Chapter_15_Q&P.ppt

Chapter 15•Cost of Capital McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All Questions and Problems • 1. With the information given, we can find the cost of equity using the dividend growth model. Using this model, the cost of equity is: • RE = [420(1.06)/ 6500] + .06 = .1285 or 12.85% (See Eq. 15.1) • 2. Calculating Cost of Equity • The Tubby Ball Corporation's common stock has a beta of 1.2. If the risk-free rate is 4.5 percent and the expected return on the market is 13 percent, what is Tubby Ball's cost of equity capital? • 2. Here we have information to calculate the cost of equity using the CAPM. The cost of equity is: • RE = .045 + 1.20 (.12 – .045) = .1470 or 14.70% 80 per share. The market risk premium is 8 percent. and T-bills are currently yielding 4 percent. what is your best estimate of Parrothead's cost of equity? . Calculating Cost of Equity • Stock in Parrothead Industries has a beta of 1. and dividends are expected to grow at a 5 percent annual rate indefinitely.15. Parrothead's most recent dividend was $1.• 3. If the stock sells for $34 per share. • 3.1056 or 10. Using the CAPM.05)/$34] + .04 + 1.56% .80(1. we find: • RE = .08) = .1320 or 13.20% • And using the dividend growth model. We have the information available to calculate the cost of equity using the CAPM and the dividend growth model.05 = . the cost of equity is • RE = [$1.15(. we will use the average of the two. and the estimate from the dividend growth model is about one percent lower than the historical average.1320 + . Given this.1188 or 11.• Both estimates of the cost of equity seem reasonable. the estimate from the CAPM model is about one percent higher than average.1056)/2 = .88% . If we remember the historical return on large capitalization stocks. so: • RE = (. so we cannot definitively say one of the estimates is incorrect. 00 per share in the last four years. a company based in New Zealand. If the stock currently sells for $52. Estimating the DCF Growth Rate • Suppose Massey Ltd. $. and $1. $.. just issued a dividend of $1.91.78. The company paid dividends of $. what is your best estimate of the company's cost of equity capital using the arithmetic average growth rate in dividends? What if you use the geometric average growth rate? .22 per share on its common stock.• 4.93. we find the cost of equity is: • RE = [$1. the increase in dividends each year was: • g1 = ($.93 = .91 = .1473 or 14.0220 or 2.93 – .10% • Using this growth rate in the dividend growth model.1210 = .00 = .67% • g2 = ($.00 – . we first need to find the growth rate in dividends.1667 or 16.1210)/$52.0753 + .93)/$.91)/$.0753 or 7. To use the dividend growth model.73% .22 – 1.1667 + .53% • g4 = ($1.2200)/4 = .78 = .00% • So.00)/$1.1210 or 12.00] + .20% • g3 = ($1.22(1.78)/$.• 4. So.91 – .2200 or 22. the average arithmetic growth rate in dividends was: • g = (.0220 + . 1183)/$52.1183 or 11.22(1.22 = $0.00] + . we find: $1.46% .83% The cost of equity using the geometric dividend growth rate is: RE = [$1.• • • • • Calculating the geometric growth rate in dividends.78(1 + g)4 g = .1183 = 14. What is the bank's cost of preferred stock? .• 5. Calculating Cost of Preferred Stock • Nanning Bank has an issue of preferred stock with a 48 yuan stated dividend that just sold for 725 yuan per share. so: • • RP = CNY 48/CNY 725 = . The cost of preferred stock is the dividend payment divided by the price.62% .0662 or 6.• 5. • 6. what is the after tax cost of debt? . What is Minsk's pretax cost of debt? If the tax rate is 35 percent. The firm has a debt issue outstanding with 12 years to maturity that is quoted at 104 percent of face value. The issue makes semiannual payments and has an embedded cost of 8 percent annually. Calculating Cost of Debt • Minsk Diamonds is trying to determine its cost of debt. 0487 or 4.87% .745% • YTM = 2 × 3.49% • • And the aftertax cost of debt is: • RD = .0749(1 – .04)) • Coupon = 40 (1.000*8%*0.040 (1. The pretax cost of debt is the YTM of the company’s bonds.5) • T=24 • R = 3.000*(1+0.745% = 7.