We propose a novel approach to enable the coexistence between Multi-Input-Multi-Output (MIMO) radar and downlink multi-user Multi-Input-Single-Output (MU-MISO) communication system. By exploiting the constructive multi-user interference (MUI), the proposed approach trades-off useful MUI power for reducing the transmit power, to obtain a power efficient transmission. This paper focuses on two optimization problems: a) Transmit power minimization at the base station (BS) while guaranteeing the receive signal-to-interference-plus-noise ratio (SINR) level of downlink users and the interference-to-noise ratio (INR) level to radar; b) Minimization of the interference from BS to radar for a given requirement of downlink SINR and transmit power budget. To reduce the computational overhead of the proposed scheme in practice, an algorithm based on gradient projection is designed to solve the power minimization problem. In addition, we investigate the trade-off between the performance of radar and communication, and analytically derive the key metrics for MIMO radar in the presence of the interference from the BS. Finally, a robust power minimization problem is formulated to ensure the effectiveness of the proposed method in the case of imperfect Channel State Information (CSI). Numerical results show that the proposed method achieves a significant power saving compared to conventional approaches, while obtaining a favorable performance-complexity trade-off.