How to price a note: yield vs discount

How do you price a note?

You price a note by working out what its remaining payments are worth today at the yield you want. That number, the present value of the payments, is the most you should pay. Pay less and you earn more; pay more and you earn less.

A note here means a promissory note that someone is paying off in monthly installments, often from a seller-financed sale of a home or land. The person who holds it may want cash now instead of payments for years, so notes change hands, usually for less than the balance owed. That gap is the discount. The yield is the yearly return the buyer earns at that price.

This guide uses one note throughout: $6,000 owed at 10%, with 60 monthly payments of $127.48 left. Bought at face value ($6,000), it yields the note rate, 10%: about $1,649 of profit on $6,000 of cash at risk, with your cash back in month 48. Every dollar under $6,000 pushes the yield and the profit up.

Note pricing calculator

Enter the balance, the note rate, the payments left and the yield you want. It shows the price for that yield, the yield at an asking price, the yield if the note is paid off early, and the price of buying only the first few payments.

With the defaults, a 20% yield means paying about $4,812, close to 20% under the balance. At an asking price of $4,500, the yield is 23.2% as a note rate, for about $3,149 of profit on $4,500 of cash at risk, with your cash back in month 36.

What is the formula for the price of a note?

The price is the payment × the present value factor for the number of payments left, at your target yield per month.

Going the other way, from a price to a yield, has no neat formula. You find the monthly rate that makes the payments’ present value equal the price by trial, which is what a calculator or the RATE function does. That rate is the note’s internal rate of return.

Yield vs discount: what is the difference?

The discount is how far below the balance you buy. The yield is the return that discount produces once it is spread over the payments, on top of the note’s own interest. They move together, but they are not the same number.

Here is the same $6,000 note at five prices. Your cash at risk is the price you pay.

Every $500 off the price adds $500 of profit and pulls your cash back about four months sooner. The yield climbs faster than the discount, because you are earning the same payments on less money.

Working from the yield you want instead, the same note prices like this:

Why does the same discount yield more on a short note?

Because the discount is earned when the payments arrive. On a short note it arrives quickly, so it counts for more per year; on a long note it is spread thin. Here is a $6,000 note at 10% bought for $4,500 (a 25% discount, $4,500 of cash at risk) with different numbers of payments left:

This is where yield and dollars pull apart. The 24-month note has the best yield and the smallest profit. The 360-month note has the lowest yield and almost seven times the profit, but your cash is tied up for 86 months before it is back, and 30 years is a long time to count on one payer. Judge a note by all three: the yield, the dollars and how long your cash is out.

How does an early payoff change your yield?

When a note you bought at a discount is paid off early, you collect the whole remaining balance at once, so the discount arrives sooner and the yield jumps. The dollars go down, because the interest stops.

At face value an early payoff does not change the yield at all: buy the note for $6,000 and it earns 10% whenever it ends (paid off after 12 payments, that is about $556 of profit on $6,000 of cash at risk, back in month 12). The jump only happens because of the discount. That is why note buyers like payers who are likely to sell or refinance, and why the 43.5% in the first row is a best case, not a plan.

What is a partial note purchase?

A partial is buying only some of a note’s payments, usually the next 12 to 60, while the original holder keeps the rest. You price it the same way, using only the payments you are buying.

Buying the first 36 payments at 20% instead costs $3,430 for $4,589 of payments: about $1,159 of profit, with your cash back in month 27.

Partials suit both sides for a few reasons:

• Less cash, shorter wait. You put up a fraction of the price and your money comes back in months, not years.
• A cushion. The payments you own come first. The value of the property stands behind a balance much larger than what you paid.
• The holder keeps the back end. They raise the cash they need without giving up the whole note at a deep discount.

A partial needs a written agreement that says who gets what if the note is paid off early, who services the payments, and what happens if the payer defaults. Have an attorney draft it.

Seasoning, payment history and what can go wrong

The yield you need depends on how likely the payments are to keep coming. A few things move that, and none of them shows up in the formula.

• Seasoning. How long the payer has been paying. A note with a long on-time history is safer than one signed last month. It also has fewer payments left, so the same yield needs a smaller discount: after 12 payments, the 36-month $6,000 note at 15% has a balance of $4,289.68, and its 24 remaining payments cost $4,087 at a 20% yield, about 4.7% under the balance (about $905 of profit on $4,087 of cash at risk, back in month 20).
• Payment history. Ask for a record of every payment and its date. Late or partial payments are a warning.
• Equity. A larger down payment means the payer has more to lose by walking away, and the property is worth more than what is owed.
• The property. Its condition and value are what you fall back on after a default. Taxes and insurance should be current.
• The paperwork. The original signed note, the security document (mortgage, deed of trust or lien on a title), proper recording, and a transfer that your state recognizes. How notes and security documents are transferred is set by state law; check yours.

The person paying the note is not affected by the sale. On this note they still pay $127.48 a month and about $1,649 of interest over 60 months, just to a different holder, under the same terms. A buyer of notes should treat that payer fairly: the note’s terms do not change because it was sold.

Selling a note for cash

Selling your own note turns payments over years into cash today, at the buyer’s yield. It is the same math from the other side, and it is expensive.

Before you sell, ask for offers in writing, compare the yield each one implies (put the price into the calculator above), and check whether the buyer can come back to you if the payer defaults. Sometimes the cheaper move is a partial, or borrowing against something else, or simply keeping the note.

Note pricing in Excel and Google Sheets

Two functions do almost all of it. Divide the yield by 12 and count payments in months; a minus sign means money paid out.

• Price for a target yield: =PV(20%/12, 60, 127.48) returns −4,811.68. That is the price for a 20% yield.
• Yield from a price: =RATE(60, 127.48, −4500)*12 returns 0.2324, a 23.2% note rate.
• Compounded: =EFFECT(23.24%, 12) returns about 0.2588, or 25.9%.
• Yield with an early payoff: =RATE(12, 127.48, −4500, 5026.39)*12 returns about 0.4354, the 43.5% from the table above. The fourth number is the balance paid off with payment 12.
• Uneven payments or a partial: put the payments in cells B2:B13 and use =NPV(20%/12, B2:B13). With twelve payments of 127.48 it returns about 1,376.16, the price of the partial above.

Excel’s PRICE function sounds like the right tool but is built for bonds that pay interest only and return their face value at maturity, quoted per $100. For an amortizing note, use PV and RATE.

Before buying any note, check that you are not carrying debt at a higher rate than the note would pay you. The leak check is a quick way to find it.

Further reading: yield vs discount, buying notes in pieces and prepayment profits are among the topics of Lonnie Scruggs’s Taking the Mystery Out of Money.