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How IRR Is Calculated
The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows equal to zero. In other words, it is the annualized effective compounded return rate that an investment earns over its holding period.
For a series of cash flows CF0, CF1, ... CFn, the IRR is the value of r that satisfies:
NPV = CF0 + CF1/(1+r)1 + CF2/(1+r)2 + ... + CFn/(1+r)n = 0
This calculator uses the Newton-Raphson iterative method with up to 100 iterations and a tolerance of 0.00001. The algorithm starts with an initial guess of 10% and refines the estimate by computing both the NPV and its derivative at each step.
Limitations
- Reinvestment assumption: IRR assumes that all intermediate cash flows are reinvested at the IRR rate itself, which may not reflect reality. For a more conservative measure, consider MIRR (Modified IRR).
- Multiple solutions: Non-conventional cash flows (where the sign changes more than once) can produce multiple valid IRR values. This calculator returns the first solution found.
- No time weighting: IRR treats each period as equal. If your cash flow periods are not evenly spaced, the result may be misleading.
- Scale-independent: IRR does not account for the absolute size of the investment. A $1M investment at 20% IRR is very different from a $10K investment at 20% IRR. Use MOIC alongside IRR for a fuller picture.
For a simpler conversion between MOIC and IRR, see the MOIC to IRR Calculator.
This calculator is for educational and planning purposes only. Consult a financial professional for investment decisions.
