Prepayment rates or prepayment speeds are essential in projecting the cash flow of a mortgage.

**Par Sunil K. Parameswaran**

Mortgages are called amortized loans. Equal payments are calculated for the remaining term of the loan at the start of a period, usually the month. Most mortgages are repaid in equal installments at evenly spaced intervals.

This is where the terms Equal Monthly Payments (EMI) come from. Each payment will have an interest component and a principal component. Thus, the outstanding principal and interest of the tranche will decrease with each payment. However, since the tranche is fixed, the principal component will increase.

In practice, we have both fixed rate and variable rate mortgages. In the first case, the interest rate remains fixed for the duration of the loan. However, in the case of variable rate mortgages, the rates are usually reset at the start of each year. Each time the rate is reset, the principal outstanding at that time will be amortized over the remaining term until maturity. If the interest rate has fallen, so will the EMI. Otherwise, if the interest rate has increased, the EMI will increase.

A practical problem with loans is the possibility of prepayment. This is a principal payment at the end of the month that exceeds the expected principal. If the interest rate is constant, future IMEs will decrease due to prepayment, which serves to reduce the outstanding principal. In the case of a variable rate mortgage, the new EMI will be influenced by two factors, the unexpected drop in the outstanding principal and the new interest rate on the mortgage.

Prepayment rates or prepayment speeds are essential in projecting the cash flow of a mortgage. Single Month Mortality or SMM is the percentage of the principal delinquency expected at the end of the month that is prepaid. Suppose the outstanding amount at the beginning of the month is L. The interest rate is r% per month and the EMI is A. The main component of the EMI is A-rL.

Thus, the outstanding amount expected at the end of the month is L- (A-rL) = L (1 + r) -A. If the SMM is m%, the prepayment for the month is m[L(1+r)-A]. The actual principal delinquency at the end of the month is the expected unpaid balance minus the prepayment. The actual principal outstanding will then be written off over the remaining term to maturity, based on the prevailing interest rate. The EMI for the following month, and its division into an interest component and a principal component, is based on the actual principal at the beginning of the month. The principal expected at the end of the month is used only to calculate the prepayment amount at the end of the month.

The annual prepayment rate is called the conditional prepayment rate (CPR). One minus the CPR is equivalent to one minus the SMM raised to the power 12. Thus, this prepayment at the rate of SMM 12 times per year is equivalent to prepaying once at the end of the year to the CPR.

**The author is CEO, Tarheel Consultancy Services**

Get live stock quotes for BSE, NSE, US market and latest NAV, mutual fund portfolio, see latest IPO news, top performing IPOs , calculate your tax by income tax calculator, know the best market winners, the best losers and the best equity funds. Like us on Facebook and follow us on Twitter.

Financial Express is now on Telegram. Click here to join our channel and stay up to date with the latest news and updates from Biz.