NPV and IRR Calculator

What net present value and internal rate of return actually tell you

Net present value answers one question: after paying for a project and waiting for the money to come back, how much value is left in today's dollars? Every future cash flow is divided by (1 + r) raised to the power of the year it arrives, which strips out the return you could have earned elsewhere. The initial investment is already in today's money, so it is subtracted at full face value. If what remains is positive, the project beats the alternative use of the same capital.

The internal rate of return flips the question around. Instead of assuming a discount rate and solving for value, it assumes zero value and solves for the rate. The IRR is the discount rate at which NPV equals exactly zero — the break-even cost of capital. Anything cheaper than the IRR and the project makes money; anything more expensive and it loses money.

Worked example: a 00,000 project at a 10% discount rate

Suppose a piece of equipment costs 00,000 today and produces $25,000, $30,000, $35,000, $30,000 and $25,000 of net cash over the next five years. At a 10% hurdle rate the discounting looks like this:

The last cumulative figure is the NPV: $9,830.12. The undiscounted total is 45,000, which looks like a 45% gain until you charge for the five years of waiting. The profitability index is the present value of the inflows divided by the outlay, 09,830.12 / 00,000 = 1.098 — you get about .10 of value per dollar committed. Simple payback ignores discounting entirely: cumulative cash reaches $90,000 after year three and 20,000 after year four, so the break-even lands a third of the way through year four, at 3.33 years.

How the IRR gets found, one guess at a time

There is no closed-form formula for the IRR of an arbitrary cash flow series, so calculators search for it. NPV falls as the rate rises: at 0% this project is worth $45,000, at 10% it is worth $9,830, at 12% it is $4,401, and at 14% it has turned negative at -$616. The root sits between 12% and 14%. Bisection repeatedly halves that bracket — 13%, 13.5%, 13.75% — until NPV is within a cent of zero, arriving at an IRR of 13.75%. Any cost of capital below that leaves the project profitable; anything above it does not.

When NPV and IRR point different ways

Take two mutually exclusive options with the same 10% cost of capital. Project A costs 0,000 and returns $20,000 in one year: IRR of 100%, NPV of $8,181.82. Project B costs 00,000 and returns 50,000 in one year: IRR of 50%, NPV of $36,363.64. Project A wins on IRR by a mile and loses on value by a factor of four. Percentages cannot tell you how big the pot is, and shareholders are paid in dollars, not in rates of return. When the two measures conflict and you can only pick one project, NPV is the tie-breaker.

Test the discount rate before you trust the answer

The discount rate is usually the shakiest input in the whole model. Run the same equipment project across a range and watch the verdict move: NPV is 5,718 at 8%, $9,830 at 10%, $4,401 at 12%, and -$616 at 14%. A project with that little headroom flips from accept to reject on a two-point change in the cost of capital. If your WACC estimate could plausibly be wrong by that much, the honest conclusion is that the project is marginal rather than good. Projects with an IRR far above the hurdle rate survive this test; ones sitting a point or two above it do not.

Limitations worth remembering

This calculator assumes annual, end-of-year cash flows and a single constant discount rate. Real projects have mid-year timing, changing risk profiles, tax shields, working capital swings and terminal values, and each of those has to be baked into the cash flow figures you enter. Cash flow series that change sign more than once can have multiple IRRs, in which case the number shown is one root among several and NPV is the only reliable guide. And the whole exercise is only as good as the forecast: precision to the cent in the table does not make year-five revenue any more certain than it was when you guessed it.