chap012 - Chapter 12 Risk Return and Capital Budgeting 12.1...

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Unformatted text preview: Chapter 12: Risk, Return, and Capital Budgeting 12.1 Cost of equity R = 5 + 0.95 (9) = 13.55% NPV of the project 5 $340,000 = -$1.2 million + t . t=1 11355 = -$20,016.52 Do not undertake the project. S 12.2 a. b. 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 = 0.02 RD - RD -0.116 -0.016 0.014 0.084 0.034 R M - RM -0.14 -0.01 0.04 0.08 0.03 ( R M - R M )2 0.0196 0.0001 0.0016 0.0064 0.0009 0.0286 ( R D - R D )( R M - R M ) 0.01624 0.00016 0.00056 0.00672 0.00102 0.02470 Beta of Douglas = 0.02470 / 0.0286 = 0.864 12.3 R R a. b. S B = 6% + 1.15 10% = 17.5% = 6% + 0.3 10% = 9% Cost of equity = R = 17.5% B / S = 0.25 B / (B + S) = 0.2 S / (B + S) = 0.8 WACC = 0.8 17.5% + 0.2 9% (1 - 0.35) = 15.17% S 12.4 C = ( 0.04225) 2 = 0.065 1 1 = ( 0.01467 ) 2 = 0.0383 Beta of ceramics craftsman = CM C M / M 2 = CM C / M = (0.675) (0.065) / 0.0383 = 1.146 M 12.5 a. 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 of the market's returns from their mean. The mechanics of computing the means and the deviations were presented in an earlier chapter. Answers to End-of-Chapter Problems B-123 R T = 0.196 / 12 = 0.016333 R M = 0.236 / 12 = 0.019667 E( R T - R T ) ( R M - R M ) = 0.038711 E( R M - R M )2 = 0.038588 = 0.038711 / 0.038588 = 1.0032 The beta of the average stock is 1. Mercantile's beta is close to 1, indicating that its stock has average risk. RM can have three values, 0.16, 0.18 or 0.20. The probability that R M takes one of these values is the sum of the joint probabilities of the return pair that include particular value of R M . For example, if R M is 0.16, RJ will be 0.16, 0.18 or The probability that R M is 0.16 and RJ is 0.16 is 0.10. The probability that 0.16 and RJ is 0.18 is 0.06. The probability that R M is 0.16 and RJ is 0.22 is The probability that R M is 0.16 is, therefore, 0.10 + 0.06 + 0.04 = 0.20. The procedure is used to calculate the probability that R M is 0.18 and the b. 12.6 a. the 0.22. RM is 0.04. same probability that R M is 0.20. Remember, the sum of the probability must be one. RM 0.16 0.18 0.20 b. i. ii. RM Probability 0.20 0.60 0.20 2 M = 0.16 (0.20) + 0.18 (0.60) + 0.20 (0.20) = 0.18 = (0.16 - 0.18) 2 (0.20) + (0.18 - 0.18) 2 (0.60) + (0.20 - 0.18) 2 (0.20) = 0.00016 1 iii. c. RJ .16 .18 .20 .22 .24 M = ( 0.00016) 2 = 0.01265 Probability .10 .20 .40 .20 .10 d. i. E j = .16 (.10) + .18 (.20) + .20 (.40) + .22 (.20) + .24(.10) = .20 ii. j2 = (.16 - .20)2 (.10) + (.18 - .20)2 (.20) + (.20 - .20)2 (.40) + (.22 - .20)2 (.20) + (.24 - .20)2 (.10) = .00048 iii. j = ( 0.00048) 2 = .02191 1 B-124 Answers to End-of-Chapter Problems e. 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) = .000176 Corrmj = (0.000176) / (0.01265) (0.02191) = 0.635 f. 12.7 i. ii. 12.8 a. b. j = (.635) (.02191) / (.01265) = 1.10 The risk of the new project is the same as the risk of the firm without the project. The firm is financed entirely with equity. 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. 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 the perfume project. A good way to estimate the beta of the project would be to average the betas of many perfume producing firms. 12.9 E(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% State 1 2 3 4 Sum M 2 a. b. c. {RS - E(RS)}{RM - E(RM)}Pr (0.03-0.137)(0.05-0.135)0.1 (0.08-0.137)(0.10-0.135)0.3 (0.20-0.137)(0.15-0.135)0.4 (0.15-0.137)(0.20-0.135)0.2 0.002056 = Cov(RS, RM) {RB - E(RB)}{RM - E(RM)}Pr (0.08-0.092)(0.05-0.135)0.1 (0.08-0.092)(0.10-0.135)0.3 (0.10-0.092)(0.15-0.135)0.4 (0.10-0.092)(0.20-0.135)0.2 0.00038 = Cov(RB, RM) = 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 = 0.002025 Beta of debt = Cov(RB, RM) / M2 = 0.00038 / 0.002025 = 0.188 Beta of stock = Cov(RS, RM) / M2 = 0.002055 / 0.002025 = 1.015 B / S = 0.5 Thus, B / (S + B) = 1 / 3 = 0.3333 S / (S + B) = 2 / 3 = 0.6667 Beta of asset = 0.188 0.3333 + 1.015 0.6667 = 0.739 12.10 The 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 firm's cost of equity, using only the stock's beta yields a discount rate that is too high. The Answers to End-of-Chapter Problems B-125 concept and practical uses of a weighted average discount rate will be in a later chapter. 