Dynamics of cash holdings, learning about profitability, and access to the market

We study a dynamic model of a firm whose shareholders learn about its profitability, 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 the firm has no access to capital markets, and a “mature stage” where the firm does have access to capital markets. The cash target level is nonmonotonic in the belief about the profitability and reaches its highest value at the access threshold to the market. It follows new insights on the firm’s volatility and its payout ratio which depend on the firm’s stage in its life cycle.