Question

Your firm has issued 35,000 bonds with a market price of $100 per bond. The firm also has 50,000 common shares outstanding at a price of $65 per share. If the common shares will pay a dividend of $2.50 at the end of the year and thereafter dividends will grow at a rate of 3%. If the after-tax yield on the firm's bonds is 6%, what is the firm's weighted average cost of capital?

Answer 1

Solution:

Calculation of Cost of Equity:

The price of a share of a firm is calculated using the following formula:

P0 = D1 / ( ke – g )

Where

P0 = Price of the share;      D1 = Dividend paid at the end of the year ; g = growth rate ;

ke = Cost of equity

As per the information given in the question we have ;

D1 = $ 2.50 ;       g = 3 % = 0.03 ; P0 = $ 65   ;   ke = To find

Applying the above values in the formula we have

65 = 2.50 / (ke – 0.03)                                

65 * (ke – 0.03) = 2.50                                

ke – 0.03 = 2.50 / 65

ke – 0.03 = 0.038462

ke = 0.03 + 0.038462 = 0.068462

ke = 6.8462 %

The cost of equity of the company = 6.8462 %

Calculation of weights of Debt and Equity :

As per the information given in the question             

Market value of the Equity shares or Common stock = No. of shares outstanding * Market price per share

= 50,000 shares * $ 65 = $ 3,250,000

Market value of the bonds = No. of bonds issued * Market price per bond

= 35,000 bonds * $ 100 = $ 3,500,000

Thus Weight of equity shares or Common stock = [ $ 3,250,000 / ( $ 3,250,000 + $ 3,500,000 ) ]

= $ 3,250,000 / $ 6,750,000 = 0.4815

Thus Weight of bonds = [ $ 3,500,000 / ( $ 3,250,000 + $ 3,500,000 ) ]

= $ 3,500,000 / $ 6,750,000 = 0.5185

Calculation of Weighted Average Cost of Capital :

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

WACC = [ Ke * We ] + [ Kd * Wd ]

Ke = Cost of equity ; We = Weight of equity ; Kd = After tax Cost of debt    ; Wd = Weight of debt

Cost of equity or common stock = 6.8462 %   ; After tax yield of corporate bonds = After tax cost of debt = 6 %

Thus as per the information available in the question we have

Ke = 6.8462 % ; We = 0.4815   ;   Kd = 6 % ; Wd = 0.5185

Applying the above values in the formula we have

= [ 6.8462 % * 0.4815 ] + [ 6 % * 0.5185 ]

= 3.2963 % + 3.1111 %

= 6.4074 %

= 6.41 % ( when rounded off to two decimal places )

Thus the firm’s Weighted Average Cost of Capital is = 6.41 %