Net Present Value (NPV) Formula
Reference for Net Present Value: sum of discounted cash flows minus initial investment.
The gold standard formula for comparing investment decisions.
The Formula
NPV calculates whether an investment will create or destroy value. A positive NPV means the investment earns more than the required return rate.
Variables
| Symbol | Meaning |
|---|---|
| NPV | Net Present Value (in currency) |
| CF_t | Cash flow in period t |
| r | Discount rate (required rate of return) |
| t | Time period (years) |
| C₀ | Initial investment cost |
Example 1
Investment of $10,000 returns $3,000/year for 5 years. Discount rate = 8%.
NPV = 3000/1.08 + 3000/1.08² + 3000/1.08³ + 3000/1.08⁴ + 3000/1.08⁵ - 10000
NPV = 2778 + 2572 + 2381 + 2205 + 2042 - 10000
NPV = $1,978 (positive — the investment adds value)
Example 2
Same investment but discount rate = 15%
NPV = 3000/1.15 + 3000/1.15² + 3000/1.15³ + 3000/1.15⁴ + 3000/1.15⁵ - 10000
NPV = 2609 + 2268 + 1972 + 1715 + 1492 - 10000
NPV = $56 (barely positive — marginal at 15%)
When to Use It
Use the NPV formula when:
- Deciding whether to accept or reject an investment project
- Comparing multiple investment opportunities
- Valuing businesses or income-producing assets
- Capital budgeting and strategic planning
Key Notes
- The discount rate r is the most influential input — small changes drastically affect NPV; a project with NPV = +$50,000 at 8% may turn negative at 10%; always run a sensitivity analysis (vary r ± 2–5%) before making a decision based on NPV alone
- Positive NPV means the investment earns more than the hurdle rate — it does NOT mean the investment is risk-free or that projected cash flows will materialize; NPV is only as reliable as the underlying cash flow forecasts
- NPV vs IRR conflict: for mutually exclusive projects, NPV is the correct decision criterion because it measures absolute value added; IRR measures percentage return and can favor a smaller, higher-percentage project over a larger, higher-NPV one
- NPV implicitly assumes intermediate cash flows are reinvested at the discount rate r — if that is unrealistic (e.g., you cannot actually earn 15% on reinvested cash), the Modified IRR (MIRR) or adjusted NPV gives a more accurate picture