公司理财第12章.doc

Chapter 12: Risk, Return, and Capital BudgetingConcept Questions - Chapter 1212.1What is the disadvantage of using too few observations when estimating beta?Small samples can lead to inaccurate estimations. What is the disadvantage of using too many observations when estimating beta?Firms may change their industries over time making observations from the distant past out-of-date. What is the disadvantage of using the industry beta as the estimate of the beta of an individual firm?The operations of a particular firm may not be similar to the industry average.12.2What are the determinants of equity betas?1. The responsiveness of a firms revenues to economy wide movements.2. The degree of a firms operating leverage.3. The degree of a firms financial leverage.What is the difference between an asset beta and an equity beta?Financial leverage.12.6h What is liquidity?Liquidity in this context means the cost of buying and selling stocks. Those stocks that are expensive to trade are considered less liquid. h What is the relation between liquidity and expected return?There is a high expected return for illiquid stocks with high trading costs.h What is adverse selection?Adverse selection occurs when individuals have ignorance about traits, trends, or other information hidden in a population. For instance, a trader may suffer from adverse selection if certain market knowledge is hidden from him but is available to some investors.h What can a corporation do to lower its cost of capital?A corporation can be proactive in taking actions that will lower trading costs, thereby lowering its cost of capital.Answers to End-of-Chapter Problems12.1Cost of equityRS = 5 + 0.95 (9) = 13.55%NPV of the project= -$1.2 million + = -$20,016.52Do not undertake the project.12.2a. = (-0.05 + 0.05 + 0.08 + 0.15 + 0.10) / 5 = 0.066 = (-0.12 + 0.01 + 0.06 + 0.10 + 0.05) / 5 = 0.02b. - -( -)2( -)( -)-0.116-0.140.01960.01624-0.016-0.010.00010.000160.0140.040.00160.000560.0840.080.00640.006720.0340.030.00090.001020.02860.02470Beta of Douglas= 0.02470 / 0.0286= 0.86412.3RS= 6% + 1.15 10% = 17.5%RB= 6% + 0.3 10% = 9%a.Cost of equity = RS = 17.5%b.B / S = 0.25B / (B + S) = 0.2S / (B + S) = 0.8WACC = 0.8 17.5% + 0.2 9% (1 - 0.35) = 15.17%12.4= = 0.065= = 0.0383Beta of ceramics craftsman= / 2= / = (0.675) (0.065) / 0.0383= 1.14612.5a.To compute the beta of Mercantile Manufacturings stock, you need the product of the deviations of Mercantiles returns from their mean and the deviations of the markets returns from their mean. You also need the squares of the deviations of the markets returns from their mean.The mechanics of computing the means and the deviations were presented in an earlier chapter. = 0.196 / 12 = 0.016333 = 0.236 / 12 = 0.019667E( -) ( -) = 0.038711E( -)2 = 0.038588b = 0.038711 / 0.038588 = 1.0032b.The beta of the average stock is 1. Mercantiles beta is close to 1, indicating that its stock has average risk. 12.6a.RM can have three values, 0.16, 0.18 or 0.20. The probability that takes one of these values is the sum of the joint probabilities of the return pair that include the particular value of . For example, if is 0.16, RJ will be 0.16, 0.18 or 0.22.The probability that is 0.16 and RJ is 0.16 is 0.10. The probability that RM is 0.16 and RJ is 0.18 is 0.06. The probability that is 0.16 and RJ is 0.22 is 0.04. The probability that is 0.16 is, therefore, 0.10 + 0.06 + 0.04 = 0.20. The same procedure is used to calculate the probability that is 0.18 and the probability that is 0.20. Remember, the sum of the probability must be one.Probability80.600.200.20b.i. = 0.16 (0.20) + 0.18 (0.60) + 0.20 (0.20) = 0.18ii. = (0.16 - 0.18) 2 (0.20) + (0.18 - 0.18) 2 (0.60) + (0.20 - 0.18) 2 (0.20)= 0.00016iii. = = 0.01265c.RJProbability.0d.i. = .16 (.10) + .18 (.20) + .20 (.40) + .22 (.20) + .24(.10) = .20ii. sj2 = (.16 - .20)2 (.10) + (.18 - .20)2 (.20) + (.20 - .20)2 (.40) + (.22 - .20)2 (.20) + (.24 - .20)2 (.10) = .00048iii. sj = = .02191e.Covmj = (.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)= .000176Corrmj = (0.000176) / (0.01265) (0.02191) = 0.635f.bj = (.635) (.02191) / (.01265) = 1.1012.7i.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.12.8a.Pacific Cosmetics should use its stock beta in the evaluation of the project only if the 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 firms stock beta. If the risk differs, then use the beta of an all-equity firm with similar risk as the perfume project. A good way to estimate the beta of the project would be to average the betas of many perfume producing firms.12.9E(RS) = 0.1 3 + 0.3 8 + 0.4 20 + 0.2 15 = 13.7%E(RB) = 0.1 8 + 0.3 8 + 0.4 10 + 0.2 10 = 9.2%E(RM) = 0.1 5 + 0.3 10 + 0.4 15 + 0.2 20 = 13.5%StateRS - E(RS)RM - E(RM)PrRB - E(RB)RM - E(RM)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)0.2Sum0.0020560.00038= Cov(RS, RM)= Cov(RB, RM)sM 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(RB, RM) / sM2 = 0.00038 / 0.002025= 0.188b.Beta of stock = Cov(RS, RM) / sM2 = 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= 0.73912.10The discount rate for the project should be lower than the rate implied by the use of the Security Market Line. The appropriate discount rate for such projects is the weighted average of the interest rate on debt and the cost of equity. Since the interest rate on the debt of a given firm is generally less than the firms cost of equity, using only the stocks beta yields a discount rate that is too high. The concept and practical uses of a weighted average discount rate will be in a later chapter. 