How to calculate yield on a mortgage note

The interest rate printed on a note is the borrower's contractual coupon. Investor yield is the return implied by the price you pay for the remaining cash flow. If you buy a note at a discount, your yield can be higher than the coupon. If you pay a premium, it can be lower.

The clean way to calculate yield is to solve for the discount rate that makes the present value of the future cash flows equal your purchase price.

The core equation

For monthly cash flows:

Purchase price = Σ CF(t) / (1 + r)^t

where CF(t) is the cash flow received in month t, r is the monthly investor yield you are solving for, and the final cash flow includes any contractual balloon or remaining principal due at maturity. This is an internal-rate-of-return, present-value problem. There usually is not a useful shortcut based on coupon minus discount.

Complete example: a fully amortizing note

Assume the remaining contractual cash flow is a purchase price of $85,000, a monthly payment of $1,110.21, 120 payments remaining, and no balloon at maturity. We solve for the monthly rate r such that the present value of 120 payments of $1,110.21 equals $85,000.

The important point is not which annual convention you prefer. It is that you label the convention. A 9.72% nominal annualized monthly rate and a 10.17% effective annual rate describe the same solved monthly cash flow in different ways.

Spreadsheet formulas

In Excel or Google Sheets, one way to solve the example is =RATE(120,-1110.21,85000,0), which returns the monthly rate. For a nominal annualized rate: =RATE(120,-1110.21,85000,0)*12. For an effective annual rate: =(1+RATE(120,-1110.21,85000,0))^12-1.

Keep the signs consistent: money you pay to acquire the note and money you receive from the note must have opposite signs in a cash-flow model.

Yield is not “coupon plus discount”

Suppose a note with $100,000 of principal is offered for $80,000. The $20,000 discount is not automatically an extra 20% return. The actual yield depends on when principal and interest come back. A $20,000 discount returned next month is very different from a $20,000 discount recovered ten years from now. Time is the entire reason present-value math is necessary.

Add a balloon when the contract requires one

If the note makes monthly payments but still has principal due at maturity, the final cash flow is the final regular payment plus the balloon principal. For example, if the payment is $775.30 for 120 months and a contractual residual of $66,774 is due in month 120, month 120's modeled cash flow is approximately $67,549.30.

Leaving the balloon out of the cash-flow model can destroy the yield calculation. Adding a balloon that the contract does not actually require is equally wrong. How to tell an implied residual from a contractual balloon, and what each does to the solved return, is covered in Mortgage note balloon payment risk.

Verify the cash flow before solving the rate

A yield formula assumes the inputs describe the contract you are buying. Before relying on the result, reconcile:

• current UPB;
• interest rate;
• contractual payment;
• number of payments remaining;
• maturity date;
• amortization period, if different from maturity;
• any balloon, interest-only period or modification;
• payment frequency;
• purchase price.

Yield to maturity is still a scenario

Even when the contract math is correct, yield to maturity assumes the modeled cash flows occur as scheduled. Real notes can prepay, default, modify, incur servicing costs or resolve early. So keep two questions separate. What return does this contractual cash flow imply at this purchase price? That is math. How likely is the actual deal to produce that cash flow? That is underwriting and diligence.

Yield also answers a different question from the collateral ratios. A corrected property value changes LTV and ITV, your cushion if performance breaks; it does not change the coupon or the solved yield. The calculation was correct. The input was wrong. covers why a correct yield can still rest on unsupported contractual inputs.

Common mistakes

• Using UPB instead of purchase price. Investor yield is measured against the acquisition basis, not merely the borrower's outstanding principal.
• Treating the coupon as the yield. Coupon describes the borrower's rate. Yield describes the investor's return at the price paid.
• Ignoring a residual balance. A maturity date that arrives before amortization is complete may create a major final cash flow.
• Guessing missing inputs. A missing price, payment or maturity is not zero. Keep it unresolved.
• Mixing annual conventions. State whether an annual yield is nominal annualized monthly or effective annual.

Once the yield is solved, the next question is what price a target return allows, and what the evidence lets you actually bid; How to price a mortgage note offer takes it from there. The software-by-job guide covers which tool fits each step.

FAQ

Why can a 7% note produce a 10% investor yield?

Because the investor may be buying the remaining payments for less than their present value at 7%. The discount increases the solved return on the acquisition price.

Does a lower purchase price always increase yield?

Holding the cash flows and timing constant, yes. But a lower price may reflect greater risk, weaker evidence or a different recovery expectation. The formula does not tell you why the price is lower.

Should I include servicing costs in yield?

If you are modeling net investor return, include the cash costs and timing assumptions that belong in that model. Label gross contractual yield separately from a net-return scenario.