The constant is what the debt costs the property's cash flow, and it sizes the loan as much as the interest rate does.
The mortgage constant is annual debt service divided by the loan amount: interest and scheduled principal together, as a percentage of the balance. A $30.0m loan at 6.0 per cent on a 25-year monthly amortisation pays $2.32m a year, a constant of 7.73 per cent, not 6.0. It is the number a lender divides into the NOI it will allow for debt service, so it sets loan proceeds as much as the interest rate does.
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 →
An illustrative stabilised commercial property and a fixed-rate senior loan at 70 per cent loan-to-value. The figures are illustrative, not market terms.
| Input | Value |
|---|---|
| Net operating income | 3.00 |
| Cap rate | 7.0% |
| Property value | 42.86 |
| Loan amount (70.0% LTV) | 30.0 |
| Interest rate, fixed | 6.0% |
| Amortisation, years, monthly payments | 25 |
| Lender's minimum DSCR | 1.25 |
Monthly payment = L x i / (1 - (1 + i)-n), with i = 6.0% / 12 = 0.5% and n = 300 months: $193,290
Annual debt service = 12 x 193,290 = $2.32m
Mortgage constant = annual debt service / loan = 2.319 / 30.0 = 7.73%
Equivalently, constant = 12 x i / (1 - (1 + i)-n), independent of the loan size.
In Excel: =-PMT(6%/12, 300, 1)*12 returns 0.0773; multiply by the loan for annual debt service.
Of the $2.32m paid in year 1, $1.785m is interest and $0.534m is principal, 1.78 per cent of the loan. The constant bundles both because the borrower pays both out of the same NOI, and the lender's coverage test does not care which is which.
| Amortisation | Constant | Debt service, $m | DSCR | Cash-on-cash | Max loan at 1.25x DSCR alone, $m |
|---|---|---|---|---|---|
| Interest only | 6.00% | 1.80 | 1.67 | 9.33% | 40.0 |
| 30 years | 7.19% | 2.16 | 1.39 | 6.55% | 33.4 |
| 25 years | 7.73% | 2.32 | 1.29 | 5.29% | 31.0 |
| 20 years | 8.60% | 2.58 | 1.16 | 3.27% | 27.9 |
Three readings follow from the one number. Coverage: DSCR is NOI / (constant x loan), so 3.00 / 2.32 = 1.29. Proceeds: the maximum loan on a coverage test is NOI / DSCR / constant, so $2.40m of permitted debt service supports $31.0m at 7.73 per cent, $40.0m interest-only and only $27.9m on a 20-year schedule. Moving from 25 to 20 years costs the borrower $3.1m of coverage-based proceeds at the same interest rate. These are DSCR limits only: a lender capping LTV at 70.0 per cent would stop at $30.0m, so the interest-only and 30-year figures would never be reached, and the 20-year schedule would cost $2.1m against that cap rather than $3.1m.
The constant is the price of the debt as the property's cash flow sees it. When it is above the cap rate, here 7.73 against 7.0 per cent, every dollar borrowed costs more cash than the property yields on it, and leverage pulls the cash-on-cash return down: 5.29 per cent against 7.0 unlevered.
The constant is also the bridge between the two coverage measures lenders quote. Debt yield is NOI divided by the loan, here 3.00 / 30.0 = 10.0 per cent. DSCR is NOI divided by debt service. Since debt service is the constant times the loan, DSCR = debt yield / constant: 10.0 / 7.73 = 1.29. A lender that sets a minimum debt yield is therefore setting a minimum DSCR that changes with every move in the rate and the amortisation, while a lender that sets a minimum DSCR is setting a debt yield floor of DSCR times constant. When rates rise, the DSCR test tightens and the debt yield test does not, which is why the binding test tends to switch from debt yield to DSCR as rates go up. Reading the constant first tells you which of the two will bind before the full sizing is run; the full three-test sizing, with LTV, is worked in the maximum loan on a commercial property. Many loan agreements go further and test the covenant DSCR on a notional constant rather than on actual debt service, which is how an interest-only loan can still fail its covenant, as shown in how to calculate DSCR under a loan agreement.
The constant falls more slowly than the rate, because the principal component does not shrink with it.
| Interest rate | Interest only | 30 years | 25 years | 20 years |
|---|---|---|---|---|
| 5.0% | 5.00% | 6.44% | 7.02% | 7.92% |
| 6.0% | 6.00% | 7.19% | 7.73% | 8.60% |
| 7.0% | 7.00% | 7.98% | 8.48% | 9.30% |
| 8.0% | 8.00% | 8.81% | 9.26% | 10.04% |
On a 25-year schedule the constant matches the 7.0 per cent cap rate only when the interest rate falls to 4.98 per cent. Above that, an amortising loan on this property is cash-negative leverage, however attractive the rate looks against the cap rate.
=PMT(6%,25,...), gives 7.82 per cent instead of 7.73, and sizes the loan at $30.68m instead of $31.04m. The term sheet's payment frequency belongs in the formula.Divide annual debt service by the loan, using the actual payment frequency: 7.73 per cent here. Compare it with the cap rate to judge leverage, divide it into permitted debt service to size the loan, and remember it moves with amortisation as much as with the rate. The book's sizing and exit-test model, which runs every limit on your own loan, is in the free workbook for this case; and for what the same loan leaves to refinance at maturity, see how to calculate a balloon payment.
The interest rate prices the balance; the constant adds scheduled principal and expresses total debt service as a share of the loan. At 6.0 per cent interest-only the two are equal. On a 25-year amortisation with monthly payments the constant is 7.73 per cent, and on 20 years 8.60 per cent.
If the constant is above the cap rate, leverage reduces the cash-on-cash return. On the illustrative property at a 7.0 per cent cap rate, a 7.73 per cent constant cuts cash-on-cash to 5.29 per cent at 70.0 per cent LTV. Interest-only at 6.00 per cent raises it to 9.33 per cent.
Maximum loan = NOI / minimum DSCR / constant. With $3.00m of NOI and a 1.25x minimum, permitted debt service is $2.40m, so on the coverage test alone the loan is $31.0m at a 7.73 per cent constant, $33.4m on a 30-year schedule and $27.9m on 20 years, all at the same 6.0 per cent rate, before any LTV cap.
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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