Optimal Lending Contracts and Firm Dynamics

Abstract

We develop a general model of lending in the presence of endogenous borrowing constraints. Borrowing constraints arise because borrowers face limited liability and debt repayment cannot be perfectly enforced. In the model, the dynamics of debt are closely linked with the dynamics of borrowing constraints. In fact, borrowing constraints must satisfy a dynamic consistency requirement: the value of outstanding debt restricts current access to short-term capital, but is itself determined by future access to credit. This dynamic consistency is not guaranteed in models of exogenous borrowing constraints, where the ability to raise short-term capital is limited by some prespecified function of debt. We characterize the optimal default-free contract-which minimizes borrowing constraints at all histories-and derive implications for firm growth, survival, leverage and debt maturity. The model is qualitatively consistent with stylized facts on the growth and survival of firms. Comparative statics with respect to technology and default constraints are derived. REVIEW OF ECONOMIC STUDIEScapital 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 constraints 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 o...

Asset Pricing Implications of Firms' Financing Constraints

“…2 Our results are also consistent with the view that financial distress is mostly an idiosyncratic phenomenon that does not affect returns in a systematic way. 3 Finally, our findings can also be interpreted as providing additional evidence against models of financing frictions that rely on costly external finance.…”

“…3 Finally, our findings can also be interpreted as providing additional evidence against models of financing frictions that rely on costly external finance. 4 Second, in the macroeconomic literature, several authors have argued that financing 1 For example Chan, Chen, and Hsieh (1985), Chen, Roll, and Ross (1986) and Chan and Chen (1991) 2 Berk, Green, and Naik (1999), Gomes, Kogan, and Zhang (2002), and Zhang (2002). 3 For example, Opler and Titman (1994), Asquith, Gertner, and Sharfstein (1994) and Lamont, Polk, and Saá-Requejo (2001).…”

“…4 For example a recent strand of literature has focused instead on "quantity" constraints (e.g. Kehoe and Levine (1993), Kotcherlakotta (1996), Zhang (1997), Alvarez and Jermann (2000), Albuquerque and Hopenhayn (2001), Clementi and Hopenhayn (2001), Cooley, Quadrini, and Marimon (2001), and Almeida and Campello (2002)). …”

Impatience versus Incentives

“…Oscillation emerges. 2 Our setting is broadly applicable, in the spirit of Ray (2002), and nests environments studied in many influential papers, such as Thomas and Worrall (1988), Thomas and Worrall (1994), and Albuquerque and Hopenhayn (2004). Yet, we show that by adding even an infinitesimal amount of relative impatience on the agent side, virtually all Pareto-optimal contracts oscillate around a focal Pareto-optimal steady state.…”

“…Theorem 1 now holds for all sufficiently low O P . 6 Example 1 is drawn from Thomas and Worrall (1994) and Opp (2012); Example 2 is a modified version of Albuquerque and Hopenhayn (2004) or Clementi and Hopenhayn (2006); Example 3 is inspired by Ray (2002) and Thomas and Worrall (1988).…”