Switching tax structure and payouts in endogenous bankruptcy models

Abstract

In the spirit of Leland (H.E. Leland, Corporate Debt Value, Bond Covenant, and Optimal Capital Structure, J. Finance 49 (1994), pp. 1213–1252), we consider a structural credit risk model with tax provisions under the assumption of a positive payout rate. By defining a more general tax structure than in (Leland, 1994), we introduce a general switching corporate tax rate function and analytically derive the value of the tax benefits claim, the whole capital structure and the smooth pasting condition. In this set-up, the endogenous failure level is derived and both the singular and joint effect of the two introduced risk factors (payouts and tax asymmetry) on optimal managerial financing decisions are studied. Results show a quantitatively significant impact on optimal debt issuance and leverage ratios, bringing them to values more in line with historical norms and providing a way to explain differences in observed leverage across firms.

Keywords::

• structural model
• corporate debt
• endogenous default
• optimal stopping
• tax benefits of debt

Keywords::

• 60J60
• 62L15
• 91G40
• 91G20

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

^1. Instantaneous coupon payments can be written as , where F is face value of debt, supposed to be constant through time, as in Leland [12].

^2. In the special case of a switch to zero tax benefits, e.g. τ₂ = 0, we obtain the optimal failure V_B(C;τ₁,0;δ) as implicit solution of

(38)

This result completes the analysis in [14] Appendix B, in the case where we let the maturity T → ∝ since the authors analyse the switch to a zero tax rate only in case of no payouts.

^3. EBIT is modelled in [12] as a linear function of V; in [13] as a constant fraction of firm's assets value.

^4. The independence with respect to α means that bankruptcy costs do not directly affect the endogenous failure level, since the strict priority rule holds. Bankruptcy costs will instead affect the optimal failure level through the choice of the optimal coupon C^* which maximizes total firm value. In [4] a study is conducted by removing the strict priority rule under the assumption of a constant corporate tax rate.

^5. This condition is always satisfied with our parameter values, since we always consider and .

^6. Leland [12] in his Section D observes that a leverage of 52% is quite in line with historical norms.

^7. As noted in [12] for , and also supported by results in [2] for , the firm will always chose a coupon level which is lower than that one corresponding to the maximum capacity of debt. As a consequence, a lower coupon means a lower debt value. Moreover, as in [12] we are assuming the face value of debt being constant.

^8. As in Leland [12] this model does not consider tax loss carry forwards which could be an interesting point to develop, since they will introduce path dependence, making the model even more realistic.