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A Dynamic Theory of the Balance Sheet

We analyze dynamic corporate financing under moral hazard. In the optimal contract, financiers provide funds in exchange for bonds and outside equity. The entrepreneur is incentivized by a fraction of the equity. Retained earnings are the state variable governing the payoff and liquidation decisions. When they reach a prespecified threshold dividends are paid, when they fall to zero the firm is liquidated. We characterize the continuous time dynamics of stock and bond prices. The volatility of stock prices is stochastic, and decreases as the value of the firm increases. Default risk also decreases as the value of the firm increases, but it never goes to zero, and is factored in the bond price. Small firms have high default risk, but large upside potential and thus high market to book ratio. Large firms have high liquidity and low market to book ratios. Finally, leverage decreases as a function of the value of the firm.