Present Value Formula
Calculate present value using PV = FV / (1+r)^n.
Determine what any future sum of money is worth today given a discount rate and number of time periods.
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
Key Notes
- Formula: PV = FV / (1 + r)^n: Discounts a future cash flow back to today's equivalent value at discount rate r over n periods. A dollar received in the future is worth less than a dollar today — this is the time value of money principle.
- Choosing the discount rate: The discount rate should reflect the risk and opportunity cost of the investment. Risk-free rate (~government bond yield) for certain cash flows; a higher rate for risky projects. A higher discount rate means lower PV — future cash flows matter less.
- PV of an annuity: PV = PMT × [1 − (1+r)^(−n)] / r: Sums the PV of equal periodic payments. This formula is used to calculate mortgage loan amounts, where PMT is the monthly payment, r is the monthly rate, and n is the number of payments.
- PV of a perpetuity: PV = C / r: For an infinite stream of equal payments (e.g., preferred stock dividends, consol bonds), PV simplifies to cash flow divided by the discount rate. A $100/year perpetuity at 5% is worth PV = $2,000.
- Applications: PV is the foundation of Net Present Value (NPV) analysis for capital budgeting, bond pricing (sum of coupon PVs + face value PV), loan payment calculation, and retirement planning.