Question

In the problems below, you can use a risk premium of 5.5 percent and a tax rate of 40 percent if none is specified.

1. Union Pacific Railroad reported net income of $770 million after interest expenses of $320 million in a recent financial year. (The corporate tax rate was 36 percent.) It reported depreciation of $960 million in that year, and capital spending was $1.2 billion. The firm also had $4 billion in debt outstanding on the books, was rated AA (carrying a yield to maturity of 8 percent), and was trading at par (up from $3.8 billion at the end of the previous year). The beta of the stock is 1.05, and there were 200 million shares outstanding (trading at $60 per share), with a book value of $5 billion. Union Pacific paid 40 percent of its earnings as dividends and working capital requirements are negligible. (The Treasury bond rate is 7 percent.)

a. Estimate the FCFF for the most recent financial year.

b. Estimate the value of the firm now.

c. Estimate the value of equity and the value per share now.

Answer 1

a). Free cash flow to the firm (FCFF) = (net income/(1-Tax rate) + interest expense)*(1-Tax rate) + depreciation - capital expenditure

= (770/(1-36%) +320)*(1-36%) + 960 - 1,200

= 734.8 million

b). Reinvestment rate = (Capex - depreciation)/EBIT*(1-Tax rate)

= (1,200 - 960)/(770/(1-36%) + 320)*(1-36%) = 24.62%

Return on capital = EBIT*(1-36%)/Total book capital = 1,523.125*(1-36%)/(4,000 + 5,000) = 10.83%

Expected growth rate = reinvestment rate*ROC = 24.62%*10.83% = 2.67%

Cost of equity = risk-free rate + (beta*market risk premium) = 7%+(1.05*5.5%) = 12.775%

After-tax cost of debt = yield*(1-Tax rate) = 8%*(1-36%) = 5.12%

Total capital (at market value) = debt value (D) + equity value (E)

= 4,000 + (200*60) = 16,000

WACC = sum of weighted costs = (4,000/16,000)*5.12% + (12,000/16,000)*12.775% = 10.86%

Firm value (assuming perpetual growth) = FCFC*(1+growth rate)/WACC - growth rate)

= 734.8*(1+2.67%)/(10.86%-2.67%) = 9,211.47 million

c). Equity value = firm value - last year's debt value = 9,211.47 - 3,800 = 5,411.47 million

Value per share = equity value/number of shares = 5,11.47/200 = $27.06 per share