Chapter

McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.

15

•Cost of Capital•Cost of Capital

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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)

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• 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?

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• 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%

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• 3. Calculating Cost of Equity• Stock in Parrothead Industries has a beta

of 1.15. The market risk premium is 8 percent, and T-bills are currently yielding 4 percent. Parrothead's most recent dividend was $1.80 per share, and dividends are expected to grow at a 5 percent annual rate indefinitely. If the stock sells for $34 per share, what is your best estimate of Parrothead's cost of equity?

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• 3. We have the information available to calculate the cost of equity using the CAPM and the dividend growth model. Using the CAPM, we find:

• RE = .04 + 1.15(.08) = .1320 or 13.20%

• And using the dividend growth model, the cost of equity is

• RE = [$1.80(1.05)/$34] + .05 = .1056 or 10.56%

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• Both estimates of the cost of equity seem reasonable. If we remember the historical return on large capitalization stocks, the estimate from the CAPM model is about one percent higher than average, and the estimate from the dividend growth model is about one percent lower than the historical average, so we cannot definitively say one of the estimates is incorrect. Given this, we will use the average of the two, so:

• RE = (.1320 + .1056)/2 = .1188 or 11.88%

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• 4. Estimating the DCF Growth Rate• Suppose Massey Ltd., a company based in New

Zealand, just issued a dividend of $1.22 per share on its common stock. The company paid dividends of $.78, $.91, $.93, and $1.00 per share in the last four years. If the stock currently sells for $52, 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?

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• 4. To use the dividend growth model, we first need to find the growth rate in dividends. So, the increase in dividends each year was:

• g1 = ($.91 – .78)/$.78 = .1667 or 16.67% • g2 = ($.93 – .91)/$.91 = .0220 or 2.20%• g3 = ($1.00 – .93)/$.93 = .0753 or 7.53%• g4 = ($1.22 – 1.00)/$1.00 = .2200 or 22.00%• So, the average arithmetic growth rate in dividends

was:• g = (.1667 + .0220 + .0753 + .2200)/4 = .1210 or

12.10%• Using this growth rate in the dividend growth

model, we find the cost of equity is:• RE = [$1.22(1.1210)/$52.00] + .1210 = .1473 or

14.73%

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• Calculating the geometric growth rate in dividends, we find:

• $1.22 = $0.78(1 + g)4

• g = .1183 or 11.83%

• The cost of equity using the geometric dividend growth rate is:

• RE = [$1.22(1.1183)/$52.00] + .1183 = 14.46%

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• 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. What is the bank's cost of preferred stock?

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• 5. The cost of preferred stock is the dividend payment divided by the price, so:

•

• RP = CNY 48/CNY 725 = .0662 or 6.62%

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• 6. Calculating Cost of Debt• Minsk Diamonds is trying to determine its

cost of debt. 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. What is Minsk's pretax cost of debt? If the tax rate is 35 percent, what is the after tax cost of debt?

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• 6. The pretax cost of debt is the YTM of the company’s bonds, so:

• P0 = RUR 1,040 (1,000*(1+0.04))• Coupon = 40 (1,000*8%*0.5)• T=24 • R = 3.745%• YTM = 2 × 3.745% = 7.49%•• And the aftertax cost of debt is:• RD = .0749(1 – .35) = .0487 or 4.87%

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• 7. Calculating Cost of Debt• Moldova Beef Farm issued a 25-year, 9

percent semiannual bond 7 years ago. The bond currently sells for 108 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

after tax cost of debt? Why?

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• 7. a.The pretax cost of debt is the YTM of the company’s bonds, so:

• P0 = $1,080 • Coupon = 45 (1,000*9%*0.5)• T=(25-7)*2 • R = 4.075%• YTM = 2 × 4.075% = 8.15%• b. The aftertax cost of debt is:• RD = .0815(1 – .35) = .0529 or

5.29%• c. The after-tax rate is more relevant

because that is the actual cost to the company.

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• 8. Calculating Cost of Debt• For the firm in Problem 7, suppose the book

value of the debt issue is 50 million lei. 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 170 million lei and the bonds sell for 58 percent of par. 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?

