.2

3.2

6.6

14.8

20.5

24.1

30.6

18.0

Mean = 9.8%

9.8%

σ= 19.6%

13.8%

Construct a scatter diagram showing the relationship between returns on Stock Y and the market. Use a spreadsheet or a calculator with a linear regression function to estimate beta. Give a verbal interpretation of what the regression line and the beta coefficient show about Stock Y’s volatility and relative risk as compared with those of other stocks. Suppose the regression line were exactly as shown by your graph from part b but the scatter plot of points was more spread out. How would this affect (1) the firm’s risk if the stock is held in a oneasset portfolio and (2) the actual risk premium on the stock if the CAPM holds exactly? Suppose the regression line were downward sloping and the beta coefficient were negative. What would this imply about (1) Stock Y’s relative risk, (2) its correlation with the market, and (3) its probable risk premium?

Solution: a. The regression graph is shown below. Using a spreadsheet, we find b = 0.6171  0.62.

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Because b = 0.62, Stock Y is about 62% as volatile as the market; thus, its relative risk is about 62% of that of an average firm.

Total risk ( 2Y ) would be greater because the second term of the firm’s risk equation, 2 2 2Y  b 2YM  eY , would be greater.

CAPM assumes that company-specific risk will be eliminated in a portfolio, so the risk premium under the CAPM would not be affected.

The stock’s variance would not change, but the risk of the stock to an investor holding a diversified portfolio would be greatly reduced.

It would now have a negative correlation with rM.

Because of a relative scarcity of such stocks and the beneficial net effect on portfolios that include it, its ―risk premium‖ is likely to be very low or even negative. Theoretically, it should be negative.

SOLUTION TO SPREADSHEET PROBLEM 25-7 Feasible Portfolios. Start with the partial model in the file Ch25 P07 Build a Model.xlsx from the textbook’s website. Following is information for the required returns and standard deviations of returns for A, B, and C: ri

σi

7.0%

33.11%

10.0

53.85

20.0

89.44

Stock

The correlation coefficients for each pair are shown in the following matrix, with each cell in the matrix giving the correlation between the stock in that row and column. For example, ρAB = 0.1571 is in the row

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for A and the column for B. Notice that the diagonal values are equal to 1 because a variable is always perfectly correlated with itself.

1.0000

0.1571

0.1891

0.1571

1.0000

0.1661

0.1891

0.1661

1.0000

Suppose a portfolio has 30% invested in A, 50% in B, and 20% in C. What are the expected return and standard deviation of the portfolio? The partial model lists six different combinations of portfolio weights. For each combination of weights, find the required return and standard deviation. The partial model provides a scatter diagram showing the required returns and standard deviations already calculated. This provides a visual indicator of the feasible set. If you seek a return of 10.5%, then what is the smallest standard deviation that you must accept?

b. c.

Solution: The detailed solution for the spreadsheet problem is available in the file Ch25 P07 Build a Model Solution.xlsx on the textbook’s website.

MINI CASE You have been hired at the investment firm of Bowers & Noon. One of its clients doesn’t understand the value of diversification or why stocks with the biggest standard deviations don’t always have the highest expected returns. Your assignment is to address the client’s concerns by showing the client how to answer the following questions: a.

Suppose Asset A has an expected return of 10% and a standard deviation of 20%. Asset B has an expected return of 16% and a standard deviation of 40%. If the correlation between A and B is 0.35, what are the expected return and standard deviation for a portfolio comprised of 30% Asset A and 70% Asset B? Inputs:

Expected return = Standard deviation = Correlation coefficient =

Asset A 10% 20%

Asset B 16% 40% 0.35

Answer:

ˆrP  w A ˆrA  (1 w A )rˆB  0.3(0.1)  0.7(0.16)  0.142  14.2%. p  

WA2 2A  (1 WA )2 B2  2WA (1 WA ) AB A B 0.32 (0.22 )  0.72 (0.4 2 )  2(0.3)(0.7)(0.35)(0.2)(0 .4)

 0.306

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Plot the attainable portfolios for a correlation of 0.35, for a correlation of +1.0, and for a correlation of −1.0. Answer: Attainable portfolios for ρ = 0.35:

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Attainable portfolios for ρ = +1:

Attainable portfolios for ρ = −1:

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Suppose a risk-free asset has an expected return of 5%. By definition, its standard deviation is zero, and its correlation with any other asset is also zero. Using only Asset A and the risk-free asset, plot the attainable portfolios. Answer:

Construct a plausible graph that shows risk (as measured by portfolio standard deviation) on the x-axis and expected rate of return on the y-axis. Now add an illustrative feasible (or attainable) set of portfolios and show what portion of the feasible set is efficient. What makes a particular portfolio efficient? Don't worry about specific values when constructing the graph—merely illustrate how things look with ―reasonable‖ data. Answer:

The figure above shows the feasible set of portfolios within the area having orange boundaries.

