年 金 现 值 系 数 表.doc

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
0.8065
0.8000
0.7937
0.7874
0.7813
0.7752
0.7692
2
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
1.3609
3
2.9410
2.8839
2.8286
2.7751
2.7232
2.6730
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
1.8161
4
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
2.6386
2.5887
2.5404
2.4936
2.4483
2.4043
2.3616
2.3202
2.2800
2.2410
2.2031
2.1662
5
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
2.4356

6
5.7955
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
2.6427
7
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
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
2.8021
8
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
3.1564
3.0758
2.9986
2.9247
9
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
3.0190
10
9.4713
8.9826
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.8892
5.6502
5.4262
5.2161
5.0188
4.8332
4.6586
4.4941
4.3389
4.1925
4.0541
3.9232
3.7993
3.6819
3.5705
3.4648
3.3644
3.2689
3.1781
3.0915

11
10.3676
9.7868
9.2526
8.7605
8.3064
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
4.1769
4.0354
3.9018
3.7757
3.6564
3.5435
3.4365
3.3351
3.2388
3.1473
12
11.2551
10.5753
9.9540
9.3851
8.8633
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
4.2784
4.1274
3.9852
3.8514
3.7251
3.6059
3.4933
3.3868
3.2859
3.1903
13
12.1337
11.3484
10.6350
9.9856
9.3936
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
4.3624
4.2028
4.0530
3.9124
3.7801
3.6555
3.5381
3.4272
3.3224
3.2233
14
13.0037
12.1062
11.2961
10.5631
9.8986
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
4.4317
4.2646
4.1082
3.9616
3.8241
3.6949
3.5733
3.4587
3.3507
3.2487
15
13.8651
12.8493
11.9379
11.1184
10.3797
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
4.4890
4.3152
4.1530
4.0013
3.8593
3.7261
3.6010
3.4834
3.3726
3.2682

16
14.7179
13.5777
12.5611
11.6523
10.8378
10.1059
9.4466
8.8514
8.3126
7.8237
7.3792
6.9740
6.6039
6.2651
5.9542
5.6685
5.4053
5.1624
4.9377
4.7296
4.5364
4.3567
4.1894
4.0333
3.8874
3.7509
3.6228
3.5026
3.3896
3.2832
17
15.5623
14.2919
13.1661
12.1657
11.2741
10.4773
9.7632
9.1216
8.5436
8.0216
7.5488
7.1196
6.7291
6.3729
6.0472
5.7487
5.4746
5.2223
4.9897
4.7746
4.5755
4.3908
4.2190
4.0591
3.9099
3.7705
3.6400
3.5177
3.4028
3.2948
18
16.3983
14.9920
13.7535
12.6593
11.6896
10.8276
10.0591
9.3719
8.7556
8.2014
7.7016
7.2497
6.8399
6.4674
6.1280
5.8178
5.5339
5.2732
5.0333
4.8122
4.6079
4.4187
4.2431
4.0799
3.9279
3.7861
3.6536
3.5294
3.4130
3.3037
19
17.2260
15.6785
14.3238
13.1339
12.0853
11.1581
10.3356
9.6036
8.9501
8.3649
7.8393
7.3658
6.9380
6.5504
6.1982
5.8775
5.5845
5.3162
5.0700
4.8435
4.6346
4.4415
4.2627
4.0967
3.9424
3.7985
3.6642
3.5386
3.4210
3.3105
20
18.0456
16.3514
14.8775
13.5903
12.4622
11.4699
10.5940
9.8181
9.1285
8.5136
7.9633
7.4694
7.0248
6.6231
6.2593
5.9288
5.6278
5.3527
5.1009
4.8696
4.6567
4.4603
4.2786
4.1103
3.9539
3.8083
3.6726
3.5458
3.4271
3.3158

21
18.8570
17.0112
15.4150
14.0292
12.8212
11.7641
10.8355
10.0168
9.2922
8.6487
8.0751
7.5620
7.1016
6.6870
6.3125
5.9731
5.6648
5.3837
5.1268
4.8913
4.6750
4.4756
4.2916
4.1212
3.9631
3.8161
3.6792
3.5514
3.4319
3.3198
22
19.6604
17.6580
15.9369
14.4511
13.1630
12.0416
11.0612
10.2007
9.4424
8.7715
8.1757
7.6446
7.1695
6.7429
6.3587
6.0113
5.6964
5.4099
5.1486
4.9094
4.6900
4.4882
4.3021
4.1300
3.9705
3.8223
3.6844
3.5558
3.4356
3.3230
23
20.4558
18.2922
16.4436
14.8568
13.4886
12.3034
11.2722
10.3711
9.5802
8.8832
8.2664
7.7184
7.2297
6.7921
6.3988
6.0442
5.7234
5.4321
5.1668
4.9245
4.7025
4.4985
4.3106
4.1371
3.9764
3.8273
3.6885
3.5592
3.4384
3.3254
24
21.2434
18.9139
16.9355
15.2470
13.7986
12.5504
11.4693
10.5288
9.7066
8.9847
8.3481
7.7843
7.2829
6.8351
6.4338
6.0726
5.7465
5.4509
5.1822
4.9371
4.7128
4.5070
4.3176
4.1428
3.9811
3.8312
3.6918
3.5619
3.4406
3.3272
25
22.0232
19.5235
17.4131
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
4.7213
4.5139
4.3232
4.1474
3.9849
3.8342
3.6943
3.5640
3.4423
3.3286

