The Biltmore Garage has lights in places that are difficult to reach. Management estimates that it costs about $2 to change a bulb. Standard 100-watt bulbs with an expected life of 1000 hours are now used. Standard bulbs cos $1. A long-life bulb that requires 90 watts for the same effective level of light is available. Long-life bulbs cost $3. The bulbs that are difficult to reach are in use for about 500 hours a month. Electricity costs $0.07/kilowatt-hour payable at the end of each month. Biltmore uses a 12 percent MARR (1 percent per month) for projects involving supplies. a. What minimum life for the long-life bulb would make it the lower cost option? b. If the cost of changing bulbs is ignored, what is the minimum life for the long-life bulb to be the lower cost alternative? c. If the solutions are obtained by linear interpolation of the capital recovery factor, will the approximations understate or overstate the required life? Click the icon to view the table of compound interest factors for discrete compounding periods when i = 1%. hours a. The minimum life that would make the long-life bulb the lower cost option is (Round to the nearest whole number as needed.) Compound interest factors for discrete compounding, discrete cash flows (i=1%) N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Single Payment Compound Present Amount Worth Factor Factor (F/P,1,N) (P/F,1,N) 1.0100 0.99010 1.0201 0.98030 1.0303 0.97059 1.0406 0.96098 1.0510 0.95147 1.0615 0.94205 1.0721 0.93272 1.0829 0.92348 1.0937 0.91434 1.1046 0.90529 1.1157 0.89632 1.1268 0.88745 1.1381 0.87866 1.1495 0.86996 Sinking Fund Factor (A/F,i,N) 1.00000 0.49751 0.33002 0.24628 0.19604 0.16255 0.13863 0.12069 0.10674 0.09558 0.08645 0.07885 0.07241 0.06690 Uniform Series Series Uniform Capital Present Series Recovery Worth Factor Factor Factor (FIA,1,N) (A/P,1,N) (PIA,1,N) 1.0000 1.0100 0.99010 2.0100 0.50751 1.9704 3.0301 0.34002 2.9410 4.0604 0.25628 3.9020 5.1010 0.20604 4.8534 6.1520 0.17255 5.7955 7.2135 0.14863 6.7282 8.2857 0.13069 7.6517 9.3685 0.11674 8.5660 10.462 0.10558 9.4713 11.567 0.09645 10.368 12.683 0.08885 11.255 13.809 0.08241 12.134 14.947 0.07690 13.004 Arithmetic Gradient Series Factor (A/G,1,N) 0.00000 0.49751 0.99337 1.4876 1.9801 2.4710 2.9602 3.4478 3.9337 4.4179 4.9005 5.3815 5.8607 6.3384 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2324 1.2447 1.2572 1.2697 1.2824 1.2953 1.3082 1.3213 1.3345 1.3478 1.3613 1.3749 1.3887 1.4026 0.86135 0.85282 0.84438 0.83602 0.82774 0.81954 0.81143 0.80340 0.79544 0.78757 0.77977 0.77205 0.76440 0.75684 0.74934 0.74192 0.73458 0.72730 0.72010 0.71297 nrnrnd 0.06212 0.05794 0.05426 0.05098 0.04805 0.04542 0.04303 0.04086 0.03889 0.03707 0.03541 0.03387 0.03245 0.03112 0.02990 0.02875 0.02768 0.02667 0.02573 0.02484 16.097 17.258 18.430 19.615 20.811 22.019 23.239 24.472 25.716 26.973 28.243 29.526 30.821 32.129 33.450 34.785 36.133 37.494 38.869 40.258 0.07212 0.06794 0.06426 0.06098 0.05805 0.05542 0.05303 0.05086 0.04889 0.04707 0.04541 0.04387 0.04245 0.04112 0.03990 0.03875 0.03768 0.03667 0.03573 0.03484 annana 13.865 14.718 15.562 16.398 17.226 18.046 18.857 19.660 20.456 21.243 22.023 22.795 23.560 24.316 25.066 25.808 26.542 27.270 27.990 28.703 i Ann 6.8143 7.2886 7.7613 8.2323 8.7017 9.1694 9.6354 10.100 10.563 11.024 11.483 11.941 12.397 12.852 13.304 13.756 14.205 14.653 15.099 15.544 nnnn Ann 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2324 1.2447 1.2572 1.2697 1.2824 1.2953 1.3082 1.3213 1.3345 1.3478 1.3613 1.3749 1.3887 1.4026 0.86135 0.85282 0.84438 0.83602 0.82774 0.81954 0.81143 0.80340 0.79544 0.78757 0.77977 0.77205 0.76440 0.75684 0.74934 0.74192 0.73458 0.72730 0.72010 0.71297 nrnrnd 