期11% 2% 3% 4% 5% 6% 7% 8% 9% 012% 13% 415% 16% 17% 819% 20% 21% 223% 24% 25% 627% 28% 29% 0数 % % % % % % % 00.90.9901 804 0.9709 0.90.90.9615 524 434 0.9346 .0.90.99259 174 091 11.91.9704 416 1.9135 1.81.81.8861 594 334 1.8080 .1.71.77833 591 355 22.92.8410 839 2.8286 2.72.72.6751 232 730 2.6243 .2.52.54771 313 869 33.93.8020 077 3.7171 3.63.53.4299 460 651 3.3872 .3.33.21121 397 699 34.84.7534 135 4.5797 4.44.34.2518 295 124 4.1002 .3.93.87927 897 908 3.6959 3.1024 2.4437 1.7125 0.9009 0.0.0.0.0.11112231 0.80.880.80.80.880.80.80.880.80.80.870.70.70.77929 850 7696 621 547 4403 333 264 1130 065 000 9874 813 752 672 1.75 1.97 1.37 1.92 1.2 1.61.661.61.61.551.51.51.541.41.41.441.41.31.33901 681 4257 052 852 6465 278 095 9740 568 400 2074 916 761 667 2.56 2.15 2.35 1.09 1.3 2.42.332.22.22.212.12.12.002.01.91.991.81.81.88018 612 2832 459 096 7399 065 739 4114 813 520 2956 684 420 116 2.43 2.22 2.34 2.61 2.4 3.02.992.82.72.762.62.52.542.42.42.332.22.22.21373 745 1550 982 432 9386 887 404 9483 043 616 2800 410 031 637 3.01 3.36 2.02 2.62 2.5 3.63.543.33.23.113.02.92.982.82.72.662.52.52.44048 172 3522 743 993 2576 906 260 6035 454 893 3827 320 830 331 72 36 51 56 45.75.6955 014 5.4172 5.25.04.9421 757 173 4.7665 .4.64.43229 859 553 7 4.2305 3.3.3.2.2.6 4.13.983.73.63.543.43.33.213.03.02.982.82.72.76114 975 8845 847 892 9098 255 446 6923 205 514 8210 594 000 487 76 69 50 27 6.76.46.6.05.75.55.5.25.044.4.54.444.14.03.933.73.63.533.33.23.133.02.92.82282 720 23021 864 824 38064 330 .71638 226 .604 386 224 .057 046 079 .270 423 611 .087 370 682 .03 93 822 684 52883 48115 4.4155 3.0833 3.8021 2.8 7.67.3517 255 7.0197 6.76.46.2327 632 098 5.9713 .5.75.53466 348 349 55.1461 .4.94.764.44.34.203.93.83.763.53.43.323.13.02.99676 988 3873 436 072 7544 372 256 1179 212 289 4564 758 986 289 476 4.93 3.07 3.47 3.9 8.58.1660 622 7.7861 7.47.16.8353 078 017 6.5152 .6.25.97469 952 590 65.5370 .5.35.194.74.64.434.14.03.973.63.53.433.23.13.00282 317 4716 065 506 0633 310 054 8731 655 631 6728 842 997 164 530 4.63 3.57 3.90 3.19.48.90 713 826 8.5302 8.17.77.3109 217 601 7.0236 .6.76.41101 177 446 5.8892 .5.65.425.04.84.644.34.14.093.73.63.543.33.23.10502 262 1188 332 586 9389 925 541 2993 819 705 6644 689 781 961 41 32 48 15 611 10.3676 9.7868 9.2526 8.78.37.8605 064 869 7.4987 .7.16.84390 052 951 612 11.10.9.255575951 3 40 9.38.88.3851 633 838 7.9427 .7.57.18361 607 