12.11 i. Revenues The 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 leverage Operating 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 leverage Financial 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. 12.12 a. b. Cost of equity for National Napkin = 7 + 1.29 (13 - 7) = 14.74% B / (S + B) = S / (S + B) = 0.5 WACC = 0.5 7 0.65 + 0.5 14.74 = 9.645% 12.13 B = $60 million 1.2 = $72 million S = $20 5 million = $100 million B / (S + B) = 72 / 172 = 0.4186 S / (S + B) = 100 / 172 = 0.5814 WACC = 0.4186 12% 0.75 + 0.5814 18% = 14.23% 12.14 S = $25 20 million = $500 million B = 0.95 $180 million = $171 million 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 B-126 Answers to End-of-Chapter Problems S / (S + B) = 4 / 7 WACC = (4 / 7) 15% + (3 / 7) 9% (1 - 0.35) = 11.08% 5 $7 million NPV = -$25 million + t t =1 (1 + 0.1108) = $819,299.04 Undertake the project. 12.16 WACC = (0.5) x 28% + (0.5) x 10% x (1 - 0.35) = 17.25% 5 NPV = - $1,000,000 + (1 - 0.35) $600,000 0.1725 = $240,608.50 Answers to End-of-Chapter Problems B-127 Mini Case: Allied Products Assumptions PP&E Investment Useful life of PP&E Investment (years) Salvage Value of PP&E Investment Annual Depreciation Expense (7 year MACRS) Year 1 2 3 4 5 6 7 8 MACRS % 14.29% 24.49% 17.49% 12.49% 8.93% 8.93% 8.93% 4.45% Depreciation 6,001,800 10,285,800 7,345,800 5,245,800 3,750,600 3,750,600 3,750,600 1,869,000 42,000,000 7 12,000,000 Ending Book Value 35,998,200 25,712,400 18,366,600 13,120,800 9,370,200 5,619,600 1,869,000 0 70,000 50,000 35,000 22,000 3,000,000 3.00% 40.00% 1.20 6.20% 14.50% 16.16% 9.9400% Year 1 350 250 150 50 215 Year 2 403 275 159 52 237 Year 3 463 303 169 53 261 15.00% 10.00% 6.00% 3.00% 2,500 45.00% Year 4 532 333 179 55 289 Year 5 612 366 189 56 319 Last year of project NEW GPWS price/unit (Year 1) NEW GPWS variable cost/unit (Year 1) UPGRADE GPWS price/unit (Year 1) UPGRADE GPWS variable cost/unit (Year 1) Year 1 marketing and admin costs Annual inflation rate Corporate Tax rate Beta (9/27 Valueline) Rf (30 year U.S. Treasury Bond) Rm (S&P 500 30 year average) Re (from CAPM) RS = 6.2% + 1.2 (14.5% - 6.2%) WACC = 0.5(6.2%)(1-40%) + 0.5(16.16%) New Aircraft Production (i.e. NEW GPWS Market) Probability Strong Growth 0.15 Moderate Growth 0.45 Mild Recession 0.30 Severe Recession 0.10 Expected New Airplane Production NEW GPWS Market Growth (Strong Growth) NEW GPWS Market Growth (Moderate Growth) NEW GPWS Market Growth (Mild Recession) NEW GPWS Market Growth (Severe Recession state of economy) Total Annual Market for UPGRADE GPWS (units) Allied Signal Market Share in each market B-128 Answers to End-of-Chapter Problems Year Sales NEW Units Price Total NEW UPGRADE Units Price Total UPGRADE Total Sales Variable Costs NEW UPGRADE Total Variable Costs SG&A Depreciation EBIT Interest Tax Net Income EBIT + Dep - Taxes Less: Change in NWC Less: Captial Spending CF from Assets: Discounted CF from Assets Total Discounted CF from Assets Less: Investment Net Present Value 0 1 2 3 4 5 144 78,786 11,308,721 97 107 118 130 70,000 72,100 74,263 76,491 6,772,500 7,688,654 8,736,317 9,935,345 1,125 1,125 1,125 1,125 1,125 35,000 36,050 37,132 38,245 39,393 39,375,000 40,556,250 41,772,938 43,026,126 44,316,909 46,147,500 48,244,904 50,509,254 52,961,470 55,625,630 4,837,500 5,491,896 6,240,226 7,096,675 8,077,658 24,750,000 25,492,500 26,257,275 27,044,993 27,856,343 29,587,500 30,984,396 32,497,501 34,141,668 35,934,001 3,000,000 3,090,000 3,182,700 3,278,181 6,001,800 10,285,800 7,345,800 5,245,800 3,376,526 3,750,600 7,558,200 3,884,708 7,483,253 10,295,821 12,564,503 0 0 0 0 0 3,023,280 1,553,883 2,993,301 4,118,329 5,025,801 4,534,920 2,330,825 4,489,952 6,177,493 2,000,000 42,000,000 (44,000,000) 7,538,702 10,536,720 12,616,625 11,835,752 11,423,293 11,289,302 307,375 104,870 113,218 122,611 (2,648,074) (10,948,080) 10,229,345 12,511,755 11,722,534 11,300,682 24,885,455 9,304,480 10,351,583 8,821,741 7,735,381 51,707,305 (44,000,000) $ 7,707,305 15,494,120 Answers to End-of-Chapter Problems B-129 Results Payback Discounted Payback AAR IRR NPV PI 3.93 years 4.50 years 20.81% 15.76% $7,707,305 1.18 B-130 Answers to End-of-Chapter Problems ...
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This note was uploaded on 05/07/2010 for the course FIN 302 taught by Professor Corporationfinance during the Spring '10 term at Uni Potsdam.

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