University of California, Merced ENGR 155: Engineering Economic Analysis Final Exam - Summer 2022 Name: UCM ID: Part I: ----------------------------------------- /10 Part II: ---------------------------------------- /10 Part III: ---------------------------------------- /30 Total: ------------------------------------------ /50 Exam Time: 5:30 PM - 7:20 PM Submission Time: 7:20 PM - 7:35 PM Submission Time with 15% penalty: 7:35 PM - 7:45 PM Calculator policy To protect the integrity of exams, The following calculator models are the only ones acceptable for use during the exams: Casio: All fx-115 and fx-991 models (Any Casio calculator must have “fx-115” or “fx-991” in its model name.) Hewlett Packard: The HP 33s and HP 35s models, but no others Texas Instruments: All TI-30X and TI-36X models (Any Texas Instruments calculator must have “TI-30X” or “TI-36X” in its model name.) Uploading exam to Catcourse You will have 15 min to upload the exam back to Catcourse midterm submission folder. If you submit after 7:35 pm but before 7:45 pm, 15% of grade penalty will be applied. After 7:45 pm, your exam will not be accepted. Email submissions will not be accepted for grading. Part – I: Multiple-choice Questions (No Partial Credit) Each Multiple-choice question worth 2 points 1. Depreciation is the reduction in purchase value of a tangible business asset over its useful life due to the following reasons. Select all that apply. A) Age B) Wear C) Deterioration D) Obsolescence 2. An earthwork contractor installed a water main that was completed in March 2018 with an actual project cost of $1250/LF. A similar project is being bid in June 2021. The contractor’s estimate using an annual construction inflation factor of 3.5% is most nearly. A) $1,398/LF B) $1,420/LF C) $1,278/LF D) $1,447/LF 3. The construction of a new Indian restaurant in Merced requires the property development firm to pay the municipality the cost to expand its sewage treatment plant. In addition to the expansion costs, the developer must pay $120,000 annually toward the plant operating costs. The developer plans to finance the annual costs by placing money into a fund that earns 10% per year to pay its share of the plant operating cost forever. The amount to the fund is most nearly. A) $120,000 B) $1,200,000 C) $625,000 D) None 4. Given the following, calculate the third-year book value using straight-line depreciation? Cost basis of the asset = $12000; Useful life = 5 years; Estimated salvage value = $4,000 A) $7,200 B) $10,400 C) $8,800 D) $5,600 5. A distribution center purchased an equipment for $100,000 and has depreciated the equipment using the MACRS depreciation schedule as a 7-year property. The operating income in year 2 was $200,000 and the expenses were $87,000. If the company is in the 40% income tax bracket, determine the income tax in year 2 A) $87,520 B) $48,545 C) $35,404 D) $57840 Part - II: Fill-in-the-blank Questions (No Partial Credit) Each Fill-in-the blank question worth 2 points 6. Excel functions to be used for the following methods. a) Straight Line: _________________ b) Double Declining Balance: ______________ c) Sum of Years Digits: _______________ d) Variable Declining Balance: _____________ 7. For simplicity, assume that Engineered Industries will not pay dividends in 2018 and did not sell any capital equipment. It did purchase $965,000 in capital equipment. Total fixed assets in dollars _____________________at the end of 2018. 