### DEFINITION of Yield Maintenance

Yield maintenance is a prepayment premium that allows investors to attain the same yield as if the borrower made all scheduled interest payments up until the maturity date.

Yield maintenance premiums are designed to make investors indifferent to prepayment. Furthermore, it also makes refinancing unattractive and uneconomical to borrowers.

### BREAKING DOWN Yield Maintenance

When a borrower takes out a loan either by issuing bonds to investors and lenders or by receiving a loan (e.g. mortgage, auto loan, business loan, etc.) from a lending institution, the lenders are periodically paid interest as compensation for lending their funds for a period of time. The interest that is expected constitutes a rate of return for the lender who projects his earnings based on the rate. For example, an investor who purchases a 10-year bond with $100,000 face value and annual coupon rate of 7%, intends to have his account credited annually by 7% x $100,000 = $7,000. Likewise, a bank that approves a $350,000 at a fixed interest rate expects to receive interest payments monthly until the borrower completes his or her mortgage payments years down the line. However, there are situations in which the borrower prepays the loan prior to the maturity date, exposing the lender to prepayment risk.

To compensate lenders in the event that a borrower repays the loan earlier than scheduled, a prepayment fee or premium, known as a yield maintenance, is charged. The most common reason for loan prepayment is a drop in interest rates, which provides an opportunity for a borrower or debt issuer to refinance its debt at a lower interest rate. In effect, the yield maintenance allows the bank to earn their original yield without suffering any loss due to lower interest rates. The bank can reinvest the money returned to them, plus the penalty amount, in safe Treasury securities and receive the same cash flow as they would if they had received all scheduled loan payments for the entire duration of the loan.

### How to Calculate Yield Maintenance

The formula for yield maintenance premium is:

**Yield Maintenance = Present Value of Remaining Payments on the Mortgage x (Interest Rate - Treasury Yield)**

The Present Value factor in the formula can be calculated as (1 – (1+r)^{-n/12})/r

where r = Treasury yield

n = number of months

For example, assume a borrower has a $60,000 balance remaining on a loan with 5% interest. The remaining term of the loan is exactly 5 years, or 60 months. If the borrower decides to pay off the loan when the yield on 5-year Treasury notes drops to 3%, let’s calculate the yield maintenance.

Step 1: PV = [(1 – (1.03)^{-60/12})/0.03] x $60,000

PV = 4.58 x $60,000

PV = $274,782.43

Step 2: Yield Maintenance = $274,782.43 x (0.05 – 0.03)

Yield Maintenance = $274,782.43 x (0.05 – 0.03)

Yield Maintenance = $5,495.65

The borrower will have to pay an additional $5,495.65 to prepay his debt.

If Treasury yields go up from where they were when a loan was taken out, the lender can actually make a profit by accepting the early loan repayment amount and lending the money out at a higher rate or investing the money in higher paying treasury bonds. In this case, there is no yield loss to the lender but it will still charge you a prepayment penalty on the principal balance.

Yield maintenance is most common in the commercial mortgage industry.