OPTIMAL INVESTMENT AND FINANCE IN A DYNAMIC MODEL OF THE FIRM

Abstract

Within the context of dynamic policies of the firm, an optimal control problem is formulated to find the investment and borrowing policies that maximize dividend payments. lt is assumed that the firm's income per unit of debt increases with the capital/debt ratio at diminishing rates and the investment is financed through retained earnings and external borrowings. The interest rate on debt is defined as an increasing function of the debt/equity ratio, while the cost of investment per unit of debt is assumed to be convex. Also, the cost of increasing or decreasing the debt level is a convex function of the rate of borrowing per unit of debt. It is shown in this paper that, for such a firm, the optimal debt/equity ratio and the corresponding optimal trajectories for the investment and borrowing rates can be uniquely determined through out various initial conditions.