Question

Fama's Llamas has a weighted average cost of capital of 11.5 percent. The company's cost of equity is 17 percent, and its pretax cost of debt is 8.5 percent. The tax rate is 35 percent. What is the company's target debt-equity ratio?

A. 0.8745

B. 1.8333

C. 0.9573

D. 0.9665

E. 0.9205

Answer 1

Solution :

Calculation of weight of debt and equity in WACC :

The formula for calculating the weighted average cost of capital is =

WACC = [ K_e * W_e ] + [ ( K_d * ( 1- t ) ) * W_d ]

K_e = Cost of equity ; W_e = Weight of equity ;       

K_d = Cost of debt  ; t = Income tax rate ; W_d = Weight of debt

As per the information available in the question we have

K_e = 17 %    ;   K_d = 8.50 %    ; t = 35 % = 0.35     ; WACC = 11.50 %

Let weight of equity = X ; Let weight of debt = ( 1 – X )

W_e = X ;   W_d = ( 1 – X )

Applying the above values in the formula we have

11.50 = [ 17 * X ] + [ 8.50 * ( 1 – 0.35 ) * ( 1 – X ) ]

11.50 = [ 17 * X ] + [ 8.50 * 0.65 * ( 1 – X ) ]

11.50 = [ 17 * X ] + [ 5.5250 * ( 1 – X ) ]

11.50 = 17X + 5.5250 - 5.5250X

11.50 – 5.5250 = 17X – 5.5250X

5.9750 = 11.4750X

11.4750X = 5.9750

X = 5.9750 / 11.4750 = 0.5207

Thus weight of equity = X = 0.5207

Therefore weight of debt = ( 1 – X ) = 1 – 0.5207 = 0.4793

Thus weight of equity = 0.5207

And weight of debt = 0.4793

Thus the target debt equity ratio is

=Weight of debt / Weight of equity

= 0.4793 / 0.5207 = 0.9205

Thus the solution is E. 0.9205