Question

Styles 1) A mortgage loan of $1,875,000 has just been made on a property valued at $2,500,000. The interest rate is 5% with 2 points. The loan will require level monthly payments to amortize the principal over 30 years. The mortgage also carries a 1% prepayment penalty. a. What is the indicated loan-to-value ratio? 75.00% b. What is the monthly mortgage payment? ($10,065.41) c. How much interest is paid in the fifth year? $87,011.11 d. If the mortgage is paid off after 8 years what will the effective yield be?

Answer 1

As you have answered the first three questions correctly, I assume you have built a mortgage repayment schedule and want help with question d.

The borrower has made payments till year 8, so if we divide the cashflows monthly, we have a cash flow of $1,875,000 at month 0 (when the mortgage is made) and for next 96, we have a cash flow of -$10,065.41

If the mortgage is repaid at the end of 8^th year, there will be cash flow equal to -(outstanding loan amount)
From the schedule, we find this value as $1,609,741.76

If the mortgage is repaid at the end of the 8^th year, there will be a prepayment penalty of 1%, which will be charged on the outstanding balance at that time. Hence it would be 1% of $1,609,741.76 = $16,097.42

Hence, we have the following stream of cash flows

Month 0: $1,875,000
Month 1 through Month 95: -$10,065.41
Month 96: Payment + Principal repayment + Prepayment penalty
-$10,065.41 - $1,609,741.76 - $16,097.42

We calculate the IRR of this cash flow using Excel function to get the yield. Note, this will be monthly yield, we annualize it by multiplying by 12

Hence the effective yield will be 5.09%