Time-to-build and capacity expansion

In this study, we investigate a firm’s optimal investment timing and capacity decisions in the presence of uncertain time-to-build. The firm raises revenue from the investment after an uncertain amount of time elapses, while the time-to-build of the follow-up investment is expectedly shorter than that of the initial investment due to learning by doing. We derive the optimal investment strategies and examine the impact of time-to-build on the investment dynamics. We show that both the initial and 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 dominates that of the initial project in the presence of time-to-build, whereas the latter dominates the former in the absence of lags. The capacity choice of each project, however, is nonmonotone with respect to the size of the lags. We also show that uncertainty delays investment even when the investment involves lags but the negative impact softens in the presence of time-to-build and learning effects.