Chapter 9 problems

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Chapter 9 Risk and the Cost of Capital 249 ! [ ] [ ] [ ] For a useful survey of the issues covered in this chapter, see: FURTHER R.Jagannathan, J. Liberti, B. Liu, and I. Meier, “A Firm’s Cost of Capital,” Annual Review of Financial READING Economics 9 (November 2017), pp. 259-282. Levi and Welch provide some recommendations for estimating betas in: Y. Levi and I. Welch, “Best Practice for Cost-of-Capital Estimates,” Journal of Financial and Quanti- tative Analysis 52 (April 2017), pp. 427-463. [ ] [ ] [ ] e m‘meCt Select problems are available in McGraw-Hill’s Connect. PROBLEM SETS - Please see the preface for more information. . Definitions Define the following terms: a. Cost of debt. b. Cost of equity. . After-tax WACC. [y . Equity beta. c d e. Asset beta. f. Pure-play comparable. g. Certainty equivalent. 2. True/false* True or false? a. The company cost of capital is the correct discount rate for all projects because the high risks of some projects are offset by the low risk of other projects. o . Distant cash flows are riskier than near-term cash flows. Therefore, long-term projects require higher risk-adjusted discount rates. c. Adding fudge factors to discount rates undervalues long-lived projects compared with quick-payoff projects. 3. Company cost of capital Quark Productions (“Give your loved one a quark today.”) uses its company cost of capital to evaluate all projects. Will it underestimate or overestimate the value of high-risk projects? 4. Company cost of capital The total market value of the common stock of the Okefenokee Real Estate Company is $6 million, and the total value of its debt is $4 million. The treasurer estimates that the beta of the stock is currently 1.5 and that the expected risk premium on the market is 6%. The Treasury bill rate is 4%. Assume for simplicity that Okefenokee debt is risk-free and the company does not pay tax. a. What is the required return on Okefenokee stock? b. Estimate the company cost of capital. c. What is the discount rate for an expansion of the company’s present business? d. Suppose the company wants to diversify into the manufacture of rose-colored spectacles. The beta of unleveraged optical manufacturers is 1.2. Estimate the required return on Okefenokee’s new venture. 1 250 Part Two Risk 5. 6. Company cost of capital You are given the following information for Golden Fleece Financial: Long-term debt outstanding: $300,000 Current yield to maturity (ryep): 8% Number of shares of common stock: 10,000 Price per share: $50 Book value per share: §25 Expected rate of return on stock {requity): 15% Calculate Golden Fleece’s company cost of capital. Ignore taxes. Company cost of capital Nero Violins has the following capital structure: “tal L B CLA AT ecuri ($ millions) Debt Preferred stock Common stock a. What is the firm’s asset beta? (Hint: What is the beta of a portfolio of all the firm’s securities?) b. Assume that the CAPM is correct. What discount rate should Nero set for investments that expand the scale of its operations without changing its asset beta? Assume a risk-free interest rate of 5% and a market risk premium of 6%. Ignore taxes. . WACC* A company is 40% financed by risk-free debt. The interest rate is 10%, the expected market risk premium is 8%, and the bela of the company’s common stock is .5. Whalt is the after-tax WACC, assuming that the company pays tax at a 20% rate? . WACC Binomial Tree Farm’s financing includes $5 million of bank loans. Its common equity is shown in Binomial’s Annual Report at $6.67 million. It has 500,000 shares of com- mon stock outstanding, which trade on the Wichita Stock Exchange at $18 per share. What debt ratio should Binomial use to calculate its WACC or asset beta? Explain. . Measuring risk Refer to the top-right panel of Figure 9.2. What proportion of U.S. Steel’s returns was explained by market movements? What proportion of risk was diversifiable? How does the diversifiable risk show up in the plot? What is the range of possible errors in the estimated beta? . Measuring risk Figure 9.4 shows plots of monthly rates of return on three stocks versus those of the market index. The beta and standard deviation of each stock is given beside the plot. a. Which stock is safest for a diversified investor? b. Which stock is safest for an undiversified investor who puts all her money in one of these stocks? . Consider a portfolio with equal investments in each stock. What would be this portfolio’s beta? d. Consider a well-diversified portfolio composed of stocks with the same beta and standard deviation as Ford. What are the beta and standard deviation of this portfolio’s return? The standard deviation of the market portfolio’s return is 20%. @] . Use the capital assel pricing model 1o estimate the expectled return on each stock. The risk-free rate is 4%, and the market risk premium is 8%. o

