Ebook Exit Options and Dividend Policy under Liquidity Constraints
In the standard entry exit problem of a firm with stochastic cash flow, the optimal policy requires the firm to sustain negative cash flows indefinitely. Our main question is how firms should behave if they have a limited capability of paying for losses. The solution is a policy for exit and dividend payments that depends on the current levels of both cash flow and cash holdings.
In the standard problem, the potential for future profits and the irreversibility of exit make it optimal for a firm to accept negative cash flows up to some point. In the absence of financial constraints cash holdings are irrelevant, and the optimal policy is simply a negative threshold level of cash flow below which the firm exits. However, the value of continuation is partly due to future paths where cash flow remains negative for arbitrarily long periods of time. It seems realistic in many contexts that a firm with a long history of losses would find it difficult to keep raising more funds. But as soon as there is a limit to a firm's ability to sustain losses the firm's problem changes in a fundamental way.
To make our point clear, we initially model the liquidity constraint as the complete inability to raise new funds. The firm has an initial stock of cash that can only be augmented with retained earnings. A firm without cash and with a negative cash flow is forced to exit immediately regardless of its future prospects, so firms have an incentive to hoard cash in order to avoid inefficient exit in the future. This precautionary saving is costly due to the liquidity premium cash holdings earn interest at a rate below the discount rate. Therefore, if the firm is sufficiently safe from forced exit with sufficiently high cash flow and/or cash holdings it is optimal to pay out some of the cash to the owners. Thus, besides affecting the optimal exit policy, the liquidity constraint also generates the optimal dividend policy. We characterize the optimal policy and analyze its dependence on the properties of the cash flow process. Our numerical results show that a small liquidity premium has a large impact on optimal firm behavior.
We do not explicitly model the causes behind the liquidity constraint. One natural cause of liquidity constraints is asymmetric information: it can be difficult for a firm or a manager to credibly convey to investors that it has potential for profits. Aside from the liquidity constraint, our model has no other imperfections such as agency problems. The optimal policy maximizes the value of the firm to its owners, taking as given the lack of further cash injections by the owners. In an extension to our model we assume that raising external funds incurs a transaction cost; in effect the basic model assumes that this cost is prohibitive.
Our model builds on elements from the literature on the optimal exercise of options, where the seminal papers are by McDonald and Siegel (1986) who model the optimal timing of investment under uncertain cash flow, and by Dixit (1989) who analyzes the firm's optimal entry and exit decisions in the same framework. A large number of extensions to various directions is summarized by Dixit and Pindyck (1993). Our paper extends this line of research further by adding a liquidity constraint that may prevent the firm from covering operating losses.
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