NPV Calculator (Net Present Value)
Calculate net present value from an initial investment and a series of cash flows at a given discount rate, to determine whether a project creates value.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| NPV Calculator (Net Present Value) | — | NPV = Σ CFₜ / (1 + r)ᵗ − initial investment | currency |
Step-by-Step Examples
Invest 100,000, returns of 30,000 / 35,000 / 40,000 / 45,000 over four years, 10% discount rate.
- Year 1: 30,000 / 1.10 = 27,273
- Year 2: 35,000 / 1.21 = 28,926
- Year 3: 40,000 / 1.331 = 30,053
- Year 4: 45,000 / 1.4641 = 30,735
- PV total = 116,987, NPV = 16,987
Invest 200,000, returns of 60,000 annually for four years, 12% discount rate.
- PV = 60,000 × annuity factor at 12% for 4 years (3.0373)
- PV = 182,238
- NPV = 182,238 − 200,000 = −17,762
Same 200,000 project at 6% instead of 12%.
- Annuity factor at 6% for 4 years = 3.4651
- PV = 60,000 × 3.4651 = 207,906
- NPV = +7,906
- The same cash flows flip from negative to positive on discount rate alone
Real-World Applications
Common Mistakes to Avoid
The discount rate should reflect the cost of capital and project risk. As the third example shows, the rate alone can flip the decision.
Projects generating cash beyond the modelled period need a terminal value, or NPV substantially understates the true result.
NPV inherits all the uncertainty in the projections feeding it. A precise-looking output built on optimistic forecasts is precisely wrong.