IDEAS home Printed from https://ideas.repec.org/p/col/000463/006653.html
   My bibliography  Save this paper

Average internal rate of return and investment decisions: A new perspective

Author

Listed:
  • Carlo Alberto Magni

Abstract

The internal rate of return (IRR) is often used by managers and practitioners for investment decisions. Unfortunately, it has serious flaws: (i) multiple real-valued IRRs may arise, (ii) complex-valued IRRs may arise, (iii) the IRR is, in general, incompatible with the net present value (NPV) in accept/reject decisions (iv) the IRR ranking is, in general, different from the NPV ranking, (v) the IRR criterion is not applicable with variable costs of capital. The efforts of economists and management scientists in providing a reliable project rate of return have generated over the decades an immense bulk of contributions aiming to solve these shortcomings. This paper offers a solution to this long-standing issue by changing the usual perspective: the IRR equation is dismissed and the evaluator is allowed to describe the project as an investment or a borrowing at his discretion. This permits to show that any arithmetic mean of the one-period return rates implicit in a project reliably informs about a project profitability and correctly ranks competing projects. With such a measure, which we name Average Internal Rate of Return"), complex-valued numbers disappear and all the above mentioned problems are wiped out. The traditional IRR notion may be found back as a particular case.*This article has been selected for the Grant award, given annually by the Engineering Economy Division of the American Society for Engineering Education to the author of the best paper in the journal The Engineering Economist. The papers was judged based on its originality, importance of the problem, logic and clarity, and adequacy of proposed solution. This award is named after Eugene L. Grant, a professor at Stanford."

Suggested Citation

  • Carlo Alberto Magni, 2010. "Average internal rate of return and investment decisions: A new perspective," Proyecciones Financieras y Valoración 6653, Master Consultores.
  • Handle: RePEc:col:000463:006653
    as

