We propose a stylized monopolistic competition model of international trade where firms differ with respect to the expected economic lifetime of their innovations. Upon entry, they receive a commonly observed signal which is updated over time. Jointly with partial irreversibility of investment, this generates heterogeneity in effective discount rates and, thus, in the cost of finance. In line with evidence, the model predicts a negative correlation between firms' financing costs and their age. Over a firm's life-cycle, per period net profits and the export participation probability grow. Exporters are less likely to exit than purely domestic firms. Belief updating entails excessive financing of incumbents relative to entrants and too much exporting. Asymptotically, trade liberalization reduces overall general equilibrium exit rates, but it does not necessarily increase welfare. With multiple asymmetric export markets, firms gradually expand their market coverage and total sales. A confidence crisis modeled by belief reversion causes an over-proportional decrease in exports, thereby offering a novel interpretation of the recent trade slump.