Ari Tagor Sihombing (Hal 650-672)
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Transcript of Ari Tagor Sihombing (Hal 650-672)
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TABLE C-17 Discrete Compounding; i= 20%
Single Payment Uniform Series Uniform Gradient
Compound Present Compound Present Sinking capital Gradient Gradient
Amount Worth Amount Worth Fund recovery Present Worth Uniform Series
Factor Factor Factor Factor Factor Factor Factor Factor
To Find F To Find P To Find F To Find P To Find A To Find A To Find P To Find A
Given P Given F Given A Given A Given F Given P Given G Given G
N F/P P/F F/A P/A A/F A/P P/G A/G N
1 1.2000 0.8333 1.0000 0.8333 1.0000 1.2000 0.000 0.0000 1
2 1.4400 0.6944 2.2000 1.5278 0.4545 0.6545 0.694 0.4545 2
3 1.7280 0.5787 3.6400 2.1065 0.2747 0.4747 1.852 0.8791 34 2.0736 0.4823 5.3680 2.5887 0.1863 0.3863 3.299 1.2742 4
5 2.4883 0.4019 7.4416 2.9906 0.1344 0.3344 4.906 1.6405 5
6 2.9860 0.3349 9.9299 3.3255 0.1007 0.3007 6.581 1.9788 6
7 3.5832 0.2791 12.9159 3.6046 0.0774 0.2774 8.255 2.2902 7
8 4.2998 0.2326 16.4991 3.8372 0.0606 0.2606 9.883 2.5756 8
9 5.1598 0.1938 20.7989 4.0310 0.0481 0.2481 11.434 2.8364 9
10 6.1917 0.1615 25.9587 4.1925 0.0385 0.2385 12.887 3.0739 10
11 7.4301 0.1346 32.1504 4.3271 0.0311 0.2311 14.233 3.2893 11
12 8.9161 0.1122 39.5805 4.4392 0.0253 0.2253 15.467 3.4841 12
13 10.6993 0.0935 48.4966 4.5327 0.0206 0.2206 16.588 3.6597 13
14 12.8392 0.0779 59.1959 4.6106 0.0169 0.2169 17.601 3.8175 14
15 15.4070 0.0649 72.0351 4.6755 0.0139 0.2139 18.510 3.9588 15
16 18.4884 0.0541 87.4421 4.7296 0.0114 0.2114 19.321 4.0851 16
17 22.1861 0.0451 105.9306 4.7746 0.0094 0.2094 20.042 4.1976 17
18 26.6233 0.0376 128.1167 4.8122 0.0078 0.2078 20.681 4.2975 18
19 31.9480 0.0313 154.7400 4.8435 0.0065 0.2065 21.244 4.3861 19
20 38.3376 0.0261 186.6880 4.8696 0.0054 0.2054 21.740 4.4643 20
21 46.0051 0.0217 225.0256 4.8913 0.0044 0.2044 22.174 4.5334 21
22 55.2061 0.0181 271.0307 4.9094 0.0037 0.2037 22.555 4.5941 22
23 6.2474 0.0151 326.2369 4.9245 0.0031 0.2031 22.887 4.6475 23
24 79.4968 0.0126 392.4842 4.9371 0.0025 0.2025 23.176 4.6943 24
25 95.3962 0.0105 471.9811 4.9476 0.0021 0.2021 23.428 4.7352 25
30 237.3763 0.0042 1181.8816 4.9789 0.0008 0.2008 24.263 4.8731 30
35 590.6682 0.0017 2948.3411 4.9915 0.0003 0.2003 24.661 4.9406 35
40 1469.7716 0.0007 7343.8578 4.9966 0.0001 0.2001 24.847 4.9728 40
45 3657.2620 0.0003 18281.3099 4.9986 0.0001 0.2001 24.932 4.9877 45
50 9100.4382 0.0001 45497.1908 4.9995 a 0.2000 24.970 4.9945 50
60 56347.5144 a 281732.5718 4.9999 a 0.2000 24.994 4.9989 60
80 2160228.4620 a 10801137.3101 5.0000 a 0.2000 25.000 5.0000 80
5.0000 0.2000
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lnterest and Annuity
Tables for Continuous
compounding
For various values of r from 8% to 20%,
r = nominal interest rate per period, compounded continuourty
N = number of compounding periods
(F/P,r%,N) =
(P/F,1%,N) = =
(F/ A,r%,N) =
(P / A,r%,N) =
APPENDIXD
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TABLE C-18 Discrete Compounding; i= 25%
Single Payment Uniform Series Uniform Gradient
Compound Present Compound Present Sinking capital Gradient Gradient
Amount Worth Amount Worth Fund recovery Present Worth Uniform Series
Factor Factor Factor Factor Factor Factor Factor Factor
To Find F To Find P To Find F To Find P To Find A To Find A To Find P To Find A
Given P Given F Given A Given A Given F Given P Given G Given G
N F/P P/F F/A P/A A/F A/P P/G A/G N
1 1.2500 0.8000 1.0000 0.8000 1.0000 1.2500 0.000 0.0000 1
2 1.5625 0.6400 2.2500 1.4400 0.4444 0.6944 0.640 0.4444 2
3 1.9531 0.5120 3.8125 1.952 0.2623 0.5123 1.664 0.8525 34 2.4414 0.4096 5.7656 2.3616 0.1734 0.4234 2.893 1.2249 4
5 3.0518 0.3277 8.2070 2.6893 0.1218 1.3718 4.204 1.5631 5
6 3.8147 0.2621 11.2588 2.9514 0.0888 0.3388 5.514 1.8683 6
7 4.7684 0.2097 15.0735 3.1611 0.0663 0.3163 6.773 2.1424 7
8 5.9605 0.1678 19.8419 3.3289 0.0504 0.3004 7.947 2.3872 8
9 7.4506 0.1342 25.8023 3.4631 0.0388 0.2888 9.021 2.6048 9
10 9.3132 0.1074 33.2529 3.5705 0.0301 0.2801 9.987 2.7971 10
11 11.6415 0.859 42.5661 3.6564 0.0235 0.2735 10.846 2.9663 11
12 14.5519 0.687 54.2077 3.7251 0.0184 0.2684 11.602 3.1145 12
13 18.1899 0.0550 68.7596 3.7801 0.0145 0.2645 12.262 3.2437 13
14 22.7374 0.0440 86.9495 3.8241 0.0115 0.2615 12.833 3.3559 14
15 28.4217 0.0352 109.6868 3.8593 0.0091 0.2591 13.326 3.4530 15
16 35.5271 0.0281 138.1085 3.8874 0.0072 0.2572 13.748 3.5366 16
17 44.4089 0.0225 173.6357 3.9099 0.0058 0.2558 14.109 3.6084 17
18 55.5112 0.018 218.0446 3.9279 0.0046 0.2546 14.415 3.6698 18
19 69.3889 0.0144 273.5558 3.9424 0.0037 0.2537 14.674 3.7222 19
20 86.7362 0.0115 342.9447 3.9539 0.0029 0.2529 14.893 3.7667 2021 108.4202 0.0092 429.6809 3.9631 0.0023 0.2523 15.078 3.8045 21
22 135.5253 0.0074 538.1011 3.9764 0.0019 0.2519 15.233 3.8365 22
23 16.4066 0.0059 673.6264 3.9764 0.0015 0.2515 15.363 3.8634 23
24 211.7582 0.0047 843.0329 3.9811 0.0012 0.2512 15.471 3.8861 24
25 264.6978 0.0038 1054.7912 3.9849 0.0009 0.2509 15.562 3.9052 25
30 807.7936 0.0012 3227.1743 3.9950 0.0003 0.2503 15.832 3.9628 30
35 2465.1903 0.0004 9856.7613 3.9984 0.0001 0.2501 15.937 3.9858 35
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40 7523.1638 0.0001 30088.6554 3.9995 a 0.2500 15.977 3.9947 40
45 22958.874 a 91831.4962 3.9998 a 0.2500 15.992 3.9980 45
50 70064.9232 a 280255.6929 3.9999 a 0.2500 15.997 3.9993 50
60 652530.4468 a 2610117.7872 4.0000 a 0.2500 16.0000 3.9999 60
4.0000 0.2500
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INTEREST AND ANNUITY TABLES FOR CONTINOUS COMPOUNDING 651
TABLE D-1 Continous Compounding; r = 8%
Discrete Flows
Single Payment Uniform Series
Compound Present Compound Present
Amount Worth Amount Worth
