Energy costs from Heating, Ventilation and Air Conditioning (HVAC) systems can be greater than 50% of the total operational expenditure of a commercial building. Demand side strategies such as pre-cooling and supply side strategies such as using renewable energy resources (e.g. solar panels) have the potential to reduce the operating energy costs. Several optimization frameworks have been proposed that use these strategies in an efficient manner. However, incorporating the dynamics of HVAC in an optimization framework often renders the framework computationally intractable - due to the inherent non-linearities - for large buildings. In this paper, we focus on the demand side strategy and develop a closed form expression for the optimal pre-cooling time assuming a 1R, 1C model of a building. Using simulations, we demonstrate that the optimal pre-cooling time obtained from the closed form expression matches the one from the optimization framework. Furthermore, we show that the expression - when used in conjunction with existing HVACoptimization frameworks to determine the optimal schedule of set-point temperatures - reduces the computation time of the optimization by two orders of magnitude, without loss of optimality.