IRR Calculator
Calculate the internal rate of return for a series of cash flows.
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About
IRR Calculator
Anyone weighing one project against another runs into the same problem: each comes with a different pattern of money going out and coming back, over a different stretch of time. The internal rate of return compresses all of it into a single annual percentage you can compare directly. Two calculators sit above. The first handles a fixed recurring withdrawal or deposit against an opening and closing balance. The second takes an initial outlay and uneven yearly cash flows, and reports the IRR alongside further investments, investment length, total return, and gross return.
What the internal rate of return is
The IRR is the discount rate at which a project's net present value comes out to exactly zero. Money arriving in five years is worth less than the same money today, so future cash flows have to be discounted back before they can be compared with what you paid upfront. The rate that makes those discounted inflows exactly cancel the outflows is the IRR.
Read it as the break-even return once the timing of money is accounted for. If a project's IRR clears your cost of capital or hurdle rate, it earns more than the money costs and is generally worth doing. If it falls short, the project does not pay for the capital it consumes. A machine returning 19.438% is attractive to a firm borrowing at 12% and a bad idea for one borrowing at 20%, and nothing about the machine changed between those two sentences.
How IRR is calculated
The IRR uses the net present value equation, but backward. Rather than picking a discount rate and computing NPV, you set NPV to zero and solve for the rate:
0 = ฮฃ [ CFt รท (1 + r)t ]
where:
CFt : the cash flow in period t (CF0 is normally negative, the initial investment)
r : the discount rate, which here is the IRR being solved for
t : the time period, running from 0 to n
n : the final period
For anything beyond a couple of periods there is no algebraic solution. The rate has to be found by iteration: try a rate, see whether NPV lands above or below zero, adjust, repeat. That is what the calculators above do, and it is why spreadsheets ship a dedicated IRR function rather than a formula you type out.
Where IRR gets used
- Investment decisions. Compare a project's IRR against the hurdle rate. Above it, the opportunity clears the bar; below it, the money is better used elsewhere.
- Capital budgeting. When several projects compete for one budget, ranking them by IRR is a common first cut.
- Loan and lease analysis. Lenders and lessors use it to check that a financing structure actually earns what it should once payments are spread over time.
- Private equity and venture capital. Fund performance is routinely quoted as an IRR, since capital goes in and comes back at irregular intervals over years.
- Real estate. Purchase price, rental income, maintenance, and an eventual sale price form exactly the kind of uneven series IRR was built for. The Rental Property Calculator runs that case in detail.
Example: a single project
A manufacturer is considering a $40,000 machine expected to return $10,000, $20,000, and $30,000 at the end of years one, two, and three. Put $40,000 in the initial investment field of the irregular cash flow calculator above, then $10,000, $20,000, and $30,000 in the year 1 to 3 fields.
The IRR comes out at 19.438%. Adjusted for the time value of money, the machine earns an annualised 19.438% on the money tied up in it. At a 12% cost of capital that is comfortably worth doing. At 20% it is not, even though the machine returns $60,000 in total on a $40,000 outlay.
Example: two projects, same total return
Two property deals each need $100,000 upfront and each pay back $150,000 over five years. Investment A returns $5,000, $20,000, $25,000, $40,000, and $60,000. Investment B returns nothing in year one, then $10,000, $30,000, $30,000, and $80,000.
On simple ROI they are identical: $50,000 of profit on $100,000, or 50% each. IRR separates them, because A returns more of its money sooner and that money can be put back to work:
- Investment A: 11.290%
- Investment B: 10.259%
A full percentage point of annualised return, entirely down to timing. This is the case where ROI misleads and IRR does not, and it is the reason IRR is standard in capital budgeting rather than a simple profit percentage.
IRR on a personal portfolio
IRR is useful well outside corporate finance. Applied to your own account it answers a question a fund fact sheet cannot: what did your money actually earn, given when you paid it in and took it out. Put the opening balance in as the initial investment, each contribution as a negative figure and each withdrawal as a positive one, and the closing balance as the final inflow.
