Question

Graham Inc. has a WACC of 10%. The company’s cost of equity is 15% and its pre-tax cost of debt is 6%. The tax rate is 35%. What is the firm’s target debt-to-equity ratio?

Answer 1

Here, we will use the following formula of weighted average cost of capital (WACC) to calculate the proportions invested in debt and equity first.

WACC = w_e * r_e + w_d * r_d * (1 - t)

where, w_e = Proportion of equity

w_d = Proportion of debt

r_e = Cost of equity = 15%

r_d = Cost of debt = 6%

t = tax rate = 35%

WACC= Weighted average cost of capital = 10%

w_e + w_d = 100%

w_e = 100% - w_d

Now, putting these values in the WACC formula, we get,

10% = ((100% - w_d) * 15%) + (w_d * 6%  * (1 - 0.35))

0.10 = 0.15 - 0.15w_d + (0.06 * w_d * 0.65)

0.10 - 0.15 = - 0.15w_d + 0.039w_d

-0.05 = -0.111w_d

w_d = 0.05 / 0.111

w_d = 0.45

So, weight of debt is 0.45 or 45%

Now, w_e = 100% - w_d

w_e = 1005 - 45% = 55%

Now, we will calculate the target debt to equity ratio as per below:

Target debt to equity ratio = Weight of debt / Weight of equity

Putting the values in the above formula, we get,

Target debt to equity ratio = 45% / 55% = 0.81