APPENDIX 2 Table 1 : Present value of a regular annuity of $1 per period for n periods : PVFA (k,n) Σ= i=1 n = 1 (1+ K) 1 (1 + k)n k Number of Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 1 2 3 4 5 3.9020 4.8534 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 1.9704 1.9416. 1.9135 1.8861 1.8594 1.8334 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 3.8077 3.7171 3.6299 3.5460 3.4651 4.7135 4.5797 4.4518 4.3295 4.2124 0.9346 0.9259 1.8080 1.7833 2.6243 2.5771 3.3872 3.3121 4.1002 3.9927 17% 18% 19% 20% 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333 1.7591 1.7355 1.7125 1.6901 1.6681 1.6467 1.6257 1.6052 1.5852 1.5656 1.5465 1.5278 2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.2459 2.2096 2.1743 2.1399 2.1065 3.2397 3.1699 3.1024 3.0373 2.9745 2.9137 2.8550 2.7982 2.7432 2.6901 2.6386 2.5887 3.8897 3.7908 3.6959 3.6048 3.5172 3.4331 3.3522 3.2743 3.1993 3.1272 3.0576 2.9906 15% 16% 6 5.7955 5.6014 7 5.4172 6.7282 6.4720 6.2303 5.2421 6.0021 8 7.6517 7.3255 7.0197 6.7327 9 8.5660 8.1622 7.7861 7.4353 7.1078 10 9.4713 8.9826 8.5302 8.1109 7.7217 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 6.8017 6.5152 6.2469 5.9952 5.7590 7.3601 7.0236 6.7101 6.4177 6.1446 4.2305 4.1114 3.9975 4.7122 4.5638 4.4226 5.1461 4.9676 4.7988 5.5370 5.3282 5.1317 5.8892 5.6502 5.4262 3.8887 3.7845 3.6847 3.5892 3.4976 3.4098 3.3255 4.2883 4.1604 4.0386 3.9224 3.8115 3.7057 3.6046 4.6389 4.4873 4.3436 4.2072 4.0776 3.9544 3.8372 4.9464 4.7716 4.6065 4.4506 4.3038 4.1633 4.0310 5.2161 5.0188 4.8332 4.6586 4.4941 4.3389 4.1925 11 10.3676 9.7868 9.2526 8.7605 8.3064 12 11.2551 10.5753 9.9540 9.3851 13 12.1337 11.3484 10.6350 9.9856 8.8633 9.3936 14 13.0037 15 13.8651 12.1062 11.2961 10.5631 9.8986 12.8493 11.9379 11.1184 10.3797 7.8869 7.4987 7.1390 6.8052 6.4951 6.2065 5.9377 5.6869 5.4527 5.2337 5.0286 4.8364 4.6560 4.4865 4.3271 8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 6.1944 5.9176 5.6603 5.4206 5.1971 4.9884 4.7932 4.6105 4.4392 8.8527 8.3577 7.9038 7.4869 7.1034 6.7499 6.4235 6.1218 5.8424 5.5831 5.3423 5.1183 4.9095 4.7147 4.5327 9.2950 8.7455 8.2442 7.7862 7.3667 6.9819 6.6282 6.3025 6.0021 5.7245 5.4675 5.2293 5.0081 4.8023 4.6106 9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 6.8109 6.4624 6.1422 5.8474 5.5755 5.3242 5.0916 4.8759 4.6755 16 17 18 14.7179 13.5777 12.5611 15.5623 14.2919 13.1661 16.3983 14.9920 13.7535 19 20 11.6523 10.8378 10.1059 9.4466 8.8514 12.1657 11.2741 10.4773 9.7632 9.1216 12.6593 11.6896 10.8276 10.0591 9.3719 17.2260 15.6785 14.3238 13.1339 12.0853 11.1581 10.3356 9.6036 18.0456 16.3514 14.8775 13.5903 12.4622 11.4699 10.5940 9.8181 25 30 22.0232 19.5235 17.4131 25.8077 22.3965 19.6004 40 50 60 8.3126 7.8237 7.3792 6.9740 6.6039 6.2651 5.9542 5.6685 5.4053 5.1624 4.9377 4.7296 8.5436 8.0216 7.5488 7.1196 6.7291 6.3729 6.0472 5.7487 5.4746 5.2223 4.9897 4.7746 8.7556 8.2014 7.7016 7.2497 6.8399 6.4674 6.1280 5.8178 5.5339 5.2732 5.0333 4.8122 8.9501 8.3649 7.8393 