0.06212 0.05794 0.05426 0.05098 0.04805 0.04542 0.04303 0.04086 0.03889 0.03707 0.03541 0.03387 0.03245 0.03112 0.02990 0.02875 0.02768 0.02667 0.02573 0.02484 16.097 17.258 18.430 19.615 20.811 22.019 23.239 24.472 25.716 26.973 28.243 29.526 30.821 32.129 33.450 34.785 36.133 37.494 38.869 40.258 0.07212 0.06794 0.06426 0.06098 0.05805 0.05542 0.05303 0.05086 0.04889 0.04707 0.04541 0.04387 0.04245 0.04112 0.03990 0.03875 0.03768 0.03667 0.03573 0.03484 annana 13.865 14.718 15.562 16.398 17.226 18.046 18.857 19.660 20.456 21.243 22.023 22.795 23.560 24.316 25.066 25.808 26.542 27.270 27.990 28.703 i Ann 6.8143 7.2886 7.7613 8.2323 8.7017 9.1694 9.6354 10.100 10.563 11.024 11.483 11.941 12.397 12.852 13.304 13.756 14.205 14.653 15.099 15.544 nnnn Ann 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.3345 1.3478 1.3613 1.3749 1.3887 1.4026 1.4166 1.4889 1.5648 1.6446 1.7285 1.8167 1.9094 2.0068 2.1091 2.2167 2.3298 2.4486 2.5735 2.7048 0.74934 0.74192 0.73458 0.72730 0.72010 0.71297 0.70591 0.67165 0.63905 0.60804 0.57853 0.55045 0.52373 0.49831 0.47413 0.45112 0.42922 0.40839 0.38857 0.36971 0.02990 0.02875 0.02768 0.02667 0.02573 0.02484 0.02400 0.02046 0.01771 0.01551 0.01373 0.01224 0.01100 0.00993 0.00902 0.00822 0.00752 0.00690 0.00636 0.00587 33.450 34.785 36.133 37.494 38.869 40.258 41.660 48.886 56.481 64.463 72.852 81.670 90.937 100.68 110.91 121.67 132.98 144.86 157.35 170.48 0.03990 0.03875 0.03768 0.03667 0.03573 0.03484 0.03400 0.03046 0.02771 0.02551 0.02373 0.02224 0.02100 0.01993 0.01902 0.01822 0.01752 0.01690 0.01636 0.01587 25.066 25.808 26.542 27.270 27.990 28.703 29.409 32.835 36.095 39.196 42. 147 44.955 47.627 50.169 52.587 54.888 57.078 59.161 61.143 63.029 13.304 13.756 14.205 14.653 15.099 15.544 15.987 18.178 20.327 22.436 24.505 26.533 28.522 30.470 32.379 34.249 36.080 37.872 39.626 41.343 The Biltmore Garage has lights in places that are difficult to reach. Management estimates that it costs about $2 to change a bulb. Standard 100-watt bulbs with an expected life of 1000 hours are now used. Standard bulbs cos $1. A long-life bulb that requires 90 watts for the same effective level of light is available. Long-life bulbs cost $3. The bulbs that are difficult to reach are in use for about 500 hours a month. Electricity costs $0.07/kilowatt-hour payable at the end of each month. Biltmore uses a 12 percent MARR (1 percent per month) for projects involving supplies. a. What minimum life for the long-life bulb would make it the lower cost option? b. If the cost of changing bulbs is ignored, what is the minimum life for the long-life bulb to be the lower cost alternative? c. If the solutions are obtained by linear interpolation of the capital recovery factor, will the approximations understate or overstate the required life? Click the icon to view the table of compound interest factors for discrete compounding periods when i = 1%. hours a. The minimum life that would make the long-life bulb the lower cost option is (Round to the nearest whole number as needed.) Compound interest factors for discrete compounding, discrete cash flows (i=1%) N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Single Payment Compound Present Amount Worth Factor Factor (F/P,1,N) (P/F,1,N) 1.0100 0.99010 1.0201 0.98030 1.0303 0.97059 1.0406 0.96098 1.0510 0.95147 1.0615 0.94205 1.0721 0.93272 1.0829 0.92348 1.0937 0.91434 1.1046 0.90529 1.1157 0.89632 1.1268 0.88745 1.1381 0.87866 1.1495 0.86996 Sinking Fund Factor (A/F,i,N) 1.00000 0.49751 0.33002 0.24628 0.19604 0.16255 0.13863 0.12069 0.10674 0.09558 0.08645 0.07885 0.07241 0.06690 Uniform Series Series Uniform Capital Present Series Recovery Worth Factor Factor Factor (FIA,1,N) (A/P,1,N) (PIA,1,N) 