Sparkling Water, Inc., expects to sell 3.7 million bottles of drinking water each year in perpetuity. This year each bottle will sell for $1.46 in real terms and will cost $.82 in real terms. Sales income and costs occur at year-end. Revenues will rise at a real rate of 1.7 percent annually, while real costs will rise at a real rate of .8 percent annually. The real discount rate is 5 percent. The corporate tax rate is 25 percent. What is the company worth today?

approximately $65,238,286

Explanation:

gross profit year 0 = $2,368,000, after tax profit = $1,776,000

gross profit year 1 = [($1.46 x 1.017) - ($0.82 x 1.008)] x 3,700,000 = $2,435,562, after tax profit = $1,826,672

gross profit year 2 = [($1.46 x 1.017²) - ($0.82 x 1.008²)] x 3,700,000 = $2,540,491, after tax profit = $1,905,368

gross profit year 3 = [($1.46 x 1.017³) - ($0.82 x 1.008³)] x 3,700,000 = $2,574,812, after tax profit = $1,931,109

gross profit year 4 = $2,646,550, after tax profit = $1,984913

gross profit year 5 = $2,691,542, after tax profit = $2,018,657

gross profit year 6 = $2,737,298, after tax profit = $2,052,974

gross profit year 7 = $2,783,832, after tax profit = $2,087,368

gross profit year 8 = $2,831,157, after tax profit = $2,123,368

gross profit year 9 = $2,879,287, after tax profit = $2,159,465

gross profit year 10 = $2,928,535, after tax profit = $2,16,401

Using linear regression (using an excel spreadsheet and the data from the first 20 years), the slope of the constant growth line is 39,078x, which represents a $39,078/$1,776,000 = 2.2% growth rate

once we are able to determine an approximate constant growth rate, we can use the formula for the present value of a growing perpetuity:

company's value = NCF year 1 / (Re - g) = $1,826,672 / (5% - 2.2%) = $65,238,286

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