Debt sizing with the binding constraint calculator
This calculator sizes a commercial mortgage by running three lender tests side by side and keeping the smallest result. It answers a plain question for a sponsor: how much debt the property will support once every test is applied, and which test sets the limit.
Calculator
Net operating income is whatever figure you enter. State its basis before comparing results: trailing or in-place or forward or sponsor-adjusted, and which reserves and management fees are in or out.
| Loan allowed by loan to value | |
|---|---|
| Loan allowed by coverage | |
| Loan allowed by debt yield | |
| Loan proceeds (smallest of the three) | |
| Binding constraint |
Formulas
- Loan by loan to value = value x maximum loan to value
- Loan by coverage = (net operating income / minimum debt service coverage) / loan constant, where loan constant = annual debt service on one dollar of loan at the entered rate and amortization
- Loan by debt yield = net operating income / minimum debt yield (shown as n/a when no minimum is entered)
- Proceeds = the smallest of the three; lender thresholds vary by lender and cycle
Worked example with the starting inputs
With the starting inputs in the form (net operating income $1,000,000; property value $14,000,000; interest rate 6.5 percent; amortization 30 years; maximum loan to value 65 percent; minimum debt service coverage 1.25; minimum debt yield 9 percent), the results are: loan allowed by loan to value: $9,100,000; loan allowed by coverage: $10,547,388; loan allowed by debt yield: $11,111,111; loan proceeds (smallest of the three): $9,100,000; binding constraint: LTV.
These inputs are hypothetical and are shown only so the arithmetic can be checked by hand.
What the loan proceeds mean in a real deal
The lender does. Its credit committee works from a term sheet that applies several tests at once. The smallest figure becomes the proceeds, so the valuation test sets the loan here and the other two have room to spare.
The gap between the three results tells the limited partners how much slack the capital stack has. Equity must fill whatever the loan leaves, so the binding test also sets the check size.
How to read and stress the sizing result
Change one input at a time. Raise the interest rate and the coverage loan falls first, because only that test reacts to the rate. Lower net operating income and the coverage and debt yield loans shrink together.
Then stress the appraiser’s side. An appraisal at a higher cap rate lowers value, and the loan to value result drops with it while the other two stay put. Compare the new binding constraint with the old one, because a switch shows that the deal’s risk has moved from price to cash flow. Run the covenant levels in the loan agreement next to the sizing tests, since lenders often retest coverage after closing on trailing income. Record each case in the investment memo so the limited partners see the full range of outcomes.
Where the sizing result misleads
The result is only as sound as the net operating income behind it. A lender underwrites its own figure, which may reserve for capital expenditures and vacancy that the sponsor’s pro forma ignores. The appraiser may land on a different value than the purchase price. Definitions differ. Coverage is often measured on a fully amortizing payment even when the loan is interest only for part of the term, so the calculator’s payment can differ from the one in the note. Recourse carve outs, reserves, origination fees and lender specific floors on the rate all sit outside this arithmetic.
Treat the output as a first screen. The term sheet and then the loan agreement settle the real terms, and each lender and market cycle moves its thresholds.