Question

a firm has total debt of $900 an total equity of $1600. the cost of debt is 10% and the unlevered rate of return is 13%. The tax rate is 34%. What is the cost equity?

A) 14.69%

B)14.11%

C) 13.88%

D)12.29%

E) 12.69%

Answer 1

Solution :

The formula for calculating the Cost of equity capital is

K_e = R_u + [ ( R_u – K_d ) * ( 1 – t ) * ( D/E) ]

Where

K_e = Cost of equity capital ;   R_u = Unlevered Rate of Return    ;   K_d = Cost of debt    ;

t = Tax rate   ;   D = Value of debt   ; E = Value of equity

As per the information given in the question we have

R_u = 13 %    ;   K_d = 10 %     ; t = 34 %   ;   D = $ 900   ; E = $ 1,600 ;    K_e = To find

Applying the above values in the formula we have :

= 13 % + [ ( 13 % – 10 % ) * ( 1 – 0.34 ) * ( 900 / 1600 ) ]

= 13 % + [ 3 % * 0.66 * ( 900 / 1600 ) ]

= 13 % + [ 3 % * 0.66 * 0.5625 ]

= 13 % + 1.11375 %

= 14.11375 %

= 14.11 % ( when rounded off to two decimal places)

The cost of equity capital = 14.11 %

Thus the solution is Option B) = 14.11 %