Vehicle scrappage subsidy programs have been widely applied by governments to replace old cars by newer, more fuel-efficient ones. While these programs have been implemented to motivate earlier replacement, they may not be as effective as expected. From a cost-benefit perspective, the consumers who would have replaced anyway, even without the program, need to be addressed when evaluating the net benefits of the program. This requires accounting for variations in consumers' willingness to replace. Considering consumer heterogeneity in net trade-in valuation, this study investigates a dynamic vehicle-replacement problem based on a life cycle optimization (LCO) approach. We theoretically demonstrate that although increasing the subsidy level motivates low-value consumers to replace earlier, it also induces consumers with a high net trade-in valuation to replace later to become eligible for the subsidy program. We have also developed a simulation program based on real data to show the application of our general model. According to the simulation results, ignoring consumer heterogeneity could result in an overestimation of the net benefits of the scrappage program.