IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v53y2013i3p747-756.html
   My bibliography  Save this article

Generalized Makeham’s formula and economic profitability

Author

Listed:
  • Magni, Carlo Alberto

Abstract

This paper generalizes Makeham’s formula, allowing for varying interest rates and for a non-flat structure of valuation rates. An average interest rate (AIR) is introduced, as well as an average valuation rate (AVR), both of which exist and are unique for any asset. They can be computed either as principal-weighted arithmetic means or as interest-weighted harmonic means of period rates. Economic profitability of an asset or a portfolio of assets is captured by the spread between AIR and AVR, which has the same sign as the Net Present Value. This makes (i) AIR a more reliable tool for valuation and decision than the venerable Internal Rate of Return, and (ii) AVR a natural generalization of the cost-of-capital notion.

Suggested Citation

  • Magni, Carlo Alberto, 2013. "Generalized Makeham’s formula and economic profitability," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 747-756.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:747-756
    DOI: 10.1016/j.insmatheco.2013.09.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668713001479
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2013.09.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dirk Brounen & Abe de Jong & Kees Koedijk, 2004. "Corporate Finance in Europe: Confronting Theory with Practice," Financial Management, Financial Management Association, vol. 33(4), Winter.
    2. Sandahl, Gert & Sjogren, Stefan, 2003. "Capital budgeting methods among Sweden's largest groups of companies. The state of the art and a comparison with earlier studies," International Journal of Production Economics, Elsevier, vol. 84(1), pages 51-69, April.
    3. Carlo Alberto Magni, 2010. "Average internal rate of return and investment decisions: A new perspective," PROYECCIONES FINANCIERAS Y VALORACION 006653, MASTER CONSULTORES.
    4. Kenneth B. Gray, Jr. & Robert B. K. Dewar, 1971. "Axiomatic Characterization of the Time-Weighted Rate of Return," Management Science, INFORMS, vol. 18(2), pages 32-35, October.
    5. Graham, John R. & Harvey, Campbell R., 2001. "The theory and practice of corporate finance: evidence from the field," Journal of Financial Economics, Elsevier, vol. 60(2-3), pages 187-243, May.
    6. Lindblom, Ted & Sjögren, Stefan, 2009. "Increasing goal congruence in project evaluation by introducing a strict market depreciation schedule," International Journal of Production Economics, Elsevier, vol. 121(2), pages 519-532, October.
    7. Dybvig, Philip H & Ingersoll, Jonathan E, Jr, 1982. "Mean-Variance Theory in Complete Markets," The Journal of Business, University of Chicago Press, vol. 55(2), pages 233-251, April.
    8. Austin J. Jaffe, 1977. "Is There A “New” Internal Rate of Return Literature?," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 5(4), pages 482-502, December.
    9. Magni, Carlo Alberto, 2009. "Correct or incorrect application of CAPM? Correct or incorrect decisions with CAPM?," European Journal of Operational Research, Elsevier, vol. 192(2), pages 549-560, January.
    10. 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.
    11. Brounen, D. & de Jong, A. & Koedijk, C.G., 2004. "Corporate Finance In Europe Confronting Theory With Practice," ERIM Report Series Research in Management ERS-2004-002-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    12. Ramlau-Hansen, Henrik, 1988. "Yields on lottery bonds," Insurance: Mathematics and Economics, Elsevier, vol. 7(2), pages 95-101, April.
    13. Carlo Alberto Magni, 2010. "Average internal rate of return and investment decisions: A new perspective," Proyecciones Financieras y Valoración 6653, Master Consultores.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Magni, Carlo Alberto, 2014. "Arithmetic returns for investment performance measurement," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 291-300.
    3. Magni, Carlo Alberto & Marchioni, Andrea & Baschieri, Davide, 2023. "The Attribution Matrix and the joint use of Finite Change Sensitivity Index and Residual Income for value-based performance measurement," European Journal of Operational Research, Elsevier, vol. 306(2), pages 872-892.
    4. Carlo Alberto Magni & Andrea Marchioni, 2022. "Performance attribution, time-weighted rate of return, and clean finite change sensitivity index," Journal of Asset Management, Palgrave Macmillan, vol. 23(1), pages 62-72, February.

