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

Answer and Explanation:

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

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%

Therefore, The annualized IRR = .38367784*12 = 4.60413409%.