公司理财习题答案第十二章Chapter 12: Risk, Return, and Capital Budgeting12.1 Cost of equity R S = 5 + 0.95 (9) = 13.55% NPV of the project= -$1.2 million + $340,.0001135515tt =∑= -$20,016.52Do not undertake the project. 12.2 a. R D= (-0.05 + 0.05 + 0.08 + 0.15 + 0.10) / 5 = 0.066 R M = (-0.12 + 0.01 + 0.06 + 0.10 + 0.05) / 5 = 0.02b.DR- D R M R -R M(M R -M R )2 (D R -R D )(M R -R M )-0.116 -0.14 0.0196 0.01624 -0.016 -0.01 0.0001 0.00016 0.014 0.04 0.0016 0.00056 0.084 0.08 0.0064 0.00672 0.034 0.03 0.0009 0.001020.02860.02470Beta of Douglas = 0.02470 / 0.0286 = 0.86412.3 R S = 6% + 1.15 ⨯ 10% = 17.5% R B = 6% + 0.3 ⨯ 10% = 9% a. Cost of equity = R S = 17.5% b. B / S = 0.25 B / (B + S) = 0.2 S / (B + S) = 0.8WACC = 0.8 ⨯ 17.5% + 0.2 ⨯ 9% (1 - 0.35)= 15.17%12.4 C σ = ()2104225.0 = 0.065M σ = ()2101467.0 = 0.0383Beta of ceramics craftsman = CM ρC σ M σ / M σ2 = CM ρC σ/ M σ = (0.675) (0.065) / 0.0383 = 1.146 12.5a. To compute the beta of Mercantile Manufacturing’s stock, you need the product of the deviations of Mercantile’s returns from their mean and the deviations of the market’s returns from their mean. You also need the squares of the deviations ofthe market’s returns from their mean.The mechanics of computing the means and the deviations were presented in an earlier chapter.R T = 0.196 / 12 = 0.016333 R M = 0.236 / 12 = 0.019667 E(T R -R T ) (M R -R M ) = 0.038711 E(M R -R M )2 = 0.038588 β = 0.038711 / 0.038588= 1.0032b.The beta of the average stock is 1. Mercantile’s beta is close to 1, indicating that its stock has average risk.12.6 a.R M can have three values, 0.16, 0.18 or 0.20. The probability that M R takes one of these values is the sum of the joint probabilities of the return pair that include theparticular value of M R . For example, if M R is 0.16, R J will be 0.16, 0.18 or 0.22. The probability that M R is 0.16 and R J is 0.16 is 0.10. The probability that R M is 0.16 and R J is 0.18 is 0.06. The probability that M R is 0.16 and R J is 0.22 is 0.04. The probability that M R is 0.16 is, therefore, 0.10 + 0.06 + 0.04 = 0.20. The same procedure is used to calculate the probability that M R is 0.18 and the probability that M R is 0.20. Remember, the sum of the probability must be one.M RProbability 0.16 0.20 0.18 0.60 0.20 0.20 b. i.RM= 0.16 (0.20) + 0.18 (0.60) + 0.20 (0.20) = 0.18ii. 2M σ = (0.16 - 0.18) 2 (0.20) + (0.18 - 0.18) 2 (0.60) + (0.20 - 0.18) 2 (0.20)= 0.00016iii. M σ = ()2100016.0 = 0.01265c. R J Probability .18 .20 .20 .40 .22 .20 .24.10d. i. E j = .16 (.10) + .18 (.20) + .20 (.40) + .22 (.20) + .24(.10) = .20 ii. σj 2 = (.16 - .20)2 (.10) + (.18 - .20)2 (.20) + (.20 - .20)2 (.40)+ (.22 - .20)2 (.20) + (.24 - .20)2 (.10) = .00048公司理财习题答案第十二章iii. σj = ()21.0 = .0219100048e. Cov mj= (.16 - .18) (.16 - .20) (.10) + (.16 - .18) (.18 - .20) (.06)+ (.16 - .18) (.22 - .20) (.04) + (.20 - .18) (.18 - .20) (.02)+ (.20 - .18) (.22 - .20) (.04) + (.20 - .18) (.24 - .20) (.10)= .000176Corr mj = (0.000176) / (0.01265) (0.02191) = 0.635f. βj = (.635) (.02191) / (.01265) = 1.1012.7 i. The risk of the new project is the same as the risk of the firm without the project.ii. The firm is