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 $$250,000.$ The investor has determined that if it were sold today, she would earn an IRR of $15$ percent on equity for the past five years. If not sold, the property is expected to produce after$-$tax cash flow of $$50,000$ over the next year. At the end of the year, the property value is expected to increase to $$2\mathrm{.}1$ million, the loan balance will decrease to $$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 advice would you give the investor?

$2.$ Refer to Problem $1.$ The owner determines that if the property were renovated instead of sold, after$-$tax cash flow over the next year would increase to $$60,000$ and the property could be sold after one year for $$2\mathrm{.}4$ million. Renovation would cost $$250,000.$ The investor would not borrow any additional funds to renovate the property.

a$.$ What is the rate of return that the investor would earn on the additional funds invested in renovating the property?

b$.$ Would you recommend that the property be renovated