This study provides a formal analysis of the customer targeting decision problem in settings where the cost for marketing action is stochastic and proposes a framework to efficiently estimate the decision variables for campaign profit optimization. Targeting a customer is profitable if the positive impact of the marketing treatment on the customer and the associated profit to the company is higher than the cost of the treatment. While there is a growing literature on developing causal or uplift models to identify the customers who are impacted most strongly by the marketing action, no research has investigated optimal targeting when the costs of the action are uncertain at the time of the targeting decision. Because marketing incentives are routinely conditioned on a positive response by the customer, e.g. a purchase or contract renewal, stochastic costs are ubiquitous in direct marketing and customer retention campaigns. This study makes two contributions to the literature, which are evaluated on a coupon targeting campaign in an e-commerce setting. First, the authors formally analyze the targeting decision problem under response-dependent costs. Profit-optimal targeting requires an estimate of the treatment effect on the customer and an estimate of the customer response probability under treatment. The empirical results demonstrate that the consideration of treatment cost substantially increases campaign profit when used for customer targeting in combination with the estimation of the average or customer- level treatment effect. Second, the authors propose a framework to jointly estimate the treatment effect and the response probability combining methods for causal inference with a hurdle mixture model. The proposed causal hurdle model achieves competitive campaign profit while streamlining model building. The code for the empirical analysis is available on Github.