7.3658 6.9380 6.5504 6.1982 5.8775 5.5845 5.3162 5.0700 4.8435 9.1285 8.5136 7.9633 7.4694 7.0248 6.6231 6.2593 5.9288 5.6278 5.3527 5.1009 4.8696 15.6221 14.0939 12.7834 11.6536 10.6748 9.8226 9.0770 8.4217 7.8431 7.3300 6.8729 6.4641 6.0971 5.7662 5.4669 5.1951 4.9476 17.2920 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269 8.6938 8.0552 7.4957 7.0027 6.5660 6.1772 5.8294 5.5168 5.2347 4.9789 32.8347 27.3555 23.1148 19.7928 17.1591 15.0463 13.3317 11.9246 10.7574 9.7791 8.9511 8.2438 7.6344 7.1050 6.6418 6.2335 5.8713 5.5482 5.2582 4.9966 39.1961 31.4236 25.7298 21.4822 18.2559 15.7619 13.8007 12.2335 10.9617 9.9148 9.0417 8.3045 7.6752 7.1327 6.6605 6.2463 5.8801 5.5541 5.2623 4.9995 44.9550 34.7609 27.6756 22.6235 18.9293 16.1614 14.0392 12.3766 11.0480 9.9672 9.0736 8.3240 7.6873 7.1401 6.6651 6.2402 5.8819 5.5553 5.2630 4.9999 END OF PAPER Table 1: Present value of $1: PVFA (k,n) = 1 (1 + k)n APPENDIX 1 Number of 1% 2% 3% 4% 5% 6% 7% 8% 9% 12% 13% Periods 1 0.9901 0.9804 0.9709 0.9615 2 0.9524 0.9434 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 3 4 5 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.8163 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 10% 11% 15% 25% 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333 0.8000 0.8734 0.8573 0.8417 0.8264 0.8116 0.7972 0.7831 0.7695 0.7561 0.7432 0.7305 0.7182 0.7062 0.6944 0.6400 0.7938 0.7722 0.7513 0.7312 0.7118 0.6931 0.6750 0.6575 0.6407 0.6244 0.6086 0.5934 0.5787 0.5120 0.7350 0.7084 0.6830 0.6587 0.6355 0.6133 0.5921 0.5718 0.5523 0.5337 0.5158 0.4987 0.4823 0.4096 0.6806 0.6499 0.6209 0.5935 0.5674 0.5428 0.5194 0.4972 0.4761 0.4561 0.4371 0.4190 0.4019 0.3277 14% 16% 17% 18% 19% 20% 6 7 8 9 10 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584. 0.5083 0.6302 0.5963 0.5645 0.5346 0.5066 0.4803 0.4556 0.4323 0.4104 0.3898 0.3704 0.3521 0.5835 0.5470 0.5132 0.4817 0.4523 0.4251 0.3996 0.3759 0.3538 0.3332 0.3139 0.2959 0.5403 0.5019 0.4665 0.4339 0.4039 0.3762 0.3506 0.3269 0.3050 0.2848 0.2660 0.5002 0.4604 0.4241 0.3909 0.3606 0.3329 0.3075 0.2843 0.2630 0.2434 0.4632 0.4224 0.3855 0.3522 0.3220 0.2946 0.2697 0.2472 0.2267 0.2080 0.3349 0.2621 0.2791 0.2097 0.2487 0.2326 0.1678 0.2255 0.2090 0.1938 0.1342 0.1911 0.1756 0.1615 0.1074 11 12 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.3173 0.2875 0.2607 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2858 0.2567 0.2307 13 14 15 0.2366 0.2149 0.1954 0.1778 0.1619 0.1476 0.1346 0.0859 0.2076 0.1869 0.1685 0.1520 0.1372 0.1240 0.1122 0.0687 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2575 0.2292 0.1821 0.1625 0.1452 0.1299 0.1163 0.1042 0.0935 0.0550 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.2320 0.2046 0.1807 0.1597 0.1413 0.1252 0.1110 0.0985 0.0876 0.0779 0.0440 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 0.2090 0.1827 0.1599 0.1401 0.1229 0.1079 0.0949 0.0835 0.0736 0.0649 0.0352 0.2042 16 17 18 19 20 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.0929 