Points on the right side of the figure represent single securities (or portfolios containing only one security).

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All the other points within the orange boundary, including the boundaries, represent portfolios of two or more securities. The shaded area is called the feasible, or attainable, set. The boundary with the blue curve defines the efficient set of portfolios, which is also called the efficient frontier. Portfolios to the left of the efficient set are not possible because they lie outside the attainable set. Portfolios to the right of the boundary line (interior portfolios) are inefficient because some other portfolio would provide either a higher return with the same degree of risk or a lower level of risk for the same rate of return. e.

Add a set of indifference curves to the graph created for part b. What do these curves represent? What is the optimal portfolio for this investor? Add a second set of indifference curves that leads to the selection of a different optimal portfolio. Why do the two investors choose different portfolios?

Answer: The figure above shows the indifference curves for two hypothetical investors, A and B. To determine the optimal portfolio for a particular investor, we must know the investor’s attitude towards risk as reflected in his or her risk/return trade-off function, or indifference curve. Curves I a1, Ia2, and Ia3 represent the indifference curves for individual A, with the higher curve (I a3) denoting a greater level of satisfaction (or utility). Thus, Ia3 is better than Ia2 for any level of risk. The optimal portfolio is found at the tangency point between the efficient set of portfolios and one of the investor's indifference curves. This tangency point marks the highest level of satisfaction the investor can attain. The arrows point toward the optimal portfolios for both investors A and B.

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The investors choose different optimal portfolios because their risk aversion is different. Investor A chooses the portfolio with the lower expected return, but the riskiness of that portfolio is also lower than investor's B optimal portfolio, because investor A is more risk averse. f.

Now add the risk-free asset. What impact does this have on the efficient frontier?

Answer: The risk-free asset by definition has zero risk, and hence σ = 0%, so it is plotted on the vertical axis. Now, given the possibility of investing in the risk-free asset, investors can create new portfolios that combine the risk-free asset with a portfolio of risky assets. This enables them to achieve any combination of risk and return that lies along any straight line connecting rRF with any portfolio in the feasible set of risky portfolios. However, the straight line connecting rRF with m, the point of tangency between the line and the portfolio's efficient set curve, is the one that all investors would choose. Since all portfolios on the line r RFZ are preferred to the other risky portfolio opportunities on the efficient frontier AB, the points on the line rRFMZ now represent the best attainable combinations of risk and return. Any combination under the rRFMZ line offers less return for the same amount of risk, or offers more risk for the same amount of return. Thus, everybody wants to hold portfolios which are located on the rRFMZ line. g.

Write out the equation for the Capital Market Line (CML) and draw it on the graph. Interpret the CML. Now add a set of indifference curves and illustrate how an investor's optimal portfolio is some combination of the risky portfolio and the risk-free asset. What is the composition of the risky portfolio? Answer: The line rRFMZ in the figure above is called the capital market line (CML). It has an intercept of rRF and a slope of (rˆM  rRF ) / M . Therefore, the equation for the capital market line may be expressed as follows:

 r̂  r  CML: r̂p  rRF   M RF  p .    M   The CML tells us that the expected rate of return on any efficient portfolio (that is, any portfolio on the CML) is equal to the risk-free rate plus a risk premium, and the risk premium is equal to (rˆM  rRF ) / M multiplied by the portfolio’s standard deviation, p . Thus, the CML specifies a linear relationship between

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expected return and risk, with the slope of the CML being equal to the expected return on the market portfolio of risky stocks, r̂M , minus the risk-free rate, rRF, which is called the market risk premium, all divided by the standard deviation of returns on the market portfolio, σm.

The figure above shows a set of indifference curves (i1, i2, and i3), with i1 touching the CML. This point of tangency defines the optimal portfolio for this investor, and he or she will buy a combination of the market portfolio and the risk-free asset. The risky portfolio, m, must contain every asset in exact proportion to that asset's fraction of the total market value of all assets; that is, if security g is x percent of the total market value of all securities, x percent of the market portfolio must consist of security g. h.