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• 8. The book value of debt is the total par value of all outstanding debt, so:

• BVD = 50M + 170M = 220M• To find the market value of debt, we find

the price of the bonds and multiply by the number of bonds. Alternatively, we can multiply the price quote of the bond times the par value of the bonds. Doing so, we find:

• MVD = 1.08* 50M + .58*170M = 152.6M

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• The YTM of the zero coupon bonds is:

• PZ = 580 = 1,000

• T=7

• R = 8.09%

• So, the after tax cost of the zero coupon bonds is:

• RZ = .0809(1 – .35) = .0526 or 5.26%

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• 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. We need to use the market value weights of the bonds. The total after tax cost of debt for the company is:

• RD = .0529*(54/152.6) + .0526*(98.6/ 152.6) = .0527 or 5.27%

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• 9. Calculating WACC• Mullineaux Corporation has a target capital

structure of 50 percent common stock, 10 percent preferred stock, and 40 percent debt. Its cost of equity is 16 percent, the cost of preferred stock is 7.5 percent, and the cost of debt is 9 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?

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• 9. a. Using the equation to calculate the WACC, we find:

• WACC = .50(.16) + .10(.075) + .40(.09)(1 – .35) = .1109 or 11.09%

• b. Since interest is tax deductible and dividends are not, we must look at the after-tax cost of debt, which is:

•• .09(1 – .35) = .0585 or 5.85% • Hence, on an after-tax basis, debt is

cheaper than the preferred stock.

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• 10. Taxes and WACC

• Oman Manufacturing has a target debt-equity ratio of .70. Its cost of equity is 18 percent and its cost of debt is 10 percent. If the tax rate is 35 percent, what is Oman's WACC?

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• 10. Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find:

• WACC = .18(1/1.70) + .10(.70/1.70)(1 – .35) = .1326 or 13.26%

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• 11. Finding the Target Capital Structure

• Sao Paulo Llamas has a weighted average cost of capital of 11.5 percent. The company's cost of equity is 15 percent and its cost of debt is 9 percent. The tax rate is 35 percent. What is Captain's target debt-equity ratio?

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• 11. Here we have the WACC and need to find the debt-equity ratio of the company. Setting up the WACC equation, we find:

• WACC = .1150 = .15(E/V) + .09(D/V)(1 – .35)• Rearranging the equation, we find:• .115(V/E) = .15 + .09(.65)(D/E)• Now we must realize that the V/E is just the equity

multiplier, which is equal to:• V/E = 1 + D/E• .115(D/E + 1) = .15 + .0585(D/E) • Now we can solve for D/E as:• .0565(D/E) = .0350 • D/E = .6195

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• 15. Finding the WACC• Given the following information for Alexandria Power

Company find the WACC. Assume the company's tax rate is 35 percent.

• Debt: 4,000 7 percent coupon bonds outstanding, EGP 1,000 par value, 20 years to maturity, selling for 105 percent of par; the bonds make semiannual payments.

• Common stock: 90,000 shares outstanding, selling for EGP 60 per share; the beta is 1.10.

• Preferred stock: 13,000 shares of 6 percent preferred stock outstanding, currently selling for EGP 110 per share.

• Market: 8 percent market risk premium and 6 percent risk-free rate.

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• 15. We will begin by finding the market value of each type of financing. We find:

• • MVD = 4,000(EGP 1,000)(1.03) = EGP

4.12M • MVE = 90,000(EGP 60) = EGP 5.40M• MVP = 13,000(EGP 110) = EGP 1.430M • And the total market value of the firm is:• V = EGP 4.12M + 5.40M + 1.430M = EGP

10.95M

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• Now, we can find the cost of equity using the CAPM. The cost of equity is:

• RE = .06 + 1.10(.08) = .1480 or 14.80%

15-30

• The cost of debt is the YTM of the bonds, so:

• P0 = EGP 1,030 = • Coupon= 1,000*7%*0.5• T=40 • R = 3.36%• YTM = 3.36% × 2 = 6.72%• And the aftertax cost of debt is:• RD = (1 – .35)(.0672) = .0437 or 4.37%

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• The cost of preferred stock is:

• RP = EGP 6/EGP 110 = .0546 or 5.46%

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• Now we have all of the components to calculate the WACC. The WACC is:

• WACC = .0437(4.12/10.95) + .1480(5.40/10.95) + .0546(1.43/10.95) = 9.57%

• Notice that we didn’t include the (1 – tC) term in the WACC equation. We simply used the aftertax cost of debt in the equation, so the term is not needed here.

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• 17. 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. 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?

