We study a dynamic model of a firm whose shareholders learn about its profitability, face costs of external nancing 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 non-monotonic in the belief about the profitability and reaches its highest value on the edge between the two stages. It follows new insights on the firm's volatility and its payout ratio which depend on the firm's stage in its life cycle.
Corporate cash management; Corporate life cycle; Learning; Singular control;
- C02: Mathematical Methods
- C11: Bayesian Analysis: General
- C61: Optimization Techniques • Programming Models • Dynamic Analysis
- G32: Financing Policy • Financial Risk and Risk Management • Capital and Ownership Structure • Value of Firms • Goodwill
- G33: Bankruptcy • Liquidation
- G35: Payout Policy
Jean-Paul Décamps et Stéphane Villeneuve, « Learning about profitability and dynamic cash management », TSE Working Paper, n° 22-1301, février 2022.
Jean-Paul Décamps et Stéphane Villeneuve, « Learning about profitability and dynamic cash management », Journal of Economic Theory, vol. 205, n° 105522, octobre 2022.
Journal of Economic Theory, vol. 205, n° 105522, octobre 2022