This paper presents a cost-efficient video multicast method for live video streaming to heterogeneous mobile terminals over a content delivery network (CDN), where CDN consists of a video server, several proxies with wireless access points, and overlay links among the server and proxies. In this method, the original video sent from the server is converted into multiple versions with various qualities by letting proxies execute transcoding services based on the users' requirements, and delivered to mobile terminals along video delivery paths. To suppress the required computation and transfer costs in CDN, we propose an algorithm to calculate cost-efficient video delivery paths which minimizes the sum of the computation cost for proxies and the transfer cost on overlay links. Our basic idea for deriving cost-efficient delivery paths is to place transcoding service on different proxies in load-balancing manner, and to construct a minimal Steiner tree from all transcoding points of requested qualities. The overall goal of the placement is the balance between computation and transfer cost. Through simulations, we show that our algorithm can calculate more costefficient video delivery paths and achieve lower request rejections than other algorithms.