The NPV formula
NPV = Σ (CFt ÷ (1 + r)t) − Initial Investment, where CFt is the cash flow in year t, r is the discount rate, and the sum runs over every year of the project. Each cash flow is divided by (1 + r) raised to its year — that division is the "discounting" step that shrinks distant money to its present-day value. Discounting reflects three realities: inflation erodes purchasing power, money today could be invested elsewhere, and the future is uncertain.
The decision rule
| NPV result | Meaning | Decision |
|---|---|---|
| NPV > 0 | The project earns more than your required return | ✅ Accept — it creates value |
| NPV < 0 | Returns fall short of the required return | ❌ Reject — it destroys value |
| NPV = 0 | The project exactly meets the required return | ↔ Indifferent — it breaks even |
A worked example
A café owner in Lisbon considers a €30,000 equipment upgrade expected to generate €9,000 a year for 4 years, with a required return (discount rate) of 8%:
- Year 1: €9,000 ÷ 1.081 = €8,333.33
- Year 2: €9,000 ÷ 1.082 = €7,716.05
- Year 3: €9,000 ÷ 1.083 = €7,144.49
- Year 4: €9,000 ÷ 1.084 = €6,615.27
- Present value of inflows: €8,333.33 + €7,716.05 + €7,144.49 + €6,615.27 = €29,809.14
- NPV = €29,809.14 − €30,000 = −€190.86 → reject (barely)
Notice what happened: the project generates €36,000 of total cash against a €30,000 cost — a €6,000 "profit" on paper. But because the cash arrives years later and 8% could be earned elsewhere, its present value is only €29,809.14. The discount rate flipped the verdict. At a 6% rate, the same project would have a positive NPV of roughly €1,182.
NPV vs IRR vs payback
- NPV measures value in money terms: how many euros a project creates above the required return.
- IRR (internal rate of return) measures efficiency: the discount rate at which NPV equals exactly zero, as a percentage. A project with an IRR above your required return is acceptable — but for competing projects of different sizes, NPV is the better judge: a tiny project can have a huge IRR while creating almost no value.
- Payback period only asks how fast you get your money back. It ignores every cash flow after payback and ignores the time value of money entirely — a project that pays back fast then earns nothing can beat a great project on payback while destroying value.
Common mistakes
- Using profit instead of cash flow: NPV is a cash tool — depreciation, accruals and other non-cash items distort it.
- Forgetting the opportunity cost: a 5% discount rate when your alternative earns 8% makes bad projects look good.
- Inflating later cash flows: distant projections are the least reliable — sensitivity-check them against a higher rate.
❓ Net Present Value FAQs
What is the net present value formula?
NPV = the sum of CF_t ÷ (1 + r)^t, minus the initial investment. CF_t is the cash flow in year t, r is the discount rate, and the initial investment is the cash you put in at time zero. Each future cash flow is divided by (1 + r) raised to its year, converting it to today's euros, then everything is added up and the upfront cost is subtracted.
What does a positive NPV mean?
A positive NPV means the project is expected to earn more than your required rate of return — it creates value. An NPV of €8,500 at a 5% discount rate means the project is worth €8,500 more than simply investing the money at 5% instead. A negative NPV means the project destroys value, and zero means it exactly breaks even at the required return.
What is the NPV decision rule?
The NPV decision rule is simple: accept any standalone project with NPV greater than zero, reject projects with NPV below zero, and be indifferent at exactly zero. When choosing between competing projects, pick the one with the highest positive NPV, because it creates the most value.
How do you choose the discount rate?
The discount rate should reflect your required return and the project's risk: a risk-free bank rate for safe cash flows, your cost of capital for business projects, or a higher rate for risky ventures. A higher discount rate makes future cash worth less and shrinks the NPV, so the same project can look good at 5% and bad at 10%.
What is the difference between NPV and IRR?
NPV measures value in money terms — how many euros a project creates above the required return. IRR measures efficiency — the discount rate at which the NPV equals exactly zero, expressed as a percentage. For one standalone project they agree, but for competing projects of different sizes NPV is the better judge: a tiny project can have a huge IRR while creating almost no value.
Why is NPV better than the payback period?
The payback period only asks how fast you get your money back — it ignores everything that happens after payback and ignores the time value of money entirely. NPV accounts for every cash flow over the project's whole life and discounts them properly. A project that pays back fast but then earns nothing can beat a slower project on payback while destroying value.
Can a profitable project have a negative NPV?
Yes. A project can show accounting profit on paper and still have a negative NPV if the cash arrives too late or the upfront cost is too high. NPV discounts future cash and compares it against the required return, while accounting profit ignores timing. That is why NPV is a cash-flow tool, not an income-statement tool.
Related: What Is Compound Interest? · What Is Amortization? · What Is APR? · Compound Interest Calculator · Savings Goal Calculator