10.10.5 Water Pumps 1. Why are the two alternatives compared based on NPV rather than EAC? 2. If the decision criterion is the EAC, is the analyst making the assumption of repeatability?" 3. Is the decision sensitive to the discount rate? 4. Create a spreadsheet of the water pumps case and determine the sensitivity of the decision to the following items: (i) Refurbishment costs (ii) Regular maintenance costs (iii) Off-peak energy costs (iv) On-peak energy costs 10.6 Bakersfield Water Pumps 10.6.1 Introduction A water pumping station in Bakersfield, California, delivers water over the Tehachapi Mountains into Southern California. (See Hamilton, 2004. All values in this case study are fictitious.) The plant consists of fourteen pumps. Each pump is a four- stage, 60 MW, 600 rpm unit. The capacity of each pump is 8.92 m/s with a static head of 587m. Discharge from the pumping station is through two pipelines with a diameter of 4.26m that feed a tunnel with a diameter of 7.16m. The energy consumption is 840 MW with all fourteen pumps running. There are four Allis- Chalmers pumps, seven Baldwin Lima Hamilton pumps, and three Voith pumps. The Allis-Chalmers pumps were installed in 1971, the Baldwin Lima Hamilton pumps were installed in 1973, and the Voith pumps were installed in 1982. The Voith pumps have a pumping efficiency of 92%, whereas the Allis-Chalmers pumps have an efficiency of 89.7%. The water flow through the pumping station is projected to double over the next thirty years. The pumps currently operate for 10 hours a day during the off-peak electricity period of 10pm to sam providing 117 million m /yr of water each. The off-peak time is completely used. To meet the increasing demand for water, it will be necessary to use on-peak electricity Maintenance of the pumps is a major function. The pumping station only has an availability of 70%, which may be too low as the water demand increases. Over the years, there have been numerous maintenance problems with the pumps, mainly related to electrical issues. All of the motor stators have been rewound. Other prob- lems are related to the impellers, caused by flow-induced erosion, corrosion, and cracking. Officials of the California Department of Water Resources are concerned about the older Allis-Chalmers units. Two major proposals have emerged. The first proposal is to replace the Allis Chalmers units with new Voith units, which are expected to have an efficiency of 92%. The Voith pumps will only require major maintenance every ten years, whereas the Allis-Chalmers pumps undergo a major refurbishment every five years. The second proposal is retain the Allis-Chalmers pumps, redesign the suction bend, and replace the stage one impellers. Project Management Solutions has been retained by the California Department of Water Resources to assess which of the two solutions is more economically de- sirable. 10.6.2 Project Financials The project is an equipment replacement study with cost saving as the measure of economic performance. The alternative with the lowest present value of costs is the preferred alternative. The project financials for the alternative to replace the existing pumps with new pumps are presented in Table 10.30. The delivery of water increases linearly from 117 million m'/year for each pump to 234 million m'/year. The current load of 117 million m'/year is at the off-peak 1.000 Table 10.30 Project financials for the alternative to replacement the existing the pumps with new pumps (all amounts in thousands) Year Off-peak On-peak Regular New and Total Discount PV(costs) energy costs energy costs maintenance refurbish costs factor capital 0 0 -32.600 -32,600 -32,600 1 -3.335 - 162 -1,014 -4,511 0.943 -4.256 2 -3.502 -341 -1,055 -4.897 0.890 -4.358 -3.677 --537 - 1.097 -5,310 0.840 -4.459 -3.861 -752 -1.141 -5.753 0.792 -4557 -4,054 -987 -1.186 -6,227 0.747 -4.653 6 -4.256 -1.243 -1.234 -6,733 0.705 -4.747 7 -1.523 -1,283 -7.275 0.665 -4.838 8 -4.693 -1.828 -1.334 -7.855 0.627 -4.928 9 -4.927 -2.159 -1.388 -8.474 0.592 -9,861 10 --5.174 -2.519 -1.443 -9.651 -18,787 0.558 -29.881 11 -5.432 -2.909 -1.501 -9.842 0.527 -5.185 12 -5,704 -3,332 -1.561 -10.597 0.497 -5.266 13 -5.989 -3.790 -1.623 -11,403 0.469 -5,346 14 6.288 -4,286 -1.688 - 12.263 0.442 -9,693 15 -6,603 -4.822 -1.756 -13.181 0.417 - 5.500 16 -6.933 -5.400 -1.826 - 14.160 0.394 -5,574 17 -7.280 -6,025 -1.899 --15.204 0.371 -5,646 18 -7,644 -6,698 -1.975 -16,317 0.350 -5,717 19 -8,026 -7.424 -2.054 -17.504 0.331 -5.785 20 -8.427 -8.205 -2.136 -14.286 -33.085 0.312 -10,307 21 -8.848 -9,046 -2.222 -20.117 0.294 -5.917 22 -9.291 -9.951 -2,311 -21.553 0.278 -5.981 23 -9.755 -10,924 -2.403 -23,082 0.262 -6,043 24 -10,243 - 11.968 -2.499 -24,711 0.247 -6,103 25 -10.755 -13,091 -2.599 - 26,445 0.233 -6.162 26 - 11.293 -14.295 -2.703 -28,291 0.220 -6,219 27 - 11.858 -15,587 -2.811 - 30.256 0.207 -6,274 28 -12.451 --16,972 -2,924 -32,347 0.196 -6,328 29 -13,073 -18.457 -3.041 -34.571 0.185 -6,380 30 -13.727 -20.049 -3.162 -36.938 0.174 -6,431 NPV ---234.995 rate for electricity, while all of the increase is at peak electricity rates. The off-peak rate is currently $13.27/MWhr and the peak rate is 19/MWh. The energy inflation is expected to rise at 5% pa. The off-peak cost in the first year is calculated as follows: Offpeak energy cost = (60MW)(1Ohr/day)(365days/year) (513.27/MWhr) (1 +he)/(91.5% efficiency) Ofpeak energy cost = $3,334.903/year where he is the inflation rate for energy prices. The on-peak cost is calculated simi- larly. In addition to energy costs, the pumps require regular maintenance. The cost of this maintenance amounts to $975,012 each year. The rate of increase of mainten- ance is expected to be 4% pa. The capital cost of the new pumps is expected to be $32.6 million. The pumps will require major refurbishment every ten years. The cost of this refurbishment is expected to be 20% of the capital cost of the pump. The cost of this refurbishment is expected to increase at the same inflation rate as the maintenance costs. The total costs are sum of the energy costs, the maintenance costs, and the new and refurbishment capital costs. The present value of these costs is determined using a discount rate of 6% pa. There are no tax considerations since the California Department of Water Re- sources is not liable for tax. -162 Table 10.31 Project financials for the alternative to refurbish the existing the pumps (all amounts in thousands) Year Off-peak On peak Regular Refurbish Total Discount PV(costs) energy costs energy costs maintenance cost factor 0 0 -22,600 -22,600 1.000 -22,600 1 --3,402 - 1.014 -4,578 0.943 -4,319 2 -3.572 - 1,055 -4,967 0.890 3 -3.751 -1.097 -5,384 0.840 -4,521 4 -3.938 -1.141 -5,830 0.792 -4,618 -4.135 -987 -1.186 - 15.123 -21.431 0.747 - 16,014 6 -4.342 - 1.243 -1.234 -6,819 0.705 -4,807 7 -4.559 -1.523 -1.283 -7.365 0.665 -4,898 8 -4.787 -1.828 -1,334 -7.949 0.627 -4.987 9 -5,026 -2.159 -1,388 -8.573 0.592 -5,074 10 -5.277 -2,519 -1.443 -18,399 -27.639 0.558 -15.433 11 -5.541 -2.909 -1.501 -9.951 0.527 -5.242 12 --5,818 -3.332 -1.561 -10,712 0.497 -5,323 13 -6,109 -3.790 -1.623 -11.523 0.469 -5,402 14 -6,415 -4.286 -1.688 -12.389 0.442 --5,480 15 -6,735 -4,822 -1.756 - 22,386 -35,699 0.417 -14,896 16 -7,072 -5,400 -1.826 --14.299 0.394 -5,629 17 -7,426 -6,025 -1.899 -15.350 0.371 -5,700 18 -7.797 -6,698 -1.975 -16,471 0.350 -5,770 19 -8.187 -7424 -2,054 -17,665 0.331 -5.839 20 -8.596 -8.205 -2.136 -27,236 -46,174 0.312 - 14.397 21 -9.026 -9.046 -2.222 -20.294 0.294 -5,970 22 -9.477 -9.951 -2,311 -21,739 0.278 -6,033 23 -9.951 -10.924 -2.403 -23.278 0.262 -6,094 24 -10.449 - 11.968 -2.499 - 24,917 0.247 -6,154 25 -10.971 -13.091 -2.599 -33.136 -59,797 0.233 -13.933 26 -11.520 -14.295 -2.703 -28.518 0.220 -6,269 27 -12,096 -15.587 -2,811 -30,494 0.207 28 -12,701 - 16,972 -2.924 -32.597 0.196 -6,377 29 -13.336 -18.457 -3.041 -34.834 0.185 -6,429 30 - 14.002 -20.049 -3.162 -37.213 0.174 -6,479 NPV --235.432 The project financials for the alternative to refurbish the existing pumps are pre- sented in Table 10.31. It is estimated that it will cost $22.6 million to refurbish each of the pumps, and that the pumps will require refurbishment every five years at a cost of 55% of the current refurbishment. The costs for the other items are calculated in a manner that is similar to those represented in Table 10.30. The present values for these two alternatives suggest that the Allis-Chalmers pumps should be replaced, although there is not much difference between the two alternatives. The two alternatives have been compared based on the net present value of their costs. They could have been compared based on the equivalent annual charge (EAC). The equivalent annual charge is also called annual worth, amongst others. The EAC for the refurbishment of the existing pumps is -$17,104,000 per pump and that for replacing the pumps is -$17,072,000. The difference between these two figures is slight, indicating that either of the alternatives could be justified. 10.6.3 Sensitivity Analysis The effect of the discount rate, the maintenance inflation and the energy inflation on the preferred option was investigated. The results of this investigation are shown in Figures 10.13 to 10.15. These results are shown as the difference in their present values. Since the present values are those of costs, positive values indicate that re- furbishing the pumps is the preferred option. For low discount rates, replacement favoured. If the discount rate chosen is greater than 6.1%, the refurbishment of the units is favoured. 30.0 20.0 10.01 0.0 PV(Existing-New) -10.0 -20.01 30.0 -40.0 Replace Refurbish -50.0 -60.0 -70.0+ 0% 2% 4% 6% 8% 10% 12% 14% Discount Rate Figure 10.13 Effect of the discount rate on the difference in PV for the refurbishment of the existing pumps less that of replacing the pumps with new ones 20.0 100 0.0 PV(Existing-New) -10.00 -2004 -30.0 Refurbish Replace 40.04 -50.0 -60.0 -70.0 0% 6% 8% 10% 12% 14% Maintenance Inflation Figure 10.14 Effect of the rate of inflation of the maintenance items on the difference in PV for the refurbishment of the custing pumps less that of replacing the pumps with news If the rate of inflation of the maintenance costs is less than 3.9%, the refurbish ment of the units is recommended, and if the rate of inflation of the energy costs is higher then 6.3%.replacement of the units is recommended. 2.0 1.5 1.0 0.5 0.0 PV(Existing-New) -0.5 - 1.0 -1.5 Refurbish Replace -20 -2.5 0% 2% 6% 8% 10% 12% 14% Energy Inflation Figure 10.15 Effect of the rate of inflation of the energy prices on the difference in PV for the refurbishment of the existing pumps less that of replacing the pumps with new ones 10.7 Combine Harvester 10.6.4 Recommendation The decision is sensitive to the values for the discount rate, the maintenance inflation and the energy inflation. For the current set of values, the replacement of the units is recommended. However, this is a marginal decision, since the difference between the alternatives is slight