ACCORDING TO THE FLIGHT INSTRUCTOR, THE STUDENT WAS PRACTICING AUTO ROTATIONS TO A POWER RECOVERY. ON THE LAST PRACTICE AUTO ROTATION, THE ENGINE QUIT WHEN THE STUDENT ROLLED THE THROTTLE TO IDLE. THE INSTRUCTOR TOOK OVER CONTROL OF THE HELICOPTER AND EXECUTED A COMPLETE AUTO ROTATION TO TOUCH DOWN. DURING THE LANDING FLARE THE TAIL BOOM CONTACTED THE GROUND AND THE HELICOPTER LANDED HARD. THE HELICOPTER WAS EXAMINED AND NO DISCREPANCIES WERE FOUND.