Solve for the internal rate of return of a cash-flow series with an initial investment and irregular future cash inflows. Use it to test different inputs quickly, compare outcomes, and understand the main factors behind the result before moving on to related tools or deeper guidance.
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Capital Budgeting
The Internal Rate of Return (IRR) is the discount rate that makes the net present value of a series of cash flows equal to zero. It is one of the most widely used capital budgeting metrics for evaluating project profitability.
IRR tells you the annualised effective return implied by a set of cash flows. If a project’s IRR exceeds the company’s cost of capital (hurdle rate), the project creates value.
Unlike NPV, IRR expresses the result as a percentage, making it intuitive for comparing projects of different sizes.
IRR is the rate r that satisfies the NPV equation.
0 = Σ CFₜ / (1+IRR)ᵗ
Solved numerically (Newton-Raphson). No closed-form solution exists for more than 2 cash flows.
Cash flows: −100,000, 30,000, 35,000, 40,000, 50,000. The IRR is approximately 12.5% — the rate at which the discounted inflows exactly equal the initial outflow.
Assumes reinvestment of interim cash flows at the IRR itself (often unrealistic). Can produce multiple solutions for non-conventional cash flow patterns (multiple sign changes). Does not indicate the scale of value creation — use NPV for that. MIRR addresses the reinvestment rate assumption.
Frequently asked questions
Compare IRR to your hurdle rate (typically WACC). If IRR > hurdle rate, the project creates value. But always check NPV too — a high IRR on a tiny project may create less total value than a lower IRR on a large project.
Yes. If cash flows change sign more than once (e.g. investment, returns, then another investment), the equation can have multiple mathematical solutions. Use MIRR or NPV for non-conventional cash flows.
IRR assumes you can reinvest interim cash flows at the IRR rate. If IRR is 30% but you can only reinvest at 8%, the true return is lower. MIRR fixes this by using separate finance and reinvestment rates.
The Newton-Raphson solver may not converge for certain cash flow patterns. Try adjusting the cash flows or use NPV analysis instead. Non-convergence often indicates an unusual cash flow pattern.
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