Question

Given the following: the risk-free rate is 8% and the market risk premium is 6.5%. Which projects should be accepted if the firm’s beta is 1.2?
Project Beta Expected return
I 0.50 12%
II 0.90 13%
III 1.40 16%
A) I only
B) II only
C) III only
D) I and II only
E) None of the projects are acceptable

Answer 1

The expected Rate of firm  = Risk Free Rate + beta* Market = 8%+1.2*6.5% = 15.8%
The Risk to Volatility ratio of Firm =(Expected return - risk Free Rate)/Beta =(15.8%-8%)/1.2 = 6.5%

Risk To volatility  ratio of Project 1 =(expected return-Risk Free Rate)/Beta =(12%-8%)/0.5 =8%
Risk To volatility  ratio of Project 2 =(expected return-Risk Free Rate)/Beta =(13%-8%)/0.9 =5.56%
Risk To volatility  ratio of Project 3 =(expected return-Risk Free Rate)/Beta =(16%-8%)/1.40 = 5.71%

Only project 1 should be selected because Return to Volatility ratio of Project 1 is higher than Risk to volatility ratio of firm

Hence option A ) I only