Question

You have been managing a $5 million portfolio that has a beta of 1.05 and a required rate of return of 8.675%. The current risk-free rate is 5%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.35, what will be the required return on your $5.5 million portfolio? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Required Return on Stock = Risk-Free Return + (Market Risk Premium)(Stock’s Beta)

8.675% = 5% + (Market Risk Premium) (1.05)

3.675% = (Market Risk Premium) (1.05)

Market Risk Premium = 3.5%

Now, we will calculate the beta of the new portfolio.

Total investment = $5,500,000

Beta of new portfolio = ($500,000 / $5,500,000) (1.35) + ($5,000,000 / $5,500,000) (1.05)

Beta of new portfolio = 1.077

Required return on the new portfolio = 5% + (3.5%) (1.077)

Required return on the new portfolio = 8.77%