Net Present Value (NPV)
NPV measures the value today of all future cash flows discounted at the required rate of return. A positive NPV means the investment creates value; negative means it destroys value.
NPV Formula
NPV = Σ [CF_t / (1+r)^t] - Initial Investment
CF_t = cash flow in period t
r = discount rate (cost of capital)
t = time period
Or: NPV = -C₀ + CF₁/(1+r) + CF₂/(1+r)² + ...Worked Example
Project: -$100,000 initial, r=10%
Year 1: $30,000 → PV = 30,000/1.10 = $27,273
Year 2: $40,000 → PV = 40,000/1.21 = $33,058
Year 3: $50,000 → PV = 50,000/1.331 = $37,566
Year 4: $30,000 → PV = 30,000/1.464 = $20,492
NPV = -100,000 + 27,273 + 33,058 + 37,566 + 20,492
NPV = +$18,389 → Accept (positive NPV)Decision Rules
- NPV > 0: Accept — project adds value
- NPV < 0: Reject — destroys value at this discount rate
- NPV = 0: IRR = discount rate (break-even)
- When comparing projects: choose highest positive NPV
Calculate NPV and DCF: Free NPV Calculator
NPV Quick-Reference Table
| Year | Cash Flow ($) | Discount factor (10%) | PV ($) |
|---|---|---|---|
| 0 (initial) | −100,000 | 1.000 | −100,000 |
| 1 | 30,000 | 0.909 | 27,273 |
| 2 | 35,000 | 0.826 | 28,926 |
| 3 | 40,000 | 0.751 | 30,053 |
| 4 | 25,000 | 0.683 | 17,075 |
| NPV | +3,327 | ||
How NPV Works
Net Present Value discounts all future cash flows back to today using NPV = Σ [CF_t / (1+r)^t] − Initial Investment. A positive NPV means the project returns more than the required rate of return (discount rate r) and creates value. NPV = 0 means exactly break-even at the discount rate. The discount rate typically reflects the cost of capital or minimum acceptable return.
NPV is considered the most theoretically sound capital budgeting method because it accounts for the time value of money, uses all cash flows, and produces an absolute dollar value of wealth created. Unlike IRR, NPV correctly handles projects with unconventional cash flow patterns (multiple sign changes). For mutually exclusive projects of different scales, NPV is superior to IRR and payback period.
Common Mistakes
- Double-counting the initial investment: The initial outflow at t=0 has discount factor 1.0 — it is already in present value. Don't discount it again.
- Using the wrong discount rate: Use after-tax cost of capital, not borrowing rate or target ROI. For risky projects, add a risk premium to the discount rate.
- Ignoring terminal value: Long-lived projects may need a terminal value (continuing value beyond the forecast horizon) discounted to present value and added to NPV.
Frequently Asked Questions
IRR (Internal Rate of Return) is the discount rate that makes NPV = 0. NPV tells you how much value a project creates in dollars; IRR tells you the percentage return. For independent projects both give the same accept/reject decision. For mutually exclusive projects with different scales, NPV is more reliable — a small project with high IRR may have lower NPV than a large project with slightly lower IRR.
For corporate projects, use the Weighted Average Cost of Capital (WACC) — a blend of the after-tax cost of debt and cost of equity, weighted by their proportions in the capital structure. For personal investments, use your opportunity cost (what you would earn in the next-best investment). For government projects, social discount rates (2–8%) reflect societal time preferences.
Yes, but you must account for the difference. Methods include: (1) Equivalent Annual Annuity (EAA) — convert each project's NPV to an equal annual value and compare; (2) Least Common Multiple — repeat both projects until they end at the same time; (3) assume indefinite chain replacement. Simply comparing NPV of a 3-year and a 6-year project is misleading without adjustment.