0.0802 0.0693 0.0600 0.0520 0.0451 0.0225 0.8360 0.7002 0.5874 0.4936 0.4155 0.3503 0.2959 0.2502 0.2120 0.1799 0.1528 0.1300 0.1108 0.0946 0.0808 0.0691 0.0592 0.0508 0.0437 0.0376 0.0180 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2765 0.2317 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.0703 0.0596 0.0506 0.0431 0.0367 0.0313 0.0144 0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 0.1240 0.1037 0.0868 0.0728 0.0611 0.0514 0.0433 0.0365 0.0308 0.0261 0.0115 0.2176 0.1883 0.1631 0.1415 0.1229 0.1069 0.0930 0.0811 0.0708 0.0618 0.0541 0.0281 25 0.7798 0.6095 30 0.7419 0.5521 0.4776 0.3751 0.2953 0.4120 0.3083 0.2314 40 0.2330 0.1842 0.1460 0.1160 0.0923 0.0736 0.1741 0.1314 0.0994 0.0754 0.0573 0.0437 0.6717 0.4529 0.3066 0.2083 0.1420 0.0972 0.0668 0.0460 0.0318 0.0221 0.0154 0.0588 0.0334 0.0471 0.0378 0.0304 0.0245 0.0197 0.0160 0.0129 0.0105 0.0038 50 60 0.6080 0.3715 0.2281 0.1407 0.0872 0.0543 0.0339 0.0213 0.0134 0.0085 0.0054 0.5504 0.3048 0.1697 0.0951 0.0535 0.0303 0.0173 0.0099 0.0057 0.0033 0.0019 0.0256 0.0196 0.0151 0.0116 0.0090 0.0070 0.0054 0.0042 0.0012 0.0107 0.0075 0.0053 0.0037 0.0026 0.0019 0.0013 0.0010 0.0007 0.0001 0.0035 0.0022 0.0014 0.0009 0.0006 0.0004 0.0003 0.0002 0.0001 0.0007 0.0011 0.0004 0.0002 0.0001 0.0001 ** * • The factor is zero to four decimal places
APPENDIX 2 Table 1 : Present value of a regular annuity of $1 per period for n periods : PVFA (k,n) Σ= i=1 n = 1 (1+ K) 1 (1 + k)n k Number of Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 1 2 3 4 5 3.9020 4.8534 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 1.9704 1.9416. 1.9135 1.8861 1.8594 1.8334 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 3.8077 3.7171 3.6299 3.5460 3.4651 4.7135 4.5797 4.4518 4.3295 4.2124 0.9346 0.9259 1.8080 1.7833 2.6243 2.5771 3.3872 3.3121 4.1002 3.9927 17% 18% 19% 20% 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333 1.7591 1.7355 1.7125 1.6901 1.6681 1.6467 1.6257 1.6052 1.5852 1.5656 1.5465 1.5278 2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.2459 2.2096 2.1743 2.1399 2.1065 3.2397 3.1699 3.1024 3.0373 2.9745 2.9137 2.8550 2.7982 2.7432 2.6901 2.6386 2.5887 3.8897 3.7908 3.6959 3.6048 3.5172 3.4331 3.3522 3.2743 3.1993 3.1272 3.0576 2.9906 15% 16% 6 5.7955 5.6014 7 5.4172 6.7282 6.4720 6.2303 5.2421 6.0021 8 7.6517 7.3255 7.0197 6.7327 9 8.5660 8.1622 7.7861 7.4353 7.1078 10 9.4713 8.9826 8.5302 8.1109 7.7217 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 6.8017 6.5152 6.2469 5.9952 5.7590 7.3601 7.0236 6.7101 6.4177 6.1446 4.2305 4.1114 3.9975 4.7122 4.5638 4.4226 5.1461 4.9676 4.7988 5.5370 5.3282 5.1317 5.8892 5.6502 5.4262 3.8887 3.7845 3.6847 3.5892 3.4976 3.4098 3.3255 4.2883 4.1604 4.0386 3.9224 3.8115 3.7057 3.6046 4.6389 4.4873 4.3436 4.2072 4.0776 3.9544 3.8372 4.9464 4.7716 4.6065 4.4506 4.3038 4.1633 4.0310 5.2161 5.0188 4.8332 4.6586 4.4941 4.3389 4.1925 11 10.3676 9.7868 9.2526 8.7605 8.3064 12 11.2551 10.5753 9.9540 9.3851 13 12.1337 