Why is IRR solved by iteration instead of a formula?

Once more than one future cash flow is involved, the NPV=0 equation becomes a higher-degree polynomial with no general closed-form solution.

Can a set of cash flows have more than one IRR?

Yes, mathematically, whenever the cash flows change sign more than once. This tool detects that case and flags it.

What if there's no IRR at all?

If every cash flow points the same direction, no real IRR exists — the calculator reports this explicitly.

How is IRR different from a simple return-on-investment percentage?

IRR accounts for the timing of cash flows, while a simple ROI just compares total money in vs. out with no time-value adjustment.

It depends entirely on your alternative use of capital — generally attractive if it clearly exceeds your cost of capital.

Does IRR account for risk or reinvestment realistically?

Not directly — it implicitly assumes interim cash flows get reinvested at the same IRR, which can overstate real-world returns.

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Finance

Internal Rate of Return (IRR) Calculator

The break-even discount rate for a series of cash flows, solved numerically like Excel's IRR.

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Last reviewed 2026-08-30

About the Internal Rate of Return (IRR) Calculator

Solves numerically for the Internal Rate of Return (IRR) — the discount rate at which a series of cash flows has a Net Present Value of exactly zero — using the same Newton-Raphson iteration Excel's IRR function relies on internally, with a bisection-search fallback.

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How to use it

Enter the Initial investment (cash outflow today).
Enter each future period's expected cash flow.
Read the IRR, total invested vs. total returned, and net cash flow in the result panel.

Formula

IRR is the rate r that solves: 0 = −Initial investment + Σ [Cash flow_t ÷ (1 + r)^t]. Solved iteratively via Newton-Raphson from a 10% starting guess, falling back to a bounded bisection search between −99% and +1,000% if Newton-Raphson fails to converge.

Worked example

A $100,000 initial investment returning $10,000/$20,000/$30,000/$40,000/$50,000 over 5 years: total cash returned is $150,000, and the solver converges to an IRR of about 12.0%.

Interpreting your result

For a typical project — one upfront outflow followed only by inflows — there's a single well-defined IRR. If cash flows change sign more than once, more than one mathematically valid IRR can exist; this tool reports the root nearest its starting guess and flags multiple sign changes explicitly. IRR also implicitly assumes interim cash flows are reinvested at the IRR itself.

Recommendations

• IRR is most useful for ranking similarly-sized projects by percentage return; for comparing projects of very different sizes, NPV is the more reliable dollar-value comparison.
• A cash-flow series with more than one sign change can mathematically have multiple valid IRRs — treat a flagged result with extra caution.
• IRR assumes cash flows are reinvested at the IRR itself, which can be unrealistic for a very high computed IRR.

Frequently asked questions

It means this series of cash flows has the same value-generating effect as an investment that steadily compounds at exactly 12% per period.