Mezzanine sits where most bad outcomes land, so its price is set by the value distribution, not by the senior spread.
Charge the return you need on the capital plus the expected loss of the slice, spread over the term. On an illustrative three-year mezzanine loan from 55 to 70 per cent of value, with 15 per cent value volatility and 8 per cent enforcement costs, the slice has a 7.03 per cent chance of being under water at maturity and an expected loss of 5.17 per cent of its principal. To earn a 10.00 per cent expected return it must carry a coupon of 11.56 per cent, 156 basis points of it for expected loss.
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 →
A senior loan to 55 per cent of value loses money only in a collapse, and its expected loss is a rounding error: 4 basis points on these inputs. That is why senior pricing is mostly about funding cost, operating cost and competition. A mezzanine loan sits in the slice where most of the realistic bad outcomes land. Its expected loss is large, it depends on where the slice starts and how thick it is, and it is very sensitive to how volatile the property's value is. Adding a fixed premium to the senior spread ignores all three.
The method here treats the mezzanine loan as what it is: a claim on the property's value between two points, after the costs of getting the value out.
| Input | Value |
|---|---|
| Senior loan, interest-only (attachment point of the mezzanine) | 55 |
| Mezzanine loan, interest-only | 15 |
| Detachment point | 70 |
| Term, years | 3 |
| Expected value growth a year | 2.0% |
| Value volatility a year | 15% |
| Enforcement and sale costs, share of value | 8% |
| Target expected return on the mezzanine capital | 10.0% |
Interest is assumed to be paid in full until maturity, so the risk sits in repayment: if the property is worth less than 70 when the loans fall due, the borrower cannot refinance, the mezzanine lender takes control and sells, and it receives what is left after costs and the senior loan. Value at maturity is lognormal. The target return is an input: the return a mezzanine investor wants for tying up the capital before counting any loss.
Value at maturity: ln VT ~ Normal( ln 100 + (2.0% − σ²/2) × 3, σ² × 3 )
If VT ≥ 70: repaid in full. Otherwise recovery = min(15, max(0, VT × (1 − 8%) − 55))
Expected loss rate = E[15 − recovery] ÷ 15
Coupon c solves: 1 = c × annuity(10%, 3) + (1 − expected loss rate) ÷ 1.103
Excel, once the expected loss rate is in B1: =(1-(1-B1)/1.1^3)/PV(10%,3,-1)
The expected loss is an integral over the value distribution, done numerically over a fine grid of outcomes. Two features drive it. The probability of ending below 70 is 7.03 per cent. And the loss when that happens is never small: at a value of exactly 70, the lender sells for 64.40 after costs, repays the senior 55 and keeps 9.40 of its 15, a loss of 37 per cent of the loan on the first dollar of shortfall. A value of 59.78, a fall of 40.2 per cent, wipes the slice out.
| Line | Value |
|---|---|
| Probability value is below 70 at maturity | 7.03% |
| Expected loss, share of the mezzanine principal | 5.17% |
| Expected loss, simple annual rate | 1.72% |
| Annuity factor, 10 per cent, three years | 2.4869 |
| Required coupon | 11.56% |
| of which expected loss premium | 156 bp |
On a 40 million mezzanine loan the expected loss is 2.07 million over the term, against 4.62 million a year of coupon. The premium is lower than the simple 1.72 per cent a year because the loss is only suffered at maturity and is discounted.
| Slice, per cent of value | Chance under water | Expected loss of slice | Coupon | Loss premium, bp |
|---|---|---|---|---|
| 50 to 65 | 3.93% | 2.67% | 10.81% | 81 |
| 55 to 65 | 3.93% | 3.39% | 11.02% | 102 |
| 55 to 70 | 7.03% | 5.17% | 11.56% | 156 |
| 55 to 75 | 11.34% | 7.40% | 12.24% | 224 |
| 60 to 75 | 11.34% | 8.92% | 12.69% | 269 |
| 65 to 75 | 11.34% | 10.55% | 13.19% | 319 |
The same 55 per cent attachment needs 102 basis points of loss premium for a slice to 65 and 224 for a slice to 75: thickness at the top of the stack matters as much as where the slice starts. A thin slice high in the stack, 65 to 75, needs 319. Volatility matters even more: at 10 per cent the 55 to 70 slice needs a coupon of 10.19 per cent, at 20 per cent it needs 13.74, with expected loss of 0.62 and 12.39 per cent of the principal respectively. Volatility is the input to argue about at credit committee.
Pricing by the attachment point, or by the equity cushion. A 55 to 70 slice "with 30 per cent of equity below it" sounds safe, and losses are often pictured as starting gently once value falls through 70. They do not: enforcement costs come off the top, so the first dollar of shortfall costs the lender 37 per cent of its loan. The cushion that matters is measured after costs and accrued interest, as in how to calculate mezzanine attachment and detachment points.
The model ignores interest defaults before maturity and treats value as the only risk. Both make it generous. Use the result as a floor for the coupon, then add what you need for operating cost and for the capital the position ties up.
How a margin turns into a return on the lender's capital is the subject of margin versus return on capital on a real estate loan, and the book's return model and sizing workbook are in the free workbooks for this book.
It depends on the slice and the asset, so derive it rather than quote it. On illustrative inputs, a 10.0 per cent target return gives 10.81 per cent for a 50 to 65 per cent slice and 13.19 per cent for 65 to 75. Raising value volatility from 15 to 20 per cent lifts the 55 to 70 slice from 11.56 to 13.74 per cent.
Because they come off the top of the value before the mezzanine is paid. At a value of 70, 8 per cent costs leave 64.40; after the senior 55, the mezzanine keeps 9.40 of its 15. The first dollar of shortfall therefore costs 37 per cent of the loan, and a 40.2 per cent fall in value wipes it out.
A thicker slice reaches higher into the stack, where losses are more likely. With the attachment fixed at 55 per cent, a slice to 65 needs 102 basis points of expected loss premium, a slice to 70 needs 156 and a slice to 75 needs 224, at a 10.0 per cent target return.
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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