11.3484 10.6350 9.9856 8.8633 9.3936 14 13.0037 15 13.8651 12.1062 11.2961 10.5631 9.8986 12.8493 11.9379 11.1184 10.3797 7.8869 7.4987 7.1390 6.8052 6.4951 6.2065 5.9377 5.6869 5.4527 5.2337 5.0286 4.8364 4.6560 4.4865 4.3271 8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 6.1944 5.9176 5.6603 5.4206 5.1971 4.9884 4.7932 4.6105 4.4392 8.8527 8.3577 7.9038 7.4869 7.1034 6.7499 6.4235 6.1218 5.8424 5.5831 5.3423 5.1183 4.9095 4.7147 4.5327 9.2950 8.7455 8.2442 7.7862 7.3667 6.9819 6.6282 6.3025 6.0021 5.7245 5.4675 5.2293 5.0081 4.8023 4.6106 9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 6.8109 6.4624 6.1422 5.8474 5.5755 5.3242 5.0916 4.8759 4.6755 16 17 18 14.7179 13.5777 12.5611 15.5623 14.2919 13.1661 16.3983 14.9920 13.7535 19 20 11.6523 10.8378 10.1059 9.4466 8.8514 12.1657 11.2741 10.4773 9.7632 9.1216 12.6593 11.6896 10.8276 10.0591 9.3719 17.2260 15.6785 14.3238 13.1339 12.0853 11.1581 10.3356 9.6036 18.0456 16.3514 14.8775 13.5903 12.4622 11.4699 10.5940 9.8181 25 30 22.0232 19.5235 17.4131 25.8077 22.3965 19.6004 40 50 60 8.3126 7.8237 7.3792 6.9740 6.6039 6.2651 5.9542 5.6685 5.4053 5.1624 4.9377 4.7296 8.5436 8.0216 7.5488 7.1196 6.7291 6.3729 6.0472 5.7487 5.4746 5.2223 4.9897 4.7746 8.7556 8.2014 7.7016 7.2497 6.8399 6.4674 6.1280 5.8178 5.5339 5.2732 5.0333 4.8122 8.9501 8.3649 7.8393 7.3658 6.9380 6.5504 6.1982 5.8775 5.5845 5.3162 5.0700 4.8435 9.1285 8.5136 7.9633 7.4694 7.0248 6.6231 6.2593 5.9288 5.6278 5.3527 5.1009 4.8696 15.6221 14.0939 12.7834 11.6536 10.6748 9.8226 9.0770 8.4217 7.8431 7.3300 6.8729 6.4641 6.0971 5.7662 5.4669 5.1951 4.9476 17.2920 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269 8.6938 8.0552 7.4957 7.0027 6.5660 6.1772 5.8294 5.5168 5.2347 4.9789 32.8347 27.3555 23.1148 19.7928 17.1591 15.0463 13.3317 11.9246 10.7574 9.7791 8.9511 8.2438 7.6344 7.1050 6.6418 6.2335 5.8713 5.5482 5.2582 4.9966 39.1961 31.4236 25.7298 21.4822 18.2559 15.7619 13.8007 12.2335 10.9617 9.9148 9.0417 8.3045 7.6752 7.1327 6.6605 6.2463 5.8801 5.5541 5.2623 4.9995 44.9550 34.7609 27.6756 22.6235 18.9293 16.1614 14.0392 12.3766 11.0480 9.9672 9.0736 8.3240 7.6873 7.1401 6.6651 6.2402 5.8819 5.5553 5.2630 4.9999 END OF PAPER Table 1: Present value of $1: PVFA (k,n) = 1 (1 + k)n APPENDIX 1 Number of 1% 2% 3% 4% 5% 6% 7% 8% 9% 12% 13% Periods 1 0.9901 0.9804 0.9709 0.9615 2 0.9524 0.9434 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 3 4 5 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.8163 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 10% 11% 15% 25% 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333 0.8000 0.8734 0.8573 0.8417 0.8264 0.8116 0.7972 0.7831 0.7695 0.7561 0.7432 0.7305 0.7182 0.7062 0.6944 0.6400 0.7938 0.7722 0.7513 0.7312 0.7118 0.6931 0.6750 0.6575 0.6407 0.6244 0.6086 0.5934 0.5787 0.5120 0.7350 0.7084 0.6830 0.6587 0.6355 0.6133 0.5921 0.5718 0.5523 0.5337 0.5158 0.4987 0.4823 0.4096 0.6806 0.6499 0.6209 0.5935 0.5674 0.5428 0.5194 0.4972 0.4761 0.4561 0.4371 0.4190 0.4019 0.3277 14% 16% 17% 18% 19% 20% 6 7 8 9 10 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584. 