IRR Calculator
Find the internal rate of return (IRR) on an investment with equal annual cash inflows — the discount rate that makes its net present value zero.
How it works
Solve 0 = −initial + Σ cash inflow ÷ (1 + IRR)^t for t = 1…n · Solved numerically by bisection
The internal rate of return is the annual discount rate at which an investment’s net present value is exactly zero — the rate at which the future cash inflows, discounted back to today, just repay the initial outlay. There is no closed-form solution for more than a couple of periods, so IRR is found numerically; this calculator uses bisection, narrowing the rate between −90% and 1000% until NPV crosses zero. A higher IRR means a more attractive investment, and a project is generally worth pursuing when its IRR exceeds your required rate of return (hurdle rate).
Worked example
Investing $10,000 that returns $3,000 a year for 5 years pays back $15,000 undiscounted. The IRR is the rate r where 10,000 = 3,000 ÷ (1+r) + 3,000 ÷ (1+r)² + … + 3,000 ÷ (1+r)⁵. Solving numerically gives an IRR of about 15.2% — meaning those cash flows are equivalent to earning roughly 15.2% a year on the $10,000.
Frequently asked questions
What does IRR actually mean?
IRR is the annualized return implied by a series of cash flows — the single discount rate that makes their net present value zero. If an investment’s IRR is 15%, its cash flows are financially equivalent to earning a steady 15% per year on the money invested.
How is IRR different from ROI?
ROI is a simple total return that ignores timing — total gain divided by cost. IRR accounts for when each cash flow arrives by discounting it, so it reflects the time value of money. Two investments can share the same ROI but have very different IRRs if one returns cash sooner.
Why does the calculator say “no positive IRR”?
If the total undiscounted cash inflows do not exceed the initial investment, there is no positive rate at which the investment breaks even — the project loses money in nominal terms, so no positive IRR exists. Increase the annual inflow or the number of years.
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Educational estimate, not financial advice.