Question

A property could be sold today for $2 million. It has a loan balance of $1 million and, if sold, the investor would incur a capital gains tax of $250,000.The investor has determined that if it were sold today, she would earn an IRR of 15% on equity for the past 5 years.If not sold, the property is expected to produce an after-tax cash flow of $50,000 over the next year.At the end of the year, the property value is expected to increase to $2.1 million, the loan balance will decrease to $900,000, and the amount of capital gains tax due is expected to increase to $255,000.a. What is the marginal rate of return for keeping the property one additional year?b. What is the decision to make by the investor?

Answer 1

The marginal rate of return is calculated by considering the net difference in proceeds from selling the property today versus after one year, including the net cash flow from holding on to it. The decision whether to sell or keep the property would depend on how the marginal rate of return compares to the investor's required return.

Step-by-step explanation:

To calculate the marginal rate of return for keeping the property an additional year, you need to compare the net proceeds from selling today to what the investor would receive in total if the property is sold after one year, including the additional net cash flow from retaining it. The net proceeds from selling today are $2 million (sale price) - $1 million (loan balance) - $250,000 (capital gains tax) = $750,000. If the property is sold after one more year, the proceeds would be $2.1 million (expected future sale price) - $900,000 (expected future loan balance) - $255,000 (expected future capital gains tax) + $50,000 (net cash flow from holding the property for the year) = $995,000. The marginal rate of return is then calculated on the equity difference, which is $995,000 in one year versus $750,000 today.

As for the decision the investor should make, it would depend on comparing this marginal rate of return to the investor's required return or opportunity cost of capital. If the marginal rate exceeds the investor's threshold, she should keep the property; otherwise, she should sell it.

Answer 2

a. What is the marginal rate of return for keeping the property one additional year?

• 1.82

b. What is the decision to make by the investor?

• the investor should keep the property one more year since the returns generated by doing so are much higher than the returns the investor requires.

Step-by-step explanation:

the current gains from selling the property = selling price - loan balance - capital gains tax = $2,000,000 - $1,000,000 - $250,000 = $750,000

if he investor keeps the property for one more year, h/she can earn = selling price - loan balance - capital gains tax + after tax cash flow = $2,100,000 - $900,000 - $255,000 + $50,000 = $955,000

marginal return from holding the investment one more year = $955,000 - $750,000 = $205,000

marginal cost = net investment x IRR = $750,000 x 15% = $112,500

marginal rate of return = $205,000 / $112,500 = 1.82