Sparkling Water Inc expects to sell 282 million bottles of d

Sparkling Water, Inc., expects to sell 2.82 million bottles of drinking water each year in perpetuity. This year each bottle will sell for $1.35 in real terms and will cost $.92 in real terms. Sales income and costs occur at year-end. Revenues will rise at a real rate of 6 percent annually, while real costs will rise at a real rate of 5 percent annually. The real discount rate is 12 percent. The corporate tax rate is 34 percent. What is the company worth today? (Do not round intermediate calculations. Enter your answer in dollars, not millions of dollars, e.g., 1,234,567.) Value of the firm

Solution

Value of Firm = PV of Revenue (net of taxes) - PV of Expenses(net of taxes)

Where Value of perpetuity with Growth = C₁/ (r -g)

PV of Revenue(net of taxes)

Revnue for 1st Year = Units sold * Selling Price = 2,820,000 * 1.35 = 3,807,000
Revenue Net of Taxes = 3,807,000* (1 - 34%) = 2,512,620

r = 12%
g = 6%

Present Value of Revenue = 2,512,620 / (12% - 6%)
Present Value of Revenue = 2,512,620 / 6%
Present Value of Revenue = 41,877,000

PV of Cost (net of taxes)

Cost for 1st Year = Units sold * Cost per Unit = 2,820,000 * 0.92 = 2,594,400
Cost Net of Taxes = 2,594,400 * (1 - 34%) = 1,712,304

r = 12%
g = 5%

Present Value of Cost = 1,712,304 / (12% - 5%)
Present Value of Cost = 1,712,304 / 7%
Present Value of Cost = 24,461,486

Value of Firm = PV of Revenue (net of taxes) - PV of Expenses(net of taxes)
Value of Firm = 41,877,000 - 24,461,486
Value of Firm = 17,415,514