Question

What is a firm's weighted-average cost of capital if the stock has a beta of 1.1, Treasury bills yield 4%, and the market portfolio offers an expected return of 16%? In addition to equity, the firm finances 70% of its assets with debt that has a yield to maturity of 10%. The firm is in the 35% marginal tax bracket.

Answer 1

Solution:

Calculation of Cost of Equity of the firm:

As per the Capital Asset Pricing Model ( CAPM), the Cost of equity of a firm is calculated using the following formula :

Cost of equity = R_F + [ β * ( R_M - R_F ) ]

Where

R_F = Risk free rate of return   ; β = Beta of the stock;   R_M = Expected return on the market

As per the information given in the question we have

R_F = Risk free rate of Return = Treasury bills yield = 4 %   ;

R_M = Expected Return of the market portfolio = 16 %   ;

β = 1.1

Applying the above values in the formula we have

= 4 % + [ 1.1 * ( 16 % - 4 % ) ]

= 4 % + [ 1.1 * 12 % ]

= 4 % + 13.20 %

= 17.20 %

Thus the cost of equity for the firm is = 17.20 %

Calculation of Weighted Average Cost of Capital:

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

Weight of debt = 70 % = 0.70

Thus the weight of equity = ( 1 – Weight of debt ) = 1 – 0.70 = 0.30 = 30 %

Therefore we have

K_e = 17.20 % = 0.1720   ; W_e = 30 % = 0.30   ;  

K_d = 10 % = 0.10 ; t = 35 % = 0.35; W_d =70 % = 0.70

Applying the above values in the formula we have

= [ 17.20 % * 0.30 ] + [ ( 10 % * ( 1 – 0.35 ) ) * 0.70 ]

= [ 17.20 % * 0.30 ] + [ ( 10 % * 0.65 * 0.70 ]

= [ 5.16 % + 4.55 % ]

= 9.71 %

Thus the Weighted average cost of the capital of the firm = 9.71 %.