The achievable capacity index (ACI) can measure the profitability of a newsboy-type product with probabilistic distributed demand. This criterion has been employed to deal with the problem of profitability evaluation by implementing statistical hypothesis testing. However, due to sampling errors, the point estimate of ACI probably overestimates the profitability. To this end, we derive a lower confidence bound of ACI (LCBA) to give a conservative evaluation of profitability. Since the complex sampling distribution of ACI makes it difficult to obtain an explicit closed-form expression of LCBA, we characterise the relationship between LCBA and estimator of ACI under given confidence level and sample size. A computational algorithm is proposed to obtain LCBA. Extensive numerical results of LCBA for various sample sizes, confidence levels and estimates are tabulated. Finally, we illustrate the practicality and applicability of the proposed method in an application example. Some managerial insights are also discussed.