Sparkling Water, Inc., expects to sell 2.98 million bottles of drinking water each year in perpetuity....

Sparkling Water, Inc., expects to sell 2.98 million bottles of drinking water each year in perpetuity. This year each bottle will sell for $2.15 in real terms and will cost $1.08 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           $ ____________

Expert Solution

We need to calculate the present value of the sales revenues.

For year 1: Revenue=Number of bottles sold*Price per bottle
Number of bottles sold=2.98 million=2.98*1000000=2980000

Price per bottle=$2.15
Revenue=$2.15*2980000=$6407000

For year 1:
Tax rate=34%.
Real after tax revenue in year 1= $6407000*(1-34%)=$4228620
The present value of revenue (in perpetuity)
Present value of revenues=(After tax revenue in real terms)/(Real discount rate−Real growth rate of revenue)
Real discount rate=12%
Real growth rate of revenue=6%
Present value of revenues=$4228620/(12%-6%)=$70477000

Real after tax costs in year 1=Number of bottles purchased*Cost per bottle*(1-Tax rate)
Number of bottles purchased=2980000
Cost per bottle=$1.08
Real after tax costs in year 1=2980000*$1.08*(1-34%)=$2124144

Present value of cost=Real after tax costs in year 1/(Real discount rate−Real growth rate of cost)
Real discount rate=12%
Real growth rate of cost=5%
Real after tax costs in year 1=$2124144

Present value of cost=$2124144/(12%-5%)=$2124144/(7%)=$30344914.29
Value of the firm = Present value of revenues - Present Value of costs
=$70477000-$2124144=$68,352,856

jeff jeffy answered 1 year ago

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