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Capital Project Analysis When Cash Flows Evolve as a Continuous Time Branching Process

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  • IAN DAVIDSON
  • YOSHIKATSU SHINOZAWA
  • MARK TIPPETT

Abstract

Optimal capital budgeting criteria now exist for a variety of applications when project cash flows (or present values) evolve in terms of the well‐known geometric Brownian motion. However, relatively little is known about the capital budgeting procedures that ought to be implemented when cash flows are generated by stochastic processes other than the geometric Brownian motion. Given this, our purpose here is to develop optimal investment criteria for capital projects with cash flows that evolve in terms of a continuous time branching process. Branching processes are compatible with an empirical phenomenon known as ‘volatility smile’. This occurs when there are systematic fluctuations in the implied volatility of a capital project's cash flows as the cash flow grows in magnitude. A number of studies have shown that this phenomenon characterizes the cash flow streams of the capital projects in which firms typically invest. We implement optimal capital budgeting procedures for both the continuous time branching process and the geometric Brownian motion using cost and revenue data for the Stuart oil shale project in central Queensland, Australia. This example shows that significant differences can arise between the optimal investment criteria for cash flows based on a branching process and those based on the geometric Brownian motion. This underscores the need for the geometric Brownian motion broadly to reflect the way a given capital project's cash flows actually evolve if serious errors in valuation and/or capital budgeting decisions are to be avoided.

Suggested Citation

  • Ian Davidson & Yoshikatsu Shinozawa & Mark Tippett, 2009. "Capital Project Analysis When Cash Flows Evolve as a Continuous Time Branching Process," Abacus, Accounting Foundation, University of Sydney, vol. 45(1), pages 44-65, March.
    • Handle: RePEc:bla:abacus:v:45:y:2009:i:1:p:44-65
    DOI: 10.1111/j.1467-6281.2009.00277.x
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    1. Metcalf, Gilbert E. & Hassett, Kevin A., 1995. "Investment under alternative return assumptions Comparing random walks and mean reversion," Journal of Economic Dynamics and Control, Elsevier, vol. 19(8), pages 1471-1488, November.
    2. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    3. Michael J. Alderson & Brian L. Betker, 1996. "Liquidation Costs and Accounting Data," Financial Management, Financial Management Association, vol. 25(2), Summer.
    4. David G. Laughton & Henry D. Jacoby, 1993. "Reversion, Timing Options, and Long-Term Decision-Making," Financial Management, Financial Management Association, vol. 22(3), Fall.
    5. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    6. David Ashton & Mark Tippett, 2006. "Mean Reversion and the Distribution of United Kingdom Stock Index Returns," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 33(9-10), pages 1586-1609.
    7. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    8. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    9. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    10. Paul Klumpes & Mark Tippett, 2004. "A Modified 'Square Root' Process for Determining the Value of the Option to (Dis)invest," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(9-10), pages 1449-1481.
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