IRR Calculator

How IRR Is Calculated

The Internal Rate of Return is the discount rate that makes an investment's net present value equal to exactly zero. Every period's cash flow is discounted back at a candidate rate and summed alongside the initial investment (entered as a negative cash flow at time zero); IRR is whatever rate makes that sum vanish: $$NPV(r) = -C_0 + \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} = 0$$

Unlike present value or compound interest, this equation has no algebraic solution for r once there are more than a couple of cash flow periods — it's a polynomial in r with no general closed form. This calculator solves it numerically with Newton-Raphson iteration: starting from a guess rate, it repeatedly refines the guess using the function's slope until NPV lands close enough to zero, the same iterative approach spreadsheet software uses internally for its own IRR function.

IRR vs. NPV

Net present value and IRR are two views of the same underlying cash flow stream. NPV picks a discount rate you choose — usually your required rate of return or cost of capital — and tells you the dollar value the investment creates or destroys at that rate. IRR instead solves for the break-even rate itself, the exact return the cash flows produce. A project is generally attractive when its IRR exceeds your required rate of return, which is the same condition as its NPV being positive at that same required rate. See the Present Value Calculator for the single-cash-flow version of the same discounting idea.

Worked Examples

1. This calculator's default case. A 10,000-dollar investment returning 3,000 dollars a year for 5 years produces an IRR of about 15.24 percent — the rate at which those five 3,000-dollar inflows discount back to exactly 10,000 dollars today.
2. Uneven cash flows. A 5,000-dollar investment returning 1,000, 1,500, 2,000, and 2,500 dollars over four years produces an IRR of about 12.83 percent, illustrating that the cash flows don't need to be equal from period to period — the solver handles any sequence.
3. No real solution. If every entered cash flow is positive (no negative outflow anywhere in the series), there's no discount rate that brings NPV to zero, and the calculator reports that it could not converge rather than returning a misleading number.

Why Newton-Raphson Can Fail to Converge

Newton-Raphson iteration refines a guess using the function's local slope, which works reliably when the cash flow series changes sign once (a typical outflow-then-inflows pattern). It can fail to converge, or converge to a rate that isn't economically meaningful, when the cash flows never change sign at all, when they change sign several times (which can produce multiple valid IRRs mathematically), or when the numbers are extreme enough that each iteration overshoots further instead of settling down. This calculator caps the iteration count and reports a clear message rather than looping indefinitely or silently showing a wrong number. It also checks your entered cash flows for more than one sign change and flags it directly — a mathematically real situation where more than one rate can satisfy NPV = 0, so the single rate shown is whichever one the iteration happened to land on, not proof that it's the only valid answer.

The Reinvestment-Rate Assumption

IRR implicitly assumes every positive cash flow the investment throws off gets reinvested at that same IRR for the rest of the period — an assumption that gets less realistic the higher the computed IRR is, since few real opportunities exist to keep reinvesting at, say, a 30 percent annual return. This is the classic critique of using IRR alone for a real multi-year business or project decision: a very high IRR on paper can overstate the actual return you'll realize if you can't actually find comparably good places to put the interim cash flows. NPV avoids this specific issue since it doesn't assume anything about reinvestment, which is part of why comparing IRR against your required rate of return (rather than trusting IRR as a standalone number) is the safer way to use it.

Comparing Multiple Investment Options

To decide between two or more opportunities, run each one's cash flows through this calculator separately and compare both figures side by side: the computed IRR against your own required rate of return, and each option's NPV at that same required rate. Since every field here updates the page's own URL live as you type, the address bar itself becomes a shareable snapshot of one scenario — open a second browser tab with this same calculator, enter the other option's numbers, and keep both tabs' URLs (or bookmark them) to compare the two side by side or share them with someone else.

IRR Terms You Should Know

NPV (Net Present Value) — the sum of all discounted cash flows at a chosen rate; IRR is the specific rate at which this sum equals zero.

Discount Rate — the rate used to shrink a future cash flow down to what it's worth today; IRR is solved for, not chosen.

Cost of Capital — the return a business or investor requires to make a project worthwhile; comparing IRR against this figure is the usual way IRR gets used in a decision.

Sign Change — a cash flow series switching from negative to positive (or back); at least one sign change is required for a real-valued IRR to exist.

This calculator provides estimates for educational and planning purposes only. Actual results may vary. Consult a qualified financial advisor for guidance specific to your situation.