Factor Factor Factor Factor
To Find F To Find P To Find F To Find P
Given P Given F Given A Given A
N F/P P/F F/A P/A N
1 1.0833 0.9231 1.0000 0.9231 1
2 1.1735 0.8521 2.0833 1.7753 2
3 1.2712 0.7866 3.2568 2.5619 3
4 1.3771 0.7261 4.5280 3.2880 4
5 1.4918 0.6703 5.9052 3.9584 5
6 1.6161 0.6188 7.3970 4.5771 6
7 1.7507 0.5712 9.0131 5.1483 7
8 1.8965 0.5273 10.7637 5.6756 8
9 2.0544 0.4868 12.6602 6.1624 9
10 2.2255 0.4493 14.7147 6.6117 10
11 2.4109 0.4148 16.9402 7.0265 11
12 2.6117 0.3829 19.3511 7.4094 12
13 2.8292 0.3535 21.9628 7.7629 13
14 3.0649 0.3263 24.7920 8.0891 14
15 3.3201 0.3012 27.8569 8.3903 15
16 3.5966 0.2780 31.1770 8.6684 16
17 3.8962 0.2567 34.7736 8.9250 17
18 4.2207 0.2369 38.6698 9.162 18
19 4.5722 0.2187 42.8905 9.3807 19
20 4.9530 0.2019 47.4627 9.5826 20
21 5.3656 0.1864 52.4158 9.7689 21
22 5.8124 0.172 57.7813 9.9410 22
23 6.2965 0.1588 63.5938 10.0998 23
24 6.812 0.1466 69.8903 10.2464 24
25 7.3891 0.1353 76.7113 10.3817 25
26 8.0045 0.1249 84.1003 10.5067 26
27 8.6711 0.1153 92.1048 10.6220 27
28 9.3933 0.1065 100.776 10.7285 28
29 10.1757 0.0983 110.1690 10.8267 29
30 11.0232 0.907 120.345 10.9174 30
35 16.4446 0.0608 185.439 11.2765 35
40 24.5325 0.0408 282.547 11.5172 40
45 36.5982 0.0273 427.416 11.6786 45
50 54.5982 0.0183 643.535 11.7868 5055 81.4509 0.0123 965.947 11.8593 55
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60 121.510 0.0082 1446.93 11.9078 60
65 181.272 0.0055 2164.47 11.9404 65
70 270.426 0.0037 3234.91 11.9623 70
75 403.429 0.0025 4831.83 11.9769 75
80 601.845 0.0017 7214.15 11.9867 80
85 897.847 0.0011 10768.1 11.9933 85
90 1339.43 0.0007 16070.1 11.9977 90
95 1998.20 0.0005 23979.7 12.0007 95 10
0 2980.96 0.0003 35779.3 12.0026
10
0
652 APPENDIX D/ INTEREST AND ANNUITY TABLES FOR CONTINOUS COMPOUNDING
TABLE D-2 Continous Compounding; r = 10%
Discrete Flows
Single Payment Uniform Series
Compound Present Compound Present
Amount Worth Amount Worth
Factor Factor Factor Factor
To Find F To Find P To Find F To Find P
Given P Given F Given A Given A
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N F/P P/F F/A P/A N
1 1.1052 0.9048 1.0000 0.9048 1
2 1.2214 0.8187 2.1052 1.7236 2
3 1.3499 0.7408 3.3266 2.4644 3
4 1.4918 0.6703 4.6764 3.1347 4
5 1.6487 0.6065 6.1683 3.7412 5
6 1.8221 0.5488 7.8170 4.2900 6
7 2.0138 0.4966 9.6391 4.7866 7
8 2.2255 0.4493 11.6528 5.236 8
9 2.4596 0.4066 13.8784 5.6425 9
10 2.7183 0.3679 16.3380 6.0104 10
11 3.0042 0.3329 19.0536 6.3433 11
12 3.3201 0.3012 22.0604 6.6445 12
13 3.6693 0.2725 25.3806 6.9170 13
14 4.0552 0.2466 29.0499 7.1636 14
15 4.4817 0.2231 33.1051 7.3867 15
16 4.953 0.2019 37.5867 7.5886 16
17 5.4739 0.1827 42.5398 7.7713 17
18 6.0496 0.1653 48.0137 7.9366 18
19 6.6859 0.1496 54.0634 8.0862 19
20 7.3891 0.1353 60.7493 8.2215 20
21 8.1662 0.1225 68.1383 8.3440 21
22 9.025 0.1108 76.3045 8.4548 22
23 9.9742 0.1003 85.3295 8.5550 23
24 11.0232 0.0907 95.3037 8.6458 2425 12.1825 0.0821 106.327 8.7278 25
26 13.4637 0.0743 118.509 8.8021 26
27 14.8797 0.0672 131.973 8.8693 27
28 16.4446 0.0608 146.853 8.9301 28
29 18.1741 0.0550 163.298 8.9852 29
30 20.0855 0.0498 181.472 9.0349 30
35 33.1155 0.0302 305.364 9.2212 35
40 54.5981 0.0183 509.629 9.3342 40
45 90.0171 0.0111 846.404 9.4027 45
50 148.413 0.0067 1401.65 9.4443 5055 244.692 0.0041 2317.10 9.4695 55
60 403.429 0.0025 3826.43 9.4848 60
65 665.142 0.0015 6314.88 9.4940 65
70 1096.63 0.0009 1401.65 9.4997 70
75 1808.04 0.0006 17182.0 9.5031 75
80 2980.96 0.0003 28334.4 9.5051 80
85 4914.77 0.0002 46721.7 9.5064 85
90 8103.08 0.0001 77037.7 9.5072 90
95 13359.7 a 127019.0 9.5076 95
100 22026.5 a 209425.0 9.5079 100
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INTEREST AND ANNUITY TABLES FOR CONTINOUS COMPOUNDING 653
TABLE D-3 Continous Compounding; r = 20%
Discrete Flows
Single Payment Uniform Series
Compound Present Compound Present
Amount Worth Amount Worth
Factor Factor Factor Factor
To Find F To Find P To Find F To Find P
Given P Given F Given A Given A
N F/P P/F F/A P/A N
1 1.2214 0.8187 1.0000 0.8187 1
2 1.4918 0.6703 2.2140 1.4891 2
3 1.8221 0.5488 3.7132 2.0379 3
4 2.2255 0.4493 5.5353 2.4872 4
5 2.7183 0.3679 7.7609 2.8551 5
6 3.3201 0.3012 10.4792 3.1563 6
7 4.0552 0.2466 13.7993 3.4029 7
8 4.9530 0.2019 17.8545 3.6048 8
9 6.0496 0.1653 22.8075 3.7701 9
10 7.3891 0.1353 28.8572 3.9054 1011 9.0250 0.1108 36.2462 4.0162 11
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12 11.0232 0.0907 45.2712 4.1069 12
13 13.4637 0.0743 56.2944 4.1812 13
14 16.4446 0.0608 69.7581 4.2420 14
15 20.0855 0.0498 86.2028 4.2918 15
16 24.5325 0.0408 106.288 4.3325 16
17 29.9641 0.0334 130.8210 4.3659 17
18 36.5982 0.0273 160.785 4.3932 18
19 44.7012 0.0224 197.383 4.4156 19
20 54.5981 0.0183 242.0840 4.4339 20
21 66.6863 0.0150 296.6820 4.4489 21
22 81.4509 0.0123 363.3690 4.4612 22
23 99.4843 0.0101 444.820 4.4713 23
24 121.510 0.0082 544.3040 4.4795 24
25 148.413 0.0067 665.814 4.4862 25
26 181.272 0.0055 814.227 4.4917 26
27 221.406 0.0045 995.500 4.4963 27
28 270.426 0.0037 1216.910 4.5000 28
29 330.299 0.0030 1487.33 4.5030 29
30 403.429 0.0025 1817.63 4.5055 30
35 1096.63 0.0009 4948.60 4.5125 35
40 2980.96 0.0003 13459.4 4.5151 40
45 8103.08 0.0001 36594.3 4.5161 45
50 22026.5 a 99481.4 4.5165 50
55 59874.1 a 270426.0 4.5166 55
60 162755.0 a 735103.0 4.5166 60
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Standard NormalDistribution
The standard normal distribution is a normal (Gaussian) distribution with a mean of 0
and a variance of 1. It is a continuous diskibution with a range of - to +. The
tabled values denote the probability of observing a value from minus infinity to the Z
value indicated by the left column and top row.lhezvalue is determined by applying the
following formula to the observed data:
Z:(X- )/.
