On September 5, 2012, about 1555 central daylight time, a Cessna model 175B airplane, N8260T, was substantially damaged during a forced landing at Hamilton Municipal Airport (MNZ), Hamilton, Texas. The student pilot, who was the sole occupant, was not injured. The airplane was registered to and operated by the pilot, under the provisions of 14 Code of Federal Regulations Part 91, without a flight plan. Day visual meteorological conditions prevailed for the local flight that was originating at the time of the accident.The student pilot reported that the accident occurred on the first flight since the airplane had been refueled (topped-off) a couple days earlier. He did not observe any water or particulate contamination of the fuel samples obtained from the gascolator bowl or both wing tanks during his preflight inspection. He stated that he always operated the airplane with the fuel tank selector valve positioned to draw fuel from both fuel tanks. Before takeoff, he verified that no anomalies existed with the engine operation during two separate run-up checks and while he applied power for takeoff. He stated that liftoff was achieved at about 65 knots after the airplane had accelerated normally on the takeoff roll. The initial climb after liftoff was uneventful until 400 feet above ground level when he reportedly sensed that the airplane was not climbing normally, at which time he identified that the engine was not producing takeoff power and was unresponsive to his throttle movements. He verified that the mixture lever was in the full rich position before he focused on completing a forced landing. He reported that the airplane impacted a small tree during touchdown and subsequently descended a small hill before coming to a stop. The fuselage, engine firewall, and both wings were substantially damaged during the forced landing. The engine, a Continental model GO-300-D, serial number 16126-0-D, was examined by investigators with the National Transportation Safety Board and the engine manufacturer. The rotation of the engine crankshaft produced cylinder compression and suction to all cylinders except the No. 3 cylinder. Valve train continuity was confirmed to each cylinder except the No. 3 exhaust valve. A lighted boroscope inspection of the cylinders revealed normal combustion deposits on the cylinder domes and piston heads. Further examination of the No. 3 cylinder revealed that the exhaust valve was stuck in the full open position. There was no visible debris noted under the valve seat that would have kept the valve from closing. No additional anomalies were revealed during the engine examination that would have prevented normal operation. The recording tachometer indicated 809.02 hours after the accident. According to maintenance logbook information, the engine had accumulated 26.44 hours since the last annual inspection that was completed on October 5, 2011, and 698.22 hours since its last major overhaul.