financed entirely with equity.12.8 a. Pacific Cosmetics should use its stock beta in the evaluation of the project only ifthe risk of the perfume project is the same as the risk of Pacific Cosmetics.b. If the risk of the project is the same as the risk of the firm, use the firm’s stock beta.If the risk differs, then use the beta of an all-equity firm with similar risk as theperfume project. A good way to estimate the beta of the project would be toaverage the betas of many perfume producing firms.12.9 E(R S) = 0.1 ⨯ 3 + 0.3 ⨯ 8 + 0.4 ⨯ 20 + 0.2 ⨯ 15 = 13.7%E(R B) = 0.1 ⨯ 8 + 0.3 ⨯ 8 + 0.4 ⨯ 10 + 0.2 ⨯ 10 = 9.2%E(R M) = 0.1 ⨯ 5 + 0.3 ⨯ 10 + 0.4 ⨯ 15 + 0.2 ⨯ 20 = 13.5%State {R S - E(R S)}{R M - E(R M)}Pr {R B - E(R B)}{R M - E(R M)}Pr1 (0.03-0.137)(0.05-0.135)⨯0.1 (0.08-0.092)(0.05-0.135)⨯0.12 (0.08-0.137)(0.10-0.135)⨯0.3 (0.08-0.092)(0.10-0.135)⨯0.33 (0.20-0.137)(0.15-0.135)⨯0.4 (0.10-0.092)(0.15-0.135)⨯0.44 (0.15-0.137)(0.20-0.135)⨯0.2 (0.10-0.092)(0.20-0.135)⨯0.2Sum 0.002056 0.00038= Cov(R S, R M) = Cov(R B, R M)σM 2= 0.1 (0.05 - 0.135)2 + 0.3 (0.10-0.135)2+ 0.4 (0.15-0.135)2 + 0.2 (0.20-0.135)2= 0.002025a. Beta of debt = Cov(R B, R M) / σM2 = 0.00038 / 0.002025= 0.188b. Beta of stock = Cov(R S, R M) / σM2 = 0.002055 / 0.002025= 1.015c. B / S = 0.5Thus, B / (S + B) = 1 / 3 = 0.3333S / (S + B) = 2 / 3 = 0.6667Beta of asset = 0.188 ⨯ 0.3333 + 1.015 ⨯ 0.6667= 0.73912.10 The discount rate for the project should be lower than the rate implied by the use ofthe Security Market Line. The appropriate discount rate for such projects is theweighted average of the interest rate on debt and the cost of equity. Since theinterest rate on the debt of a given firm is generally less than the firm’s cost ofequity, using only the stock’s beta yields a discount rate that is too high. Theconcept and practical uses of a weighted average discount rate will be in a laterchapter.12.11i. RevenuesThe gross income of the firm is an important factor in determining beta. Firmswhose revenues are cyclical (fluctuate with the business cycle) generally have highbetas. Firms whose revenues are not cyclical tend to have lower betas.ii. Operating leverageOperating leverage is the percentage change in earnings before interest and taxes(EBIT) for a percentage change in sales, [(Change in EBIT / EBIT) (Sales / Changein sales)]. Operating leverage indicates the ability of the firm to service its debt andpay stockholders.iii. Financial leverageFinancial leverage arises from the use of debt. Financial leverage indicates theability of the firm to pay stockholders. Since debt holders must be paid beforestockholders, the higher the financial leverage of the firm, the riskier its stock.The beta of common stock is a function of all three of these factors. Ultimately, theriskiness of the stock, of which beta captures a portion, is determined by thefluctuations in the income available to the stockholders. (As was discussed in thechapter, whether income is paid to the stockholders in the form of dividends or it isretained to finance projects are irrelevant as long as the projects are of similar riskas the firm.) The income available