Question

Colt Manufacturing has two divisions: 1) pistols; and 2) rifles. Betas for the two divisions have been determined to the beta (pistol)= 0.8 and beta (rifle)= 1.2. The current risk-rate of return is 1.5%, and the expected market rate of return is 7.5%. The after-tax cost of debt for Colt is 5%. The pistol division's financial proportions are 32.5% debt and 67.5% equity, and the rifle division's are 42.5% debt and 57.5% equity.

a. What is the pistol's division's WACC?

b. What is the rifle division's WACC?

Round to two decimal places.

Answer 1

Solution:                                                                                                                                  

Calculation of Pistol’s Division WACC :

As per the information given in the question we have

As per the CAPM the cost of equity can be obtained using the formula

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

Where

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

As per the information given in the question we have

R_F = 1.5 %   ; R_M = 7.5 %   ; β = 0.8

Applying the above values in the formula we have

= 1.5 % + [ 0.8 * ( 7.5 % - 1.5 % ) ]

= 1.5 % + ( 0.8 * 6 % )

= 1.5 % + 4.8 % = 6.3 %

Thus cost of equity of Pistol’s Division = 6.3 %

Thus the cost of equity = 6.3 %. The after-tax cost of debt for Colt is 5%. The pistol division's financial proportions are 32.5% debt and 67.5% equity

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

WACC = [ K_e * W_e ] + [ ( K_d * W_d ]

K_e = Cost of equity ; W_e = Weight of equity ;

K_d = After tax Cost of debt   ; W_d = Weight of debt

As per the information available in the question we have

K_e = 6.3 %    ; W_e = 67.5 % = 0.675 ;   K_d = 5 %    ; W_d = 32.5 % = 0.325

Applying the above values in the formula we have

= [ ( 6.3 * 0.675 ) + ( 5 * 0.325 ) ]

= 4.2525 + 1.6250 = 5.8775 %

Thus the WACC of Pistol’s Division = 5.8775 %

= 5.88 % ( when rounded off to two decimal places )

Calculation of Rifle’s Division WACC :

As per the information given in the question we have

As per the CAPM the cost of equity can be obtained using the formula

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

Where

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

As per the information given in the question we have

R_F = 1.5 %   ; R_M = 7.5 %   ; β = 1.2

Applying the above values in the formula we have

= 1.5 % + [ 1.2 * ( 7.5 % - 1.5 % ) ]

= 1.5 % + ( 1.2 * 6 % )

= 1.5 % + 7.2 % = 8.7 %

Thus cost of equity of Rifle’s Division = 8.7 %

Thus the cost of equity = 8.7 %. The after-tax cost of debt for Colt is 5%. The Rifle’s division's financial proportions are 42.5% debt and 57.5% equity

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

WACC = [ K_e * W_e ] + [ ( K_d * W_d ]

K_e = Cost of equity ; W_e = Weight of equity ;

K_d = After tax Cost of debt   ; W_d = Weight of debt

As per the information available in the question we have

K_e = 8.7 %    ; W_e = 57.5 % = 0.575 ;   K_d = 5 %    ; W_d = 42.5 % = 0.425

Applying the above values in the formula we have

= [ ( 8.7 * 0.575 ) + ( 5 * 0.425 ) ]

= 5.0025 + 2.1250 = 7.1275 %

Thus the WACC of Rifle’s Division = 7.1275 %

= 7.13 % ( when rounded off to two decimal places )