Optimal Dividend and Investment Policies for a Self-Financing Business Enterprise

For a self-financing business enterprise (or for an underdeveloped economy subject to constraints on the availability of foreign investment funds), three theorems are presented. Each result is based upon the assumption that the firm's investment opportunities follow constant returns-to-scale, and are of the "point input--stream output" type. Theorem 1 shows that if the enterprise is attempting to maximize a linear function of the cash dividends paid out, the optimization model cannot explain a readily observed phenomenon: both investment expenditures and also cash dividends at the same point in time. Theorems 2 and 3 explore the consequences of supposing that the maximand is a concave, nonlinear function of the cash dividends paid out, and that the optimal solution consists of positive investment expenditures over time. (The optimal policy may or may not call for positive dividends during each time period.) Then Theorem 2 shows that the optimal dual variable price ratios are determined uniquely by the set of investment opportunities available, and Theorem 3 shows that the optimal policy can be evaluated numerically through optimization of the original utility function subject to a specially constructed single linear equality constraint on the cash withdrawals. An economic decentralization interpretation is attached to this auxiliary maximization problem.