We analyze the welfare cost of inflation in a model with a cash-in-advance constraint and an endogenous distribution of establishments' productivities. Inflation distorts aggregate productivity through firm entry dynamics. The model is calibrated to the U.S. economy and the long-run equilibrium properties are compared at low and high inflation. When the period over which the cash-in-advance constraint is binding is one quarter, an annual inflation rate of 10% leads to a decrease in average productivity of roughly 0.5% compared to the optimum. This decrease is not innocuous: it leads to a doubling of the welfare cost of inflation.