Chapter 12

If the stock currently sells for $55, what is your best estimate of the company's cost of equity capital using arithmetic and geometric growth rates?

Calculating the geometric growth rate in dividends, we find: $1.82 = $1.36(1 + g)^4 g = .0756, or 7.56% The cost of equity using the geometric dividend growth rate is: RE = [$1.82(1.0756)/$55] + .0756 RE = .1111, or 11.11%

Masterson, Inc., has 4.1 million shares of common stock outstanding. The current share price is $84, and the book value per share is $11. The company also has two bond issues outstanding. The first bond issue has a face value of $70 million, has a coupon rate of 5.1 percent, and sells for 98 percent of par. The second issue has a face value of $50 million, has a coupon rate of 5.60 percent, and sells for 108 percent of par. The first issue matures in 20 years, the second in 12 years. The most recent dividend was $3.95 and the dividend growth rate is 5 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 21 percent. What is the company's WACC?

First, we will find the cost of equity for the company. The information provided allows us to solve for the cost of equity using the dividend growth model, so: RE = [$3.95(1.05)/$84] + .05 RE = .0994, or 9.94% Next, we need to find the YTM on both bond issues. Doing so, we find: P1 = $980 = $25.50(PVIFAR%,40) + $1,000(PVIFR%,40) R = 2.631% YTM = 2.631% × 2 YTM = 5.26% P2 = $1,080 = $28(PVIFAR%,24) + $1,000(PVIFR%,24) R = 2.360% YTM = 2.360% × 2 YTM = 4.72% To find the weighted average aftertax cost of debt, we need the weight of each bond as a percentage of the total debt. We find: xD1 = .98($70,000,000)/$122,600,000 xD1 = .5595 xD2 = 1.08($50,000,000)/$122,600,000xD2 = .4405 Now we can multiply the weighted average cost of debt times one minus the tax rate to find the weighted average aftertax cost of debt. This gives us: RD = (1 - .21)[(.5595)(.0526) + (.4405)(.0472)] RD = .0397, or 3.97% The market value of equity is the share price times the number of shares, so: MVE = 4,100,000($84) = $344,400,000 Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is: MVD = .98($70,000,000) + 1.08($50,000,000) = $122,600,000 This makes the total market value of the company: V = $344,400,000 + 122,600,000 = $467,000,000 And the market value weights of equity and debt are: E/V = $344,400,000/$467,000,000 = .7375 D/V = 1 − E/V = .2625 Using the costs we have found and the weight of debt, the WACC is: WACC = .7375(.0994) + .2625(.0397) WACC = .0837, or 8.37%

Hoolahan Corporation's common stock has a beta of .87. Assume the risk-free rate is 3.6 percent and the expected return on the market is 11 percent. What is the company's cost of equity capital?

Here we have information to calculate the cost of equity, using the CAPM. The cost of equity is: RE = .036 + .87(.11 - .036) RE = .1004, or 10.04%

Fama's Llamas has a WACC of 8.95 percent. The company's cost of equity is 10.4 percent, and its pretax cost of debt is 5.3 percent. The tax rate is 21 percent. What is the company's target debt-equity ratio?

Here, we have the WACC and need to find the debt-equity ratio of the company. Setting up the WACC equation, we find: WACC = .0895 = .104(E/V) + .053(D/V)(1 - .21) Rearranging the equation, we find: .0895(V/E) = .104 + .053(.79)(D/E) Now we must realize that the V/E is just the equity multiplier, which is equal to: V/E = 1 + D/E .0895(D/E + 1) = .104 + .04187(D/E) Now, we can solve for D/E as: .04763(D/E) = .0145D/E = .3044

Suppose Potter Ltd. just issued a dividend of $1.82 per share on its common stock. The company paid dividends of $1.36, $1.46, $1.53, and $1.68 per share in the last four years, respectively. If the stock currently sells for $55, what is your best estimate of the company's cost of equity capital using arithmetic growth rates?

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 = ($1.46 - 1.36)/$1.36 g1 = .0735, or 7.35% g2 = ($1.53 - 1.46)/$1.46 g2 = .0479, or 4.79% g3 = ($1.68 - 1.53)/$1.53 g3 = .0980, or 9.80% g4 = ($1.82 - 1.68)/$1.68 g4 = .0833, or 8.33% So, the average arithmetic growth rate in dividends was: g = (.0735 + .0479 + .0980 + .0833)/4 g = .0757, or 7.57% Using this growth rate in the dividend growth model, we find the cost of equity is: RE = [$1.82(1.0757)/$55] + .0757 RE = .1113, or 11.13%

The Pierce Co. just issued a dividend of $2.35 per share on its common stock. The company is expected to maintain a constant 5 percent growth rate in its dividends indefinitely. If the stock sells for $44 a share, what is the company's cost of equity?

