IRR Calculator
Find the internal rate of return that zeros the NPV from irregular cash flows of up to 10 periods.
Input Data
Results
At a glance:The internal rate of return (IRR) is the discount rate that makes a project's NPV exactly zero — the rate at which discounted future net cash flows just equal the initial investment, i.e. the project's own annualised return. Rule: IRR above the cost of capital (borrowing rate / required return) means the project is theoretically worth it; below, be cautious. As a percentage it is easy to compare with time-deposit rates, mortgage rates or other returns, used for shops, acquisitions, rental property or any multi-period cash-flow project.
Formula
IRR is the rate zeroing NPV: 0 = C₀ + Σ Cᵢ ÷ (1 + IRR)^i, i = 1..n.
C₀ is the initial investment (usually negative), Cᵢ the period-i cash flow.
IRR has no closed form; this calculator solves numerically (Newton + bisection).
$$0 = C_0 + \sum_{i=1}^{n} \dfrac{C_i}{(1+IRR)^i}$$How to Use
- Enter the initial investment as a negative outflow.
- Enter periodic cash flows (in +, out −); 0 for periods with none, up to 10.
- View the IRR that zeros the NPV instantly.
Case Studies
Case 1: Evaluating a small shop
Ms Li plans a shop: HK$500,000 fit-out and stock (outflow), net inflows HK$120k, 140k, 160k, 180k, 200k over 5 years.
Solving numerically, the rate zeroing NPV is about 16.36% — the project's IRR. If funded by a 6% loan, IRR far exceeds the cost of capital, theoretically worth it; but watch over-optimistic cash-flow forecasts.
FAQ
How is IRR related to NPV?
IRR is the discount rate that makes NPV exactly zero. Discount below IRR → NPV positive; above IRR → NPV negative. Set the rate to IRR and NPV is near zero.
How high must IRR be to be worth it?
Compare with the cost of capital (borrowing rate / required return). IRR above cost → theoretically profitable; below → cautious.
Why sometimes no IRR?
If cash flows never turn from negative to positive (all outflows), the equation has no sign change in the reasonable range and no real solution; the calculator shows not computable. Mixed-sign flows may yield multiple IRRs — prefer NPV then.
High IRR means a good project?
Not necessarily. IRR is a percentage, not an amount. A HK$10k project at 40% IRR may earn far less than a HK$5m project at 12%. IRR also assumes interim cash is reinvested at the same IRR (often untrue). Use NPV, payback and cost of capital together.
IRR vs MIRR?
MIRR (modified IRR) fixes IRR's reinvestment assumption: interim inflows are reinvested at a safe rate (e.g. deposit) and the final value is discounted at the finance rate, giving a single, more realistic return. IRR assumes reinvestment at the IRR itself, which can overstate results. For large, long, complex flows prefer MIRR.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.