APPENDIXE
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Interested readers are referred to any introductory statistics text book for an In-depth
discussion of the use of the standard normal distribution function.
654
STANDART NORMAL DISTRIBUTION 655
z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-3.4 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0002
-3.3 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004 0.0004 0.0004 0.0003
-3.2 0.0007 0.0007 0.0006 0.0006 0.0006 0.0006 0.0006 0.0005 0.0005 0.0005
-3.1 0.0010 0.0009 0.0009 0.0009 0.0008 0.0008 0.0008 0.0007 0.0007 0.0007
-3.0 0.0013 0.0013 0.0013 0.0012 0.0012 0.0011 0.0011 0.0011 0.0010 0.0010
-2.9 0.0019 0.0018 0.0017 0.0017 0.0016 0.0016 0.0015 0.0015 0.0014 0.0014
-2.8 0.0026 0.0025 0.0024 0.0023 0.0023 0.0022 0.0021 0.0021 0.0020 0.0019
-2.7 0.0035 0.0034 0.0033 0.0032 0.0031 0.0030 0.0029 0.0028 0.0027 0.0026
-2.6 0.0047 0.0045 0.0044 0.0043 0.0041 0.0040 0.0039 0.0038 0.0037 0.0036
-2.5 0.0062 0.0060 0.0059 0.0057 0.0055 0.0054 0.0052 0.0051 0.0049 0.0048
-2.4 0.0082 0.0080 0.0078 0.0075 0.0073 0.0071 0.0069 0.0068 0.0066 0.0064
-2.3 0.0107 0.0104 0.0103 0.0099 0.0096 0.0094 0.0091 0.0089 0.0087 0.0084
-2.2 0.0139 0.0136 0.0132 0.0129 0.0125 0.0122 0.0119 0.0116 0.0113 0.0110
-2.1 0.0179 0.0174 0.0170 0.0166 0.0162 0.0158 0.0154 0.0150 0.0146 0.0143
-2.0 0.0228 0.0222 0.0217 0.0212 0.0207 0.0202 0.0197 0.0192 0.0118 0.0183
-1.9 0.0287 0.0281 0.0274 0.0268 0.0262 0.0256 0.0250 0.0244 0.0239 0.0233
-1.8 0.0359 0.0352 0.0344 0.0336 0.0329 0.0322 0.0314 0.0307 0.0301 0.0294
-1.7 0.0446 0.0436 0.0427 0.0418 0.0409 0.0401 0.0392 0.0384 0.0375 0.0367
-1.6 0.0548 0.0537 0.0526 0.0516 0.0505 0.0495 0.0485 0.0475 0.0465 0.0455
TABLE E-1 Areas under the normal curve
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-1.5 0.0668 0.0655 0.0643 0.0630 0.0618 0.0606 0.0594 0.0582 0.0571 0.0559
-1.4 0.0808 0.0793 0.0778 0.0764 0.0749 0.0735 0.0722 0.0708 0.0694 0.0681
-1.3 0.0968 0.0951 0.0934 0.0918 0.0901 0.0885 0.0869 0.0853 0.0838 0.0823
-1.2 0.1151 0.1131 0.1112 0.1093 0.1075 0.1056 0.1038 0.1020 0.1003 0.0985
-1.1 0.1357 0.1335 0.1314 0.1292 0.1271 0.1251 0.1230 0.1210 0.1190 0.1170
-1.0 0.1587 0.1562 0.1539 0.1515 0.1492 0.1469 0.1446 0.1423 0.1401 0.1379
-0.9 0.8141 0.1841 0.1788 0.1762 0.1736 0.1711 0.1685 0.1660 0.1635 0.1611
-0.8 0.2119 0.2090 0.2061 0.2033 0.2005 0.1977 0.1949 0.1922 0.1894 0.1867
-0.7 0.2420 0.2389 0.2358 0.2327 0.2296 0.2266 0.2236 0.2206 0.2177 0.2148
-0.6 0.2743 0.2709 0.2676 0.2643 0.2611 0.2578 0.2546 0.2514 0.2483 0.2451
-0.5 0.3085 0.3050 0.3015 0.2981 0.2946 0.2912 0.2877 0.2843 0.2810 0.2776
-0.4 0.3446 0.3409 0.3372 0.3336 0.3300 0.3264 0.3228 0.3192 0.3156 0.3121
-0.3 0.3821 0.3783 0.3745 0.3707 0.3669 0.3632 0.3594 0.3557 0.3520 0.3483
-0.2 0.4207 0.4168 0.4129 0.4090 0.4052 0.4013 0.3974 0.3936 0.3897 0.3859
-0.1 0.4602 0.4562 0.4522 0.4483 0.4443 0.4404 0.4364 0.4325 0.4286 0.4247
0.0 0.5000 0.4960 0.4920 0.4880 0.4840 0.4801 0.4761 0.4721 0.4681 0.4641
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656 APPENDIX E / STANDART NORMAL DISTRIBUTION
z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359
0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753
0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141
0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.648 0.6517
0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879
0.5 0.6915 0.695 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.719 0.7224
0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549
0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852
0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133
0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389
1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621
1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.879 0.8810 0.883
1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015
1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177
1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9278 0.9292 0.9306 0.9319
1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441
1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545
1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633
1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706
1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.975 0.9756 0.9761 0.9767
2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817
2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.985 0.9854 0.9857
2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.989
2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916
2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936
2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952
2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964
2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974
TABLE E-1 (continued)
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2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981
2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986
3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.999
3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993
3.2 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995
3.3 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997
3.4 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9997 0.9998
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APPENDIXF
Selected References
Au, T., and T.P. Au. Engineering Economic for capital Investment Analysis,2nd ed.
(Boston: Allyn and Bacon, 1992).
BARISH, N.N., and S. KAPLAN. Economic analysis for Engineering and Managerial
Decision Making (New York McGraw-Hill,1978).
BIERMAN, H., JR., and S. SMIDT. The capital Budgeting Decision,8th ed. (New york:
Macmillan, L993).
BLANK, L.T., and AJ. TARQUIN. Engineering Economy,6th ed. (New york: McGraw-
Hill,2005).
