[15 Points] A lighting system is being designed for an outdoor sports field. There are two choices of lighting fixtures under consideration, each of which will give the same light output. A. Install 30 Metal Halide luminaries, each with a power consumption of 400 Watts. The cost of these fixtures is $450 each. B. Install 40 LED luminaries, each with a power consumption of 150 Watts. The cost of these fixtures is $725 each. Energy is priced at a cost of S0.09/kWh; the cost of money is 5% per year. The fixtures will be used for 2,000 hours per year. Use the Interest Tables attached as the last sheet of this Exam to determine the point in time (years) between which the more expensive fixture will actually be the most cost-effective choice. Compound Interest Factors Uniform Payment Series 5% 5% Single Payment Arithmetic Gradient Compound Amount Factor Present Sinking Fund Factor Capital Compound Amount Factor Present Gradient Gradient Recovery Factor Uniform Worth Factor Worth Factor Present Worth Series Find F Given P F/P Find P Find A Find A Given P A/P Find F Find P Find A Given A P/A Find P Given G P/G Given F Given F Given A Given G n P/F A/F F/A A/G 1.050 .9524 1.0000 1.0500 1.000 0.952 1.102 9070 4878 5378 2.050 1.859 0.488 0.907 1.158 .8638 3672 3.152 2.635 3 .3172 .2320 2.723 3.546 0.967 1.439 1.902 1.216 .8227 .2820 4.310 5.103 1.276 7835 1810 2310 5.526 4.329 8.237 5 6. 1.340 .7462 1470 .1970 6.802 5.076 2.358 5.786 6.463 I1.968 16,232 20.970 7 1.407 1.477 .7107 2.805 .1228 1047 .1728 1547 1407 8.142 9.549 .6768 3.244 11.027 12.578 6. 1.551 1.629 .6446 .6139 .0907 .0795 7.108 3.676 4.099 26.127 31.652 9. 10 10 1295 7.722 .0704 .0628 .0565 1.710 5847 1204 1128 11 14.207 8.306 4.514 37.499 11 8.863 9.394 9.899 12 1.796 5568 5303 .5051 15.917 4.922 43.624 12 1065 1010 49.988 56.553 13 1.886 17.713 13 5.321 5.713 14 1.980 .0510 19.599 14 15 2.079 4810 .0463 .0963 21.579 10.380 6.097 63.288 15 .0923 .0887 16 2.183 2.292 4581 4363 .0423 23.657 25.840 10.838 6.474 6.842 70.159 77.140 16 17 17 .0387 11.274 11.690 18 2.407 4155 .0355 .0855 28.132 7.203 84.204 18 .3957 .3769 .0827 19 20 2.527 2.653 .0327 .0302 30.539 33.066 12.085 12.462 7.557 7.903 91.327 98.488 19 20 .0802 8.242 8.573 8.897 21 2.786 3589 .0280 .0780 .0760 .0741 .0725 35.719 12.821 13.163 13.489 105.667 112.846 21 22 23 2.925 3.072 .3419 .0260 38.505 41.430 44.502 22 .0241 23 3256 .3101 .2953 120.008 24 3.225 .0225 13.799 9.214 127.140 24 25 3.386 .0210 .0710 47.727 14.094 9.524 134.227 25 3.556 3.733 .2812 2678 .0696 .0683 .0671 51.113 141.258 26 27 .0196 .0183 .0171 14.375 14.643 9.827 10.122 10.411 26 27 54.669 148.222 14,898 15.141 28 3.920 2551 58.402 155.110 28 29 30 4.116 4.322 .2429 .2314 .0160 .0660 62.323 66.439 10.694 161.912 168.622 29 30 0151 .0651 15.372 10.969 15.593 15.803 16.003 16.193 31 4.538 2204 0141 .0641 70.761 11.238 175.233 31 75.299 80.063 85.067 32 4.765 5.003 5.253 .2099 .1999 .1904 .0133 .0633 .0625 .0618 I1.501 181.739 32 11.757 12.006 33 .0125 188.135 33 34 34 .0118 194.416 1234 5 35 5.516 1813 0111 ,0611 90.320 16.374 12.250 200.580 35 40 45 7.040 8.985 .1420 .1113 .0872 .0683 .00828 .00626 .0583 .0563 120.799 17.159 17.774 13.377 14.364 229.545 40 45 159,699 255.314 .00478 .00367 .0548 .0537 .0528 50 11.467 209.347 18.256 15.223 15.966 16.606 277.914 50 14.636 55 60 272.711 353.582 18.633 297.510 55 60 18.679 .0535 .00283 18.929 314.343 19.161 19.343 65 23.840 .0419 00219 .0522 456.795 17.154 328.691 65 70 30.426 .0329 .00170 .0517 588.525 756.649 971.222 1 245.1 17.621 18.018 340.841 70 .00132 .00103 19.485 19.596 75 351.072 38.832 49.561 63.254 0258 .0202 .0158 .0513 .0510 .0508 75 80 18.353 18.635 359.646 80 85 .00080 19.684 366.800 85 .0506 90 95 80.730 103.034 90 95 .0124 00063 .00049 1594.6 2040.7 19.752 19.806 18.871 19.069 372.749 .0505 .0504 .00971 377.677 100 131.500 .00760 00038 2610.0 19.848 19.234 381.749 100