Kulatilaka '88 as a Cvp Analysis in a Real Option Framework: A Review, Gauss Codes and Numerical Examples

Abstract

In this short paper, (Kulatilaka 1988) model of FMS management is reinterpreted as a real options dynamic programming (DP) version of traditional Cost Volume Profit (CVP) analysis. Computational aspects of the Bellman DP algorithm solution are investigated and some simple solutions are suggested for computing both the value function and operational mode boundaries through the whole life of the investment project. A GAUSS code has been written and it is reported and commented in the text for both pedagogical and practical uses. Numerical examples replicate results reported in chapter 4 example 1.H. and chapter 7 of (Dixit and Pindyck 1994). Moreover, a different version of (Kulatilaka 1988) numerical example is analyzed. Results include not only the value of the flexible plant, decomposed into its base value and the value of the flexibility options (namely abandonment option, production mode switching option, mothballing option and waiting to invest option), but also mode bounds (threshold curves). In conclusion, this paper shows how much powerful is Kulatilaka's General Real Option Pricing Model (GROPM) in reaching through simple numerical methods results that others, (e.g. Dixit and Pindyck 1994), get through very difficult symbolic stochastic algebra. For this reason it is very much likely that GROPM would become widely applied to real business problems and, as a consequence, taught in business school classes where stochastic calculus is not a prerequisite. For the same reason GROPM could be "easily" extended to higher degrees of sophistication (and applicability to real business problems) which are unmanageable with symbolic stochastic calculus.

Keywords: Real options, Switching option, Abandonment option, Mothballing option, Bellman Dynamic Programming, hysteresis, Ornstein Uhlenbeck, GAUSS codes

JEL Classification: G13, G31, M40, M46