# chap012

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```					Solutions to Chapter 12 The Cost of Capital 1. The yield to maturity for the bonds (since maturity is now 19 years) is the interest rate (r) that is the solution to the following equation: [\$80  annuity factor(r, 19 years)] + [\$1,000/(1 + r)19] = \$1,050 Using a financial calculator, enter: n = 19, FV = 1000, PV = (-)1050, PMT = 90, and then compute i = 7.50% Therefore, the after-tax cost of debt is: 7.50%  (1 – 0.35) = 4.88%

2.

r = DIV/P0 = \$4/\$40 = 0.10 = 10%
D  P  E     r debt  (1  T C )     r preferred     r equity  V  V  V 

3.

WACC

= [0.3  7.50%  (1 – 0.35)] + [0.2  10%] + [0.5  12.0%] = 9.46%
DIV 1 P0 DIV 0 (1  g ) P0 \$ 5  1 . 05 \$ 60

4.

r 

g 

g 

 0 . 05  0 . 1375  13 . 75 %

5.

The total value of the firm is \$80 million. The weights for each security class are as follows: Debt: Preferred: Common:
WACC

D/V = 20/80 = 0.250 P/V = 10/80 = 0.125 E/V = 50/80 = 0.625
D  P  E     r debt  (1  T C )     r preferred     r equity  V  V  V 

= [0.250  6%  (1 – 0.35)] + [0.125  8%] + [0.625  12.0%] = 9.475%

6.

Executive Fruit should use the WACC of Geothermal, not its own WACC, when evaluating an investment in geothermal power production. The risk of the project determines the discount rate, and in this case, Geothermal’s WACC is more reflective of the risk of the project in question. The proper discount rate, therefore, is not 12.3%. It is more likely to be 11.4%.

7.

The flotation costs reduce the NPV of the project by \$1.2 million. Even so, project NPV is still positive, so the project should be undertaken. 12-1

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8.

The rate on Buildwell’s debt is 5 percent. The cost of equity capital is the required rate of return on equity, which can be calculated from the CAPM as follows: 4% + (0.90  8%) = 11.2% The weighted average cost of capital, with a tax rate of zero, is:
WACC D  E     r debt  (1  T C )     r equity  V  V 

= [0.30  5%  (1 – 0)] + [0.70  11.2%] = 9.34%

9.

The internal rate of return, which is 12%, exceeds the cost of capital. Therefore, BCCI should accept the project. The present value of the project cash flows is: \$100,000  annuity factor(9.34%, 8 years) = \$546,556.08 This is the most BCCI should pay for the project.

10. Security Debt Equity Total Market Value \$ 5.5 million \$15.0 million \$20.5 million Explanation 1.10  par value of \$5 million \$30 per share  500,000 shares *
book value per share  500 , 000

*Number of shares =

\$ 10 million

\$ 20 book value
WACC

D  E     r debt  (1  T C )     r equity  V  V   5 .5   15     9 %  (1  0 . 40 )     15 %   12 . 42 %  20 . 5   20 . 5 

11. Since the firm is all-equity financed: asset beta = equity beta = 0.8 The WACC is the same as the cost of equity, which can be calculated using the CAPM: requity = rf + (rm – rf) = 4% + (0.80  10%) = 12% 12. The 12.5% value calculated by the analyst is the current yield of the firm’s outstanding debt: interest payments/bond value. This calculation ignores the fact that bonds selling at discounts from, or premiums over, par value provide expected returns determined in part by expected price appreciation or depreciation. The analyst should be using yield to maturity instead of current yield to calculate cost of debt. [This answer assumes the value of the debt provided is the market value. If it is the book value, then 12.5% would be the

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average coupon rate of outstanding debt, which would also be a poor estimate of the required rate of return on the firm’s debt.]

13. a.

Using the recent growth rate of 30% and the dividend yield of 2%, one estimate would be: DIV1/P0 + g = 0.02 + 0.30 = 0.32 = 32% Another estimate, based on the CAPM, would be: r = rf + (rm – rf) = 4% + (1.2  8%) = 13.6%

b.

