Why the rate that zeroes NPV is the rate you earn
Every investment is a stream of cash flows spread across time — money out at the start, money back later. Discounting those flows at some rate gives their net present value: discount at a low rate and distant inflows still look large, so NPV is high; discount at a high rate and they shrink, pulling NPV down. Somewhere in between sits the rate that makes the positives and negatives cancel exactly, leaving NPV at zero. That break-even rate is the IRR, and because it is the rate at which the project just pays for itself, it is the effective compound return on the capital you have committed. You can explore the dollar side of the same idea with the NPV calculator.
The IRR definition
0 = Σ CFt / (1 + IRR)t
where CFt is the cash flow in period t(negative for outflows, positive for inflows) and the sum runs over every period from t = 0 to the end of the project. IRR is the rate that satisfies this equation. There is no closed form — it is solved numerically — and unconventional cash flows that change sign more than once can satisfy it at more than one rate.
What makes this calculator different
- Fully editable cash flows. Add, remove, and edit each period’s cash flow directly — model an upfront outlay followed by any pattern of inflows and outflows you like.
- It solves IRR numerically. Because the equation has no algebraic solution, the calculator finds the zero of NPV by bisection, narrowing the rate from both sides until the crossing is pinned down.
- It draws the NPV profile. A chart of NPV against discount rate shows the curve sloping down and the exact point where it crosses zero — making the IRR visual, not just a figure.
- It compares against your hurdle rate. Enter the minimum return you require and the calculator tells you whether the IRR clears it, so the accept/reject decision is explicit.
Frequently asked questions
What is IRR and how is it found?+
The internal rate of return is the single discount rate at which a project’s net present value is exactly zero — in other words, the compound annual rate the project earns on the capital tied up in it. Because the NPV equation sums each cash flow divided by (1 + IRR) raised to its period, IRR appears inside a polynomial and there is no closed-form algebraic solution. It must be solved numerically: you search for the rate that drives NPV to zero. This calculator does that with bisection, narrowing the rate from both sides until NPV crosses zero.
How do you use IRR to make a decision?+
Compare the IRR against your hurdle rate — the minimum return you require, usually your cost of capital or the return on the next-best alternative. The rule is simple: accept the project if IRR exceeds the hurdle rate and reject it if IRR falls short. When IRR beats the hurdle, discounting at the hurdle rate produces a positive NPV, so the two tests agree for a single conventional project. The bigger the gap between IRR and the hurdle, the more cushion the project has against estimation error.
What is the difference between IRR and NPV?+
NPV is a dollar amount — the present value of all cash flows discounted at your chosen rate — while IRR is a percentage rate intrinsic to the cash flows themselves. NPV tells you how much value a project adds; IRR tells you the rate it earns. They usually point the same way, but they can conflict when ranking mutually exclusive projects of different sizes or timing. When they disagree, trust NPV: it measures the actual wealth created and does not suffer from IRR’s reinvestment assumption or multiple-solution problem.
Can a project have more than one IRR?+
Yes. A conventional cash flow has one sign change — an outflow followed by inflows — and yields a single IRR. But if the cash flows switch sign more than once (for example, a large cleanup cost at the end of a mining or energy project), the NPV polynomial can cross zero at several rates, giving multiple valid IRRs. It is also possible to have no real IRR at all. When the cash flows are unconventional, IRR becomes ambiguous and NPV is the more reliable guide.
What are IRR’s limitations?+
IRR implicitly assumes every interim cash flow is reinvested at the IRR itself, which is often unrealistic when the IRR is high. It can produce multiple values or none when cash flows change sign more than once, and it can rank projects incorrectly when they differ in scale or timing. The modified internal rate of return (MIRR) addresses the worst of these by reinvesting positive flows at an explicit finance/reinvestment rate, producing a single unambiguous figure. For decisions, IRR is best read alongside NPV rather than in isolation.
Disclaimer: This calculator is foreducation and illustration only. IRR rests on simplifying assumptions (notably that interim cash flows are reinvested at the IRR) and can be ambiguous when cash flows change sign more than once; its output should be read alongside NPV, not in isolation. Nothing here is investment, tax, or financial advice.