Tobin’s Q and Optimal Dividends, Investment, and Liquidity in a Financially-Constrained Firm

We analyze the payout decision of a financially-constrained firm that cannot raise external funds. Exogenous cash flows are generated by a two-state Markov regime-switching process and are positive in one regime and negative in the other regime. The firm is motivated to pay out dividends to impatient shareholders but is also motivated to accumulate cash within the firm to make required payments when cash flow is negative. If the cash on hand is insufficient to make these payments, the firm terminates, thereby losing its claim on future cash flows. The optimal payout policy can be described as a form of precautionary saving. However, contrary to conventional wisdom about precautionary saving, we find that such saving falls in response to a mean-preserving increase in the variance of cash flows.
 
We extend the model to include a capital investment decision. Instead of smooth and convex adjustment costs, we introduce an upper bound on the investment-capital ratio, which leads to a bang-bang solution for investment. Thus optimal investment and dividends are each governed by trigger policies. We derive and interpret analytic solutions for these triggers. The trigger for optimal investment equates marginal q to the "static cost of funds," which is technically the marginal valuation of a dollar of cash within the firm. Despite the linear homogeneity of the value function in the state variables (capital and cash on hand), average q and marginal q are not equal. At the optimal trigger for investment, a broader measure of average q, equal to the value of the firm divided by the sum of the replacement cost of its capital and its cash on hand, equals marginal q. Finally, we analyze a particular myopic value of a unit of capital, and show that if this myopic value of capital is sufficiently high, specifically when the myopic value exceeds one, the firm can ignore the financing constraint when making its investment decision. Otherwise, the firm will invest in capital only if its cash on hand is greater than or equal to an optimally-derived trigger.