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IRR Calculator

Calculate the internal rate of return for a series of cash flows against an initial investment.

Result

Internal Rate of Return
15.24%

IRR is the discount rate at which this investment's NPV equals zero - compare it to your required rate of return or cost of capital to judge whether the project is worthwhile.

About the IRR Calculator

What single rate of return would make a series of future cash flows exactly worth their initial cost today? That's the question internal rate of return answers, and it's one of the most-cited metrics in investment and capital budgeting decisions. Our IRR Calculator solves for it numerically from an initial investment and up to five years of projected cash flows.

How It Works

You enter an initial investment (treated as a cash outflow) and up to five years of expected cash inflows. Rather than solving IRR algebraically, which has no closed-form solution for more than a couple of cash flows, the calculator uses a binary search: it repeatedly tests a discount rate, computes the net present value of all cash flows at that rate, and narrows the range between a low and high guess until it finds the rate where NPV lands at essentially zero.

IRR is the rate r that solves: NPV = Σ [CFₜ ÷ (1 + r)ᵗ] = 0, for t = 0 to 5

Formula & Methodology

The calculator starts with a wide bracket, roughly negative 90% to 500%, and checks whether NPV at the low end and NPV at the high end have opposite signs, confirming a root exists somewhere between them. It then repeatedly bisects that range: testing the midpoint rate's NPV, and keeping whichever half of the range still brackets a sign change, for up to 100 iterations or until NPV is within a cent of zero. This binary search approach reliably finds IRR even though there's no direct algebraic formula for it once you have more than two or three cash flow periods.

Step-by-Step: Calculating It By Hand

  1. 1List your initial investment as a negative cash flow at time zero.
  2. 2List each subsequent year's expected cash inflow.
  3. 3Test a candidate discount rate by computing NPV: sum each cash flow divided by (1 + rate) raised to its year number.
  4. 4Adjust the rate up or down and repeat until NPV lands at zero; that rate is the IRR.

Examples

Solid return

A $50,000 initial investment followed by $15,000 in cash flow each year for 5 years produces an IRR of roughly 15.2%, meaning that's the annual return rate at which the investment exactly breaks even in present-value terms.

Comparing to cost of capital

If your required rate of return or cost of capital is 10%, an IRR of 15.2% suggests the project clears that hurdle comfortably; an IRR below 10% would suggest passing on it in favor of other opportunities.

Advantages

  • Expresses investment attractiveness as a single, comparable percentage rather than a dollar figure
  • Useful for ranking projects or investments of different sizes
  • Solves numerically via binary search, handling cash flow patterns that have no simple algebraic answer
  • Directly comparable to a required rate of return or cost of capital

Common Mistakes

  • Comparing IRR across projects of very different sizes or durations without also checking NPV in dollar terms
  • Assuming reinvestment at the IRR rate is realistic for very high returns, which can overstate a project's true attractiveness
  • Ignoring the "No solution found" result and assuming a data entry error rather than checking for multiple sign changes in cash flows
  • Treating IRR as the only decision metric instead of pairing it with NPV, payback period, and risk assessment

Edge Cases to Watch For

  • If cash flows never turn positive, or if they change sign more than once (for example, a big cash outflow midway through the projection), the binary search may fail to find a solution and the calculator reports "No solution found."
  • Unconventional cash flow patterns can technically produce more than one mathematically valid IRR, though this calculator's search returns just one within its bracketed range.
  • IRR assumes all interim cash flows get reinvested at the IRR itself, an assumption that can be unrealistic for very high IRRs, which is why some analysts prefer NPV or a modified IRR for large projects.
  • A very small or negative IRR still gets reported as long as a solution exists within the search bracket, it isn't automatically flagged as "reject."

Common Use Cases

  • Evaluating whether a business investment or capital project clears your required return
  • Ranking multiple investment opportunities by their implied rate of return
  • Comparing an investment's IRR against its cost of capital or a benchmark return
  • Sanity-checking projected cash flows before committing capital
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

How is IRR different from NPV?

NPV gives you a dollar amount of value created at a rate you choose, while IRR gives you the percentage return the investment itself generates - IRR is useful for comparing opportunities of different sizes, but can be misleading with unconventional cash flow patterns (multiple sign changes).

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Conclusion

IRR distills a multi-year cash flow projection into one percentage you can compare against your required return, but it works best alongside NPV rather than in isolation. Run the same cash flows through our NPV Calculator to see the dollar value created at your actual discount rate, not just the breakeven rate.

References