In standard models, expected inflation on its own does not affect the real investment decisions of firms, unless the real cost of capital or investment opportunities also change. We highlight a new mechanism, which implies that this inflation neutrality breaks down when firms’ discount rates (which determine the nominal marginal product of capital) are sticky with respect to expected inflation. Sticky discount rates generate theoretical predictions that are consistent with stylized empirical facts but distinct from the New Keynesian textbook and other standard models: increases in expected inflation directly raise real investment; demand shocks generate investment consumption comovement; and the sensitivity of investment to real interest rates is low. Sticky discount rates imply monetary non-neutrality, even when all other prices are flexible. In the New Keynesian optimal monetary policy problem, the central bank steers long-run inflation expectations, even in response to temporary shocks.