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Calculate the Internal Rate of Return (IRR) for an investment using a bisection algorithm.
IRR Definition:
IRR is the discount rate r that makes NPV = 0:
0 = −Investment + Σ [CFt / (1 + r)t]
Solved numerically using bisection over rates from −50% to 500%.
IRR is the annualized rate of return that makes the net present value of an investment equal to zero. It represents the project's intrinsic return regardless of external financing costs.
Compare the IRR to your hurdle rate (required rate of return or cost of capital). If IRR exceeds the hurdle rate, the investment adds value and should generally be accepted. If IRR is below the hurdle rate, the investment should be rejected.
It depends on the type of investment and risk level. For real estate, 10-15% is often considered good. For venture capital, 20-30%+ is typical. For corporate projects, IRR is usually compared to the company's WACC.
Yes. When cash flows change sign more than once (e.g., negative, positive, negative again), there can be multiple rates that set NPV to zero. In these cases, NPV analysis is more reliable than IRR.
ROI measures total return as a simple percentage without accounting for the time value of money or the duration of the investment. IRR is an annualized rate that properly accounts for timing, making it more suitable for comparing investments of different durations.
The payback period is the time it takes for cumulative cash flows to recover the initial investment. It is a simple liquidity measure but does not account for time value of money or returns after the payback point.