Chapter 9 Risk and the Cost of Capital 251 ! 1 252 IBM Newmont B=0.10 o=42.2% D FIGURE 9.4 11. Measuring risk* The following table shows estimates of the risk of two well-known Cana- dian stocks: _ Standard : ndard Error CELL LA a of Beta Sun Life Financial 18.7 0.12 0.86 0.30 Loblaw 19.5 0.06 0.63 0.33 a. What proportion of each stock’s risk was market risk, and what proportion was specific risk? . What is the variance of the returns for Sun Life Financial stock? What is the specific variance? o c. What is the confidence interval on Loblaw’s beta? (See page 234 for a definition of “con- fidence interval.”) oL . If the CAPM is correct, what is the expected return on Sun Life? Assume a risk-free inter- est rate of 5% and an expected market return of 12%. . Suppose that next year, the market provides a 20% return. Knowing this, what return would you expect from Sun Life? o Part Two Risk 12. Measuring risk Look again at Table 9.1. This time we will concentrate on Union Pacific. a. Calculate Union Pacific’s cost of equity from the CAPM using its own beta estimate and the industry beta estimate. How different are your answers? Assume a risk-free rate of 2% and a market risk premium of 7%. b. Can you be confident that Union Pacific’s true beta is not the industry average? c. Under what circumstances might you advise Union Pacific to calculate its cost of equity based on its own beta estimate? d. You now discover that the estimated beta for Union Pacific in the period 2008-2012 was 1.3. Does this influence your answer to part (c)? . Asset betas Which of these projects is likely to have the higher asset beta, other things equal? Why? a. The sales force for project A is paid a fixed annual salary. Project B’s sales force is paid by commissions only. b. Project C is a first-class-only airline. Project D is a well-established line of breakfast cereals. . Asset betas* EZCUBE Corp. is 50% financed with long-term bonds and 50% with common equity. The debt securities have a beta of .15. The company’s equity beta is 1.25. What is EZCUBE’s asset beta? . Asset betas What types of firms need to estimate industry asset betas? How would such a firm make the estimate? Describe the process step by step. . Betas and operating leverage You run a perpetual encabulator machine, which generates revenues averaging $20 million per year. Raw material costs are 50% of revenues. These costs are variable—they are always proportional to revenues. There are no other operating costs. The cost of capital is 9%. Your firm’s long-term borrowing rate is 6%. Now you are approached by Studebaker Capital Corp., which proposes a fixed-price contract to supply raw materials at $10 million per year for 10 years. a. What happens to the operating leverage and business risk of the encabulator machine if you agree to this fixed-price contract? b. Calculate the present value of the encabulator machine with and without the fixed-price contract. . Diversifiable risk Many investment projects are exposed to diversifiable risks. What does “diversifiable” mean in this context? How should diversifiable risks be accounted for in proj- ect valuation? Should they be ignored completely? . Fudge factors John Barleycorn estimates his firm’s after-tax WACC at only 8%. Neverthe- less, he sets a 15% companywide discount rate to offset the optimistic biases of project spon- sors and to impose “discipline” on the capital budgeting process. Suppose Mr. Barleycorn is correct about the project sponsors, who are, in fact, optimistic by 7% on average. Explain why the increase in the discount rate from 8% to 15% will not offset the bias. . Fudge factors Mom and Pop Groceries has just dispatched a year’s supply of groceries to the government of the Central Antarctic Republic. Payment of $250,000 will be made one year hence after the shipment arrives by snow train. Unfortunately, there is a good chance of a coup d’état, in which case the new government will not pay. Mom and Pop’s controller there- fore decides to discount the payment at 40%rather than at the company’s 12% cost of capital. a. What’s wrong with using a 40% rate to offset political risk? b. How much is the $250,000 payment really worth if the odds of a coup d’état are 25%? . Fudge factors* An oil company is drilling a series of new wells on the perimeter of a pro- ducing oil field. About 20% of the new wells will be dry holes. Even if a new well strikes oil, there is still uncertainty about the amount of oil produced: 40% of new wells that strike oil produce only 1,000 barrels a day; 60% produce 5,000 barrels per day.

