Question

2. XYZ has total assets of $3,000,000 financed by debt of $2,000,000 and equity capital of $1,000,000. The pretax cost of debt is 6% and the cost of equity capital is given at 10%. XYZ has pretax income (before deduction of interest expense) of $300,000 and is taxed at 40%. Calculate residual income in year 1 (after deducting an equity charge).

3. Same facts as problem 2. XYZ is expected to earn pretax income (before deduction of interest expense) of $300,000 in perpetuity. The book value of XYZ shares is $20 per share. XYZ has 50,000 shares of common stock outstanding. What is the intrinsic value of one share of XYZ common stock.

4. Same facts as problem 3. XYZ expects long term earnings growth to average 7% a year. What is the intrinsic value of XYZ common stock.

Answer 1

2) EBIT = $300,000

I = 6%*$2,000,000 = $120,000

PBT = $180,000

Tax = 0.4 * 180,000 = $72,000

Net Income = $108,000

Equity Charge = Equity Capital * Cost of equity = $1,000,000 * 10% = $100,000

Residual Income = Net Income - Equity Charge = $8,000

3) Present value of expected future residual incomes = RI/r = $8,000/0.1 = $80,000

Intrinsic Value per share = $20 + $80,000/50000 = $21.6

4) Present value of expected future residual incomes = RI(1+g)/(r-g) = $8,000*1.07/(0.1-0.07) = $285,333.33

Intrinsic Value per share = $20 + $285,333.33/50000 = $25.71