The estimate of 32% seems far less reasonable. It is based on an historic growth rate that is impossible to sustain. The [DIV1/P0 + g] rule requires that the growth rate of dividends per share must be viewed as highly stable over the foreseeable future. In other words, it requires the use of the sustainable growth rate.

14. a.

The 9% coupon bond has a yield to maturity of 10% and sells for 93.86% of face value: n = 10, i = 10%, PMT = 90, FV = 1000, compute PV = \$938.55 Therefore, the market value of the issue is: 0.9386  \$20 million = \$18.77 million The 10% coupon bond sells for 94% of par value, and has a yield to maturity of 10.83%: n = 15, PV = ()940, PMT = 100, FV = 1000, compute i = 10.83% The market value of the issue is: 0.94  \$25 million = \$23.50 million Therefore, the weighted-average before-tax cost of debt is:
18 . 77 23 . 50      18 . 77  23 . 50  10 %    18 . 77  23 . 50  10 . 83 %   10 . 46 %    

b.

The after-tax cost of debt is: (1 – 0.35)  10.46% = 6.80%

15. The bonds are selling below par value because the yield to maturity is greater than the coupon rate. The price per \$1,000 par value is: [\$80  annuity factor(9%, 10 years)] + (\$1,000/1.0910) = \$935.82 The total market value of the bonds is:

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\$10 million par value 

\$ 935 . 82 market val ue \$ 1, 000 par value

 \$ 9 . 36 million

There are: \$2 million/\$20 = 100,000 shares of preferred stock. The market price of the preferred stock is \$15 per share, so that the total market value of the preferred stock is \$1.5 million.

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There are: \$0.1 million/\$0.10 = 1 million shares of common stock. The market price of the common stock is \$20 per share, so that the total market value of the common stock is \$20 million. Therefore, the capital structure is: Security Bonds Preferred Stock Common Stock Total Market Value \$ 9.36 million \$ 1.50 million \$20.00 million \$30.86 million Percent 30.3% 4.9% 64.8% 100.0%

16. The yield to maturity for the firm’s debt is: rdebt = 9% The rate for the preferred stock is: rpreferred = \$2/\$15 = 0.1333 = 13.33% The rate for the common stock is: requity = rf + (rm – rf) = 6% + 0.8  10% = 14% Using the capital structure derived in the previous problem, we can calculate WACC as:
WACC D  P  E     r debt  (1  T C )     r preferred     r equity  V  V  V 

= [0.303  9%  (1 – 0.40)] + [0.049  13.33%] + [0.648  14%] = 11.36%

17. The IRR on the computer project is less than the WACC of firms in the computer industry. Therefore, the project should be rejected. However, the WACC of the firm (based on its existing mix of projects) is only 11.36%. If the firm uses this figure as the hurdle rate, it will incorrectly go ahead with the venture in home computers. r = rf + (rm – rf) r = 4% + (1.2  10%) = 16% Weighted average beta = (0.4  0) + (0.6  1.5) = 0.9
WACC D  E     r debt  (1  T C )     r equity  V  V 

18. a. b. c.

= [0.4  4%  (1 – 0.4)] + [0.6  16%] = 10.56% d. If the company plans to expand its present business, then the WACC is a reasonable estimate of the discount rate since the risk of the proposed project is similar to the risk of the existing projects. Use a discount rate of 10.56%. The WACC of optical projects should be based on the risk of those projects. Using a beta of 1.4, the discount rate for the new venture is: r = 4% + 1.4  10% = 18% 12-6

e.

