Question

Problem 12.

Using the information below, answer the questions:

 Firm named Galaxy has a free cash flow (FCF) of $13 million.

 Galaxy's net income is $50million and total book equity is $105million

 Galaxy's debt-to-equity ratio is 1.25

 Galaxy's market value of debt is 150 million

 Galaxy's tax rate is 25%

 Galaxy's FCF and earnings will grow at a constant rate of 3%

 Galaxy's equity beta is 1.3

 US 3 month T-bill rate is 1.5%

 S&P 500 market return is 7.5%

 Currently Galaxy Interiors do not pay dividends.

 There are 10 million shares outstanding.

#1) What should be the fair stock value per share using the Residual Income Model (RIM) ?

#2) What should be the fair stock value per share using the Free Cash Flow (FCF) Valuation

model?

Multiple choices

#1)  stock price per share with RIM = approx. $24

#1)  stock price per share with RIM = approx. $77

#1)  stock price per share with RIM = approx. $15

#1)  stock price per share with RIM = approx. $69

#2) stock price per share with FCF model = approx. $59

#2) stock price per share with FCF model = approx. $84

#2) stock price per share with FCF model = approx. $38

#2) stock price per share with FCF model = approx. $41

Answer 1

Residual income = RI0 = Net income - cost of equity x book value of equity

Cost of equity = Ke = Rf + Beta x (Rm - Rf) = 1.5% + 1.3 x (7.5% - 1.5%) = 9.30%

Hence, RI0= 50 - 9.30% x 105 = $ 40.24 million

Growth rate, g = 3%

RI1 = RI0 x (1 + g) = 40.24 x (1 + 3%) = $ 41.44 million

Hence, the equity value using the Residual Income Model (RIM) = Ve = Book value of equity + PV of RI1 in perpetuity = Book value of equity + RI1 / (Ke - g) = 105 + 41.44 / (9.30% - 3%) = $ 762.81 million

Number of shares, N = 10 million

Hence, stock price per share with RIM = Ve / N = 762.81 / 10 = $ 76.28 = approx. $ 77

-----------------

D/E = 1.25; Wd = D/ (D + E) = 1.25 / (1.25 + 1) = 0.5556

We = 1 - Wd = 1 - 0.5556 = 0.4444

Kd = risk free rate = 1.5%

Tax rate, T = 25%

WACC= r = Wd x Kd x (1 - T) + We x ke = 0.5556 x 1.5% x (1 - 25%) + 0.4444 x 9.30% = 4.76%

Hence, value of the firm = Vf = PV of FCF as perpetuity = FCF / (r - g) = 13 / (4.76% - 3%) = $ 739.34 million

Value of equity = Ve = Vf - Market value of debt = 739.34 - 150 = $ 589.34 million

Hence, stock price per share with FCF model = Ve / N = 589.34 / 10 = 58.93 = approx. $ 59