Borrowing constraints are an important determinant of firm growth and survival. Such constraints may arise in connection to the financing of investment opportunities faced by firms or temporary liquidity needs, such as those required to survive a recession. This paper develops a theory of endogenous borrowing constraints and studies its implications for firm dynamics. In our model, debt is constrained by the firm’s limited liability and option to default.
A lending contract specifies an initial loan size, future financing, and a repayment schedule. The choice of these variables in turn determines future growth, the firm’s future borrowing capacity, and its ability and willingness to repay. Hence, borrowing constraints and firm dynamics are jointly determined. We study this dynamic design problem.
Our model builds on Thomas and Worral’s (1994) model of foreign direct investment. At time zero a risk neutral borrower (firm or entrepreneur) has a project which requires a fixed initial set-up cost. Every period the project yields revenues that increase with the amount of capital input and a revenue shock, which follows a Markov process. A risk neutral lender (bank) finances the initial investment and provides liquidity to support the firm’s growth process. At any point in time the project may be liquidated.
A lending contract specifies transfers to and payments from the borrower and a liquidation decision, contingent on all past shocks. The firm, has limited commitment and can choose to default at any time. Default gives the firm an outside value which increases with the amount of capital financed and the current revenue shock. We study the contract that maximizes total firm value subject to the no-default and limited liability constraints.
The optimal contract defines a Pareto frontier between the value for the lender (which we call long-term debt) and the value for the entrepreneur (which we call equity). By defaulting, the entrepreneur obtains an outside value but loses its equity. Thus, the firm’s ability to expand is constrained by the entrepreneurs entitlement. Equity grows over time as the firm pays-off the long term debt. This weakens borrowing constraints, as the increased equity provides the bonding necessary to accumulate increasing amounts of capital.
Competition by lenders determines an initial long term debt equal to the initial set-up cost. The equilibrium contract maximizes the entrepreneur’s equity value (and total firm value) subject to expected repayment of this set-up cost. A unique debt maturity structure attains this initial equity value. Any other debt maturity either leads to default or a lower initial firm value.
In the optimal lending contract equity grows at the maximum possible rate (the interest rate), eventually reaching a level at which borrowing constraint are no longer binding. Along this path, dividends are zero. As equity grows, so does the size of the firm and its probability of survival. Our model is thus consistent with the firm age and size effects found in the literature on firm dynamics. In addition, it implies that the capital structure is an important determinant of the firm’s growth and exit decisions, in accordance with the evidence presented in Zingales (1998).
Moreover, we show that investment of a financially constrained firm responds to Tobin’s Q as well as the current level of cash flows. Finally, we show that firms with higher market-to-book ratio of assets display a lower ratio of long term debt to short term debt,conditional on the revenue shock (e.g. Barclay and Smith 1995). This property arises because conditional on the revenue shock, a firm with higher market-to-book value of assets is also a firm with higher equity entitlement, weaker borrowing constraints, and lower long term debt.
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