Most previous studies on real options are confined to the realm of continuous modelling while more practical discrete models are restricted by the methodology of solutions. This thesis applies the discount factor methodology to solve two scaling capacity choice problems: one is the scaling capacity expansions without switching options raised from Dxit and Pindyck (1994) and the other one is the case adding switching opportunities raised from Pindyck (1988). We respectively establish two discrete models for these two problems and examine their convergence to the continuous case by narrowing the discrete intervals. We verify with analytical inference and numerical results that the discrete models are soundly consistent with the continuous models, supporting the validity of the discount factor methodology.