8. Book value is the value of an asset that measures the influence of _________________ 9. The financial data below for Tech Engineering in 2016. Determine the working capital for the company is_______________________ & Current ratio is ____________________ Category Dollar Amount Cash $800,000 Account receivable $1,000,000 Inventories $600,000 Intangibles $100,000 Accounts payable $650,000 Accrued Expenses $180,000 10. Find the expected EUAW from the financial data provided in the table for a new equipment. Because of the uncertainty of technology being used in this equipment, it has not been possible to get the initial cost accurately. The annual benefit, however, is estimated to be $25,000 with a possible equipment life of 5 years. The salvage value is expected to be 10% of the initial cost. MARR =8% Expected EUAW is ____________________ First Cost, $ $60,000 $80,000 $100,000 $120,000 Probability 0.25 0.35 0.30 0.10 PART – III: Problem Solving Questions (Have Partial Credit) Problem # 11 through 15, don't use excel to solve the problems 11. A project has the following cost, benefit data, and life probability distribution. Compute the conventional B/C ratio using the expected EUAC. (10 Points) Initial Cost = $15M Annual O&M Cost = $500K Annual Benefit = $4M MARR = 8% Life 7 8 9 Probability 0.20 0.50 0.30 12. A company that manufactures food and beverages in the vending industry has purchased some handling equipment that cost $70,000 and will be depreciated using 3-year MACRS. Show in a table the yearly depreciation amount and book value of the asset over its depreciable life. (5 Points) 13. Florida Construction Equipment Rentals (FCER) purchases a new 12,000-pound-rated crane for rental to its customers. This crane costs $1,125,000 and is expected to last for 25 years, at which time it will have an expected salvage value of $150,000. FCER earns $200,000 before-tax cash flow each year in rental income from this crane, and its total taxable income each year is between $10,000,000 and $15,000,000. If FCER uses straight-line depreciation and a MARR of 15%, what is the present worth of the after -tax cash flow for this equipment? Should the crane invest in this crane? (5 Points) Use tax rate as 35% 14. Samantha receives a starting salary offer of $105,000 for Year 1. If inflation is 5% each year, what must her salary to be to have the same purchasing power in Year 5, Year 10, Year 15, Year 20? (5 Points) 15. Compute the equivalent annual inflation rate based on the Consumer Price Index, for the period from 1990 to 2017? (5 Points) Book Value = Asset cost – Depreciation charges made to date Straight – line depreciation Double declining balance (DDB) πππ πππππππππ‘πππ ππ πππ¦ π¦πππ = πππππ’ππ‘πππ πππ π¦πππ (π΅ − π) πππ‘ππ πππππ‘πππ πππππ’ππ‘πππ Combined incremental tax rate = οState tax rate + (οFederal tax rate) (1 - οState tax rate) βΌ Taxable income = Before-tax cash flow − Depreciation βΌ Income taxes = Taxable income × Incremental tax rate βΌ After-tax cash flow = Before-tax