We numerically investigate the effect of magnetic and electrical damages at the edge of a perpendicular magnetic random access memory (MRAM) cell on the spin-transfer-torque (STT) efficiency that is defined by the ratio of thermal stability factor to switching current. We find that the switching mode of an edge-damaged cell is different from that of an undamaged cell, which results in a sizable reduction in the switching current. Together with a marginal reduction of the thermal stability factor of an edge-damaged cell, this feature makes the STT efficiency large. Our results suggest that a precise edge control is viable for the optimization of STT-MRAM.