The simplest broadcasting scheme in the mobile ad hoc networks (MANETs) uses flooding which may result in the broadcast storm problem. The MultiPoint Relays (MPR) is another broadcasting scheme for solving the broadcast storm problem. In MPR, the mobile hosts (MHs) use a greedy algorithm to find a connected dominating set (CDS) by the exchange of 2-hop neighbor information. In order to reduce the size of CDS, the greedy algorithm used by MPR usually selects the farthest nodes from the source called the border nodes as the forwarding nodes. Since the border nodes have a higher probability of moving out the transmission range, the routing paths in MPR from the source to some destinations may be unstable. In this paper, we propose a broadcasting scheme called Dynamic Power-aware and Stability-aware MultiPoint Relays (DPS-MPR) which avoids selecting the border nodes as the forwarding nodes. As a result, the transmission range of MHs can be reduced for saving energy and the negative impact of unstable forwarding nodes can also be reduced. In addition, we use a range buffer to further enhance the stability of the forwarding nodes. We evaluate the performance of the proposed DPS-MPR by using NS2 and compared it with the existing schemes. The experimental result shows that DPS-MPR saves 20%-25% of energy and increases the lifetime of forwarding nodes by several seconds.