12.11i.RevenuesThe gross income of the firm is an important factor in determining beta. Firms whose revenues are cyclical (fluctuate with the business cycle) generally have high betas. 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 / Change in sales). Operating leverage indicates the ability of the firm to service its debt and pay stockholders.iii.Financial leverageFinancial leverage arises from the use of debt. Financial leverage indicates the ability of the firm to pay stockholders. Since debt holders must be paid before stockholders, 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, the riskiness of the stock, of which beta captures a portion, is determined by the fluctuations in the income available to the stockholders. (As was discussed in the chapter, whether income is paid to the stockholders in the form of dividends or it is retained to finance projects are irrelevant as long as the projects are of similar risk as 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 leverage indicates how much of each dollar of revenue will become EBIT. Financial leverage indicates how much of each dollar of EBIT will become net income.12.12a.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%12.13B = $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%12.14S = $25 20 million = $500 millionB = 0.95 $180 million = $171 millionB / (S + B) = 0.2548S / (S + B) = 0.7452WACC = 0.7452 20% + 0.2548 10% 0.60 = 16.43%12.15 B / S = 0.75B / (S + B) = 3 / 7S / (S + B) = 4 / 7WACC = (4 / 7) 15% + (3 / 7) 9% (1 - 0.35) = 11.08%NPV = -$25 million + = $819,299.04Undertake 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 = $240,608.50Mini Case: Allied ProductsAssumptionsPP&E Investment42,000,000 Useful life of PP&E Investment (years)7 Salvage Value of PP&E Investment12,000,000 Annual Depreciation Expense (7 year MACRS)Ending BookYearMACRS %DepreciationValue114.29%6,001,800 35,998,200 224.49%10,285,800 25,712,400 317.49%7,345,800 18,366,600 412.49%5,245,800 13,120,800 Last year of project 58.93%3,750,600 9,370,200 68.93%3,750,600 5,619,600 78.93%3,750,600 1,869,000 84.45%1,869,000 0 NEW 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)22,000 Year 1 marketing and admin costs3,000,000 Annual inflation rate3.00%Corporate Tax rate40.00%Beta (9/27 Valueline)1.20Rf (30 year U.S. Treasury Bond)6.20%Rm (S&P 500 30 year average)14.50%Re (from CAPM) RS = 6.2% + 1.2 (14.5% - 6.2%) 16.16%WACC = 0.5(6.2%)(1-40%) + 0.5(16.16%)9.9400%New Aircraft Production (i.e. NEW GPWS Market)ProbabilityYear 1Year 2Year 3Year 4Year 5Strong Growth0.15350403463532612Moderate Growth0.45250275303333366Mild Recession0.30150159169179189Severe Recession0.105052535556Expected New Airplane Production215237261289319NEW 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)2,500 Allied Signal Market Share in each market45.00%Year012345SalesNEW Units97 107 118 130 144 Price70,000 72,100 74,263 76,491 78,786 Total NEW6,772,500 7,688,654 8,736,317 9,935,345 11,308,721 UPGRADE Units1,125 1,125 1,125 1,125 1,125 Price35,000 36,050 37,132 38,245 39,393 Total UPGRADE39,375,000 40,556,250 41,772,938 43,026,126 44,316,909 Total Sales46,147,500 48,244,904 50,509,254 52,961,470 55,625,630 Variable Costs NEW4,837,500 5,491,896 6,240,226 7,096,675 8,077,658 UPGRADE24,750,000 25,492,500 26,257,275 27,044,993 27,856,343 Total Variable Costs29,587,500 30,984,396 32,497,501 34,141,668 35,934,001 SG&A3,000,000 3,090,000 3,182,700 3,278,181 3,376,526 Depreciation6,001,800 10,285,800 7,345,800 5,245,800 3,750,600 EBIT7,558,200 3,884,708 7,483,253 10,295,821 12,564,503 Interest0 0 0 0 0 Tax3,023,280 1,553,883 2,993,301 4,118,329 5,025,801 Net Income4,534,920 2,330,825 4,489,952 6,177,493 7,538,702 EBIT + Dep - Taxes10,536,720 12,616,625 11,835,752 11,423,293 11,289,302 Less: Change in NWC2,000,000 307,375 104,870 113,218 122,611 (2,648,074)Less: Captial Spending42,000,000 (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 Assets9,304,480 10,351,583 8,821,741 7,735,381 15,494,120 Total Discounted CF from Assets51,707,305 Less: Investment(44,000,000)Net Present Value $ 7,707,305 ResultsPayback3.93 yearsDiscounted Payback4.50 yearsAAR20.81%IRR15.76%NPV$7,707,305 PI1.18Year012345SalesNEW Units113 124 136 150 165 Price70,000 72,100 74,263 76,491 78,786 Total NEW7,875,000 8,962,030 10,129,473 11,443,054 12,999,690 UPGRADE Units1,125 1,1