Question

Wolff Enterprises must consider several investment projects, A through E, using the capital asset pricing model (CAPM) and its graphical representation, the security market line (SML). Relevant information is presented in the following table

ITEM                            RATE OF RETURN                     BETA

Risk-free asset                          9%                                0.0

Market portfolio                       14%                              1.0

Project A                                  -                                   1.5

Project B                                   -                                   0.75

Project C                                   -                                   2.00

Project D                                  -                                   0.0

Project E                                   -                                   -0.50

1. Calculate (1) the required rate of return and (2) the risk premium for each project, given its level of nondiversifiable risk.
2. Use your findings in part a to draw the security market line (required rate of return relative to nondiversifiable risk)
3. Discuss the relative nondiversifiable risk of projects A through E.
4. Assume that recent economic events have caused investors to become less risk-averse, causing the market return to decline to 12%. Calculate the new required returns fcor assets A through E and draw the new security market line on the same graph you drew for b.
5. 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 required returns of risky assets?

Answer 1

(a) CAPM return = risk free rate of return + beta ( Return from market - risk free rate of return )

Risk free rate of return = 9% ; Return from the market = 14%

A = 0.09 + 1.5 ( 0.14 - 0.09 ) = 0.165 = 16.5%

B = 0.09 + 0.75 ( 0.14 - 0.09 ) = 0.1275 = 12.75%

C = 0.09 + 2 ( 0.14 - 0.09 ) = 0.19 = 19%

D = 0.09 + 0( 0.14 - 0.09 ) = 0.09 = 9%

E = 0.09 - 0.5 ( 0.14 - 0.09 ) = 0.065 = 6.5%

Risk premium = return from market - risk free rate of return

(c)

Project A                                  -                                   1.5

Project B                                   -                                   0.75

Project C                                   -                                   2.00

Project D                                  -                                   0.0

Project E                                   -                                   -0.50

Project C has the maximum beta which entails maximum risk and project A and B have a beta of 1.5 and 0.75 the risk is comparatively less in case of these projects.

Project D has a beta of zero which means no risk. It's as good as a risk free asset.

Project E has a negative beta which means it performs opposite to that of the market forces.

(d) If return from market =12%

A = 0.09 + 1.5 ( 0.12 - 0.09 ) = 0.135 = 13.5%

B = 0.09 + 0.75 ( 0.12 - 0.09 ) = 0.1125 = 11.25%

C = 0.09 + 2 ( 0.12 - 0.09 ) = 0.15 = 15%

D = 0.09 + 0( 0.12 - 0.09 ) = 0.09 = 9%

E = 0.09 - 0.5 ( 0.12 - 0.09 ) = 0.075 = 7.5%

We can answer maximum 4 parts.

(hope you have understood. In case any doubt please comment. I will reply in the comments)