26 CFR § 1.167(b)-3

26 CFR · Internal Revenue

§ 1.167(b)-3 — Sum of the years-digits method.

26 CFR § 1.167(b)-3

TitleTitle 26: Internal Revenue PartPart 1: Income Taxes

SourceeCFR (current through Mar 20, 2026)

This text of 26 C.F.R. § 1.167(b)-3 (Sum of the years-digits method.) is published on Counsel Stack Legal Research, covering United States primary law. Counsel Stack provides free access to over 12 million legal documents including statutes, case law, regulations, and constitutions.

Bluebook

26 C.F.R. § 1.167(b)-3 (2026).

Text

§ 1.167(b)-3 Sum of the years-digits method.

(a)Applied to a single asset—

(1)General rule. Under the sum of the years-digits method annual allowances for depreciation are computed by applying changing fractions to the cost or other basis of the property reduced by estimated salvage. The numerator of the fraction changes each year to a number which corresponds to the remaining useful life of the asset (including the year for which the allowance is being computed), and the denominator which remains constant is the sum of all the years digits corresponding to the estimated useful life of the asset. See section 167(c) and § 1.167(c)-1 for restrictions on the use of the sum of the years-digits method.

(i)Illustrations. Computation of depreciation allowances on a single asset under the sum o

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§ 1.167(b)-3 Sum of the years-digits method.

(a) Applied to a single asset—(1) General rule. Under the sum of the years-digits method annual allowances for depreciation are computed by applying changing fractions to the cost or other basis of the property reduced by estimated salvage. The numerator of the fraction changes each year to a number which corresponds to the remaining useful life of the asset (including the year for which the allowance is being computed), and the denominator which remains constant is the sum of all the years digits corresponding to the estimated useful life of the asset. See section 167(c) and § 1.167(c)-1 for restrictions on the use of the sum of the years-digits method.

(i) Illustrations. Computation of depreciation allowances on a single asset under the sum of the years-digits method is illustrated by the following examples:

Example 1.A new asset having an estimated useful life of five years was acquired on January 1, 1954, for $1,750. The estimated salvage is $250. For a taxpayer filing his returns on a calendar year basis, the annual depreciation allowances are as follows:

Year	Cost or other basis less salvage	Fraction¹	Allowable depreciation	Depreciation reserve
1954	$1,500	⁵⁄₁₅	$500	$500
1955	1,500	⁴⁄₁₅	400	900
1956	1,500	³⁄₁₅	300	1,200
1957	1,500	²⁄₁₅	200	1,400
1958	1,500	¹⁄₁₅	100	1,500
Unrecovered value (salvage)				$250
¹ The denominator of the fraction is the sum of the digits representing the years of useful life, i.e., 5, 4, 3, 2, and 1, or 15.

Example 2.Assume in connection with an asset acquired in 1954 that three-fourths of a year's depreciation is allowable in that year. The following illustrates a reasonable method of allocating depreciation:

	Depreciation for 12 months	Allowable depreciation
	Depreciation for 12 months	1954	1955	1956
1st year	$500	(³⁄₄) $375	(¹⁄₄) $125
2d year	400		(³⁄₄) 300	(¹⁄₄) $100
3d year	300			(³⁄₄) 225
Total		375	425	325

(ii) Change in useful life. Where in the case of a single asset, a change is justified in the useful life, subsequent computations shall be made as though the remaining useful life at the beginning of the taxable year of change were the useful life of a new asset acquired at such time and with a basis equal to the unrecovered cost or other basis of the asset at that time. For example, assume that a new asset with an estimated useful life of ten years is purchased in 1954. At the time of making out his return for 1959, the taxpayer finds that the asset has a remaining useful life of seven years from January 1, 1959. Depreciation for 1959 should then be computed as though 1959 were the first year of the life of an asset estimated to have a useful life of seven years, and the allowance for 1959 would be 7/28 of the unrecovered cost or other basis of the asset after adjustment for salvage.

