ABSTRACT Corporate credit lines are drawn more heavily when funding markets are stressed. This elevates expected bank funding costs. We show that credit supply is dampened by the associated debt‐overhang cost to bank shareholders. Until 2022, this impact was reduced by linking the interest paid on lines to a credit‐sensitive reference rate like the London interbank offered rate (LIBOR). We show that transition to risk‐free reference rates may exacerbate this friction. The adverse impact on credit supply is offset if drawdowns are expected to be deposited at the same bank, which happened at some of the largest banks during the global financial crisis and COVID recession.