A property is expected to have NOI of $100,000 the first year. The NOI is expected...

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.

Solutions

Expert Solution

Part A)

NOI income for the Year 1 = $100,000, and the subsequent NOI can be calculated by increasing the NOI by 3% every year.

IRR is the rate that equates the cash inflows and cash outflows.

Since IRR of the property 12.81% is higher than 9.38% effective interest rates on the loan hence the property should be purchased.

Note: This value of IRR is based on the appraised value at the end of Year 10. The IRR will vary based on the appraised value of the property.

Part B)

Step 1: We have to calculate the loan amount and the monthly EMIs

Step 2: Calculate the IRR for the lender

Annual income = Monthly EMIs * 12

Value of Equity = 60% of value of appraised property

Part C)

Only change in this part will be that the market value of property at the Year 10 will be different and hence will impact the value of equity.

Part D)
In this case market value of the property will be $500,000 and hence will impact the value of equity of the lender.

jeff jeffy answered 1 year ago

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