Abstract - The Dynamic Trade-Off Theory with Real Investment: An Analytical Approach

We develop a simple model of dynamic capital structure with real investment in presence of corporate debt tax shields and bankruptcy costs. In each period, a firm inherits an output price and free cash flow minus existing debt obligations before making investment and one-period net (of cash) debt issue decisions, which pins down net equity issue. We provide closed-form solutions for investment, debt, net equity issue, and the market value of equity. We point out that the priority of the principal over the interest in bankruptcy leads to a debt ratio that is significantly lower, and hence more reasonable, than in the traditional trade-off theory with perpetual debt. We also show that output price dynamics can generate a negative correlation between investment and debt in place, a positive correlation between cash flow and investment, a correlation between profitability and leverage, and mean-reversion in leverage. We show that debt ratios exhibit no persistence, and that they are non monotonic in the corporate tax rate. We derive predictions on investment and capital structure dynamics over the business cycle. We examine the effect of capital accumulation and of an equity underwriting cost on our results. In addition to being consistent with well-documented empirical regularities, our dynamic trade-off model is consistent with a pecking-order theory, and it is simple enough to embed and quantify agency issues.

Gilles Chemla
Imperial College London, Tanaka Business School
27.Jun 2006

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