# Several years ago, River City built a water purification plant to remove toxins and filter the citys

## Question:

Several years ago, River City built a water purification plant to remove toxins and filter the city€™s drinking water. Because of population growth, the demand for water next year will be more than the plant€™s capacity of 120 million gallons per year. Therefore, the city must expand the facility. The estimated demand over the next 20 years is given in Table.

The city planning commission is considering three alternatives.
€¢ Alternative 1: Expand enough at the end of year 0 to last 20 years, which means an 80 million gallon increase (200€” 120).
€¢ Alternative 2: Expand at the end of year 0 and at the end of year 10.
€¢ Alternative 3: Expand at the end of years 0, 5, 10, and 15,
Each alternative would provide the needed 200 million gallons per year at the end of 20 years, when the value of the plant would be the same regardless of the alternative chosen. Significant economies of scale can be achieved in construction costs: A 20 million gallon expansion would cost $18 million: a 40 million gallon expansion.$30 million; and an 80 million gallon expansion, only \$50 million. The level of future interest rates is uncertain, leading to uncertainty about the hurdle rate. The city believes that it could be as low as 12 percent and as high as 16 percent
a. Compute the cash flows for each alternative, compared to a base case of doing nothing.
b. Which alternative minimizes the present value of construction costs over the next 20 years if the discount rate is 12 percent? Sixteen percent?
c. Because the decision involves public policy and compromise, what political considerations does the planning commissionface?

Discount Rate
Depending upon the context, the discount rate has two different definitions and usages. First, the discount rate refers to the interest rate charged to the commercial banks and other financial institutions for the loans they take from the Federal...
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