Present Value Formula
Reference for the present value formula PV = FV / (1+r)^n.
Calculate what any future sum is worth today using discount rate tables and worked 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
Key Notes
- Formula: PV = FV / (1 + r)^n: The present value of a future cash flow shrinks as the discount rate r increases or as it is further in the future (larger n). A dollar received 10 years from now at 8% discount is worth only $0.463 today.
- Net Present Value (NPV): NPV = Σ CF_t / (1+r)^t: Sum the present value of all cash flows (including the initial investment as a negative outflow). NPV > 0 means the project creates value above the required return; accept it. NPV < 0 means it destroys value; reject it.
- Discount rate reflects opportunity cost and risk: For corporate projects, use the Weighted Average Cost of Capital (WACC). For risk-free government projects, use the risk-free rate. A higher discount rate gives lower NPV — it embeds a higher hurdle for the project to clear.
- PV of a perpetuity: PV = C/r: An infinite, constant cash flow has a finite present value. At r = 5%, a $1,000/year perpetuity is worth $20,000 today. Real estate capitalization rates work on this principle.
- Applications: Present value analysis underpins all of finance: bond pricing (PV of coupon stream + face value), mortgage qualification, business valuation (discounted cash flow model), lease vs buy decisions, and government cost-benefit analysis of infrastructure projects.