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The Internal Rate of Return (IRR) is the annualised rate of return that makes the Net Present Value (NPV) of all cash flows equal to zero. It is one of the most widely used metrics in capital budgeting and investment analysis.
IRR formula
IRR is the value of r that satisfies:
0 = CF₀ + CF₁/(1+r) + CF₂/(1+r)² + ... + CFₙ/(1+r)ⁿ
There is no closed-form solution — IRR is found iteratively (Newton-Raphson method).
IRR decision rule
- IRR > WACC (hurdle rate): Accept the project — it creates value
- IRR < WACC: Reject the project — it destroys value
- IRR = WACC: Break-even — indifferent
IRR limitations
- Multiple IRRs: cash flows that change sign more than once can yield multiple IRRs
- Scale blindness: IRR ignores project size — a 50% IRR on $1,000 is worth less than 20% on $1M
- Reinvestment assumption: assumes interim cash flows are reinvested at the IRR rate, which may be unrealistic
For these reasons, IRR is often used alongside NPV rather than in isolation.