Inverting a leaseback price into the tenant default rate it assumes, with rent, recovery and residual valued separately.
Solve for the annual tenant default rate at which the lease cash flows, the re-letting value on default and the residual are worth exactly the price. On an illustrative 20-year leaseback priced at a 6.75 per cent yield, 148.15 million for 10.0 million of rent, the price implies a default rate of 1.66 per cent a year. The tenant's own bonds imply 6.42 per cent, at which the same lease is worth 122.78 million, 17.1 per cent less than the price.
Worked in full in Sale and Leaseback by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A sale and leaseback is quoted as a yield, and yields are compared with other yields: comparable leasebacks, prime industrial, the tenant's bonds. None of those comparisons says what the buyer is assuming about the one thing that decides the outcome, which is whether the tenant is still paying in year 12. Inverting the price into a default rate makes that assumption explicit. It can then be set against what the credit market charges for the same company, and an investment committee can ask whether the buyer knows something the bond market does not.
| Input | Value |
|---|---|
| Passing rent, a year | 10.0 |
| Deal yield / price | 6.75% / 148.15 |
| Firm lease term, years | 20 |
| Rent-leg discount rate: risk-free 2.60% + illiquidity 1.25% | 3.85% |
| Recovery and residual discount rate | 7.50% |
| Market rent for a new occupier | 8.5 |
| Re-letting yield / vacant value | 8.5% / 100.00 |
| Void, letting fees and costs on a default | 15% |
| Tenant bond spread / bond recovery | 3.85% / 40% |
Two discount rates, not one. The rent leg carries no default premium, because default is in the cash flow through the survival probability; charging for it again in the rate would count it twice. The property legs, what the building is worth empty, carry a property risk premium. The passing rent is 17.6 per cent above market rent, so the building is worth less empty than let to this tenant.
Survival to year t: S(t) = (1 − h)t
Rent leg = Σ S(t) × 10.0 ÷ 1.0385t
Recovery leg = Σ S(t−1) × h × 85.00 ÷ 1.075t, where 85.00 is the vacant value of 100.00 less 15% of costs
Residual = S(20) × 100.00 ÷ 1.07520
Value(h) = rent leg + recovery leg + residual. Solve Value(h) = 148.15 with Goal Seek on h.
Step 1: value with no default. At h = 0 the rent leg is worth 137.73 and the residual 23.54: 161.27 in all. That is the most the lease can be worth, and the price is below it, so the price does assume some default.
Step 2: solve for h. Raising h shrinks the rent leg and the residual and grows the recovery leg. At h = 1.66 per cent the rent leg is 118.50, the recovery leg 12.80 and the residual 16.85, which add to the 148.15 price. Over the 20 years that is a cumulative default probability of 28.4 per cent.
Step 3: compare with the bonds. A simple bond-implied default rate is spread ÷ (1 − recovery) = 3.85% ÷ 0.60 = 6.42 per cent a year, or 73.5 per cent over 20 years. Put 6.42 per cent into the same model and the lease is worth 122.78: rent leg 79.79, recovery leg 36.74, residual 6.25. That is 25.37 million below the price, equivalent to an 8.14 per cent yield.
| Default rate a year | Value | Reading |
|---|---|---|
| 0.0% | 161.27 | Ceiling: tenant never fails |
| 1.0% | 153.03 | |
| 1.66% | 148.15 | The price |
| 2.0% | 145.78 | |
| 3.0% | 139.41 | |
| 5.0% | 128.84 | |
| 6.42% | 122.78 | Tenant's bonds |
The buyer at 6.75 per cent is assuming the tenant is about 3.9 times safer than the bond market says. Part of the gap is explainable: the bond spread also carries a liquidity premium, which this model has already charged separately on the rent leg. But do not excuse the rest by saying that a bond-implied rate overstates actual defaults. Because the rent leg here carries no credit premium, the 1.66 per cent is also a price-implied rate: it has to cover both the defaults the buyer expects and its reward for bearing them. A gap of that size should be argued for in the committee paper, not left inside a yield.
| Deal yield | Price | Implied default rate |
|---|---|---|
| 6.25% | 160.00 | 0.15% |
| 6.75% | 148.15 | 1.66% |
| 7.25% | 137.93 | 3.25% |
| 8.00% | 125.00 | 5.87% |
Half a point on the yield moves the implied default rate by about 1.55 points a year. At 6.25 per cent the buyer is pricing the tenant as almost riskless. The building's own value matters too: at a 7.5 per cent re-letting yield (vacant value 113.33) the price implies 2.28 per cent, and at 9.5 per cent (89.47) it implies 1.25 per cent. A weaker building leaves less room for tenant risk at the same price.
Discounting the whole lease at a single rate that already contains a default premium and then also deducting expected losses, or, more often, comparing the deal yield with the tenant's bond yield and concluding that the leaseback “pays more”. A leaseback yield includes a building the bondholder does not own, and a bond yield includes a recovery the landlord does not get. Only a cash-flow model that separates rent, recovery and residual compares like with like.
This is a simplified annual model: flat rent, no indexation, no renewal at expiry, and default treated as an immediate vacancy. The companion model works quarter by quarter with indexation and a renewal assumption; the logic is the same.
Invert the price: at 6.75 per cent this lease assumes a 1.66 per cent annual default rate against 6.42 per cent in the tenant's bonds. If you cannot explain the difference, the price is paying for covenant strength the credit market does not see. The free workbooks for this case run the hazard-rate cash flow with its two discount rates on the book's nine-building portfolio. See also whether a sale and leaseback pays more than the tenant's bonds and how to calculate rent cover.
Value the lease as rent weighted by the tenant's survival probability, plus the re-letting value of the building if the tenant defaults, plus the residual at expiry, then solve for the annual default rate that makes the total equal the price. In the worked case a 148.15 million price implies 1.66 per cent a year.
Because both price the same company's default risk. A simple bond-implied default rate is spread divided by one minus recovery: 3.85 per cent over 0.60 gives 6.42 per cent a year. At that rate the worked leaseback is worth 122.78 million, an 8.14 per cent yield, against a 6.75 per cent asking yield.
No. It is a risk-neutral rate that includes the market's premium for bearing credit risk and some liquidity, so it overstates actual default frequency. But a rate implied from a leaseback price, with the rent discounted free of any credit premium, is risk-neutral in the same way. In the worked case the leaseback assumes a rate 3.9 times lower than the bonds, which needs an argument rather than an assumption.
This article is one calculation from Sale and Leaseback. 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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