    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. 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.
    2. Magni, Carlo Alberto, 2015. "Aggregate Return On Investment for investments under uncertainty," International Journal of Production Economics, Elsevier, vol. 165(C), pages 29-37.
    3. Carlo Alberto Magni & Ken V. Peasnell, 2015. "The Term Structure of Capital Values:An accounting-based framework for measuring economic profitability," Department of Economics 0060, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    4. Carlo Alberto Magni, 2007. "Project valuation and investment decisions: CAPM versus arbitrage," Applied Financial Economics Letters, Taylor & Francis Journals, vol. 3(2), pages 137-140.
    5. Pasqual, Joan & Padilla, Emilio & Jadotte, Evans, 2013. "Technical note: Equivalence of different profitability criteria with the net present value," International Journal of Production Economics, Elsevier, vol. 142(1), pages 205-210.
    6. Weber, Thomas A., 2014. "On the (non-)equivalence of IRR and NPV," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 25-39.
    7. Magni, Carlo Alberto, 2015. "Investment, financing and the role of ROA and WACC in value creation," European Journal of Operational Research, Elsevier, vol. 244(3), pages 855-866.
    8. Cuthbert, James R. & Magni, Carlo Alberto, 2016. "Measuring the inadequacy of IRR in PFI schemes using profitability index and AIRR," International Journal of Production Economics, Elsevier, vol. 179(C), pages 130-140.
    9. Magni, Carlo Alberto & Marchioni, Andrea, 2020. "Average rates of return, working capital, and NPV-consistency in project appraisal: A sensitivity analysis approach," International Journal of Production Economics, Elsevier, vol. 229(C).
    10. Siziba, Simiso & Hall, John Henry, 2021. "The evolution of the application of capital budgeting techniques in enterprises," Global Finance Journal, Elsevier, vol. 47(C).
    11. Peter Markovič & Michal Šinský, 2009. "Trends in application of capital budgeting methods for investment projects evaluation," Ekonomika a Management, Prague University of Economics and Business, vol. 2009(1).
    12. Tor Brunzell & Eva Liljeblom & Mika Vaihekoski, 2013. "Determinants of capital budgeting methods and hurdle rates in Nordic firms," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 53(1), pages 85-110, March.
    13. Horn, Anders & Kjærland, Frode & Molnár, Peter & Steen, Beate Wollen, 2015. "The use of real option theory in Scandinavia's largest companies," International Review of Financial Analysis, Elsevier, vol. 41(C), pages 74-81.
    14. Carlo Alberto Magni, 2015. "Investment, financing and the role of ROA and WACC in value creation," Department of Economics 0050, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    15. Guedes, José & Santos, Pedro, 2016. "Valuing an offshore oil exploration and production project through real options analysis," Energy Economics, Elsevier, vol. 60(C), pages 377-386.
    16. Koedijk, Kees & Mahieu, Ronald & van Toor, Joris & Horst, Jenke, 2017. "The World We Live In: Local or Global?," CEPR Discussion Papers 11831, C.E.P.R. Discussion Papers.
    17. Osborne, Michael J., 2010. "A resolution to the NPV-IRR debate?," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(2), pages 234-239, May.
    18. Chao, Ching-Hsiang & Huang, Chih-Jen, 2022. "Firm performance following actual share repurchases: Effects of investment crowding out and financial flexibility," Pacific-Basin Finance Journal, Elsevier, vol. 73(C).
    19. Hoang, Daniel & Gatzer, Sebastian & Ruckes, Martin E., 2018. "The economics of capital allocation in firms: Evidence from internal capital markets," Working Paper Series in Economics 115, Karlsruhe Institute of Technology (KIT), Department of Economics and Management.
    20. Anastassiadis, Friederike & Liebe, Ulf & Musshoff, Oliver, 2012. "Finanzielle Flexibilität In Landwirtschaftlichen Investitionsentscheidungen: Ein Discrete Choice Experiment," 52nd Annual Conference, Stuttgart, Germany, September 26-28, 2012 137142, German Association of Agricultural Economists (GEWISOLA).

    More about this item

    Keywords

    Makeham’s formula; Net present value; Average interest rate;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

    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:eee:insuma:v:53:y:2013:i:3:p:747-756. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.