This paper examines whether a central bank digital currency (CBDC) reinforces inefficiencies in transactions with cash. In this case, the gap between the traded quantity and the welfare-maximizing one, which arises due to discounting or a suboptimal amount of money, increases further. To get some answers, the monetary search model of Trejos and Wright (1995) is extended by a CBDC. We show that an interest-bearing CBDC reinforces inefficiencies in transactions with cash since opportunity costs for cash holders and money supply increase. Nevertheless, a CBDC is able to increase welfare as long as the share of CBDC holders is limited.