Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $40,000 or $135,000, with equal probabilities of 0.5. The alternative riskless investment in T-bills pays 4%.

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 15%. What is the price you will be willing to pay now? (Round your answer to the nearest dollar amount.)

Answer 1

a. The amount is computed as follows:

Required return will be as follows:

= Risk premium + Risk free rate

= 10% + 4%

= 14%

So, the value of the portfolio will be as follows:

= ($ 40,000 x 0.50 + 135,000 x 0.50) / (1 + required return)

= $ 87,500 / 1.14

= $ 76,754

b. The return will be as follows:

= ($ 40,000 x 0.50 + 135,000 x 0.50 - value computed in part a above) / value computed in part a above

= ($ 87,500 - $ 76,754.38596) / $ 76,754.38596

= $ 10,745.61404 / $ 76,754.38596

= 14%    

c. The amount is computed as follows:

Required return will be as follows:

= Risk premium + Risk free rate

= 15% + 4%

= 19%

So, the value of the portfolio will be as follows:

= ($ 40,000 x 0.50 + 135,000 x 0.50) / (1 + required return)

= $ 87,500 / 1.19

= $ 73,529

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