This paper analyzes the potential effect of a European Central Bank Digital Currency (CBDC) on banks' profitability. We use a large sample of EU banks that span the period from 2007 to 2021 to assess the sensitivity of banks' profits to the deposits. Using quantile regression, we estimate the conditional profit distribution of a representative bank. We then introduce a shock on the amount of deposits that would be replaced by the CBDC. Our results show that, for a large take-up of CBDC, there might be substantial challenges for the profitability of banks, especially for small banks, that mostly rely on deposits as a source of funding.