Numerical solution of the sequential investment model: a note on Dixit and Pindyck's (1994) analysis

Abstract

This paper discusses the model and solution approach adopted by Majd and Pindyck (1987. Time to build, option value, and investment decisions. Journal of Financial Economics 18, March: 7–27) and Dixit and Pindyck (1994. Investment under uncertainty. Princeton, NJ: Princeton University Press), when considering the sequential investment decision. It is shown that specific results presented in these two sources are based on invalid solutions to the relevant partial differential equation. The problem stems from the possibility that economically feasible parameter values and apparently acceptable step sizes for the explicit finite difference approach used can combine to generate non-convergent, invalid solutions.

Keywords:

• real options
• sequential investment
• time to build
• stability and convergence
• explicit finite difference
• sensitivity analysis

Notes

The authors are grateful to an anonymous reviewer for suggesting that this distinction be made.

The Maple code is available from the authors on request.