6. A property management company plans to replace the existing water pumps and has the choice of two options. Pump A has an expected life of 8 years. The initial cost is $100,000 and the annual Operation, Maintenance and Repair (OMR) cost is $10,000. This option has an expected additional energy cost of $240 per annum over the existing pumping system. An additional overhaul is required every 3 years at a cost of $15,000. The salvage value at the end of its life will be $5,000. Pump B has an expected life of 10 years. The initial cost is $125,000 and the annual Operation, Maintenance and Repair (OMR) cost is $9,500. This option has an expected energy saving of $360 per annum over the existing pumping system. An additional overhaul is required every 5 years at a cost of $20,000. The salvage value at the end of its life will be $3,500. Assuming that the annual discount rate is 9%, calculate (i) the annualised life cycle cost (ii) determine which option has the lower life cycle cost and (ii) list out the factor(s) affecting accuracy. (20 marks) Present Worth Factor (pwf) n periods 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 45 50 55 60 1 Present Worth Factor (pwf) pwf (1+i)" Discount Rate (1001) 5 6 7 8 9 10 12 15 20 0.97087 0.96154 0.95238 0.94340 0.93458 0.92593 0.91743 0.90909 0.89286 0.86957 0.83333 0.94260 0.92456 0.90703 0.89000 0.87344 0.85734 0.84168 0.82645 0.79719 0.75614 0.69444 0.91514 0.88900 0.86384 0.83962 0.81630 0.79383 0.77218 0.75131 0.71178 0.65752 0.57870) 0.88849 0.85480 0.82270 0.79209 0.76290 0.73503 0.70843 0.68301 0.63552 0.57175 0.48225 0.86261 0.82193 0.78353 0.74726 0.71299 0.68058 0.64993 0.62092 0.56743 0.49718 0.40188 0.83748 0.79031 0.74622 0.70496 0.66634 0.63017 0.59627 0.56447 0.50663 0.43233 0.33490 0.81309 0.75992 0.71068 0.66506 0.62275 0.58349 0.54703 0.51316 0.45235 0.37594 0.27908 0.78941 0.73069 0.67684 0.62741 0.58201 0.54027 0.50187 0.46651 0.40388 0.32690 0.23257 0.76642 0.70259 0.64461 0.59190 0.54393 0.50025 0.46043 0.42410 0.36061 0.28426 0.19381 0.74409 0.67556 0.61391 0.55839 0.50835 0.46319 0.42241 0.38554 0.32197 0.24718 0.16151 0.72242 0.64958 0.58468 0.52679 0.47509 0.42888 0.38753 0.35049 0.28748 0.21494 0.13459 0.70138 0.62460 0.55684 0.49697 0.44401 0.39711 0.35553 0.31863 0.25668 0.18691 0.11216 0.68095 0.60057 0.53032 0.46884 0.41496 0.36770 0.32618 0.28966 0.22917 0.16253 0.09346 0.66112 0.57748 0.50507 0.44230 0.38782 0.34046 0.29925 0.26333 0.20462 0.14133 0.07789 0.64186 0.55526 0.48102 0.41727 0.36245 0.31524 0.27454 0.23939 0.18270 0.12289 0.06491 0.62317 0.53391 0.45811 0.39365 0.33873 0.29189 0.25187 0.21763 0.16312 0.10686 0.05409 0.60502 0.51337 0.43630 0.37136 0.31657 0.27027 0.23107 0.19784 0.14564 0.09293 0.04507 0.58739 0.49363 0.41552 0.35034 0.29586 0.25025 0.21199 0.17986 0.13004 0.08081 0.03756 0.57029 0.47464 0.39573 0.33051 0.27651 0.23171 0.19449 0.16351 0.11611 0.07027 0.03130 0.55368 0.45639 0.37689 0.31180 0.25842 0.21455 0.17843 0.14864 0.10367 0.06110 0.02608 0.47761 0.37512 0.29530 0.23300 0.18425 0.14602 0.11597 0.09230 0.05882 