Question

Carmona Inc. is a firm with no debt, with expected free cash flows to the firm of $10 million next year growing at 2% a year in perpetuity. The firm has no cash and its current market capitalization is $200 million. Assuming that the company is correctly priced right now, estimate the value of the firm if it decides to borrow money at 4% (pre-tax) and move to a debt to capital (D/ (D+E)) ratio of 20%. (You can assume that the risk free rate is 3%, the equity risk premium is 5%, and that the tax rate for all firms is 40%). A. $ 200 B. $ 212 C. $ 219 D. $ 231 E. $ 245

Answer 1

Calculation of cost of equity when there is no debt:

Ke = (Expected free cash flow/Market price)+growth rate

= ($10/$200)+.02

= 7%

Calculation of unlevered Beta:

CAPM = Rf + β(Rm - Rf)

7% = 3%+β*5%

β = 0.80

Calculation of unlevered Beta:

βj = βuj[1+(D/S)(1-T)]

βj = Levered Beta

βuj = Unlevered Beta

D/S = Debt/Equity ratio = 20/80 = 1/4

βj = 0.80*[1+(1/4)(1-.40)]

= 0.80*[1+0.15]

βj = 0.92

New Beta (levered Beta) after borrow money is 0.92

CAPM = Rf + β(Rm - Rf)

= 3%+0.92*5%

= 7.60%

Calculation of cost of equity (Ke) when there is debt of 20%:

CAPM = Rf + β(Rm - Rf)

=3%+0.92*5%

Cost of Equity (Ke) =7.6%

Cost of the firm using WACC:

WACC =(Kd*Wd)+(Ke*We)

Where Kd = Cost of Debt = 4% (pre-tax)

= 4%*(1-0.40) = 2.4%

Wd = Weightage of Debt = 0.20

Ke = Cost of Equity = 7.60%

We = Weightage of Debt = 0.80

WACC =7.60%*0.80+2.40%*0.20

= 6.56%

Value of the Firm = Expected free cash flow/(Market price - growth rate)

= $10/0.0656-0.02

= $219

So the correct option is (C) $219