# Answers to Chapter Review and Self-Test Problems

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1 CHAPTER 15 Cost of Capital 517 Chapter Review and Self-Test Problems 15.1 Calculating the Cost of Equity Suppose stock in Watta Corporation has a beta of.80. The market risk premium is 6 percent, and the risk-free rate is 6 percent. Watta s last dividend was \$1.20 per share, and the dividend is expected to grow at 8 percent indefinitely. The stock currently sells for \$45 per share. What is Watta s cost of equity capital? 15.2 Calculating the WACC In addition to the information given in the previous problem, suppose Watta has a target debt-equity ratio of 50 percent. Its cost of debt is 9 percent, before taxes. If the tax rate is 35 percent, what is the WACC? 15.3 Flotation Costs Suppose in the previous problem Watta is seeking \$30 million for a new project. The necessary funds will have to be raised externally. Watta s flotation costs for selling debt and equity are 2 percent and 16 percent, respectively. If flotation costs are considered, what is the true cost of the new project? Answers to Chapter Review and Self-Test Problems 15.1 We start off with the SML approach. Based on the information given, the expected return on Watta s common stock is: R E R f E (R M R f ) 6%.80 6% 10.80% We now use the dividend growth model. The projected dividend is D 0 (1 g) \$ \$1.296, so the expected return using this approach is: R E D 1 /P 0 g \$1.296/ % Because these two estimates, percent and percent, are fairly close, we will average them. Watta s cost of equity is approximately percent Because the target debt-equity ratio is.50, Watta uses \$.50 in debt for every \$1 in equity. In other words, Watta s target capital structure is 1/3 debt and 2/3 equity. The WACC is thus: WACC (E/V) R E (D/V) (1 T C ) 2/ % 1/3 9% (1.35) 9.177%% 15.3 Because Watta uses both debt and equity to finance its operations, we first need the weighted average flotation cost. As in the previous problem, the percentage of equity financing is 2/3, so the weighted average cost is: f A (E/V) f E (D/V) f D 2/3 16% 1/3 2% 11.33% If Watta needs \$30 million after flotation costs, then the true cost of the project is \$30 million/(1 f A ) \$30 million/.8867 \$33.83 million.

3 CHAPTER 15 Cost of Capital 519 Dow has a beta of 1.25, whereas Superior has a beta of.75. The expected risk premium on the market is 8 percent, and risk-free bonds are yielding 12 percent. Should either company proceed? Should both? Explain. 10. Divisional Cost of Capital Under what circumstances would it be appropriate for a firm to use different costs of capital for its different operating divisions? If the overall firm WACC were used as the hurdle rate for all divisions, would the riskier divisions or the more conservative divisions tend to get most of the investment projects? Why? If you were to try to estimate the appropriate cost of capital for different divisions, what problems might you encounter? What are two techniques you could use to develop a rough estimate for each division s cost of capital? 1. Calculating Cost of Equity The Wind Rider Co. just issued a dividend of \$2.10 per share on its common stock. The company is expected to maintain a constant 7 percent growth rate in its dividends indefinitely. If the stock sells for \$40 a share, what is the company s cost of equity? 2. Calculating Cost of Equity The Tubby Ball Corporation s common stock has a beta of If the risk-free rate is 5 percent and the expected return on the market is 12 percent, what is Tubby Ball s cost of equity capital? 3. Calculating Cost of Equity Stock in Parrothead Industries has a beta of The market risk premium is 8 percent, and T-bills are currently yielding 5.5 percent. Parrothead s most recent dividend was \$2.20 per share, and dividends are expected to grow at a 5 percent annual rate indefinitely. If the stock sells for \$32 per share, what is your best estimate of Parrothead s cost of equity? 4. Estimating the DCF Growth Rate Suppose Massey Ltd. just issued a dividend of \$.68 per share on its common stock. The company paid dividends of \$.40, \$.45, \$.52, and \$.60 per share in the last four years. If the stock currently sells for \$12, what is your best estimate of the company s cost of equity capital? 5. Calculating Cost of Preferred Stock Holdup Bank has an issue of preferred stock with a \$5 stated dividend that just sold for \$92 per share. What is the bank s cost of preferred stock? 6. Calculating Cost of Debt Legend, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 12 years to maturity that is quoted at 107 percent of face value. The issue makes semiannual payments and has an embedded cost of 10 percent annually. What is Legend s pretax cost of debt? If the tax rate is 35 percent, what is the aftertax cost of debt? 7. Calculating Cost of Debt Jiminy s Cricket Farm issued a 30-year, 9 percent semiannual bond 8 years ago. The bond currently sells for 105 percent of its face value. The company s tax rate is 35 percent. a. What is the pretax cost of debt? b. What is the aftertax cost of debt? c. Which is more relevant, the pretax or the aftertax cost of debt? Why? 8. Calculating Cost of Debt For the firm in Problem 7, suppose the book value of the debt issue is \$20 million. In addition, the company has a second debt issue on the market, a zero coupon bond with seven years left to maturity; the book value of this issue is \$70 million and the bonds sell for 61 percent of par. Questions and Problems Basic (Questions 1 19)

