Comparative dynamics in a life cycle theory of the firm

Abstract

Important insights and contributions to the corporate financial manager's decision problem have been provided by the balanced-growth financial modeling literature, e.g., see [4, 5, 8, 10, 11, 13, 15]. In the spirit of this research, the objective of this paper is twofold. First, a normative model of the dynamic financial planning process in a deterministic environment is constructed wherein the traditional, steady-state assumptions are relaxed. In contrast to prior models, the firm is allowed to pay a liquidating dividend and faces a time-dependent investment rate of return, interest rate, and equity discount rate. Necessary and sufficient conditions for the levered firm's optimal investment-financing-dividend policy decisions which maximize the wealth of its investors are developed, and a solution synthesis technique is employed to catalogue the different decisions at each time instant in terms of three earnings-growth stages over the firm's life cycle. Over this life cycle, the firm experiences high, low, and negative growth stages, with the latter stage distinguished by a liquidating dividend payout and retirement of debt outstanding. Secondly, the life cycle depiction further permits an analysis of the effects, in terms of both direction and magnitude, on the optimal duration of the firm's different growth stages and optimal growth rates due to changes in the firm's return on investment, debt-equity ratio, borrowing rate, equity discount rate, depreciation rate, and flotation costs via a comparative dynamics and simulation framework. Changes in the return on investment are found to have the most influence on the duration of the firm's growth periods and their respective earnings growth rates, while changes in the mix of financing and depreciation rate tend to have the least effect. Furthermore, the magnitudinal impact of marginal changes in any of the above firm variables is greatest at low levels of debt-to-equity and growth-in-earnings and quickly dissipates as the degree of leverage increases.