Sequential Capacity Expansion Options

Abstract

This paper considers a firm's capacity expansion decisions under uncertainty. The firm has leeway in timing investments and in choosing how much capacity to install at each investment time. We model this problem as the sequential exercising of compound capacity expansion options with embedded optimal capacity choices. We employ the impulse control methodology and obtain a quasi-variational inequality that involves two state variables: an exogenous, stochastic price process and a controlled capacity process (without a diffusion term). We provide a general verification theorem and identify-and prove the optimality of-a two-dimensional (s, S)-type policy for a specific (admittedly restrictive) choice of the model parameters and of the running profit. The firm delays investment in capacity to ensure that the perpetuity value of newly installed capacity exceeds the total opportunity cost, including the fixed cost component, by a sufficient margin. Our general model for "the option to expand" transcends a single-option exercise and yields predictions of both the optimal investment timing and the optimal scale of production.