On Optimal Dividend, Reinvestment, and Liquidation Policies for the Firm

We consider the liquid asset management problem of a firm with a fixed business. Two questions are addressed: How much, if any, of the firm's liquid assets should be paid to the owners as dividends? If the liquid asset level is negative (resulting from a net loss in the previous period), should sufficient funds be raised to pay off the corresponding short-term debts, or should the benefit of limited liability be applied by liquidating the firm (declaring it bankrupt)? These questions are addressed in a multiperiod environment under uncertainty. The owners seek to maximize the present expected value of the after-tax returns from dividends less funds invested over the lifetime of the firm. Since the owners must pay income taxes on dividends they receive but cannot deduct the expenses of paying off short-term debts when needed, they have an incentive to have the firm retain some liquid assets as a hedge against having to raise funds to pay off such short-term debts. The form of the optimal policy in the general case is found to be surprisingly complex. A numerical example is used to illustrate the possible complexities. The main thrust of the paper is the presentation of three sets of conditions that are sufficient to prove that there exists an optimal policy with a certain intuitively pleasing and simple form.