Recent empirical analyses on different datasets have revealed a common exponential behaviour in the shape of the probability density of the corporate growth rates. We briefly review these analyses and present new evidence on this topic based on corporate data from Italian Manufacturing Industry. We then propose a very simple model that, under rather general assumptions, provides a robust explanation of the observed regularities. The model is based on a very simple stochastic process describing the random partition of a number of business opportunities among a population of identical firms. A theoretical result is presented for the limiting case in which the number of firms and opportunities go to infinity. Moreover, using simulations, we show that even in a moderately small industry the agreement with asymptotic results is almost complete.