# Why is there inconsistency in WACC vs unlevered return?

To evaluate an enterprise we can discount free cash flow by either the unlevered required rate of return or the WACC.

With Tax we have:

$$WACC=R_e \frac{E}{E+D}+R_f\frac{D}{E+D}(1-t)$$

where $$R_e$$ is return on equity, $$R_f$$ is return on debt or risk free rate, $$E$$ is market value of equity, $$D$$ is market value of debt and $$t$$ is tax.

If the equity beta of the firm is $$\beta_e$$ we have the unlevered beta or asset beta as: $$\beta_A=\beta_e/(1+\frac{D}{E+D}(1-t))$$. Also by CAPM:

$$R_e=Rf+\beta_e(R_m-R_f)$$

$$R_A=Rf+\beta_A(R_m-R_f)$$

by plugging in the expression for $$\beta_A$$ and simplifying I get:

$$R_A=R_e\frac{E}{E+D(1-t)}+R_f\frac{D(1-t)}{E+D(1-t)}$$

This is different from the WACC expression while I think it should be the same. What am I doing wrong?

1. You are allowed to apply the CAPM to calculate the cost of equity $$R_e$$. However, one of the CAPM assumptions is, that taxes are not taken into account into the model.
2. The unlevered WACC gives a theoretical solution under the assumption that there is no debt at all. In conventional WACC, the tax part $$t$$ only impacts the cost of debt, but if the weight of debt is zero, tax is not relevant any more.
In summary, the difference from your formulas arises, because the WACC-approach explicitly includes the tax-shield $$t$$ and the CAPM is an economic model without taxes.