NPV Calculator — cash flows discounted against the outlay

How it works

Two steps. Discount: PV = Σ CFt ÷ (1+r)^t across the five annual slots, each flow landing at the end of its year — the same present-value arithmetic that prices any payment stream, generalized to unequal amounts (negative years are allowed; a mid-life reinvestment is just a negative flow). Net: NPV = PV − C₀. The rate sweep reruns the same flows at 5/10/15/20% — NPV falls as the hurdle rises, and the rate where it crosses zero is the IRR, which its own calculator solves for directly. The outputs keep the pieces visible: the stream's worth today, the undiscounted total (what the flows sum to with time ignored), and the net.

Worked example

The anchor is CFI's resolved case: an investment returning $10,000 per year for ten years at a 10% required rate is worth $61,446 today — CFI's published figure, the sum of ten discounted flows matching the annuity closed form to the dollar. This page holds five annual slots, so its equal-flow preset is the five-year analogue of the same method: five $10,000 flows at 10% discount to $37,908, not the ten-year $61,446. On the default inputs — $50,000 upfront against $15,000 a year for five years at 10% — this calculator discounts to about $56,862 of stream value, an NPV near $6,862: its own arithmetic on the published method.

Frequently asked questions

What does a positive NPV mean?

That the discounted cash flows exceed the upfront cost at your required rate — the project clears the hurdle you set. It is a computation about the inputs, not a verdict: the flows are forecasts and the rate is your judgment, and the result inherits both.

What discount rate should I use?

The return the money would otherwise earn at similar risk — a cost of capital, a hurdle rate, or an opportunity cost. The sweep shows the answer at four rates precisely because the choice moves the conclusion; a project that only clears a 5% hurdle is a different proposition from one that survives 20%.

How is NPV different from just adding up the cash flows?

The undiscounted total ignores time: $15,000 arriving in year five is worth less than $15,000 today, because today's money could compound in the meantime. The gap between the undiscounted total and the PV of flows on this page is exactly the price of that waiting.

What is the relationship between NPV and IRR?

The IRR is the discount rate at which NPV equals zero — visible in the sweep where the sign flips. NPV asks "is it worth it at MY rate"; IRR asks "what rate does it earn" — the irr calculator solves that rate from the same flows.

Can cash flows be negative?

Yes — enter outflows as negatives: a year-three equipment replacement, a cleanup cost at the end. The arithmetic discounts them identically, and heavily sign-switching flows are exactly where NPV stays well-behaved while IRR can become ambiguous.

What about flows beyond five years?

This page holds five annual slots; longer projects need either aggregation into the later slots or a terminal value discounted as year five. Equal long streams have a shortcut — the present-value calculator's annuity form prices any length in one step, as the CFI ten-year case shows.

How accurate is this, and what does it exclude?

The discounting is exact for the flows and rate entered; the uncertainty lives entirely in forecasting the flows and choosing the rate. It excludes taxes and inflation unless your flows already embed them, mid-year timing (flows land at year-end), and risk beyond what the rate prices in.