IRR calculator

A project that costs $500,000 and returns $145,000 a year for five years has an IRR of 13.82%, an NPV of $17,554 at a 12.40% discount rate, and pays back in 3.45 years. Its MIRR, using a 12.4% reinvestment rate, is a more modest 12.79%. Change the cash flow to an outlay, three years of profit and a $120,000 closing cost, and there may be no single IRR at all: the sign changes twice, and the standard formula can return two answers or none.

The calculator solves IRR by numerical search from any cash flow schedule, checks for the multiple-IRR problem, and shows NPV, MIRR, payback and the profitability index alongside it, so you see the whole picture and not one number in isolation.

Who reaches for this

You enter the initial outlay and up to ten years of cash flow after it, plus a discount rate and, for MIRR, a reinvestment rate and a finance rate. The calculator searches for the rate that makes the discounted cash flows sum to zero, checks the cash flow for sign changes that could mean more than one answer, and reports NPV, MIRR, simple and discounted payback, and the profitability index from the same numbers.

IRR is one way to read a cash flow schedule. The present value calculator covers a single future payment, and the WACC calculator builds the discount rate a company should use. This page focuses on the return a whole schedule of cash flows implies, and the payback period calculator and profitability index calculator use the same engine with a different emphasis.

IRR is the break-even discount rate for a project. At any rate below it, the project has a positive NPV, and at any rate above it, a negative one. It is found by trial: guess a rate, discount every cash flow, add them up, and adjust the guess until the total is zero.

Take a $500,000 outlay and five years of $145,000. At 0% the cash flows simply add up to $225,000 more than the outlay. As the rate rises, later years are discounted more, and the total value falls. It crosses zero at 13.82%, which is the IRR.

This is why IRR does not have a formula the way an average does. It is a root of a polynomial in the discount rate, of a degree equal to the number of years, and for most projects there is exactly one economically sensible root, but not always.

A conventional project has one outflow followed only by inflows: the cash flow's sign changes once. Then IRR is well behaved and has a single answer. Some projects are not conventional. A mine, an oil well, or a facility with a real decommissioning cost has a large outflow at the end too, so the sign changes twice: negative, then positive, then negative again.

Take an outlay of $100,000, three years of $60,000 profit, and a $120,000 closing cost in year four. Descartes' rule of signs says the number of positive roots cannot exceed the number of sign changes, here two, so there can be zero, one or two IRRs. In this case, scanning the NPV at a wide range of rates never crosses zero: NPV is negative everywhere from a large negative rate to a very large positive one, so there is no IRR at all, even though the project might be a perfectly sensible one to evaluate on NPV.

NPV is negative at every rate shown, dips to its least negative point around 20%, and rises again. There is no rate that makes it zero, so the project has no IRR to report, and a spreadsheet asked to compute one will either error out or, with a different starting guess, sometimes converge on a rate found by luck that does not mean what it appears to mean. The calculator flags this rather than guess: on a cash flow like this, it tells you no rate was found and points to NPV and MIRR instead. On a cash flow with more sign changes that does have two real crossings, both are mathematically valid IRRs, and neither is more correct than the other, which is the more commonly cited version of the multiple-IRR problem.

The lesson is not that IRR is broken. It is that IRR answers a narrower question than it appears to: at what single rate does this exact sequence of cash flows break even, assuming money can be borrowed and lent at that same rate throughout. For most ordinary investments that question has one sensible answer. For cash flows with more than one change of sign, ask NPV directly, or use MIRR, which is built to always give one.

Watching the search converge

A numerical search finds IRR the same way a person would with a calculator and patience: try a rate, see whether NPV is too high or too low, and narrow the range. At 10% NPV is $49,664, too high, so the true rate is above 10%. At 15% NPV is −$13,938, too low, so the rate is between 10% and 15%. At 13% NPV is $9,999, close but still positive; at 14% it is −$2,203, just past zero. The rate is between 13% and 14%, and continuing to halve the gap homes in on 13.82% within a few dozen steps. A spreadsheet does the same halving, just far faster and to more decimal places.

Unlevered vs. levered IRR

A project financed partly with debt has two IRRs worth knowing. Unlevered IRR uses the project's own cash flows before any debt payments, and measures how the underlying asset performs regardless of financing. Levered IRR uses the cash flows left for the equity investor after debt service, which is usually higher when the project's return exceeds the cost of the debt, the same idea behind positive leverage on the cap rate and cash-on-cash pages on this site. State which one you mean: a levered IRR without saying so can look far more attractive than the project itself actually is.

IRR carries a hidden assumption: that every dollar the project throws off along the way can be reinvested at the IRR itself until the project ends. For the 13.82% example that is a mild assumption. For a project with a 60% IRR, it assumes you can find another investment paying 60% for every dollar that comes back early, which is rarely realistic.

MIRR replaces that assumption with two rates you choose. Positive cash flows are compounded forward to the end of the project at a reinvestment rate, often the company's cost of capital. Negative cash flows are discounted back to today at a finance rate, the cost of borrowing. The two totals are connected by a single rate: MIRR = (future value of the positive flows ÷ present value of the negative flows)^(1/n) − 1, where n is the number of periods.

