Question

1. A firm is considering two mutually exclusive projects, A and B. The projects are different in that they have different returns depending on general economic conditions. The firm forecasts that return on the market, and the returns on each project, along with their associated probabilities will be given by the following table. You can assume a 5% risk free rate and a 6% market risk premium. Assume the CAPM holds. Compare the expected returns to the cost of capital for each project and decide which project the firm should choose.

	Extreme Recession	Moderate Recession	Normal	Moderate Growth	Extreme Growth
Pr[economic condition]	15%	20%	30%	20%	15%
Return on the market	-12%	0%	12%	24%	36%
Return on project A	-35%	2%	10%	20%	20%
Return on project B	-9%	0%	12%	22%	28%

           

Answer 1

Expected return of Market = 15%*(-12%)+20%*0%+30%*12%+20%*24%+15%*36%=12%

Similarly, expected return for project A and Project B is given below:

Probability of Economic Scenario	0.15	0.2	0.3	0.2	0.15	Expected Return
Return on the market	-0.12	0	0.12	0.24	0.36	12%
Return on project A	-0.35	0.02	0.1	0.2	0.2	5%
Return on project B	-0.09	0	0.12	0.22	0.28	11%

Beta calculation for A and Bis given below:

Hence, cost of capital for Project A= Risk Free Rate+Beta*Risk Premium=5%+0.853*6%=10.11% and expected return is 5%

Whereas, cost of capital for project B=5%+0.64*6%=8.84% and expected return is 11%.

Hence, Project B should be chosen as expected return is greater than cost of capital here.