SuperVal Enhanced Deferreds capped cash commutation

Start with member's commutable pension rights from our example on Tuesday, summed by NRA and pension-increase type.

Commutation tables shown here as vectors. The axis is NRA. They are tabulated as comtabs by sex and pension-increase type.

      ⌊mcrb ⍝ member's commutable pension rights by NRA and M,S,3,4
  716 1433 2150  2646
  770 1540 2310  2843
  826 1653 2480  3053
  887 1775 2662  3276
  952 1904 2856  3515
 1021 2042 3063  3769
 1094 2188 3283  4040
 1172 2345 3517  4329
 1255 2511 3767  4636
 1344 2688 4033  4964
 1438 2877 4316  5312
 1539 3078 4617  5683
 1646 3292 4938  6078
 1759 3519 5279  6498
 1880 3761 5642  6944
 2009 4019 6028  7420
 2146 4292 6439  7925
 2292 4584 6876  8462
 2446 4893 7340  9034
 2611 5222 7833  9641
 2785 5571 8357 10286
 2971 5943 8915 10972
 3212 6425 9638 11862
      X ⍝ member's NRA
43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
      ages ⍝ all ages tabulated
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
      ⍴¨comtabs ⍝ M/F by M, S, P3, P4
 45  45  45  45
 45  45  45  45
      ⍴ages ⍝ all ages tabulated
45

1. Commuting pension rights to cash

Commutation method A

% of pension × commutation factor

      SEX
M
      X,(↑,(SEX='MF')⌿comtabs)[ages⍳X;] ⍝ gendered commutation tables for X
 43 25.68888889 51.37777778 25.68888889 25.68888889
 44 25.06666667 50.13333333 25.06666667 25.06666667
 45 24.44444444 48.88888889 24.44444444 24.44444444
 46 23.82222222 47.64444444 23.82222222 23.82222222
 47 23.2        46.4        23.2        23.2
 48 22.57777778 45.15555556 22.57777778 22.57777778
 49 21.95555556 43.91111111 21.95555556 21.95555556
 50 21.33333333 42.66666667 21.33333333 21.33333333
 51 20.71111111 41.42222222 20.71111111 20.71111111
 52 20.08888889 40.17777778 20.08888889 20.08888889
 53 19.46666667 38.93333333 19.46666667 19.46666667
 54 18.84444444 37.68888889 18.84444444 18.84444444
 55 18.22222222 36.44444444 18.22222222 18.22222222
 56 17.6        35.2        17.6        17.6
 57 16.97777778 33.95555556 16.97777778 16.97777778
 58 16.35555556 32.71111111 16.35555556 16.35555556
 59 15.73333333 31.46666667 15.73333333 15.73333333
 60 15.11111111 30.22222222 15.11111111 15.11111111
 61 14.48888889 28.97777778 14.48888889 14.48888889
 62 13.86666667 27.73333333 13.86666667 13.86666667
 63 13.24444444 26.48888889 13.24444444 13.24444444
 64 12.62222222 25.24444444 12.62222222 12.62222222
 65 12          24          12          12
      ⍝ say percentage is 25%
      X, ⌊mcrb × 0.25 × (↑,(SEX='MF')⌿comtabs)[ages⍳X;] ⍝ total cash by NRA and M,S,3,4
 43 4602 18410 13807 16994
 44 4825 19301 14476 17816
 45 5053 20212 15159 18657
 46 5285 21142 15856 19516
 47 5522 22089 16567 20390
 48 5763 23052 17289 21279
 49 6007 24028 18021 22180
 50 6253 25015 18761 23090
 51 6502 26009 19507 24009
 52 6752 27009 20256 24931
 53 7002 28009 21007 25855
 54 7251 29007 21755 26776
 55 7499 29997 22498 27689
 56 7743 30974 23231 28592
 57 7983 31934 23950 29477
 58 8217 32868 24651 30340
 59 8442 33771 25328 31173
 60 8658 34634 25976 31970
 61 8862 35450 26587 32723
 62 9052 36208 27156 33423
 63 9224 36898 27673 34060
 64 9377 37509 28132 34624
 65 9638 38554 28915 35588

