Toward a Generalization of the Leland-Toft Optimal Capital Structure Model

Details Toward a Generalization of the Leland-Toft Optimal Capital Structure Model Toward a Generalization of the Leland-Toft Optimal Capital Structure Model

2011-09-05

arxiv.org/abs/1109.0897v2

Economy

Quantitative Finance

General Finance

22 pages, 3 figures

Scientific paper

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 generalizes the problem by allowing the values of bankruptcy costs, coupon rates and tax benefits dependent on the firm's asset value. 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 coupon rate is decreasing, 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 values and optimal leverage ratios.

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