137 713 12.11.1333487 4 10.69.99.38.835856 936 527 0 8.3577 .7.97.41038 869 034 13.12.0031067 2 11.2961 10.5631 8.7455 78.27.7.442 862 366.9819 6.7499 6.4924 6.2065 5.4.4.3.3.5.95.645.25.04.864.44.34.103.93.73.653.43.33.21377 869 5337 286 364 5865 271 769 3018 757 564 4365 351 388 427 5.60 4.54 4.35 3.73 3.6.15.965.45.14.974.64.44.213.93.83.763.43.33.21944 176 6206 971 884 9105 392 784 2852 514 251 0933 868 859 903 5.32 4.74 4.59 3.03 3.6.46.185.55.35.194.74.54.324.03.93.763.53.43.32235 218 4831 423 183 0147 327 624 0530 124 801 5381 272 224 224 695 528 455 333 314 9.89.2986 950 6.66.3.5.75.45.2.4.84.64.4.4.13.93.8.3.53.43.3.282 025 0245 675 293 0023 106 317 2082 616 241 6733 587 507 20069467 715 13.12.8658491 3 11.9379 11.10.1183794 7 9.7122 9.1079 .8.58.06595 607 061 7.1909 21 6.81 5.46 4.49 3.87 3.6.86.415.85.55.304.84.64.434.14.03.873.63.43.32109 624 4474 755 242 9759 755 890 1530 013 593 2010 834 726 622 16 52 61 82 716 14.13.7175779 7 12.5611 11.10.10.9.652837105443 8 9 66 .8.88.38514 126 237 817 15.14.5622913 9 13.1661 12.11.10.9.165274477767 1 3 32 .9.18.50216 436 216 818 16.14.3989923 0 13.7535 12.11.10.6596898273 6 6 10..09.38.7259719 556 01 14 819 17.15.2266780 5 14.3238 13.12.11.1330851589 3 1 10..39.68.9335036 501 66 49 820 18.16.0453516 4 14.8775 13.12.11.5904624693 2 9 10..59.89.1594181 285 10 36 7.9633 7.8393 7.7016 7.5488 7.3792 6.5.4.3.3.6.96.625.95.65.414.94.74.534.14.03.873.63.53.32740 039 6542 685 053 6377 296 364 5894 333 874 5228 026 896 851 6.24 5.67 4.09 3.32 3.7.16.736.05.75.424.94.74.534.24.03.973.63.53.42196 291 7472 487 746 2897 746 755 9190 591 099 7400 177 028 929 6.23 5.08 4.05 3.48 3.7.26.846.15.85.525.04.84.644.24.03.973.63.53.43497 399 6280 178 339 7333 122 079 1431 799 279 8536 294 130 074 6.32 5.87 4.61 3.37 3.7.36.956.15.85.535.04.84.644.24.03.973.63.53.43658 380 5982 775 845 1700 435 346 4627 967 424 9642 386 210 104 6.62 5.15 4.85 3.05 3.7.47.066.25.95.635.14.84.644.24.13.983.63.53.43694 248 2593 288 278 5009 696 567 6786 103 539 0726 458 271 131 27 03 83 58 21 18.17.8570110 2 15.4150 14.12.11.0298217642 2 1 10.8355 10.0168 89.2.922 648.0751 654337.57.1.6.35.95.6.5.14.84.6.4.24.13.9.3.63.53.4.620 016 6125 731 648 3268 913 750 4916 212 631 8792 514 319 38871187 822 19.17.6606584 0 15.9369 14.13.12.4511630411 0 6 11.0612 10.2007 .9.47424 715 823 20.18.4552928 2 16.4436 14.13.12.8564883038 6 4 11.2722 