In this work, we consider a multiple-input single-output system in which an access point (AP) performs a simultaneous wireless information and power transfer (SWIPT) to serve a user terminal (UT) that is not equipped with external power supply. In order to assess the efficacy of the SWIPT, we target a practically relevant scenario characterized by imperfect channel state information (CSI) at the transmitter, the presence of penalties associated to the CSI acquisition procedures, and non-zero power consumption for the operations performed by the UT, such as CSI estimation, uplink signaling and data decoding. We analyze three different cases for the CSI knowledge at the AP: no CSI, and imperfect CSI in case of time-division duplexing and frequency-division duplexing communications. Closed-form representations of the ergodic downlink rate and both the energy shortage and data outage probability are derived for the three cases. Additionally, analytic expressions for the ergodically optimal duration of power transfer and channel estimation/feedback phases are provided. Our numerical findings verify the correctness of our derivations, and also show the importance and benefits of CSI knowledge at the AP in SWIPT systems, albeit imperfect and acquired at the expense of the time available for the information transfer.