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
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 100 million gallons per year. Therefore, the city must expand the facility. The estimated demand over the next 20 years is given in table given below.
YEAR | DEMAND | YEAR | DEMAND | YEAR | DEMAND |
0 | 100 | 7 | 124 | 14 | 156 |
1 | 104 | 8 | 132 | 15 | 160 |
2 | 108 | 9 | 136 | 16 | 164 |
3 | 112 | 10 | 140 | 17 | 168 |
4 | 116 | 11 | 144 | 18 | 172 |
5 | 120 | 12 | 148 | 19 | 176 |
6 | 120 | 13 | 148 | 20 | 180 |
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 (180minus100).
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 180million 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 20million gallon expansion would cost $38million; a 40million gallon expansion, $57million; and an 80million gallon expansion, only $71million. 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 14 percent and as high as 20 percent.
a. Compute the cash flows for each alternative, compared to a base case of doing nothing. (Note: As a municipal utility, the operation pays no taxes.)
For alternative 1, the total cash flow over 20 years is $___million. (Enter your response as an integer.)
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