Internal Rate of Return (IRR) Calculator
The Internal Rate of Return (IRR) is the discount rate at which a project's NPV equals zero — i.e. the break-even return the project earns on the money tied up in it. Enter the upfront investment, projected yearly cash flows and your hurdle rate (required rate of return). The calculator returns the IRR, the NPV at the hurdle rate, and a clear accept/reject verdict. The solver uses interval scanning plus bisection — the same approach as Excel/Sheets IRR() and standard investment-banking models.
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Internal Rate of Return (IRR)
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Cash flow stream has more than one sign change (non-conventional). Multiple IRRs may mathematically exist; this tool reports the first root found — prefer NPV for the decision.
Year-by-year discounting at hurdle rate
| Year | Cash flow | Discount factor | Present value | Cumulative NPV |
|---|
Cash flows are assumed to occur at the end of each period. IRR is unreliable for non-conventional flows — trust NPV when signs alternate more than once.
Formula
Solve: Σₜ₌₀ⁿ CFₜ / (1 + IRR)ᵗ = 0 // CF₀ = − C₀ Decision: IRR > hurdle → accept; IRR < hurdle → reject NPV at hurdle = − C₀ + Σₜ₌₁ⁿ CFₜ / (1 + r)ᵗ
- · IRR is the rate that makes NPV = 0 and shares all of NPV's assumptions — cash flows occur at period-end (year-end convention), identical to Excel/Sheets IRR().
- · Search range: this tool scans −99.9 % to +1000 % in 0.1 % steps for the first sign change in NPV, then bisects to better than 1e-10 before reporting the answer in percent.
- · Sign-change count (Descartes' rule of signs): a conventional project starts negative then turns positive — one sign change → unique IRR. Non-conventional flows (multiple sign changes) may have multiple IRRs or none at all; the tool flags this with a warning banner.
- · IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself — unrealistic for very high IRRs. The Modified IRR (MIRR) was created to address this.
- · IRR and NPV give the same accept/reject signal for a single conventional project, but rank mutually exclusive or differently-sized projects differently — defer to NPV in those cases (IRR is scale-blind).
- · References: Brealey, Myers & Allen, Principles of Corporate Finance, Ch. 5; Excel/Sheets IRR() and XIRR(); CFA Level I Corporate Finance reading on capital budgeting.
Frequently asked
IRR vs NPV — which should I use for investment decisions?
NPV expresses value in absolute dollars (e.g. +$50,000), is additive, and respects project size — the academic consensus is to use NPV for the final decision. IRR is the discount rate at which NPV = 0, intuitively used as "accept if IRR beats the hurdle rate." For a conventional project (one outflow then inflows), the two methods agree. They diverge when projects are mutually exclusive or non-conventional, in which case NPV wins because IRR is scale-blind and may have multiple solutions. In practice, report both: IRR for intuition, NPV for the decision.
Why does my cash flow stream show "IRR undefined"?
Mathematically, IRR requires the cash flow stream to have at least one sign change (a negative-then-positive or positive-then-negative crossing). If the initial investment plus the subsequent flows are all in the same direction (e.g. all inflows, or all outflows), the NPV function is monotonic and never crosses zero — so no IRR exists. The most common mistakes are: forgetting the initial investment, entering it as zero, or writing an outflow as a positive number. Re-check the signs of every input and try again.
When can a project have multiple IRRs, and how should I handle it?
By Descartes' rule of signs, every sign change in a cash flow stream may correspond to an IRR. A conventional project (initial outflow followed by inflows only) has one sign change and one IRR. But projects with mid-life reinvestments (e.g. -100, +300, -250) have two sign changes and up to two IRRs. The tool flags this with a warning and reports the first root found — because both IRRs are mathematically valid but neither has a unique economic meaning. The fix: use NPV with an explicit discount rate, or use the Modified IRR (MIRR) which discounts intermediate flows at a separate reinvestment rate.
If IRR is much higher than the hurdle rate, is the project definitely worth doing?
Usually yes, but watch for two traps. First, IRR implicitly assumes intermediate cash flows can be reinvested *at the IRR itself*. If IRR = 50 %, where else are you going to find a 50 % return? This reinvestment assumption inflates the realised return — the Modified IRR (MIRR) uses a more realistic reinvestment rate (often WACC) instead. Second, a high IRR on a small project can produce a smaller NPV than a moderate IRR on a large project, so you should always check NPV and the profitability index (PI) alongside IRR before making a final call.
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