On June 25, 2001, at 0920 hours Pacific daylight time a Cessna 172M, N1409V, experienced a loss of engine power and made a forced landing at the Napa County Airport, Napa, California. The airplane was operated by Airline Transport Professionals Corp. of USA, located in Florida, under the provisions of 14 CFR Part 91, and sustained substantial damage. The certified flight instructor (CFI) and private pilot were not injured. Visual meteorological conditions prevailed for the local area instructional flight and a flight plan had not been filed. The flight departed the Sacramento Executive Airport, Sacramento, California, at 0815. The flight was scheduled to terminate at the Sacramento airport. The Safety Board investigator interviewed the CFI. The CFI stated that the purpose of the flight to was to conduct instrument training at Napa and other local area airports. The accident occurred on the first approach into Napa. The CFI reported that they were on the localizer approach for runway 36L. The student leveled the airplane at the minimum descent altitude (MDA). Prior to reaching the runway, she instructed the student to conduct the missed approach. They climbed straight ahead to 500 feet msl. As the student initiated a left-hand turn for the missed approach procedure, the engine started to lose power. They conducted the emergency procedures per the airplane flight manual for loss of engine power. The CFI contacted Napa tower and declared an emergency. The flight was cleared to land on any runway. She turned the airplane towards runway 6, and slipped the airplane to make it down to the runway. The airplane did not have enough time to descend and land on the runway, so she attempted to land in a grassy area past the departure end of the runway. She noted that the airplane was still too high to land in the grassy area, and they were approaching the airport perimeter fence. The CFI initiated a left turn to avoid the fence, and as she leveled the wings the wheels touched down. As the nose wheel contacted the ground it dug into the soft dirt and the airplane came to rest inverted. The engine was examined by a Federal Aviation Administration (FAA) inspector, with the assistance of an airframe and power plant mechanic at the Napa airport on June 25, 2001. The examination revealed that the exhaust push rod housing and exhaust push rod for the number 1 cylinder was bent. The FAA inspector noted that the rocker arm and shaft were in good condition. The valve was manually depressed to ascertain that it was not stuck. The valve functioned normally. The engine was manually rotated on July 2, 2001. Manual rotation of the crankshaft produced thumb compression of the cylinders as well as valve train continuity of the engine. There was no binding of the valve on the number 1 cylinder observed during the rotation of the crankshaft. There were no more mechanical abnormalities observed with the engine.