CHAPTER 12
RISK AND THE COST OF CAPITAL
Answers to Concepts Review and Critical Thinking Questions
1. It is the minimum rate of return the firm must earn overall on its existing assets. If it earns more than
this, value is created.
2. Book values for debt are likely to be much closer to market values than are equity book values.
3. No. The cost of capital depends on the risk of the project, not the source of the money.
4. Interest expense is tax-deductible. There is no difference between pretax and aftertax equity costs.
5. You are assuming that the new project’s risk is the same as the risk of the firm as a whole, and that
the firm is financed entirely with equity.
6. Two primary advantages of the SML approach are that the model explicitly incorporates the relevant
risk of the stock and the method is more widely applicable than is the DCF model, since the SML doesn’t make any assumptions about the firm’s dividends. The primary disadvantages of the SML method are (1) three parameters (the risk-free rate, the expected return on the market, and beta) must be estimated, and (2) the method essentially uses historical information to estimate these parameters. The risk-free rate is usually estimated to be the yield on very short maturity T-bills and is, hence, observable; the market risk premium is usually estimated from historical risk premiums and, hence, is not observable. The stock beta, which is unobservable, is usually estimated either by determining some average historical beta from the firm and the market’s return data, or by using beta estimates provided by analysts and investment firms.
7. The appropriate aftertax cost of debt to the company is the interest rate it would have to pay if it
were to issue new debt today. Hence, if the YTM on outstanding bonds of the company is observed, the company has an accurate estimate of its cost of debt. If the debt is privately-placed, the firm could still estimate its cost of debt by (1) looking at the cost of debt for similar firms in similar risk classes, (2) looking at the average debt cost for firms with the same credit rating (assuming the firm’s private debt is rated), or (3) consulting analysts and investment bankers. Even if the debt is publicly traded, an additional complication is when the firm has more than one issue outstanding; these issues rarely have the same yield because no two issues are ever completely homogeneous.
8. a. This only considers the dividend yield component of the required return on equity. b. This is the current yield only, not the promised yield to maturity. In addition, it is based on the
book value of the liability, and it ignores taxes.
c. Equity is inherently riskier than debt (except, perhaps, in the unusual case where a firm’s assets
have a negative beta). For this reason, the cost of equity exceeds the cost of debt. If taxes are considered in this case, it can be seen that at reasonable tax rates, the cost of equity does exceed the cost of debt.
B-2 SOLUTIONS
9. RSup = .12 + .75(.08) = .1800 or 18.00% Both should proceed. The appropriate discount rate does not depend on which company is investing;
it depends on the risk of the project. Since Superior is in the business, it is closer to a pure play. Therefore, its cost of capital should be used. With an 18% cost of capital, the project has an NPV of $1 million regardless of who takes it.
10. If the different operating divisions were in much different risk classes, then separate cost of capital
figures should be used for the different divisions; the use of a single, overall cost of capital would be inappropriate. If the single hurdle rate were used, riskier divisions would tend to receive more funds for investment projects, since their return would exceed the hurdle rate despite the fact that they may actually plot below the SML and, hence, be unprofitable projects on a risk-adjusted basis. The typical problem encountered in estimating the cost of capital for a division is that it rarely has its own securities traded on the market, so it is difficult to observe the market’s valuation of the risk of the division. Two typical ways around this are to use a pure play proxy for the division, or to use subjective adjustments of the overall firm hurdle rate based on the perceived risk of the division.
11. The discount rate for the projects should be lower that the rate implied by the security market line.
The security market line is used to calculate the cost of equity. The appropriate discount rate for projects is the firm’s weighted average cost of capital. Since the firm’s cost of debt is generally less that the firm’s cost of equity, the rate implied by the security market line will be too high.
