We measure the tax advantage of public firms over private firms, which operate at municipality level in the German household solid waste disposal industry. Public firms with sovereign duties pay no taxes, but equivalent private firms have to. In a simple risk-free setting, we develop a measure of the percentage difference of the charges of both types of firms demanded under their respective tax treatments. We model a cost-covering public firm and a net present value maximizing private firm. For sensible model parameters from the German waste disposal industry the private firm has to demand an about 16% to 18% higher charge. The by far biggest impact on the measure has the value added tax, with revenues as a much larger tax base than profits. Tax savings, which directly affect pre-tax profits, only alleviate the disadvantage bit. There is some evidence that at least one type of private firms—that is, private law firms that are also majority privately owned, are productive enough to overcome the tax advantage of public firms and be able to charge a lower price than public firms.

Standard models on firm valuation, incorporating risky debt, assume a certain tax treatment of a cancellation of indebtedness (COD). Most valuation procedures solely discuss two polar cases: either the COD is strictly taxed on its entirety or not taxed at all. Considering the predominant national tax jurisdictions in G7 and many other countries, this assumption is far from being realistic. We model a state dependent taxation of a COD considering the firm's state in default and further contingencies, including a partial taxation. We show how to include this stochastic interdependency into the pricing of the value of the tax shield and the WACC. Compared to the case of full taxation of a COD this potentially increases the value of tax savings and decreases the discount rate, since less taxes are paid in states with exceptions of a tax on a COD, vice versa for the case of no taxation on a COD. Furthermore, in case of an exemption from taxation of a COD, pricing equations depend on the distribution of total losses on interest and principal payments.

This paper aims at identifying the appropriate discount rate for tax shield valuation in a setting where a partial default is possible and either principal or interest payments are prioritized in default. As a general valuation framework we use the stochastic discount factor. We assume a tax framework with corporate taxes, tax-deductible interest payments of the firm, no taxes on the cancellation of debt and no personal taxes. We strictly decompose the payments owed to the debtholders into interest and principal payments and analyze discount rates of those claims for the different priorities. As a result of the single-period analysis we find that the discount rate for tax savings, i.e., the conditional expected return on tax savings, is always equal to the discount rate of debt only for a proportional loss distribution on interest and principal payments. If losses are distributed according to one of the priority assumptions, the discount rate of tax savings behaves different from the discount rate of debt and both discount rates are equal only in very special cases. Furthermore, we derive qualitative statements for the relation between the discount rate of debt and the discount rate of tax savings assuming certain correlations between the stochastic discount factor and the debt repayments. Finally, we show how the prioritization assumptions can be implemented in a multi-period setting. We obtain for the presented set of assumptions a pricing equation equivalent to the one by Miles and Ezzell (J Finance 40:1485–1492, <link http://link.springer.com/article/10.1007%2Fs11573-015-0782-4#CR26>1985</link>).