BOWMAN, M.S. Applied Economic Analysis for Technologists,Engineersa, and
Managers, 2nd ed. (Upper Saddle River, NJ: Prentice Hall, 2003).
BRIMSON, J.A.Activity Accounting: An Activity-Based Approach( New york John Wiley
& Sons,1991).
BUSSEY,L .E., and T.G. ESCHENBACH. The Economic Analysis of lndustrial Projects,
2nd ed. (Upper Saddle River, N]: Prentice Hall,1992).
CAMPEN, J.T.Benefit, cost, and Beyond (cambridge, MA: Ballinger publishing
Company, 1986).
CANADA, J.R., and W.G. SULLIVAN. Economic and Multiattribute Analysis of Advanced
Manufacturing systems(Upper Saddle River, NJ: prentice Hall, 1989).
CANADA, J.R., and W.G. SULLIVAN, D.J. KULONDA and J.A. WHITE. Capital
Investment Decision Analysis for Engineering and Management, 3rd ed. (upper
saddle River, NJ: Prentice Hall, 2005).
CLARK, J.J.,T.J. HINDELANG, and R.E. PRITCHARD. Capital Budgeting: planning and
Control of Capital Expenditures (upper saddle River, NJ: prentice Hall,1979).
COLIER, C.A., and C.R. GRAGADA. Engineering Cost Analysis, 3rd ed. (New york:
Harper & Row, 1998).
Engineering Economist,The. A quarterly journal jointly published by the Engineering
Economy Division of the American Society for Engineering Education and the
Institute of Industrial Engineers. Published by IIE, Norcross, GA.
Engineering News-Record. Published monthly by McGraw-Hill, New York.
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ESCHENBACH, T.G. Engineering Economy: Applaying Theory to Practice (Chicago:
Richard D. Irwin, 1995)
FABRYCKY,W.J., G.J. THUESEN, and D. VERMA. Economic decision Analysis,3rd ed.
(Upper Saddle River, NJ: Prentice Hall, 1998).
FLEISCHER, G.A. lntroduction to Engineering Economy(Boston: PWS Publishing
Company,1994).
GOICOECHEA, G.A., D.R. HANSEN, and L. DDUCKSTEIN. Multiobjective decision
Analysis with Engineering and Busines Applications ( New York: John Wiley &
Sons,1982).
GRANT, E.L., W.G. IRESON, and R.S. Leavenworth. Principeles of Engineering
Economy, 8th ed. (New York: John Wiley & Sons, 1990).
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658 APPENDIX F / SELECTED REFERENCES
HULL, J.C. The Evaluation of Risk in Business Investment(New York: Pergamon Press
1980).
Industrial Engineering A monthly magazine published by the Institute of Industrial
Engineers, Norcross, GA.
lnternal Revenue Service Publication 534. Depreciation. U.S. Government Printing
Office, revised periodically.
JELEN, F.C., and J.H. BLACK. Cost and Optimization Engineering, 3rd ed. (New York:
McGraw-Hill,1991).
JONES, B.W. lnflation in Engineering Economic Analysis (New York: John wiley &
Sons,1982).
KAHL, A.L., and W.F. Rentz. Spreadsheet Applications in Engineering Economics (St.
Paul, MN West Publishing Company, 1992).
KAPLAN, R.S., and R. Cooper. The Design of Cost Management Systems (Upper Saddle
River, NJ: Prentice Hall, 1999).
KEENEY, R.L., and H. RRAIFFA. Decisions with Multiple Objectives Preferences and
Value Trade-offs (New York: John Wiley & Sons, 1976).
LASSER ,J.K. Your lncome Tax[New York Simon & Schuster (see latest edition)].
MALLIK, A.K.Engineering Economy with Computer Applications (Mahomet, IL:
Engineering Technology, 1979 ).
MATTEWS L.M. Estimating Manufacturing Casts: A Practical Guide for Managers and
Estimators ( New York McGraw-Hill, 1983).
MERRETT, A.J., and A. SYKES. The Finance and Analysis of Capital Projects (New York:
John Wiley & Sons, 1963).
MISHAN, E.J. Cost-Benefit analysis (New York Praeger Publishers,1976).
MORRIS, W.T. Engineering Economic analiysis (Reston, V A: Reston Publishing, 1976).
NEWNAN, D.G., T.G. ESCHENBACH, and J.P. LAVELLE, Engineering Economic Analysis,
9th ed. (San ]ose, CA: Engineering Press, 2004).
OSTWARD, P.F. Engineering Cost Estimating, 3rd ed. (Upper Saddle River, NJ:
Prentice Hall,l992).
PARK, C.S. Contemporary Engineering Economics (Upper Saddle River, NJ: Prentice
Hall,2002).
PARK, C.S., and G.P. SHARP-BETTE. Advanced Engineering Economics (New York: ]
ohn Wiley & Sons, 1990)
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Selected references 659
PARK, W.R., and D.E. JACKSON. Cost Engineering Analysis: A Guide to Economic
Evaluation of Engineering Projects,2nd ed. (New York John Wiley & Sons,1984).
PORTER, M.E. Competitive Strategy: Techniques for Analyzing lndustries and
Competitors (New York: The Free Press, 1980).
RIGGS, J.L., D.D. BEDWORTH, and S.V. RANDHAWA. Engineering Economics, 4th ed
(New York McGraw-Hill, 1996).
SMITH, G.W. Engineering Economy: The Analysis of Capital Expenditures, 4th ed.
(Ames,IO: Iowa State University Press, 1987).
STEINER, H.M. Engineering Economic Principles, 2nd ed. (New York: McGraw-Hill,
1996)
STERMOLE, F.J., and J.M. STERMOLE. Economic Evaluation and lnvestment Decision
Methods,6th ed. (Golden, CO: investment Evaluations Corp., 1997).
STEWART, R.D. Cost Estimating (New York John Wiley & Sons, 1982).
STEWART, R.D., R.M. Wyskida, and J.D. JOHANNES, eds. Cost Estimators' Reference
Manual, 2nd ed. (New York John Wiley & Sons, 1995).
TAYLOR, G.A. Managerial and Engineering Economy, 3rd ed. (New York Van Nostrand
Reinhold, 1980).
THUESEN, G.J., and W.J. FABRYCKY. Engineering Economy, 9th ed. (Upper Saddle
River, NJ: Prentice Hall 2001).VANHORNE, J.C. Financial Management and Policy,8th ed. (Upper Saddle River, NJ:
Prentice Hall, 1989).
WEINGARTNER, H.M. Mathematical Programming and the analysis of Capital
Budgeting Problems (Englewood Cliffs, NJ: Prentice-Hall, 1975).
WHITE, J.A., K.E. Case, D.B. PRATT, and M.H. AGEE. Principles of Engineering
Economic Analysis, 4th ed. (New York: John Wiley & Sons, 1998).
WOODS, D.R. Financial Decision Making in the Process Industry (Englewood Cliffs,
NJ): Prentice-Hall, 1975).
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APPENDIXG
Answers to Selected
Problems
CHAPTER 2
2-12 a. D* = 2,425 circuit
boards/month
b. Profit = $75,612.50/month
(maximum profit)
c. D = 480.6 481 circuit
boards/month
D = 4,369.4 4,369
circuit boards/month
d. 481 to 4,369 circuit boards
per month
2-14 D* 240 units per month
Profit = $4,960 per monthD = 18 units/month
D= 462 units/month
2-18 a. D* 50 units per month
b.
for D > 1. Therefore, D* = 50
is a point of maximum profit.