0.5083 0.6302 0.5963 0.5645 0.5346 0.5066 0.4803 0.4556 0.4323 0.4104 0.3898 0.3704 0.3521 0.5835 0.5470 0.5132 0.4817 0.4523 0.4251 0.3996 0.3759 0.3538 0.3332 0.3139 0.2959 0.5403 0.5019 0.4665 0.4339 0.4039 0.3762 0.3506 0.3269 0.3050 0.2848 0.2660 0.5002 0.4604 0.4241 0.3909 0.3606 0.3329 0.3075 0.2843 0.2630 0.2434 0.4632 0.4224 0.3855 0.3522 0.3220 0.2946 0.2697 0.2472 0.2267 0.2080 0.3349 0.2621 0.2791 0.2097 0.2487 0.2326 0.1678 0.2255 0.2090 0.1938 0.1342 0.1911 0.1756 0.1615 0.1074 11 12 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.3173 0.2875 0.2607 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2858 0.2567 0.2307 13 14 15 0.2366 0.2149 0.1954 0.1778 0.1619 0.1476 0.1346 0.0859 0.2076 0.1869 0.1685 0.1520 0.1372 0.1240 0.1122 0.0687 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2575 0.2292 0.1821 0.1625 0.1452 0.1299 0.1163 0.1042 0.0935 0.0550 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.2320 0.2046 0.1807 0.1597 0.1413 0.1252 0.1110 0.0985 0.0876 0.0779 0.0440 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 0.2090 0.1827 0.1599 0.1401 0.1229 0.1079 0.0949 0.0835 0.0736 0.0649 0.0352 0.2042 16 17 18 19 20 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.0929 0.0802 0.0693 0.0600 0.0520 0.0451 0.0225 0.8360 0.7002 0.5874 0.4936 0.4155 0.3503 0.2959 0.2502 0.2120 0.1799 0.1528 0.1300 0.1108 0.0946 0.0808 0.0691 0.0592 0.0508 0.0437 0.0376 0.0180 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2765 0.2317 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.0703 0.0596 0.0506 0.0431 0.0367 0.0313 0.0144 0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 0.1240 0.1037 0.0868 0.0728 0.0611 0.0514 0.0433 0.0365 0.0308 0.0261 0.0115 0.2176 0.1883 0.1631 0.1415 0.1229 0.1069 0.0930 0.0811 0.0708 0.0618 0.0541 0.0281 25 0.7798 0.6095 30 0.7419 0.5521 0.4776 0.3751 0.2953 0.4120 0.3083 0.2314 40 0.2330 0.1842 0.1460 0.1160 0.0923 0.0736 0.1741 0.1314 0.0994 0.0754 0.0573 0.0437 0.6717 0.4529 0.3066 0.2083 0.1420 0.0972 0.0668 0.0460 0.0318 0.0221 0.0154 0.0588 0.0334 0.0471 0.0378 0.0304 0.0245 0.0197 0.0160 0.0129 0.0105 0.0038 50 60 0.6080 0.3715 0.2281 0.1407 0.0872 0.0543 0.0339 0.0213 0.0134 0.0085 0.0054 0.5504 0.3048 0.1697 0.0951 0.0535 0.0303 0.0173 0.0099 0.0057 0.0033 0.0019 0.0256 0.0196 0.0151 0.0116 0.0090 0.0070 0.0054 0.0042 0.0012 0.0107 0.0075 0.0053 0.0037 0.0026 0.0019 0.0013 0.0010 0.0007 0.0001 0.0035 0.0022 0.0014 0.0009 0.0006 0.0004 0.0003 0.0002 0.0001 0.0007 0.0011 0.0004 0.0002 0.0001 0.0001 ** * • The factor is zero to four decimal places
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Crown Limited aims to expand its operations and increase its market share in the football industry by boosting its annual production capacity of 100,000 soccer balls by at least 6% over the next five years, while considering two football making machines.
