Cognitive radio networks (CRNs) promise solutions to increase the spectrum utilization in wireless systems. In underlay cognitive radio spectrum sharing, the non-licensed users referred to as secondary users (SUs) are allowed to transmit simultaneously over the same frequency of licensed users known as primary users (PUs) as long as the interference to the primary receiver (PU-Rx) caused by the secondary transmitter (SU-Tx) remains below a predefined threshold. In this work, we investigate a downlink model for CRN. In particular, we assume that the SU-Tx sends common packets to secondary receivers (SU-Rx) under the outage constraint of a single PU and the peak transmit power constraint of the SU-Tx. All channels undergo Rayleigh fading. Given these settings, an adaptive transmit power policy for the SU-Tx is obtained. Moreover, we derive the cumulative distribution function (CDF) for minimum packet transmission time to analyze the timeout probability for SU-Rx having the best channel condition. Numerical results are provided to investigate the impact of PU transmit power and channel mean power gain on secondary network performance. The secondary system performance does not only depend on the outage constraint imposed by the PU and the SU peak transmit power but also on the interference from PU-Tx to SU-Rx. By increasing the number of SU-Rx, the timeout probability decreases to a minimum value.