Electric Vehicles (EV) are drawing tremendous attention, as part of the transition toward environment-friendly transportation. While EV recharging represents a considerable extra load on the grid, they also offer new opportunities in terms of consumption flexibility. In this paper, we use the recharging process of EVs to provide regulation to the grid by varying the instantaneous recharging power. We provide an economic analysis of the incentives at play, including the EV owners point of view (longer recharging durations and impact on battery lifetime versus cheaper energy) and the aggregator point of view (revenues from recharging versus regulation gains). In particular, we analyze the range of regulation rewards such that offering a regulation-oriented recharging benefits both EV owners and the aggregator. Interestingly, we observe that under current market conditions in France, an aggregator could offer regulating EV owners to recharge for 50% cheaper, and still be better off than offering only constant-power recharging.