Why might IRR be undefined?

For "non-conventional" cash flows (sign changes beyond initial outflow), there can be 0, 1, or multiple IRRs. Use MIRR or NPV in those cases.

How accurate is the numeric solver?

Newton with bisection fallback converges to ~10⁻⁹ precision typically. Reported as a percentage to 4 decimal places.

Above your hurdle rate. Corporate projects: WACC + 2-5%. VC investing: 25%+. Real estate: 12-20%.

Why might IRR be undefined?

For "non-conventional" cash flows (sign changes beyond initial outflow), there can be 0, 1, or multiple IRRs. Use MIRR or NPV in those cases.

How accurate is the numeric solver?

Newton with bisection fallback converges to ~10⁻⁹ precision typically. Reported as a percentage to 4 decimal places.

Above your hurdle rate. Corporate projects: WACC + 2-5%. VC investing: 25%+. Real estate: 12-20%.

IRR (Internal Rate of Return) Calculator

IRR = the discount rate that makes NPV = 0. Solved numerically via Newton's method.

Result

IRR

20.5259%

Compare to your hurdle rate.

Initial$100,000.00
Cash flows$25,000, $30,000, $35,000, $40,000, $50,000
IRR20.5259%
NPV at IRR (sanity)0.0000

High IRR — verify reinvestment-rate realism (use MIRR cross-check)

IRR

Discount rate at which NPV exactly equals zero.

20.5259%

NPV at 10% benchmark

Standard corporate hurdle rate cross-check.

$32,183

NPV at 15% (VC threshold)

Typical VC required-return floor.

$15,165

Sign changes (non-conventional flag)

Descartes' rule of signs: each sign change permits an additional real IRR. >1 → use MIRR or NPV.

Source: Brealey, Myers & Allen, "Principles of Corporate Finance" 13e — IRR decision rule + reinvestment-assumption critique (Ch. 5); Newton-Raphson convergence per any standard numerical-analysis text.

Not financial advice — Standard IRR implicitly assumes intermediate cash flows are reinvested at the IRR itself — usually unrealistic for high-IRR projects. For mutually exclusive projects of different scale or timing, IRR can rank wrong; NPV always picks the wealth-maximizing choice.

Step-by-step

Solve r where NPV(r) = -100000 + Σ CF_t / (1+r)^t = 0.
Newton's method converges to r ≈ 20.5259%.
Verify: NPV(0.2053) ≈ 0.00 (should be near 0).

How to use this calculator

Enter initial investment.
List annual cash flows.
Read IRR; compare to your hurdle rate.

About this calculator

IRR is the discount rate that makes NPV exactly zero — the project's break-even rate. If IRR > your required return (hurdle rate), accept. Solved numerically because there's no closed-form for general cash flows. Beware: with non-conventional flows (sign changes), IRR can be multiple-valued or undefined; use NPV instead in those cases.