While practicing emergency procedures on a recurrent instructional flight, the pilot receiving instruction and the flight instructor completed several takeoffs and circuits around the airport traffic pattern where the pilot demonstrated various emergency procedures. During a subsequent takeoff, the flight instructor simulated a loss of engine power at an altitude of about 50 feet above the ground. As the airplane began to slow, the pilot receiving instruction pulled back on the control yoke to flare. Around this time, the flight instructor attempted to take control of the airplane after stating, “I have the aircraft,” and then tried to decrease the airplane’s pitch attitude, but the pilot receiving instruction was still trying to pull back on the controls, which ultimately resulted in hard landing and subsequent bounce. After the airplane bounced back into the air, the pilot receiving instruction added partial power to ease the second bounce while the flight instructor assumed the control of the airplane and added full power. The airplane then departed the right side of the runway while the flight instructor attempted to avoid an aerodynamic stall. The airplane touched down in the grass on the right side of the runway and bounced again while still at full power, striking a taxiway sign, and resulting in substantial damage to the right side of the empennage, the bottom of the right horizontal stabilizer, and separating the nose wheel from the nose landing gear. The airplane remained in ground effect at low speed while both the flight instructor and the pilot provided control inputs. The pilot then reassumed control of the airplane and maneuvered the airplane back onto the runway where it came to rest. The pilot and the flight instructor both reported that there were no preaccident mechanical failures or malfunctions of the airplane that would have precluded normal operation.