Commutation method B

multiple of pension, say 3

      X, ⌊mcrb × 3 ⍝ total cash
 43 2150  4300  6450  7938
 44 2310  4620  6930  8529
 45 2480  4961  7441  9159
 46 2662  5325  7987  9830
 47 2856  5712  8569 10546
 48 3063  6126  9189 11309
 49 3283  6566  9849 12122
 50 3517  7035 10553 12988
 51 3767  7535 11302 13910
 52 4033  8066 12100 14892
 53 4316  8633 12949 15938
 54 4617  9235 13853 17050
 55 4938  9877 14815 18234
 56 5279 10559 15839 19494
 57 5642 11285 16928 20834
 58 6028 12057 18086 22260
 59 6439 12878 19318 23776
 60 6876 13752 20628 25388
 61 7340 14680 22020 27102
 62 7833 15667 23500 28923
 63 8357 16715 25073 30859
 64 8915 17830 26745 32917
 65 9638 19277 28915 35588

2. Capping the commuted cash

      ⍝ say total cash is as above, from commutation method B
      tc←mcrb × 3 ⍝ total cash
      X, ⌊tc,+/tc ⍝ with totals on R
 43 2150  4300  6450  7938 20838
 44 2310  4620  6930  8529 22389
 45 2480  4961  7441  9159 24042
 46 2662  5325  7987  9830 25806
 47 2856  5712  8569 10546 27685
 48 3063  6126  9189 11309 29688
 49 3283  6566  9849 12122 31822
 50 3517  7035 10553 12988 34095
 51 3767  7535 11302 13910 36515
 52 4033  8066 12100 14892 39093
 53 4316  8633 12949 15938 41837
 54 4617  9235 13853 17050 44758
 55 4938  9877 14815 18234 47866
 56 5279 10559 15839 19494 51173
 57 5642 11285 16928 20834 54691
 58 6028 12057 18086 22260 58433
 59 6439 12878 19318 23776 62413
 60 6876 13752 20628 25388 66644
 61 7340 14680 22020 27102 71143
 62 7833 15667 23500 28923 75925
 63 8357 16715 25073 30859 81007
 64 8915 17830 26745 32917 86407
 65 9638 19277 28915 35588 93419
      ⍝ say cash cap is £25,000
      X,[1.5] ctcc ← ⌊ 25000 ⌊ +/tc ⍝ capped total cash commuted
 43 20838
 44 22389
 45 24042
 46 25000
 47 25000
 48 25000
 49 25000
 50 25000
 51 25000
 52 25000
 53 25000
 54 25000
 55 25000
 56 25000
 57 25000
 58 25000
 59 25000
 60 25000
 61 25000
 62 25000
 63 25000
 64 25000
 65 25000

