IRR calculator
Find the rate that makes an investment break even in present value.
- Formula and assumptions shown
- Table and CSV export
- Runs in your browser
How it works
IRR is the discount rate that makes the net present value of the entered cash flows equal to zero. The model restricts inputs to a conventional initial outflow followed by inflows so the result has a clear interpretation.
Find r such that cash flow at time 0 + Σ(cash flow at time t ÷ (1 + r)^t) = 0.
IRR is a comparison measure, not a guarantee. It can be misleading when projects have different sizes, durations, reinvestment assumptions, or multiple sign changes.
Assumptions
- Cash flows are equally spaced.
- The first cash flow is negative and later flows are non-negative.
- The model searches for one conventional solution.
- Taxes, financing costs, irregular dates, and reinvestment outcomes are excluded unless entered in the cash flows.
Worked example
$1,000 now and $1,100 in one year
The IRR is 10%, because −$1,000 + $1,100 ÷ 1.10 = $0.
Step by step
- List the cash flows by period. Period 0 is −$1,000, the initial outlay; period 1 is +$1,100. The results show total inflows of $1,100 and 1 inflow.
- Set net present value to zero. −$1,000 + $1,100 ÷ (1 + r) = 0, so 1 + r = $1,100 ÷ $1,000 = 1.10.
- Solve for the rate. r = 1.10 − 1 = 0.10, the headline IRR of 10%.
- Check it with NPV. At 10%, $1,100 ÷ 1.10 = $1,000 and NPV is $0. At 5% NPV is +$47.62 and at 12% it is −$17.86, so the zero point sits between them at 10%.
- Longer series need a search. With several inflows there is usually no direct formula, so the calculator narrows the rate step by step until NPV reaches zero. For the default series, −$10,000 followed by $3,000, $3,500, $4,000, and $4,500, the IRR is 17.09%.
How to read your result
The headline is the IRR as an annual percentage, because each period is a year. Initial outlay repeats the amount entered, Total inflows is the undiscounted sum of the later cash flows, and Number of annual periods counts every year after the outlay, including any with a zero cash flow. The table lists each period and its cash flow; there is no chart.
IRR is most useful compared with a required return. If the IRR is above that rate, NPV at that rate is positive; if below, negative. It says nothing about size: $1,000 growing to $1,100 and $1,000,000 growing to $1,100,000 both have a 10% IRR, although the second adds far more dollars.
The calculator accepts only a negative outlay followed by non-negative inflows, which has a single IRR. Projects with later negative cash flows, such as a large repair in year 3, can have more than one IRR and are rejected. Irregular dates need a date-based method such as a spreadsheet XIRR function. IRR is sometimes read as assuming interim cash is reinvested at the IRR itself; the modified IRR (MIRR) replaces that with a stated reinvestment rate.
What changes the result most
- Timing
- The same $1,100 received in year 2 instead of year 1 (cash flows "0, 1100") lowers the IRR from 10% to 4.88%, because 1.10 is now spread over two years: √1.10 − 1 = 0.0488.
- Size of the inflows
- Receiving $1,200 instead of $1,100 in year 1 doubles the IRR to 20%.
- How inflows are spread
- Splitting the $1,100 into $550 in each of two years gives an IRR of 6.60%. Total inflows are identical, but half the money arrives a year later.
Questions
What does IRR measure?
It is the periodic rate that makes the entered cash flows' NPV equal to zero. Annualize it only when the periods are years or when the model converts them.
Can IRR have more than one answer?
Yes, cash flows with multiple sign changes can produce multiple roots. This calculator restricts the pattern to a conventional single-outflow case.
Should I choose the highest IRR?
Not automatically. Compare NPV, scale, risk, timing, and the assumptions behind each cash-flow series.
What is the IRR formula?
IRR is the rate r that solves 0 = CF0 + CF1 ÷ (1 + r) + CF2 ÷ (1 + r)² + … + CFn ÷ (1 + r)ⁿ, where CF0 is the negative initial outlay. With a single later cash flow there is a direct answer, r = CF1 ÷ outlay − 1. Longer series are solved numerically, as spreadsheet IRR functions do.
What is the difference between IRR and NPV?
NPV is a dollar amount at a chosen discount rate; IRR is the rate at which NPV equals zero. For a single conventional project they agree on the basic test, since an IRR above the discount rate means a positive NPV, but they can rank two projects differently when the projects differ in size or timing.
What is modified internal rate of return (MIRR)?
MIRR discounts outflows at a stated finance rate and compounds inflows at a stated reinvestment rate, then finds the single rate linking the two. It always has one answer. This calculator reports standard IRR only.
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Sources
These references explain the concepts behind the calculation. They do not endorse this site. Estimates leave out any cost or condition you did not enter.