I present a dynamic fixed cost model of export participation extended by a capital theoretic concept of the customer stock. Plants that want to start exporting have to invest into a market specific factor which serves as input into a decreasing returns to scale technology generating sales demand. Customer capital, like phyical capital, depreciates over time and its accumulation is subject to adjustment costs. It allows the model to reproduce the empirical fact that new exporters show above average revenue growth rates and a declining exit hazard in the years after entry. I structurally estimate the model on a rich panel data set of German manufacturing plants between 1995 and 2008. During the observed time span, plants in the sample saw a strong increase in export activity which provides a suitable case study for the predictive power of the model. Unlike a pure fixed cost version, the model correctly forecasts a steep rise in exports after 2003. It is also able to reconcile a strong export reaction to trade liberalizations with a low elasticity of aggregate exports to exchange rate movements. Customer capital accumulation therefore offers a potential resolution to the elasticity puzzle in international economics.