In the classical literature of innovation-based endogenous growth, the main engine of long- run economic growth is firm entry. Nevertheless, when projects are heterogeneous, and good ideas are scarce, a mass-composition trade-off is introduced into this link: larger cohorts have a lower average quality. As one of the roles of the financial system is to screen the quality of projects, the ability of financial intermediaries to detect promising projects shapes the strength of this trade-off. We build a general equilibrium endogenous growth model with project heterogeneity, and financial screening to study this relationship. We use two quantitative experiments to illustrate the relevance of our analytic results. First, we show that accounting for heterogeneity and selection allows the model to conciliate two well documented and apparently contradictory effects of corporate taxation. Corporate taxation has a strong detrimental effect on firm entry while affecting the long-run growth only mildly. A second illustration studies the effects of financial development on growth. This experiment shows that size based measures of financial development (e.g. domestic credit over GDP) are not good proxies for the ability of the financial system to select the most promising projects. Finally, we propose a novel firm level measure to assess the accuracy of financial selection across countries.