Benoit Chevalier-Roignant

Sequential Capacity Expansion Options

This article considers a firm's capacity expansion decisions under uncertainty. The firm has leeway in timing investments as well as in choosing how much capacity to install at each investment time. We model this as the sequential exercises of compound capacity expansion options with embedded optimal capacity choices. We follow the methodology of impulse control and obtain a quasi-variational inequality (QVI) involving two state variables, an (uncontrolled) price process driven by a Brownian motion and a controlled capacity process (without a diffusion term). We provide a general verification theorem, construct and prove the optimality of a two-dimensional (s,S) policy for a specific case. The firm delays capacity investment to ensure that the perpetuity value of the installed capacity lump exceeds the total opportunity cost, including the fixed cost component, by a sufficient margin. Real options analysis provides no prediction on the level of investment, while models of capital accumulation do not explain ``investment bursts" (by lump sums).

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