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 0.5. 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?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

Answer:

(A) The price you will be willing to pay for the portfolio is $194,690.

(B) The expected rate of return is 13%.

(C) The price you will be willing to pay for the portfolio is $181,818.

Explanation:

A. If you require a risk premium of 7%, how much will you be willing to pay for the portfolio?

The amount you be willing to pay for the portfolio can be calculated using the following formula:

The price you will be willing to pay for the portfolio = Expected cash flow / (1 + Required rate of return) ................... (1)

Where;

Expected cash flow = ($150,000 * 0.5) + ($290,000 * 0.5) = $220,000

Required rate of return = Risk free rate + Risk premium = 6% + 7% = 13%, or 0.13

Therefore, we have:

The price you will be willing to pay for the portfolio = $220,000 / (1 + 0.13) = $220,000 / 1.13 = $194,690

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?

The expected rate of return (E(r)) can be calculated using the following formula:

Amount to be paid for the portfolio * [1 + E(r)] = Expected cash flow

Therefore, we have:

$194,690 * [1 + E(r)] = $220,000

$194,690 + ($194,690 * E(r)) = $220,000

$194,690 * E(r) = $220,000 - $194,690

$194,690 * E(r) = $25,310

E(r) = $25,310 / $194,690 = 0.13, or 13%

Therefore, the expected rate of return is 13%.

C. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now?

Required rate of return = Risk free rate + Risk premium = 6% + 15% = 21%, or 0.21

Using equation (1) in part A, we have:

The price you will be willing to pay for the portfolio = $220,000 / (1 + 0.21) = $220,000 / (1.21) = $181,818