cash flow − Income taxes (1 + i) = (1 + i′) (1 + f) i = i′ + f +(i′) (f) π΄πππ’ππ % πππππππ ππ = πΌππππ₯π − πΌππππ₯π−1 × 100 πΌππππ₯π−1 Assets = Liabilities + Equity Working Capital = Current assets – Current liabilities 608 APPENDIX C: COMPOUND INTEREST TABLES 5% Compound Interest Factors Single Payment 5% Uniform Payment Series Compound Amount Factor Find F Given P F/P Present Worth Factor Find P Given F P/F 1 2 3 4 5 1.050 1.102 1.158 1.216 1.276 .9524 .9070 .8638 .8227 .7835 1.0000 .4878 .3172 .2320 .1810 1.0500 .5378 .3672 .2820 .2310 1.000 2.050 3.152 4.310 5.526 0.952 1.859 2.723 3.546 4.329 0 0.488 0.967 1.439 1.902 0 0.907 2.635 5.103 8.237 1 2 3 4 5 6 7 8 9 10 1.340 1.407 1.477 1.551 1.629 .7462 .7107 .6768 .6446 .6139 .1470 .1228 .1047 .0907 .0795 .1970 .1728 .1547 .1407 .1295 6.802 8.142 9.549 11.027 12.578 5.076 5.786 6.463 7.108 7.722 2.358 2.805 3.244 3.676 4.099 11.968 16.232 20.970 26.127 31.652 6 7 8 9 10 11 12 13 14 15 1.710 1.796 1.886 1.980 2.079 .5847 .5568 .5303 .5051 .4810 .0704 .0628 .0565 .0510 .0463 .1204 .1128 .1065 .1010 .0963 14.207 15.917 17.713 19.599 21.579 8.306 8.863 9.394 9.899 10.380 4.514 4.922 5.321 5.713 6.097 37.499 43.624 49.988 56.553 63.288 11 12 13 14 15 16 17 18 19 20 2.183 2.292 2.407 2.527 2.653 .4581 .4363 .4155 .3957 .3769 .0423 .0387 .0355 .0327 .0302 .0923 .0887 .0855 .0827 .0802 23.657 25.840 28.132 30.539 33.066 10.838 11.274 11.690 12.085 12.462 6.474 6.842 7.203 7.557 7.903 70.159 77.140 84.204 91.327 98.488 16 17 18 19 20 21 22 23 24 25 2.786 2.925 3.072 3.225 3.386 .3589 .3419 .3256 .3101 .2953 .0280 .0260 .0241 .0225 .0210 .0780 .0760 .0741 .0725 .0710 35.719 38.505 41.430 44.502 47.727 12.821 13.163 13.489 13.799 14.094 8.242 8.573 8.897 9.214 9.524 105.667 112.846 120.008 127.140 134.227 21 22 23 24 25 26 27 28 29 30 3.556 3.733 3.920 4.116 4.322 .2812 .2678 .2551 .2429 .2314 .0196 .0183 .0171 .0160 .0151 .0696 .0683 .0671 .0660 .0651 51.113 54.669 58.402 62.323 66.439 14.375 14.643 14.898 15.141 15.372 9.827 10.122 10.411 10.694 10.969 141.258 148.222 155.110 161.912 168.622 26 27 28 29 30 31 32 33 34 35 4.538 4.765 5.003 5.253 5.516 .2204 .2099 .1999 .1904 .1813 .0141 .0133 .0125 .0118 .0111 .0641 .0633 .0625 .0618 .0611 70.761 75.299 80.063 85.067 90.320 15.593 15.803 16.003 16.193 16.374 11.238 11.501 11.757 12.006 12.250 175.233 181.739 188.135 194.416 200.580 31 32 33 34 35 40 45 50 55 60 7.040 8.985 11.467 14.636 18.679 .1420 .1113 .0872 .0683 .0535 .00828 .00626 .00478 .00367 .00283 .0583 .0563 .0548 .0537 .0528 120.799 159.699 209.347 272.711 353.582 17.159 17.774 18.256 18.633 18.929 13.377 14.364 15.223 15.966 16.606 229.545 255.314 277.914 297.510 314.343 40 45 50 55 60 65 70 75 80 85 23.840 30.426 38.832 49.561 63.254 .0419 .0329 .0258 .0202 .0158 .00219 .00170 .00132 .00103 .00080 .0522 .0517 .0513 .0510 .0508 456.795 588.525 756.649 971.222 1 245.1 19.161 19.343 19.485 19.596 19.684 17.154 17.621 18.018 18.353 18.635 328.691 340.841 351.072 359.646 366.800 65 70 75 80 85 90 95 100 80.730 103.034 131.500 .0124 .00971 .00760 .00063 .00049 .00038 .0506 .0505 .0504 1 594.6 2 040.7 2 610.0 19.752 19.806 19.848 18.871 19.069 19.234 372.749 377.677 381.749 90 95 100 n Sinking Fund Factor Find A Given F A/F Capital Recovery