1、表 格 名 称： 年 金 现 值 系 数 表期数 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 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 0.8264 0.8197 0.8130 0.
2、8065 0.8000 0.7937 0.7874 0.7813 0.7752 0.76922 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.7125 1.6901 1.6681 1.6467 1.6257 1.6052 1.5852 1.5656 1.5465 1.5278 1.5095 1.4915 1.4740 1.4568 1.4400 1.4235 1.4074 1.3916 1.3761 1.36093 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730
3、 2.6243 2.5771 2.5313 2.4869 2.4437 2.4018 2.3612 2.3216 2.2832 2.2459 2.2096 2.1743 2.1399 2.1065 2.0739 2.0422 2.0114 1.9813 1.9520 1.9234 1.8956 1.8684 1.8420 1.81614 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.1024 3.0373 2.9745 2.9137 2.8550 2.7982 2.7432 2.6901 2.63
4、86 2.5887 2.5404 2.4936 2.4483 2.4043 2.3616 2.3202 2.2800 2.2410 2.2031 2.16625 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6959 3.6048 3.5172 3.4331 3.3522 3.2743 3.1993 3.1272 3.0576 2.9906 2.9260 2.8636 2.8035 2.7454 2.6893 2.6351 2.5827 2.5320 2.4830 2.43566 5.7955 5
5、.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.2305 4.1114 3.9975 3.8887 3.7845 3.6847 3.5892 3.4976 3.4098 3.3255 3.2446 3.1669 3.0923 3.0205 2.9514 2.8850 2.8210 2.7594 2.7000 2.64277 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.7122 4.5638 4.4226 4.2883
6、 4.1604 4.0386 3.9224 3.8115 3.7057 3.6046 3.5079 3.4155 3.3270 3.2423 3.1611 3.0833 3.0087 2.9370 2.8682 2.80218 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 5.1461 4.9676 4.7988 4.6389 4.4873 4.3436 4.2072 4.0776 3.9544 3.8372 3.7256 3.6193 3.5179 3.4212 3.3289 3.2407 3.15
7、64 3.0758 2.9986 2.92479 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.5370 5.3282 5.1317 4.9464 4.7716 4.6065 4.4506 4.3030 4.1633 4.0310 3.9054 3.7863 3.6731 3.5655 3.4631 3.3657 3.2728 3.1842 3.0997 3.0190109.47138.98268.53028.11097.72177.36017.02366.71016.41776.14465.88
8、925.65025.42625.21615.01884.83324.65864.49414.33894.19254.05413.92323.79933.68193.57053.46483.36443.26893.17813.09151110.36769.78689.25268.76058.30647.88697.49877.13906.80526.49516.20655.93775.68695.45275.23375.02864.83644.65604.48654.32714.17694.03543.90183.77573.65643.54353.43653.33513.23883.14731
9、211.255110.57539.95409.38518.86338.38387.94277.53617.16076.81376.49246.19445.91765.66035.42065.19714.98844.79324.61054.43924.27844.12743.98523.85143.72513.60593.49333.38683.28593.19031312.133711.348410.63509.98569.39368.85278.35777.90387.48697.10346.74996.42356.12185.84245.58315.34235.11834.90954.71
10、474.53274.36244.20284.05303.91243.78013.65553.53813.42723.32243.22331413.003712.106211.296110.56319.89869.29508.74558.24427.78627.36676.98196.62826.30256.00215.72455.46755.22935.00814.80234.61064.43174.26464.10823.96163.82413.69493.57333.45873.35073.24871513.865112.849311.937911.118410.37979.71229.1
11、0798.55958.06077.60617.19096.81096.46246.14225.84745.57555.32425.09164.87594.67554.48904.31524.15304.00133.85933.72613.60103.48343.37263.26821 14. 13. 12. 11. 10. 10. 9.4 8.8 8.3 7.8 7.3 6.9 6.6 6.2 5.9 5.6 5.4 5.1 4.9 4.7 4.5 4.3 4.1 4.0 3.8 3.7 3.6 3.5 3.3 3.26 717957775611652383781059466 514 126
12、237 792 740 039 651 542 685 053 624 377 296 364 567 894 333 874 509 228 026 896 8321715.562314.291913.166112.165711.274110.47739.76329.12168.54368.02167.54887.11966.72916.37296.04725.74875.47465.22234.98974.77464.57554.39084.21904.05913.90993.77053.64003.51773.40283.29481816.398314.992013.753512.659
