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Transcoding is an important technology which adapts the same multimedia object to diverse mobile appliances; thus, users' requests for a specified version of a multimedia object could be served by a more detailed version cached according to transcoding. Therefore, it is of particularly theoretical and practical necessity to determine the proper versions to be cached at a node such that the specified objective is achieved. In this paper, we address the problem of multimedia object placement. The performance objective is to minimize the total access cost by considering both transmission cost and transcoding cost. We present an optimal dynamic programming-based solution for this problem. The performance of the proposed solutions is evaluated with a set of carefully designed simulation experiments for various performance metrics over a wide range of system parameters. The simulation results show that our solution consistently and significantly outperforms comparison solutions in terms of all the performance metrics considered.