The rate only enters the cover test, so proceeds hold flat under the LTV cap and then fall almost in line with the mortgage constant.
Higher interest rates cut a commercial loan through the debt service cover test: the lender caps debt service at NOI ÷ minimum DSCR, and a higher rate buys less loan for the same payment. On an illustrative 40,000,000 property with 2,400,000 of NOI, a 65 per cent LTV and a 1.25x DSCR on 25-year amortisation, rates up to 5.52 per cent leave the loan at 26,000,000, capped by LTV. Above that, every 100 basis points removes roughly 8 to 9 per cent of the loan: 24,833,098 at 6.00 per cent, 22,637,905 at 7.00 and 20,730,324 at 8.00.
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 effect is not gradual from the first basis point. While the loan-to-value test binds, rates can rise with no change in proceeds; once the cover test takes over, proceeds fall almost in proportion to the mortgage constant. Knowing where that switch sits is the first thing to know about any financing in a rising-rate market. The three-test sizing itself is set out in how to calculate the maximum loan on a commercial property; the question here is narrower: what a rate move alone does to proceeds, to the equity cheque and to the NOI a refinancing needs.
| Input | Value |
|---|---|
| Net operating income | 2,400,000 |
| Value, at a 6.00% cap rate | 40,000,000 |
| Maximum loan-to-value | 65% |
| Minimum DSCR, amortising debt service | 1.25x |
| Minimum debt yield | 8.0% |
| Amortisation, monthly payments | 25 years |
LTV loan = value × maximum LTV = 40,000,000 × 65% = 26,000,000
DSCR loan = NOI ÷ minimum DSCR ÷ mortgage constant = 1,920,000 ÷ constant
Debt yield loan = NOI ÷ minimum debt yield = 2,400,000 ÷ 8.0% = 30,000,000
The loan is the lowest of the three. In Excel, the constant at the rate in B2 is =-PMT(B2/12,25*12,1)*12 and the loan =MIN(Value*65%, NOI/1.25/constant, NOI/8%). Only the middle test contains the rate.
The cover test allows 2,400,000 ÷ 1.25 = 1,920,000 of debt service a year whatever the rate. The rate reaches the loan only through the mortgage constant. At 6.00 per cent the constant is 7.73 per cent, so 1,920,000 supports 24,833,098. At 7.00 per cent the constant is 8.48 per cent and the same payment supports 22,637,905.
| Rate | Constant | LTV loan | DSCR loan | Maximum loan | Binds | Change |
|---|---|---|---|---|---|---|
| 4.00% | 6.33% | 26,000,000 | 30,312,397 | 26,000,000 | LTV | |
| 5.00% | 7.02% | 26,000,000 | 27,369,608 | 26,000,000 | LTV | 0.0% |
| 6.00% | 7.73% | 26,000,000 | 24,833,098 | 24,833,098 | DSCR | -4.5% |
| 7.00% | 8.48% | 26,000,000 | 22,637,905 | 22,637,905 | DSCR | -8.8% |
| 8.00% | 9.26% | 26,000,000 | 20,730,324 | 20,730,324 | DSCR | -8.4% |
The debt yield test, at 30,000,000, never binds here because it does not depend on the rate. The switch from LTV to DSCR happens where the DSCR loan equals 26,000,000, which needs a constant of 1,920,000 ÷ 26,000,000 = 7.38 per cent: a rate of 5.52 per cent.
From 4.00 to 8.00 per cent the loan falls from 26,000,000 to 20,730,324, a loss of 5,269,676 or 20.3 per cent. A buyer paying the same 40,000,000 must put in 19,269,676 of equity instead of 14,000,000, 37.6 per cent more. The LTV slides from 65.0 per cent to 51.8 per cent without anyone deciding to borrow less.
Put the other way, to borrow the full 26,000,000 at 7.00 per cent the property would need NOI of 2,756,439, 14.9 per cent more than it earns. That is the gap a value-add business plan is sometimes asked to close before refinancing, and the reason maturing loans struggle to refinance at par when rates have risen.
In practice a rate rise rarely leaves the cap rate alone. If the cap rate moves from 6.00 to 6.50 per cent as the rate goes from 6.00 to 7.00, the value falls to 36,923,077 and the LTV loan to 24,000,000, but the DSCR loan of 22,637,905 still binds. Both tests point the same way; the cover test simply gets there first.
Interest-only debt service is the loan times the rate, so the DSCR loan is 1,920,000 ÷ rate: 32,000,000 at 6.00 per cent and 27,428,571 at 7.00. The switch from LTV moves out to a rate of 7.38 per cent, and at 8.00 per cent the loan is 24,000,000, a 60.0 per cent LTV. Interest-only terms protect proceeds against rate rises, which is why borrowers ask for them, and why lenders who grant them usually tighten the DSCR or the LTV in return.
| Rate | Amortising | Interest-only |
|---|---|---|
| 5.00% | 26,000,000 | 26,000,000 |
| 6.00% | 24,833,098 | 26,000,000 |
| 7.00% | 22,637,905 | 26,000,000 |
| 8.00% | 20,730,324 | 24,000,000 |
The mistake is to model the rate only in the interest line and keep the loan fixed. A business plan that assumes 65 per cent leverage at refinancing, with rates at 7.00 per cent, has assumed 3,362,095 of proceeds the lender will not provide. The second mistake is to look only at the rate the loan is fixed at: a lender sizing a floating loan often tests cover at a stressed rate, or at the strike of a required hedge, and the binding constant is that one, which is why an interest rate cap does not always protect the DSCR.
Size the loan on all three tests and find the rate at which cover takes over from loan-to-value: 5.52 per cent here. Below it, rate rises cost interest but not proceeds; above it, each 100 basis points cuts the loan by roughly 8 to 9 per cent. Real Estate Finance runs the same three tests side by side on three loans so the ranking can be watched as the yield and the rate move; the free workbooks for this case carry them as live formulas.
Because the lender's cover test caps debt service, not the loan. At a 1.25x DSCR, 2,400,000 of NOI allows 1,920,000 of payments a year. At 8.00 per cent on 25-year amortisation that supports only 20,730,324, a 51.8 per cent LTV on a 40,000,000 property, against 65.0 per cent when rates were 5.00 per cent.
Largely. With no principal in the payment the DSCR loan is 1,920,000 divided by the rate, so the 65 per cent LTV still binds up to 7.38 per cent. At 8.00 per cent the interest-only loan is 24,000,000 against 20,730,324 amortising. Lenders usually ask for a tighter DSCR or LTV in exchange.
Solve the cover test for NOI: loan times the mortgage constant times the minimum DSCR. Keeping 26,000,000 at 7.00 per cent with a 1.25x DSCR and 25-year amortisation needs 2,756,439 of NOI, 14.9 per cent more than the 2,400,000 the property earns.
Sizing a loan on loan-to-value, debt service cover and debt yield, and naming the test that binds, is the subject of 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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