Internal Rate of Return (IRR) Calculator
Find the discount rate that zeroes the NPV to compute an investment's internal rate of return.
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 the discounted future net cash flows just equal the initial investment, representing the project's own annualised return. Rule: IRR above the cost of capital (borrowing rate or required return) means the project is theoretically worth it; below, be cautious. As a percentage, IRR is easy to compare with deposit rates, mortgage rates or other returns, so HK businesses and individuals use it for shops, acquisitions, rental property or any multi-year 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, Cᵢ the year-i net 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 (year-0 outflow).
- Enter yearly net cash flows (in +, out −); 0 for years with none.
- View the IRR that zeros the NPV instantly.
Initial HK$100,000, equal net cash flow for 5 years — IRR by amount
| Annual cash flow | 5-yr total | IRR | vs cost of capital (6%) |
|---|---|---|---|
| HK$22,000 | HK$110,000 | 3.26% | Below cost, avoid |
| HK$25,000 | HK$125,000 | 7.93% | Slightly above, consider |
| HK$28,000 | HK$140,000 | 12.38% | Clearly profitable |
| HK$30,000 | HK$150,000 | 15.24% | Attractive |
Case Studies
Case 1: Evaluating a small shop
Ms Li plans a shop: HK$500,000 fit-out and stock, 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.
Case 2: IRR near the cost of capital is a warning
A project invests HK$200,000, then HK$60,000/year for 4 years (total HK$240,000). IRR ≈ 7.71%.
On paper it 'earns' HK$40,000, but IRR is only 7.71%. If the cost of capital is also ~7%, after risk and inflation there is almost no profit. 'Surplus' ≠ 'worth it' — IRR must beat the cost of capital; a thin gap means a thin safety margin.
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 or 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.
Multiple IRRs with mixed-sign cash flows?
Yes. When the cash-flow sign changes more than once (e.g. invest, earn, then large re-invest), there can be multiple real solutions — the 'multiple IRR' problem. Then IRR alone misleads; use NPV or MIRR. This calculator returns one solution in range; for atypical flows prefer NPV as the decision basis.
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 in absolute terms than a HK$5m project at 12%. IRR also assumes interim cash can be reinvested at the same IRR (often untrue). Use NPV (absolute value), payback period and cost of capital together; do not decide on IRR alone.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.