Non-monotonic NPV Function Leads to Spurious NPVs and Multiple IRR Problems: A Critical Analysis to Resolve These Problems

Forthcoming in the Australian Economic Papers Journal

22 Pages Posted: 21 Aug 2018 Last revised: 15 Dec 2018

Date Written: August 3, 2018


This analysis is conducted using some popular non-normal net cash flow (NNCF) investment data available in public domain and other hypothetical NNCF data. The methodology is mainly based on capital amortization schedule (CAS) and modified CAS (MCAS) methods along with a comparison of the results with the common DCF method. The findings are summarised here: a. The problem of multiple IRR is caused by reinvestment income and the resultant non-monotonic NPV function. The CAS methods clearly indicate whether there is any reinvestment. Non-monotonic NPV function of NNCF investment leads to multiple IRRs or spurious IRRs, NPVs and MIRRs. With non-monotonic NPV functions the DCF estimated criteria are all spurious. b. The MCAS method eliminates the reinvestment thereby leads to monotonic NPV function and resolves the problem of reinvestment, spurious NPVs, MIRRs, IRRs and or multiple IRR. c. Neither the NPV nor the MIRR could resolve the problem of multiple IRR. With normal NCFs and some of the NNCFs also, there are no reinvestment at IRR or at hurdle rate as wrongly asserted in many published works. d. It is normal for the estimated IRR to be either ‘nil or zero or negative’ when the sum of net benefits or NCF is zero or negative. Such IRRs are consistent with NCF or net benefit. IRR of ‘zero or negative or no’ is not a weakness or problem but it reveals the real or consistent return. e. MCAS is an appropriate method to estimate the rate of return (IRR and NPV) for both normal NCF and NNCF and resolves the multiple IRR problem and eliminates spurious NPVs and MIRRS. The estimated IRR and NPV by MCAS method are consistent with NCF. f. Ultimately, IRR and NPV, estimated by MCAS, are the best criteria available to investment, project and cost-benefit analysis. In summary, NPV and IRR estimated by MCAS method are equally appropriate and therefore one cannot be the best substitute for the other. The multilateral and bilateral organizations and corporate managements may wish to revisit their recommendation to use the NPV only and not the IRR while dealing with multiple IRRs associated with NNCF investments.

Keywords: Capital Budgeting, Investment Analysis, Non-Normal NCF Investments, Non-Monotonic NPV Functions, Multiple IRR and Spurious NPVs and MIRR, New Method Resolves These Problems

JEL Classification: D, D61, G3, G31, O2, O22, O12

Suggested Citation

Arjunan, Kannapiran, Non-monotonic NPV Function Leads to Spurious NPVs and Multiple IRR Problems: A Critical Analysis to Resolve These Problems (August 3, 2018). Forthcoming in the Australian Economic Papers Journal. Available at SSRN: or

Kannapiran Arjunan (Contact Author)

Independent ( email )

No Address Available

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