A problem of optimally purchasing electricity at a real-valued spot price (that is, with

potentially negative cost) has been recently addressed in De Angelis, Ferrari and Moriarty

(2015) [SIAM J. Control Optim. 53(3)]. This problem can be considered one of irreversible

investment with a cost functional which is non convex with respect to the control variable.

In this paper we study the optimal entry into this investment plan. The optimal entry policy

can have an irregular boundary arising from this non convexity, with a kinked shape.