Question

P8-30 Integrative—Risk, return, and CAPM Wolff Enterprises must consider several investment projects, A through E, using the capital asset pricing model (CAPM) and itsgraphical representation, the security market line (SML). Relevant information is presented in the following table.
Item Rate of return Beta, ?
Risk-free asset 9% 0.00
Market portfolio 14% 1.00
Project A — 1.50
Project B — 0.75
Project C — 2.00
Project D — 0.00
Project E — -0.5

a) Calculate (1) the required rate of return and (2) the risk premium for each project, given its level of nondiversifiable risk.
b) Use your findings in part a) to draw the security market line (required return relative to nondiversifiable risk).
c) Discuss the relative nondiversifiable risk of projects A through E.
d) Assume that recent economic events have caused investors to become less risk- averse, causing the market return to decline by 2%, to 12%. Calculate the new requiredreturns for assets A through E, and draw the new security market line on the same set of axes that you used in part b)
e) Compare your findings in parts a) and b) with those in part d) What conclusion can you draw about the impact of a decline in investor risk aversion on the requiredreturns of risky assets?

Answer 1

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Market premium = 14% - 9% = 5%

Stock A return = 9% + 0.5 * 5% = 11.5%
Stock B return = 9% + 0.75 * 5% = 12.75%
Stock C return = 9% + 2 * 5% = 19%
Stock D return = 9% + 0 * 5% = 9%
Stock E return = 9% - 0.5 * 5% = 6.5%

SML will be a straight line from 9% to 14% with weights varying from 0 to 100%

Answer 2

a.

1. Required Return = RF + beta* [RM - RF]

= 9% + 1.0 [14% - 9%]

= 9% + 1.0 [5%]

= 9% + 5%

= 14%

2. Risk premium for the market = RM - RF

= 14% - 9%

= 5%

d. RM = 12% - 2% = 10%

Required Return (A) = RF + beta* [RM - RF]

= 9% + 1.50 [10% - 9%]

= 9% + 1.50 [1%]

= 9% + 1.5%

= 10.5%

Required Return (B) = RF + beta* [RM - RF]

= 9% + 0.75 [10% - 9%]

= 9% + 0.75 [1%]

= 9% + 0.75%

= 9.75%

Required Return (C) = RF + beta* [RM - RF]

= 9% + 2 [10% - 9%]

= 9% + 2 [1%]

= 9% + 2%

= 11%

Required Return (D) = RF + beta* [RM - RF]

= 9% + 0 [10% - 9%]

= 9% + 0 [1%]

= 9% + 0%

= 9%

Required Return (E) = RF + beta* [RM - RF]

= 9% + -0.5 [10% - 9%]

= 9% + -0.5 [1%]

= 9% + -0.5%

= 8.5%