Dividend and Stock Repurchase Policy with Transaction Costs

Firms mainly distribute cash flows to shareholders in the form of dividends or stock repurchases. Stock repurchase has become an important method of distributing cash flows to shareholders. Firms repurchase stock for the following reasons: to distribute cash flow; to announce that firms' managers think their firms' stocks are undervalued; to avoid unwanted takeover attempts; and, to counter the dilution effects of employee and management stock options. In this paper, we examine an optimal dividend and stock repurchase policy with transaction costs under uncertainty. We assume that when the firm pays out dividends it incurs proportional transaction costs, while when it repurchases stock it incurs both fixed and proportional transaction costs. The firm's problem is to choose the dividend and stock repurchase policy in order to maximize the firm's expected total discounted dividends and stock repurchases function. To this end, we formulate it as a combined stochastic control problem: a mixed absolutely continuous and impulse control problem. Then, we show an optimal dividend and stock repurchase policy such that the firm pays out dividend at every instantaneous time, while, whenever the cash flow reaches a certain level, the firm repurchases stock