Unlevered firm (Firm U) which has EBIT of $2m/year in perpetuity

Question: An unlevered firm (Firm U) which has EBIT of $2m/year in perpetuity

Key Formulas

1. Free Cash Flow = EBIT (1-T) – (Change in NOWC+ Change in NFA)
2. WACC = (D/V) (R_{D *} (1 – T)) + (S/V) (R_S) ; V = D + S
3.    Value of debt tax shields (assuming perpetual debt)

= PV of taxes saved on a perpetuity of annual interest payments of (R_D * D)

= (T * R_D * D)/ R_D   = T*D

Modigliani-Miller Relationships

4. Value of levered firm = Value of unlevered firm + Value of debt tax shields

V_L  = V_U + T*D   (ignoring costs of financial distress)

5. Risk of levered equity (Beta: B):

B_S,L = B_S,U + (B_S,U – B_D) (1 – T) (D/S)

6. Required return on levered equity (R_S,L )

R_S,L = R_S,U + (R_S,U – R_D) (1 – T) (D/S)

Consider an unlevered firm (Firm U) which has EBIT of $2m/year in perpetuity. The cost of equity for Firm U is 10%; equity beta is 1.0. It has 1 million shares outstanding. The firm is considering issuing $10m of perpetual debt at an interest rate of 5% and buying back stock. At this debt level, the debt is considered to be riskless; therefore, ignore costs of financial distress. Firm L denotes the firm under the levered capital structure. The firm does not have to make additional investments in operating working capital or net fixed assets to sustain this EBIT. Every year, it distributes the entire net income as dividends to stockholders.

What is the Free Cash Flow of the firm? Does it depend upon the capital structure?

Fill in the following table: assume 40% tax rate

	Firm U	Firm L
EBIT
– Interest
EBT
-Tax
NI
CF to debt
Cost of debt
Value of debt
CF to equity
Cost of equity
Value of equity
FCF
WACC
Firm Value using FCF
CCF
Pre-tax WACC
Firm Value using CCF