[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 $0.09/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. 5% 5% n n 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 6 7 8 9 10 11 12 13 14 15 Single Payment Compound Present Amount Worth Factor Factor Find F Find P Given P Given F F/P P/F 1.050 9524 1.102 9070 1.158 .8638 1.216 .8227 1.276 .7835 1.340 .7462 1.407 7107 1.477 .6768 1.551 .6446 1.629 .6139 1.710 -5847 1.796 .5568 1.886 -5303 1.980 .5051 2.079 4810 2.183 .4581 2.292 .4363 2.407 4155 2.527 .3957 2.653 .3769 2.786 .3589 2.925 .3419 3,072 -3256 3.225 .3101 3.386 .2953 3.556 .2812 3.733 2678 3.920 2551 4.116 .2429 4.322 .2314 4.538 .2204 4.765 .2099 5.003 .1999 5.253 .1904 -1065 Compound Interest Factors Uniform Payment Series Capital Compound Recovery Amount Factor Factor Find A Find F Given P Given A A/P F/A 1.0500 1.000 .5378 2.050 .3672 3.152 .2820 4.310 .2310 5.526 .1970 6.802 .1728 8.142 .1547 9.549 .1407 11.027 .1295 12.578 .1204 14.207 .1128 15.917 17.713 .1010 19.599 .0963 21.579 .0923 23.657 .0887 25.840 .0855 28.132 .0827 30.539 .0802 33.066 .0780 35.719 .0760 38.505 .0741 41.430 .0725 44.502 .0710 47.727 .0696 51.113 .0683 54.669 .0671 58.402 .0660 62.323 .0651 66.439 .0641 70.761 .0633 75.299 .0625 80.063 .0618 85.067 Sinking Fund Factor Find A Given F A/F 1.0000 .4878 .3172 .2320 .1810 .1470 .1228 .1047 .0907 .0795 .0704 .0628 .0565 .0510 .0463 .0423 .0387 .0355 .0327 .0302 .0280 .0260 0241 .0225 .0210 .0196 .0183 .0171 .0160 20151 .0141 .0133 .0125 .0118 Present Worth Factor Find P Given A P/A 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 9.899 10.380 10.838 11.274 11.690 12.085 12.462 12.821 13.163 13.489 13.799 14.094 14.375 14.643 14.898 15.141 15.372 15.593 15.803 16.003 16.193 Arithmetic Gradient Gradient Gradient Uniform Present Series Worth Find A Find P Given G Given G A/G P/G 0 0 0.488 0.907 0.967 2.635 1.439 5.103 1.902 8.237 2.358 11.968 2.805 16.232 3.244 20.970 3.676 26.127 4.099 31.652 4.514 37.499 4.922 43.624 5.321 49.988 5.713 56.553 6.097 63.288 6.474 70.159 6.842 77.140 7.203 84.204 7.557 91.327 7.903 98.488 8.242 105.667 8.573 112.846 8.897 120.008 9.214 127.140 9.524 134.227 9.827 141.258 10.122 148.222 10.411 155.110 10.694 161.912 10.969 168.622 11.238 175.233 11.501 181.739 11.757 188.135 12.006 194.416 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 15 35 40 45 5516 7.40 8.985 || 467 14.65 18.679 23.84) 30426 38.832 9.56] 63.254 200581) 229.45 255.314 277914 2975100 14.34 55 d) 5 70 1813 14200 1113 0877 IMG.B1 0535 0419 0329 105258 0202 15% 0124 (TWD97] 00760 III 00828 2010626 00478 (010307 00283 00219 00170 20132 00 103 CUMABI) (TMD63 (17MM9 2018038 0611 0583 10563 0548 0537 0528 0522 0517 1513 05 10 15108 2015/hr 1505 0504 0371) | 20.799 10. 6634) 2009.347 272.711 353.582 456.705 588.525 756.49 971222 1245.1 1594.6 20140.7 2610.0 16374 17.19 17.774 18.156 18.6.35 18.920 19.16L 19.343 19.485 195415 19.68] 19.752 19.8065 19.848 12.150 13.377 14.34 15.223 15 its 15. fly; 17.154 17.621 18.148 18.353 18.1635 18.871 19.069 19.234 45 0 55 6) 65 7) 75 80 85 75 328.691 340.841 35.1.172 359,646 3finio. 