Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $70,000 or $200,000 with equal probabilities of 0.5. The alternative risk-free investment in T-bills pays 6 percent per year.

a) If you require a risk premium of 12 percent, how much will you be willing to pay for the portfolio?

b) Suppose that the portfolio can be purchased for the amount in a). What will be the expected rate of return on the portfolio?

a) 118,421.05

b) 14%

To answer these questions, we need to apply some concepts of finance, including risk premium and expected rate of return. Let's explain step by step how to calculate each answer:

a) To determine how much you would be willing to pay for the portfolio, we first need to calculate the expected cash flow from the risky portfolio. The expected cash flow is the sum of the possible cash flows weighted by their probabilities:

Expected Cash Flow = ($70,000 * 0.5) + ($200,000 * 0.5) = $135,000

Now, we can calculate the risk premium by multiplying the expected cash flow by the risk premium rate:

Risk Premium = $135,000 * 12% = $16,200

Finally, the amount you would be willing to pay for the portfolio is the sum of the expected cash flow and the risk premium:

Amount to Pay = Expected Cash Flow + Risk Premium = $135,000 + $16,200 = $151,200

Therefore, you would be willing to pay $151,200 for the portfolio.

b) The expected rate of return on the portfolio can be calculated as the weighted average of the possible returns, given their respective probabilities.

The potential returns from the risky portfolio are $70,000 and $200,000 with equal probabilities.

Expected Rate of Return = ($70,000 * 0.5) + ($200,000 * 0.5) = $135,000 / $151,200 = 0.8914 or 89.14%

Therefore, the expected rate of return on the portfolio is 89.14%.