(2) Remaining life—(i) Application. Under the sum of the years-digits method, annual allowances for depreciation may also be computed by applying changing fractions to the unrecovered cost or other basis of the asset reduced by estimated salvage. The numerator of the fraction changes each year to a number which corresponds to the remaining useful life of the asset (including the year for which the allowance is being computed), and the denominator changes each year to a number which represents the sum of the digits corresponding to the years of estimated remaining useful life of the asset. For decimal equivalents of such fractions, see Table I of subdivision (ii) of this subparagraph. For example, a new asset with an estimated useful life of 10 years is purchased January 1, 1954, for $6,000. Assuming a salvage value of $500, the depreciation allowance for 1954 is $1,000 ($5,500 × 0.1818, the applicable rate from Table I). For 1955, the unrecovered balance is $4,500, and the remaining life is 9 years. The depreciation allowance for 1955 would then be $900 ($4,500 × 0.2000, the applicable rate from Table I).

(ii) Table I. This table shows decimal equivalents of sum of the years-digits fractions corresponding to remaining lives from 1 to 100 years.

Table I—Decimal Equivalents for Use of Sum of the Years-Digits Method, Based on Remaining Life
Remaining life (years)	Decimal equivalent
100.0	0.0198
99.9	.0198
99.8	.0198
99.7	.0199
99.6	.0199
99.5	.0199
99.4	.0199
99.3	.0199
99.2	.0200
99.1	.0200
99.0	.0200
98.9	.0200
98.8	.0200
98.7	.0201
98.6	.0201
98.5	.0201
98.4	.0201
98.3	.0201
98.2	.0202
98.1	.0202
98.0	.0202
97.9	.0202
97.8	.0202
97.7	.0203
97.6	.0203
97.5	.0203
97.4	.0203
97.3	.0203
97.2	.0204
97.1	.0204
97.0	.0204
96.9	.0204
96.8	.0204
96.7	.0205
96.6	.0205
96.5	.0205
96.4	.0205
96.3	.0206
96.2	.0206
96.1	.0206
96.0	.0206
95.9	.0206
95.8	.0207
95.7	.0207
95.6	.0207
95.5	.0207
95.4	.0207
95.3	.0208
95.2	.0208
95.1	.0208
95.0	.0208
94.9	.0209
94.8	.0209
94.7	.0209
94.6	.0209
94.5	.0209
94.4	.0210
94.3	.0210
94.2	.0210
94.1	.0210
94.0	.0211
93.9	.0211
93.8	.0211
93.7	.0211
93.6	.0211
93.5	.0212
93.4	.0212
93.3	.0212
93.2	.0212
93.1	.0213
93.0	.0213
92.9	.0213
92.8	.0213
92.7	.0213
92.6	.0214
92.5	.0214
92.4	.0214
92.3	.0214
92.2	.0215
92.1	.0215
92.0	.0215
91.9	.0215
91.8	.0216
91.7	.0216
91.6	.0216
91.5	.0216
91.4	.0216
91.3	.0217
91.2	.0217
91.1	.0217
91.0	.0217
90.9	.0218
90.8	.0218
90.7	.0218
90.6	.0218
90.5	.0219
90.4	.0219
90.3	.0219
90.2	.0219
90.1	.0220
90.0	.0220
89.9	.0220
89.8	.0220
89.7	.0221
89.6	.0221
89.5	.0221
89.4	.0221
89.3	.0221
89.2	.0222
89.1	.0222
89.0	.0222
88.9	.0222
88.8	.0223
88.7	.0223
88.6	.0223
