On November 9, 2023, about 0930 mountain daylight time, a Textron Aviation Inc. 172S, N1817E, was substantially damaged when it was involved in an accident near Erie, Colorado. The flight instructor and the student pilot were not injured. The airplane was operated as a Title 14 Code of Federal Regulations Part 91 instructional flight. After a thorough pre-flight inspection, the flight instructor started the engine and the engine began to shake; also, the alternator was not charging the battery. The flight instructor shut the engine down and inspected both the engine and alternator belt. Everything appeared to be normal, so he decided to restart the engine. After the second engine start, all indications were “in the green” and the engine no longer shook. All systems during the run-up appeared normal. The flight instructor and student pilot departed and, after completing several maneuvers, the instructor gave the student a simulated engine fire. After completing the appropriate checklists, they entered a simulated emergency descent starting about 7,000 ft msl. The flight instructor reported that they transitioned into a simulated emergency landing and the student pilot chose a field, taking the simulated emergency descent down to about 700 ft agl. As the student pilot applied full power to recover from the simulated emergency, the engine started to shake again. The flight instructor took the flight controls and observed that the engine rpm started to drop. Since the engine was still running, and they were near an airport, the flight instructor maneuvered the airplane toward the airport. He set up to land on the runway, but the airplane was too high and fast. Engine rpm reduced to about 1,900, and the flight instructor decided to land the airplane in a field to avoid houses near the airport. The flight instructor maneuvered the airplane to land in a field, and the touchdown was uneventful. However, the field where the airplane landed sloped downward and during the landing roll the airplane rolled nose-first into a culvert. During the impact with the culvert, the airplane sustained substantial damage to the right wing and engine firewall. During the engine examination, compression was observed at cylinder Nos. 1, 2, and 3. However, no compression was observed in the No. 4 cylinder. Further examination revealed that the No. 4 exhaust valve was stuck open and the No. 4 push rod was bent. A borescope examination revealed no additional anomalies. Both magnetos produced sparks at all leads when the engine was rotated by hand at the propeller flange. The spark plugs appeared normal as compared to the Champion Aviation Check-a-Plug Chart AV-27. All the fuel injectors were found clear. A review of the maintenance records revealed that Lycoming Mandatory Service Bulletin 388C, Procedure to Determine Exhaust Valve and Guide Condition, had not been complied with, as suggested by the engine manufacturer. The SB stated that an inspection should be performed at every 1,000 hours of operation if Hi-Chrome exhaust valve guides are installed. The inspection is intended to identify excessive carbon build up between the valve stem and the valve guide to prevent sticking valves or valve failure. The Hi-Chrome exhaust valve guides were installed on the accident airplane, as identified by the letter "C" stamped inside a circle on the engine cylinders.