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Application of the calculus of variations to financing alternatives

Author

Listed:
  • Grubbström, RW
  • Ashcroft, SH

Abstract

The problem considered is to choose from a finite set of inter-related investment and financing alternatives and also levels of consumption/work over time in order to maximise a utility functional. Each investment and financing option is characterised by its cash flow over time. An inter-temporal budget requirement operates continuously. Application of Calculus of Variations leads to consideration of the Euler-Lagrange equations combined with Kulm-Tucker conditions. It is shown that the solution (also when there are logical dependencies present) requires the maximisation of a Generalised Net Present Wealth measure in which the discount factor is formed from an integral of the Lagrangean multiplier function.

Suggested Citation

  • Grubbström, RW & Ashcroft, SH, 1991. "Application of the calculus of variations to financing alternatives," Omega, Elsevier, vol. 19(4), pages 305-316.
    • Handle: RePEc:eee:jomega:v:19:y:1991:i:4:p:305-316
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    Citations

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    Cited by:

    1. Borgonovo, E., 2008. "Differential importance and comparative statics: An application to inventory management," International Journal of Production Economics, Elsevier, vol. 111(1), pages 170-179, January.
    2. Marchioni, Andrea & Magni, Carlo Alberto, 2018. "Investment decisions and sensitivity analysis: NPV-consistency of rates of return," European Journal of Operational Research, Elsevier, vol. 268(1), pages 361-372.
    3. Borgonovo, E. & Peccati, L., 2007. "Global sensitivity analysis in inventory management," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 302-313, July.
    4. 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.
    5. Luciano, Elisa & Peccati, Lorenzo, 1999. "Capital structure and inventory management:: The temporary sale price problem," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 169-178, March.
    6. Borgonovo, E. & Peccati, L., 2006. "The importance of assumptions in investment evaluation," International Journal of Production Economics, Elsevier, vol. 101(2), pages 298-311, June.
    7. Molinder, Anders, 1995. "Application of calculus of variations to a continuous time aggregate production model," International Journal of Production Economics, Elsevier, vol. 41(1-3), pages 273-280, October.
    8. Cigola, Margherita & Peccati, Lorenzo, 2005. "On the comparison between the APV and the NPV computed via the WACC," European Journal of Operational Research, Elsevier, vol. 161(2), pages 377-385, March.
    9. Luciano, Elisa & Peccati, Lorenzo, 2001. "Cycles optimization: The equivalent annuity and the NPV approaches," International Journal of Production Economics, Elsevier, vol. 69(1), pages 65-83, January.

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