• 6.35) = . so: • P0 = RUR 1. What is the pretax cost of debt? • b. the pretax or the after tax cost of debt? Why? . The bond currently sells for 108 percent of its face value. • a. Calculating Cost of Debt • Moldova Beef Farm issued a 25-year. What is the aftertax cost of debt? • c. Which is more relevant. The company's tax rate is 35 percent.• 7. 9 percent semiannual bond 7 years ago. 15% • b.• 7.0529 or 5. .The pretax cost of debt is the YTM of the company’s bonds.080 • Coupon = 45 (1.5) • T=(25-7)*2 • R = 4.0815(1 – . The after-tax rate is more relevant because that is the actual cost to the company.075% • YTM = 2 × 4.35) = .000*9%*0. a.29% • c.075% = 8. The aftertax cost of debt is: • RD = . so: • P0 = $1. Calculating Cost of Debt • For the firm in Problem 7. In addition. the company has a second debt issue on the market. What is the company's total book value of debt? The total market value? What is your best estimate of the after tax cost of debt now? . a zero coupon bond with seven years left to maturity.• 8. suppose the book value of the debt issue is 50 million lei. the book value of this issue is 170 million lei and the bonds sell for 58 percent of par. 08* 50M + .• 8. we find the price of the bonds and multiply by the number of bonds.58*170M = 152. Alternatively. Doing so. we find: • MVD = 1. we can multiply the price quote of the bond times the par value of the bonds. so: • BVD = 50M + 170M = 220M • To find the market value of debt. The book value of debt is the total par value of all outstanding debt.6M . 35) = .0809(1 – .26% .0526 or 5.09% So. the after tax cost of the zero coupon bonds is: • RZ = .• • • • • The YTM of the zero coupon bonds is: PZ = 580 = 1.000 T=7 R = 8. 0527 or 5. We need to use the market value weights of the bonds.• The after tax cost of debt for the company is the weighted average of the after tax cost of debt for all outstanding bond issues.6) = .0529*(54/152.0526*(98.6) + .6/ 152. The total after tax cost of debt for the company is: • RD = .27% . 5 percent. Its cost of equity is 16 percent. and the cost of debt is 9 percent. • a. What would you tell the president? . What is Mullineaux's WACC? • b. The company president has approached you about Mullineaux's capital structure. 10 percent preferred stock. Calculating WACC • Mullineaux Corporation has a target capital structure of 50 percent common stock. The relevant tax rate is 35 percent. He wants to know why the company doesn't use more preferred stock financing. since it costs less than debt. the cost of preferred stock is 7. and 40 percent debt.• 9. 40(.35) = .09(1 – . debt is cheaper than the preferred stock. we must look at the after-tax cost of debt. we find: • WACC = . .09) (1 – . Using the equation to calculate the WACC. Since interest is tax deductible and dividends are not. a.075) + . on an after-tax basis.1109 or 11. which is: • • .• 9.85% • Hence.09% • b.0585 or 5.10(.50(.16) + .35) = . Its cost of equity is 18 percent and its cost of debt is 10 percent. Taxes and WACC • Oman Manufacturing has a target debtequity ratio of . If the tax rate is 35 percent.• 10. what is Oman's WACC? .70. Doing so.26% .Here we need to use the debt-equity ratio to calculate the WACC.• 10.10(.35) = .70) + .18(1/1. we find: • WACC = .70)(1 – .1326 or 13.70/1. Finding the Target Capital Structure • Sao Paulo Llamas has a weighted average cost of capital of 11.• 11.5 percent. What is Captain's target debtequity ratio? . The tax rate is 35 percent. The company's cost of equity is 15 percent and its cost of debt is 9 percent. 15 + .35) • Rearranging the equation.1150 = .15 + . we find: • WACC = . Setting up the WACC equation. Here we have the WACC and need to find the debtequity ratio of the company.0350 • D/E = .09(.0565(D/E) = .09(D/V)(1 – .65)(D/E) • Now we must realize that the V/E is just the equity multiplier.115(V/E) = .