NoteTools All Tools

Discounted Note Pricing Tool

Enter your target yield and the note's terms to find the maximum price you can pay — the reverse of a yield calculator.

Enter a UPB greater than $0.
Enter a note rate of 0% or higher.
Enter a whole number of months, 1 or more.
Enter a target yield of 0% or higher.
Optional
Lump sum due at the balloon month. Leave 0 for a fully amortizing note.
Balloon amount can't be negative.
Regular payments run through this month; the balloon is paid with the final payment.
Enter a balloon month between 1 and the remaining term.
Netted out of each monthly payment before discounting.
Servicing cost can't be negative.

Maximum Purchase Price

$0
0% of UPB
Monthly payment (borrower pays)
Net monthly cash flow (after servicing)
Discount from UPB ($)
Discount from UPB (%)
Total cash collected over hold
Price Sensitivity to Yield
Target YieldMax Price% of UPB

Worked Example

Suppose you're offered a performing note with $100,000 UPB (unpaid principal balance), a 7% note rate, and 240 months remaining, fully amortizing with no balloon and no servicing cost. You want an 11% annual yield. Here's the math, step by step:

Step 1 — Monthly note rate. Divide the annual note rate by 12: i = 0.07 / 12 = 0.00583333 (about 0.5833% per month).
Step 2 — Monthly payment. Apply the amortizing payment formula: PMT = 100,000 × 0.00583333 / (1 − (1.00583333)−240). Since (1.00583333)−240 = 0.247602, that's 583.33 / 0.752398 = $775.30 per month.
Step 3 — Monthly target yield. Divide the annual target yield by 12: y = 0.11 / 12 = 0.00916667 (about 0.9167% per month). This is the discount rate applied to every cash flow.
Step 4 — Present-value annuity factor. Compute (1 − (1.00916667)−240) / 0.00916667. Since (1.00916667)−240 = 0.111919, the factor is 0.888081 / 0.00916667 = 96.8815. In plain English: at an 11% yield, 240 future monthly dollars are worth about 96.88 of today's dollars.
Step 5 — Maximum price. Multiply the payment by the factor: $775.2989 × 96.8815 = $75,112.15. (We keep the unrounded payment for the multiplication and round only at the end.)
Step 6 — Express the discount. Price ÷ UPB = 75,112.15 / 100,000 = 75.11% of UPB. The discount is $100,000 − $75,112.15 = $24,887.85, or 24.89%.

So you can pay up to $75,112.15 for this note and earn exactly 11%. Pay less and your yield rises; pay more and it falls. The sensitivity table shows how steeply: at a 9% target the price is $86,170.56 (86.17% of UPB), while at 13% it drops to $66,175.74 (66.18% of UPB).

How the Math Works

Why investors bid to a yield, not a price

A note's face value (UPB) tells you what the borrower owes — not what the cash flow is worth to you. Note investors start with the return they require for the risk (their target yield) and let that produce the price. This standardizes bidding across notes with different rates, terms, and balloons: two very different notes priced to the same 11% yield are economically equivalent investments, before considering risk.

The price/yield inverse relationship

Price and yield move in opposite directions. The cash flows are fixed by the note; the only lever is what you pay for them. Pay less, and the same payments represent a higher return on a smaller investment — pay more and the return shrinks. That's also why discounts deepen as the spread between the note rate and your target yield widens, and why long-term notes are more yield-sensitive: distant payments get discounted many more times.

The formulas

All math is monthly-periodic. Monthly rates are nominal annual rates divided by 12, and the target yield is reported the same way (annualized nominal, monthly compounding):

  1. Monthly payment from the note's own terms: PMT = UPB × i / (1 − (1+i)−N), where i = note rate / 12 and N = amortization months. If the note rate is 0%, PMT = UPB / N.
  2. Net payment: PMTnet = PMT − servicing cost per month.
  3. Price = present value of the cash flows at the target monthly yield y = target yield / 12, over n months (the balloon month if there's a balloon, otherwise the full remaining term): PV = PMTnet × (1 − (1+y)−n) / y. If y = 0, the formula reduces to PV = PMTnet × n.
  4. Balloon present value, if any, due at month m: PVballoon = Balloon / (1+y)m. Maximum price = annuity PV + balloon PV.

No iterative solver is needed in this direction — pricing to a yield is a closed-form present-value calculation. (Solving the other way, yield from a known price, requires Newton–Raphson or bisection; see our Note Yield Calculator.) Intermediate values are never rounded; only the displayed results are.

ITV implications

ITV (investment-to-value) is your price divided by the property's value — your real exposure to the collateral. Because you buy at a discount, ITV sits below the borrower's LTV (loan-to-value), and that gap is an equity cushion that protects principal in a default. Many buyers enforce an ITV ceiling (commonly 65–75%) on top of their yield target: if the price this tool produces implies a higher ITV than your ceiling, the lower of the two prices governs. Check yours with the ITV / LTV Equity Coverage tool.

Assumptions and limitations

Frequently Asked Questions

How much should I pay for a mortgage note?

Pay no more than the present value of the note's remaining cash flows discounted at your required yield. Decide the annual yield you need (many performing-note buyers target roughly 8–12%), convert it to a monthly rate, and discount every remaining payment (and any balloon) back to today. That present value is your maximum price — paying more than that means accepting a lower yield. Also check collateral: keep your investment-to-value (price divided by property value) low enough that equity protects you if the borrower defaults.

How do you price a note to a target yield?

First compute the note's monthly payment from its unpaid principal balance, note rate, and remaining term. Then discount that payment stream at your target monthly yield (annual target yield divided by 12) using the present-value annuity formula PV = PMT × (1 − (1+y)−n) / y. If there is a balloon, add its present value: Balloon ÷ (1+y)m. The result is the price that makes the note yield exactly your target. This tool does that math instantly.

What discount do notes sell for?

It varies with the spread between the note rate and the buyer's target yield, the remaining term, and risk. Performing first-lien notes commonly trade around 70–95% of unpaid principal balance; the example on this page (7% note priced to an 11% yield over 240 months) prices at about 75% of UPB — a 25% discount. Non-performing notes trade far lower, often 30–60% of UPB, because cash flow must be re-created through workout or foreclosure. The longer the remaining term and the wider the yield spread, the deeper the discount.

How does a balloon affect note price?

A balloon usually raises the price (shrinks the discount) for a given target yield, because a large lump sum arrives early instead of being spread over many far-future payments that are heavily discounted. For example, a balloon at month 60 returns most of the principal in 5 years rather than 20, so less of the value sits in distant, deeply discounted payments. The trade-off is balloon risk: the borrower must refinance or sell to make the balloon payment, so underwrite their ability to do so.

Should I subtract servicing fees when pricing a note?

Yes. If a third-party servicer charges, say, $20–$30 per month, your true cash flow is the borrower's payment minus that fee. Discounting the gross payment overstates the price you can pay and quietly lowers your realized yield. Enter the monthly servicing cost in this tool and it nets the fee out of every payment before discounting, so your target yield is computed on the cash you actually keep. Also budget for one-time costs (boarding fees, collateral review, recording) outside the monthly fee.

What is ITV and why does it matter when pricing a note?

ITV (investment-to-value) is your purchase price divided by the property's value, while LTV (loan-to-value) is the loan balance divided by value. Buying at a discount pushes ITV below LTV, creating an extra equity cushion: if you pay $75,000 for a note on a $130,000 property, your ITV is about 58%, so the property could lose a lot of value before your investment is impaired. Many note buyers cap ITV (often at 65–75%) regardless of yield, because the discount is also their downside protection.

Related Tools