Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $75,000 or $330,000 with equal probabilities of 0.5. The alternative risk-free investment in T-bills pays 4% per year.

A. If you require a risk premium of 7%, how much will you be willing to pay for 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?
C. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now?

Answer 1

A. $182,432.43

B. 11%

C. $165,983.607

Step-by-step explanation:

A. The computation of value of portfolio is shown below:-

Value of portfolio = (Cash flow × equal probabilities) ÷ (1 + (Risk free rate + Risk premium))

= (($75,000 × 0.5) + ($330,000 × 0.5)) ÷ (1 + (4% + 7%))

= $202,500 ÷ 1.11

= $182,432.4324

or

= $182,432.43

B. The computation of expected rate of return on the portfolio is shown below:-

Rate of return is

= (Cash flow × equal probabilities) - (value of portfolio) ÷ (value of portfolio)

= ($202,500 - $182,432.43) ÷ $182,432.43

= $20,067.57 ÷ $182,432.43

= 0.11

or

= 11%

C. The computation of value of portfolio is shown below:-

Required rate of return = Risk free rate + Risk premium

= 7% + 15%

= 22%

Price = Expected cash flow ÷ (1 + Required rate of return)

= $202,500 ÷ (1 + 0.22)

= $202,500 ÷ 1.22

= $165,983.607