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 = $27.15, Long Run Growth rate = 4.4%, Next Year's Dividend = $1.88. 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:

As per the Gordon growth model the price of a stock can be calculated using the following formula:

P₀ = D₁ / ( K_e – g )

Where,

P₀ = Current Price of the stock    ; D₁ = Dividend payment for year 1 i.e., next year’s dividend

K_e = Cost of equity    ;     g = Dividend growth rate

As per the information given in the question we have

P₀ = $ 27.15     ;   D₁ = $ 1.88   ;    g = 4.4% = 0.044   ; K_e = to find

Applying the above values in the formula we have

27.15 = 1.88 / (K_e – 0.044 )

(K_e – 0.044 ) = 1.88 / 27.15

(K_e – 0.044 ) = 0.069245

K_e = 0.044 + 0.069245 = 0.113245

K_e = 11.3245 %

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 = 11.3245 % = 0.113245   ; 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

= [ 0.113245 * 0.60 ] + [ (0.07 * ( 1 – 0.40 ) ) * 0.40 ]

= [ 0.113245 * 0.60 ] + [ (0.07 * 0.60 * 0.40]

= [ 0.067947 + 0.016800 ]

= 0.084747

= 8.4747 %   ( when rounded off to four decimal places)

= 8.5 % ( when rounded off to nearest 1 % )

The firm's weighted average cost of capital = 8.5