800) 172.740) 377.677 81.749 80 B5 11) 15 1000 180.70 103.034 131.500 95 100 [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 $0.09/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. 5% 5% n n 1 2 3 4 5 1 2 3 4 5 6 7 8 9 10 6 7 8 9 10 11 12 13 14 15 Single Payment Compound Present Amount Worth Factor Factor Find F Find P Given P Given F F/P P/F 1.050 9524 1.102 9070 1.158 .8638 1.216 .8227 1.276 .7835 1.340 .7462 1.407 7107 1.477 .6768 1.551 .6446 1.629 .6139 1.710 -5847 1.796 .5568 1.886 -5303 1.980 .5051 2.079 4810 2.183 .4581 2.292 .4363 2.407 4155 2.527 .3957 2.653 .3769 2.786 .3589 2.925 .3419 3,072 -3256 3.225 .3101 3.386 .2953 3.556 .2812 3.733 2678 3.920 2551 4.116 .2429 4.322 .2314 4.538 .2204 4.765 .2099 5.003 .1999 5.253 .1904 -1065 Compound Interest Factors Uniform Payment Series Capital Compound Recovery Amount Factor Factor Find A Find F Given P Given A A/P F/A 1.0500 1.000 .5378 2.050 .3672 3.152 .2820 4.310 .2310 5.526 .1970 6.802 .1728 8.142 .1547 9.549 .1407 11.027 .1295 12.578 .1204 14.207 .1128 15.917 17.713 .1010 19.599 .0963 21.579 .0923 23.657 .0887 25.840 .0855 28.132 .0827 30.539 .0802 33.066 .0780 35.719 .0760 38.505 .0741 41.430 .0725 44.502 .0710 47.727 .0696 51.113 .0683 54.669 .0671 58.402 .0660 62.323 .0651 66.439 .0641 70.761 .0633 75.299 .0625 80.063 .0618 85.067 Sinking Fund Factor Find A Given F A/F 1.0000 .4878 .3172 .2320 .1810 .1470 .1228 .1047 .0907 .0795 .0704 .0628 .0565 .0510 .0463 .0423 .0387 .0355 .0327 .0302 .0280 .0260 0241 .0225 .0210 .0196 .0183 .0171 .0160 20151 .0141 .0133 .0125 .0118 Present Worth Factor Find P Given A P/A 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 9.899 10.380 10.838 11.274 11.690 12.085 12.462 12.821 13.163 13.489 13.799 14.094 14.375 14.643 14.898 15.141 15.372 15.593 15.803 16.003 16.193 Arithmetic Gradient Gradient Gradient Uniform Present Series Worth Find A Find P Given G Given G A/G P/G 0 0 0.488 0.907 0.967 2.635 1.439 5.103 1.902 8.237 2.358 11.968 2.805 16.232 3.244 20.970 3.676 26.127 4.099 31.652 4.514 37.499 4.922 43.624 5.321 49.988 5.713 56.553 6.097 63.288 6.474 70.159 6.842 77.140 7.203 84.204 7.557 91.327 7.903 98.488 8.242 105.667 8.573 112.846 8.897 120.008 9.214 127.140 9.524 134.227 9.827 141.258 10.122 148.222 10.411 155.110 10.694 161.912 10.969 168.622 11.238 175.233 11.501 181.739 11.757 188.135 12.006 194.416 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 15 35 40 45 5516 7.40 8.985 || 467 14.65 18.679 23.84) 30426 38.832 9.56] 63.254 200581) 229.45 255.314 277914 2975100 14.34 55 d) 5 70 1813 14200 1113 0877 IMG.B1 0535 0419 0329 105258 0202 15% 0124 (TWD97] 00760 III 00828 2010626 00478 (010307 00283 00219 00170 20132 00 103 CUMABI) (TMD63 (17MM9 2018038 0611 0583 10563 0548 0537 0528 0522 0517 1513 05 10 15108 2015/hr 1505 0504 0371) | 20.799 10. 6634) 2009.347 272.711 353.582 456.705 588.525 756.49 971222 1245.1 1594.6 20140.7 2610.0 16374 17.19 17.774 18.156 18.6.35 18.920 19.16L 19.343 19.485 195415 19.68] 19.752 19.8065 19.848 12.150 13.377 14.34 15.223 15 its 15. fly; 17.154 17.621 18.148 18.353 18.1635 18.871 19.069 19.234 45 0 55 6) 65 7) 75 80 85 75 328.691 340.841 35.1.172 359,646 3finio. 800) 172.740) 377.677 81.749 80 B5 11) 15 1000 180.70 103.034 131.500 95 100