4 520 PART SIX Cost of Capital and Long-Term Financial Policy Basic (continued ) What is the company s total book value of debt? The total market value? What is your best estimate of the aftertax cost of debt now? 9. Calculating WACC Mullineaux Corporation has a target capital structure of 50 percent common stock, 5 percent preferred stock, and 45 percent debt. Its cost of equity is 18 percent, the cost of preferred stock is 6.5 percent, and the cost of debt is 8 percent. The relevant tax rate is 35 percent. a. What is Mullineaux s WACC? b. The company president has approached you about Mullineaux s capital structure. He wants to know why the company doesn t use more preferred stock financing, since it costs less than debt. What would you tell the president? 10. Taxes and WACC Modigliani Manufacturing has a target debt-equity ratio of.75. Its cost of equity is 18 percent and its cost of debt is 10 percent. If the tax rate is 35 percent, what is Modigliani s WACC? 11. Finding the Target Capital Structure Fama s Llamas has a weighted average cost of capital of 12.5 percent. The company s cost of equity is 15 percent and its cost of debt is 8 percent. The tax rate is 35 percent. What is Fama s target debt-equity ratio? 12. Book Value versus Market Value Filer Manufacturing has 8.2 million shares of common stock outstanding. The current share price is \$52, and the book value per share is \$5. Filer Manufacturing also has two bond issues outstanding. The first bond issue has a face value of \$70 million, an 8 percent coupon, and sells for 104 percent of par. The second issue has a face value of \$50 million, a 7.5 percent coupon, and sells for 97 percent of par. The first issue matures in 10 years, the second in 6 years. a. What are Filer s capital structure weights on a book value basis? b. What are Filer s capital structure weights on a market value basis? c. Which are more relevant, the book or market value weights? Why? 13. Calculating the WACC In Problem 12, suppose the most recent dividend was \$4 and the dividend growth rate is 6 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 35 percent. What is the company s WACC? 14. WACC Sniffles, Inc., has a target debt-equity ratio of.90. Its WACC is 13 percent, and the tax rate is 35 percent. a. If Sniffles cost of equity is 18 percent, what is its pretax cost of debt? b. If instead you know that the aftertax cost of debt is 7.5 percent, what is the cost of equity? 15. Finding the WACC Given the following information for Dunhill Power Co., find the WACC. Assume the company s tax rate is 35 percent. Debt: 3,000 8 percent coupon bonds outstanding, \$1,000 par value, 20 years to maturity, selling for 103 percent of par; the bonds make semiannual payments. Common stock: 90,000 shares outstanding, selling for \$45 per share; the beta is Preferred stock: 13,000 shares of 7 percent preferred stock outstanding, currently selling for \$108 per share. Market: 8 percent market risk premium and 6 percent risk-free rate.

