Find the internal rate of return and NPV of an irregular cash flow series.
The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of a cash flow series equal to zero. In plain terms: it's the annualized return rate of an investment assuming all cash flows are reinvested at the same rate. A project is worth pursuing when IRR exceeds your cost of capital (hurdle rate). NPV, computed at your chosen discount rate, tells you whether the investment adds value in today's dollars. Positive NPV = value-creating; negative NPV = value-destroying at your cost of capital.
NPV
NPV = Σ Cash Flow_t / (1 + r)^t
IRR definition
IRR is the rate r where NPV = 0
Some cash flow patterns have multiple sign changes (e.g., negative-positive-negative). Such series can have multiple IRRs, and bisection may find any one of them or none. If you get a convergence error, check that you have exactly one sign change, or use the Modified IRR (MIRR) approach which avoids the multiple-root problem.
Compare IRR against your hurdle rate — typically your weighted average cost of capital (WACC) or the return you could earn on an alternative investment of similar risk. If IRR > hurdle rate, the project adds value.
CAGR measures the return on a single investment with a beginning and ending value. IRR handles irregular, multi-period cash flows — including cases where you invest in multiple tranches or receive income at uneven intervals. For a single lump-sum investment and exit, IRR and CAGR will be identical.
Yes — IRR implicitly assumes all intermediate inflows are reinvested at the IRR rate. For high-IRR projects (e.g., 40%), this assumption is often unrealistic. MIRR (Modified IRR) corrects for this by using the cost of capital as the reinvestment rate.