What is the Capital Asset Pricing Model (CAPM)? What are the assumptions that underlie the model? What is the Security Market Line (SML)? Answer: The Capital Asset Pricing Model (CAPM) is an equilibrium model that specifies the relationship between risk and required rates of return on assets when they are held in well-diversified portfolios. The CAPM requires an extensive set of assumptions:       

All investors are single-period expected utility of terminal wealth maximizers, who choose among alternative portfolios on the basis of each portfolio’s expected return and standard deviation. All investors can borrow or lend an unlimited amount at a given risk-free rate of interest. Investors have homogeneous expectations (that is, investors have identical estimates of the expected values, variances, and covariances of returns among all assets). All assets are perfectly divisible and perfectly marketable at the going price, and there are no transactions costs. There are no taxes. All investors are price takers (that is, all investors assume that their own buying and selling activity will not affect stock prices). The quantities of all assets are given and fixed.

The Security Market Line (SML) expresses a stock’s return as a function of the risk-free rate and the

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stock’s beta: ri = rRF + (RPM) bi where RPM is the market risk premium, which is amount by which the expected return on the market exceeds the risk-free rate: RPM = rM − rRF i.

What is a characteristic line? How is this line used to estimate a stock’s beta coefficient? Write out and explain the formula that relates total risk, market risk, and diversifiable risk. Answer: Betas are calculated as the slope of the characteristic line, which is the regression line formed by plotting returns on a given stock on the y axis against returns on the general stock market on the x-axis. In practice, 5 years of monthly data, with 60 observations, would be used, and a computer would be used to obtain a least squares regression line. The relationship between stock J's total risk, market risk, and diversifiable risk can be expressed as follows:

Tot al risk  Variance  Market Risk  Diversif iable Risk 2 2  2J  b J2 M   eJ

2 is the variance of the market, b is stock J's beta Here,  2J is the variance or total risk of stock j, M j

coefficient, and  2 eJ is the variance of stock J's regression error term. If stock J is held in isolation, then the investor must bear its total risk. However, when stock J is held as part of a well-diversified portfolio, the regression error term,  2 eJ is driven to zero; hence, only the market risk remains. j.

What are two potential tests that can be conducted to verify the CAPM? What are the results of such tests? What is Roll’s critique of CAPM tests? Answer: Since the CAPM was developed on the basis of a set of unrealistic assumptions, empirical tests should be used to verify the CAPM. The first test looks for stability in historical betas. If betas have been stable in the past for a particular stock, then its historical beta would probably be a good proxy for its ex ante, or expected beta. Empirical work concludes that the betas of individual securities are not good estimators of their future risk, but that betas of portfolios of ten or more randomly selected stocks are reasonably stable, hence that past portfolio betas are good estimators of future portfolio volatility. The second type of test is based on the slope of the SML. As we have seen, the CAPM states that a linear relationship exists between a security's required rate of return and its beta. Further, when the SML is graphed, the vertical axis intercept should be rRF, and the required rate of return for a stock (or portfolio) with beta = 1.0 should be rm, the required rate of return on the market. Various researchers have attempted to test the validity of the CAPM model by calculating betas and realized rates of return, plotting these values in graphs, and then observing whether or not (1) the intercept is equal to r RF, (2) the regression line is linear, and (3) the SML passes through the point b = 1.0, rm. Evidence shows a more-or-less linear relationship between realized returns and market risk, but the slope is less than predicted. Tests that attempt to assess the relative importance of market and company-specific risk do not yield definitive results, so the irrelevance of diversifiable risk specified in the CAPM model can be questioned. Roll questioned whether it is even conceptually possible to test the CAPM. Roll showed that the linear relationship which prior researchers had observed in graphs resulted from the mathematical properties of the models being tested; hence, that a finding of linearity proved nothing about the validity of the CAPM. Roll’s work did not disprove the CAPM theory, but he did show that it is virtually impossible to prove that

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investors behave in accordance with the theory. In general, evidence seems to support the CAPM model when it is applied to portfolios, but the evidence is less convincing when the CAPM is applied to individual stocks. k.

Briefly explain the difference between the CAPM and the Arbitrage Pricing Theory (APT). Answer: The CAPM is a single-factor model, while the Arbitrage Pricing Theory (APT) can include any number of risk factors. It is likely that the required return is dependent on many fundamental factors such as the GNP growth, expected inflation, and changes in tax laws, and that different groups of stocks are affected differently by these factors. Thus, the apt seems to have a stronger theoretical footing than does the CAPM. However, the apt faces several major hurdles in implementation, the most severe being that the apt does not identify the relevant factors—a complex mathematical procedure called factor analysis must be used to identify the factors. To date, it appears that only three or four factors are required in the apt, but much more research is required before the apt is fully understood and presents a true challenge to the CAPM.

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