The modeling of investment problems as being analogous to the exercise of perpetual American call options has become commonplace in economics and finance since . By exploiting the analogy with traded options, management's flexibility to decide on scale at the time of investment is generally unaccounted for; this assumption is at odds with business practice. In this paper, we study a situation in which an incumbent firm has leeway in choosing when and by how much to raise capital. We consider a general setting and prove the unicity and optimality of a threshold policy under certain conditions. The literature on real options analysis typically considers the timing of lump-sum investments wherein the change in scale is known beforehand. In another stream of the economic literature, stochastic models of capital accumulation deal with situations where, at each instant, the firm decides on its optimal level of capital goods with the aim to maximize its expected discounted revenues netted of capital expenditures; fixed adjustment costs are ignored in this perspective. We consider fixed and variable adjustment costs and allow for the optimal time of investment and choice of scale. We thus reconciliate these two distinct approaches in a unified theory of investment under uncertainty with time and scale flexibility.
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