Textbook Question on cost of capital

CFA Level II Corporate Finance
#1

Your firm has a debt-equity ratio of .60. Your cost of equity is 11% and your after-tax cost of debt is 7%. What will your cost of equity be if the target capital structure becomes a 50/50 mix of debt and equity?

Solutions given: WACC = [(1.0 / 1.6) x .11] + [(.6 / 1.6) x .07] = .095; .095 = .5Re + (.5 x .07); Re = 12%

Isn’t the above solution totally wrong? Since WACC is always going to change with a change in capital structure, in the presence of taxes.

#2

Weird… WACC rate is an output calculation. Implying a new cost of equity by changing capital structure and keeping WACC rate constant sounds like a pure exercise only. Don’t mind too much on this.