In this paper, we analytically derive an exact expression for the SINR of the two-stage parallel interference cancellation (PIC) multiuser detector in a synchronous, nonorthogonal, binary, CDMA communication system. In order to obtain an intuitive understanding, we consider an approximation to the SINR expression that is well justified in scenarios where the error probability of the matched filter detector is reasonably low. Given a specific SINR requirement for each user in the system, we derive an expression for the minimum transmit power necessary to meet this requirement when the two-stage PIC detector is used. We also derive an expression for a measure of the theoretical system capacity of PIC, defined as the maximum number of users possible in a system with finite available transmit power. Analytical results comparing PIC to successive interference cancellation (SIC) detector and matched filter (MF) detector show that PIC requires less total transmit power and has greater theoretical system capacity than the SIC of MF detectors in the cases considered.