This paper addresses the issue of discount pricing in word-of-mouth (WOM) marketing. First, we propose a novel discount strategy we refer to as the Influence-Based Discount (IBD) strategy, in which each buyer would enjoy a discount that is linearly proportional to his/her influence in the WOM network. For the purpose of evaluating the performance of an IBD strategy, we model the associated WOM spreading process as a higher-dimensional nonlinear differential dynamical system we refer to as the Dormant-Potential-Adopting (DPA) model. Next, we examine the dynamics of a DPA model through computer experiments. Thereby, we estimate the expected net profit of an IBD strategy and inspect how different factors influence this profit through numerical experiments. On this basis, we suggest some feasible promotional measures.