Interactions between real capacity expansion and shutdown options : an application to renewable energies

A renewable energy asset manager can expand the power generation capacity of a particular site by an endogenous amount but may also want to shut down the location to save on fixed operating costs if the market prospects deteriorate. The site manager does not exercise these real options in a set sequence: the decision to exit is driven by the value of a capacity expansion option, while the decision to expand depends on the value of an exit option. From our analysis, we obtain three main economic insights. First, the presence of fixed costs renders the NPV threshold nonmonotonic in the firm's existing capacity. Second, the manager further delays shutting down production to avoid killing the expansion option. Finally, it is optimal to delay the timing \emph{and} the scale of the investment in capacity compared to the case without an exit option. Mathematically, we solve a nonstandard optimal stopping problem as the sequence of stopping times is at the discretion of the decision-maker and the objective of the capacity choice problem is not concave, which leads to a gain function that is not differentiable. We find a continuously differentiable solution to this optimal stopping problem and specify the corresponding continuation and stopping sets analytically