Question

Colt Manufacturing has two? divisions: 1)? pistols; and? 2) rifles. Betas for the two divisions have been determined to be beta (pistol)= 0.7 and beta ?(rifle)=1.3 The current? risk-free rate of return is 4?%, and the expected market rate of return is 10% The? after-tax cost of debt for Colt is 3.5%. The pistol? division's financial proportions are 37.5% debt and 62.5% ?equity, and the rifle? division's are 47.5% debt and 52.5% equity.

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

b.??What is the rifle? division's WACC?

Answer 1

Solution :

A. Using the Capital Asset Pricing model for cost of equity we have R_e = R_f +? (R_m – R_f)

Thus, Cost of equity ( R_e )= Risk free rate of return ( R_f ) + Beta (? ) * ( Market rate of return ( R_m ) - Risk free rate of return (R_f ) )

As per the data given in the question:

Beta (Pistol) = 0.7 ; Beta (Rifle) = 1.3 ; Risk free rate of return = 4 % ; Expected Market rate of return = 10 %

Thus applying the above values in the formula we have Cost of equity of Pistol division as

= 4 % + 0.7 * ( 10 % - 4 % ) = 4 % + 0.7 ( 6 %) = 8.2 %

Similarly , the cost of equity of Rifles division can be derived as follows :

= 4 % + 1.3 * ( 10 % - 4 %) = 4 % + 1.3 ( 6 % ) = 11.8 %

Thus cost of equity of Pistol division = 8.2 % & the cost of equity of Rifles division = 11.8 %

B . Calculation of WACC of Pistol Division :

WACC = K_e * W_e + K_d ( 1 - Tax rate ) * W_d

           = ( Cost of equity * Weight of equity) + ( After tax cost of debt * Weight of debt )

The cost of debt given in the question is after tax. Hence K_d = 3.5 % . No tax adjustments are required.

Given that the Pistol division has 37.5 % of debt and 62.5 % equity ;

Cost of debt = K_d = 3.5 % ;

Cost of equity of Pistol division = K_e = 8.2 %

WACC of Pistol Division = [ 8.2 % * (0.625) + 3.5 % ( 0.375) ] = 5.125 % + 1.3125 % = 6.4375 % = 6.44 %

C. Calculation of WACC of Rifles Division :

WACC = K_e * W_e + K_d ( 1 - Tax rate ) * W_d

The cost of debt given in the question is after tax. Hence K_d = 3.5 % . No tax adjustments are required.

Given that the Rifles division has 47. 5% of debt and 52.5 % of equity.

Cost of debt = K_d = 3.5 % ;

Cost of equity of Rifles division = K_e = 11.8 %

WACC of Rifles Division = [ 11.8 % * (0.525) + 3.5 % ( 0.475) ] = 6.195 % + 1.6625 % = 7.8575 % = 7.86 %

Thus the Pistol Division's WACC = 6.44 %

and the Rifles Division' WACC = 7.86 %