IRR Calculator
Calculate the internal rate of return and net present value for any series of cash flows, however irregular.
How to use this calculator
- 1Enter cash flows in order, starting with the initial outlay as a negative number.
- 2Each subsequent value is one period — a year, quarter or month, as long as you are consistent.
- 3Set your required return to see whether the NPV is positive at that hurdle.
How the calculation works
IRR is the rate r where: Σ CFₜ / (1 + r)ᵗ = 0
NPV = Σ CFₜ / (1 + d)ᵗ- CFₜ
- Cash flow in period t — negative for money out
- r
- The internal rate of return being solved for
- d
- Your required return or cost of capital
There is no closed-form solution for IRR; it is found numerically. This calculator uses bisection over a bracketed range rather than Newton-Raphson, because bisection cannot diverge and IRR problems often have near-zero derivatives where Newton fails.
By Descartes’ rule of signs, a series with more than one sign change may have several real IRRs. The calculator warns when that applies.
IRR implicitly assumes interim cash flows are reinvested at the IRR itself — the assumption most often criticised, and the reason NPV is preferred for ranking mutually exclusive projects.
Worked example
$10,000 invested returning $3,000 to $5,000 over four years
- 1.The outlay is $10,000 at time zero; returns total $16,500 over four periods.
- 2.Solving Σ CFₜ / (1+r)ᵗ = 0 numerically gives r ≈ 21.41%.
- 3.Verification: discounting all flows at 21.41% gives an NPV of essentially zero. ✓
- 4.At a 10% required return the NPV is $2,829, so the project clears the hurdle comfortably.
Result: IRR 21.41%, NPV at 10% of $2,829
What IRR is trying to answer
Internal rate of return distills a whole series of cash flows — an initial outlay followed by returns spread over time — into a single percentage: the rate at which those cash flows exactly break even, neither creating nor destroying value once discounted. It answers a specific question: "what constant annual return would this investment need to deliver, given exactly when the money goes out and comes back in, to be worth exactly what was paid for it?" That makes it more informative than a simple total-return percentage, because it accounts for timing — money returned in year one is worth more than the same amount returned in year five, and IRR is sensitive to that difference in a way a plain return figure is not.
How it is used to size up a project
Businesses and investors typically compare a computed IRR against a hurdle rate — the minimum return they require to bother taking on the risk, often derived from their cost of capital or from what a safer alternative would return. A project whose IRR clears that hurdle is, by this measure, worth pursuing; one that falls short is not, at least not on financial grounds alone. Because it produces a percentage rather than a currency amount, IRR is also commonly used to communicate a project’s attractiveness in a way that is intuitive to compare across very differently sized opportunities, even though — as below — that convenience comes with a real limitation.
IRR versus NPV
The two measures usually point the same direction but are not interchangeable, and disagreements between them are informative rather than a bug.
- What each produces — IRR is a percentage rate; NPV is a currency amount — the actual value the project is expected to add at a chosen discount rate.
- Sensitivity to project size — IRR treats a 50% return on a small outlay the same as a 50% return on a huge one; NPV reflects the fact that a smaller amount of value created is worth less in absolute terms, which usually matters more to the decision.
- The reinvestment assumption — IRR implicitly assumes interim cash flows are reinvested at the IRR itself, which can be unrealistic for a very high-IRR project; NPV makes no such assumption.
- When to prefer which — IRR is useful for communicating and screening; NPV is generally the more reliable basis for an actual go/no-go decision, especially between mutually exclusive projects.
Where IRR breaks down
IRR has two well-known failure modes. The first is scale-blindness — it says nothing about how much value is actually created, only the rate at which it is created, so it can rank a tiny, high-return project above a much larger one that creates far more absolute value. The second is the possibility of multiple IRRs: when a series of cash flows changes sign more than once, for example an outlay followed by returns followed by a further cost, the underlying equation can have more than one valid solution, making a single IRR figure ambiguous or misleading. Both are reasons NPV is generally treated as the more dependable measure when the two disagree.
Hurdle rates in practice
A hurdle rate is the minimum acceptable return a business or investor sets before committing capital, and it is rarely just "whatever a bank would pay." It is typically built up from a baseline cost of capital — what it costs the organization to raise money in the first place — with a margin added for the specific risk of the project being evaluated. A speculative venture is held to a higher hurdle than a low-risk expansion of an existing, proven business line, which is why the same nominal IRR can be an easy yes for one project and a clear no for another.
What this assumes, and where it stops
Assumptions
- Cash flows occur at regular, evenly spaced intervals.
- Each flow arrives at the end of its period.
- Interim cash flows are reinvested at the IRR — an assumption inherent to the measure.
Limitations
- Multiple sign changes can produce several valid IRRs, making the measure ambiguous. NPV does not have this problem.
- IRR ignores project scale — a 50% return on $1,000 ranks above a 20% return on $1,000,000, which is rarely the right business decision.
- Irregularly timed cash flows need XIRR, which discounts by actual dates rather than equal periods.
Common questions
What is a good IRR?
One comfortably above your cost of capital, with enough margin to cover the risk. A 20% IRR on a low-risk project is excellent; the same figure on a speculative venture may be inadequate. Always compare against the return available from your next-best alternative at similar risk.
Should I use IRR or NPV?
NPV, when they disagree. IRR is intuitive because it produces a percentage, but it ignores project size and assumes reinvestment at its own rate. NPV measures the actual value created in currency terms and has no ambiguity. Use IRR to communicate, NPV to decide.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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