A five-year fixed-rate loan prepaid in each year, priced on a step-down schedule and on yield maintenance, with the treasury level at which they cross.
A 5-4-3-2-1 step-down charges a fixed percentage of the balance prepaid, falling one point a year: 5 per cent in loan year one, 4 in year two, down to 1 per cent in year five. On an illustrative $25,000,000 loan at 6.00 per cent, prepaying in year three costs 3 per cent, $750,000. The same prepayment under yield maintenance would cost $1,050,529 at a 4.50 per cent treasury, and only the $250,000 floor at 6.50 per cent: the step-down is the cheaper premium whenever the treasury sits more than about 110 basis points below the note rate.
Worked in full in The Real Estate Debt Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Prepayment protection is what a fixed-rate lender charges for the option it gives the borrower to repay early. Yield maintenance and defeasance price that option at market; a step-down replaces the market with a schedule. Lenders who hold loans on balance sheet, and borrowers who expect to sell, often prefer it because the cost is known on day one. Whether it is the better deal depends on where rates go.
| Term | Value |
|---|---|
| Loan balance | $25,000,000 |
| Note rate | 6.00% |
| Term | 5 years |
| Step-down schedule, loan years 1 to 5 | 5%, 4%, 3%, 2%, 1% |
| Alternative: yield maintenance floor | 1% of balance |
Premium = balance prepaid × percentage for the loan year of prepayment
In Excel, with the loan year in B2 and the schedule in E2:E6: =25000000*INDEX(E2:E6,B2). Loan years run from the first payment date, not the calendar year: a prepayment in month 25 is in loan year 3.
| Loan year | Months remaining | Rate | Premium |
|---|---|---|---|
| 1 | 60 | 5% | 1,250,000 |
| 2 | 48 | 4% | 1,000,000 |
| 3 | 36 | 3% | 750,000 |
| 4 | 24 | 2% | 500,000 |
| 5 | 12 | 1% | 250,000 |
Yield maintenance pays the lender the present value of the margin it loses by reinvesting at the treasury yield for the remaining term, with a floor. At the start of year three, with 36 months left and a 4.50 per cent treasury:
YM = balance × (note rate − treasury) / 12 × annuity factor at treasury / 12
25,000,000 × 1.50% / 12 = 31,250 a month; annuity factor for 36 months at 0.375% = 33.6169; YM = 1,050,529, 4.20 per cent of the balance. In Excel: =MAX(PV(4.5%/12,36,-25000000*(6%-4.5%)/12),1%*25000000).
The full derivation is in how to calculate yield maintenance. Here, the 3 per cent step-down saves the borrower $300,529 against it.
| Treasury | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Step-down | 1,250,000 | 1,000,000 | 750,000 | 500,000 | 250,000 |
| 3.50% | 2,863,020 | 2,329,725 | 1,777,462 | 1,205,557 | 613,311 |
| 4.50% | 1,676,231 | 1,370,405 | 1,050,529 | 715,958 | 366,017 |
| 5.50% | 545,342 | 447,904 | 344,970 | 250,000 | 250,000 |
| 6.50% | 250,000 | 250,000 | 250,000 | 250,000 | 250,000 |
The two structures answer different questions. Yield maintenance makes the lender whole on its margin whatever happens to rates, so it is expensive when rates have fallen and costs only the floor when they have risen. The step-down ignores rates: the borrower pays the same $750,000 in year three whether the treasury is 3.50 or 6.50 per cent.
| Loan year | Break-even treasury | Below the note rate |
|---|---|---|
| 1 | 4.87% | 113 bp |
| 2 | 4.90% | 110 bp |
| 3 | 4.92% | 108 bp |
| 4 | 4.95% | 105 bp |
| 5 | 4.97% | 103 bp |
A 5-4-3-2-1 schedule on this loan is equivalent to yield maintenance with the treasury roughly 110 basis points below the note rate. If the note rate was set at a spread wider than that over the treasury at origination, the step-down is cheaper for the borrower even with rates unchanged; the lender is then accepting less protection than yield maintenance would give, in return for certainty and simplicity.
For a lender, the step-down's weakness is the scenario in which borrowers prepay most: a large fall in rates. At a 3.50 per cent treasury, a year-one prepayment pays $1,250,000 against $2,863,020 of lost margin in present value.
A step-down premium is balance times the year's percentage: $750,000 in year three on $25,000,000. It beats yield maintenance for the borrower whenever the treasury sits more than about 110 basis points below the note rate, and loses to it whenever rates have risen. The Real Estate Debt Investor treats prepayment protection as the margin compression a lender can survive on early repayment, and the free workbook for this case prices exactly that round trip.
A prepayment premium set as a fixed percentage of the balance repaid, declining with each loan year. On a 5-4-3-2-1 schedule, prepaying $25,000,000 costs $1,250,000 in year one, $750,000 in year three and $250,000 in year five. Unlike yield maintenance, it does not depend on interest rates at the time of prepayment, so both sides know the cost in advance.
When rates have fallen, usually yes; when they have risen, no. What decides it is the gap between the treasury and the note rate, not the direction of travel. Yield maintenance pays the lender the lost interest margin over the treasury, so it grows as rates fall and drops to its floor as they rise. In the example the two cross at a treasury of about 4.92 per cent in year three: below it, the 3 per cent step-down is the cheaper premium.
Many fixed-rate commercial loans have an open period, often the last three to six months of the term, in which the loan can be repaid at par so the borrower can refinance before maturity. The schedule should say so explicitly; otherwise the final step, 1 per cent or $250,000 on a $25,000,000 loan in the example, applies up to maturity.
This article is one calculation from The Real Estate Debt Investor. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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