Production, Capacity, and Liquidity of a Self-Financed Firm

We develop and analyze a dynamic stochastic model of a self-financed firm that optimizes its expected present value of dividends, profits, or a mixture of both. Each period the firm chooses how much to produce, to invest in capacity expansion, to distribute as a dividend, and to retain as liquidity subject to constraints from existing capacity and capital. Product-market prices and yields of capacity-enhancing investments are Markov-modulated. We show that linearity assumptions regarding investment yield and production cost imply that the value function has an affine structure. This leads to a complete characterization of an optimal policy and a linear program that exorcises the curse of dimensionality. We clarify the linkage between capacity and capital in a dynamic framework and provide real option interpretations. We prove that profit maximization induces a more aggressive investment attitude than does maximization of dividends.