the beta corporation has an optimal debt ratio of

Question

The Beta Corporation has an optimal debt ratio of 40%. Its cost of equity capital is 12% and its before-tax borrowing rate is 8%.  Given a marginal tax rate of 35%, calculate

(1) The weighted-average cost of capital and,

(2) The cost of equity for an equivalent all-equity financed firm.

Solution: 

(1) K = (1 - .40).12 + (.40).08(1 - .35)      

      = .0928 or 9.28% 

(2) A weighted-average cost of capital of 9.28% for a levered firm implies:       

K =.0928 = K_u (1-(.35)(.40)).  Solving for K_u yields .1079 or 10.79%.