Internal rate of return (IRR) is the discount rate at which an investment breaks even — the rate that makes the present value of all its cash flows equal zero. It is the single number most often used to compare projects with different sizes, timelines and payment patterns.
Cash flow
Leave a year blank to count it as 0. Only the years you fill are used.
Result
Discounted cash flows
How IRR is found
Every cash flow is discounted at rate r and summed:
NPV(r) = CF0 + CF1/(1+r) + CF2/(1+r)2 + … + CFN/(1+r)N
The IRR is the value of r that makes NPV zero. There is no closed-form solution for most cash flow patterns, so the calculator scans for a change of sign and then bisects the interval until the answer is stable to ten decimal places.
Worked example
Invest $1,000 today and receive $300 a year for five years. Set NPV to zero:
0 = −1000 + 300/(1+r) + 300/(1+r)2 + … + 300/(1+r)5
The solution is r ≈ 15.24%. Because the project returns about 15% a year on the money still tied up in it, any cost of capital below 15.24% makes it worth doing.
IRR versus NPV
- NPV is an amount of money — what the project adds in today’s terms. It depends on the discount rate you choose.
- IRR is a rate — the return the project earns. It does not need a discount rate, which is why it is popular for quick comparisons.
- When the two disagree, NPV is usually the better decision rule: a very small project can have a spectacular IRR and still add less value than a large project with a modest one.
Limitations worth knowing
- Multiple roots. Cash flows that alternate sign (invest, withdraw, invest again) can produce more than one IRR. This calculator returns the root closest to zero.
- No root. If every cash flow is positive or every one is negative, there is no rate that balances them — the calculator says so instead of inventing a number.
- Reinvestment assumption. IRR implicitly assumes interim cash flows are reinvested at the IRR itself, which is rarely true.
- Scale. IRR ignores the size of the investment; pair it with NPV before deciding.
IRR calculator FAQ
What counts as a good IRR?
There is no universal threshold. Compare it with your cost of capital or the return available on a comparable investment: an IRR above that hurdle is attractive, below it is not.
Why does my IRR come out as zero?
If the sum of the undiscounted cash flows is exactly zero — for example, invest $1,000 and receive $1,000 back over the following years — the break-even rate is 0%.
Can IRR be negative?
Yes. A project that returns less than it costs has a negative IRR; the calculator reports it rather than hiding it.
How many cash flows can I enter?
Up to ten annual periods plus the initial investment, which covers the usual project appraisal horizon.
Related tools
- Present Value Calculator — discount a future amount and a payment stream to today.
- Future Value Calculator — compound today’s money forward.
- Payback Period Calculator — how long until the cash flows recover the outlay.
