This work introduces a new approach to solve the joint precoding and power allocation for sum rate maximization problem in the downlink multiuser MIMO by a combination of random matrix theory and optimization theory. The new approach results in a simplified problem that, though non-convex, obeys a simple separable structure. The sum rate maximization problem is decomposed into different single-variable optimization problems that can be solved in parallel. A water-filling-like solution is found, which can be applied under some mild conditions on the SNRs of the users. The proposed scheme provides large gains over heuristic solutions when the number of users in the cell is large, which suggests the applicability in massive MIMO systems.