IRR — Internal Rate of Return

Internal Rate of Return (IRR) is the discount rate that, when applied to a project's cash flows, makes its Net Present Value (NPV) equal to zero. Mathematically the IRR is the rate solving sum_{t=0..T} CF_t / (1+IRR)^t = 0, where the initial investment CF_0 is negative and subsequent annual cash flows are positive. The interpretation is straightforward: IRR is the annual compound return the project intrinsically earns. The decision rule compares IRR with the firm's cost of capital (WACC or hurdle rate) — accept if IRR > hurdle rate, reject otherwise. IRR's appeal lies in producing a single percentage figure that is easier than NPV to convey to non-finance stakeholders. It has, however, well-known pathologies: (1) non-conventional cash-flow patterns — for example a mid-life refurbishment that creates a second outflow — can yield multiple IRR solutions (the multiple-IRR problem); (2) when comparing mutually exclusive projects of different scale, IRR can rank them incorrectly while NPV gives the right order; (3) IRR implicitly assumes that interim cash flows are reinvested at the IRR rate, which is often unrealistic — hence the Modified IRR (MIRR) correction. An SMB finance manager typically reports IRR alongside NPV so that both project attractiveness and absolute value creation are visible.