Electric Vehicles (EVs), though appealing for an increasing number of users, suffer from known limitations of battery energy storage. We analyze a rentable plug-in Range Extender (RE) concept as a viable way to increase the EV range only when really needed, avoiding its encumbrance in normal urban usage. This concept leads to the formulation of an original energy management problem: in addition to usual operating constraints, the rental decision must be taken in the least costly way from the user's perspective. The original problem is solved offline by Dynamic Programming to provide the best achievable performance; a mixed integer convex reformulation is shown to yield the same results in much less time. The performance is compared by means of a thorough simulation study.