    Download full text from publisher

    File URL: http://ssrn.com/abstract=1545815
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Richard H. Bernhard, 1967. "Communications to the Editor--Probability and Rates of Return: Some Critical Comments," Management Science, INFORMS, vol. 13(7), pages 598-600, March.
    2. Carlo Alberto Magni, 2009. "Accounting and economic measures:An integrated theory of capital budgeting," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0019, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    3. Dorfman, Robert, 1981. "The Meaning of Internal Rates of Return," Journal of Finance, American Finance Association, vol. 36(5), pages 1011-1021, December.
    4. Thomas Pfeiffer, 2004. "Net Present Value-Consistent Investment Criteria Based on Accruals: A Generalisation of the Residual Income-Identity," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(7-8), pages 905-926.
    5. Weingartner, H. Martin, 1966. "The Generalized Rate of Return*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 1(3), pages 1-29, September.
    6. Yuri Biondi, 2006. "The double emergence of the Modified Internal Rate of Return: The neglected financial work of Duvillard (1755 - 1832) in a comparative perspective," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 13(3), pages 311-335.
    7. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    8. Davide Ferrari & Sandra Paterlini, 2009. "The Maximum Lq-Likelihood Method: An Application to Extreme Quantile Estimation in Finance," Methodology and Computing in Applied Probability, Springer, vol. 11(1), pages 3-19, March.
    9. William H. Jean, 1968. "On Multiple Rates Of Return," Journal of Finance, American Finance Association, vol. 23(1), pages 187-191, March.
    10. Carlo Alberto Magni, 2009. "Investment decisions, net present value and bounded rationality," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 967-979.
    11. Arrow, Kenneth J & Levhari, David, 1969. "Uniqueness of the Internal Rate of Return with Variable Life of Investment," Economic Journal, Royal Economic Society, vol. 79(315), pages 560-566, September.
    12. Bernhard, Richard H., 1979. "A More General Sufficient Condition for A Unique Nonnegative Internal Rate of Return," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 14(2), pages 337-341, June.
    13. Gallo, Paolo & Peccati, Lorenzo, 1993. "The appraisal of industrial investments: A new method and a case study," International Journal of Production Economics, Elsevier, vol. 30(1), pages 465-476, July.
    14. Ramsey, James B, 1970. "The Marginal Efficiency of Capital, the Internal Rate of Return and Net Present Value: An Analysis of Investment Criteria," Journal of Political Economy, University of Chicago Press, vol. 78(5), pages 1017-1027, Sept.-Oct.
    15. Paul A. Samuelson, 1964. "Tax Deductibility of Economic Depreciation to Insure Invariant Valuations," Journal of Political Economy, University of Chicago Press, vol. 72(6), pages 604-604.
    16. Thiemo Krink & Sandra Paterlini, 2008. "Differential Evolution for Multiobjective Portfolio Optimization," Center for Economic Research (RECent) 021, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    17. Gronchi, Sandro, 1986. "On Investment Criteria Based on the Internal Rate of Return," Oxford Economic Papers, Oxford University Press, vol. 38(1), pages 174-180, March.
    18. K. E. Boulding, 1935. "The Theory of a Single Investment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 49(3), pages 475-494.
    19. Tim Baldenius & Stefan Reichelstein, 2005. "Incentives for Efficient Inventory Management: The Role of Historical Cost," Management Science, INFORMS, vol. 51(7), pages 1032-1045, July.
    20. Seymour Kaplan, 1967. "Computer Algorithms for Finding Exact Rates of Return," The Journal of Business, University of Chicago Press, vol. 40, pages 389-389.
    21. Magni, Carlo Alberto, 2009. "Splitting up value: A critical review of residual income theories," European Journal of Operational Research, Elsevier, vol. 198(1), pages 1-22, October.
    22. James E. Smith & Robert F. Nau, 1995. "Valuing Risky Projects: Option Pricing Theory and Decision Analysis," Management Science, INFORMS, vol. 41(5), pages 795-816, May.
    23. Gordon Hazen, 2009. "An Extension of the Internal Rate of Return to Stochastic Cash Flows," Management Science, INFORMS, vol. 55(6), pages 1030-1034, June.
    24. Ross, Stephen A. & Spatt, Chester S. & Dybvig, Philip H., 1980. "Present values and internal rates of return," Journal of Economic Theory, Elsevier, vol. 23(1), pages 66-81, August.
    25. Daniel Teichroew & Alexander A. Robichek & Michael Montalbano, 1965. "An Analysis of Criteria for Investment and Financing Decisions Under Certainty," Management Science, INFORMS, vol. 12(3), pages 151-179, November.
    26. Kierulff, Herbert, 2008. "MIRR: A better measure," Business Horizons, Elsevier, vol. 51(4), pages 321-329.
    27. David Promislow, S. & Spring, David, 1996. "Postulates for the internal rate of return of an investment project," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 325-361.
    28. Graziani, Rebecca & Veronese, Piero, 2009. "How to Compute a Mean? The Chisini Approach and Its Applications," The American Statistician, American Statistical Association, vol. 63(1), pages 33-36.
    29. J. Hirshleifer, 1958. "On the Theory of Optimal Investment Decision," Journal of Political Economy, University of Chicago Press, vol. 66(4), pages 329-329.
    30. Richard D. MacMinn, 2005. "The Fisher Model," World Scientific Book Chapters, in: The Fisher Model And Financial Markets, chapter 2, pages 12-21, World Scientific Publishing Co. Pte. Ltd..
    31. Federico M. Mucciarelli, 2009. "Exclusion of US-holders in cross-border takeover bids and the principle of equality in tender offers," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0018, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    32. Martin J. Bailey, 1959. "Formal Criteria for Investment Decisions," Journal of Political Economy, University of Chicago Press, vol. 67(5), pages 476-476.
    33. William Fairley & Henry D. Jacoby, 1975. "Investment Analysis Using the Probability Distribution of the Internal Rate of Return," Management Science, INFORMS, vol. 21(12), pages 1428-1437, August.
    34. Marianna Brunetti, 2007. "Population Ageing, Household Portfolios and Financial Asset Returns: a Survey of the Literature," Politica economica, Società editrice il Mulino, issue 2, pages 171-208.
    35. Herbst, Anthony, 1978. "The Unique, Real Internal Rate of Return: Caveat Emptor!," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(2), pages 363-370, June.
    36. Silvia Muzzioli, 2009. "The skew pattern of implied volatility in the DAX index options market," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0020, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    37. Flemming, J S & Wright, J F, 1971. "Uniqueness of the Internal Rate of Return: A Generalisation," Economic Journal, Royal Economic Society, vol. 81(322), pages 256-263, June.
    38. Daniel Teichroew & Alexander A. Robichek & Michael Montalbano, 1965. "Mathematical Analysis of Rates of Return Under Certainty," Management Science, INFORMS, vol. 11(3), pages 395-403, January.
    39. Ezra Solomon, 1956. "The Arithmetic of Capital-Budgeting Decisions," The Journal of Business, University of Chicago Press, vol. 29, pages 124-124.
    40. Bellerby, J.R. & Mujumdar, N.A., 1961. "Agricultural Economic Theory and the Indian Economy," Indian Journal of Agricultural Economics, Indian Society of Agricultural Economics, vol. 16(3), pages 1-4.
