Question

Market value of debt of YTU Co. is equal to market value of its equity. Company has no preferred stock. If cost of equity of the company is four times its before-tax cost of debt and weighted average cost of capital is 2.4 times its before-tax cost of debt, what must be the corporate tax rate?

Answer 1

Solution:

WACC = Kd (1 - T) * Wd + Ke * We + Kp * Wp

WACC => Weighted average cost of capital , Kd => cost of debt , Wd => weight of debt , Ke => cost of equity , We => weight of equity , Kp => cost of preferred stock , Wp => weights of preferred stock

We are given ,

Market value of equity = Market value of debt

Also We = Market value of equity / total market value of debt and equity

We = Market value of equity / 2 market value of equity = .5

Similarly, Wd = .5

Kp = 0 (no preferred stock) , Ke = 4Kd (cost of equity is four times the before tax cost of debt) , WACC = 2.4 Kd , T =??

Putting all the values in the WACC equation we get,

2.4Kd = Kd (1-T) .5 + Ke * .5 + 0

2.4 Kd = Kd(1-T).5 + 4Kd*.5

2.4Kd = .5Kd(1-T)+2Kd

Dividing by kd both sides

2.4 = .5(1-T)+2

.4 = .5(1-T)

.8 = 1-T

T = 1-.8 = .2

The tax rate comes out to be 20%