Present Value Formula
Calculate the present value of future cash flows with PV = FV / (1+r)^n.
Understand the time value of money with examples.
The Formula
Present value tells you what a future sum of money is worth today. A dollar today is worth more than a dollar tomorrow because you can invest it and earn interest.
Variables
| Symbol | Meaning |
|---|---|
| PV | Present value (what the future amount is worth today) |
| FV | Future value (the amount you will receive in the future) |
| r | Discount rate per period (as a decimal) |
| n | Number of periods (usually years) |
Present Value of an Annuity
When receiving equal payments over multiple periods, use the annuity formula. PMT is the payment amount received each period.
Example 1
You will receive $25,000 in 5 years. With a 7% discount rate, what is it worth today?
PV = FV / (1 + r)ⁿ = 25,000 / (1.07)⁵
PV = 25,000 / 1.40255
PV = $17,824.65 (the future $25,000 is worth about $17,825 today)
Example 2
You will receive $5,000 per year for 4 years. At a 6% discount rate, what is the present value?
PV = PMT × [(1 - (1 + r)⁻ⁿ) / r]
PV = 5,000 × [(1 - (1.06)⁻⁴) / 0.06]
PV = 5,000 × [(1 - 0.79209) / 0.06]
PV = 5,000 × [0.20791 / 0.06]
PV = 5,000 × 3.46511
PV = $17,325.55
When to Use It
Use the present value formula for financial decision-making:
- Evaluating investment opportunities (is $100,000 in 10 years worth investing $60,000 now?)
- Comparing lump-sum vs. annuity payment options (lottery, settlements)
- Valuing bonds, leases, and other financial instruments
- Capital budgeting — deciding if a project's future returns justify today's cost