Debt yield and loan sizing

LTV depends on the value, which depends on a cap rate someone chose. DSCR depends on the interest rate and the amortisation, which can be stretched (a longer amortisation or an interest-only period lowers the payment and flatters DSCR). Debt yield depends on neither.

Debt yield = NOI ÷ loan amount. A $5,000,000 loan on a property with $450,000 of NOI has a 9% debt yield. It says: if the lender took the property back on day one, the income would pay it 9% a year on what it lent. Lenders often want something like 8% to 10% or more, depending on the property and the market.

noi = 450_000
for loan in (4_500_000, 5_000_000, 5_625_000):
    print(f"${loan:,}: debt yield {noi / loan:.1%}")

Flip it round to size a loan: the largest loan a debt-yield test allows is NOI ÷ minimum debt yield. With $450,000 of NOI and a 9% minimum, that's $5,000,000.

So a full sizing runs three tests and takes the smallest answer: value × maximum LTV; the loan whose payments equal NOI ÷ minimum DSCR; and NOI ÷ minimum debt yield. The one that gives the smallest loan is the binding constraint, and it tells the borrower what would have to change for a bigger loan: a higher value, a lower rate, or more income.

value, noi = 9_000_000, 560_000
by_ltv = value * 0.70
by_debt_yield = noi / 0.09
print(round(by_ltv), round(by_debt_yield), round(min(by_ltv, by_debt_yield)))