12. Beta measures the responsiveness of a security's returns to movements in the market. Beta is
determined by the cyclicality of a firm's revenues. This cyclicality is magnified by the firm's operating and financial leverage. The following three factors will impact the firm’s beta. (1) Revenues. The cyclicality of a firm's sales is an important factor in determining beta. In general, stock prices will rise when the economy expands and will fall when the economy contracts. As we said above, beta measures the responsiveness of a security's returns to movements in the market. Therefore, firms whose revenues are more responsive to movements in the economy will generally have higher betas than firms with less-cyclical revenues. (2) Operating leverage. Operating leverage is the percentage change in earnings before interest and taxes (EBIT) for a percentage change in sales. A firm with high operating leverage will have greater fluctuations in EBIT for a change in sales than a firm with low operating leverage. In this way, operating leverage magnifies the cyclicality of a firm's revenues, leading to a high beta. (3) Financial leverage. Financial leverage arises from the use of debt in the firm's capital structure. A levered firm must make fixed interest payments regardless of its revenues. The effect of financial leverage on beta is analogous to the effect of operating leverage on beta. Fixed interest payments cause the percentage change in net income to be greater than the percentage change in EBIT, magnifying the cyclicality of a firm's revenues. Thus, returns on highly-levered stocks should be more responsive to movements in the market than the returns on stocks with little or no debt in their capital structure.
CHAPTER 12 B-3
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic
1. With the information given, we can find the cost of equity using the CAPM. The cost of equity is: RE = .05 + 1.30 (.12 – .05) = .1410 or 14.10%
2. The pretax cost of debt is the YTM of the company’s bonds, so: P0 = $1,050 = $40(PVIFAR%,24) + $1,000(PVIFR%,24) R = 3.683% YTM = 2 × 3.683% = 7.37% And the aftertax cost of debt is: RD = .0737(1 – .40) = .0442 or 4.42%
3. a. The pretax cost of debt is the YTM of the company’s bonds, so: P0 = $1,080 = $50(PVIFAR%,46) + $1,000(PVIFR%,46) R = 4.58% YTM = 2 × 4.58% = 9.16% b. The aftertax cost of debt is: RD = .0916(1 – .40) = .05496 or 5.50% c. The aftertax rate is more relevant because that is the actual cost to the company.
4. The book value of debt is the total par value of all outstanding debt, so: BVD = �20M + 80M = �100M 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(�20M) + .58(�80M) = �68M
B-4 SOLUTIONS
5. 6. 7.
The YTM of the zero coupon bonds is: PZ = �580 = �1,000(PVIFR%,7) R = 8.09%
So, the aftertax cost of the zero coupon bonds is: RZ = .0809(1 – .35) = .0526 or 5.26%
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 = .0595(�21.6/�68) + .0526(�46.4/�68) = .0548 or 5.48% Using the equation to calculate the WACC, we find: WACC = .60 (.16) + .40(.09)(1 – .35) = .1194 or 11.94%
Here we need to use the debt-equity ratio to calculate the WACC. Doing so, we find: WACC = .18(1/1.60) + .10(.60/1.60)(1 – .35) = .1369 or 13.69%
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 = .16(E/V) + .075(D/V)(1 – .35) Rearranging the equation, we find: .115(V/E) = .16 + .075(.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) = .16 + .04875(D/E) Now we can solve for D/E as: .06625(D/E) = .0450 D/E = .6792
CHAPTER 12 B-5
8. a.
The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company’s debt, so: BVE = 9.5M(￡5) = ￡47.5M BVD = ￡75M + 60M = ￡135M So, the total value of the company is: V = ￡47.5M + 135M = ￡182.5M
And the book value weights of equity and debt are: E/V = ￡47.5/￡182.5 = .2603 D/V = 1 – E/V = .7397
The market value of equity is the share price times the number of shares, so: MVE = 9.5M(￡53) = ￡503.5M
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 = .93(￡75M) + .965(￡60M) = ￡127.65M This makes the total market value of the company: V = ￡503.5 + 127.65M = ￡631.15
And the market value weights of equity and debt are: E/V = ￡503.5/￡631.15 = .7978 D/V = 1 – E/V = .2024
The market value weights are more relevant.
b.
c.
英文版罗斯公司理财习题答案Chap012
