The headline loan-to-value measures the distance to the owner's valuation. The lender is repaid from a forced sale, and the cushion has to be measured against that.
Not as far as the loan-to-value suggests. Rebuild the value the lender would actually recover in an enforcement, strip any rent above market, capitalise at a forced-sale yield and deduct realisation costs, then divide the loan by that figure. On an illustrative logistics asset worth 120,000,000 with a 72,000,000 loan, the headline 60 per cent LTV implies a 40 per cent cushion; the lender in fact starts to lose after a 12.4 per cent fall in value, and after only 7.1 per cent once a year of unpaid interest is added to its claim.
Worked in full in Real Estate Finance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The 40 per cent is the distance between the loan and the owner's valuation. The lender does not get the owner's valuation. It gets whatever a receiver can sell the building for, to a buyer who knows it is a forced sale, after the over-rent has been priced out and the agents and lawyers have been paid. That is a different number, and the cushion has to be measured against it.
| Input | Value |
|---|---|
| Passing rent under the lease | 6,420,000 |
| Market rent for the same space today | 5,900,000 |
| Non-recoverable owner's costs | 120,000 |
| Market yield, properly marketed | 5.25% |
| Forced-sale yield (market plus 150 bp) | 6.75% |
| Realisation costs, share of the sale price | 4.0% |
| Senior loan, interest-only | 72,000,000 |
| All-in interest rate | 6.10% |
The owner's net operating income is 6,300,000 and, at 5.25 per cent, the market value is 120,000,000. The loan is 60.0 per cent of it. The lease pays 520,000 a year more than the space would let for today, 8.1 per cent of the passing rent.
Recovery value = (market rent − owner's costs) ÷ forced-sale yield × (1 − realisation costs)
Distance to loss = 1 − loan ÷ recovery value
In Excel: =1-Loan/((MarketRent-Costs)/FSYield*(1-RealCosts))
| Step | Value | Change | Share of market value |
|---|---|---|---|
| Market value, passing NOI at 5.25% | 120,000,000 | ||
| 1. Strip the over-rent: market NOI of 5,780,000 at 5.25% | 110,095,238 | −9,904,762 | 8.3% |
| 2. Capitalise at the 6.75% forced-sale yield | 85,629,630 | −24,465,608 | 20.4% |
| 3. Deduct 4.0% realisation costs | 82,204,444 | −3,425,185 | 2.9% |
| Recovery value | 82,204,444 | −37,795,556 | 31.5% |
Step 1: the over-rent. A buyer from a receiver will not pay for rent the tenant has every reason to renegotiate or walk away from at expiry. Capitalising the market rent instead of the passing rent removes 9,904,762.
Step 2: the forced-sale yield. An enforcement sale reaches fewer bidders, with less information and no warranties, so the yield widens. 150 basis points on a 5.25 per cent yield takes 24,465,608 off the value, the largest single step. Yield moves bite hardest where yields are tightest.
Step 3: realisation costs. Receiver, agents, legal fees and holding costs at 4.0 per cent of the price: another 3,425,185.
The recovery value is 82,204,444, a factor of 0.685 on market value. The loan is 87.6 per cent of that figure, not 60.0 per cent, so the cushion is 1 − 72,000,000 ÷ 82,204,444 = 12.4 per cent.
Read the loan as the lender's credit committee should: a written put on the building, struck where recovery value equals the claim. The probability of default from LTV uses the loan as the strike on market value; the bridge shows the strike sits much closer.
The loan is not the claim. A borrower in default stops paying interest months before the building is sold, and the arrears rank with the principal. At 6.10 per cent, twelve months of unpaid interest adds 4,392,000, so the claim is 76,392,000, 92.9 per cent of recovery value, and the cushion falls to 7.1 per cent. Six months of arrears leaves 9.7 per cent; eighteen leaves 4.4; twenty-four leaves 1.7.
| Widening over 5.25% | Costs 3.0% | Costs 4.0% | Costs 6.0% | Recovery at 4.0% |
|---|---|---|---|---|
| 100 bp (6.25%) | 19.7% | 18.9% | 17.2% | 88,780,800 |
| 150 bp (6.75%) | 13.3% | 12.4% | 10.5% | 82,204,444 |
| 200 bp (7.25%) | 6.9% | 5.9% | 3.9% | 76,535,172 |
| 300 bp (8.25%) | −5.9% | −7.1% | −9.3% | 67,258,182 |
The widening is the judgement that matters. At 300 basis points the recovery is 67,258,182 and the same loan loses 4,741,818 with no fall in the market at all. Building the forced-sale figure line by line, as in how to calculate forced sale value, is what makes that judgement arguable.
To give itself a real cushion of 20 per cent on these assumptions, the lender would advance 65,763,556, an LTV of 54.8 per cent. For 25 per cent, 61,653,333, or 51.4 per cent.
Reading 1 − LTV as the cushion. It measures the distance to the owner's valuation, which includes rent the market will not pay and a yield no forced seller achieves. Skipping only the over-rent step, and keeping the forced-sale yield and costs, still gives a recovery of 89,600,000 and a cushion of 19.6 per cent, more than half as large again as the true 12.4. Over-rented, single-let assets are exactly where the headline LTV flatters most, because the over-rent sits inside the value the ratio is computed on.
Divide the loan, and then the loan plus a year of arrears, by recovery value rather than market value. Here a 60 per cent LTV loan is 87.6 per cent of what the lender would recover, with 12.4 per cent of room before a loss and 7.1 per cent once interest stops. The free workbook for this case puts each step of the bridge on its own switch, and the loan sizing template sets LTV, cover and debt yield side by side.
Because the lender recovers a forced-sale price, not market value. On an illustrative 120,000,000 asset, stripping 520,000 of over-rent, widening the yield 150 basis points and paying 4.0 per cent of costs leaves 82,204,444. A 72,000,000 loan is 87.6 per cent of that, so the lender starts to lose after a 12.4 per cent fall.
Yes. Interest payments stop in a default, but interest keeps accruing and the arrears rank with principal. Twelve months at 6.10 per cent adds 4,392,000 to a 72,000,000 loan, taking the claim to 76,392,000, 92.9 per cent of an 82,204,444 recovery value. The cushion falls from 12.4 to 7.1 per cent, and to 1.7 per cent after twenty-four months.
It is a judgement, so test a range. On an illustrative asset at a 5.25 per cent market yield, a 100 basis point widening leaves the lender an 18.9 per cent cushion, 150 basis points 12.4 per cent, 200 basis points 5.9 per cent, and 300 basis points a loss of 4,741,818 on a 72,000,000 loan with no fall in market value.
This article is one calculation from Real Estate Finance. 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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