Optimal Security Design and Dynamic Capital Structure in a Continuous‐Time Agency Model

Abstract

We derive the optimal dynamic contract in a continuous-time principal-agent setting, and implement it with a capital structure (credit line, long-term debt, and equity) over which the agent controls the payout policy. While the project's volatility and liquidation cost have little impact on the firm's total debt capacity, they increase the use of credit versus debt. Leverage is nonstationary, and declines with past profitability. The firm may hold a compensating cash balance while borrowing (at a higher rate) through the credit line. Surprisingly, the usual conflicts between debt and equity (asset substitution, strategic default) need not arise. Copyright 2006 by The American Finance Association.

Ambiguity in Dynamic Contracts

“…Generally, it is possible to interpret the agent's continuation value in a dynamic contracting environment as the amount of cash the firm has at hand, either in a money market account as in DeMarzo et al (2010), or as a draw on a credit line as in DeMarzo and Sannikov (2006). Consequently, we can identify the expected growth of the firm's cash stock as γW + η (W ), and at the optimal contract, the growth of the firm's free cash will be lower when the cash stock itself is low, or alternatively, when the draw on the firm's credit line is close to the limit.…”

“…A related setting which features a risk neutral principal and agent and linear effort cost is studied in DeMarzo and Sannikov (2006). The existence of the over-and under-compensating regions, and the fact that the agent is over-incentivized are novel to my paper and due to the introduction of ambiguity.…”

“…Contrary to DeMarzo and Sannikov (2006), I assume that the agent's effort cost varies over time. Let η ≡ {η t } t≥0 denote the stochastic process governing the agent's effort cost.…”

“…In DeMarzo and Sannikov (2006) as well as numerous other works in dynamic contracting, the agent's continuation value plays a crucial role in determining the properties of the contract. In the case without ambiguity, it can be shown that the continuation value…”

“…In general, J ′ (W ) can be either positive or negative. Let us conjecture that the principal's value function has the same shape as in DeMarzo and Sannikov (2006), that is, it is concave, first increasing and then decreasing, and satisfies J ′ (W ) = −1, whereW is the maximal continuation value of the agent in the contract. We have µ+J…”