13、311.689610.827610.05919.37198.75568.20147.70167.24976.83996.46746.12805.81785.53395.27325.03334.81224.60794.41874.24314.07993.92793.78613.65363.52943.41303.30371917.226015.678514.323813.133912.085311.158110.33569.60368.95018.36497.83937.36586.93806.55046.19825.87755.58455.31625.07004.84354.63464.441
14、54.26274.09673.94243.79853.66423.53863.42103.31052018.045616.351414.877513.590312.462211.469910.59409.81819.12858.51367.96337.46947.02486.62316.25935.92885.62785.35275.10094.86964.65674.46034.27864.11033.95393.80833.67263.54583.42713.31582118.857017.011215.415014.029212.821211.764110.835510.01689.29
15、228.64878.07517.56207.10166.68706.31255.97315.66485.38375.12684.89134.67504.47564.29164.12123.96313.81613.67923.55143.43193.31982219.660417.658015.936914.451113.163012.041611.061210.20079.44248.77158.17577.64467.16956.74296.35876.01135.69645.40995.14864.90944.69004.48824.30214.13003.97053.82233.6844
16、3.55583.43563.32302320.455818.292216.443614.856813.488612.303411.272210.37119.58028.88328.26647.71847.22976.79216.39886.04425.72345.43215.16684.92454.70254.49854.31064.13713.97643.82733.68853.55923.43843.32542421.243418.913916.935515.247013.798612.550411.469310.52889.70668.98478.34817.78437.28296.83
17、516.43386.07265.74655.45095.18224.93714.71284.50704.31764.14283.98113.83123.69183.56193.44063.32722522.023219.523517.413115.622114.093912.783411.653610.67489.82269.07708.42177.84317.33006.87296.46416.09715.76625.46695.19514.94764.72134.51394.32324.14743.98493.83423.69433.56403.44233.32862622.795220.
18、121017.876815.982814.375213.003211.825810.81009.92909.16098.48817.89577.37176.90616.49066.11825.78315.48045.20604.95634.72844.51964.32784.15113.98793.83673.69633.56563.44373.32972723.559620.706918.327016.329614.643013.210511.986710.935210.02669.23728.54787.94267.40866.93526.51356.13645.79755.49195.2
19、1514.96364.73424.52434.33164.15423.99033.83873.69793.56693.44473.33052824.316421.281318.764116.663114.898113.406212.137111.051110.11619.30668.60167.98447.44126.96076.53356.15205.80995.50165.22284.96974.73904.52814.33464.15663.99233.84023.69913.56793.44553.33122925.065821.844419.188516.983715.141113.
20、590712.277711.158410.19839.36968.65018.02187.47016.98306.55096.16565.82045.50985.22924.97474.74304.53124.33714.15853.99383.84143.70013.56873.44613.33173 25. 22. 19. 17. 15. 13. 12. 11. 10. 9.4 8.6 8.0 7.4 7.0 6.5 6.1 5.8 5.5 5.2 4.9 4.7 4.5 4.3 4.1 3.9 3.8 3.7 3.5 3.4 3.30 80773965600429203725764840
21、9025782737269 938 552 957 027 660 772 294 168 347 789 463 338 391 601 950 424 009 693 466 321年金现值系数表（PVIFA 表）http:/ 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 15% 16% 18% 20% 22% 24% 25% 30% 35% 40% 45% 50%1 0.99 0.98 0.970.9610.9520.9430.9250.9090.8920.8770.8690.8620.8470.8330.8190.8060.7990.7690.740.7140.68
22、90.6662 1.971.9411.9131.8861.8591.8331.7831.7351.691.6461.6251.6051.5651.5271.4911.4561.44 1.361.2891.2241.1651.1113 2.942.8832.8282.7752.7232.6732.5772.4862.4012.3212.2832.2452.1742.1062.0421.9811.9521.8161.6951.5881.4931.40743.9013.8073.7173.6293.5453.4653.3123.1693.0372.9132.8542.7982.692.5882.49
23、32.4042.3612.1661.9961.8491.7191.60454.8534.7134.5794.4514.3294.2123.9923.793.6043.4333.3523.2743.1272.992.8632.7452.6892.4352.2192.0351.8751.73665.7955.6015.4175.2425.0754.9174.6224.3554.1113.8883.7843.6843.4973.3253.1663.022.9512.6422.3852.1671.9831.82476.7286.4716.236.0025.7865.5825.2064.8684.563
24、4.2884.164.0383.8113.6043.4153.2423.1612.8022.5072.2622.0571.88287.6517.3257.0196.7326.4636.2095.7465.3344.9674.6384.4874.3434.0773.8373.6193.4213.3282.9242.5982.332.1081.92198.5668.1627.7867.4357.1076.8016.2465.7595.3284.9464.7714.6064.3034.033.7863.5653.4633.0192.6652.3782.1431.947109.4718.9828.53
