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Mathematical Analysis of Rates of Return Under Certainty


  • Daniel Teichroew

    (Case Institute of Technology, Cleveland, Ohio)

  • Alexander A. Robichek

    (Stanford University, Stanford, California)

  • Michael Montalbano

    (International Business Machines Corporation and Industrial Research Fellow (1963-1964), Graduate School of Business, Stanford University)


The purpose of this paper is to prove certain properties of the present and future values of a sequence of cash flows which have applications in the theory of capital budgeting. This is done in Theorems III, IV and V. As an introduction, certain previously available results about the present value function are stated and proved as Theorems I and II. A summary of the relevance of these results in capital budgeting is given in the Summary.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormnsc:v:11:y:1965:i:3:p:395-403

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    Cited by:

    1. 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.
    2. Roberto Ghiselli Ricci & Carlo Alberto Magni, 2014. "Axiomatization of residual income and generation of financial securities," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1257-1271, July.
    3. 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.
    4. 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.
    5. 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".
    6. 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.
    7. Magni, Carlo Alberto, 2015. "Aggregate Return On Investment for investments under uncertainty," International Journal of Production Economics, Elsevier, vol. 165(C), pages 29-37.
    8. Magni, Carlo Alberto, 2010. "Residual income and value creation: An investigation into the lost-capital paradigm," European Journal of Operational Research, Elsevier, vol. 201(2), pages 505-519, March.
    9. 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".
    10. Weber, Thomas A., 2014. "On the (non-)equivalence of IRR and NPV," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 25-39.
    11. Carlo Alberto Magni, 2010. "Average Internal Rate of Return and investment decisions: A new perspective," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0021, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    12. 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.
    13. 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.
    14. Edgar Achong V., 1988. "An approach to find the return rate on non-simple investment projects," Economía, Instituto de Investigaciones Económicas y Sociales (IIES). Facultad de Ciencias Económicas y Sociales. Universidad de Los Andes. Mérida, Venezuela, vol. 13(2), pages 7-33, January-D.
    15. Carlo Alberto Magni, 2006. "Zelig and the Art of Measuring Excess Profit," Frontiers in Finance and Economics, SKEMA Business School, vol. 3(1), pages 103-129, June.
    16. Gaponenko, A.L. (Гапоненко, А.) & Savelyeva, Marina (Савельева, Марина), 2016. "Modern Factors of Competitiveness of Socio-Economic Systems: Organizations, Regions and Cities
      [Современные Факторы Конкурентоспособности Социально-Экономических Систем: Организаций, Регионов И Гор
      ," Working Papers 453, Russian Presidential Academy of National Economy and Public Administration.
    17. Magni, Carlo Alberto, 2004. "Modelling excess profit," Economic Modelling, Elsevier, vol. 21(3), pages 595-617, May.
    18. repec:eee:ejores:v:268:y:2018:i:1:p:361-372 is not listed on IDEAS
    19. Alexander Alexeev & Mikhail Sokolov, 2011. "A Note on Indices of Return," EUSP Department of Economics Working Paper Series Ec-02/11, European University at St. Petersburg, Department of Economics, revised 21 Feb 2011.
    20. repec:nos:bedcdu:nc11 is not listed on IDEAS
    21. Magni, Carlo Alberto, 2005. "On decomposing net final values: EVA, SVA, and shadow project," MPRA Paper 12357, University Library of Munich, Germany.

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