IRR (Internal Rate of Return) Calculator
Find the discount rate that makes a project break even — the IRR. Universal corporate-finance formula used in capital budgeting, project appraisal, and private-investment screening.
Internal rate of return
15.24%
- Hurdle rate
- 10%
- Initial investment
- £10,000.00
- Total cash returned
- £15,000.00
- Net cash gain
- £5,000.00
- Simple payback (years)
- 3.33
Accept — IRR of 15.24% clears the 10% hurdle rate. IRR is the discount rate at which the present value of all future cash inflows equals the upfront investment — the project's break-even cost of capital. A project clears its hurdle when IRR exceeds your required rate of return; otherwise the same money would earn more in the next-best alternative of equal risk.
How to use this calculator
Enter the upfront cost of the project as the initial investment, the cash flow you expect each year, the project horizon in years, and your hurdle rate (the minimum return you require). The calculator solves for the discount rate that makes net present value equal to zero — the project's break-even cost of capital. If the IRR exceeds your hurdle rate, accept the project; if it falls short, reject it. Use the same currency for investment and cash flow — the IRR is a rate, so it is currency-independent.
How the calculation works
IRR is defined by the equation NPV(r) = -C0 + Σ CF_t / (1 + r)^t = 0. For a constant annual cash flow this reduces to -C0 + CF × (1 − (1 + r)^(-n)) / r = 0. The equation has no closed-form solution in general, so the calculator uses Newton-Raphson iteration starting at r = 10% and falls back to bisection between -99% and 1000% if Newton-Raphson does not converge. An IRR only exists when the cash-flow series changes sign — an outflow followed by inflows that, in total, exceed the outflow over the project horizon.
Worked example
A factory upgrade costs $10,000 today and is expected to save $3,000 a year for 5 years. The IRR is the rate r that solves -10,000 + 3,000 × (1 − (1 + r)^(-5)) / r = 0. Iterating from r = 10%: at 15.24% the present value of the five $3,000 inflows is exactly $10,000, so IRR ≈ 15.24%. At a 10% hurdle rate the project clears comfortably and would be accepted. If the same $3,000 ran for only 4 years instead of 5, IRR would fall to 7.71% and fail the same hurdle.
Frequently asked questions
What does IRR tell me that NPV does not?
IRR is a rate, so it is comparable across projects of different sizes and durations in a way a raw NPV figure is not. A $1m project with $50k NPV and a $50k project with $50k NPV have very different capital efficiency, but both have the same NPV. IRR captures that — the small project might have an IRR of 35% while the big one is at 6%. The flip side: IRR is silent on the absolute dollars of value created, so for ranking mutually exclusive projects, NPV is the better tool.
What hurdle rate should I use?
The hurdle rate is your required rate of return — the return you could earn on an investment of equivalent risk. For a public company this is usually the weighted average cost of capital (WACC), typically 8–12% for stable businesses. For a private project or personal investment, use the opportunity cost: maybe 10–15% for a small business, 6–8% for a defensive real-estate hold, 4–5% for a Treasury-grade cash flow. A project earns its keep when IRR exceeds the hurdle rate; otherwise the same money does better elsewhere.
Can a project have more than one IRR?
Yes, if the cash-flow series changes sign more than once. Descartes' rule of signs says a polynomial can have as many positive real roots as sign changes in its coefficients — so a project with an outflow, inflows, then a large terminal outflow (decommissioning a mine, dismantling a turbine) can have two IRRs. Both rates set NPV = 0, but neither is a meaningful hurdle. For non-conventional cash flows, fall back to NPV at your hurdle rate or use Modified IRR (MIRR), which assumes reinvestment at the cost of capital.
Why might no IRR exist?
IRR is the rate that makes NPV zero, so it only exists when the cash-flow series crosses zero NPV somewhere. If every cash flow is positive (no upfront cost) or every cash flow is negative (a money-pit project), NPV never crosses zero and IRR is undefined. The calculator returns "no IRR" in that case rather than guessing. Practically: check that the initial investment is positive and that the total of all cash inflows exceeds it over the project horizon.
How does the calculator handle uneven cash flows?
This calculator assumes a constant annual cash flow for n years — the most common back-of-envelope setup and the one that matches typical rental property, bond-like, or simple-savings investments. For lumpy real-world cash flows (ramp-up periods, terminal values, irregular inflows), lay out the series in a spreadsheet and use Excel's IRR or XIRR function. The underlying maths and decision rule are unchanged; only the polynomial degree grows.
What is the relationship between IRR and payback period?
They are different lenses on the same project. Payback period asks "how long until I recover the upfront cost?" — IRR asks "what rate of return does the whole stream earn?" A short payback often correlates with high IRR, but not always: a project with a fast payback and then nothing earns less than one with a slower payback and a long tail of cash flows. Payback ignores everything after breakeven and ignores the time value of money entirely; IRR uses every cash flow. Treat payback as a liquidity / risk check, not a profitability metric.