Factor Find A Given P A/P Compound Amount Factor Find F Given A F/A Arithmetic Gradient Present Worth Factor Find P Given A P/A Gradient Uniform Series Find A Given G A/G Gradient Present Worth Find P Given G P/G n APPENDIX C: COMPOUND INTEREST TABLES 8% Compound Interest Factors Single Payment 8% Uniform Payment Series Present Worth Factor Find P Given F P/F 1 2 3 4 5 1.080 1.166 1.260 1.360 1.469 .9259 .8573 .7938 .7350 .6806 1.0000 .4808 .3080 .2219 .1705 1.0800 .5608 .3880 .3019 .2505 1.000 2.080 3.246 4.506 5.867 0.926 1.783 2.577 3.312 3.993 0 0.481 0.949 1.404 1.846 0 0.857 2.445 4.650 7.372 1 2 3 4 5 6 7 8 9 10 1.587 1.714 1.851 1.999 2.159 .6302 .5835 .5403 .5002 .4632 .1363 .1121 .0940 .0801 .0690 .2163 .1921 .1740 .1601 .1490 7.336 8.923 10.637 12.488 14.487 4.623 5.206 5.747 6.247 6.710 2.276 2.694 3.099 3.491 3.871 10.523 14.024 17.806 21.808 25.977 6 7 8 9 10 11 12 13 14 15 2.332 2.518 2.720 2.937 3.172 .4289 .3971 .3677 .3405 .3152 .0601 .0527 .0465 .0413 .0368 .1401 .1327 .1265 .1213 .1168 16.645 18.977 21.495 24.215 27.152 7.139 7.536 7.904 8.244 8.559 4.240 4.596 4.940 5.273 5.594 30.266 34.634 39.046 43.472 47.886 11 12 13 14 15 16 17 18 19 20 3.426 3.700 3.996 4.316 4.661 .2919 .2703 .2502 .2317 .2145 .0330 .0296 .0267 .0241 .0219 .1130 .1096 .1067 .1041 .1019 30.324 33.750 37.450 41.446 45.762 8.851 9.122 9.372 9.604 9.818 5.905 6.204 6.492 6.770 7.037 52.264 56.588 60.843 65.013 69.090 16 17 18 19 20 21 22 23 24 25 5.034 5.437 5.871 6.341 6.848 .1987 .1839 .1703 .1577 .1460 .0198 .0180 .0164 .0150 .0137 .0998 .0980 .0964 .0950 .0937 50.423 55.457 60.893 66.765 73.106 10.017 10.201 10.371 10.529 10.675 7.294 7.541 7.779 8.007 8.225 73.063 76.926 80.673 84.300 87.804 21 22 23 24 25 26 27 28 29 30 7.396 7.988 8.627 9.317 10.063 .1352 .1252 .1159 .1073 .0994 .0125 .0114 .0105 .00962 .00883 .0925 .0914 .0905 .0896 .0888 79.954 87.351 95.339 103.966 113.283 10.810 10.935 11.051 11.158 11.258 8.435 8.636 8.829 9.013 9.190 91.184 94.439 97.569 100.574 103.456 26 27 28 29 30 31 32 33 34 35 10.868 11.737 12.676 13.690 14.785 .0920 .0852 .0789 .0730 .0676 .00811 .00745 .00685 .00630 .00580 .0881 .0875 .0869 .0863 .0858 123.346 134.214 145.951 158.627 172.317 11.350 11.435 11.514 11.587 11.655 9.358 9.520 9.674 9.821 9.961 106.216 108.858 111.382 113.792 116.092 31 32 33 34 35 40 45 50 55 60 21.725 31.920 46.902 68.914 101.257 .0460 .0313 .0213 .0145 .00988 .00386 .00259 .00174 .00118 .00080 .0839 .0826 .0817 .0812 .0808 259.057 386.506 573.771 848.925 1 253.2 11.925 12.108 12.233 12.319 12.377 10.570 11.045 11.411 11.690 11.902 126.042 133.733 139.593 144.006 147.300 40 45 50 55 60 65 70 75 80 85 148.780 218.607 321.205 471.956 693.458 .00672 .00457 .00311 .00212 .00144 .00054 .00037 .00025 .00017 .00012 .0805 .0804 .0802 .0802 .0801 1 847.3 2 720.1 4 002.6 5 887.0 8 655.7 12.416 12.443 12.461 12.474 12.482 12.060 12.178 12.266 12.330 12.377 149.739 151.533 152.845 153.800 154.492 65 70 75 80 85 .00098 .00067 .00045 .00008 .00005 .00004 .0801 .0801 .0800 12 724.0 18 701.6 27 484.6 12.488 12.492 12.494 12.412 12.437 12.455 154.993 155.352 155.611 90 95 100 90 95 100 1 018.9 1 497.1 2 199.8 Capital Recovery Factor Find A Given P A/P Compound Amount Factor Find F Given A F/A Arithmetic