Question

Lone Star Industries just issued $800 of perpetual 12% debt and used the proceeds to repurchase stock. The company expects to generate $185 of earnings before interest and taxes in perpetuity. Lone Star distributes all of its earnings as dividends at the end of each year. The firm’s unlevered cost of capital is 18% and the corporate tax rate is 40%.

A.What is the value of Lone Star as an unlevered firm?

                                                

            B.Use the Adjusted Present Value Method to calculate the value of Lone Star with leverage.

C.What is the value of the firm’s equity?

D.What is the required return on the firm’s levered equity (r_S)?

            E.  Use the Flow-to-Equity method to calculate the value of Lone Star’s equity.

Answer 1

(a) Unlevered Cost of Capital = 18%, Tax Rate = 40 % and EBIT = $ 185

NOPAT = EBIT x (1-Tax Rate) = 185 x (1-0.4) = $ 111

Value of Unlevered Firm = 111/0.18 = $ 616.667

(b) Perpetual Debt = $ 800, Interest Expense = 12 % and Tax Rate = 40 %

Interest Tax Shield = 0.4 x 0.12 x 800 = $ 38.4

Present Value (PV) of Interest Tax Shield = 38.4 / 0.12 = $ 320

Value of Levered Firm = 320 + 616.667 = $ 936.667

(c) Perpetual Debt = $ 800 and Firm Value = 936.667

Equity Value = 936.667 - 800 = $ 136.667

(d) Debt to Equity Ratio = DE = 800 / 136.667 = 5.85364

Cost of Levered Equity = Unlevered Cost of Capital + DE x (1-Tax Rate) x (Unlevered Cost of Capital - Cost of Debt) = 18 + 5.85364 x (1-0.4) x (18 - 12) = 39.0731 % ~ 39.07 %

(e) EBIT = $ 185

Less: Interest Expense = 800 x 0.12 = $ 96

PBT = 89

Less: Tax Expense = 0.4 x 89 = $ 35.6

Net Income = $ 53.4

Levered Cost of Equity= 39.07 %

Therefore, Equity Value = 53.4 / 0.3907 = $ 136.678