Numerous influential finance and accounting studies describe how to reverse engineer cost of equity capital (COEC) estimates. A key motivation of these studies is that the COEC is important for capital budgeting and investment. Indeed, we show that there is a tautological relation between the COEC, market-to-book, and future ROE. Given this relation, one would expect future firm accounting returns to be correlated with cost of equity capital estimates. We find that very few of the implied COEC estimates which are commonly employed in academic studies are positively associated with future return on equity (ROE); in fact some implied COEC estimates are significantly negatively correlated with future ROE. A subset of COEC estimates based on the residual income model are positively associated with future ROE, as is the earnings-to-price ratio; however, contrary to intuition and theoretical predictions, all the COEC estimates based on the abnormal earnings growth model of Ohlson and Juettner-Nauroth (2005) are negatively associated with future ROE.