2-19 X = l5.64 megawatts
2-21 D' = 3,112pumps/month;
D' = 2,404pumps/month;
22.75% reduction
2-27 R-30; LCC = $19,513.00
2-30 $4,448
2-37 a. Either machine
b. Machine A
2-39 Process 1 ; Profit : $2,640/ day
2-39 a. Speed B; cost/piece : $0.104
2-43 Method 1; Profit - $10,974,A0A
2-53 Select (a)
2-54 Select (b)
2-55 Select (c)
2-59 Select (d)
CHAPTER 3
3-4 = $262,78A.27
3-6 a. = 154.9
= 203.4
b. = $412,710
3-7 a. = 176
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b. = 144.5
= $797,696
3-l I a. $630A/year
3-15 $11,54
3-22 a. y = 31.813 + 0.279 x
b. R = 0.99
c. y = $101.56
3-26 x = 4,497 units
3-29 Total Cost = $2,239,046
3-30 s = 0.9 (90% learning curve)
3-38 Select (d)
3-39 Select (c)
3-40 Select (b)
3-42 Select (d)
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ANSWERS TO SELECTED PROBLEMS 661
CHAPTER 4
I = $4,250
I = $7,560
F = $13,382
P = $31,775
i = 2.17% per yearA = $2,925
P = $8,865
A = $3,397.50
Fr= $124,966
a. N8years.
b. I = 15.11%
c.P = $720.96
d. A= $277.40
Select D; F = $13,490
A = -$581.86
P = $33,511.70
Z = $3,848.15
i' /year = 11.55% per year
W = $714.25
P= -$165,104
A = $1,203.69
Z = $608.21
P = $100(P / A,10%,4 + $100(P/G ,
10%,8)
A = $124.34
Q= $435.75
N = 8 years
A = $2,790.73
X = $5,573.25
a. 10.25%
b. 10.38%
c. 10.51%
Select D; A = $1,430
P = $4,729.87
N = 30 months
i/yr = 8.24%
F = $6,340.50
Select (c); A = $312
F = $17,303.19
a. False; b. False; c. False;
d. True; e. False; f. True;
g. False; h. False; i, False;
4-99 Z = $1,421.67
4-103 A = $1,320.66
4-106 a. True b. True c. False
d. False e. False
4-114 Select( e)
4-116 Select(d )
4-717 Select (c)
4-1 19 Select(d )
4-121 Select (c)
4-122 Select (a)
4-123 Select (c)
CHAPTER 5
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5-2 N = 72 months
5-4 PW (12%) = $13,423.57
5-5 PW (15%) = $2,911.60
Fw (15%) = $5,855.60
AW (15%) = $868.70
5-8 PW (15%) = $352,650> 0;
Invest in the new product line.
5-12 a. = $7,688.96
b. A = $150,992.90
5- 14 i'% = 7.5% per six months
5-17 PW of 5 yr lining = $5,514.72
PW 10 yr lining = $9,003.56
5-21 A = $4,490/year
5-25 AW (of costs) = $20,736.30 per
year
5-27 a. As i , the PW approaches -
$3,000
b. = 6 years
c. PW(0%) = -$1,000
AW(0%) = -$166.70
5-30 APR = 22.8% compounded monthly
5-33 = 51.1% Per year.
5-34 i = 14 %
5-38 a. I5.2% b. 18.8% c. 21.5%
d. 20%
5-41 i = 1.24% per year
5-43 a. ' = 6 years
b. i'%= 29.4% per year
5-49 a. i = 1/2% and 28.8% per year.b. i' = 21.15%;ERR > 20% accept
project.
5-51 a. PW = 1.710 X + 26.006Y
b. AW = 0.2732X + 4.1558Y
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ANSWER TO SELECTED PROBLEMS
CHAPTER 4
1 I= $4,250
2 I= $7,560
3 F = $13,382
9 P = $31,775
11 i = 2.17% per year
14 A = $2,925
17 P = $8,865
20 A = $3,397.50
24 F4 = $124,966
25 a. N - 8 years.
b. i =15.11%
c. P = $720.96
d. A = $277.40
29 Select D; F4 = $13,490
33 A = - $681.86
35 P = $33,511.70
38 Z $3,848.15
42 i'/year =11.55% per year
45 W = $714.25
48 Po = $165,104 1 A = $1,203.69
53 Z = $608.21
58 Po = $100(P/A, 10%, 4) + $100(P/G,
10%, 8)
60 A = $124.34
64 Q = $435.75
65 N = 8 years ;
69 A = $2,790.73
73 X = $5,573.25
77 a. 10.25%
4-99 Z = $1,421.67
4-103 A = $1,320.66
4-106 a. True b. Truec.
False
d. False e. False
4-114 Select (e)
4-116 Select (d)
4-117 Select (c)
4-119 Select (d)
4-121 Select (c)
4-122 Select (a)
4-123 Select (c)
CHAPTER 5
5-2 N = 72 months
5-4 PW(12%) = -$13,423.57
5-5 PW(15%) = $2,911.60
FW(15%) = $5,855.60
AW(15%) $868.70
5-8 PW(15%) $352,650 > 0;
invest in the new product line.
5-12 a. VN = $7,688.96
b. A = $150,892.90
5-14 i'% = 7.5% per six months
5-17 PW of 5 yr lining = $5,614.72
PW 10 yr lining = $9,003.56
5-21 A = 54,490/year
5-25 AW (of costs) = $20,736.30 per
149
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ANSWER TO SELECTED PROBLEMS
5-52 a. IIW = 59.91 Y
b. A = 9.908Y
5-63 Select (d)
5-64 Select (a)
5-67 Select (c)
5-69 Select (e)
5-70 Select (c)
5-72 Select (d)
CHAPTER 6
6-2 Select Design D3 for PW, FW, and AW
6-4 Select Design C; AW,(20%) = $16,245
6-7 Select Alternative B; PWB(20%) $9,180
6-12 Select Alternative Al; AW(18%)
$13,492
6-14 Select Design A; AWA(6%) = -
$48,594/mile, PWA (6%) = -
$557,273/mile
6-17 Select Alternative Y; PWy(5%) =
$40,885.54
6-21 a. Standard light bulb is less expensive
by $0.44 per year
6-25 a. Select A; AWA = -$12,053.60
b. Select A; AWA = -$12,053.60
6-27 a. Select Alternative El; AWE,(15%)
= -$16,990
b. Select Alternative El; AWE'(15%)
= -$16,990
6-30 Select Bridge Design L; CWL(15%)
7-7 a. $180,550.50
b. $14,449.50c. $43,329
7-11 a. d3 = $3,428.57; BV5 =
$42,857.15
b. d3 = $6,297.38; BV5 = $27,759.86
c. d- = $10,494; BV5, = $13,386
d. d2 = d3=. =d14_$4,285.71
BV5 = $40,714.30
7-16 a. Income taxes = $18,850
b. Depreciation + Expenses $130,000
7-19 t =37.96%;
t = 41.92%
7-22 Alternative A: Plastic; AWA = -
$1,184
7-25 PW(15%) = $363,690 > > 0;
investment should be made
7-27 Design S1; AW(10%) = -$290
7-31 N = 6 years
7-33 X = $864,135 / year
7-34 a. PW $171,592
b. AW $37,115
7-37 AW(12%) = $3,468 for both ATCF
and EVA
7-39 Accept Quotation II, PW = -
$136,848
7-46 Select (b)
7-48 Select (c)
7-51 Select (d)
7-53 Select (d)
150
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ANSWER TO SELECTED PROBLEMS
= -$378,733 6-32 Recommend Design
ER1
6-38 Select Alternative 2
6-40 Select Design 4; PW4 = $23,433.23
6-48 i' 21.6%; Select (c)
6-49 X = 6.26 or 7 planes per year; Select
(a)
6-52 i' = 13.4% > 10%; Select (c)
6-54 Select (e)
6-55 Select (a)
6-57 Select (b); PWA(15%) = $42,848
CHAPTER7
7-6 a. $7,142.86
b. $11,200
c. $5,000
7-56 Select (d)
7-59 Select (a)
7-61 Select (e)
CHAPTER 8
8-2 N 18 years
8-4 Alternative B, PW = -$369,080
8-5 Alternative I, PW = $10,000
8-11 PO(A$) = $43,755
8-14 a. FW(A$) = $144,105
b. FW(R$) = $44,932
8-20 a. if, = 36.08% per year
b. if, = 18.44% per year
8-25 PW(18%) = -$12,233
8-30 Select Purchase alternative;
FW -$1,952,551
8-38 Select (d)
840 Select (c)
42 Select (c)
CHAPTER 9
9-1 Keep the old lift truck; PW = $23,331
9-5 Economic life = 3 years
9-9 Keep the defender, AW = $15,383
9-11 Reinforce the existing bridge
9-16 Keep the defender, PW
56,542.40, Anti
11-14 b. Retain the steel pier, AW =
$29,332
11-17 Construct the levee
11-19 a. Select Design 3
b. Select Design 3
11-21 Select Design B
11-22 B-C Ratio = 1.1; Select (d)
11-23 Select (b)
11-25 Select (b)
151
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ANSWER TO SELECTED PROBLEMS
$1,725.89
9.19 Select Alternative B, PW S1,440,4239-23 Lease the challenger
9-25 Relocate the existing transformers
(Alterna tive B); CW = $54,239
9-32 Select (a)
9-33 Select (c)
9-35 Select (d)
CHAPTER 10
10-3 =0.818
10-5 a. MV(Alternative 2) 2,050
b. N = 7.3 years
10-9 X = $933,953 in annual revenues year
10-13 a. At themost likely estimates, Design is
marginally- preferred to B,
b. X = 11,872 units/year
10-18 X = 362,500,000 Btu per year
10-21 Select
the ABC brand motor, AW,
