Question

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $150,000 or $290,000 with equal probabilities of .5. The alternative risk-free investment in T-bills pays 6% per year.

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 whole dollar amount.)
b. Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? (Round your answer to the nearest whole number.)
c. Now suppose that you require a risk premium of 12%. What is the price that you will be willing to pay? (Round your answer to the nearest whole dollar amount.)

Answer 1

a. $194,690

b. 13%

c. $186,441

Step-by-step explanation:

The computation is shown below:

a. The amount willing to pay would be equal to

= (Expected return) ÷ (1 + return)

where,

Expected return equals to

= ($150,000 + $290,000) ÷ 2

= $220,000

And, the required rate would be

= 6% + 7%

= 13%

So, amount willing to pay would be

= $220,000 ÷ 1.13

= $194,690

b. The expected return on the portfolio would be

= Alternative risk-free investment in T-bills + risk premium

= 6% + 7%

= 13%

c. The price that willing to pay would be

= (Expected return) ÷ (1 + return)

= $220,000 ÷ 1.18

= $186,441

The return would be

= Alternative risk-free investment in T-bills + risk premium

= 6% + 12%

= 18%