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Problem (8): A water pump, to be used by the city's maintenance department, costs $12,000
Problem (8): A water pump, to be used by the city's maintenance department, costs $12,000. Operating and maintenance costs are $700 in the first year, increasing by $400 per year thereafter. The salvage value of the pump is declining by 25% each year. MARR is 12%. How often should the pump be replaced if the expected service life is 10 years?
Expert Solution
It should be replaced in year 8 because then its EUAC is minimum at 4183. Before year 8 EUAC is declining so the pump is useful / cost effective
Firstly, you need to find the PV of annual cost using P/A notation
Next you find the PV of salvage value using P/F notation
Finally use NPV as the difference between PV of costs and PV salvage value
Now use A/P notation for EUAC. This is given by EUAC = (A/P, 12%, n) (NPV) for n = 1 to 10
| Year | Annual cost | Salvage value | PV of the annual cost | PV of the market value | Net present value | EUAC |
| 1 | 700 | 9000 | 625 | 8036 | 4589 | 5140 |
| 2 | 1100 | 6750 | 1502 | 5381 | 8121 | 4805 |
| 3 | 1500 | 5063 | 2570 | 3603 | 10966 | 4566 |
| 4 | 1900 | 3797 | 3777 | 2413 | 13364 | 4400 |
| 5 | 2300 | 2848 | 5082 | 1616 | 15466 | 4291 |
| 6 | 2700 | 2136 | 6450 | 1082 | 17368 | 4224 |
| 7 | 3100 | 1602 | 7852 | 725 | 19128 | 4191 |
| 8 | 3500 | 1201 | 9266 | 485 | 20781 | 4183 |
| 9 | 3900 | 901 | 10672 | 325 | 22347 | 4194 |
| 10 | 4300 | 676 | 12057 | 218 | 23839 | 4219 |
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