Consider a risky portfolio that delivers an end-of-year cash flow of either $70,000 or $195,000, each outcome having a probability of 0.5. An alternative risk-free investment in T-bills yields a 4% return. If you require a risk premium of 8%, what amount would you be willing to pay for the portfolio?

To calculate the amount you would be willing to pay for the risky portfolio, given the required risk premium of 8%, we first need to calculate the expected return of the portfolio and then discount it at the required rate of return (which includes the risk-free rate plus the risk premium).

1. Calculate the expected return (ER) of the risky portfolio: ER = (Probability of low outcome * Cash flow of low outcome) + (Probability of high outcome * Cash flow of high outcome) ER = (0.5 * $70,000) + (0.5 * $195,000) ER = $35,000 + $97,500 ER = $132,500

2. Determine the required rate of return: Required rate of return = Risk-free rate + Risk premium Required rate of return = 4% + 8% Required rate of return = 12% (or 0.12 in decimal terms)

3. Calculate the present value (PV) of the expected cash flow using the required rate of return: PV = ER / (1 + Required rate of return) PV = $132,500 / (1 + 0.12) PV = $132,500 / 1.12 PV = $118,303.57 (approximately)

You would be willing to pay $118,303.57 for the portfolio. This is the price at which the expected return from the portfolio, discounted at the rate equal to the risk-free rate plus your required risk premium, equals the expected cash flow.