Question

A firm has a debt-equity ratio of 0.6 and pretax cost of debt of 10 percent. The industry average cost of unlevered equity is 12.6 percent. What is the cost of levered equity if tax rate is 20 percent?

A. 13.85%

B. 15.90%

C. 8.51%

D. 7.23%

Answer 1

Solution:

As per the Modigilani & Miller Theorem the formula for calculating the cost of levered equity is

rL = ru + [ ( D/ E ) * ( 1 – t ) * ( ru – rd ) ]

Where

rL= Levered cost of equity ; ru = Unlevered cost of equity ; D/E = Debt of equity ratio ; t = Tax rate ;

rd = Pre tax Cost of debt ;

As per the information given in the question we have

ru = 12.6 % = 0.126 ; ( D/ E ) = 0.60 ; t = tax rate = 20 % = 0.20 ; rd = 10 %

rL = Levered cost of equity = To find

Applying the above information in the formula we have

= 12.6 % + [ 0.6 * ( 1 – 0.20 ) * ( 12.6 % – 10 % ) ]

= 12.6 % + ( 0.6 * 0.8 * 2.6 % )

= 12.6 % + 1.25 %

= 13.85 %

Thus the cost of levered equity if tax rate is 20 percent = 13.85 %

The solution is Option A. 13.85 %