0.03038 0.01048 0.41199 0.30832 0.23138 0.17411 0.13137 0.09938 0.07537 0.05731 0.03338 0.01510 0.00421 0.35538 0.25342 0.18129 0.13011 0.09366 0.06763 0.04899 0.03558 0.01894 0.00751 0.00169 0.30656 0.20829 0.14205 0.09722 0.06678 0.04603 0.03184 0.02209 0.01075 0.00373 0.00068 0.26444 0.17120 0.11130 0.07265 0.04761 0.03133 0.02069 0.01372 0.00610 0.00186 0.00027 0.22811 0.14071 0.08720 0.05429 0.03395 0.02132 0.01345 0.00852 0.00346 0.00092 0.00011 0.19677 0.11566 0.06833 0.04057 0.02420 0.01451 0.00874 0.00529 0.00196 0.00046 0.00004 0.16973 0.09506 0.05354 0.03031 0.01726 0.00988 0.00568 0.00328 0.00111 0.00023 0.00002 Uniform Series Present Worth Factor (uspwf) Uniform Series Present Worth Factor (uspwf) Discount Rate (= 100") 1-(1+i)" i n periods 3 4 5 6 7 8 9 10 12 15 20 1 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.8929 0.8696 0.8333 2 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.75911 1.7355 1.6901 1.6257 1.5278 3 2.8286 2.7751 2.7232 2.6730 2.6243 4 3.7171 3.6299 3.5460 3.4651 5 4.5797 6 5.4172 4.4518 5.2421 5.0757 4.3295 4.2124 4.9173 4.7665 2.5771 2.5313 2.4869 3.3872 3.3121 3.2397 3.1699 3.0373 4.1002 3.9927 3.8897 3.7908 3.6048 4.6229 4.4859 4.3553 4.1114 2.4018 2.2832 2.1065 2.8550 2.5887 3.3522 2.9906 3.7845 3.3255 7 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638 4.1604 3.6046 8 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676 4.4873 3.8372 9 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 10 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.7590 5.3282 4.7716 4.0310 5.6502 5.0188 4.1925 11 9.2526 8.7605 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 5.9377 5.2337 4.3271 12 9.9540 9.3851 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.1944 5.4206 4.4392 13 10.6350 9.9856 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.4235 5.5831 4.5327 14 11.2961 10.5631 9.8986 9.2950 8.7455 8.2442 7.7862 7.3667 6.6282 5.7245 4.6106 15 11.9379 11.1184 10.3797 9.7122 9.1079 8.5595 8.0607 7.6061 6.8109 16 12.5611 11.6523 10.8378 10.1059 9.4466 8.8514 8.3126 5.8474 4.6755 7.8237 6.9740 5.9542 4.7296 17 18 13.1661 12.1657 11.2741 10.4773 9.7632 13.7535 12.6593 11.6896 10.8276 10.0591 9.3719 9.1216 8.5436 8.7556 8.0216 8.2014 7.2497 7.1196 6.0472 4.7746 6.1280 4.8122 19 14.3238 13.1339 12.0853 11.1581 20 25 30 35 40 45 10.3356 9.6036 14.8775 13.5903 12.4622 11.4699 10.5940 9.8181 17.4131 15.6221 14.0939 12.7834 11.6536 10.6748 9.8226 19.6004 17.2920 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269 21.4872 18.6646 16.3742 14.4982 12.9477 11.6546 10.5668 9.6442 23.1148 19.7928 17.1591 15.0463 13.3317 11.9246 10.7574 9.7791 24.5187 20.7200 17.7741 15.4558 13.6055 12.1084 10.8812 9.8628 8.9501 9.1285 9.0770 8.2438 8.3649 7.3658 6.1982 4.8435 8.5136 7.4694 6.2593 4.8696 7.8431 6.4641 4.9476 8.0552 6.5660 4.9789 8.1755 6.6166 4.9915 6.6418 4.9966 8.2825 6.6543 4.9986 50 25.7298 21.4822 18.2559 15.7619 13.8007 12.2335 10.9617 9.9148 55 26.7744 22.1086 18.6335 15.9905 13.9399 12.3186 8.3045 6.6605 4.9995 60 27.6756 22.6235 18.9293 16.1614 14.0392 12.3766