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

In this question, required rate of return will be calculated by using Capital Asset Pricing Model.

Required rate of return = Risk free return + Beta of project ( Return from Market - Risk free return)

a) Required rate of return of

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

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

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

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

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

risk premium = return from market - risk free rate of return = 0.14 - 0.09 = 0.05

(c) Non diversible risk refers to beta of the project

Project A                                              -                                              1.5

Project B                                              -                                              0.75

Project C                                              -                                              2.00

Project D                                              -                                              0.0

Project E                                              -                                              -0.50

Project C has the highest beta of 2 i.e. Maximum volatility in its price with respect to swing in the market return as compared to A and B which have beta of 1.5 and 0.75 respectively. Project D has a beta of 0 which means that it does not entail any risk. It is as good as a risk free asset. Project E has a negative beta which means that its movement will be inverse with that of movement in the market.

(d) if the market rate of return is 12%

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

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

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

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

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

( Maximum 4parts can be answered, in case of query please post in comments. I will respond to you)