On July 10, 2015, about 0900 mountain standard time, a Mooney M20G, N9152V, experienced a partial loss of engine power while on short final to the Phoenix Deer Valley Airport (DVT), Phoenix, Arizona, and subsequently landed short of the runway. The private pilot undergoing instruction and the certified flight instructor (CFI) sustained no injuries; the airplane sustained substantial damage to the right wing. The airplane is registered to a private individual and operated by the private pilot under the provisions of 14 Code of Federal Regulations Part 91 as an instructional flight. Visual meteorological conditions prevailed and no flight plan was filed. The private pilot undergoing instruction reported that when they passed the approach end of the runway on the downwind leg of the traffic pattern, he reduced power to idle to conduct a practice 180o power off landing. The pilot maintained glide speed until about 40 feet above the ground when the pilot observed the airplane was slightly below the intended glide path. The pilot increased power to initiate a go around, however, the engine sputtered and did not increase RPM. The pilot executed a forced landing short of the runway surface; the airplane touched down hard and bounced. When it settled back onto the ground, the right main landing gear and nose landing gear collapsed and the airplane came to rest to the right of the runway surface. The CFI reported that when the private pilot decided to conduct a go around, he looked at the throttle quadrant to confirm that the throttle was full forward and the propeller and mixture levers were also positioned correctly. A postaccident engine run was conducted by a mechanic and inspectors from the Federal Aviation Administration (FAA). The spark plugs were removed and examined; they displayed signatures consistent with a rich running engine. The spark plugs were reinstalled and an undamaged propeller was installed. The engine started without hesitation; after idling temporarily, the RPM was increased and a magneto check was completed with no abnormalities noted. The power was decreased to idle for two minutes to simulate a 180o power off landing. The throttle was abruptly increased to full power; it hesitated for a split second and went to full RPM for a couple minutes. This sequence was conducted twice with no anomalies noted. The engine was shutdown uneventfully. The engine data monitor download showed that shortly before the engine lost power, the engine was at idle for about 1.5 minutes; during which, the cylinder exhaust gas temperatures were decreasing. At the end of the 1.5 minutes, there was an increase in RPM and subsequent small spike in the exhaust gas temperatures before they continued to decrease. In addition, the RPMs continued to zero, and the manifold pressure adjusted to barometric pressure. At the time of the accident, the reported temperature was 29o C and the dew point was 7o C. According to the FAA carburetor icing Special Airworthiness Information Bulletin, the condition was conducive to carburetor icing at glide and cruise power settings.