Gross and net tax shield valuation
Authors: Kolari James 
Published: June 2018

Purpose
The purpose of this paper is to show that distinguishing between gross and net tax shields arising from interest deductions is important to firm valuation. The distinction affects the interpretation but not valuation of tax shields for the famous Miller’s (1977) model with corporate and personal taxes. However, for the well-known Miles and Ezzell’s (1985) model, the authors show that the valuation of tax shields can be materially affected. Implications to the cost of equity and optimal capital structure are discussed.

Design/methodology/approach
This paper proposed a simple tax shield clarification that distinguishes between gross and net tax shields. Net tax shields equal gross tax shields minus personal taxes on debt. When an after-tax riskless rate is used to discount shareholders’ tax shields, this distinction affects the interpretation but not valuation results of the Miller’s model. However, when the after-tax unlevered equity rate is used to discount tax shields under the well-known Miles and Ezzell’s (1985) model, the difference between gross and net tax shields can materially affect valuation results. According to the traditional ME model, both gross tax shields and debt interest tax payments (i.e. net tax shields) are discounted at the after-tax unlevered equity rate. By contrast, the proposed revised ME model discounts gross tax shields at the unlevered equity rate but personal taxes on debt income at the riskless rate (like debt payments). Because personal taxes on debt are nontrivial, traditional ME valuation results can noticeably differ from the revised ME model to the extent that after-tax unlevered equity and debt rates differ from one another.

Findings
For comparative purposes, the authors provide numerical examples of the traditional and revised ME models. The following constant tax rates and market discount rates are assumed: Tc=0.30, Tpb=0.20, Tps=0.10, r=0.06, and ρ=0.10. Table I compares these two models’ valuation results. Maximum firm value for the traditional ME model is 7.89 compared to 7.00 for the revised ME model. At a 50 percent leverage ratio, equity value is reduced from 3.71 to 3.49, respectively. Importantly, the traditional ME model suggests that firm value linearly increases with leverage and implies an all-debt capital structure, whereas firm value stays relatively constant as leverage increases in the revised ME model. These capital structure differences arise due to discounting debt tax payments with the unlevered equity rate (riskless rate) in the traditional ME (revised ME) model. Figure 1 graphically summarizes these results by comparing the traditional ME model (thin lines) to the revised ME model (bold lines).

Research limitations/implications
Textbook treatments of leverage gains to firms or projects with corporate and personal taxes should be amended to take into account this previously unrecognized tradeoff. Also, empirical analyses of capital structure are recommended on the sensitivity of leverage ratios to the gross-tax-gain/debt-personal taxes tradeoff.

Practical implications
Financial managers need to understand how to value interest tax shields on debt in making capital structure decisions, computing the cost of capital, and valuing the firm.

Social implications
The valuation of interest tax shields in finance is a long-standing controversy. Nobel prize winners Modigliani and Miller (MM) wrote numerous papers on this subject and gained fame from their ideas in this area. However, application of their ideas has changed over time due to the Miles and Ezzell’s (ME) model of firm valuation. The present paper adapts the pathbreaking ideas of MM to the valuation framework of ME. Students and practitioners in finance can benefit by the valuation results in the paper.

Originality/value
No previous studies have recognized the valuation issues resolved in the paper on the application of the popular and contemporary ME model of firm valuation to the MM valuation concepts. The new arguments in the paper are easy to understand and readily applied to firm valuation.