The number that comes back is a money-weighted return, and it will differ from the fund's published figure, which is time-weighted. The published return measures the manager's performance with contributions stripped out. IRR measures yours, including the effect of buying more in a good month or a bad one. If you added heavily just before a fall, your IRR trails the fund's headline return, and that gap is real rather than an error. The first calculator above handles the simple version of this, where deposits or withdrawals are a fixed amount on a regular schedule.
Where IRR falls short
It ignores scale. A 40% IRR on $10,000 makes less money than a 15% IRR on $500,000. IRR is a rate, not an amount, so a small project can outrank a far more valuable one. Check the total return alongside it, which is why both calculators above report it.
It ignores risk. The math treats forecast cash flows as facts. A speculative venture projecting 30% and a government-backed contract projecting 12% look unambiguous on paper, and the lower, more certain one is often the better decision.
It assumes reinvestment at the IRR. Built into the calculation is the idea that every interim cash flow is reinvested at the same rate. A project returning 30% rarely has somewhere else earning 30% to put the money. The modified internal rate of return exists to fix exactly this.
It can produce more than one answer. When cash flows change sign more than once, negative then positive then negative again, the equation can have several mathematically valid roots. In that situation a single IRR figure stops being meaningful.
None of this makes IRR a bad metric; it makes it one metric. Net present value, MIRR, and the payback period each answer a question IRR cannot, and analysts normally read them together. The Payback Period Calculator covers how long the money is at risk, and the ROI Calculator gives the plain profit percentage.
How these calculators work
Both build a cash flow series and search for the rate that drives its net present value to zero, narrowing the range by bisection until the answer is precise well past the decimals shown. A rate only exists when the series contains both a negative and a positive figure, so a set of flows that never turns positive returns no result.
The fixed cash flow calculator converts your holding period and frequency into periods, applies the recurring withdrawal or deposit at the beginning or end of each one, adds the ending balance at the finish, and compounds the periodic rate up to an annual figure. The irregular calculator treats year 0 as the initial outlay and each later year as entered, so a negative figure in any year counts as further money invested rather than a return. Its charts show each year's flow, money out in red and money back in blue, and the running cumulative total whose crossing of zero is the payback point. For projecting a single lump sum forward instead, use the Investment Calculator.
Common questions
Frequently asked questions
One that clears your cost of capital, and the answer changes by investor. A 19.438% IRR is strong for a firm borrowing at 12% and inadequate for one borrowing at 20%. Private equity often targets 20% or more; a stable property deal in the low teens can be perfectly acceptable. Compare it to your hurdle rate, not to a universal number.
ROI is total profit as a percentage of cost and ignores timing. IRR is annualised and accounts for when each dollar arrives. Two deals both returning $150,000 on $100,000 over five years show a 50% ROI each, but IRRs of 11.290% and 10.259% depending on how early the money comes back.
They use the same equation from opposite ends. NPV discounts cash flows at a rate you choose and returns a dollar amount. IRR solves for the rate that makes NPV zero and returns a percentage. NPV tells you how much value a project adds; IRR tells you the rate it earns.
Yes. A negative IRR means the cash flows never repay the money invested, so the project loses value even before the cost of capital is considered. The calculators above return no result when a series contains no positive figure at all, since there is then no rate to solve for.
Because the equation is a polynomial, and one with cash flows that change sign more than once can have several valid roots. A project that costs money, earns money, then needs a large repair or cleanup outlay is the classic case. When that happens, a single IRR figure is not meaningful and NPV or MIRR is the better guide.
The calculation implicitly assumes every interim cash flow is reinvested at the IRR itself. For a project returning 30%, that assumes you have somewhere else paying 30% to put the money, which is often unrealistic. The modified internal rate of return exists to let you set a separate, realistic reinvestment rate.
Type them as a negative number in the year they occur. A $20,000 renovation in year three is entered as -20000. The calculator adds it to the further investments total and to the invested base used for gross return, rather than treating it as a return.
Gross return is total profit as a percentage of everything you put in, including any further investments. Put in $50,000 and receive $90,000 back and the total return is $40,000, which is a gross return of 80%. Unlike IRR, it says nothing about how long the money was tied up.