A property is expected to have NOI of $100,000 the first year. The NOI is expected to increase by 3 percent per year thereafter. Assume that the appraiser would estimate the value in year 10 by using a 10 percent capitalization rate. The appraised value of the property is currently $1 million and the lender is willing to make a 90 percent LTV loan with a contract interest rate of 9 percent, and it will be amortized with fixed monthly payments over a 20-year term. It will be a convertible mortgage loan that will give the lender the option to convert the mortgage balance into a 60 percent equity position at the end of year 10. That is, instead of receiving the payoff on the mortgage, the lender would own 60 percent of the property. Assume that the borrower will default if the property value is less than the loan balance in year 10, in which case the property is transferred to the lender.

a. Calculate the investor’s before-tax IRR. Show and explain all calculations. Should the building be purchased? Why or why not?

b. Calculate the lender’s IRR. Show and explain all calculations.

c. Calculate the lender’s IRR if the property instead sells for only $1 million after 10 years. Show and explain all calculations.

d. Calculate the lender’s IRR if the property instead sells for only $500,000 after 10 years. Show and explain all calculations.