Learning about profitability and dynamic cash management

We study a dynamic model of a firm whose shareholders learn about its profitability and, face costs of external financing and costs of holding cash. The shareholders' problem involves a notoriously challenging singular stochastic control problem with a two-dimensional degenerate diffusion process. We solve it by means of an explicit construction of its value function, and derive a corporate life-cycle with two stages: a “probation stage” where it is never optimal for the firm to issue new shares, and a “mature stage” where the firm resorts to the market whenever needed. The cash target level is nonmonotonic in the belief about profitability and reaches its highest value on the edge between the two stages. This solution leads to new insights into the firm's volatility and its payout ratio which depend on the firm's stage in its life cycle.