Question

GXY Corp. has a WACC of 15%, a cost of debt capital of 5%, and a market value debt-to-equity ratio of 0.10. GXY Corp. is not subject to taxation. Suppose that GXY Corp. increased it market value debt-to-equity ratio to 0.35, What will be the change in GXY Corp’s WACC? Enter your answer as a percent; do not include the % sign. Round your final answer to two decimals.

Answer 1

Solution:

Calculation of GXY Corp.’s cost of equity capital if its market value debt-to-equity ratio is 0.10 :

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 capital ; W_e = Weight of equity capital ;

K_d = Cost of debt capital  ;   W_d = Weight of debt capital

As per the information available in the question we have

WACC = 15 % ;   K_d = 5 % = 0.05 ; K_e = To find ;

Debt equity ratio = 0.10 : 1

Thus weight of debt capital = 0.10 / ( 1 + 0.10 ) = 0.10 / 1.10 = 0.090909

Thus weight of equity capital = 1 / ( 1 + 0.10 ) = 1 / 1.10 = 0.909091

W_e = 0.909091 ;    W_d = 0.090909 ;  

Applying the above values in the formula we have

15 % = [ K_e * 0.909091 ] + [ 5 % * 0.090909 ]

15 % = [K_e * 0.909091 ] + [ 0.454545 % ]

15 % - 0.454545 % = K_e * 0.909091

14.545455 % = K_e * 0.909091

K_e * 0.909091 = 14.545455 %

K_e = 14.545455 % / 0.909091

K_e = 16 %

Thus the cost of equity capital at a market value debt - to - equity ratio of 0.10 = 16 %

Calculation of GXY Corp.’s WACC if it raises its market value debt-to-equity ratio to 0.35 :

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 capital ; W_e = Weight of equity capital ; K_d = Cost of debt capital  ;   W_d = Weight of debt capital

As per the information available in the question we have

K_d = 5 % ;       K_e = 16 % ;         WACC = To find ;  

Debt equity ratio = 0.35 : 1

Thus weight of debt capital = 0.35 / ( 1 + 0.35 ) = 0.35 / 1.35 = 0.259259

Thus weight of equity capital = 1 / ( 1 + 0.35 ) = 1 / 1.35 = 0.740741

W_e = 0.740741 ;    W_d = 0.259259 ;  

Applying the above values in the formula we have

= [ 16 % * 0.740741 ] + [ 5 % * 0.259259 ]

= 11.851852 % + 1.296296 %

= 13.148148 %

= 13.15 % ( when rounded off to two decimal places )

Thus the WACC of GXY Corp. at a market value debt - to - equity ratio of 0.35 = 13.15 %

Calculation of change in GXY Corp’s WACC :

The change in GXY Corp’s WACC is calculated as follows :

The change in GXY Corp’s WACC = WACC of GXY Corp. when market value debt-to-equity ratio is 0.10 - WACC of GXY Corp. when market value debt-to-equity ratio is 0.35

= 15 % - 13.15 %

= - 1.85 %

Thus the change in GXY Corp’s WACC = - 1.85 % ( decrease in WACC by - 1.85 % )