We study a market for equity financing with private information about start-up projects, thus producing adverse selection. The novelty lies in assuming that the alternative investment option for entrepreneurs earns them an income that correlates with the probability of succeeding as an entrepreneur. The model thereby captures conditions typically met by innovative entrepreneurs in a venture-capital market. We derive the equilibrium conditions that are found to produce under- and overinvestment simultaneously for different types of projects. We then discuss possible policy interventions using taxes and subsidies linked to observables.