10.3711 .9.58802 832 824 21.18.2439134 9 16.9355 15.13.12.2477985500 6 4 11.4693 10.5288 .9.79066 847 925 22.19.0235232 5 17.4131 15.14.12.6220937831 9 4 11.6536 10.6748 .9.80226 770 8.4217 8.3481 8.2664 8.1757 70 6.37 5.56 4.61 3.98 3.7.67.176.36.05.645.14.94.644.34.13.983.63.53.43446 695 4587 113 964 0486 094 900 8021 300 705 2844 558 356 229 6.99 5.82 4.23 3.30 3.7.77.276.36.05.745.14.94.744.34.13.983.63.53.43184 297 9988 442 234 3668 245 025 9106 371 764 2885 592 384 221 6.21 5.85 4.73 3.54 3.7.77.286.46.05.745.14.94.754.34.13.983.63.53.43843 829 3338 726 465 5822 371 128 0176 428 811 3918 619 406 251 6.09 5.70 4.12 3.72 3.7.87.386.46.05.745.14.94.754.34.13.983.63.53.43431 300 7641 971 662 6951 476 213 1232 474 849 3943 640 423 229 69 39 42 86 926 22.20.7951212 0 17.8768 15.14.13.9823750038 2 2 11.8258 10.8100 .9.91290 609 927 23.20.5597066 9 18.3270 16.14.13.3296432106 0 5 11.9867 10.10.9350262 6 .2372 928 24.21.3162814 3 18.7641 16.14.13.6638984061 1 2 12.1371 11.10.0511161 1 .3066 8.6016 8.5478 8.4881 6.5.4.3.3.7.87.396.46.15.745.24.94.754.34.13.983.63.53.43957 717 0906 182 831 8060 563 284 1278 511 879 3963 656 437 261 6.04 5.96 4.67 3.97 3.7.97.496.56.15.745.24.94.754.34.13.983.63.53.43426 086 3135 364 975 9151 636 342 2316 542 903 3979 669 447 352 6.19 5.43 4.87 3.05 3.7.97.496.56.15.855.24.94.754.34.13.983.63.53.43844 412 6335 520 099 0228 697 390 2346 566 923 4991 679 455 307 16 81 02 12 929 25.21.0658448 4 19.1885 16.15.13.9831415907 1 7 12.2777 11.10.1581984 3 .3696 930 25.22.8073967 5 19.6004 17.15.13.2923727640 5 8 12.4090 11.10.2572738 7 .4269 8.6938 8.6501 6.5.4.3.3.8.07.496.56.15.855.24.94.754.34.13.983.73.53.43218 701 8509 656 204 0292 747 430 3371 585 938 4001 687 461 330 7.98 5.12 4.14 3.17 3.8.07.406.56.15.855.24.94.754.34.13.983.73.53.43552 957 0660 772 294 1347 789 463 3391 601 950 4009 693 466 327 68 38 24 21
12n 1% 2% 3% 4% 5% 6% 8% 10% % 0.0.1 99 0.98 97 1 1.1.2 97 3 2.2.3 94 8 3.4 901 4.5 853 5.6 795 6.6.7 728 7.8 651 8.9 568.162 78437.325 7.019 7.6.471 23 2 6.732 7.7.107 806 59 326.463 2 6.5.74206 9 6.6.245.734 7 5.4.946 77607 4.3 4.4.303 03 787 4.9 3.3.565 46018 3.4 3.2.665 371447 2.5.3964.638 48344.077 83613.421 32922.598 33 8 2.1.9005.786 586 68 3 4.4.5.601 4.713 3.807 3.717 4.579 5.417 5 3.629 4.451 5.242 6.5.075 4.329 3.545 3 3.3.31462 5 4.3.99212 2 4.4.62912 7 5.5.204.8564.288 16 8 4.4 3.5 3.1 3.2 