= -$1,831
10-30 Select (b)
10-31 Select (a)
10-34 Select (b)install Machine A
10-38 True
10-39 False
CHAPTER 11
CHAPTER 12
12-2 The four-lane bridge should be builtnow, PW = $3-500,000
12-4 E(X) 1,350 cubic yards
V(X) 66,500(cubic yards)
SD(X) = 258 cubic yards
12-6 Select Design E, PW = $239,414
12-7 Alternative T, Annual Cost =
$52,435
12-10 E(PWAT) = 533,403; implement
the project
12-13 a. V(PW) = 1,097.7 x 106($)2
SD(PW) = 533,131
b.Pr/PW > 0) = 0.57
c. E(AW)Rs = $1,866
The project appears questionable.
The E(PW) is positive but the
SD(PW) is approximately two times
the expected value. Also the Pr[PW
> 01 = 0.57 is only somewhat
attractive.
12-16 Pr(X 171) = 0.7881
12-19 E[PW(B A)] = $5,228
(PWA B) = $1,183.97
12-25 Select new product, PW = $62,125
12-27 Choose to build
CHAPTER 13
13-2 a. Leasing a tuck is better.
b. The annual cost of having to
operate without a truck, $2,000,
is less than the minimum cost
152
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ANSWER TO SELECTED PROBLEMS
11-1 Select B
11-2 Alternative C
11-5 Alternative B
11-8 Expand the present facility (Alt. A)
11-13Recommend building the dam (II)
alternative in (a). Hence, it is
better to operate without a truck.
13-5 Leasing is better for case a, but
buying is better for case b.
13-6 Leasing is better if the life is 3
years. It appears that a breakeven
life is 4 years (to the nearest whole
year).
13-8 Objective function value = $219.89
13-11 Objective function value= $8,822
13-12 Recommendations differ for Projects
A and C 13-13 R, = 10%
CHAPTER 14
14-5 a. Alternative 2
b.Alternative 2
c. Alternative 2
14-7 Dominanceno alternatives
eliminated SatisficinAlternative A
eliminated
Lexicographyno alternatives
eliminated
Hurwicz procedureAlternative Aeliminated
Additive weightingAlternative B
selected
14-9 Alternative A
14-11 The solution involves subjective
factors which will vary from one
student to another.
14-13 Dominanceno selection
Feasible rangesno selection
LexicographyDomestic 2
Additive weighting Domestic 2
14-14 Xij 0.7 (keep tool)
1.0 (purchase new)
153
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ANSWER TO SELECTED PROBLEMS
A
Abandonment 383, 399
Accounting
cost 72
depreciation 72, 302
fundamental equation of 71
as source of estimates 89
Accounting fundamentals 71
Accuracy of cost estimates 88
Actual dollars, definition 354
Additive weighting method 595
Adjusted (cost) basis 304
After-tax cash flow analyses
general procedure for 327
impact of inflation on 362
sensitivity analysis in 448
spreadsheet example 332
After-tax cash flow table 329
After-tax comparisons
equations for ATCF 328
illustration using different methods 331-
341 After-tax economic life 400
Allocation of capital 548, 567
Alternative Depreciation System (ADS)
development of
brainstorming, 12, 115
Nominal Group Technique 12,115
do-nothing (no change) 6, 263, 566
202 essential 202
feasible 10
independent 480, 568
investment 248
mutually exclusive 247, 482, 568
repeatability assumption 252, 274, 396,
486
rules for comparing by rate of return
methods
260
Analysis (study) period 202, 252
infinite 252, 397
as a source of uncertainty 426
Annual percentage rate (APR) 169
Annual worth (AW) method 213, 254,
339 spreadsheet example 220, 257, 618
unequal lives 279, 283
Annuity 142 d
deferred 149
fixed and responsive (to inflation) 360
INDEX
154
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ANSWER TO SELECTED PROBLEMS
310, 311 Alternatives
comparison of 247, 270, 339, 387, 482
basic philosophy 248, 251
by benefit/cost ratio method 482
by capitalized worth method 211, 259
by equivalent worth methods 253 3
by rate of return methods 260, 283
with different useful lives 274
contingent 572
cost 249, 339
coterminated assumption 252, 274, 396
decision (selection) 14
ordinary 149
Answers to problems 660
Arithmetic sequences
interest formulas for 158-159
modeling expenses 281
spreadsheet example 617
Assets 71, 327 Assumed certainty 424
Attributes 582
selection of 584
weighting of 595
Augmentation versus replacement 383,
410 Avoidable difference 136
B
Balance sheet 71, 74
Base alternative 248, 262 Base time
period 354 Basis (cost) 304, 316
Before-tax cash flow 328 Before-tax MARK
322
Benefit-cost ratio method 486, 473 :)
after-the-fact justifications 487
case study 489
conventional ratio 474-476 criticisms of
487
distributional considerations 488
independent projects /alternatives 480
modified ratio 474-476 mutually
return to 129, 201
sources 550
Capital allocation 548-550, 567
Capital asset pricing model (CAPM) 553-
555 Capital financing 548-550 Capital
gains and losses 327
Capital investment, fundamental purpose
of 248 Capital rationing 203, 480 Capital
recovery
depreciation plus interest 214 factor
147
Capital sources 550
borrowed (debt) capital 129, 551
equity capital 129, 552
155
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ANSWER TO SELECTED PROBLEMS
exclusive alternatives 482
omitting qualitative (no monetary)
information 489
spreadsheet example 485
Beta (volatility) 554
Bibliography 657
Bond rate 209
Bond valuation 209
Book cost (value) 29, 304 Borrowed
capital 129, 551 Borrowing-lending
terminology 139 Brainstorming 12, 115
Breakeven analysis 38, 43, 339, 427, 615
Breakeven chart 38, 43, 341, 431, 433,
616 Breakeven life 230, 428 Breakeven
point 38, 43, 341, 427
Budget constraints 568, 572
Budget (semi-detailed) estimates 88
Burden 28, 74
C
Capacity utilization 428, 452
Capital 128
allocation 548-550, 567
average weighted cost of 322, 552, 555
borrowed 129, 322, 551
budgets 568, 572, 564
debt 129, 322, 551
equity 129, 322, 552
financing 548-550
investment 33, 248
leasing 564-567
Capitalized cost 211
Capitalized worth (CW) method 211, 259,
397 Case (comprehensive) studies
after taxes 338
automobile financing 575
benefit-cost ratio 489
cost estimating 116
decision tree analysis 535
depreciation 317
economic equivalence 179
incremental analysis 285
inflation 371, 410
no monetary attributes 60, 587
present economy 60
process yield 231
replacement 410
sensitivity 450
Cash flow(s)
after-tax 328
approach 13
developing 79, 81, 116
diagrams 133-135
estimating 79, 81, 91
tables 133, 136
Certainty (assumed) 424
Challenger (new asset) 383
economic life 386, 390, 400
156
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ANSWER TO SELECTED PROBLEMS
Charts
breakeven 38, 43, 341, 431, 433, 616
sensitivity 435, 438, 440, 442
Class life 305, 310, 311, 314
Combinations, mutually exclusive 568
Combined (market) interest rate 354
Common errors
in inflation analyses 357
in rate of return analyses 265
in replacement analyses 412, 414
Common unit of measurement 7
Communication 562
Comparison of alternatives 247, 339, 387,
482 Compensatory models 586, 591
Competition 36
Compound interest 131, 168
Compounding
continuous, with discrete cash flows
172, discrete 149
more often than cash flows 170