26
22.7952
20.1210
17.8768
15.9828
14.3752
13.0032
11.8258
10.8100
9.9290
9.1609
8.4881
7.8957
7.3717
6.9061
6.4906
6.1182
5.7831
5.4804
5.2060
4.9563
4.7284
4.5196
4.3278
4.1511
3.9879
3.8367
3.6963
3.5656
3.4437
3.3297
27
23.5596
20.7069
18.3270
16.3296
14.6430
13.2105
11.9867
10.9352
10.0266
9.2372
8.5478
7.9426
7.4086
6.9352
6.5135
6.1364
5.7975
5.4919
5.2151
4.9636
4.7342
4.5243
4.3316
4.1542
3.9903
3.8387
3.6979
3.5669
3.4447
3.3305
28
24.3164
21.2813
18.7641
16.6631
14.8981
13.4062
12.1371
11.0511
10.1161
9.3066
8.6016
7.9844
7.4412
6.9607
6.5335
6.1520
5.8099
5.5016
5.2228
4.9697
4.7390
4.5281
4.3346
4.1566
3.9923
3.8402
3.6991
3.5679
3.4455
3.3312
29
25.0658
21.8444
19.1885
16.9837
15.1411
13.5907
12.2777
11.1584
10.1983
9.3696
8.6501
8.0218
7.4701
6.9830
6.5509
6.1656
5.8204
5.5098
5.2292
4.9747
4.7430
4.5312
4.3371
4.1585
3.9938
3.8414
3.7001
3.5687
3.4461
3.3317
30
25.8077
22.3965
19.6004
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
4.7463
4.5338
4.3391
4.1601
3.9950
3.8424
3.7009
3.5693
3.4466
3.3321

