Flight Instructor on training flight with student reported runway excursion during landing sequence.

Narrative

On the above date and time I was giving a high performance endorsement to an experienced Mooney pilot.The taxi; takeoff and enroute flight were uneventful except the pilot had a tendency to taxi left of centerline. I mentioned this to him several times and gave him corrections back to centerline. Enroute the VFR flight went directly to ZZZ with minor course changes for aircraft over ZZZ1. The pilot flying flew an ILS to minimums in VFR conditions. At minimums the aircraft was slightly left of centerline and the pilot initially corrected back. After flying the practice ILS into ZZZ the pilot flying initially was low over the displaced threshold. I reminded him that he can not land on the displaced threshold and needed to land on the numbers at the earliest. The pilot added power and made it to the runway end. The Pilot Flying was again drifting left of centerline and at approximately 20 ft. AGL. He proceeded to flare high and bounce the airplane. During the bounce the pilot applied full power but did not apply enough rudder to maintain runway centerline. I took control of the aircraft and brought it back onto the runway however my intervention was not early enough to keep the aircraft on the runway. The aircraft left the prepared surface. Several runway edge lights were struck as a result of the aircraft departing the runway. Post flight inspection discovered damage to the propeller and forward landing gear door. Airfield operations discovered three damaged runway edge lights. The problem arose with an inexperienced pilot in high performance aircraft not anticipating the yaw required to counteract a rapid increase in power and late intervention.