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19. If Big Oil does not pay taxes, then the after-tax and before-tax costs of debt are identical. WACC would then become:
WACC D  E     r debt  (1  T C )     r equity  V  V 

= [0.243  9%  (1 – 0)] + [0.757  12.8%] = 11.88% If Big Oil issues new equity and uses the proceeds to pay off all of its debt, the cost of equity will decrease. There is no longer any leverage, so the equity becomes safer and therefore commands a lower risk premium. In fact, with allequity financing, the cost of equity would be the same as the firm’s WACC, which is 11.88%. This is less than the previous value of 12.8%. (We use the WACC derived in the absence of interest tax shields since, for the all-equity firm, there is no interest tax shield.) 20. The net effect of Big Oil’s transaction is to leave the firm with \$200 million more debt (because of the borrowing) and \$200 million less equity (because of the dividend payout). Total assets and business risk are unaffected. The WACC will remain unchanged because business risk is unchanged. However, the cost of equity will increase. With the now higher leverage, the business risk is spread over a smaller equity base, so each share is now riskier. The new financing mix for the firm is: E = \$1,000 and D = \$585.7 Therefore:
D V  \$ 585 . 7 \$ 1,585 . 7  0 . 369 and E V  \$ 1, 000 \$ 1,585 . 7  0 . 631

If the cost of debt is still 9%, then we solve for the new cost of equity as follows. Use the fact that, even at the new financing mix, WACC must still be 12.41%.
WACC D  E     r debt  (1  T C )     r equity  V  V 

= [0.369  9%  (1 – 0)] + [0.631  r equity] = 12.41% We solve to find that: requity = 13.56% 21. Even if the WACC were lower when the firm’s tax rate is higher, this does not imply that the firm would be worth more. The after-tax cash flows the firm would generate for its owners would also be lower. This would reduce the value of the firm even if the cash flows were discounted at a lower rate. If the tax authority is collecting more income from the firm, the value of the firm will fall.

22. This reasoning is faulty in that it implicitly treats the discount rate for the project as the cost of debt if the project is debt financed, and as the cost of equity if the project is equity

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financed. In fact, if the project poses risk comparable to the risk of the firm’s other projects, the proper discount rate is the firm’s cost of capital, which is a weighted average of the costs of both debt and equity.

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Solution to Minicase for Chapter 12 Bernice needs to explain to her boss, Mr. Brinestone, that appropriate rates of return for cost of capital calculations are the rates of return that investors can earn on comparable risk investments in the capital market. Mr. Brinestone’s estimate of the cost of equity is his target value for the book return on equity; it is not the expected rate of return that investors demand on shares of stock with the same risk as Sea Shore Salt. Bernice’s CAPM calculation indicates that the correct value for the equity rate is 11%. This value is broadly consistent with the rate one would infer from the constant growth dividend discount model (which seems appropriate for a mature firm like this one with stable growth prospects). The dividend discount model implies a cost of equity of a bit more than 11 percent: requity 
DIV 1 P0 g  \$2 \$ 40  0 . 067  0 . 117  11 . 7 %

Thus, it appears that Bernice’s calculation is correct. Similarly, Mr. Brinestone’s returns for other securities should be modified to reflect the expected returns these securities currently offer to investors. The bank loan and bond issue offer pre-tax rates of 8% and 7.75%, respectively, as in Mr. Brinestone’s memo. The preferred stock, however, is not selling at par, so Mr. Brinestone’s assertion that the rate of return on preferred is 6% is incorrect. In fact, with the preferred selling at \$70 per share, the rate of return is: rpreferred 
DIV P0  \$6 \$ 70  0 . 086  8 . 6 %

This makes sense: the pre-tax return on preferred should exceed that on the firm’s debt. Finally, the weights used to calculate the WACC should reflect market, not book, values. These are the prices that investors would pay to acquire the securities. The market value weights are computed as follows: Comment Bank loan Bond issue Preferred stock Common stock valued at face amount valued at par \$70  1 million shares \$40  10 million shares Amount (millions) \$120 80 70 400 \$670 Percent of total 17.91 11.94 10.45 59.70 100.00 Rate of return (%) 8.00 7.75 8.60 11.00

Therefore, the WACC, which serves as the corporate hurdle rate, should be 9%: WACC = [0.1791  8%  (1 – 0.35)] + [0.1194  7.75%  (1 – 0.35)] + (0.1045  8.6%) + (0.5970  11%) = 9.00%

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