Optimal Capital Structure with Scale Effects under Spectrally Negative Levy Models

Abstract

The optimal capital structure model with endogenous bankruptcy was first studied by Leland (1994) and Leland and Toft (1996), and was later extended to the spectrally negative Levy model by Hilberink and Rogers (2002) and Kyprianou and Surya (2007). This paper incorporates scale effects by allowing the values of bankruptcy costs and tax benefits to be dependent on the firm's asset value. These effects have been empirically shown, among others, in Warner (1976), Ang et al. (1982), and Graham and Smith (1999). By using the fluctuation identities for the spectrally negative Levy process, we obtain a candidate bankruptcy level as well as a sufficient condition for optimality. The optimality holds in particular when, monotonically in the asset value, the value of tax benefits is increasing, the loss amount at bankruptcy is increasing, and its proportion relative to the asset value is decreasing. The solution admits a semi-explicit form, and this allows for instant computation of the optimal bankruptcy levels, equity/debt/firm values and optimal leverage ratios. A series of numerical studies are given to analyze the impacts of scale effects on the default strategy and the optimal capital structure.