Option One: involves importing a football machine at a landed purchase cost of R200,000, which is expected to last for five years. The net cash flow from the sale of the additional production is expected to be R50,000, R60,000, R65, R75, and R40,000, enabling Crown Limited to increase its productive capacity by 4%.
Option Two: involves purchasing a football machine locally for R200,000 with a 5-year useful life. The machine will not have a resale value and will be disposed of. Net
- Cown Limited mandates a 12% return on capital for all investments, with a straight-line
- The capital expenditure committee has allocated R400,000 for the company's capital expenditure, with projects with a payback period of less than four years being accepted.
Required
As the
Transcribed Image Text:APPENDIX 2
Table 1 : Present value of a regular annuity of $1 per period for n periods : PVFA (k,n)
Σ=
i=1
n
=
1
(1+ K)
1
(1 + k)n
k
Number
of
Periods
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
1
2
3
4
5
3.9020
4.8534
0.9901 0.9804 0.9709 0.9615 0.9524 0.9434
1.9704 1.9416. 1.9135 1.8861 1.8594 1.8334
2.9410 2.8839 2.8286 2.7751 2.7232 2.6730
3.8077 3.7171 3.6299 3.5460 3.4651
4.7135 4.5797 4.4518 4.3295 4.2124
0.9346 0.9259
1.8080 1.7833
2.6243 2.5771
3.3872 3.3121
4.1002 3.9927
17% 18% 19% 20%
0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333
1.7591 1.7355 1.7125 1.6901 1.6681 1.6467 1.6257 1.6052 1.5852 1.5656 1.5465 1.5278
2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.2459 2.2096 2.1743 2.1399 2.1065
3.2397 3.1699 3.1024 3.0373 2.9745 2.9137 2.8550 2.7982 2.7432 2.6901 2.6386 2.5887
3.8897 3.7908 3.6959 3.6048 3.5172 3.4331 3.3522 3.2743 3.1993 3.1272 3.0576 2.9906
15%
16%
6
5.7955 5.6014
7
5.4172
6.7282 6.4720 6.2303
5.2421
6.0021
8
7.6517 7.3255 7.0197
6.7327
9
8.5660 8.1622 7.7861
7.4353
7.1078
10
9.4713 8.9826 8.5302
8.1109
7.7217
5.0757 4.9173 4.7665 4.6229 4.4859 4.3553
5.7864 5.5824 5.3893 5.2064 5.0330 4.8684
6.4632 6.2098 5.9713 5.7466 5.5348 5.3349
6.8017 6.5152 6.2469 5.9952 5.7590
7.3601 7.0236 6.7101 6.4177 6.1446
4.2305 4.1114 3.9975
4.7122 4.5638 4.4226
5.1461 4.9676 4.7988
5.5370 5.3282 5.1317
5.8892 5.6502 5.4262
3.8887 3.7845 3.6847 3.5892 3.4976 3.4098 3.3255
4.2883 4.1604 4.0386 3.9224 3.8115 3.7057 3.6046
4.6389 4.4873 4.3436 4.2072 4.0776 3.9544 3.8372
4.9464 4.7716 4.6065 4.4506 4.3038 4.1633 4.0310
5.2161
5.0188 4.8332 4.6586 4.4941 4.3389 4.1925
11
10.3676 9.7868
9.2526
8.7605
8.3064
12
11.2551 10.5753 9.9540
9.3851
13
12.1337
11.3484 10.6350 9.9856
8.8633
9.3936
14
13.0037
15
13.8651
12.1062 11.2961 10.5631 9.8986
12.8493 11.9379 11.1184 10.3797
7.8869 7.4987 7.1390 6.8052 6.4951 6.2065 5.9377 5.6869 5.4527 5.2337 5.0286 4.8364 4.6560 4.4865 4.3271
8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 6.1944 5.9176 5.6603 5.4206 5.1971 4.9884 4.7932 4.6105 4.4392
8.8527
