Question

Suppose a firm has 34 million shares of common stock outstanding at a price of $15.5 per share. The firm also has 100,000 bonds outstanding with a current price of $1171.1. The outstanding bonds have yield to maturity 7.8%. The firm's common stock beta is 2.5 and the corporate tax rate is 38%. The expected market return is 12% and the T-bill rate is 1%. What is the WACC for this firm?

Weight of Equity (3 decimals):  

Weight of Debt (3 decimals):  

Cost of Equity (4 decimals):  

After tax Cost of Debt (4 decimals):  

WACC (4 decimals):  

Answer 1

Solution :

1. Calculation of weight of equity :

The formula for calculating the weight of equity is

= Value of Equity / ( Value of Equity + Value of Debt )

As per the information given in the question

No. of shares of comon stock outstanding = 34 Million ; Market price per share = $ 15.5 ;

                                                                                               

Thus Market value of Common stock = No. of shares of common stock outstanding * Market price per share

= 34 Million shares * $ 15.5 = $ 527 Million = $ 527,000,000

Thus the value of equity = Market value of common stock = $ 527,000,000

As per the information given in the question

No. of bonds outstanding = 100,000 ; Market price of bond = $ 1,171.10 ;

Market value of the bonds = No. of bonds outstanding * Market price of bond

= 100,000 * $ 1171.10   = $ 117,110,000

Thus the value of debt = Market value of bonds = $ 117,110,000

Applying the above information in the formula for weight of equity we have

Weight of equity shares or Common stock = [ 527,000,000 / ( 527,000,000 + 117,110,000 ) ]

= 527,000,000 / 644,110,000

= 0.818183

= 81.8183 %

= 81.818 % ( when rounded off to three decimal places )

Thus the weight of equity = 81.818 %

2.Calculation of weight of debt :

The formula for calculating the weight of debt is

= Value of Debt / ( Value of Equity + Value of Debt )

As per the information given in the question

No. of shares of common stock outstanding = 34 Million ; Market price per share = $ 15.5 ;           

Thus Market value of Common stock = No. of shares of common stock outstanding * Market price per share

= 34 Million shares * $ 15.5 = $ 527 Million = $ 527,000,000

Thus the value of equity = Market value of common stock = $ 527,000,000

As per the information given in the question

No. of bonds outstanding = 100,000 ; Market price of bond = $ 1,171.10 ;

Market value of the bonds = No. of bonds outstanding * Market price of bond

= 100,000 * $ 1171.10   = $ 117,110,000

Thus the value of debt = Market value of bonds = $ 117,110,000

Applying the above information in the formula for weight of debt we have

Thus Weight of debt = weight of corporate bonds = [ 117,110,000 / ( 527,000,000 + 117,110,000 ) ]

= 117,110,000 / 644,110,000

= 0.181817

= 18.1817 %

= 18.182 % ( when rounded off to three decimal places )

Thus the weight of debt = 18.182 %

3.Calculation of cost of equity :

Cost of equity as per Capital Asset Pricing Model is calculated using the following formula :

R_E = R_F + [ β * ( R_M - R_F ) ]

Where

R_E = Cost of equity    ; R_F = Risk free rate of return   ; β = Beta of the stock ; R_M = Expected market return ;

As per the information given in the question we have

R_F = T – Bill rate = 1 %   ; R_M = 12 % ; β = 2.5   ;

Applying the above values in the formula we have

= 1 % + [ 2.5 * ( 12 % - 1 % ) ]

= 1 % + [ 2.5 * 11 % ]

= 1 % + 27.5 % = 28.5 %

Thus the cost of equity = 28.5000 % (when rounded off to four decimal places )

4. Calculation of After tax Cost of Debt :

The formula for calculating the After tax cost of debt is

= K_d * ( 1- t )

where K_d = Pre tax cost of debt ; t = tax rate ;

As per the information given in the question we have

K_d = 7.8 %    ;   t = 38 % = 0.38 ;

Applying the above information in the formula we have after tax cost of debt as

= 7.8 % * ( 1 - 0.38 ) = 7.8 % * 0.62 = 4.8360 %

Thus the after tax cost of debt = 4.8360 %

5. 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 = 28.5 % = 0.285   ; W_e = 81.818 % = 0.81818 ;   K_d = 7.8 % = 0.078 ; t = 38 % = 0.38   ;

W_d = 18.182 % = 0.18182

Applying the above values in the formula we have the WACC as

= [ 0.285 * 0.81818 ] + [ (0.078 * ( 1 – 0.38 ) ) * 0.18182 ]

= [ 0.285 * 0.81818 ] + [ (0.078 * 0.62 * 0.18182 ]

= [ 0.233181 + 0.008793 ]

= 0.241974

= 24.1974 % ( when rounded off to four decimal places)

Thus the WACC of the firm is = 24.1974 %