to common stock, the net income of the firm,depends initially on the revenues or sales of the firm. The operating leverageindicates how much of each dollar of revenue will become EBIT. Financialleverage indicates how much of each dollar of EBIT will become net income.12.12 a. Cost of equity for National Napkin= 7 + 1.29 (13 - 7)= 14.74%b. B / (S + B) = S / (S + B) = 0.5WACC = 0.5 ⨯ 7 ⨯ 0.65 + 0.5 ⨯ 14.74= 9.645%12.13 B = $60 million ⨯ 1.2 = $72 millionS = $20 ⨯ 5 million = $100 millionB / (S + B) = 72 / 172 = 0.4186S / (S + B) = 100 / 172 = 0.5814WACC = 0.4186 ⨯ 12% ⨯ 0.75 + 0.5814 ⨯ 18%= 14.23%12.14 S = $25 ⨯ 20 million = $500 millionB = 0.95 ⨯ $180 million = $171 million公司理财习题答案第十二章B / (S + B) = 0.2548 S / (S + B) = 0.7452 WACC = 0.7452 ⨯ 20% + 0.2548 ⨯ 10%⨯ 0.60 = 16.43%12.15 B / S = 0.75 B / (S + B) = 3 / 7 S / (S + B) = 4 / 7 WACC = (4 / 7) ⨯ 15% + (3 / 7) ⨯ 9%⨯ (1 - 0.35) = 11.08%NPV = -$25 million + $7(.)m illion tt 10110815+=∑= $819,299.04 Undertake the project.12.16 WACC = (0.5) x 28% + (0.5) x 10% x (1 - 0.35)= 17.25%NPV = - $1,000,000 + (1 - 0.35) $600,000 51725.0A = $240,608.50Mini Case: Allied ProductsAssumptionsPP&E Investment 42,000,000 Useful life of PP&E Investment (years) 7NEW GPWS price/unit (Year 1) 70,000 NEW GPWS variable cost/unit (Year 1) 50,000 UPGRADE GPWS price/unit (Year 1) 35,000 UPGRADE GPWS variable cost/unit (Year 1) 22,000Year 1 marketing and admin costs 3,000,000 Annual inflation rate 3.00% Corporate Tax rate 40.00%Beta (9/27 Valueline) 1.20 Rf (30 year U.S. Treasury Bond) 6.20%NEW GPWS Market Growth (Strong Growth) 15.00%NEW GPWS Market Growth (Moderate Growth) 10.00%NEW GPWS Market Growth (Mild Recession) 6.00%NEW GPWS Market Growth (Severe Recession state of economy) 3.00%Total Annual Market for UPGRADE GPWS (units) 2,500Allied Signal Market Share in each market 45.00%公司理财习题答案第十二章Year 0 1 2 3 4 5 SalesNEWUnits 97 107 118 130 144 Price 70,000 72,100 74,263 76,491 78,786 Total NEW 6,772,500 7,688,654 8,736,317 9,935,345 11,308,721 UPGRADEUnits 1,125 1,125 1,125 1,125 1,125 Price 35,000 36,050 37,132 38,245 39,393 Total UPGRADE 39,375,000 40,556,250 41,772,938 43,026,126 44,316,909 Total Sales 46,147,500 48,244,904 50,509,254 52,961,470 55,625,630 Variable CostsNEW 4,837,500 5,491,896 6,240,226 7,096,675 8,077,658 UPGRADE 24,750,000 25,492,500 26,257,275 27,044,993 27,856,343 Total Variable Costs 29,587,500 30,984,396 32,497,501 34,141,668 35,934,001SG&A 3,000,000 3,090,000 3,182,700 3,278,181 3,376,526 Depreciation 6,001,800 10,285,800 7,345,800 5,245,800 3,750,600EBIT 7,558,200 3,884,708 7,483,253 10,295,821 12,564,503 Interest 0 0 0 0 0 Tax 3,023,280 1,553,883 2,993,301 4,118,329 5,025,801 Net Income 4,534,920 2,330,825 4,489,952 6,177,493 7,538,702EBIT + Dep - Taxes 10,536,720 12,616,625 11,835,752 11,423,293 11,289,302 Less: Change in NWC 2,000,000 307,375 104,870 113,218 122,611 (2,648,074) Less: Captial Spending 42,000,000 (10,948,080) CF from Assets: (44,000,000) 10,229,345 12,511,755 11,722,534 11,300,682 24,885,455 Discounted CF from Assets 9,304,480 10,351,583 8,821,741 7,735,381 15,494,120Total Discounted CF from Assets 51,707,305Results。