8.3577 7.9038 7.4869 7.1034 6.7499 6.4235 6.1218 5.8424 5.5831 5.3423 5.1183 4.9095 4.7147 4.5327
9.2950 8.7455 8.2442 7.7862 7.3667 6.9819 6.6282 6.3025 6.0021 5.7245 5.4675 5.2293 5.0081 4.8023 4.6106
9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 6.8109 6.4624 6.1422 5.8474 5.5755 5.3242 5.0916 4.8759
4.6755
16
17
18
14.7179 13.5777 12.5611
15.5623 14.2919 13.1661
16.3983 14.9920 13.7535
19
20
11.6523 10.8378 10.1059 9.4466 8.8514
12.1657 11.2741 10.4773 9.7632 9.1216
12.6593 11.6896 10.8276 10.0591 9.3719
17.2260 15.6785 14.3238 13.1339 12.0853 11.1581 10.3356 9.6036
18.0456 16.3514 14.8775 13.5903 12.4622 11.4699 10.5940 9.8181
25
30
22.0232 19.5235 17.4131
25.8077 22.3965 19.6004
40
50
60
8.3126 7.8237 7.3792 6.9740 6.6039 6.2651 5.9542 5.6685 5.4053 5.1624 4.9377 4.7296
8.5436 8.0216 7.5488 7.1196 6.7291 6.3729 6.0472 5.7487 5.4746 5.2223 4.9897 4.7746
8.7556 8.2014 7.7016 7.2497 6.8399 6.4674 6.1280 5.8178 5.5339 5.2732 5.0333 4.8122
8.9501 8.3649 7.8393 7.3658 6.9380 6.5504 6.1982 5.8775 5.5845 5.3162 5.0700 4.8435
9.1285 8.5136 7.9633 7.4694 7.0248 6.6231 6.2593 5.9288 5.6278 5.3527 5.1009 4.8696
15.6221 14.0939 12.7834 11.6536 10.6748 9.8226 9.0770 8.4217 7.8431 7.3300 6.8729 6.4641 6.0971 5.7662 5.4669 5.1951 4.9476
17.2920 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269 8.6938 8.0552 7.4957 7.0027 6.5660 6.1772 5.8294 5.5168 5.2347 4.9789
32.8347 27.3555 23.1148 19.7928 17.1591 15.0463 13.3317 11.9246 10.7574 9.7791 8.9511 8.2438 7.6344 7.1050 6.6418 6.2335 5.8713 5.5482 5.2582 4.9966
39.1961 31.4236 25.7298 21.4822 18.2559 15.7619 13.8007 12.2335 10.9617 9.9148 9.0417 8.3045 7.6752 7.1327 6.6605 6.2463 5.8801 5.5541 5.2623 4.9995
44.9550 34.7609 27.6756 22.6235 18.9293 16.1614 14.0392 12.3766 11.0480 9.9672 9.0736 8.3240 7.6873 7.1401 6.6651 6.2402 5.8819 5.5553 5.2630 4.9999
END OF PAPER
Transcribed Image Text:Table 1: Present value of $1: PVFA (k,n) =
1
(1 + k)n
APPENDIX 1
Number
of
1%
2%
3%
4%
5%
6%
7%
8%
9%
12%
13%
Periods
1
0.9901 0.9804 0.9709 0.9615
2
0.9524 0.9434
0.9803 0.9612 0.9426 0.9246 0.9070 0.8900
3
4
5
0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.8163
0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629
0.9515 0.9057 0.8626 0.8219
0.7835 0.7473 0.7130
10% 11%
15%
25%
0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333 0.8000
0.8734 0.8573 0.8417 0.8264 0.8116 0.7972 0.7831 0.7695 0.7561 0.7432 0.7305 0.7182 0.7062 0.6944 0.6400
0.7938 0.7722 0.7513 0.7312 0.7118 0.6931 0.6750 0.6575 0.6407 0.6244 0.6086 0.5934 0.5787 0.5120
0.7350 0.7084 0.6830 0.6587 0.6355 0.6133 0.5921 0.5718 0.5523 0.5337 0.5158 0.4987 0.4823 0.4096
0.6806 0.6499 0.6209
0.5935 0.5674 0.5428 0.5194 0.4972 0.4761 0.4561 0.4371 0.4190 0.4019 0.3277
14%
16% 17% 18% 19% 20%
6
7
8
9
10
0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663
0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227
