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Decomposition of a Certain Cash Flow Stream: Differential Systemic Value and Net Final Value

Author

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  • Magni, Carlo Alberto

Abstract

This paper proposes a new way of decomposing net present values and net final values in periodic shares. Such a decomposition generates a new notion of residual income, radically different from the classical one available in the financial and accounting literature. While the standard residual income is formally computed as profit minus cost of capital times actual capital invested, the new paradigm introduces a fourth element: the capital invested in the so-called shadow project. Such a capital is the counterfactual capital that the investor would own if, at time 0, he invested his funds at the cost of capital, rather than in the project. Two important features are found: in primis, the new residual income is obtained as the sum of the standard residual incomes and the interest earned on past standard residual incomes; in secundis, the new paradigm is shown to be additive: the net final value of the project is computed as the sum of all periodic shares (residual incomes) with no capitalization process (abnormal earnings aggregation). A generalization is provided for a levered portfolio of projects, and a fourthfold decomposition is reached: (i) periodic decomposition, (ii) opportunity account decomposition, (iii) project decomposition, (iv) financing decomposition.

Suggested Citation

  • Magni, Carlo Alberto, 2000. "Decomposition of a Certain Cash Flow Stream: Differential Systemic Value and Net Final Value," MPRA Paper 7308, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:7308
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    File URL: https://mpra.ub.uni-muenchen.de/7898/1/MPRA_paper_7898.pdf
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    Citations

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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. Carlo Alberto Magni, 2007. "A Sum&Discount Method for Appraising Firms: An Illustrative Example," Department of Economics 572, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    4. 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.
    5. Magni, Carlo Alberto, 2001. "Valore Aggiunto Sistemico: un'alternativa all'EVA quale indice di sovraprofitto periodale," MPRA Paper 7525, University Library of Munich, Germany.
    6. 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.
    7. Magni, Carlo Alberto, 2000. "Systemic Value Added, Residual Income and Decomposition of a Cash Flow Stream," MPRA Paper 5900, University Library of Munich, Germany.
    8. Carlo Magni, 2005. "On Decomposing Net Final Values: Eva, Sva and Shadow Project," Theory and Decision, Springer, vol. 59(1), pages 51-95, August.

    More about this item

    Keywords

    net present value; net final value; decomposition; residual income; systemic value; finance; accounting; quantitative methods;

    JEL classification:

    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • M41 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Accounting - - - Accounting
    • C0 - Mathematical and Quantitative Methods - - General
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • M21 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics - - - Business Economics

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