Exit Options and Dividend Policy under Liquidity Constraints
We introduce a liquidity constraint to the standard model of a firm with stochastic cash flow and an irreversible exit decision. A firm with no cash holdings and negative cash flow is forced to exit regardless of its option value. This creates a precautionary motive for holding cash, which has a liquidity cost because the return on cash is below the discount rate of interest. We characterize the optimal exit and dividend policy and show how it can be solved numerically. We show that the firm almost surely exits voluntarily to preempt forced exit. Numerical results show that the optimal policy is very sensitive to a small liquidity cost. We also study the implications of the liquidity constraint on an industry with idiosyncratic productivity shocks and endogenous entry. Equilibrium inefficiency has three channels: 1) cross-section of firm productivity is distorted as some firms exit too early and others too late, 2) turnover rate is distorted, 3) precautionary cash holdings are socially inefficient. The effect of the liquidity constraint on average productivity is in principle ambiguous. Monte-Carlo simulation shows that when entry costs are low the liquidity constraint lowers average productivity, as old but currently unproductive firms that have succeeded in accumulating a lot of cash then continue at inefficiently low productivity levels.
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