年金现值系数表（PVIFA表）

n
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
0.97
0.961
0.952
0.943
0.925
0.909
0.892
0.877
0.869
0.862
0.847
0.833
0.819
0.806
0.799
0.769
0.74
0.714
0.689
0.666
2
1.97
1.941
1.913
1.886
1.859
1.833
1.783
1.735
1.69
1.646
1.625
1.605
1.565
1.527
1.491
1.456
1.44
1.36
1.289
1.224
1.165
1.111
3
2.94
2.883
2.828
2.775
2.723
2.673
2.577
2.486
2.401
2.321
2.283
2.245
2.174
2.106
2.042
1.981
1.952
1.816
1.695
1.588
1.493
1.407
4
3.901
3.807
3.717
3.629
3.545
3.465
3.312
3.169
3.037
2.913
2.854
2.798
2.69
2.588
2.493
2.404
2.361
2.166
1.996
1.849
1.719
1.604
5
4.853
4.713
4.579
4.451
4.329
4.212
3.992
3.79
3.604
3.433
3.352
3.274
3.127
2.99
2.863
2.745
2.689
2.435
2.219
2.035
1.875
1.736
6
5.795
5.601
5.417
5.242
5.075
4.917
4.622
4.355
4.111
3.888
3.784
3.684
3.497
3.325
3.166
3.02
2.951
2.642
2.385
2.167
1.983
1.824
7
6.728
6.471
6.23
6.002
5.786
5.582
5.206
4.868
4.563
4.288
4.16
4.038
3.811
3.604
3.415
3.242
3.161
2.802
2.507
2.262
2.057
1.882
8
7.651
7.325
7.019
6.732
6.463
6.209
5.746
5.334
4.967
4.638
4.487
4.343
4.077
3.837
3.619
3.421
3.328
2.924
2.598
2.33
2.108
1.921
9
8.566
8.162
7.786
7.435
7.107
6.801
6.246
5.759
5.328
4.946
4.771
4.606
4.303
4.03
3.786
3.565
3.463
3.019
2.665
2.378
2.143
1.947
10
9.471
8.982
8.53
8.11
7.721
7.36
6.71
6.144
5.65
5.216
5.018
4.833
4.494
4.192
3.923
3.681
3.57
3.091
2.715
2.413
2.168
1.965
11
10.367
9.786
9.252
8.76
8.306
7.886
7.138
6.495
5.937
5.452
5.233
5.028
4.656
4.327
4.035
3.775
3.656
3.147
2.751
2.438
2.184
1.976
12
11.255
10.575
9.954
9.385
8.863
8.383
7.536
6.813
6.194
5.66
5.42
5.197
4.793
4.439
4.127
3.851
3.725
3.19
2.779
2.455
2.196
1.984
13
12.133
11.348
10.634
9.985
9.393
8.852
7.903
7.103
6.423
5.842
5.583
5.342
4.909
4.532
4.202
3.912
3.78
3.223
2.799
2.468
2.204
1.989
14
13.003
12.106
11.296
10.563
9.898
9.294
8.244
7.366
6.628
6.002
5.724
5.467
5.008
4.61
4.264
3.961
3.824
3.248
2.814
2.477
2.209
1.993
15
13.865
12.849
11.937
11.118
10.379
9.712
8.559
7.606
6.81
6.142
5.847
5.575
5.091
4.675
4.315
4.001
3.859
3.268
2.825
2.483
2.213
1.995
16
14.717
13.577
12.561
11.652
10.837
10.105
8.851
7.823
6.973
6.265
5.954
5.668
5.162
4.729
4.356
4.033
3.887
3.283
2.833
2.488
2.216
1.996
17
15.562
14.291
13.166
12.165
11.274
10.477
9.121
8.021
7.119
6.372
6.047
5.748
5.222
4.774
4.39
4.059
3.909
3.294
2.839
2.491
2.218
1.997
18
16.398
14.992
13.753
12.659
11.689
10.827
9.371
8.201
7.249
6.467
6.127
5.817
5.273
4.812
4.418
4.079
3.927
3.303
2.844
2.494
2.219
1.998
19
17.226
15.678
14.323
13.133
12.085
11.158
9.603
8.364
7.365
6.55
6.198
5.877
5.316
4.843
4.441
4.096
3.942
3.31
2.847
2.495
2.22
1.999
20
18.045
16.351
14.877
13.59
12.462
11.469
9.818
8.513
7.469
6.623
6.259
5.928
5.352
4.869
4.46
4.11
3.953
3.315
2.85
2.497
2.22
1.999
21
18.856
17.011
15.415
14.029
12.821
11.764
10.016
8.648
7.562
6.686
6.312
5.973
5.383
4.891
4.475
4.121
3.963
3.319
2.851
2.497
2.221
1.999
22
19.66
17.658
15.936
14.451
13.163
12.041
10.2
8.771
7.644
6.742
6.358
6.011
5.409
4.909
4.488
4.129
3.97
3.322
2.853
2.498
2.221
1.999
23
20.455
18.292
16.443
14.856
13.488
12.303
10.371
8.883
7.718
6.792
6.398
6.044
5.432
4.924
4.498
4.137
3.976
3.325
2.854
2.498
2.221
1.999
24
21.243
18.913
16.935
15.246
13.798
12.55
10.528
8.984
7.784
6.835
6.433
6.072
5.45
4.937
4.507
4.142
3.981
3.327
2.855
2.499
2.221
1.999
25
22.023
19.523
17.413
15.622
14.093
12.783
10.674
9.077
7.843
6.872
6.464
6.097
5.466
4.947
4.513
4.147
3.984
3.328
2.855
2.499
2.222
1.999
26
22.795
20.121
17.876
15.982
14.375
13.003
10.809
9.16
7.895
6.906
6.49
6.118
5.48
4.956
4.519
4.151
3.987
3.329
2.855
2.499
2.222
1.999
27
23.559
20.706
18.327
16.329
14.643
13.21
10.935
9.237
7.942
6.935
6.513
6.136
5.491
4.963
4.524
4.154
3.99
3.33
2.856
2.499
2.222
1.999
28
24.316
21.281
18.764
16.663
14.898
13.406
11.051
9.306
7.984
6.96
6.533
6.152
5.501
4.969
4.528
4.156
3.992
3.331
2.856
2.499
2.222
1.999
29
25.065
21.844
19.188
16.983
15.141
13.59
11.158
9.369
8.021
6.983
6.55
6.165
5.509
4.974
4.531
4.158
3.993
3.331
2.856
2.499
2.222
1.999
30
25.807
22.396
19.6
17.292
15.372
13.764
11.257
9.426
8.055
7.002
6.565
6.177
5.516
4.978
4.533
4.16
3.995
3.332
2.856
2.499
2.222
1.999
40
32.834
27.355
23.114
19.792
17.159
15.046
11.924
9.779
8.243
7.105
6.641
6.233
5.548
4.996
4.543
4.165
3.999
3.333
2.857
2.499
2.222
1.999
50
39.196
31.423
25.729
21.482
18.255
15.761
12.233
9.914
8.304
7.132
6.66
6.246
5.554
4.999
4.545
4.166
3.999
3.333
2.857
2.499
2.222
1.999

大多数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%