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 = [$2.35(1.05)/$44] + .05 RE = .1061, or 10.61%

An all-equity firm is considering the following projects: Project Beta IRR W .80 9.3% X .90 11.4 Y 1.10 12.1 Z 1.35 15.1 The T-bill rate is 4 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 will be incorrectly accepted/rejected or correctly accepted/rejected if the firm's overall cost of capital were used as a hurdle rate?

a. Projects 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 lower than the project expected return, we should accept the project; if not, we reject the project. After considering risk via the CAPM: E(W) = .04 + .80(.12 - .04) = .1040 > .0930, so reject W E(X) = .04 + .90(.12 - .04) = .1120 < .1140, so accept X E(Y) = .04 + 1.10(.12 - .04) = .1280 > .1210, so reject Y E(Z) = .04 + 1.35(.12 - .04) = .1480 < .1510, so accept Z

Jiminy's Cricket Farm issued a 30-year, 6.3 percent semiannual bond eight years ago. The bond currently sells for 110 percent of its face value. The book value of the debt issue is $135 million. In addition, the company has a second debt issue, a zero coupon bond with 12 years left to maturity; the book value of this issue is $65 million, and it sells for 64.3 percent of par. The company's tax rate is 22 percent. a. What is the total book value of debt? b. What is the total market value of debt? c. What is the aftertax cost of debt?

a. The book value of debt is the total par value of all outstanding debt, so: BVD = $135,000,000 + 65,000,000 BVD = $200,000,000 b. 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 = 1.10($135,000,000) + .643($65,000,000) MVD = $190,295,000 c. The YTM of the coupon bonds is: P0 = $1,100 = $31.50(PVIFAR%,44) + $1,000(PVIFR%,44)R = 2.755% YTM = 2 × 2.755% YTM = 5.51% The aftertax cost of debt is: RD = .0551(1 - .22)RD = .0430, or 4.30% The YTM of the zero coupon bonds is (Remember, even on zero coupon bonds, for consistency, the "payments" are assumed to be semiannual): PZ = $643 = $1,000(PVIFR%,24) R = .01857, or 1.857% Which means the YTM is: YTM = 1.857% × 2 YTM = 3.71% So, the aftertax cost of the zero coupon bonds is: RZ = .0371(1 - .22) RZ = .0290, or 2.90% The aftertax cost of debt for the company is the weighted average of the aftertax cost of debt for all outstanding bond issues. We need to use the market value weights of the bonds. The total aftertax cost of debt for the company is: RD = .0430[(1.10)($135,000,000)/$190,295,000] + .0290[(.643)($65,000,000)/$190,295,000] RD = .0399, or 3.99%

ICU Window, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with seven years to maturity that is quoted at 103 percent of face value. The issue makes semiannual payments and has an embedded cost of 5.1 percent annually. a. What is ICU's pretax cost of debt? b. If the tax rate is 21 percent, what is the aftertax cost of debt?

a. The pretax cost of debt is the YTM of the company's bonds, so: P0 = $1,030 = $25.50(PVIFAR%,14) + $1,000(PVIFR%,14) R = 2.297% YTM = 2 × 2.297% YTM = 4.59% b. And the aftertax cost of debt is: RD = .0459(1 - .21) RD = .0363, or 3.63%

Jiminy's Cricket Farm issued a 30-year, 6.3 percent semiannual bond eight years ago. The bond currently sells for 110 percent of its face value. The company's tax rate is 22 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?

a. The pretax cost of debt is the YTM of the company's bonds, so: P0 = $1,100 = $31.50(PVIFAR%,44) + $1,000(PVIFR%,44) R = 2.755% YTM = 2 × 2.755% YTM = 5.51% b. The aftertax cost of debt is: RD = .0551(1 - .22) RD = .0430, or 4.30% c. The aftertax rate is more relevant because that is the actual cost to the company.

Baron Corporation has a target capital structure of 75 percent common stock, 5 percent preferred stock, and 20 percent debt. Its cost of equity is 11.3 percent, the cost of preferred stock is 4.9 percent, and the pretax cost of debt is 5.8 percent. The relevant tax rate is 23 percent. a. What is the company's WACC? b. What is the aftertax cost of debt?

a. Using the equation to calculate the WACC, we find: WACC = .75(.1130) + .05(.049) + .20(.058)(1 - .23) WACC = .0961, or 9.61% b. Since interest is tax deductible and dividends are not, we must look at the aftertax cost of debt, which is: RD = .058(1 - .23) RD = .0447, or 4.47%