IRR Calculator
The internal rate of return of any series of cash flows, with the net present value and a warning when the answer is not unique.
Results
What this tool does
The internal rate of return is the rate at which a project exactly breaks even: discount every future flow by it and the whole thing comes to zero. It is the natural way to compare an investment against a borrowing cost, and it has no closed-form solution — it has to be searched for, which is what this page does. Paste the flows in order, negative for money out and positive for money in. You also get the net present value at your own required rate, and a count of how many times the flows change sign, because that is the one thing that can make an internal rate of return quietly meaningless.
Formula
IRR = the rate r for which Σ flow_t ÷ (1+r)^t = 0 · found by bisection
Variables
| Symbol | Meaning | Unit |
|---|---|---|
flows | The cash flows, in order | — |
rate | Discount rate | % |
IR | Internal rate of return | % |
NV | Net present value at your rate | — |
UQ | Is this the only answer? | — |
SC | Times the flows change sign | — |
TI | Everything that comes in | — |
TO | Everything that goes out | — |
NF | In minus out | — |
MU | Times the money back | x |
PB | Payback ignoring the discount | — |
NP | Periods | — |
Worked example
- The cash flows, in order-50000, 12000, 15000, 18000, 20000, 14000
- Discount rate10 %
- Internal rate of return16.5962 %
- Net present value at your rate9182.62
- Is this the only answer?Yes
- Times the flows change sign1
- Everything that comes in79,000.00
- Everything that goes out50,000.00
- In minus out29,000.00
- Times the money back1.580 x
- Payback ignoring the discount3.250
- Periods5
Limitations
- This is an informational calculator, not personalised financial advice. Rates, fees, taxes and contract conditions vary between institutions and countries.
- The tool works with whatever currency you use for the inputs; it does not convert between currencies.
Frequently asked questions
How do I write the cash flows?
In order, starting with today. Money going out is negative, money coming in is positive, and the first figure is usually the investment itself. Separate them with commas or put one per line. The gap between figures must be a constant period — every year, or every month — because the rate that comes out is per period. A yearly list gives a yearly rate; a monthly list gives a monthly rate, which you would then convert to annual, not multiply by twelve.
What does the warning about sign changes mean?
That there may be more than one right answer. The internal rate of return is the root of a polynomial, and a polynomial can have as many roots as it has sign changes in its coefficients. The ordinary case — one payment out, then money coming in — has exactly one change and one rate. But a project that needs more money partway through, or leaves a clean-up cost at the end, changes sign twice and can genuinely have two internal rates, both correct and neither meaningful. This page finds one and tells you how many changes there were; when there is more than one, judge the project by its net present value instead.
Should I prefer the project with the higher IRR?
Not on its own. The internal rate of return is a percentage, and percentages are blind to size: a project returning 40 per cent on 1,000 creates far less value than one returning 15 per cent on a million. It also implicitly assumes every interim cash flow is reinvested at the same high rate, which is rarely available. When two projects disagree — one wins on rate, the other on net present value — the net present value is the one to follow, because it is measured in money rather than in ratios.