IRR calculator – internal rate of return
Calculate the discount rate that makes the net present value of a cash-flow series equal to zero.
This choice applies to every calculator; amounts are not converted.
Internal rate of return
Enter the initial investment and one cash flow per period to estimate IRR.
One amount per line. IRR assumes equal-length periods.
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How does this tool work?
IRR is the implicit return rate of periodic cash flows: the discount rate at which NPV equals zero.
The calculation searches for the discount rate that makes the net present value of all cash flows equal to zero. The initial investment and each periodic cash flow are included according to their position in time, then the algorithm tests and refines the rate until NPV is sufficiently close to zero. The result is expressed as a percentage per period. It still requires careful interpretation because multiple sign changes in the cash-flow series can produce several mathematical solutions or prevent a single meaningful IRR from being found.
How to use this tool
Enter the investment
Provide the initial cash outflow.
Add cash flows
Enter one flow per period.
Read IRR
The result is estimated automatically when a solution exists.
Good to know
Several IRRs are possible
When cash flows change sign more than once (investment, income, then a large decommissioning cost), the equation may have several solutions or none. The tool flags it: in that case, rely on NPV at a chosen discount rate.
IRR or NPV to choose
IRR expresses a return as a percentage, handy for comparing with a cost of capital. But between two projects of different sizes, the one with the higher IRR does not necessarily create more value: compare their NPVs too.
Internal rate of return formula
Internal rate of return (IRR)
−I₀ + Σ CFₜ / (1 + IRR)ᵗ = 0
IRR is the discount rate that makes NPV zero. The tool finds it by successive approximation and shows no result when the series does not have exactly one sign change.
- I₀
- initial investment, paid at t = 0
- CFₜ
- cash flow of period t
- IRR
- internal rate of return per period
- n
- number of periods entered
Use cases
Compare projects
Compare IRRs across investments built with consistent periods and comparable cash-flow assumptions.
Test profitability
Compare the calculated IRR with a relevant hurdle rate or cost of capital for the project.
Analyse cash flows
See how the timing and amount of future cash flows change the project’s implicit rate of return.
Examples
€10,000 project returning €3,000, €4,000 then €5,000
The IRR is the rate that brings NPV to zero: at 8.9% a year, the three discounted flows are worth exactly the €10,000 invested.
Input
Initial investment: €10,000; Future cash flows: €3,000, €4,000, €5,000Result
Estimated IRR: 8.9%; Total net cash flow: €2,000Tips and best practices
- IRR assumes equal-length periods.
- Multiple sign changes can lead to multiple IRRs or no unique result.
- Compare IRR with a hurdle rate appropriate to the project.
Sources and references
Frequently asked questions
How is IRR different from ROI?
ROI is a simple overall return, while IRR considers the timing of cash flows and expresses an implicit periodic return rate.
Why is no IRR shown?
Some cash-flow series do not have a unique solution in the searched range, especially when the sign changes more than once.
Does IRR include risk?
Not directly; risk is reflected mainly in the benchmark rate used for comparison and in the cash-flow assumptions.
Why can IRR be misleading?
Cash flows that switch signs several times can produce multiple IRRs. Compare NPV at an appropriate discount rate as well.
What does an IRR above the discount rate mean?
For an initial outflow followed only by inflows, IRR above the discount rate implies positive NPV, provided both rates use the same period. Do not extend this rule automatically to cash flows with repeated sign changes: multiple IRRs may exist. Check NPV directly at the chosen discount rate.
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