On July 2, 2014, about 0842 central daylight time, a Piper PA-28-140, N9898W, sustained substantial damage during a forced landing after a loss of engine power during takeoff at the Granbury Regional Airport (GDJ), Granbury, Texas. The flight instructor and passenger were not injured. The airplane was registered to Thunderbolt Aviation LLC and operated by Iron Compass Aviation under the provisions of the 14 Code of Federal Regulations Part 91 as an instructional flight. Visual meteorological conditions prevailed at the time of the accident, and a visual flight rules flight plan was filed. The airplane was departing GDJ and was en route to the Waco Regional Airport (ACT), Waco, Texas. The flight instructor reported that the airplane was about 500 feet above ground level when the engine started to run rough along with a loss of engine power. The engine rpm decreased to about 1,100 rpm as the flight instructor attempted to complete a 180-degree turn back to the airport. However, he was unable to land on the airport, so he completed a forced landing to a field short of the runway. The airplane's right wing hit a tree during the landing roll, which resulted in substantial damage to the wing. The on-site examination of the airplane by Federal Aviation Administration inspectors revealed that there appeared to be no damage to the engine and no apparent reason for the loss of engine power. The airplane wreckage was transported to an aircraft storage facility for further examination and an engine run. An engine run was conducted using an external fuel supply. After priming the fuel system with the electric fuel pump, the engine was started. The engine sounded like it was running rough, and some black smoke could be seen from the exhaust. After a brief warm up, the engine would not operate more than about 1,600 rpm at full throttle. The engine run was stopped and a compression check was performed. The No. 3 cylinder did not have any compression. The examination of the No. 3 cylinder revealed that the exhaust valve was broken in several pieces and some fragments remained in the cylinder. The broken exhaust valve, spring, exhaust valve keepers, and rotator cap all exhibited carbon build-up. The piston and cylinder head exhibited gouging and scraping consistent with secondary damage from the fragments. The examination of the No. 3 cylinder exhaust valve rotator cap revealed that it had a wear pattern on the top of the cap that was consistent with rocker arm wear, and no rotational signatures along the edge of the cap where there was heavy carbon build-up. The engine was a 150-horsepower Lycoming O-320-E2A. The last annual maintenance inspection was conducted on June 2, 2014, with at total aircraft time of 3,464 hours. At the time of the accident, the engine had about 2,040 hours since the last overhaul. The airplane had flown about 46 hours since the annual/100-hour maintenance inspection. The recommended time between overhauls (TBO) is 2,000 hours, but it is not a mandatory requirement under Part 91 regulations.