Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $60,000 or $170,000, with equal probabilities of 0.5. The alternative riskless investment in T-bills pays 6%.

a. If you require a risk premium of 10%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest dollar amount.)

b. Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be? (Do not round intermediate calculations. Round your answer to the nearest whole percent.)

c. Now suppose you require a risk premium of 14%. What is the price you will be willing to pay now? (Round your answer to the nearest dollar amount.)

Answer 1

Answer (a):

Required rate of return = Risk free return + Risk premium = 6% + 10% = 16%

Expected end-of-year cash flow = 60000 * 0.5 + 170000 * 0.5 = $115,000

Present value = 115000 / (1 + 16%) = $99,137.93

Amount you will be willing to pay for the portfolio = $99,137.93

Answer (b):

Expected rate of return on the portfolio = (115000 - 99137.93) / 99137.93 = 16%

Expected rate of return on the portfolio = 16%

Answer (c):

Assuming you require a risk premium of 14%:

Required rate of return = Risk free return + Risk premium = 6% + 14% = 20%

Price you will be willing to pay now = 115000 / (1 + 20%) = 95833.33

Amount you will be willing to pay for the portfolio = $95,833.33