• 11.115(D/E + 1) = .15(E/V) + . we find: • .6195 .0585(D/E) • Now we can solve for D/E as: • . which is equal to: • V/E = 1 + D/E • . • 15. EGP 1.000 shares outstanding. selling for 105 percent of par. • Market: 8 percent market risk premium and 6 percent risk-free rate. • Common stock: 90. the beta is 1. • Preferred stock: 13. selling for EGP 60 per share. the bonds make semiannual payments. Assume the company's tax rate is 35 percent. currently selling for EGP 110 per share. • Debt: 4.000 par value.10. . 20 years to maturity.000 shares of 6 percent preferred stock outstanding. Finding the WACC • Given the following information for Alexandria Power Company find the WACC.000 7 percent coupon bonds outstanding. 12M + 5.12M • MVE = 90. We find: • • MVD = 4.03) = EGP 4.430M = EGP 10.95M .40M + 1.000(EGP 110) = EGP 1.000(EGP 60) = EGP 5. We will begin by finding the market value of each type of financing.430M • And the total market value of the firm is: • V = EGP 4.• 15.000)(1.000(EGP 1.40M • MVP = 13. 80% .10(.06 + 1. we can find the cost of equity using the CAPM.• Now.08) = . The cost of equity is: • RE = .1480 or 14. 030 = Coupon= 1.35)(.0437 or 4.36% × 2 = 6.• • • • • • • • The cost of debt is the YTM of the bonds.5 T=40 R = 3.0672) = .72% And the aftertax cost of debt is: RD = (1 – .000*7%*0.37% . so: P0 = EGP 1.36% YTM = 3. • • The cost of preferred stock is: RP = EGP 6/EGP 110 = .0546 or 5.46% . 0437(4. 1480(5. The WACC is: • WACC = .12/10.40/10.95) + . . We simply used the aftertax cost of debt in the equation.57% • Notice that we didn’t include the (1 – tC) term in the WACC equation.95) = 9. so the term is not needed here.0546(1.• Now we have all of the components to calculate the WACC.43/10.95) + . Which projects would be incorrectly accepted or rejected if the firm's overall cost of capital were used as a hurdle rate? . SML and WACC • An all-equity firm is considering the following projects: The T-bill rate is 5 percent. and the expected return on the market is 13 percent. • a.• 17. Which projects have a higher expected return than the firm's 12 percent cost of capital? • b. Which projects should be accepted? • c. . Y and Z.0980 < . If the return calculated using the CAPM is higher than the project expected return. After considering risk via the CAPM: E[W] = .16. so reject Y E[Z] = .13 – .13 – . we should accept the project.05) = .05 + 1.20(. so reject Z Project W would be incorrectly rejected.13.05) = .13 – . This expected return should then be compared to the expected return of the project. we reject the project.1860 > .1220 < .90(. b. Using the CAPM to consider the projects.13 – .60(. Projects Y and Z would be incorrectly accepted. if not. a. we need to calculate the expected return of the project given its level of risk. Projects X.05) = .05 + .• • • • • • • 17.11.05) = .70(. .05 + .14.05 + 1.1460 > . so accept W E[X] = . so accept X E[Y] = . • a. Calculating Flotation Costs • Suppose your company needs 15 million Czech koruny to build a new assembly line. What is your company's weighted average flotation cost? • c. The notation cost for new equity is 10 percent.• 18. 90. but the flotation cost for debt is only 4 percent. because the flotation costs are lower and the needed funds are relatively small. What do you think about the rationale behind borrowing the entire amount? • b. 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? . Your target debt-equity ratio is . Your boss has decided to fund the project by borrowing money. 9) = .• 18.9) + . The weighted average floatation cost is the weighted average of the floatation costs for debt and equity.20% .9/1.04(. • b. He should look at the weighted average flotation cost. not just the debt cost.072 or 7.10(1/1.a. so: • fT = . .463 • Even if the specific funds are actually being raised completely from debt.072) = 15M • Amount raised = 15M/(1 – .072) = 16. should be valued as if the firm’s target capital structure is used.