Financial Risk Manager Part 1
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A junior risk analyst has been assigned by a risk manager to assess the prepayment risk for a portfolio of fixed-rate mortgages. As part of this assessment, the analyst needs to determine the conditional prepayment rate (CPR) for the portfolio, which begins with calculating the monthly prepayment for an individual mortgage. Consider a specific 30-year fixed-rate mortgage that originally amounted to USD 1,750,000, with monthly payments derived from an annual fixed interest rate of 8%. The borrower made a total monthly mortgage payment of USD 15,950.00, and the outstanding loan balance at the beginning of that month was USD 1,644,235.78. What is the precise calculation of the prepayment for that month?
Explanation:
The correct estimate of the prepayment amount for the month is USD 3,060.29, which corresponds to option A. Prepayment is calculated by taking the month's total payment and subtracting both the month's scheduled interest payment and the month's scheduled principal payment. Alternatively, it can be calculated by subtracting the scheduled total payment from the month's total payment.
In this scenario, the mortgage details are as follows:
Using these details, the scheduled total payment per month (PMT) can be calculated using a financial calculator or formula, which yields a constant payment of USD 12,889.71. This scheduled payment includes both the interest and principal components.
For the specified month, the borrower made a total payment of USD 15,950.00. The loan balance at the beginning of that month was USD 1,644,235.78. The scheduled interest payment for the month is calculated by multiplying the monthly interest rate (0.0067) by the beginning balance, resulting in USD 11,016.38.
To find the prepayment amount:
Prepayment amount = Total payment made - Scheduled total payment = USD 15,950.00 - USD 12,889.71 = USD 3,060.29.
Options B, C, and D are incorrect as they either include the scheduled principal payment or are based on incorrect calculations. Option B (USD 4,933.62) is the total payment less the scheduled interest payment, which incorrectly includes the scheduled principal payment. Option C (USD 11,016.38) is the scheduled interest payment itself, not the prepayment amount. Option D (USD 14,076.60) incorrectly subtracts the difference between the total payment and the sum of the scheduled interest and principal payments, which is not the correct method for calculating prepayment.