Present value is what your note’s future payments are worth as one sum today. Working it out takes the payment, the number of payments left and a discount rate. The first two are in your note, and the third is the yield a buyer wants, which decides the answer.
What present value means
A dollar you receive in ten years is worth less than a dollar today, because today’s dollar could be invested in the meantime and the future one might never arrive. Present value marks each future payment down for the time you wait, then adds the results together.
The markdown rate is called the discount rate. When a note buyer does the sum, the discount rate is their yield, the annual return they need to earn on the price they pay.
The inputs
- Payment amount. The principal and interest the payer sends each month. Leave out any amount collected for taxes or insurance.
- Payments left. Count them from your amortization schedule, which is the table showing how each payment splits between interest and principal.
- Discount rate per period. For monthly payments, divide the annual rate by 12.
The calculation in a spreadsheet
Any spreadsheet has a present value function, so there is no need to do this by hand. Its usual form is:
=PV(annual rate / 12, number of payments, -payment)
The minus sign in front of the payment makes the result show as a positive number.
A worked example
The example note that runs through this site pays $1,140 a month, has 168 payments left and carries a 6% interest rate.
| Discount rate used | Spreadsheet entry | Present value | What the result is |
|---|---|---|---|
| 6%, the note’s own rate | =PV(0.06/12, 168, -1140) | About $129,400 | The balance still owed |
| 8%, a buyer’s yield | =PV(0.08/12, 168, -1140) | About $115,000 | The price a buyer would pay |
Illustrative example. The 8% yield is chosen for the arithmetic, and a real buyer’s yield depends on the note, the payer and the property.
The first row is a useful check. Discount a note at its own interest rate and the answer is the balance owed, so if your result is far from your balance, one of your inputs is wrong.
The second row is the one that matters when you sell. The $14,400 between the two rows is the discount, the gap between what you are owed and what a buyer pays.
The rate is the hard part
The yield a buyer will apply to your note cannot be looked up. Each buyer sets it by judging the risk. The main things they weigh, each taken up in our guide to what your note is worth, are:
- The payment record on the note and how long it runs.
- The payer’s credit.
- The equity in the property, meaning its value above what is owed.
- Whether the note is in first lien position, meaning it is paid first if the property is sold to cover the debt.
- The type of property and the quality of the paperwork.
- Returns available on other investments at the time.
On a long note a small change in yield moves the price a good deal, so two buyers reading the same file can land thousands of dollars apart. How note buyers calculate a price follows the buyer’s side of the sum step by step. For a real figure on your own note, send it for pricing, and the offer that comes back will state the yield used, laid out as on a note pricing worksheet.
What the simple formula leaves out
A balloon, meaning a lump sum due at the end, has to be discounted separately and added in. The spreadsheet function takes a fourth entry for a future value that handles it. Uneven payments are harder: interest-only periods, adjustable rates or payments that step up need each payment discounted on its own date. The formula also assumes every payment arrives on schedule, whereas a note can be paid off early, and buyers allow for that when they choose a yield. Your own calculation is best treated as a way to understand an offer, since it cannot predict one.
Running it backwards on an offer
Given an offer, you can solve for the rate that makes the present value equal the price. That rate is the yield the buyer is earning, and it lets you compare offers on equal terms. The RATE function does this: enter the number of payments, the payment as a negative figure and the offer price, then multiply the monthly result by 12. The answer is the yield on the note at that price, and setting it beside the yield from another offer tells you which buyer is asking for more return.
Before you rely on either function, run the check from the worked example on your own note. Discount it at its own interest rate and see that the answer matches your balance. If it does, your payment and payment count are right, and a yield you solve for from an offer can be trusted.
Related questions
Is present value the same as the balance owed on my note?
Only when the discount rate equals the note's own interest rate. A buyer discounts at their yield, and whenever that yield is above the note's rate the present value to them comes out below the balance. That gap is the discount.
What discount rate should I use for my own note?
There is no single correct figure, because each buyer sets their own yield from the risk they see. Try a few rates to see how far the price moves, then compare your results with the yield shown on a real offer.
Can I work out the yield from an offer I already have?
Yes. Enter the offer price as the present value, with the payment and the number of payments left, and solve for the rate. In a spreadsheet the RATE function does this and returns a monthly rate, which you multiply by 12.