IRR Performs Better than NPV: A Critical Analysis of Cases of Multiple IRR and Mutually Exclusive and Independent Investment Projects

Abstract

This paper presents evidence to identify the appropriate investment criterion (IRR vs NPV) with emphasis on the controversial reinvestment assumption, multiple, negative, zero and no IRR, mutually exclusive investment and independent projects. The analysis is based on the estimated return of capital (ROC), return on invested capital (ROIC), capital amortization schedule (CAS) and the modified CAS (MCAS). The salient findings are: a. There is no reinvestment of intermediate income in normal net cash flow (NCF) investments. Incidences of reinvestment is evident in some of the non-normal NCF (NNCF) investments where the opening balance (OB) in the CAS is positive. The generalized assertion of reinvestment at IRR or at hurdle rate with IRR and NPV, respectively, is not valid except in the case of some NNCF. b. The problem of multiple IRR is caused by reinvestment of intermediate income in some non-normal NCF (NNCF) investments. MCAS method eliminates the reinvestment income from the NNCF data and resolves the problem of multiple IRR and leads to unique IRR. c. There is no IRR when there is no investment in zero year or investment year or there is no negative cash flow and no sign change. Negative IRR is common when the sum of NNCF is negative that and reveals capital loss (ROC not fully recovered). When the sum of NNCF is zero, the IRR will be zero. Zero IRR indicates that the NNCF is sufficient to recover the capital cost (ROC) and ROIC not recovered. d. In the case of mutually exclusive projects, selecting projects based on NPV at hurdle rate is misleading. A project selected based on higher NPV at hurdle rate ends-up with negative NPV when discounted by the higher IRR achieved by the counterpart project (with lower NPV). In the case of counterpart project, the NPV is not negative but zero at that higher IRR as the discount rate. This weakness of NPV is not exposed as NPV is a static point estimate (at hurdle rate). The NPV is not an appropriate criterion. e. Among a range of discount rates tried, IRR is the only rate that indicates the full utilization of the NCF (makes the NPV zero) and the maximum feasible ROIC (=IRR). IRR therefore performs better than the NPV to select or rank independent or mutually exclusive projects. NPV is the unutilized NCF and a static point estimate. NPV therefore provides incomplete information at hurdle rate. It fails to indicate the full ROIC that the Net cash flow (NCF) could support. NPV at hurdle rate can at best indicate whether the NCF is fully utilized (NPV = 0) or not fully utilized (positive NPV) or not adequate to cover the cost of capital (negative NPV), respectively. IRR, in contrast, explicitly indicates that the NCF is fully utilized (NPV and the closing balance (CB) in CAS are ‘0’) and the ROIC plus ROC are fully recovered. f. The modified IRR (MIRR) is not a solution to the problem of multiple IRR. MIRR assumes and includes reinvestment income without any evidence of reinvestment and therefore MIRR is a spurious estimate. The problem of reinvestment and the resultant multiple IRR is resolved by eliminating the reinvestment income under MCAS method and therefore IRR is unique. These results consistently support the conclusion that IRR is the best criterion to accept or reject or rank mutually exclusive projects as well as independent projects. NPV will still be useful in other areas to estimate the present value. Authors of finance and economic textbooks and other publications may wish to review and consider appropriately update the sections on CBA or capital investment or capital budgeting.