Ch012 - Chapter 12: Risk, Cost of Capital, and Capital...

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Chapter 12: Risk, Cost of Capital, and Capital Budgeting 12.1 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 + 0.95 (0.09) = 0.1355 Subtract the initial investment at year 0. To calculate the PV of the cash inflows, apply the annuity formula, discounted at 0.1355. NPV = C 0 + C 1 A T r = -$1,200,000 + $340,000 A 5 0.1355 = -$20,016.52 Do not undertake the project since the NPV is negative. 12.2 a. Calculate the average return for Douglas stock and the market. R D = (Sum of Yearly Returns) / (Number of Years) = (-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) = 0.020 To calculate the beta of Douglas stock, calculate the variance of the market, ( R M - R M ) 2 , and the covariance of Douglas stock’s return with the market’s return, ( R D - R D ) × ( R M - R M ). The beta of Douglas stock is equal to the covariance of Douglas stock’s return and the market’s return divided by the variance of the market. Remember to divide both the covariance of Douglas stock’s return and the market’s return and the variance of the market by 4. Because the data are historical, the appropriate denominator in the calculation of the variance is 4 (= T – 1). R D - R D R M - R M (R M - R M ) 2 (R D - R D ) (R M - 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 0.00102 0.0286 0.02470 β D = [Cov ( R D , R M ) / (T-1)] / [Var ( R M ) / (T-1)] = (0.02470 / 4) / (0.0286 / 4) = 0.864 The beta of Douglas stock is 0.864. B-236
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12.3 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 = (0.004225) 1/2 = 0.065 σ M = ( σ 2 M ) 1/2 = (0.001467) 1/2 = 0.0383 Use the formula for beta: β C = [Corr ( R C , R M ) × σ C ] / σ M = [(0.675) (0.065)] / (0.0383) = 1.146 The beta of Ceramics Craftsman is 1.146. 12.4 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. 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. 12.5
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This note was uploaded on 09/13/2011 for the course FIN 6301 taught by Professor El-asmawanti during the Fall '09 term at University of Texas at Dallas, Richardson.

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Ch012 - Chapter 12: Risk, Cost of Capital, and Capital...

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