Bank managers often claim that equity is expensive relative to debt, which contradicts the Modigliani-Miller irrelevance theorem. This paper combines dividend signalling theories and the Diamond-Dybvig bank run model. An opaque bank must signal its solvency by paying high and stable dividends in order to keep depositors tranquil. This signalling may require costly liquidations if the return on assets has been poor, but not paying the dividend might cause panic and trigger a run on the bank. The more equity has been issued, the more liquidations are needed during bad times to pay the expected dividend to each share.