more often than yearly 170
Conditional probability 532
Constant dollars 354
Constant percentage method 307
Consumer Price Index 93, 353
Consumer goods (services) 34
Contingency 426
Contingent projects 572 Continuous
compounding
nonrecurring 28
operation and maintenance 33
opportunity 30, 129, 385
overhead 28, 74
prime 76
recurring 28
standard 29
sunk 29, 385
target 110
terminology 24
variable 24
Cost accounting 72
Cost alternatives 249, 339
Cost and revenue structure 82, 87
Cost-capacity factor 97
Cost basis 304, 316
Cost-driven design optimization 45
Cost driver 45, 96
Cost estimating (see Estimating)
Cost estimating relationships (CERs) 96
development of 102
Cost indexes (see Indexes)
157
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ANSWER TO SELECTED PROBLEMS
discrete cash flows, interest formulas
for 172-174
Continuous random variables 501
evaluation of projects with 512
Conventional B-C ratio 474-476
Correlation coefficient 107
Cost(s) 24
basis 304, 316
book 29, 304
capital recovery 213-214
cash 29
concepts 24
depreciation 302 direct 28, 74
disposal 34
driver 45, 96
fixed 24
general elements of 74 incremental 25,
57 index (see Indexes) indirect 28, 74
investment 32
life cycle 31, 87, 585 marginal 387,
390, 393, 401
noncash 29, 302
Cost of capital 550-551, 555
debt 552
equity 555
weighted average 322, 552, 555
Cost recovery percentages 312
Cost terminology 24
Coterminated assumption 252, 274,
396,397 Criteria 7, 14
Current dollars 354
Cycle time 55
D
Data sources for cost estimating 89
Debt capital 129, 551
Decision analysis, multiple objectives in
583 Decision reversal (sensitivity to) 444
Decision trees
case study 535
definition 526
deterministic example 526
general principles of diagramming 528
with random outcomes 529
Declining balance method 307
Defender (old asset) 383
economic life of 387, 393, 400
investment value 385, 402
Deferred annuities 150
Deferred investments 394, 413
Definitive (detailed) estimates 88
Disjunctive resolution 587
Disposal cost 34
Disposal price (of bonds) 209 Dollars
158
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ANSWER TO SELECTED PROBLEMS
Deflation (general price) 353, 354, 355
Delphi method 90
Dependence between pairs of projects 561
Depreciable life. 305
Depreciable property 302, 387
Depreciation 72, 302
accounting for 72, 302
Alternative Depreciation System (ADS)
310, 311
basis 304, 316
class lives (MACRS) 305, 310, 311, 314
classical methods 303, 305
comprehensive example 317
constant percentage method 307
declining percentage method 307
General Depreciation System (GDS)
311 half-year convention 312
historical methods 303, 305
illustration in after-tax analysis 330
MACRS method 310
MACRS rates 313
Matheson formula 307
present worth of 320, 330
property class 313, 315
recapture 327, 332
recovery period 304, 311
recovery rate 305, 313
straight-line method 305
switchover option 308
units-of-production method 308
useful life guidelines 311
actual 354
constant 354
current 354
real 354
Dominance 586
Do-nothing alternative 6, 263, 566
E
Economic breakeven analysis 38, 43, 339,
427,615
Economic decision studies, importance of
4 Economic equivalence (case study) 179
Economic life 384, 386-387
after-tax 400
of challenger 386, 390
of defender 387, 393
spreadsheet example 392
Economic value 583
Economic value added (EVA) 341
Economy
engineering (definition) 4
present (studies) 50
Effective income tax rate 322, 325
corporate rates 324
Effective interest rate 168, 172
Elective projects 202
End-of-period cash flows 134, 202, 611
Engineering (definition of) 4
Engineering design
159
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ANSWER TO SELECTED PROBLEMS
Design (see Engineering design)
Design to cost 110
Design to price 108
Developing cash flows 79
Developing cost estimating relationships
(CERs) 102
Dimensionality 585
Direct costs 28, 74
Disbenefits 467, 477
Discounted cash flow rate of return
method 217 Discounted payback period
230
Discrete compounding 149
Discrete random variables 500
evaluation of projects with 503
cost-driven optimization 45
definition 9
for the environment 45, 285
process 9
target costing 110
value engineering 114
Engineering economic analysis procedure
8 Engineering economy
definition 4
and the design process 8 7
interest rate to use 357
origins of 5
principles of 5-8
Equity capital 71, 129, 552
Equivalence 132,152
case study 179
terminology 139
Equivalent uniform annual cost (EUAC)
214,384 Equivalent worth methods 205-
216, 253
ERR method (see External rate of
return) Essential projects 202, 250
Esteem value 583
Estimates
accounting data (as a source) 89
accuracy versus costs 89
needed for typical g engineering
economy study 87
Exponential model (for estimating) 97
External of return (ERR) method 227, 245-
246, 269
advantages over IRR method 228
F
Face value of bonds 209
Factor technique (for
estimating) 94 Feasible
alternatives 10
Financing
with debt capital 551
with equity capital 552
installment 222
160
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ANSWER TO SELECTED PROBLEMS
types of 88
ways to accomplish 90
Estimating,
by analogy 90
baseline 84
bottom-up approach 80, 108, 116
case study 116
cash flows 79, 116
comparison technique
90
components of an integrated approach
82
data (sources)
89, 93 Delphi
method 90 factor
technique 94
indexes 91
learning and improvement 98
parametric 96
power-sizing technique 97
product costs
108 purpose 88
ratio technique
91 relationships
96, 103 sellingprice 110
spreadsheet example 100, 105, 109, 113
target costing 110
techniques (models)
88, 91
top-down approach 80, 110
unit technique 93
through leasing 564-567
Fixed costs 24
Future worth (FW) method 212,
254 spreadsheet example 220,
257, 618
G
Gains and losses on capital 327
General Depreciation System (GDS) 311
General economic environment 34
General price inflation rate 353, 354
calculation of 353
Geometric sequences 143,163
modeling price changes 372
spreadsheet example 166, 617
Gradients
arithmetic (uniform) sequences 157, 28i,
617 geometric sequences 163, 372, 617
spreadsheet example 617
Graphical sensitivity displays 431, 433,
435, 438, 440,442
Graphical breakeven point solutions 38, 43,
341, 431,433
Green engineering 45, 285
Gross income 323
H
Hurdle rate 203, 231
Hurwicz procedure 593
161
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ANSWER TO SELECTED PROBLEMS
EUAC method (see Equivalent uniform
annual cost)
Exchange rates
366 Excise taxes
322
Expected value 501
Expected value of perfect information
(EVPI) 531, 536
Expenses (see Costs)
Experience curve (see Learning curve)
I
Improvement (see Learning)Imputed market value 284
In-lieu payments 468 Income statement
71, 74 Income taxes 301, 321
cash flow for 328
corporate federal tax rates 324
effect of, on average cost of capital
322, 555 effective rate 325
gains and losses 327 inflation's effect
