Question

Welling Inc. has a target debt–equity ratio of 0.78. Its WACC is 9.5%, and the tax rate is 35%.

a. If the company’s cost of equity is 14%, what is its pre-tax cost of debt? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

Cost of debt            %

b. If instead you know that the after-tax cost of debt is 6.8%, what is the cost of equity? (Do not round intermediate calculations. Round the final answer to 2 decimal places.)

Cost of equity            %

Answer 1

Solution:

a.

Calculation of pre tax xost of debt :

As per the information given in the question the target debt equity ratio is 0.78 : 1

This implies that the weight of debt in the capital structure is

= 0.78 / (0.78 + 1 )       [ Debt / ( Debt + Equity ) ]

= 0.78 / 1.78

= 0.438202

Thus the weight of debt in the capital structure is = 0.438202

Similarly we have the weight of Equity in the capital structure is

= 1 / (0.78 + 1 )       [ Debt / ( Debt + Equity ) ]

= 1 / 1.78

= 0.561798

Thus the weight of Equity in the capital structure is = 0.561798 %

Further we now that the WACC = 9.5 % ; Tax rate = 35 % ; cost of equity = 14 % ;

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 = Pre – tax Cost of debt    ;

t = Income tax rate ; W_d = Weight of debt ;

As per the information available we have

WACC = 9.5 % = 0.095 ; K_e = 14 % = 0.14 ; t = 35 % = 0.35   ; W_e = 0.561798 ;    W_d = 0.438202 ;   K_d = To find ;

Applying the above information in the formula for WACC we have

0.095 = [ 0.14 * 0.561798 ] + [ ( K_d * ( 1 - 0.35 ) ) * 0.438202 ]

0.095 = [ 0.14 * 0.561798 ] + [ ( K_d * 0.65 ) * 0.438202 ]

0.095 = [ 0.078652 ] + [ K_d * 0.65 * 0.438202 ]        

0.095 = [ 0.078652 ] + [ K_d * 0.284831 ]

0.095 – 0.078652 = [ K_d * 0.284831 ]

0.016348 = [ K_d * 0.284831 ]

[ K_d * 0.284831 ] = 0.016348

K_d = 0.016348 / 0.284831

K_d = 0.057396

K_d =5.7396 %

K_d =5.74 % ( When rounded off to two decimal places )

Thus the cost of debt = 5.74 %

b.

Calculation of cost of equity when the after tax cost of debt changes to 6.8 %

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 * ( 1 – t ) =After – tax Cost of debt    ; t = Income tax rate ; W_d = Weight of debt ;

As per the information available we have

WACC = 9.5 % = 0.095 ; W_e = 0.561798 ;    W_d = 0.438202 ;   K_d * ( 1 – t ) = 6.8 % = 0.068 ;

K_e = To find ;

Applying the above information in the formula for WACC we have

0.095 = [ K_e * 0.561798 ] + [ 0.068 * 0.438202 ]

0.095 = [ K_e * 0.561798 ] + 0.029798

0.095 – 0.029798 = [ K_e * 0.561798 ]

0.065202 = [ K_e * 0.561798 ]

[ K_e * 0.561798 ] = 0.065202

K_e = 0.065202 / 0.561798

K_e = 0.116060

K_e = 11.6060 %

K_e = 11.61   % ( When rounded off to two decimal places )

Thus the cost of equity = 11.61 %