16. 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 4.3. 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 uncer- tain, 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 (see MyLab Operations Management Supplement F, "Financial Analysis"). 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.) b. Which alternative minimizes the present value of construction costs over the next 20 years if the discount rate is 12 percent? 16 percent? c. Because the decision involves public policy and compromise, what political considerations does the planning commission face? *ABLE 4.3 WATER DEMAND Year Demand Year Demand Year Demand 0 120 7 148 14 176 1 124 8 152 15 180 2 128 9 156 16 184 3 132 10 160 17 188 4 136 11 164 18 192 5 140 12 168 19 196 6 144 13 172 20 200