In this paper, we study precoded MIMO based small cell networks. We derive the theoretical sum-rate capacity, when multi-antenna base stations transmit precoded information to its multiple single-antenna users in the presence of inter- cell interference from neighboring cells. Due to an interference limited scenario, increasing the number of antennas at the base stations does not yield necessarily a linear increase of the capacity. We assess exactly the effect of multi-cell interference on the capacity gain for a given interference level. We use recent tools from random matrix theory to obtain the ergodic sum-rate capacity, as the number of antennas at the base station, number of users grow large. Simulations confirm the theoretical claims and also indicate that in most scenarios the asymptotic derivations applied to a finite number of users give good approximations of the actual ergodic sum-rate capacity.