Consider a risky portfolio. The end-of-year cash flow derived from the portfolio

Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $70,000 or $190,000, with equal probabilities of 0.5. The alternative riskless investment in T-bills pays 5%.

a. If you require a risk premium of 7%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest dollar amount.)

Value of the portfolio= ? $

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.)

Rate of return= ? %

c.Now suppose you require a risk premium of 10%. What is the price you will be willing to pay now? (Round your answer to the nearest dollar amount.)

Value of the portfolio= ? $   

Explanation / Answer

a. If a risk premium of 7% is required , value of the portfolio: Probable Cash flow expected=(0.5*70000)+(0.5*190000)= 130000 Required rate of return= RFR+Risk Premium= 5%+7%=12% So,the Present Value of the portfolio=130000/1.12= 116071.43 Value of the portfolio= 116071.4 b. Expected Rate of return for this purchase price= 12% as 116071.43*1.12= 130000 PV is equated to the expected cash flow at this rate. c. If a risk premium of 10% is required , value of the portfolio: Probable Cash flow expected=(0.5*70000)+(0.5*190000)= 130000 Required rate of return= RFR+Risk Premium= 5%+10%=15% So,the Present Value of the portfolio=130000/1.15= 113043.48 Value of the portfolio= 113043.48 Greater the risk, lower the value or the price

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