Question

Fama's Llamas has a weighted average cost of capital of 11.5 percent. The company's cost of equity is 16 percent, and its pretax cost of debt is 7.5 percent. The tax rate is 34 percent. What is the company's target debt-equity ratio? (Do not round your intermediate calculations.)

Answer 1

Solution:

Calculation of weight of debt and weight of equity :

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 = Pre tax Cost of debt    ; t = Tax rate ; W_d = Weight of debt

As per the information available in the question we have

WACC = 11.5 % ;   K_e = 16 % ;    K_d = 7.5 % ; t = 34 % = 0.34 ;

Let the weight of Equity be “ x “ and the weight of Debt be “ ( 1 – x ) “

Thus W_e = x ;    W_d = ( 1 – x ) ;  

Applying the above values in the formula we have

11.5 = [ 16 * x ] + [ ( 7.5 * ( 1 – 0.34 ) ) *( 1 – x ) ]

11.5 = 16x + [ 7.5 * 0.66 * ( 1 – x ) ]

11.5 = 16x + [ 4.95 * ( 1 – x ) ]

11.5 = 16x + 4.95 – 4.95x

11.5 – 4.95 = 16x – 4.95x

6.55 = 11.05x

11.05x = 6.55

x = 6.55 / 11.05

x = 0.592760

The weight of equity = 0.592760

Thus the weight of debt = ( 1 – x ) = 1 – 0.592760 = 0.407240

Calculation of Debt – Equity Ratio :

The formula for calculation of Debt equity ratio is = Weight or proportion of Debt / Weight or proportion of Equity

As per the information available we have

Weight or proportion of Debt = 0.407240 ;   Weight or proportion of Equity = 0.592760    ;

Applying the above information in the formula we have Target debt equity ratio as

= 0.407240 / 0.592760

= 0.687023

Thus the Company’s Target debt - equity ratio is

= 0.6870 ( when rounded off to four decimal places )

= 0.69 ( when rounded off to two decimal places )