We challenge the idea that trade liberalizations are detrimental to non-exporters: if they expect to export in the future, larger export profits increase their present value. To do this, we develop a model of international trade, where firm productivity follows a Geometric Brownian Motion, with a drift endogenously determined by innovation. Firms export when reaching a productivity threshold, after which they grow at a constant average rate, generating a firm distribution with Pareto upper tail. Non-exporters grow at an increasing rate, lower than that of exporters. We calibrate the model to US data. The anticipation of future export profits accounts for up to 10% of the value of non-exporters. Reducing trade costs increases export profits and reduces domestic ones. As a result, small non-exporters lose value driven by domestic profits, but larger ones gain because of the anticipation of future exports. This is consistent with empirical studies that find some non-exporters expand after liberalizations. A 1% reduction in trade costs reduces the value of non-exporters by 0.01% on average, but 59% of them actually gain, up to 0.13%, which is more than some exporters.