Optimal Debt and Profitability in the Trade-Off Theory

I develop a dynamic model of leverage with tax deductible interest and an endogenous cost of default. The interest rate includes a premium to compensate lenders for expected losses in default. A borrowing constraint is generated by lenders' unwillingness to lend an amount that would trigger immediate default. When the borrowing constraint is not binding, the trade-off theory of debt holds: optimal debt equates the marginal interest tax shield and the marginal expected cost of default. Contrary to conventional interpretation, but consistent with empirical findings, increases in current or future profitability reduce the optimal leverage ratio when the trade-off theory holds.