What is the Internal Rate of Return (IRR)?

IRR is the discount rate at which the Net Present Value (NPV) of a series of cash flows equals zero. Formally, it is the value r that satisfies NPV = sum of CF_t / (1+r)^t = 0 across all periods t. A project whose IRR exceeds the cost of capital (or hurdle rate) is generally worth accepting; one below it destroys value.

How does the calculator find the IRR?

The tool uses Brent method, a robust bracketed root-finding algorithm that combines bisection, the secant method and inverse quadratic interpolation. It first scans the range -99% to +1000% in 2,000 steps to find a sign change in the NPV function (indicating a root lies within that bracket), then refines the answer to 10 decimal-place precision.

What is the difference between IRR and NPV?

NPV gives an absolute value in currency units — it tells you how much value a project adds at a given discount rate. IRR gives a rate — it tells you the break-even cost of capital. Both use the same discounted cash flow framework; IRR is simply the rate at which NPV equals zero. For mutually exclusive projects, NPV is the more reliable decision rule because IRR can give misleading rankings when project sizes differ.

Why might there be no real IRR?

IRR does not always exist as a single real number. If all cash flows have the same sign (all outflows or all inflows) the NPV curve never crosses zero. With multiple sign changes in the cash flow stream (e.g. an outflow in period 3 after a string of inflows) there may be multiple IRRs (Descartes rule of signs). In these cases the calculator reports "no real IRR" and NPV analysis at your actual cost of capital is the preferred approach.

What is a good IRR for a real-estate or business investment?

Benchmarks vary by asset class and risk. As a rough guide: property development in the UK often targets 15-20%+; private equity funds aim for 20-25%+; infrastructure projects may accept 8-12%; early-stage venture capital looks for 30%+ to compensate for failure rates. Always compare the IRR to your weighted average cost of capital (WACC) or hurdle rate, not to an absolute number.

Is the IRR the same as the annualised return (CAGR)?

They are related but not identical. CAGR measures the compound growth rate of a single lump-sum investment to a single terminal value. IRR handles any pattern of cash flows across multiple periods, including multiple outflows and inflows. For a simple two-period case (invest now, receive a lump sum later) they are mathematically equivalent, but for irregular cash flows IRR is the correct tool.

IRR Calculator — Gera Tools

The Internal Rate of Return is the single most widely used metric in capital budgeting, private equity, real estate development and project appraisal. It answers a deceptively simple question: at what annual return does this investment break even on a discounted-cash-flow basis? If the answer exceeds your cost of capital, the project creates value; if it falls short, it destroys it.

This calculator accepts up to 50 cash flow periods — enough to model a decade-long infrastructure project, a property development cycle, or a multi-year technology investment. It computes the IRR to four decimal places, draws an interactive NPV-vs-rate curve so you can see exactly how sensitive the answer is to the discount rate, and prints a period-by-period discounted cash flow table so you can verify every number.

How it works

The IRR is the rate r that satisfies:

NPV = CF_0 + CF_1/(1+r) + CF_2/(1+r)^2 + ... + CF_n/(1+r)^n = 0

Because this equation has no closed-form algebraic solution for n > 4, numerical methods are required. The calculator uses Brent’s method — a hybrid root-finding algorithm that combines bisection (guaranteed convergence), the secant method (fast near the root), and inverse quadratic interpolation (super-linear convergence). The three-step process:

Bracket search. The NPV function is evaluated at 2,000 evenly-spaced rates from -99% to +1,000%. The first adjacent pair where NPV changes sign marks a bracket containing a root.
Brent refinement. Brent’s method is applied within the bracket, iterating until the interval width falls below 10^-10 (ten decimal places of precision).
Verification. The NPV at the final rate is reported alongside the IRR. It should be effectively zero (typically below 0.001 in absolute value).

Worked example

A private investor considers a five-year development project:

Period	Description	Cash flow
0	Land purchase + build cost	-100,000
1	Phase 1 sales	+20,000
2	Phase 2 sales	+30,000
3	Phase 3 sales	+40,000
4	Phase 4 sales	+35,000
5	Final sales + land residual	+25,000

Total inflows: 150,000. Total outflows: -100,000. Net cash: +50,000.

The calculator finds IRR = 14.53%. If the investor’s cost of capital (WACC or hurdle rate) is 12%, the project creates value — proceed. If the hurdle rate is 15%, the project does not clear the bar — decline or renegotiate the land price.

The NPV at 14.53% ≈ 0, confirming the result. At 12% the NPV is approximately +6,673, representing the value added above the cost of capital in present-value terms.

Interpreting the IRR

IRR range	Typical verdict
Below 0%	Capital is destroyed — avoid
0–8%	Marginal — likely below cost of capital
8–15%	Reasonable for lower-risk projects
15%+	Strong return — check for unconventional cash flows

Always compare the IRR to your specific hurdle rate, not to a generic benchmark. A 10% IRR on a government-backed infrastructure bond may be exceptional; the same 10% on an early-stage venture is well below the risk-adjusted target.

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