Random beamforming (RBF) is a simple yet effective technique for multiuser multiple-input multiple-output systems with limited feedback. In this paper, we analyze the performance of the RBF in the presence of other cell interference (OCI), where a base station with M antennas supports Ms users (M s ≤ M) selected by scheduling among K single antenna users. Employing extreme value theory, we derive a closed-form approximation on the asymptotic ergodic sum rate by examining the limiting distribution of the largest signal-to-interference-plus-noise ratio (SINR) among K independent users. Also, we prove that even if the OCI exists, we have the same sum rate scaling law of Ms log2 log2 K as the system without OCI. Simulation results verify that our analysis provides an accurate estimation for the average sum rate performance even when K is not so large.