Question

Ann wants to buy an office building which costs $1,000,000. She obtains a 30 year fully amortizing fixed rate mortgage with 80% LTV, an annual interest rate of 4%, with monthly compounding and monthly payments. The mortgage has a 2% prepayment penalty if the borrower prepays in the first 5 years. Suppose Ann makes the required monthly payment for 3 years and prepays after her final monthly payment at the end of 3 years. What is the annualized IRR on Ann s mortgage?

Answer 1

Cost of office building= $1,000,000

LTV Ratio= 80%. Therefore, loan amount= Cost * LTV ratio= $1,000,000*85% = $800,000

Monthly payment of this mortgage for 30 years is $3819.32 as follows:

Balance outstanding after regular payment during first 36 months is $755,989.80 as shown in the relevant portion of amortization schedule below.

Rate of prepayment penalty= 2%

Therefore, amount of prepayment penalty= Balance outstanding * Rate of prepay penalty= $755,898.80*2%= $15,119.80

Hence, the cash flows of the mortgage are as follows:

Month 0 : Inflow $800,000 (Loan amount)

Months 1 to 35: $3819.32 (Monthly payments)

Month 36: $3819.32 (Monthly payment)+ $755989.80 (Balance outstanding)+ $15,119.80 (Prepayment penalty)

= $774,928.92

Monthly IRR of these cash flows is 0.38367754% as follows:

Annualized IRR=[ (1+0.38367754)^12]-1 = 1.047025414-1 = 0.047025414 Or, 4.70025414%