    41. Bernhard, Richard H., 1980. "A Simplification and an Extension of the Bernhard-deFaro Sufficient Condition for a Unique Non-Negative Internal Rate of Return," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(1), pages 201-209, March.
    42. Chiara Pederzoli, 2007. "Default risk: Poisson mixture and the business cycle," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0002, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    43. Chiara Pederzoli, 2007. "Default risk: Poisson mixture and the business cycle," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 07052, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    44. Silvia Muzzioli, 2007. "The relation between implied and realised volatility: are call options more informative than put options? Evidence from the DAX index options market," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0004, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    45. Thomas Pfeiffer & Georg Schneider, 2007. "Residual Income-Based Compensation Plans for Controlling Investment Decisions Under Sequential Private Information," Management Science, INFORMS, vol. 53(3), pages 495-507, March.
    46. Thomas Pfeiffer, 2004. "Net Present Value‐Consistent Investment Criteria Based on Accruals: A Generalisation of the Residual Income‐Identity," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(7‐8), pages 905-926, September.
    47. P. H. Karmel, 1959. "The Marginal Efficiency Of Capital," The Economic Record, The Economic Society of Australia, vol. 35(72), pages 429-434, December.
    48. de Faro, Clovis, 1978. "A Sufficient Condition for a unique Nonnegative Internal Rate of Return: Further Comments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(3), pages 577-584, September.
    49. Richard D MacMinn, 2005. "The Fisher Model and Financial Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5887, August.
    50. Bernhard, Richard B., 1977. "Unrecovered Investment, Uniqueness of the Internal Rate, and the Question of Project Acceptability," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(1), pages 33-38, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carlo Alberto Magni, 2009. "Accounting and economic measures: an integrated theory of capital budgeting," Proyecciones Financieras y Valoración 5983, Master Consultores.
    2. Magni, Carlo Alberto, 2016. "Capital depreciation and the underdetermination of rate of return: A unifying perspective," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 54-79.
    3. Magni, Carlo Alberto, 2009. "Splitting up value: A critical review of residual income theories," European Journal of Operational Research, Elsevier, vol. 198(1), pages 1-22, October.
    4. Dean Altshuler & Carlo Alberto Magni, 2015. "Introducing Aggregate Return on Investment as a Solution to the Contradiction Between Some PME Metrics and IRR," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0056, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    5. Elisabetta Gualandri & Mario Noera, 2014. "Towards A Macroprudential Policy In The Eu: Main Issues," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0049, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    6. Elena Giarda & Gloria Moroni, 2018. "The Degree of Poverty Persistence and the Role of Regional Disparities in Italy in Comparison with France, Spain and the UK," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(1), pages 163-202, February.
    7. Elisabetta Gualandri & Mario Noera, 2014. "Monitoring Systemic Risk: A Survey Of The Available Macroprudential Toolkit," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0050, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    8. Elisabetta Gualandri & Mario Noera, 2014. "Towards A Macroprudential Policy In The Eu: Main Issues," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 14110, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    9. Massimo Baldini & Giovanni Gallo & Costanza Torricelli, 2017. "Past Income Scarcity and Current Perception of Financial Fragility," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 17121, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    10. Elisabetta Gualandri & Valeria Venturelli, 2013. "The financing of Italian firms and the credit crunch: findings and exit strategies," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 13101, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    11. Enrico Rubaltelli & Sergio Agnoli & Michela Rancan & Tiziana Pozzoli, 2015. "Emotional Intelligence and risk taking in investment decision-making," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 15107, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    12. Elena Giarda & Gloria Moroni, 2018. "The Degree of Poverty Persistence and the Role of Regional Disparities in Italy in Comparison with France, Spain and the UK," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(1), pages 163-202, February.
    13. C. Pederzoli & C. Torricelli, 2013. "Efficiency and unbiasedness of corn futures markets: new evidence across the financial crisis," Applied Financial Economics, Taylor & Francis Journals, vol. 23(24), pages 1853-1863, December.
    14. Carlo Alberto Magni, 2015. "Pseudo-naïve approaches to investment performance measurement," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0051, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    15. Stefano Cosma & Francesca Pancotto & Paola Vezzani, 2018. "Customer Complaining and Probability of Default in Consumer Credit," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 18031, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    16. Francesca Arnaboldi, Francesca Gioia, 2019. "Portfolio choice: Evidence from new-borns," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0078, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    17. Elisabetta Gualandri & Valeria Venturelli, 2013. "The financing of Italian firms and the credit crunch: findings and exit strategies," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0041, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    18. Chiara Pederzoli & Costanza Torricelli, 2010. "A parsimonious default prediction model for Italian SMEs," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0022, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    19. Stefano Cosma & Francesca Pancotto & Paola Vezzani, 2018. "Customer Complaining and Probability of Default in Consumer Credit," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0068, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    20. Stefano Cosma & Elisabetta Gualandri, 2013. "The sovereign debt crisis: the impact on the intermediation model of Italian banks," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0042, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".

    More about this item

    Keywords

    Capital budgeting; decision analysis; investment criteria; internal rate of return; investment stream; mean;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • M10 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - General
    • M21 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics - - - Business Economics
    • M41 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - Accounting
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • N01 - Economic History - - General - - - Development of the Discipline: Historiographical; Sources and Methods

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:col:000463:006653. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ignacio Velez (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.