Gradient Compound Amount Factor Find F Given P F/P n Sinking Fund Factor Find A Given F A/F 611 Present Worth Factor Find P Given A P/A Gradient Uniform Series Find A Given G A/G Gradient Present Worth Find P Given G P/G n APPENDIX C: COMPOUND INTEREST TABLES 10% Compound Interest Factors Single Payment 10% Uniform Payment Series Present Worth Factor Find P Given F P/F 1 2 3 4 5 1.100 1.210 1.331 1.464 1.611 .9091 .8264 .7513 .6830 .6209 1.0000 .4762 .3021 .2155 .1638 1.1000 .5762 .4021 .3155 .2638 1.000 2.100 3.310 4.641 6.105 0.909 1.736 2.487 3.170 3.791 0 0.476 0.937 1.381 1.810 0 0.826 2.329 4.378 6.862 1 2 3 4 5 6 7 8 9 10 1.772 1.949 2.144 2.358 2.594 .5645 .5132 .4665 .4241 .3855 .1296 .1054 .0874 .0736 .0627 .2296 .2054 .1874 .1736 .1627 7.716 9.487 11.436 13.579 15.937 4.355 4.868 5.335 5.759 6.145 2.224 2.622 3.004 3.372 3.725 9.684 12.763 16.029 19.421 22.891 6 7 8 9 10 11 12 13 14 15 2.853 3.138 3.452 3.797 4.177 .3505 .3186 .2897 .2633 .2394 .0540 .0468 .0408 .0357 .0315 .1540 .1468 .1408 .1357 .1315 18.531 21.384 24.523 27.975 31.772 6.495 6.814 7.103 7.367 7.606 4.064 4.388 4.699 4.996 5.279 26.396 29.901 33.377 36.801 40.152 11 12 13 14 15 16 17 18 19 20 4.595 5.054 5.560 6.116 6.728 .2176 .1978 .1799 .1635 .1486 .0278 .0247 .0219 .0195 .0175 .1278 .1247 .1219 .1195 .1175 35.950 40.545 45.599 51.159 57.275 7.824 8.022 8.201 8.365 8.514 5.549 5.807 6.053 6.286 6.508 43.416 46.582 49.640 52.583 55.407 16 17 18 19 20 21 22 23 24 25 7.400 8.140 8.954 9.850 10.835 .1351 .1228 .1117 .1015 .0923 .0156 .0140 .0126 .0113 .0102 .1156 .1140 .1126 .1113 .1102 64.003 71.403 79.543 88.497 98.347 8.649 8.772 8.883 8.985 9.077 6.719 6.919 7.108 7.288 7.458 58.110 60.689 63.146 65.481 67.696 21 22 23 24 25 26 27 28 29 30 11.918 13.110 14.421 15.863 17.449 .0839 .0763 .0693 .0630 .0573 .00916 .00826 .00745 .00673 .00608 .1092 .1083 .1075 .1067 .1061 109.182 121.100 134.210 148.631 164.494 9.161 9.237 9.307 9.370 9.427 7.619 7.770 7.914 8.049 8.176 69.794 71.777 73.650 75.415 77.077 26 27 28 29 30 31 32 33 34 35 19.194 21.114 23.225 25.548 28.102 .0521 .0474 .0431 .0391 .0356 .00550 .00497 .00450 .00407 .00369 .1055 .1050 .1045 .1041 .1037 181.944 201.138 222.252 245.477 271.025 9.479 9.526 9.569 9.609 9.644 8.296 8.409 8.515 8.615 8.709 78.640 80.108 81.486 82.777 83.987 31 32 33 34 35 40 45 50 55 60 45.259 72.891 117.391 189.059 304.482 .0221 .0137 .00852 .00529 .00328 .00226 .00139 .00086 .00053 .00033 .1023 .1014 .1009 .1005 .1003 442.593 718.905 1 163.9 1 880.6 3 034.8 9.779 9.863 9.915 9.947 9.967 9.096 9.374 9.570 9.708 9.802 88.953 92.454 94.889 96.562 97.701 40 45 50 55 60 65 70 75 80 85 490.371 789.748 1 271.9 2 048.4 3 299.0 .00204 .00127 .00079 .00049 .00030 .00020 .00013 .00008 .00005 .00003 .1002 .1001 .1001 .1000 .1000 4 893.7 7 887.5 12 709.0 20 474.0 32 979.7 9.980 9.987 9.992 9.995 9.997 9.867 9.911 9.941 9.961 9.974 98.471 98.987 99.332 99.561 99.712 65 70 75 80 85 .00019 .00012 .00007 .00002 .00001 .00001 .1000 .1000 .1000 53 120.3 85 556.9 137 796.3 9.998 9.999 9.999 9.983 9.989 9.993 99.812 99.877 99.920 90 95 100 90 95 100 5 313.0 8 556.7 13 780.6 Capital Recovery Factor Find A Given P A/P Compound Amount Factor Find F Given A F/A Arithmetic Gradient Compound Amount