3. Calculate residual pension by NRA and peninc type

Commutation priority 1: Special, Main, Peninc3, Peninc4

      iM iS i3 i4 ⍝ axis indexes: Main, Special, Peninc3 Peninc4
1 2 3 4
      priority←iS iM i3 i4 ⍝ priority order of pen-inc types
      X, ⌊ pccc←(+\tc[;priority])[;⍋priority] ⍝ prioritised cumulative commuted cash
 43  6450  4300 12900 20838
 44  6930  4620 13860 22389
 45  7441  4961 14883 24042
 46  7987  5325 15975 25806
 47  8569  5712 17138 27685
 48  9189  6126 18378 29688
 49  9849  6566 19699 31822
 50 10553  7035 21106 34095
 51 11302  7535 22605 36515
 52 12100  8066 24200 39093
 53 12949  8633 25899 41837
 54 13853  9235 27707 44758
 55 14815  9877 29631 47866
 56 15839 10559 31678 51173
 57 16928 11285 33856 54691
 58 18086 12057 36173 58433
 59 19318 12878 38636 62413
 60 20628 13752 41256 66644
 61 22020 14680 44041 71143
 62 23500 15667 47001 75925
 63 25073 16715 50147 81007
 64 26745 17830 53490 86407
 65 28915 19277 57831 93419
      X, ⌊ pccc - pccc ⌊ 25000 ⍝ cash denied commutation
 43    0 0     0     0
 44    0 0     0     0
 45    0 0     0     0
 46    0 0     0   806
 47    0 0     0  2685
 48    0 0     0  4688
 49    0 0     0  6822
 50    0 0     0  9095
 51    0 0     0 11515
 52    0 0     0 14093
 53    0 0   899 16837
 54    0 0  2707 19758
 55    0 0  4631 22866
 56    0 0  6678 26173
 57    0 0  8856 29691
 58    0 0 11173 33433
 59    0 0 13636 37413
 60    0 0 16256 41644
 61    0 0 19041 46143
 62    0 0 22001 50925
 63   73 0 25147 56007
 64 1745 0 28490 61407
 65 3915 0 32831 68419
      X, (pccc - pccc ⌊ 25000) ÷ tc ⍝ cash denied commutation as % of commuted cash
 43 0              0 0             0
 44 0              0 0             0
 45 0              0 0             0
 46 0              0 0             0.08199982316
 47 0              0 0             0.2546249618
 48 0              0 0             0.4145312144
 49 0              0 0             0.5627550688
 50 0              0 0             0.7002380642
 51 0              0 0             0.8278366613
 52 0              0 0             0.9463309473
 53 0              0 0.06945517754 1.056432332
 54 0              0 0.1954342929  1.158790363
 55 0              0 0.3126138843  1.253998781
 56 0              0 0.4216626469  1.342600901
 57 0              0 0.5231931199  1.42509441
 58 0              0 0.6177669595  1.501935655
 59 0              0 0.7058996554  1.57354347
 60 0              0 0.7880647566  1.640302615
 61 0              0 0.8646976643  1.702566852
 62 0              0 0.9361990403  1.76066172
 63 0.008813627992 0 1.002937876   1.814887024
 64 0.1957627762   0 1.065254259   1.865519085
 65 0.4062449513   0 1.135414984   1.922524674
      X, ⌊mcrb × (pccc - pccc ˜ 25000) ÷ tc ⍝ residual pension
 43    0 0     0     0
 44    0 0     0     0
 45    0 0     0     0
 46    0 0     0   268
 47    0 0     0   895
 48    0 0     0  1562
 49    0 0     0  2274
 50    0 0     0  3031
 51    0 0     0  3838
 52    0 0     0  4697
 53    0 0   299  5612
 54    0 0   902  6586
 55    0 0  1543  7622
 56    0 0  2226  8724
 57    0 0  2952  9897
 58    0 0  3724 11144
 59    0 0  4545 12471
 60    0 0  5418 13881
 61    0 0  6347 15381
 62    0 0  7333 16975
 63   24 0  8382 18669
 64  581 0  9496 20469
 65 1305 0 10943 22806

Commutation priority 2: pro-rata

      2 ⍕ctcc ÷ +/tc ⍝ % of total after capping
 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.96 0.89 0.84 0.78 0.73 0.68 0.64 0.60 0.56 0.53 0.49 0.46 0.43
      X, ⌊ mcrb ×[1] 1-ctcc÷+/tc ⍝ residual pension by NRA and M,S,3,4
 43    0    0    0    0
 44    0    0    0    0
 45    0    0    0    0
 46   27   55   83  102
 47   92  184  277  341
 48  161  322  483  595
 49  234  469  703  866
 50  312  625  938 1154
 51  396  792 1188 1462
 52  484  969 1454 1789
 53  579 1158 1737 2138
 54  679 1359 2038 2508
 55  786 1572 2359 2903
 56  900 1800 2700 3323
 57 1021 2042 3063 3770
 58 1149 2299 3449 4245
 59 1286 2573 3860 4750
 60 1432 2864 4296 5288
 61 1586 3173 4760 5859
 62 1751 3502 5254 6466
 63 1926 3852 5778 7112
 64 2111 4223 6335 7797
 65 2353 4706 7059 8688