Time-to-Build and Capacity Expansion

Abstract

We study a firm's optimal investment timing and capacity decisions in the presence of uncertain time-to-build. Because of the time-to-build, the firm can expand its capacity before or after the initial project is completed and the lags of the follow-up investment can be shorter than those of the initial project due to learning by doing. We derive the optimal investment strategies in each scenario and examine the impact of time-to-build on the investment dynamics. We show that both the initial and the follow-up investment can be made earlier in the presence of time-to-build than they would in the absence of the lags, especially in a volatile market. This is in contrast to the case of a single investment, whose timing is always delayed by the time-to-build. Furthermore, the capacity of the follow-up project can dominate that of the initial one in the presence of time-to-build, whereas the latter always dominates the former in the absence of the lags. The capacity choice of each project, however, is non-monotone with respect to the size of the lags. We can endogenize the degree of learning by doing based on the proportion of capacity in each stage of the investment. Endogenous learning by doing is found to be non-monotone with respect to the size of the initial lags because the learning incurs costs of more investment at the earlier stage.