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• 17. a. Projects X, Y and Z.• b. Using the CAPM to consider the projects, we need

to calculate the expected return of the project given its level of risk. This expected return should then be compared to the expected return of the project. If the return calculated using the CAPM is higher than the project expected return, we should accept the project, if not, we reject the project. After considering risk via the CAPM:

• E[W] = .05 + .60(.13 – .05) = .0980 < .11, so accept W

• E[X] = .05 + .90(.13 – .05) = .1220 < .13, so accept X

• E[Y] = .05 + 1.20(.13 – .05) = .1460 > .14, so reject Y

• E[Z] = .05 + 1.70(.13 – .05) = .1860 > .16, so reject Z

• Project W would be incorrectly rejected; Projects Y and Z would be incorrectly accepted.

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• 18. Calculating Flotation Costs• Suppose your company needs 15 million Czech koruny to

build a new assembly line. Your target debt-equity ratio is .90. The notation cost for new equity is 10 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?

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• 18. a. He should look at the weighted average flotation cost, not just the debt cost.

• b. The weighted average floatation cost is the weighted average of the floatation costs for debt and equity, so:

• fT = .04(.9/1.9) + .10(1/1.9) = .072 or 7.20%

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• c. The total cost of the equipment including floatation costs is:

• Amount raised(1 – .072) = 15M • Amount raised = 15M/(1 – .072)

= 16,156,463• Even if the specific funds are

actually being raised completely from debt, the flotation costs, and hence true investment cost, should be valued as if the firm’s target capital structure is used.

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• 19. 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. The company has a target capital structure of 60 percent common stock, 20 percent preferred stock, and 20 percent debt. Flotation costs for issuing new common stock are 11 percent, for new preferred stock, 7 percent, and for new debt, 4 percent. What is the true initial cost figure Southern should use when evaluating its project?

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• 19. We first need to find the weighted average floatation cost. Doing so, we find:

• fT = .60(.11) + .20(.07) + .20(.04) = .088 or 8.8%

• And the total cost of the equipment including floatation costs is:

• Amount raised(1 – .08800) = 25M

• Amount raised = 25M/(1 – .0880) = 27,412,281

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• WACC and NPV • Davao Timber, 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, and these savings will grow at a rate of 5 percent per year indefinitely. The firm has a target debt-equity ratio of .65, a cost of equity of 15 percent, and an after tax cost of debt of 5.5 percent. The cost-saving proposal is somewhat riskier than the usual project the firm undertakes; 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?

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• 20. Using the debt-equity ratio to calculate the WACC, we find:

• WACC = (.65/1.65)(.055) + (1/1.65)(.15) = .1126 or 11.26%

• Since the project is riskier than the company, we need to adjust the project discount rate for the additional risk. Using the subjective risk factor given, we find:

• Project discount rate = 11.26% + 2.00% = 13.26%

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• 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. Since we have the costs, we just need to find the PV of inflows. The cash inflows are a growing perpetuity. If you remember, the equation for the PV of a growing perpetuity is the same as the dividend growth equation, so:

• PV of future CF = PHP 4,000,000/(.1326 – .05) = PHP 48,440,367

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• 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.

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• 21. Flotation Costs Knight, Inc., recently issued new securities to finance a new TV show. The project cost $2.1 million and the company paid $128,000 in flotation costs. In addition, the equity issued had a flotation cost of 7 percent of the amount raised, whereas the debt issued had a flotation cost of 2.5 percent of the amount raised. If Knight issued new securities in the same proportion as its target capital structure, what is the company's target debt-equity ratio?

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• 21. The total cost of the equipment including floatation costs was:

• Total costs = $2.1M + 128,000 = $2.228M • Using the equation to calculate the total cost

including floatation costs, we get:• Amount raised(1 – fT) = Amount needed

after floatation costs• $2.228M(1 – fT) = $2.1M • fT = .0575 or 5.75%

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• Now, we know the weighted average floatation cost. The equation to calculate the percentage floatation costs is:

• fT = .0575 = .07(E/V) + .025(D/V)

• We can solve this equation to find the debt-equity ratio as follows:

• .0575(V/E) = .07 + .025(D/E)

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• We must recognize that the V/E term is the equity multiplier, which is (1 + D/E), so:

• .0575(D/E + 1) = .07 + .025(D/E)

• D/E = .3867

Chapter

McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.

15

•End of Chapter•End of Chapter