The yield move is quoted in basis points, the damage is a percentage that depends on the starting yield, and the loan-to-value covenant feels it first.
Value is income divided by the cap rate, so the change in value is the old cap rate divided by the new one, minus one. At an illustrative 5.25 per cent, a 25 basis point rise to 5.50 per cent cuts value by 4.55 per cent, and a 25 basis point fall adds 5.00 per cent; on a 60 per cent loan, the rise alone takes loan-to-value to 62.9 per cent, and a move of 43.8 basis points breaches a 65 per cent covenant.
Worked in full in Real Estate Finance by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Cap rate moves are quoted in basis points; their effect on value is a percentage that depends on the starting yield. Lenders need both: the yield move is what the market does, and the percentage is what happens to the loan-to-value covenant and to the equity cushion beneath the loan. The calculation is one division, but the two usual shortcuts both get it wrong.
| Input | Value |
|---|---|
| Net operating income | 6,000,000 |
| Cap rate | 5.25% |
| Value: 6,000,000 ÷ 5.25% | 114,285,714 |
| Loan at 60% LTV | 68,571,429 |
| LTV covenant | 65% |
Value = NOI ÷ cap rate
Change in value = cap rateold ÷ cap ratenew − 1
Cap rate at which LTV hits the covenant = cap rate × covenant LTV ÷ current LTV
In Excel: =B2/(B2+0.0025)-1 for the change, and =B2*B5/B4 for the breach yield.
Outward by 25 basis points: 5.25 divided by 5.50, minus one, is minus 4.55 per cent. Value falls from 114,285,714 to 109,090,909, a loss of 5,194,805. Inward by 25 basis points: 5.25 divided by 5.00, minus one, is plus 5.00 per cent, a gain of 5,714,286. The same move in basis points is worth more inward than outward, because value is convex in the yield.
| Cap rate move | Cap rate | Value | Change | LTV |
|---|---|---|---|---|
| −25 bp | 5.00% | 120,000,000 | 5.0% | 57.1% |
| none | 5.25% | 114,285,714 | 0.0% | 60.0% |
| +25 bp | 5.50% | 109,090,909 | −4.5% | 62.9% |
| +50 bp | 5.75% | 104,347,826 | −8.7% | 65.7% |
| +75 bp | 6.00% | 100,000,000 | −12.5% | 68.6% |
| +100 bp | 6.25% | 96,000,000 | −16.0% | 71.4% |
Before the covenant, the equity. The borrower's 45,714,286 of equity absorbs the whole 5,194,805 of a 25 basis point move, 11.4 per cent of its value, and 21.7 per cent for 50 basis points. At 60 per cent leverage, every percentage point of value lost is two and a half points of equity lost.
The covenant breaks when value falls by 1 minus 60/65, 7.7 per cent. With income unchanged, that is a cap rate of 5.25 × 65 ÷ 60 = 5.6875 per cent, or 5.69: a move of 43.8 basis points. Fewer than two quarter-point moves use up the whole of the headroom, which is why the yield, not the income, is usually the first thing to break a loan-to-value covenant on a fully let asset. Add a 5 per cent fall in income to a 25 basis point rise and value falls 9.3 per cent to 103,636,364; LTV is 66.2 per cent, in breach. Which covenant breaches first runs the same test across LTV, cover and debt yield.
| Starting cap rate | Exact change | First-order estimate |
|---|---|---|
| 4.00% | −5.88% | −6.25% |
| 5.25% | −4.55% | −4.76% |
| 7.00% | −3.45% | −3.57% |
| 8.00% | −3.03% | −3.12% |
The lower the yield, the larger the percentage hit from the same basis point move. A 25 basis point rise costs a 4.00 per cent asset almost twice what it costs an 8.00 per cent one, 5.88 against 3.03 per cent of value. Low-yielding prime assets carry more value risk per basis point, even though their income is more secure, so the same loan-to-value headroom buys fewer basis points of protection on them.
The change in value is the ratio of the yields: minus 4.55 per cent for 25 basis points out from 5.25, plus 5.00 per cent for 25 in. On a 60 per cent loan with a 65 per cent covenant, the headroom is 43.8 basis points of yield. The sizing sheet in the free workbooks for this case solves every covenant for the move that breaks it, and the loan sizing template does the same for your own deal.
Because value is income divided by the yield, a convex function. From 5.25 per cent, moving to 5.00 per cent adds 5.00 per cent of value while moving to 5.50 per cent removes 4.55 per cent. The larger the move, the wider the gap: 100 basis points out costs 16.0 per cent of value.
With income unchanged, the breach yield is the current yield times the covenant over the current LTV. A loan at 60 per cent on a 5.25 per cent asset breaches at 5.69 per cent, 43.8 basis points out, a value fall of 7.7 per cent. Lower starting yields leave less room in basis points for the same LTV headroom.
In percentage terms, for prime. The same 25 basis point rise cuts value by 5.88 per cent at a 4.00 per cent yield, 4.55 per cent at 5.25, 3.45 per cent at 7.00 and 3.03 per cent at 8.00. Secondary property has other risks, but less value sensitivity per basis point.
Loan sizing and the test that binds are worked in chapter 4 of 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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