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Unformatted text preview: Solutions to EndofChapter Problems 81 r = (0.1)(50%) + (0.2)(5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%) = 11.40%. 2 = (50% 11.40%) 2 (0.1) + (5% 11.40%) 2 (0.2) + (16% 11.40%) 2 (0.4) + (25% 11.40%) 2 (0.2) + (60% 11.40%) 2 (0.1) 2 = 712.44; = 26.69%. CV = 11.40% 26.69% = 2.34. 82 Investment Beta $35,000 0.8 40,000 1.4 Total $75,000 b p = ($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12. 83 r RF = 6%; r M = 13%; b = 0.7; r = ? r = r RF + (r M r RF )b = 6% + (13% 6%)0.7 = 10.9%. 84 r RF = 5%; RP M = 6%; r M = ? r M = 5% + (6%)1 = 11%. r when b = 1.2 = ? r = 5% + 6%(1.2) = 12.2%. 85 a. r = 11%; r RF = 7%; RP M = 4%. Chapter 8: Risk and Rates of Return Answers and Solutions 1 r = r RF + (r M r RF )b 11% = 7% + 4%b 4% = 4%b b = 1. Chapter 8: Risk and Rates of Return Answers and Solutions 2 b. r RF = 7%; RP M = 6%; b = 1. r = r RF + (r M r RF )b = 7% + (6%)1 = 13%. 86 a. = = N 1 i i i r P r . Y r = 0.1(35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%) = 14% versus 12% for X. b. = = N 1 i i 2 i P ) r r ( . 2 X = (10% 12%) 2 (0.1) + (2% 12%) 2 (0.2) + (12% 12%) 2 (0.4) + (20% 12%) 2 (0.2) + (38% 12%) 2 (0.1) = 148.8%. X = 12.20% versus 20.35% for Y. CV X = X /r X = 12.20%/12% = 1.02, while CV Y = 20.35%/14% = 1.45. If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense. 87 Portfolio beta = $4,000,000 $400,000 (1.50) + $4,000,000 $600,000 (0.50) + $4,000,000 $1,000,000 (1.25) + $4,000,000 $2,000,000 (0.75) b p = (0.1)(1.5) + (0.15)(0.50) + (0.25)(1.25) + (0.5)(0.75) = 0.15 0.075 + 0.3125 + 0.375 = 0.7625. r p = r RF + (r M r RF )(b p ) = 6% + (14% 6%)(0.7625) = 12.1%. Alternative solution: First, calculate the return for each stock using the CAPM equation [r RF + (r M r RF )b], and then calculate the weighted average of these returns. r RF = 6% and (r M r RF ) = 8%. Chapter 8: Risk and Rates of Return Answers and Solutions 3 Stock Investment Beta r = r RF + (r M r RF )b Weight A $ 400,000 1.50 18% 0.10 B 600,000 (0.50) 2 0.15 C 1,000,000 1.25 16 0.25 D 2,000,000 0.75 12 .50 Total $4,000,000 1 .00 r p = 18%(0.10) + 2%(0.15) + 16%(0.25) + 12%(0.50) = 12.1%....
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This note was uploaded on 12/09/2011 for the course FIN 315 taught by Professor Hunsader during the Spring '11 term at S. Alabama.
 Spring '11
 Hunsader

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