5 CHAPTER 15 Cost of Capital Finding the WACC Titan Mining Corporation has 8 million shares of common stock outstanding,.5 million shares of 6 percent preferred stock outstanding, and 100,000 9 percent semiannual bonds outstanding, par value \$1,000 each. The common stock currently sells for \$32 per share and has a beta of 1.15, the preferred stock currently sells for \$67 per share, and the bonds have 15 years to maturity and sell for 91 percent of par. The market risk premium is 10 percent, T-bills are yielding 5 percent, and Titan Mining s tax rate is 35 percent. a. What is the firm s market value capital structure? b. If Titan Mining is evaluating a new investment project that has the same risk as the firm s typical project, what rate should the firm use to discount the project s cash flows? 17. SML and WACC An all-equity firm is considering the following projects: Basic (continued ) Project Beta Expected Return W.70 11% X Y Z The T-bill rate is 5 percent, and the expected return on the market is 12 percent. a. Which projects have a higher expected return than the firm s 12 percent cost of capital? b. Which projects should be accepted? c. Which projects would be incorrectly accepted or rejected if the firm s overall cost of capital were used as a hurdle rate? 18. Calculating Flotation Costs Suppose your company needs \$6 million to build a new assembly line. Your target debt-equity ratio is 1.0. The flotation cost for new equity is 15 percent, but the flotation cost for debt is only 4 percent. Your boss has decided to fund the project by borrowing money, because the flotation costs are lower and the needed funds are relatively small. a. What do you think about the rationale behind borrowing the entire amount? b. What is your company s weighted average flotation cost? c. What is the true cost of building the new assembly line after taking flotation costs into account? Does it matter in this case that the entire amount is being raised from debt? 19. Calculating Flotation Costs Western Alliance Company needs to raise \$12 million to start a new project and will raise the money by selling new bonds. The company has a target capital structure of 60 percent common stock, 10 percent preferred stock, and 30 percent debt. Flotation costs for issuing new common stock are 12 percent, for new preferred stock, 6 percent, and for new debt, 4 percent. What is the true initial cost figure Western should use when evaluating its project? 20. WACC and NPV Sallinger, Inc., is considering a project that will result in initial aftertax cash savings of \$4 million at the end of the first year, and these savings will grow at a rate of 5 percent per year indefinitely. The firm has a target debt-equity ratio of.75, a cost of equity of 16 percent, and an aftertax cost of debt of 6 percent. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and Intermediate (Questions 20 21)

8 524 PART SIX Cost of Capital and Long-Term Financial Policy Treasury bills? Assuming a 9.1 percent market risk premium, what is the cost of equity for Dell using CAPM? 15.3 Cost of Debt You now need to calculate the cost of debt for Dell. Go to follow the Bond Search link, and the Corporate link. Enter Dell as the company and find the yield to maturity for each of Dell s bonds. What is the weighted average cost of debt for Dell using the book value weights and using the market value weights? Does it make a difference if you use book value weights or market value weights? 15.4 WACC You now have all the necessary information to calculate the weighted average cost of capital for Dell. Calculate the weighted average cost of capital for Dell using book value weights and market value weights assuming Dell has a 35 percent marginal tax rate. Which number is more relevant? A B C D E F G H 1 2 Using a spreadsheet for time value of money calculations 3 4 If we invest \$25,000 at 12 percent, how long until we have \$50,000? We need to solve 5 for the unknown of periods, so we use the formal NPER (rate, pmt, pvfv) 6 7 Present Value (pv) \$25,000 8 Future Value (fv) \$50,000 9 Rate (rate) Periods: The formal entered in cell B 10 is = NPER: notice that pmt is zero and that pv 14 has a negative sign on it. Also notice that rate is entered as decimal, not a percentage. Spreadsheet Templates 15 4, 15 10, 15 23

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