1.0000 1.0100 0.99010 2.0100 0.50751 1.9704 3.0301 0.34002 2.9410 4.0604 0.25628 3.9020 5.1010 0.20604 4.8534 6.1520 0.17255 5.7955 7.2135 0.14863 6.7282 8.2857 0.13069 7.6517 9.3685 0.11674 8.5660 10.462 0.10558 9.4713 11.567 0.09645 10.368 12.683 0.08885 11.255 13.809 0.08241 12.134 14.947 0.07690 13.004 Arithmetic Gradient Series Factor (A/G,1,N) 0.00000 0.49751 0.99337 1.4876 1.9801 2.4710 2.9602 3.4478 3.9337 4.4179 4.9005 5.3815 5.8607 6.3384 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2324 1.2447 1.2572 1.2697 1.2824 1.2953 1.3082 1.3213 1.3345 1.3478 1.3613 1.3749 1.3887 1.4026 0.86135 0.85282 0.84438 0.83602 0.82774 0.81954 0.81143 0.80340 0.79544 0.78757 0.77977 0.77205 0.76440 0.75684 0.74934 0.74192 0.73458 0.72730 0.72010 0.71297 nrnrnd 0.06212 0.05794 0.05426 0.05098 0.04805 0.04542 0.04303 0.04086 0.03889 0.03707 0.03541 0.03387 0.03245 0.03112 0.02990 0.02875 0.02768 0.02667 0.02573 0.02484 16.097 17.258 18.430 19.615 20.811 22.019 23.239 24.472 25.716 26.973 28.243 29.526 30.821 32.129 33.450 34.785 36.133 37.494 38.869 40.258 0.07212 0.06794 0.06426 0.06098 0.05805 0.05542 0.05303 0.05086 0.04889 0.04707 0.04541 0.04387 0.04245 0.04112 0.03990 0.03875 0.03768 0.03667 0.03573 0.03484 annana 13.865 14.718 15.562 16.398 17.226 18.046 18.857 19.660 20.456 21.243 22.023 22.795 23.560 24.316 25.066 25.808 26.542 27.270 27.990 28.703 i Ann 6.8143 7.2886 7.7613 8.2323 8.7017 9.1694 9.6354 10.100 10.563 11.024 11.483 11.941 12.397 12.852 13.304 13.756 14.205 14.653 15.099 15.544 nnnn Ann 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2324 1.2447 1.2572 1.2697 1.2824 1.2953 1.3082 1.3213 1.3345 1.3478 1.3613 1.3749 1.3887 1.4026 0.86135 0.85282 0.84438 0.83602 0.82774 0.81954 0.81143 0.80340 0.79544 0.78757 0.77977 0.77205 0.76440 0.75684 0.74934 0.74192 0.73458 0.72730 0.72010 0.71297 nrnrnd 0.06212 0.05794 0.05426 0.05098 0.04805 0.04542 0.04303 0.04086 0.03889 0.03707 0.03541 0.03387 0.03245 0.03112 0.02990 0.02875 0.02768 0.02667 0.02573 0.02484 16.097 17.258 18.430 19.615 20.811 22.019 23.239 24.472 25.716 26.973 28.243 29.526 30.821 32.129 33.450 34.785 36.133 37.494 38.869 40.258 0.07212 0.06794 0.06426 0.06098 0.05805 0.05542 0.05303 0.05086 0.04889 0.04707 0.04541 0.04387 0.04245 0.04112 0.03990 0.03875 0.03768 0.03667 0.03573 0.03484 annana 13.865 14.718 15.562 16.398 17.226 18.046 18.857 19.660 20.456 21.243 22.023 22.795 23.560 24.316 25.066 25.808 26.542 27.270 27.990 28.703 i Ann 6.8143 7.2886 7.7613 8.2323 8.7017 9.1694 9.6354 10.100 10.563 11.024 11.483 11.941 12.397 12.852 13.304 13.756 14.205 14.653 15.099 15.544 nnnn Ann 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.3345 1.3478 1.3613 1.3749 1.3887 1.4026 1.4166 1.4889 1.5648 1.6446 1.7285 1.8167 1.9094 2.0068 2.1091 2.2167 2.3298 2.4486 2.5735 2.7048 0.74934 0.74192 0.73458 0.72730 0.72010 0.71297 0.70591 0.67165 0.63905 0.60804 0.57853 0.55045 0.52373 0.49831 0.47413 0.45112 0.42922 0.40839 0.38857 0.36971 0.02990 0.02875 0.02768 0.02667 0.02573 0.02484 0.02400 0.02046 0.01771 0.01551 0.01373 0.01224 0.01100 0.00993 0.00902 0.00822 0.00752 0.00690 0.00636 0.00587 33.450 34.785 36.133 37.494 38.869 40.258 41.660 48.886 56.481 64.463 72.852 81.670 90.937 100.68 110.91 121.67 132.98 144.86 157.35 170.48 0.03990 0.03875 0.03768 0.03667 0.03573 0.03484 0.03400 0.03046 0.02771 0.02551 0.02373 0.02224 0.02100 0.01993 0.01902 0.01822 0.01752 0.01690 0.01636 0.01587 25.066 25.808 26.542 27.270 27.990 28.703 29.409 32.835 36.095 39.196 42. 147 44.955 47.627 50.169 52.587 54.888 57.078 59.161 61.143 63.029 13.304 13.756 14.205 14.653 15.099 15.544 15.987 18.178 20.327 22.436 24.505 26.533 28.522 30.470 32.379 34.249 36.080 37.872 39.626 41.343