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?

	A.	0.38%
	B.	4.60%
	C.	4.00%
	D.	5.73%

Answer 1

Prepayment penalty @2% will be levied on this amount. Amount of prepayment penalty:

= $755,989 x 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 0.3836%

Therefore, The annualized IRR = 0.3836 x 12 = 4.60% i.e. Option B