Question

Suppose the HHY Corp has a WACC of 15%, a cost of debt capital of 5%, and a market value debt-to-equity ratio of 0.30. Assuming that HHY Corp. is not subject to taxation and its debt will remain risk-free, what will be HHY’s cost of equity capital if it raises its market value debt-to-equity ratio to 0.50? Enter your answer as a percent without the % sign. Round to two decimals.

Answer 1

Solution:

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 = 0.30 : 1

Thus weight of debt capital = 0.30 / ( 1 + 0.30 ) = 0.30 / 1.30 = 0.230769

Thus weight of equity capital = 1 / ( 1 + 0.30 ) = 1 / 1.30 = 0.769231

W_e = 0.769231 ;    W_d = 0.230769 ;  

Applying the above values in the formula we have

15 % = [ K_e * 0.769231 ] + [ ( 5 % * 0.230769 ]

15 % = [K_e * 0.769231 ] + [ 1.153846 % ]

15 % - 1.153856 % = K_e * 0.769231

13.846154 % = K_e * 0.769231

13.846154 % / 0.769231 = K_e

K_e = 13.846154 % / 0.769231

K_e = 18 %

Thus the cost of equity capital at a debt equity ratio of 0.30 = 18 %

Calculation of HHY’s cost of equity capital if it raises its market value debt-to-equity ratio to 0.50 :

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 = 18 % ; WACC = To find ;  

Debt equity ratio = 0.50 : 1

Thus weight of debt capital = 0.50 / ( 1 + 0.50 ) = 0.50 / 1.50 = 0.333333

Thus weight of equity capital = 1 / ( 1 + 0.50 ) = 1 / 1.50 = 0.666667

W_e = 0.666667 ;    W_d = 0.333333 ;  

Applying the above values in the formula we have

= [ 18 % * 0.666667 ] + [ 5 % * 0.333333 ]

= 12 % + 1.666667 %

= 13.666667 %

= 13.67 % ( when rounded off to two decimal places )

Thus the cost of equity capital at a debt equity ratio of 0.50 = 13.67 %