For the five-year, 13.82%-IRR example, with a 12.4% reinvestment rate and an 8% finance rate, MIRR is 12.79%, close to the IRR because the reinvestment rate is not far from it. If the reinvestment rate were more conservative, say 5%, MIRR would fall further, since the same cash could not compound as fast. MIRR is always a single number, so it never runs into the multiple-IRR problem, and it is worth reporting alongside IRR whenever a project's IRR looks unusually high.

Choosing between two projects that cannot both be done, called mutually exclusive projects, is where IRR can mislead. IRR is a percentage and ignores how much money is actually at stake.

Project S has double the IRR of Project L, and a higher profitability index. Project L has nearly three times the NPV. If only one can be funded, and capital is not the binding constraint, NPV says take Project L: it adds $33,808 of value against $12,278. IRR and PI, both percentage measures, favor the small, high-return project, which is fine as far as it goes but does not answer the question that matters, which is how much value gets created.

The crossover rate explains why. It is the discount rate at which the two projects' NPVs are equal, here 17.78%. Below it, the larger project's NPV is higher, because its bigger absolute cash flows are worth more even after discounting. Above it, the smaller project's speed wins out. At the company's 12.4% cost of capital, below the crossover, NPV correctly favors the large project.

The practical rule: when projects are independent, meaning any positive-NPV project can be taken alongside the others, IRR and NPV agree on accept or reject, and ranking barely matters. When projects are mutually exclusive, or capital is limited so that not everything positive can be funded, rank by NPV first, with the profitability index as a useful cross-check when the projects are close.

IRR is only useful next to something to compare it with. The usual benchmark is the discount rate: the company's cost of capital, or a hurdle rate set above it for a riskier project. A project clears the bar when its IRR exceeds that rate, which is the same test as NPV being positive at that rate, since IRR is defined as the rate where NPV is exactly zero.

The two tests can diverge when the discount rate itself is uncertain. A project with a 13.82% IRR clears a 12.4% hurdle and fails a 14.4% one. Since the hurdle rate is itself an estimate, built from a risk-free rate, a risk premium and a view of the project's risk, a project whose IRR sits close to the hurdle deserves a second look at the assumptions behind the rate, not just the cash flow forecast. The WACC calculator builds that rate and shows how much it can reasonably move.

IRR and NPV do not cover every question a project raises. Two more numbers from the same cash flow schedule fill in the gaps, and both are covered in depth on their own pages, which share this calculator.

A single project rarely needs all five numbers to make a decision. A quick screen often starts with payback, for a sense of how exposed the capital is, moves to IRR against the hurdle rate, and settles the close calls with NPV.

Treat the five numbers as a checklist rather than a competition. Each answers a slightly different question: NPV asks how much value, IRR asks at what rate, MIRR asks what a realistic version of that rate looks like, payback asks how exposed the capital is along the way, and PI asks how efficiently the capital is used. A project that looks strong on all five is an easy accept, and one that splits, a high IRR but a slow payback, or a good NPV but a low PI, is where the real judgment happens.

Capital rationing: choosing among several projects

Ranking gets harder still when a limited budget must be spread across more than two projects, and none of NPV, IRR or the profitability index alone answers it cleanly on its own: NPV favors large projects that use up the whole budget on one, and IRR and PI favor small, efficient ones that may leave money unspent. The usual approach ranks projects by profitability index and takes the highest-ranked ones until the budget runs out, then checks whether a different combination uses the budget more fully. The profitability index calculator works through a four-project example under a fixed budget.

There is no universal figure. Guides sometimes cite 10% to 15% for corporate capital projects, higher figures for venture and private equity investments, and lower ones for very safe, regulated assets. I could not trace a specific range to a primary source, and the right comparison is always the project's own cost of capital plus a premium for its own risk, not a borrowed number from another industry.

A useful check is not whether the IRR is high, but whether it is high enough given the risk taken, and whether the cash flows behind it are conventional enough that IRR is even a reliable measure. A 40% IRR on a one-year, single-cash-flow project, as in the ranking-conflict example, is a fine number and a small one in absolute terms. A 14% IRR on a large, ten-year infrastructure project can be an excellent one.

IRR in real estate and private equity

Two fields lean on IRR more than most. In real estate, a project's cash flows include the annual income, a sale at the end, and any refinancing along the way, and the calculator here handles exactly that pattern: enter operating cash flow each year and add the sale proceeds to the final year's number. The cap rate calculator and cash on cash return calculator on this site cover the unlevered and levered yield in a single year, and IRR extends that to the whole holding period.

In private equity, a fund's IRR is calculated on the actual dates money moves: capital calls as outflows and distributions as inflows, which can span years with no cash flow between them. The calculation is the same, but the timing matters more than the total dollars, since IRR is sensitive to how early money returns. A fund that returns capital quickly can post a higher IRR than one that returns the same total more slowly, even if the second holds more total value at the end, which is one reason the multiple on invested capital is often quoted alongside IRR rather than in place of it.

Most IRR errors trace back to one of two habits: reading the percentage without the dollars behind it, or trusting a number the underlying cash flow was never suited to produce.

See how long a project takes to repay its cost with the payback period calculator, or rank several projects under a budget with the profitability index calculator.