In order to avoid high utility demand charges from cooling during the summer and to level a building's electrical demand profile, precooling of the building's massive structure can be applied to shift cooling-related thermal loads in response to utility pricing signals. Several previous simulation and experimental studies have shown that proper precooling can attain considerable reduction of operating cost in buildings. This paper systematically evaluates the merits of the passive building thermal capacitance to minimize energy cost for a design day using optimal control. The evaluation is conducted by means of a sensitivity analysis utilizing a dynamic building energy simulation program coupled to a popular technical computing environment. The optimal controller predicts the required extent of precooling (zone temperature set-point depression), depending on the utility rate structure, occupancy and on-peak period duration and onset, internal gains, building mass, occupancy period temperature set-point range, and weather as characterized by diurnal temperature and relative humidity swings. In addition to quantifying the building response, energy consumption, and utility cost, this paper extracts the dominant features of the optimal precooling strategies for each of the investigated cases so that guidelines for near-optimal building thermal mass savings may be developed in the future.