Factor Find F Given P F/P n Sinking Fund Factor Find A Given F A/F 613 Present Worth Factor Find P Given A P/A Gradient Uniform Series Find A Given G A/G Gradient Present Worth Find P Given G P/G n APPENDIX C: COMPOUND INTEREST TABLES 15% Compound Interest Factors Single Payment 15% Uniform Payment Series Present Worth Factor Find P Given F P/F 1 2 3 4 5 1.150 1.322 1.521 1.749 2.011 .8696 .7561 .6575 .5718 .4972 1.0000 .4651 .2880 .2003 .1483 1.1500 .6151 .4380 .3503 .2983 1.000 2.150 3.472 4.993 6.742 0.870 1.626 2.283 2.855 3.352 0 0.465 0.907 1.326 1.723 0 0.756 2.071 3.786 5.775 1 2 3 4 5 6 7 8 9 10 2.313 2.660 3.059 3.518 4.046 .4323 .3759 .3269 .2843 .2472 .1142 .0904 .0729 .0596 .0493 .2642 .2404 .2229 .2096 .1993 8.754 11.067 13.727 16.786 20.304 3.784 4.160 4.487 4.772 5.019 2.097 2.450 2.781 3.092 3.383 7.937 10.192 12.481 14.755 16.979 6 7 8 9 10 11 12 13 14 15 4.652 5.350 6.153 7.076 8.137 .2149 .1869 .1625 .1413 .1229 .0411 .0345 .0291 .0247 .0210 .1911 .1845 .1791 .1747 .1710 24.349 29.002 34.352 40.505 47.580 5.234 5.421 5.583 5.724 5.847 3.655 3.908 4.144 4.362 4.565 19.129 21.185 23.135 24.972 26.693 11 12 13 14 15 16 17 18 19 20 9.358 10.761 12.375 14.232 16.367 .1069 .0929 .0808 .0703 .0611 .0179 .0154 .0132 .0113 .00976 .1679 .1654 .1632 .1613 .1598 55.717 65.075 75.836 88.212 102.444 5.954 6.047 6.128 6.198 6.259 4.752 4.925 5.084 5.231 5.365 28.296 29.783 31.156 32.421 33.582 16 17 18 19 20 21 22 23 24 25 18.822 21.645 24.891 28.625 32.919 .0531 .0462 .0402 .0349 .0304 .00842 .00727 .00628 .00543 .00470 .1584 .1573 .1563 .1554 .1547 118.810 137.632 159.276 184.168 212.793 6.312 6.359 6.399 6.434 6.464 5.488 5.601 5.704 5.798 5.883 34.645 35.615 36.499 37.302 38.031 21 22 23 24 25 26 27 28 29 30 37.857 43.535 50.066 57.575 66.212 .0264 .0230 .0200 .0174 .0151 .00407 .00353 .00306 .00265 .00230 .1541 .1535 .1531 .1527 .1523 245.712 283.569 327.104 377.170 434.745 6.491 6.514 6.534 6.551 6.566 5.961 6.032 6.096 6.154 6.207 38.692 39.289 39.828 40.315 40.753 26 27 28 29 30 31 32 33 34 35 76.144 87.565 100.700 115.805 133.176 .0131 .0114 .00993 .00864 .00751 .00200 .00173 .00150 .00131 .00113 .1520 .1517 .1515 .1513 .1511 500.957 577.100 664.666 765.365 881.170 6.579 6.591 6.600 6.609 6.617 6.254 6.297 6.336 6.371 6.402 41.147 41.501 41.818 42.103 42.359 31 32 33 34 35 40 45 50 55 60 267.864 538.769 1 083.7 2 179.6 4 384.0 .00373 .00186 .00092 .00046 .00023 .00056 .00028 .00014 .00007 .00003 .1506 .1503 .1501 .1501 .1500 1 779.1 3 585.1 7 217.7 14 524.1 29 220.0 6.642 6.654 6.661 6.664 6.665 6.517 6.583 6.620 6.641 6.653 43.283 43.805 44.096 44.256 44.343 40 45 50 55 60 .00011 .00006 .00003 .00001 .00001 .00002 .00001 .1500 .1500 .1500 .1500 .1500 58 778.6 118 231.5 237 812.5 478 332.6 962 104.4 6.666 6.666 6.666 6.667 6.667 6.659 6.663 6.665 6.666 6.666 44.390 44.416 44.429 44.436 44.440 65 70 75 80 85 65 70 75 80 85 8 817.8 17 735.7 35 672.9 71 750.9 144 316.7 Capital Recovery Factor Find A Given P A/P Compound Amount Factor Find F Given A F/A Arithmetic Gradient Compound Amount Factor Find F Given P F/P n Sinking Fund Factor Find A Given F A/F 615 Present Worth Factor Find P Given A P/A Gradient Uniform Series Find A Given G A/G Gradient Present Worth Find P Given G P/G n