We analyze the influence of monetary policy on firms' extensive margin and productivity. Our empirical evidence for the U.S. based on a macro-financial SVAR suggests that expansionary monetary policy shocks stimulate corporate profits, reduce firm exit and increase firm entry. In the medium run, exit overshoots the baseline. We rationalize these findings in a general equilibrium model featuring endogenous entry and exit. In the model, expansionary monetary policy shocks increase firm profits by stimulating aggregate demand and thereby allow less productive firms to remain in the market. As the monetary stimulus fades, these lessproductive firms become unprofitable such that exit overshoots. This exit channel of monetary policy implies a flatter aggregate supply curve and therefore amplifies output responses, but dampens inflationary effects.