The minimum energy required to transmit a bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that under a simplified layered model of wireless networks, the minimum-energy multicast problem in mobile ad hoc networks is solvable as a linear program, assuming network coding. Compared with conventional routing solutions, network coding not only promises a potentially lower energy-per-bit, but also enables finding the optimal solution in polynomial time, in sharp contrast with the NP-hardness of constructing the minimum-energy multicast tree as the optimal routing solution.