1. An electric power steering apparatus, comprising: an assist mechanism that applies assist torque from a motor to a vehicle steering mechanism; and a controller that controls driving of the motor based on an assist command value, wherein the controller includes: a first assist component calculating unit that calculates a first assist component based on a steering torque transmitted to the steering mechanism; a steered angle command value calculating unit that calculates, based on the steering torque, a steered angle command value, which is a target value of a steered angle of a steerable wheel; a second assist component calculating unit that executes steered angle feedback control so that the steered angle of the steerable wheel corresponds to the steered angle command value, thereby calculating a second assist component based on the steered angle of the steerable wheel and the steered angle command value; and an assist command value calculating unit that calculates the assist command value based on a value obtained by adding the first and second assist components, and the controller estimates a grip factor of the steerable wheel on a road surface on which the steerable wheel is traveling based on the steering torque, a first assist torque determined based on the first assist component, and a second assist torque determined based on the second assist component.