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% |
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
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