• c. The total cost of the equipment including floatation costs is: • Amount raised(1 – . and hence true investment cost.156. the flotation costs. What is the true initial cost figure Southern should use when evaluating its project? . 7 percent. and for new debt. 4 percent. for new preferred stock. and 20 percent debt. The company has a target capital structure of 60 percent common stock.• 19. Flotation costs for issuing new common stock are 11 percent. Calculating Flotation Costs • Romania Alliance Company needs to raise 25 million lei to start a new project and will raise the money by selling new bonds. 20 percent preferred stock. Doing so. we find: • fT = .0880) = 27.8% • And the total cost of the equipment including floatation costs is: • Amount raised(1 – .04) = .20(.11) + .20(.08800) = 25M • Amount raised = 25M/(1 – .• 19.412.We first need to find the weighted average floatation cost.088 or 8.07) + .60(.281 . management uses the subjective approach and applies an adjustment factor of +2 percent to the cost of capital for such risky projects. Under what circumstances should Davao take on the project? . a cost of equity of 15 percent. and an after tax cost of debt of 5. The firm has a target debt-equity ratio of .5 percent.• WACC and NPV • Davao Timber. and these savings will grow at a rate of 5 percent per year indefinitely.65. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes. is considering a project that will result in initial aftertax cash savings of 4.0 million Philippine pesos at the end of the first year. 26% + 2.65)(.• 20. we need to adjust the project discount rate for the additional risk.26% • Since the project is riskier than the company.Using the debt-equity ratio to calculate the WACC.26% .65/1. we find: • WACC = (. 1126 or 11.15) = .00% = 13.65)(.055) + (1/1. we find: • Project discount rate = 11. Using the subjective risk factor given. If you remember.• We would accept the project if the NPV is positive. The NPV is the PV of the cash outflows plus the PV of the cash inflows. so: • PV of future CF = PHP 4. we just need to find the PV of inflows.1326 – . Since we have the costs.000/(.367 .440.05) = PHP 48. the equation for the PV of a growing perpetuity is the same as the dividend growth equation.000. The cash inflows are a growing perpetuity. .• The project should only be undertaken if its cost is less than PHP 48.440.367 since costs less than this amount will result in a positive NPV. In addition.000 in flotation costs. The project cost $2. Inc. what is the company's target debt-equity ratio? .1 million and the company paid $128.• 21.5 percent of the amount raised.. whereas the debt issued had a flotation cost of 2. the equity issued had a flotation cost of 7 percent of the amount raised. Flotation Costs Knight. If Knight issued new securities in the same proportion as its target capital structure. recently issued new securities to finance a new TV show. 1M + 128.228M • Using the equation to calculate the total cost including floatation costs.1M • fT = .• 21.The total cost of the equipment including floatation costs was: • Total costs = $2.0575 or 5.75% .228M(1 – fT) = $2.000 = $2. we get: • Amount raised(1 – fT) = Amount needed after floatation costs • $2. 07 + .07(E/V) + .0575(V/E) = .• Now.0575 = . we know the weighted average floatation cost.025(D/V) • We can solve this equation to find the debt-equity ratio as follows: • .025(D/E) . The equation to calculate the percentage floatation costs is: • fT = . • We must recognize that the V/E term is the equity multiplier. which is (1 + D/E).3867 .025(D/E) • D/E = . so: • .07 + .0575(D/E + 1) = . Chapter 15 •End of Chapter McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies. Inc. All .