2.2.1021 2 7 2.1.955 1 4.4.033.811 60413.242 16802.507 260582 4 4 4.5 3.6 3.1 3.2 2.7 2.3 2.1.84.3113.888 78683.497 32163.02 95642.385 169824 9 4 4.2 3.4 3.3.3.7603.433 35273.127 99 3 3.9 2.5 2.5 2.5 1.1.869 7 3.4 3.8 3.2.862.745 68432.219 038736 8 3 2.1 2.6 2.9 2.9 1.1.73.1032.913 85792.69 58492.404 36161.996 847104 2.883 82772.723 677 86 1 3.3 2.5 2.6 2.2 2.2 2.6 2.8 1.3 1.1.66 2.3 2.2.572.4402.321 28242.174 10041.981 95811.695 584907 2.1.941 91881.859 833 35 69 5 2.5 2.7 2.1 2.1.1.1.3 1.1.781.71.1.646 62601.565 52491.456 44 36 4 1.5 1.1.40.960.952 945 09 2 9 1.2 1.3 1.9 1.1.1.1.289 221611 9 9 4 1.9 1.1.10.0.920.9890.877 86860.847 83810.806 79760.74 716866 0.14% % 0.% 0.151618% % 0.% 0.202224% % 0.% 0.253035% % 0.% 0.0.6404550% 6 9.6 5 1 8 1 5.6 4.833 5.028 5.4.656 4.494 4.192 4.327 4.4.793 439 4.4.909 532 6 3.3 9 3.8 2.2.715 413 2.2.751 438 2.3 2.1.91665 8 2.1.91876 4 2.1.91984 6 2.1.92089 4 2.1.92093 9 2.1.92195 3 2.1.92196 6 2.1.92197 8 2.1.92198 9 8.10 471 1011 .367 1112 .255 1213 .133 1314 .003 1315 .865 1416 .717 1517 .562 1618 .398 1719 .226 1820 .045 1821 .856 1922 .66 17.658 17.011 16.351 15.678 14.992 14.291 13.577 12.849 12.106 11.348 10.575 9.786 9.8.982 53 8.7.721 11 7.6.71 36 6.144 5.5.216 65 8 3 4.035 4.127 4.3.851 3.775 01923.681 3.0957 1 3.656 3.3.1942 7 5.5.842 583 5.6.002 724 5.5.342 5.4.467 5.575 5.668 5.748 5.817 5.877 5.928 5.973 6.011 5.409 5.383 5.352 5.316 5.273 5.222 5.162 5.091 4.675 4.729 4.4.7739 4 4.812 4.843 4.4.8646 9 4.891 4.909 4.475 4.3.488 4.129 97 4.121 4.11 4.418 4.441 4.096 4.079 4.059 5.008 61 7219 5 3.3.3.912 78 223 3.3.961 824 3.4.001 859 3.4.033 887 3.909 3.927 3.3.9431 2 3.953 3.963 3.315 3.319 3.322 2.853 2.851 2.85 2.847 3.248 3.268 3.283 3.294 3.303 2.844 2.839 2.833 2.825 2.814 2.799 5 2.468 2.477 2.483 2.488 2.491 2.494 2.2.4922 5 2.2.4922 7 2.497 2.498 2.2.779 453.147 7.8.7.138.306 76 888 6 9.385 9.985 10.563 11.118 11.652 12.165 12.659 13.133 13.59 14.029 14.451 13.163 12.821 12.462 12.085 11.689 11.274 10.837 10.379 9.898 9.393 8.863 8.7.536.8386 13 3 8.7.907.1853 03 2 9.8.247.3294 66 4 9.8.557.606 95 6.45.937 6.5.452 5.233 252 9.954 10.634 11.296 11.937 12.561 13.166 13.753 14.323 14.877 15.415 15.936 5.194 6.423 6.628 5.66 202 4.264 4.315 4.356 6.6.142 847 6.5.6.265 954 6.6.372 047 6.6.467 127 6.6.55 198 6.6.623 259 6.6.686 312 6.6.742 358 81 719 2 108.85.11 05 109.12.41 77 109.37.81 27 