This paper explores the role of central bank capital in ensuring that central banks focus on price stability in monetary policy decisions. The paper goes beyond the existing literature on this topic by developing a simple, but comprehensive, model of the relationship between a central bank's balance sheet structure and its inflation performance. The first part of the paper looks at solvency, i.e. under which conditions the "economic" capital (i.e. the discounted long term P&L) of a central bank always remains positive, despite adverse shocks, assuming a stability oriented monetary policy. The second part shows that in practice, capital is important for central banks beyond the issue of positive economic capital, when taking realistic assumptions regarding central bank independence. Capital thus remains a key tool to ensure that central banks are unconstrained in their focus on price stability in monetary policy decisions.