Risk vs. Proot-potential; a Model for Corporate Strategy
نویسندگان
چکیده
A rm whose net earnings are uncertain, and that is subject to the risk of bankruptcy, must choose between paying dividends and retaining earnings in a liquid reserve. Also, diierent operating strategies imply diierent combinations of expected return and variance. We model the rm's cash reserve as the diierence between the cumulative net earnings and the cumulative dividends. The rst is a diiusion (additive), whose drift/volatility pair is chosen dynamically from a nite set, A. The second is an arbitrary nondecreasing process, chosen by the rm. The rm's strategy must be nonclairvoyant. The rm is bankrupt at the rst time, T, at which the cash reserve falls to zero (T may be innnite), and the rm's objective is to maximize the expected total discounted dividends from 0 to T, given an initial reserve, x; denote this maximum by V (x). We calculate V explicitly, as a function of the set A and the discount rate. The optimal policy has the form: (1) pay no dividends if the reserve is less than some critical level, a, and pay out all of the excess above a; (2) choose the drift/volatility pairs from the upper extreme points of the convex hull of A, between the pair that minimizes the ratio of volatility to drift and the pair that maximizes the drift; furthermore, the rm switches to successively higher volatility/drift ratios as the reserve increases to a. Finally, for the optimal policy, the rm is bankrupt in nite time, with probability one. 1. A Theory of Corporate Decision Making Consider a rm with xed plant and equipment that produces an uncertain stream of net revenues. (Net revenue equals gross revenue less all costs except the cost of capital.) Part of this revenue may be paid out in dividends, with the remainder accumulated in a cash reserve. Since the net revenue can be negative as well as positive, the cash reserve can uctuate up and down. We suppose that the rm starts with a positive cash reserve, say x, and that it becomes bankrupt the rst time, if ever, that the cash reserve falls to zero. When the rm becomes bankrupt, it ceases to exist. The rm's manager controls the dividends, which must be nonnegative, and can also innu-ence the stochastic process of net revenues. In other words, the manager's policy has two parts, a dividend policy and an operating policy. (We shall give a …
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