According to chapter 17 of Ross's Corporate Finance (Brazilian translation of 2nd edition),

$$ r_{WACC} = \frac{S}{S+B}r_S + \frac{B}{S+B}r_B(1 - T) $$


$$ r_S = r_0 + \frac{B}{S}(1 - T)(r_0 - r_B) $$

where $S$ is equity, $B$ is debt, $T$ is tax rate, $r_0$ is the unlevered cost of equity, $r_S$ is the levered cost of equity, and $r_B$ is the cost of debt.

By replacing $r_S$ in the first formula and simplifying, I get

$$ r_{WACC} = \Bigg{(}\frac{S + B(1 - T)}{S + B}\Bigg{)}r_0 $$

which would mean the weighted average cost of capital does not depend on the cost of debt, $r_B$. This formula yields the same WACC as the one in the book, and I checked on some other examples as well.

Did I get this right? If so, is this because the higher tax shield compensates the additional risk from higher interest payments? If not, what am I doing wrong?


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