21. 22, 23. Chapter 9 Risk and the Cost of Capital . Forecast the annual cash revenues from a new perimeter well. Use a future oil price of $100 per barrel. . A geologist proposes to discount the cash flows of the new wells at 30% to offset the risk of dry holes. The oil company’s normal cost of capital is 10%. Does this proposal make sense? Briefly explain why or why not. =¥ o Certainty equivalents* A project has a forecasted cash flow of $110 in year 1 and $121 in year 2. The interest rate is 5%, the estimated risk premium on the market is 10%, and the project has a beta of .5. If you use a constant risk-adjusted discount rate, what is a. The PV of the project? b. The certainty-equivalent cash flow in year 1 and year 2? c. The ratio of the certainty-equivalent cash {lows to the expected cash {lows in years 1 and 2? Certainty equivalents A project has the following forecasted cash flows: Cash Flows ($ thousands Co C c, Cs -100 +40 +60 +50 I The estimated project beta is 1.5. The market return r,, is 16%, and the risk-free rate ryis 7%. a. Estimate the opportunity cost of capital and the project’s PV (using the same rate to dis- count each cash flow). o . What are the certainty-equivalent cash flows in each year? c. What is the ratio of the certainty-equivalent cash {low to the expected cash flow in each year? d. Explain why this ratio declines. Changing risk The McGregor Whisky Company is proposing to market diet scotch. The product will first be test-marketed for two years in southern California at an initial cost of $500,000. This test launch is not expected to produce any profits but should reveal consumer preferences. There is a 60% chance that demand will be satisfactory. In this case, McGregor will spend $5 million to launch the scotch nationwide and will receive an expected annual profit of $700,000 in perpetuity. If demand is not satisfactory, diet scotch will be withdrawn. Once consumer preferences are known, the product will be subject to an average degree of risk, and therefore, McGregor requires a return of 12% on its investment. However, the initial test-market phase is viewed as much riskier, and McGregor demands a return of 20% on this initial expenditure. What is the NPV of the diet scotch project? CHALLENGE 24. 25. Beta of costs Suppose that you are valuing a future stream of high-risk (high-beta) cash outflows. High risk mcans a high discount ratc. But the higher the discount rate, the less the present value. This seems to say that the higher the risk of cash outflows, the less you should worry about them! Can that be right? Should the sign of the cash flow affect the appropriate discount rate? Explain. Fudge factors An oil company executive is considering investing $10 million in one or both of two wells: Well 1 is expected to produce oil worth $3 million a year for 10 years; well 2 is expected to produce $2 million for 15 years. These are real (inflation-adjusted) cash {lows. The beta for producing wells is .9. The market risk premium is 8%, the nominal risk-free interest rate is 6%, and expected inflation is 4%. 253 ! 1 254 Part Two FINANCE ON THE WEB Risk The two wells are intended to develop a previously discovered oil field. Unfortunately there is still a 20% chance of a dry hole in each case. A dry hole means zero cash flows and a complete loss of the $10 million investment. Ignore taxes and make further assumptions as necessary. a. What is the correct real discount rate for cash flows from developed wells? b. The oil company executive proposes to add 20 percentage points to the real discount rate to offset the risk of a dry hole. Calculate the NPV of each well with this adjusted discount rate. c. What do you say the NPVs of the two wells are? d. Isthere any single fudge factor that could be added to the discount rate for developed wells that would yield the correct NPV for both wells? Explain. You can download data for the following questions from finance.yahoo.com. 1. Look at the companies listed in Table 8.2. Calculate monthly rates of return for two succes- sive five-year periods. Calculate betas for each subperiod using the Excel SLOPE function. How stable was each company’s beta? Suppose that you had used these betas to estimate expected rates of return from the CAPM. Would your estimates have changed significantly from period to period? 2. Identify a sample of food companies. For example, you could try Campbell Soup (CPB), General Mills (GIS), Kellogg (K), Mondelez International (MDLZ), and Tyson Foods (TSN). a. Estimate beta and R? for each company, using five years of monthly returns and Excel functions SLOPE and RSQ. b. Average the returns for each month to give the return on an equally weighted portfolio of the stocks. Then calculate the industry beta using these portfolio returns. How does the R? of this portfolio compare with the average R* of the individual stocks? c. Use the CAPM to calculate an average cost of equity (requiry) for the food industry. Use current interest rates—take a look at the end of Section 9-2—and a reasonable estimate of the market risk premium. The Jones Family Incorporated The Scene: 1t is early evening in the summer of 2018, in an ordinary family room in Manhat- tan. Modern furniture, with old copies of The Wall Street Journal and the Financial Times scat- tered around. Autographed photos of Jerome Powell and George Soros are prominently displayed. A picture window reveals a distant view of lights on the Hudson River. John Jones sits at a com- puter terminal, glumly sipping a glass of chardonnay and putting on a carry trade in Japanese yen over the Internet. His wife Marsha enters. Marsha: Hi, honey. Glad to be home. Lousy day on the trading floor, though. Dullsville. No vol- ume. But I did manage to hedge next year’s production from our copper mine. I couldn’t get a good quote on the right package of futures contracts, so I arranged a commodity swap. John doesn’t reply.

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