Taxes and the choice between risky and risk-free debt: on the neutrality of credit default taxation

Abstract

Shareholders can decide if their corporation issues risky or risk-free debt. We identify tax systems in which the choice between risky and risk-free debt is not distorted by taxes. These credit default neutral tax systems make it possible to make capital structure decisions and firm valuations neglecting credit default risk, even after taxes. Thus credit default neutrality is a characteristic of a tax system that helps to reduce planning costs. Moreover, credit default neutrality is a necessary condition for financial neutrality of taxation. We find one class of credit default neutral taxes that preserves and another class that modifies the expected tax distribution between creditors and debtor firm. Finally, we show the influence of personal taxation on credit default neutrality.

Appendix: Deriving Eq. (37)

We start with Eq. (32):

$$ \begin{aligned} \Updelta_s &= T_{Ds}^{{\rm mod}}- T_{Ds}^{{\rm pres}} \\ &= \tau_i\cdot {\rm Int}^{\rm mod}_s +\psi\cdot\tau_i\cdot(R^{\rm mod}_s-\lambda \cdot I_0)-\tau_i\cdot(D^{\rm pres}_s-\lambda \cdot I_0) \\ &= \tau_i\cdot(D^{\rm mod}_s-R^{\rm mod}_s)+\psi\cdot\tau_i\cdot R^{\rm mod}_s+\lambda \cdot I_0\cdot\tau_i\cdot(1-\psi)-\tau_i\cdot D^{\rm pres}_s \\ &=\tau_i\cdot(D^{\rm mod}_s-D^{\rm pres}_s)-R^{\rm mod}_s\cdot\tau_i\cdot(1- \psi)+\lambda\cdot I_0\cdot\tau_i\cdot(1-\psi). \\ \end{aligned} $$

If we consider Eq. (33) we can rearrange the above equation to:

$$ \Updelta_s=\tau_i\cdot \Updelta_s+\tau_i\cdot(1-\psi)\cdot(\lambda\cdot I_0-R^{\rm mod}_s). $$

(48)

Solving Eq. (48) to Δ _s leads to:

$$ \Updelta_s=\frac{\tau_i\cdot(1-\psi)}{1-\tau_i}\cdot(\lambda\cdot I_0-R^{\rm mod}_s). $$

(49)

In a similar way we can rearrange Eq. (34):

$$ \begin{aligned} \Updelta_s &= T_{Cs}^{{\rm pres}}- T_{Cs}^{{\rm mod}} \\&=-\tau_c\cdot(1 - z)\cdot(D^{\rm pres}_s-\lambda\cdot I_0) \\& \quad -\left(-\tau_c\cdot(1 - z)\cdot {\rm Int}^{\rm mod}_s + \tau_c\cdot\beta \cdot \left(\lambda \cdot I_0 - R^{\rm mod}_s\right)\right) \\&=\tau_c\cdot(1 - z)\cdot(\lambda\cdot I_0-D^{\rm pres}_s)+\tau_c\cdot(1 - z)\cdot(D^{\rm mod}_s-R^{\rm mod}_s) \\& \quad -\tau_c\cdot\beta \cdot \left(\lambda \cdot I_0 - R^{\rm mod}_s\right) \\&=\tau_c\cdot(1 - z)\cdot(D^{\rm mod}_s-D^{\rm pres}_s)+\tau_c\cdot(1-z- \beta)\cdot\left(\lambda\cdot I_0-R^{\rm mod}_s\right). \\\end{aligned} $$

We can simplify the above equation considering Eq. (33):

$$ \Updelta_s=\tau_c\cdot(1 - z)\cdot\Updelta_s+\tau_c\cdot(1-z-\beta)\cdot\left(\lambda\cdot I_0-R^{\rm mod}_s\right). $$

(50)

If we solve Eq. (50) to Δ _s we obtain:

$$ \Updelta_s=\frac{\tau_c\cdot(1-z-\beta)} {1-\tau_c\cdot(1-z)}\cdot\left(\lambda\cdot I_0-R^{\rm mod}_s\right). $$

(51)

Using Eqs. (49) and (51) leads to:

$$\frac{\tau_i\cdot(1-\psi)} {1-\tau_i} =\frac{\tau_c\cdot(1-z-\beta)}{1-\tau_c\cdot(1-z)}. $$

(52)

Finally, we solve Eq. (52) to τ _c :

$$ \tau_c =\frac{{\tau_i \cdot \left({1 - \psi} \right)}}{{\left( {1 - z} \right) \cdot \left({1 - \psi \cdot \tau_i} \right) - \beta \cdot \left({1 - \tau_i} \right)}}. $$