Question

A company has determined that its optimal capital structure consists of 40 percent debt and 60 percent equity. Given the following information, calculate the firm's weighted average cost of capital. Cost of Debt = 7.0%, Tax rate = 40%, Current Stock Price = $23.72, Long Run Growth rate = 3.8%, Next Year's Dividend = $2.26. Show your answer to the nearest .1%. Do not use the % sign in your answer. Enter your answer as a whole number, thus 9.2% would be 9.2 rather than .092 or 9.2%.

Answer 1

Solution:

Calculation of Cost of Equity:

As per the Gordon growth Model price of a share of a firm is calculated using the following formula:

P = D₁ / ( k_e – g )

Where

P = Price of the share;      D₁ = Dividend paid next year ; g = growth rate ;

k_e = Cost of equity

As per the information given in the question we have ;

D₁ = $ 2.26 ;       g = 3.8 % = 0.038 ; P = $ 23.72   ;   k_e = To find

Applying the above values in the formula we have

23.72 = 2.26 / (k_e – 0.038)                         

23.72 * (k_e – 0.038) = 2.26                        

k_e – 0.038 = 2.26 / 23.72

k_e – 0.038 = 0.095278

k_e = 0.038 + 0.095278 = 0.133278

k_e = 13.3278 %

The cost of equity of the company = 13.3278 %

Calculation of 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 = 13.3278 % ; W_e = 60 % = 0.60   ;   K_d = 7 % = 0.07 ; t = 40 % = 0.40   ; W_d =40 % = 0.40

Applying the above values in the formula we have

= [ 13.3278 * 0.60 ] + [ ( 7 * ( 1 – 0.40 ) ) * 0.40 ]

= [ 13.3278 * 0.60 ] + [ ( 7 * 0.60 * 0.40 ]

= [ 7.99668 + 1.68000   ]

= 9.676680

= 9.7 %   ( when rounded off to one decimal place)

Thus the Weighted average cost of capital of the company is = 9.7