on 362 replacement studies 387, 400,
410
Inconsistent ranking problem 260
Incremental analysis of alternatives 50
benefit-cost method 483 case study
285
rate of return methods 262
spreadsheet example 268, 485
unequal lives 277, 283
Incremental cash flow 249, 260, 263
fundamental role 261 Incremental cost 25,
57 Incremental revenue 25
Independent investment opportunities
/projects
480,568
compound 131,168
definition 129
factor relationships 149
origins of 130 real rate 354
simple 130
Interest factors
for continuous compounding 174
for discrete compounding 150
relationships 148
Interest rate
constant 206
effective 168
inflation-free 354
nominal 168
public projects 472
real versus combined, definition 354
risk adjusted 445
risk-free 554 time varying 167
Interest symbols 150,174
162
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ANSWER TO SELECTED PROBLEMS
Indexes 91
Indirect costs 28, 74
Inflation (and price changes) 353
analogy to foreign exchange rates 366
case studies 371, 410 common errors
357
fixed and responsive annuities 360
general price (inflation) 353, 354
impact of general price inflation onafter-tax studies 362
interest rate to use in engineering
economy studies 357
modeling with geometric cash flow
sequences 372
relationship between actual dollars and
real dollars 355
relationship between combined and real
interest rates 358
in replacement studies 410
spreadsheet example 364, 413, 414
terminology and basic concepts 354
Installment financing 222
Intangible property 303
Interest
combined (nominal) rate 354
Interest tables
continuous compounding 650
discrete compounding 631
Internal rate of return 217, 260, 332, 450,
570 assumption 227
common errors 265
difficulties 227 modified 227
multiple rates of return problem 227,
244 selecting trial rates 219
spreadsheet example 220, 221, 268,
618
Internal Revenue Service (IRS) 304
Interpolation 219, 223
Investment alternatives 248
Investment classification 560
Investment balance diagram 217, 223
Investment cost 32
IRR method (see Internal rate of return)
J
Joint probability 533-534
L
Labor costs 75
Learning
and improvement 98 Minimum attractive rate of return (MARK)
202-204, 557-559
163
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ANSWER TO SELECTED PROBLEMS
curve 98
Leasing of assets 339, 383, 410, 564-567
true lease v. conditional sale 565
Lexicography 587 Liabilities 71
tax 326
Life
of challenger 386, 390
of defender 387, 393
depreciable 305
economic 384, 386, 387,400
guideline periods 311
ownership 384 physical 384
useful 251, 274, 305, 384
Life cycle 31, 87
phases of 31-32
relationship to design 32
Life cycle cost 31, 412, 585
Linear interpolation 219, 223
Linear programming and capital allocation
571-575
Liquidity 229, 233
Lives, different, repeatability v.
coterminated assumptions 252, 274,
396-397
Loan repayment schemes 132
Luxuries 35
M
Make versus purchase (studies) 57
after-tax 322
definition 202
guidelines for 202-203
opportunity cost principle 203, 558 risk
adjusted 445, 557
Modified ACRS 303,310
flow diagram 315
Modified B-C ratio 474-476
Modified internal rate of return (MIRK) 227
Monopoly 36
Monte Carlo simulation 518
spreadsheet example 522-524 Mortgages
(see Installment financing) Multiple
alternatives
independent 480, 569
mutually exclusive 247, 482, 569
Multiple attributes, methods for considering
582, 586,591
Multiple internal rates of return 227,244
Multiple objectives 7, 13, 582
Multiple-purpose projects 468
Mutually exclusive alternatives 247, 482,
569 analysis of (see Comparison of
alternatives) ranking errors 260, 482
Mutually exclusive combinations 569
N
Necessities 35
Net cash flow 13, 134, 248
Net operating profit after taxes 341, 552
164
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ANSWER TO SELECTED PROBLEMS
Manufacturing example of cost estimating
109
Manufacturing progress function (see
Learning curve)
Marginal cost 387, 390, 393, 401
Marginal probability 533-534
Market premium 555
Market value 304,385-386
Material selection 52
Mathematical expectation 501
Matheson formula 307
Maximin and maximax rules 593-594
Measures of economic worth 34
Method of feasible ranges 586
Method of least squares 104
Net salvage value 305 Net worth 71
Nominal Group Technique 12,115
Nominal interest rate 168
No compensatory models 586
No dimensional scaling 591
No monetary factors (attributes) 7, 13,
415, 489,
582
case study 60, 587
choice of 584
selecting a measurement scale 585
Nonrecurring costs 28
Normal probability distribution 513, 515
Notation 626
O
Objectives
multiple 7,13, 582
setting minimum return 202-204
OBRA 321 Obsolescence 383 )
Operation and maintenance costs 33
Opportunity cost 30, 129
in determination of interest rates 202-
204, 472, 558
in replacement analysis 385 Optimistic-
pessimistic estimates 441
Order of magnitude estimates 88
Price index (see Indexes)
Prime costs 76
Principles of engineering economy 5-8
Probabilistic risk analysis 499
an application perspective 512
Probabilities
conditional 532
joint 533-534
marginal 533-534
revised 532
Probability functions 500
Probability tree diagram 510
165
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ANSWER TO SELECTED PROBLEMS
Ordinal ranking 589
Ordinary annuity 149
Outsider viewpoint 385-386, 387, 402
Overhead costs 28, 74-75
Overhead rate 75
Ownership life 385
P
Parametric cost estimating 96
Par value (of bonds) 209
Payback (payout) period method
discounted 230
simple 229
Perfect competition 36
Perpetual series of uniform payments 211
Personal property 303
Perspective (viewpoint)
in engineering economy studies 6, 84,
137
life cycle 45
outsider 385
public projects 467
systems 10
Physical life 384
Planning horizon 202, 252
Portfolios 553, 571
Post evaluation (of results) 8, 14, 72, 563
Postmortem project review 563
Postponement (of investment) 395
Power-sizing technique (for estimating) 97
Problem solving, efficiency 10
Producer goods (services) 34
Producer Price Index 93, 353
Profit 38-42, 53, 55, 71, 80, 110, 129,
341, 540, 549 Profit and loss statement
71
Profitability 202, 217, 229, 233, 262, 321,
327, 343, 570
index 217
Project (investment) portfolio 553, 571
Project selection 559-563
Projects
dependence between pairs of 561
elective 202 essential 202
independent (comparisons among)
480,
569-571
multiple-purpose 468
public 465
public versus privately owned 466
Property
depreciable 302, 387
intangible 303 personal 303
real 303
tangible 303
Property class 304, 310-311
Property taxes 321 Public projects 465
additional benefits v. reduced costs
477,479
benefit-cost ratio 473
166
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ANSWER TO SELECTED PROBLEMS
Present economy studies 50
case study 60
Present worth (PW) method 205, 254, 331
spreadsheet example 220, 257, 332,
436, 618
Price 34
benefits 467 costs 467
difficulties inherent in 470
disbenefits 467, 477
interest rate 472
167