In the field of inventory management, a profitability evaluation for ordered products is crucial to retailer revenue. Formulating such evaluations requires determining an appropriate order quantity, while ensuring that the product has high profitability potential. The achievable capacity index (ACI) provides a simple breakdown of profitability suitable for newsboy-type products with probabilistic distributed demand under the optimal order quantity. In this study, we investigated the lower confidence bound of ACI (LCBA) to obtain a conservative evaluation of profitability. Obtaining an explicit formula for the LCBA is difficult; therefore, we adopted parametric bootstrap methods to approximate the value for the LCBA. We also created a computational algorithm using R software to simulate the performances of various parametric bootstrap methods. Coverage rates and the corresponding ratios for various sample sizes and expected ACI values were tabulated to facilitate the selection of a suitable method and decide a required sample size with a conservative estimate. An illustrative example was presented to demonstrate the applicability of the proposed method and provide managerial insights.