0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820
0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439
0.9053 0.8203 0.7441 0.6756 0.6139 0.5584. 0.5083
0.6302 0.5963 0.5645 0.5346 0.5066 0.4803 0.4556 0.4323 0.4104 0.3898 0.3704 0.3521
0.5835 0.5470 0.5132 0.4817 0.4523 0.4251 0.3996 0.3759 0.3538 0.3332 0.3139 0.2959
0.5403 0.5019 0.4665 0.4339 0.4039 0.3762 0.3506 0.3269 0.3050 0.2848 0.2660
0.5002 0.4604 0.4241 0.3909 0.3606 0.3329 0.3075 0.2843 0.2630 0.2434
0.4632 0.4224 0.3855 0.3522 0.3220 0.2946 0.2697 0.2472 0.2267 0.2080
0.3349 0.2621
0.2791 0.2097
0.2487 0.2326 0.1678
0.2255 0.2090 0.1938 0.1342
0.1911 0.1756 0.1615 0.1074
11
12
0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.3173 0.2875 0.2607
0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2858 0.2567 0.2307
13
14
15
0.2366 0.2149 0.1954 0.1778 0.1619 0.1476 0.1346 0.0859
0.2076 0.1869 0.1685
0.1520 0.1372 0.1240 0.1122 0.0687
0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2575 0.2292
0.1821 0.1625 0.1452 0.1299 0.1163 0.1042 0.0935 0.0550
0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.2320 0.2046 0.1807 0.1597 0.1413 0.1252 0.1110 0.0985 0.0876 0.0779 0.0440
0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 0.2090 0.1827 0.1599 0.1401 0.1229 0.1079 0.0949 0.0835 0.0736 0.0649 0.0352
0.2042
16
17
18
19
20
0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519
0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.0929 0.0802 0.0693 0.0600 0.0520 0.0451 0.0225
0.8360 0.7002 0.5874 0.4936 0.4155 0.3503 0.2959 0.2502 0.2120 0.1799 0.1528 0.1300 0.1108 0.0946 0.0808 0.0691 0.0592 0.0508 0.0437 0.0376 0.0180
0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2765 0.2317 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.0703 0.0596 0.0506 0.0431 0.0367 0.0313 0.0144
0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 0.1240 0.1037 0.0868 0.0728 0.0611 0.0514 0.0433 0.0365 0.0308 0.0261 0.0115
0.2176 0.1883 0.1631 0.1415 0.1229 0.1069 0.0930 0.0811 0.0708 0.0618 0.0541 0.0281
25
0.7798 0.6095
30
0.7419 0.5521
0.4776 0.3751 0.2953
0.4120 0.3083 0.2314
40
0.2330 0.1842 0.1460 0.1160 0.0923 0.0736
0.1741 0.1314 0.0994 0.0754 0.0573 0.0437
0.6717 0.4529 0.3066 0.2083 0.1420 0.0972 0.0668 0.0460 0.0318 0.0221 0.0154
0.0588
0.0334
0.0471 0.0378 0.0304 0.0245 0.0197 0.0160 0.0129
0.0105 0.0038
50
60
0.6080 0.3715 0.2281 0.1407 0.0872 0.0543 0.0339 0.0213 0.0134 0.0085 0.0054
0.5504 0.3048 0.1697 0.0951 0.0535 0.0303 0.0173 0.0099 0.0057 0.0033 0.0019
0.0256 0.0196 0.0151 0.0116 0.0090 0.0070 0.0054 0.0042 0.0012
0.0107 0.0075 0.0053 0.0037 0.0026 0.0019 0.0013 0.0010 0.0007 0.0001
0.0035 0.0022 0.0014 0.0009 0.0006 0.0004 0.0003 0.0002 0.0001
0.0007
0.0011
0.0004 0.0002 0.0001 0.0001
**
*
•
The factor is zero to four decimal places
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