IDEAS home Printed from https://ideas.repec.org/a/taf/eurjfi/v21y2015i2p129-146.html
   My bibliography  Save this article

Time varying costs of capital and the expected present value of future cash flows

Author

Listed:
  • Ian Davidson
  • Xiaojing Song
  • Mark Tippett

Abstract

The use of an inter-temporally constant discount rate or cost of capital is a strong assumption in many ex ante models of finance and in applied procedures such as capital budgeting. We investigate how robust this assumption is by analysing the implications of allowing the cost of capital to vary stochastically over time. We use the Feynman-Kac functional to demonstrate how there will, in general, be systematic differences between present values computed on the assumption that the currently prevailing cost of capital will last indefinitely into the future and present values determined by discounting cash flows at the expected costs of capital that apply up until the point in time at which cash flows are to be received. Our analysis is based on three interpretations of the Feynman-Kac functional. The first assumes that the cost of capital evolves in terms of a state variable characterised by an Uhlenbeck and Ornstein ("On the Theory of the Brownian Motion." Physical Review 36(5): 823-841) process. The second and third interpretations of the Feynman-Kac functional are based on the continuous time branching process. The first of these assumes that the state variable tends to drift upwards over time, whilst the second assumes that there is no drift in the state variable. Our analysis shows that for all three stochastic processes there are significant differences between present values computed under the assumption that the currently prevailing cost of capital will last indefinitely into the future and present values determined by discounting cash flows at the expected costs of capital that apply up until the point in time at which cash flows are to be received. Comparisons are also made with the environmental economics literature where similar problems have been addressed by invoking a 'gamma discounting' methodology.

Suggested Citation

  • Ian Davidson & Xiaojing Song & Mark Tippett, 2015. "Time varying costs of capital and the expected present value of future cash flows," The European Journal of Finance, Taylor & Francis Journals, vol. 21(2), pages 129-146, January.
  • Handle: RePEc:taf:eurjfi:v:21:y:2015:i:2:p:129-146
    DOI: 10.1080/1351847X.2013.802248
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/1351847X.2013.802248
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/1351847X.2013.802248?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 search for a different version of it.

    Citations

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


    Cited by:

    1. J. Doyne Farmer & John Geanakoplos & Matteo G. Richiardi & Miquel Montero & Josep Perelló & Jaume Masoliver, 2024. "Discounting the Distant Future: What Do Historical Bond Prices Imply about the Long-Term Discount Rate?," Mathematics, MDPI, vol. 12(5), pages 1-25, February.

    More about this item

    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:taf:eurjfi:v:21:y:2015:i:2:p:129-146. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/REJF20 .

    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.