Electric vehicles (EVs) has tiny environmental impact and will constitute a major mean of urban transportation in the future. Shared EV is quickly becoming a new business model under the sharing economy initiatives, providing easy access for commuters who possess no private cars. In this paper, we consider a carsharing company that owns EVs and some parking lots. Passengers can hire an EV at one parking lot and drive it to another one and pay for the service at a certain price determined by the company. A dedicated EV mobility model is proposed to capture the spatial transportation of energy without tracking every single vehicle. Price elasticity is described by a linear demand-price function. The company schedules the aggregated charging of unoccupied EVs in each parking lot, aiming at maximizing the total profit. Parking lots possess relatively large capacity and have to participate in a distribution power market; energy consumption is paid at the locational marginal price. The decision-making problem of the company is formulated as a bilevel program. The lower level simulates the distribution market clearing, and the upper level represents the pricing and charging scheduling problem faced by the company. Starting from a global polyhedral approximation of the power flow model, we develop an equivalent mixed-integer program based on primal-dual optimality condition and integer algebra technique, together with a warm-start strategy which accelerates computation remarkably. Case studies demonstrate that the proposed business model can reshape the load profile by shaving the peaking and filling the valley without harming the profit of the company.