The cutoff rate of multiphase pulse position modulation (MPPM) is evaluated in a noiseless photon counting channel. The cutoff rate per slot and the cutoff rate per photon are shown for MPPM. It is found that MPPM performs better than PPM in the practical range of average number of photons per pulse. Moreover, it is shown that, in the case with binary digits, MPPM can be seen as the parallel combination of completely correlated binary erasure channels (BECs). From this perspective, both the capacity and the cutoff rate are investigated. It is found that, when a large number of bits are transmitted in one frame, coding/decoding on each BEC independently has advantages in system complexity rather than coding/decoding over BECs jointly to achieve a given bit error probability.