Researchers and design practitioners advocate building physical models of ideas at early stages of the design process. Still, the cognitive effects of physical models remain largely unknown. Some studies show that physical models possess the potential to facilitate the generation of high quality ideas. Conversely, other studies demonstrate that physical models can lead to design fixation. A prior controlled study by the authors failed to detect fixation due to early stage physical models. Based upon these conflicting results, this study hypothesizes that the fixation observed in prior studies can be explained by the Sunk Cost Effect. The Sunk Cost Effect pertains to an individual's reluctance to choose a different path of action once he/she invests a significant cost (money, time, or effort). According to this theory, as designers spend more time, money or effort in building physical models, they tend to generate ideas with lower novelty and variety. The prior observational studies use complicated design problems with higher costs compared to the controlled study, possibly explaining the difference in results. This study also hypothesizes that physical models supplement designers' erroneous mental models. The authors investigate these hypotheses through a controlled, between-subject experiment with five conditions: Sketching Only, Metal Building (low time cost), Plastic Building (high time cost), Metal Constrained Sketching, and Plastic Constrained Sketching. In each condition, subjects construct their ideas using materials specified by the name of the condition. The constrained sketching conditions assist in determining if participants tend to limit their ideas to only ones that can be built with given materials even though they are instructed to write down all ideas. The results confirm that the sunk cost of building plays a vital role in the observed fixation; thus, physical models do not inherently cause fixation. Moreover, results also show that physical models supplement designers' erroneous mental models, leading to higher quality ideas. To minimize sunk costs very early in the design process, models should be built with materials requiring minimal time, cost, and effort for the designers.