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Unformatted text preview: Bodie, Kane, Marcus, Perrakis and Ryan, Chapter 7 Answers to Selected Problems 1. What is the beta of a portfolio with E [ r p ] = 18 percent, if r f = 6 percent and E [ r M ] = 14 percent? Answer: Using the CAPM equilibrium condition, E [ r p ] = r f + p E [ r M ] r f p = E [ r p ] r f E [ r M ] r f = . 18 . 06 . 14 . 06 = 1 . 5 . 2. The market price of a security is $50. Its expected return is 14 percent. The riskfree rate is 6 percent and the market risk premium is 8.5 percent. What will be the market price of the security if its covariance with the market portfolio doubles (and all other variables remain unchanged)? Answer: The securitys risk premium is actually . 14 . 06 = 8%. According to the CAPM, doubling i will double the securitys risk premium since E [ r i ] r f = i ( E [ r M ] r f ) . That is, the new risk premium for this security will be 16%, which implies a new expected return of . 16 + . 06 = 22%. Let E [ d 1 ] and E [ p 1 ] denote the expected dividend and the expected price of the security one year from now, and let p denote todays price. Then E [ r i ] = E [ p 1 ] + E [ d 1 ] p p p (1 + E [ r i ]) = E [ p 1 ] + E [ d 1 ] . 1 If markets are efficient, then E [ p 1 ] = p and thus p = E [ d 1 ] E [ r i ] , which is the result we have obtained had we assumed that the firm were expected pay a constant dividend forever. We know that p = $50 when E [ r i ] = 14%, and thus E [ d 1 ] = 50 . 14 = $7 . Assuming that E [ d 1 ] does not change even though the security is more risky, We obtain the new price of the security by dividing E [ d 1 ] with the new expected return, i.e. p = 7 . 22 = $31 . 82 . 3. You are a consultant to a large manufacturing corporation that is considering a project with the following net aftertax cash flows (in millions of dollars): Years from now AfterTax Cash Flow 20 19 10 10 20 The projects beta is 1.7. Assuming that r f = 9 percent and E [ r M ] = 19 percent, what is the net present value of the project? What is the highest possible beta estimate for the project before its NPV becomes negative? Answer: The NPV of the project is given by NPV = 20 + 10 E [ r p ] 1 1 (1 + E [ r p ]) 9 + 20 (1 + E [ r p ]) 10 Using the CAPM equation, we can find the required return on the project, which is E [ r p ] = r f + p [ E [ r M ] r f ] = . 09 + 1 . 7( . 19 . 09) = 26% . Using this rate of return, we find that NPV = 20 + 10 . 26 1 1 (1 . 26) 9 + 20 (1 . 26) 10 = 15 . 64 . 2 The internal rate of return for this project is 49.55%. That is, the NPV of the project is zero when E [ r p ] = . 4955. Using the CAPM expectedreturnbeta relationship, this means p = E [ r p ] r f E [ r M ] r f = . 4955 . 09 . 19 . 09 = 4 . 055 ....
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 Spring '12
 Scott
 Capital Asset Pricing Model, Modern portfolio theory

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