Present Value Formula
Calculate present value with PV = FV / (1 + r)^n.
Determine what a future sum of money is worth in today's dollars.
The Formula
Present value tells you what a future amount of money is worth right now. A dollar today is worth more than a dollar in the future because of its earning potential.
Variables
| Symbol | Meaning |
|---|---|
| PV | Present value (what the money is worth today) |
| FV | Future value (the amount you will receive later) |
| r | Discount rate or interest rate per period (as a decimal) |
| n | Number of periods (usually years) |
Example 1
You will receive $50,000 in 8 years. The discount rate is 6%.
FV = $50,000, r = 0.06, n = 8
PV = 50000 / (1 + 0.06)^8
PV = 50000 / (1.06)^8
PV = 50000 / 1.5938
PV = $31,371.47 — That future $50,000 is worth about $31,371 today.
Example 2
An investment promises $20,000 in 5 years. You require a 10% return.
FV = $20,000, r = 0.10, n = 5
PV = 20000 / (1 + 0.10)^5
PV = 20000 / (1.10)^5
PV = 20000 / 1.6105
PV = $12,418.43 — You should pay no more than $12,418 for this investment.
When to Use It
Use the present value formula when:
- Deciding whether an investment is worth its asking price
- Comparing cash flows that occur at different times
- Evaluating the value of future payments from bonds or annuities
- Making business decisions about projects with future payoffs