# Unlevered firm (Firm U) which has EBIT of \$2m/year in perpetuity jagguarpaw January 18, 2017 0 Comments

## 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) (RD * (1 – T)) + (S/V) (RS) ; V = D + S
3.    Value of debt tax shields (assuming perpetual debt)

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

= (T * RD * D)/ RD   = T*D

Modigliani-Miller Relationships

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

VL  = VU + T*D   (ignoring costs of financial distress)

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

BS,L = BS,U + (BS,U – BD) (1 – T) (D/S)

1. Required return on levered equity (RS,L )

RS,L = RS,U + (RS,U – RD) (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