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= 80%

Therefore, loan amount= Cost*LTV= $1,000,000*80%= $800,000

Monthly payments on this mortgage is $3,819.32 calculated as follows:

Balance outstanding after payment of 36 installments is $755,989.30 as shown in the relevant portion of amortization schedule below:

Prepayment penalty @2% will be levied on this amount.

Hence amount of prepayment penalty= $755,989.80*2% = $15,119.80

Cash flows on this mortgage are as follows:

Month 0: $800,000

Months 1 to 35: -$3,819.32 each

Month 36: Monthly payment + Balance after monthly payment + Prepayment penalty = $3819.32.+$755,989.90+$15,119.80 = $774,928.92

Monthly IRR on this mortgage is calculated using IRR function of Excel at 0.38367784%

Hence annualized IRR = ).38367784*12 = 4.60413409%. Details as follows: