The bondholders get exactly the cash they were promised, so the price of leaving is set by the Treasury curve, not by a negotiated penalty.
Defeasance cost is the price of a portfolio of Treasuries that pays every remaining loan payment and the balloon on its due date, plus fees, less the balance it releases. On an illustrative $50.0M loan at 5.25 per cent, defeased with six years left and Treasuries at 3.90 per cent, the portfolio costs 50,213,873 against a balance of 46,944,121, so the borrower pays a premium of 3,269,752, or 3,444,752 with fees: 7.34 per cent of the balance. The premium is almost entirely the gap between the loan rate and the Treasury yield.
Worked in full in How to Read a Real Estate Loan Agreement by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Defeasance is the standard prepayment mechanism in conduit loans. The loan is not repaid: the property is released from the mortgage and replaced as collateral by government securities, and a successor borrower takes over the payments. The bondholders receive exactly the cash flows they were promised, which is why the cost depends on Treasury yields and not on any negotiated penalty.
| Input | Value |
|---|---|
| Original loan | 50,000,000 |
| Coupon, amortisation | 5.25%, 360 months |
| Term | 120 months |
| Defeased after | 48 months |
| Monthly payment | 276,102 |
| Balance at defeasance | 46,944,121 |
| Balloon at month 120 | 40,974,140 |
| Treasury yield, bond-equivalent | 3.90% |
| Fees: consultant, legal, accountant, servicer, successor borrower | 175,000 |
Portfolio cost = Σt=1..72 payment ÷ (1 + m)t + balloon ÷ (1 + m)72
Defeasance cost = portfolio cost + fees − outstanding balance
m is the monthly rate equivalent to the Treasury yield: (1 + 3.90%/2)1/6 − 1 = 0.3224 per cent. In Excel: =PV(m,72,-276102,-40974140). In practice the consultant buys actual securities maturing just before each payment date, which costs slightly more than a flat-curve PV, so treat this as the floor.
To free the property, the borrower writes a cheque of 50,388,873, 1.0734 times the balance, and in most structures gets none of it back: the portfolio belongs to the successor borrower and pays off the loan on schedule. The premium is what it costs to replace a 5.25 per cent obligation with a 3.90 per cent asset for six years, and it is large because most of the value sits in the balloon, which is discounted for the full 72 months.
Each 10 basis points of Treasury yield is worth about 242,826 here. Defeasance is a rate trade. A borrower who can choose the date, within a sale or refinancing timetable, is choosing a Treasury yield.
| Treasury yield | Portfolio cost | Premium | % of balance | With fees |
|---|---|---|---|---|
| 3.00% | 52,452,357 | 5,508,235 | 11.73% | 5,683,235 |
| 3.50% | 51,193,921 | 4,249,799 | 9.05% | 4,424,799 |
| 3.90% | 50,213,873 | 3,269,752 | 6.97% | 3,444,752 |
| 4.50% | 48,786,854 | 1,842,732 | 3.93% | 2,017,732 |
| 5.25% | 47,072,985 | 128,863 | 0.27% | 303,863 |
| 6.00% | 45,433,290 | −1,510,831 | −3.22% | −1,335,831 |
Two details are worth seeing. First, a Treasury yield equal to the coupon does not give a zero premium: Treasury yields are quoted semi-annually and the loan compounds monthly, so the portfolio only matches the balance at a yield of 5.31 per cent, and covers the fees too at 5.39. Second, when Treasury yields exceed the loan rate, the portfolio costs less than the balance. Unlike yield maintenance, which usually has a floor of a percentage of the balance, defeasance can let a borrower prepay below par.
The common mistake is to discount only the payments to the end of the term and forget that the balloon is the bulk of the cash flow: here it is 40,974,140 of the 60,853,473 to be replicated, and its PV is 65 per cent of the portfolio. The second mistake is to compare the coupon with a single Treasury yield of the wrong maturity. The portfolio's weight sits at the balloon date, so the yield that matters most is the one for the loan's remaining term, not the short end. The third is to forget that the loan agreement fixes the date to which the portfolio must run: where defeasance is allowed only to maturity rather than to the start of the open period, the premium is larger.
For the alternative formula, see how yield maintenance is calculated; the balloon itself is worked in how to calculate a balloon payment.
Defeasance cost is the PV of the remaining payments and balloon at Treasury yields, plus fees, less the balance. On this loan it is 3,444,752, 7.34 per cent, and it moves by about 242,826 for every 10 basis points. Read the defeasance clause for the date the portfolio must run to and the costs the borrower bears, then price it on the day's curve. The free workbook for this case computes the book's own defeasance figure from the live schedule rather than a typed balance.
Yes. When Treasury yields are above the loan's rate, the replicating portfolio costs less than the balance. In the illustrative case, at a 6.00 per cent Treasury yield the portfolio costs 45,433,290 against a 46,944,121 balance, 1,335,831 below it even after fees. Yield maintenance usually has a floor and cannot do this.
Usually somewhat, because defeasance buys real securities that must replicate every remaining payment and rarely match the dates exactly, adds third-party fees, and has no spread over Treasuries where some yield maintenance formulas discount at one. The difference depends on the yield maintenance formula in the agreement. In the illustrative case the fees alone are 175,000 on a 46,944,121 balance.
Roughly the portfolio's duration times the change. In the illustrative case each 10 basis point fall in the Treasury yield adds about 242,826 to the cost of a portfolio worth 50,213,873, because most of its value sits in the balloon six years out.
This article is one calculation from How to Read a Real Estate Loan Agreement. 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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