Internal Rate of Return (IRR)

Per Net Present Value, the standard way to judge whether an investment is worth its upfront cost is to discount its future cash flows at a chosen rate — usually the return you could otherwise get on a similarly risky investment — and see whether the result is positive or negative. That approach requires picking a discount rate before doing anything else. But often the more natural question runs the other way: given these cash flows, what rate of return is this investment actually producing? IRR answers exactly that.

IRR is the discount rate at which NPV comes out to precisely zero — the exact break-even point between the upfront cost and everything the investment pays back afterward, once the time value of money is accounted for. If the rate you'd actually require (or could get elsewhere at similar risk) is lower than the IRR, the investment is worth it, because it's expected to outperform the alternative; if your required rate is higher than the IRR, it isn't, because the alternative is actually the better use of the money.

This is why IRR and NPV are really two views of the same underlying cash flows, not two separate calculations: NPV assumes a rate and reports a dollar amount; IRR assumes a dollar amount of zero and reports a rate. Because IRR doesn't require picking a discount rate up front, it's useful for comparing very different investments on a single, rate-like number — but it can behave oddly, or even produce more than one mathematically valid answer, when cash flows switch sign multiple times over an investment's life. That's one reason NPV is generally treated as the more reliable of the two when they disagree.

IRR is the rate that satisfies:

0 = CF₀ + CF₁/(1+IRR)¹ + CF₂/(1+IRR)² + ... + CFₙ/(1+IRR)ⁿ

Unlike Present Value or NPV, there's no way to isolate IRR algebraically for most cash flow patterns — it has to be found by trying different rates until NPV lands on (or very near) zero, which is exactly what the calculator does automatically behind the scenes.

Using the same cash flow stream from the Net Present Value example — a $10,000 upfront cost, followed by $3,000 at the end of each of 4 years — the IRR comes out to approximately 7.71%.

This matches what was found there: at an assumed 8% discount rate — just above this 7.71% IRR — NPV was slightly negative, meaning the required rate exceeded what the investment could actually deliver. Try the IRR Calculator to see how changing any cash flow shifts this rate.