119.60.13 58 119.81.48 69 1110.0.716 64 128.7.041 10.2 71 4 6448 2 7.8.65613 9 7.8.54664 5 7.8.33601 9 7.8.22421 9 7.8.01123 3 7.7.8971.999 1.999 1.92299 1 2.1.92299 1 2023 .455 2124 .243 2225 .023 2226 .795 2327 .559 2428 .316 2529 .065 2521.844 21.281 20.706 20.121 19.523 18.913 18.292 16.443 16.935 17.413 17.876 18.327 18.764 19.188 14.856 15.246 15.622 15.982 16.329 16.663 16.983 1715.141 14.898 14.643 14.375 14.093 13.798 13.488 1210.3.371 03 1210.5.528 5 1210.6.774 83 1310.8.009 03 1310.9.235 1 1311.0.451 06 1311.1.558 9 1311.29.415.372 .757 26 64 1511.99.717.159 .024 79 46 1512.29.918.255 .733 14 61 69 9.306 9.337 9.26 9.177 9.084 8.983 8.87.718 7.784 7.843 7.6.872 6.835 6.792 6.398 6.433 6.464 6.044 6.072 6.097 6.5.466 5.45 5.432 4.924 4.937 4.947 4.5.48 956 4.5.491 963 4.5.501 969 4.5.509 974 4.5.516 978 4.5.548 996 4.5.554 999 4.498 4.507 4.513 4.519 4.4.151 4.147 4.142 4.137 3.976 3.981 3.984 3.987 3.325 3.327 3.328 3.329 2.855 2.855 2.855 2.854 2.498 2.499 2.499 2.499 2.2.1.92299 1 2.1.92299 1 2.1.92299 2 2.1.92299 2 2.1.92299 2 2.1.92299 2 2.1.92299 2 2.1.92299 2 2.1.92299 2 2.1.92299 2 6.895 7.942 7.984 8.6.021 8.055 8.243 8.6.304 7.132 66 6 5 9 3 9 24544.166 99332.857 497.105 7.002 6.565 6.641 6.983 55 5 6.177 6.233 6.1 4.533 4.543 4.4.165 4.16 3 3.995 3.999 3.1 3.332 3.333 3.2.857 2.856 9 2.499 2.499 2.16534.158 99332.856 496.96 6.935 6.513 6.533 6.906 49 8 6.136 6.152 6.113.524 4.528 4.4.156 3.992 3.4.154 99 3.2.856 33 9 3.331 3.2.856 2.499 2.491930 .807 3240 .834 3950 .196 31.423 27.355 23.114 25.729 22.396 .6 92 19.792 21.482 .2大多数项目都是在建设期集中，直到投产初期可能还出现入不敷出，为负值，但进入正常生产或达产后就能收入大于支出，净现金流量为。因而，在整个计算期内序列的符号从负值到只改变一次，我们把在计算期内，净现金流量序列的符号只变化一次的项目称为常规项目。对于常规项目，若累计大于零，一般会有一个正实数根，则其应当是该项目的内部收益率。 在计算期内，如果项目的序列的符号正负变化多次时，则称此类项目为非常规项目。一般地讲，如果在生产期大量追加，或在某些年份集中偿还债务，或经营费用支出过多等，都有可能导致序列的符号正负多次变化，构成非常规项目。非常规投资项目内部收益率方程的解显然不止一个。这些解中是否有真正的内部收益率呢?这需要按照内部收益率的经济涵义进行检验：即以这些根作为，看在内是否始终存在未被回收的。 首先看一元高次多项式是否有正实数根，如果有多个正实数根，则须经过检验，符合内部收益率经济涵义的根才是项目的内部收益率；如果只有一个正实数根，则可能是该项目的内部收益率，也可能不是，同样需要检验。如果无正实数根，或所有实数根都不能满足内部收益率的经济涵义的要求，则该项目无解。对这类投资项目，一般地讲，已失效，不能用它来进行项目的评价和选择。 目前，对于非常规投资项目内部收益率方程多根时，这些根中是否有真正的内部收益率解的问题，即解的存在性问题，还没有一个判别定理。
某项目期初200万，以后的10年每年都有30万的流，求该项目的内部收益率（IRR）。（注：插值区间宽度小于1%即可） 解答：
内部收益率（IRR），是指实际可望达到的收益率，实质上，它是能使项目的等于零时的折现率。 -200+[30/(1+IRR)+30/(1+IRR)^2+....+30/(1+IRR)^10]=0,IRR=11.923%
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