Yield Maintenance

What is yield maintenance?

Yield maintenance is a prepayment penalty designed to make lenders or investors “whole” if a borrower repays a loan or a bond is called before maturity. It compensates for the interest income the lender expected to receive over the remaining life of the loan by requiring the borrower to pay the difference in yield between the loan rate and a comparable risk-free rate (typically a Treasury yield) on the prepaid amount.

Common uses
– Frequently found in commercial mortgages and some long-term loans or bonds.
– Intended to discourage refinancing when interest rates fall and to protect lenders from prepayment risk.

Why it matters

When borrowers prepay a loan, lenders lose the anticipated stream of interest payments. Yield maintenance ensures the lender can reinvest the prepaid funds at prevailing Treasury rates and receive essentially the same cash flow as if the borrower had made all scheduled payments. If Treasury yields rise above the loan rate, lenders may not suffer a loss but may still impose a penalty per contract terms.

How yield maintenance is calculated

Basic formula:
YM = PV of remaining scheduled payments discounted at the Treasury yield × (Loan interest rate − Treasury yield)

Where:
– YM = Yield maintenance payment (prepayment premium)
– PV = Present value (discounted at the Treasury yield) of the remaining scheduled payments on the loan or bond
– Loan interest rate = the contract rate on the loan or bond (decimal)
– Treasury yield = the comparable Treasury yield (decimal)

Present value (annuity) factor (when using annual discounting and remaining years t):
PV factor = [1 − (1 + r)^(-t)] / r
– r = Treasury yield (annual, decimal)
– t = years remaining

If payments are monthly, use the monthly Treasury discount rate r/12 and number of months n:
PV factor = [1 − (1 + r/12)^(-n)] / (r/12)

Multiply the PV factor by the dollar amount of the scheduled remaining payments (or by the outstanding principal if the contract defines PV that way) to get PV, then apply the basic formula above.

Example

Assume:
– Outstanding loan amount used as the payment base: $60,000
– Loan interest rate (IR): 5% (0.05)
– Comparable 5‑year Treasury yield (TY): 3% (0.03)
– Remaining term: 5 years

Step 1 — compute the PV factor (annual discounting):
PV factor = [1 − (1 + 0.03)^(-5)] / 0.03 ≈ 4.5797

Step 2 — present value of remaining payments:
PV ≈ 4.5797 × $60,000 ≈ $274,782.42

Step 3 — yield maintenance payment:
YM = $274,782.42 × (0.05 − 0.03) = $274,782.42 × 0.02 ≈ $5,495.65

So the borrower would pay about $5,496 as the yield maintenance premium to prepay the loan.

Practical considerations

• Contract terms vary: Some agreements specify exactly how the PV is computed (monthly vs. annual discounting, which Treasury curve to use, whether certain fees or expenses are included).
• Calculation basis: Lenders often discount the remaining contractual payments (interest + principal) at a Treasury yield using the appropriate term that matches the loan’s remaining maturity.
• Economic effect: Yield maintenance can make refinancing unattractive when it would require paying a significant premium; it shifts the economic decision by internalizing the lender’s reinvestment loss.
• If Treasury yields rise above the loan rate after origination, accepting prepayment may benefit the lender; some contracts still impose a prepayment fee regardless.

Key takeaways

• Yield maintenance is a prepayment premium that compensates lenders for lost interest income when a loan or bond is paid off early.
• It is commonly used in commercial mortgages to protect investors from prepayment risk and to discourage refinancing.
• Compute it by discounting the remaining scheduled payments at the Treasury yield to get a present value, then multiply that PV by the difference between the loan rate and the Treasury yield.