Money later is worth less than money now
A dollar received in five years is worth less than a dollar today, because today’s dollar could be invested in the meantime. Net present value (NPV) applies that idea to an investment: it converts every future cash flow into today’s dollars at a chosen discount rate, then subtracts the upfront cost. A positive NPV means the project earns more than that rate.
The formula
NPV = −investment + Σ CFₜ ÷ (1 + d)ᵗ + residual value ÷ (1 + d)ᴺ
With cash flows that start at CF and grow by g each year, the sum has a closed form:
PV of cash flows = CF × (1 − ((1 + g) ÷ (1 + d))ᴺ) ÷ (d − g)
The profitability index is the present value of everything received divided by the investment: above 1, the project creates value.
Worked example: new equipment
A machine costs $100,000. It should bring in $25,000 of extra cash in year one, growing 2% a year for 6 years, and can be sold for $10,000 at the end. Your required return is 8%.
- Present value of the six cash flows: $120,969.
- Present value of the resale: $6,302.
- NPV: 120,969 + 6,302 − 100,000 = $27,271.
- Profitability index: 1.27: each dollar invested returns $1.27 in today’s money.
- Undiscounted, you receive $167,703 in total, but that figure overstates the value because it ignores timing.
NPV by discount rate
| Discount rate | NPV | Profitability index |
|---|---|---|
| 4% | $45,375 | 1.45 |
| 6% | $35,862 | 1.36 |
| 8% | $27,271 | 1.27 |
| 10% | $19,492 | 1.19 |
| 12% | $12,429 | 1.12 |
| 15% | $3,002 | 1.03 |
The NPV stays positive up to about 16%: that rate is close to the project’s internal rate of return (IRR).
Choosing the discount rate
- For a company, the weighted average cost of capital (WACC) is the usual base.
- For a small business owner, use the return you could earn elsewhere at similar risk, often 8–15%.
- Add a premium for riskier or less certain projects.
NPV vs payback
The simple payback here is 4 years (100,000 ÷ 25,000). Payback is easy to explain but ignores everything after the payback date and the time value of money. When two projects compete, choose the one with the higher NPV; when capital is limited, rank them by profitability index.
Limits
NPV is only as good as the cash flow forecast. Run a pessimistic case with lower cash flows and a higher rate: if the NPV is still positive, the decision is robust.