Opportunistic network coding (ONC) has shown high potential in enhancing the quality-of-experience (QoE) for the clients of cellular networks using their previously downloaded files. In this paper, we study the problem of offloading clients from the macrocell base station (MBS) with the help of femtocaches (FCs) and ONC. We formulate this MBS offloading problem as an optimization problem over an ONC graph, and prove that it is non-deterministic polynomial-time (NP)-hard. Thus, we propose an ONC-broadcast offloading scheme, which utilizes separate ONC graphs at the MBS and FCs in addition to uncoded broadcasting, to offload the clients from the MBS. We analyze the performance of the ONC-broadcast offloading scheme and show that it is asymptotically optimal using random graph theory. Since even this ONC-broadcast offloading scheme is still NP-hard to implement, we devise an efficient heuristic to simplify the implementation. We show that the proposed heuristic reduces the worst-case complexity of implementing the ONC-broadcast offloading scheme from an exponential to a quadratic function of the total number of vertices in the FC ONC graph. Simulation results show that, despite its low complexity, the proposed heuristic achieves similar MBS offloading performance to the ONC-broadcast offloading scheme.