A decision-maker needs to perform a task and can choose whether to do it in period 0, period 1 or period 2. If she does not do it in periods 0 or 1 she is forced to do it in period 2. The cost of performing the task depends on when she does it, where t 0, 1, 2 indexes the period. The costs are cost₀ = 2, cost₁ = 3 and cost₂ = 5. The benefit V of doing it is received in period 3 and does not depend on when she does it. Utility is linear in (discounted) costs and benefits.

Alice is time-consistent, discounting future costs and benefits exponentially with discount factor = 1. When does she do it?