25、 8.117.7217.36 6.716.1445.655.2165.0184.8334.4944.1923.9233.6813.573.0912.7152.4132.1681.9651110.3679.7869.2528.768.3067.8867.1386.4955.9375.4525.2335.0284.6564.3274.0353.7753.6563.1472.7512.4382.1841.9761211.25510.5759.9549.3858.8638.3837.5366.8136.1945.66 5.425.1974.7934.4394.1273.8513.7253.192.77
26、92.4552.1961.9841312.13311.34810.6349.9859.3938.8527.9037.1036.4235.8425.5835.3424.9094.5324.2023.9123.783.2232.7992.4682.2041.9891413.00312.10611.29610.5639.8989.2948.2447.3666.6286.0025.7245.4675.0084.614.2643.9613.8243.2482.8142.4772.2091.9931513.86512.84911.93711.11810.3799.7128.5597.6066.816.14
27、25.8475.5755.0914.6754.3154.0013.8593.2682.8252.4832.2131.9951 14.7 13.5 12.5 11.6 10.8 10.1 8.85 7.82 6.97 6.26 5.95 5.66 5.16 4.72 4.35 4.03 3.88 3.28 2.83 2.48 2.21 1.996 17 77 61 52 37 05 1 3 3 5 4 8 2 9 6 3 7 3 3 8 6 61715.56214.29113.16612.16511.27410.4779.1218.0217.1196.3726.0475.7485.2224.77
28、44.394.0593.9093.2942.8392.4912.2181.9971816.39814.99213.75312.65911.68910.8279.3718.2017.2496.4676.1275.8175.2734.8124.4184.0793.9273.3032.8442.4942.2191.9981917.22615.67814.32313.13312.08511.1589.6038.3647.3656.556.1985.8775.3164.8434.4414.0963.9423.312.8472.4952.221.9992018.04516.35114.87713.5912
29、.46211.4699.8188.5137.4696.6236.2595.9285.3524.8694.46 4.113.9533.3152.852.4972.221.9992118.85617.01115.41514.02912.82111.76410.0168.6487.5626.6866.3125.9735.3834.8914.4754.1213.9633.3192.8512.4972.2211.9992219.6617.65815.93614.45113.16312.04110.28.7717.6446.7426.3586.0115.4094.9094.4884.1293.973.32
30、22.8532.4982.2211.9992320.45518.29216.44314.85613.48812.30310.3718.8837.7186.7926.3986.0445.4324.9244.4984.1373.9763.3252.8542.4982.2211.9992421.24318.91316.93515.24613.79812.5510.5288.9847.7846.8356.4336.0725.454.9374.5074.1423.9813.3272.8552.4992.2211.9992522.02319.52317.41315.62214.09312.78310.67
31、49.0777.8436.8726.4646.0975.4664.9474.5134.1473.9843.3282.8552.4992.2221.9992622.79520.12117.87615.98214.37513.00310.8099.167.8956.9066.496.1185.484.9564.5194.1513.9873.3292.8552.4992.2221.9992723.55920.70618.32716.32914.64313.2110.9359.2377.9426.9356.5136.1365.4914.9634.5244.1543.99 3.332.8562.4992
32、.2221.9992824.31621.28118.76416.66314.89813.40611.0519.3067.9846.966.5336.1525.5014.9694.5284.1563.9923.3312.8562.4992.2221.9992925.06521.84419.18816.98315.14113.5911.1589.3698.0216.9836.556.1655.5094.9744.5314.1583.9933.3312.8562.4992.2221.9993025.80722.39619.617.29215.37213.76411.2579.4268.0557.00
33、26.5656.1775.5164.9784.5334.163.9953.3322.8562.4992.2221.9994032.83427.35523.11419.79217.15915.04611.9249.7798.2437.1056.6416.2335.5484.9964.5434.1653.9993.3332.8572.4992.2221.9995039.19631.42325.72921.48218.25515.76112.2339.9148.3047.1326.666.2465.5544.9994.5454.1663.9993.3332.8572.4992.2221.999大多数
34、项目都是在建设期集中投资，直到投产初期可能还出现入不敷出，净现金流量为负值，但进入正常生产或达产后就能收入大于支出，净现金流量为正值。因而，在整个计算期内净现金流量序列的符号从负值到正值只改变一次，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，若累计净现金流量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，如果项目的净现金流量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投资，或在某些年份集中偿还债务，或经营费用支出过多等，都有可能导致净现金流量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
35、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：即以这些根作为盈利率，看在项目寿命期内是否始终存在未被回收的投资。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，内部收益率法已失效，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。某项目期初投资 200 万，以后的 10 年每年都有 30 万的现金流，求该项目的内部收益率（IRR）。（注：利率插值区间宽度小于 1%即可）解答：内部收益率（IRR），是指项目投资实际可望达到的收益率，实质上，它是能使项目的净现值等于零时的折现率。-200+30/(1+IRR)+30/(1+IRR)2+30/(1+IRR)10=0 , IRR=11.923%
