Resolution of Tax Shield on Interest Expense in WACC


1. Tax Shields from Interest Deductibility in WACC Can Be Resolved with Gross and Net Capital Structures. The excessive discussion about how to value tax shields associated with debt is a colossal waste of time.

When you recognize that the tax shield is equivalent to a reduction in the coupon rate on debt, the proof of how to treat the tax shield becomes clear. The market value of debt to the corporation is reduced to when the coupon rate falls and the equity value increases. For example if debt was 1,000 at with an interest rate of 10% and the coupon rate is reduced to 6%, the market value of debt decreases form 1,000 to 600. If the opportunity cost of debt for providers of funds is 10% both before and after the coupon rate decrease, the value of the debt declines to 60 of interest/10% or 600.

This example is just the same as the tax effects of the interest shield at a 40% tax rate. Using the simple an basic principles that the fixed cost to the corporation is reduced from the tax shield and that the opportunity cost to providers of debt does not change from the corporate tax rate, the following equations quantify the tax shield. The second method is equivalent to the traditional WACC implementation.

Tax Shield Percent = Gross Observed Market Debt to Capital * t

Net Equity Percent = Gross Equity Observed/(1-Tax Shield Percent)

Net Debt Percent = 1- Net Debt Percent

Ku = Kd * Net Debt Percent + Ke * Net Equity Percent

Ke = [Ku – Kd * Net Debt Percent]/Net Equity Percent

Bu = Bd * Net Debt Percent + Be * Net Equity Percent

Be = [Bu – Bd * Net Debt Percent]/Net Equity Percent

3. Bd Should Vary with the Capital Structure in Computing Be and Bu. Even though this is obvious, it is virtually never done in practice. S&P standards for the leverage and credit rating and published credit spreads can be used to establish Bd that varies with capital structure. When the varying credit spreads are applied, the effects on the relationship between Be and Ke and the capital structure are dramatic. The cost of equity at high leverage is dramatically reduced which reflects the call option premium that is inherent in the Ke and the put option cost that is part of the Kd.

Bu = Bd * Net Debt Percent + Be * Net Equity Percent, where Bd is a function of Gross Debt/Capital
Be = [Bu – Bd * Net Debt Percent]/Net Equity Percent, where Bd is a function of Gross Debt/Capital

4. Circularity in WACC and Valuation from Tax Shield can Easily be Avoided. As the equity to capital ratio is computed using the market value of equity and, in turn, the market value of equity requires a value of WACC that is in turn driven in part by the equity to capital ratio. This implies a circular reference seems to exist. This is not much of a problem when the Bu and Ku is established from a comparison set of companies. The remaining circular reference from re-levering the beta can be easily resolved.

5. Target versus Actual Capital Structure Does Not Matter With No Interest Tax Shield. If there is no tax shield, the WACC should not change if you use different capital structure assumptions because the cost of equity changes to compensate for risk created by gearing. This means that without taxes, use of a target capital structure in the context of DCF is not beneficial, necessary or relevant in terms of accuracy or theory. Without the interest tax shield, when the cost of equity is derived from re-levering the unlevered beta using the market value of debt at the valuation date, the result is exactly the same as if the company moves to a target capital structure.

6. APV does not add anything new to valuation. Correct application of the WACC accounts for all items in the bridge between equity value and enterprise value in the WACC calculation. Investment bankers typically do this with using net debt rather than gross debt in computing WACC. Similar adjustments to the WACC should be made for associated investments not included in EBITDA, the fair value of derivatives, discounted operations and any other items.