Ross5eChap13sm - Chapter 13: Risk, Return, and Capital...

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Chapter 13: Risk, Return, and Capital Budgeting 13.1 The discount rate for the project is equal to the expected return for the security, R S , since the project has the same risk as the firm as a whole. Apply the CAPM to express the firm’s required return, R S , in terms of the firm’s beta, β , the risk–free rate, R F , and the expected market return, R M . R S = R F + β × ( R M R F ) = 0.05 + 1.6 (0.09) = 0.194 Subtract the initial investment at year 0. To calculate the PV of the cash inflows, apply the annuity formula, discounted at 0.194. NPV = C 0 + C 1 A T r = –$1,450,000 + $510,000 A 5 0.194 = $ 277.402.65 Undertake the project since the NPV is positive. 13.2 Apply the CAPM to express the firm’s cost of equity capital, R S , in terms of the firm’s beta, , the risk–free rate, R F , and the expected market return, R M . R S = R F + β × ( R M R F ) = 0.045 + 1.3 (0.12–0.045) = 0.1425 13.3 Calculate the square root of the stock’s variance and the market’s variance to find the standard deviation, σ , of each. σ C = ( σ 2 C ) 1/2 = (0.005112) 1/2 = 0.07149825 σ M = ( σ 2 M ) 1/2 = (0.001668) 1/2 = 0.0408412 Use the formula for beta: β C = [Corr ( R C , R M ) × σ C ] / σ M = [(0.910) (0.07149825)] / (0.0408412) = 1.593 The beta of Ceramics Craftsman is 1.593. 13.4 a. To compute the beta of Mercantile’s stock, divide the covariance of the stock’s return with the market’s return by the market variance. Since those two values are provided in the problem, the 13 quarterly returns of Mercantile’s stock and the market are not needed for the calculation. Answers to End–of–Chapter Problems B– 186
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β D = Cov ( R D , R M ) / σ 2 M = (0.038711) / (0.038588) = 1.0032 The beta of Mercantile Banking Corporation is 1.0032. b. The beta of the average stock is one. Since Mercantile’s beta is close to one, its stock has approximately the same risk as the overall market. 13.5 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. 13.6 a. Lang 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 Lang Cosmetics as a whole. b. If the risk of the project is the same as the risk of the firm, use the firm’s stock beta. Otherwise, Lang should use the beta of an all–equity firm that has similar risks as the perfume project. An effective way to estimate the beta of the perfume project is to average the betas of several all–equity, perfume–producing firms. 13.7 First, calculate the expected return on Compton’s stock. R S = Σ [ R S × Prob( R S )] = (0.04) (0.15) + (0.09) (0.25) + (0.19) (0.3) + (0.16) (0.3) = 0.1335 Calculate the expected return on Compton’s debt. R B = Σ [ R B × Prob( R B )] = (0.07) (0.15) + (0.07) (0.25) + (0.09) (0.3) + (0.11) (0.3) = 0.088 Calculate the expected return on the market. R M = Σ [ R M × Prob( R M )] = (0.06) (0.15) + (0.09) (0.25) + (0.15) (0.3) + (0.19) (0.3) = 0.1335 Calculate the covariance of the stock’s return with the market’s return. Cov ( R S , R M ) = Σ [( R S R S ) × ( R M R M ) × Prob] = (0.04 – 0.1335) (0.06 – 0.1335) (0.15) + (0.09– 0.1335) (0.09 – 0.1335) (0.25) + (0.19 – 0.1335) (0.15 – 0.1335) (0.3) + (0.16 – 0.1335) (0.19 – 0.1335) (0.3) = 0.00223275 Calculate the covariance of the debt’s return with the market’s return.
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Ross5eChap13sm - Chapter 13: Risk, Return, and Capital...

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