Albeit an important goal of caching is traffic reduction, a perhaps even more important aspect follows from the above achievement: the reduction of internet service provider (ISP) operational costs that comes as a consequence of the reduced load on transit and provider links. Surprisingly, to date this crucial aspect has not been properly taken into account in cache design. In this paper, we show that the classic caching efficiency indicator, i.e., the hit ratio, conflicts with cost. We therefore propose a mechanism whose goal is the reduction of cost and, in particular, we design a cost-aware (CoA) cache decision policy that, leveraging price heterogeneity among external links, tends to store with more probability the objects that the ISP has to retrieve through the most expensive links. We provide a model of our mechanism, based on Che's approximation, and, by means of a thorough simulation campaign, we contrast it with traditional cost-blind schemes, showing that CoA yields a significant cost saving, that is furthermore consistent over a wide range of scenarios. We show that CoA is easy to implement and robust, making the proposal of practical relevance.