Question

Currently under consideration is a project with a beta of 1.50. At this time, the risk free rate of return is 7% and the return on the market portfolio of assets is 10%.The project is actually expected to earn an annual rate of return of 11%.
a. If the return on the market portfolio were to increase by 10%, what would be the expected to happen to the project’s required return? What if the market return were to decline by 10%?
b. Use the CAPM to find the required return on this investment.
c. On the basis of your calculations in b, would you recommend this investment? Why or why not?
d. Assume that as a result of investors becoming less risk – averse, the market return drops by 1% to 9%.what impact would this change have on your response in b and c?

Answer 1

beta=1.5 Rf=7% Rm=10% E(R)=11%

a)

If rm increases by 10% then new Rm=10%*(1+10%)=11%

Required return=7+1.5*(11-7)=13%

If rm decreases by 10% then new Rm=10%*(1-10%)=9%

Required return=7+1.5*(9-7)=10%

b)Required Return= Rf+Beta*(Rm-Rf)
=7%+1.5*(10-7)=11.5%

c)We will not recommend this investment as the actual return is less than the required return by 0.5%

d)if Rm=9%

Required return=7+1.5*(9-7)=10%

and now we can go ahead with the investment as the actual return is more than the required return by 1%

Answer 2

We can use CAPM model to analyze above situation.

Return_Investment = RiskFreeRate + Beta*(R_m - RiskFreeRate) ...(1)

Given, RiskFreeRate = 7%, Beta = 1.5 ...(2)

From (1) & (2),

Return_Investment = 7% + 1.5*(R_m - 7%)

When R_m=10%

Return_Investment = 7% + 1.5*(10%- 7%) = 11.5% (nearer to 11% as given in question)

If R_m to increase 10%, R_m = 10%*1.1 = 11%

Return_Investment = 7% + 1.5*(11%- 7%) = 13%. {we expect investment's return to increase to 13%}

If R_m to fecrease 10%, R_m = 10%*0.9 = 9%

Return_Investment = 7% + 1.5*(9%- 7%) = 10%. {we expect investment's return to decrease to 10%}