88.5	.0223
88.4	.0224
88.3	.0224
88.2	.0224
88.1	.0224
88.0	.0225
87.9	.0225
87.8	.0225
87.7	.0225
87.6	.0226
87.5	.0226
87.4	.0226
87.3	.0226
87.2	.0227
87.1	.0227
87.0	.0227
86.9	.0228
86.8	.0228
86.7	.0228
86.6	.0228
86.5	.0229
86.4	.0229
86.3	.0229
86.2	.0229
86.1	.0230
86.0	.0230
85.9	.0230
85.8	.0230
85.7	.0231
85.6	.0231
85.5	.0231
85.4	.0231
85.3	.0232
85.2	.0232
85.1	.0232
85.0	.0233
84.9	.0233
84.8	.0233
84.7	.0233
84.6	.0234
84.5	.0234
84.4	.0234
84.3	.0234
84.2	.0235
84.1	.0235
84.0	.0235
83.9	.0236
83.8	.0236
83.7	.0236
83.6	.0236
83.5	.0237
83.4	.0237
83.3	.0237
83.2	.0238
83.1	.0238
83.0	.0238
82.9	.0238
82.8	.0239
82.7	.0239
82.6	.0239
82.5	.0240
82.4	.0240
82.3	.0240
82.2	.0240
82.1	.0241
82.0	.0241
81.9	.0241
81.8	.0242
81.7	.0242
81.6	.0242
81.5	.0242
81.4	.0243
81.3	.0243
81.2	.0243
81.1	.0244
81.0	.0244
80.9	.0244
80.8	.0244
80.7	.0245
80.6	.0245
80.5	.0245
80.4	.0246
80.3	.0246
80.2	.0246
80.1	.0247
80.0	.0247
79.9	.0247
79.8	.0248
79.7	.0248
79.6	.0248
79.5	.0248
79.4	.0249
79.3	.0249
79.2	.0249
79.1	.0250
79.0	.0250
78.9	.0250
78.8	.0251
78.7	.0251
78.6	.0251
78.5	.0252
78.4	.0252
78.3	.0252
78.2	.0253
78.1	.0253
78.0	.0253
77.9	.0253
77.8	.0254
77.7	.0254
77.6	.0254
77.5	.0255
77.4	.0255
77.3	.0255
77.2	.0256
77.1	.0256
77.0	.0256
76.9	.0257
76.8	.0257
76.7	.0257
76.6	.0258
76.5	.0258
76.4	.0258
76.3	.0259
76.2	.0259
76.1	.0259
76.0	.0260
75.9	.0260
75.8	.0260
75.7	.0261
75.6	.0261
75.5	.0261
75.4	.0262
75.3	.0262
75.2	.0262
75.1	.0263
75.0	.0263
74.9	.0264
74.8	.0264
74.7	.0264
74.6	.0265
74.5	.0265
74.4	.0265
74.3	.0266
74.2	.0266
74.1	.0266
74.0	.0267
73.9	.0267
73.8	.0267
73.7	.0268
73.6	.0268
73.5	.0268
73.4	.0269
73.3	.0269
73.2	.0270
73.1	.0270
73.0	.0270
72.9	.0271
72.8	.0271
72.7	.0271
72.6	.0272
72.5	.0272
72.4	.0272
72.3	.0273
72.2	.0273
72.1	.0274
72.0	.0274
71.9	.0274
71.8	.0275
71.7	.0275
71.6	.0275
71.5	.0276
71.4	.0276
71.3	.0277
71.2	.0277
71.1	.0277
71.0	.0278
70.9	.0278
70.8	.0279
70.7	.0279
70.6	.0279
70.5	.0280
70.4	.0280
70.3	.0280
70.2	.0281
70.1	.0281
70.0	.0282
69.9	.0282
69.8	.0282
69.7	.0283
69.6	.0283
69.5	.0284
69.4	.0284
69.3	.0284
69.2	.0285
69.1	.0285
69.0	.0286
68.9	.0286
68.8	.0287
68.7	.0287
68.6	.0287
68.5	.0288
68.4	.0288
68.3	.0289
68.2	.0289
68.1	.0289
68.0	.0290
67.9	.0290
67.8	.0291
67.7	.0291
67.6	.0292
67.5	.0292
67.4	.0292
67.3	.0293
67.2	.0293
67.1	.0294
67.0	.0294
66.9	.0295
66.8	.0295
66.7	.0295
66.6	.0296
66.5	.0296
66.4	.0297
66.3	.0297
66.2	.0298
66.1	.0298
66.0	.0299
65.9	.0299
65.8	.0299
65.7	.0300
65.6	.0300
65.5	.0301
65.4	.0301
65.3	.0302
65.2	.0302
65.1	.0303
65.0	.0303
64.9	.0303
64.8	.0304
64.7	.0304
64.6	.0305
64.5	.0305
64.4	.0306
64.3	.0306
64.2	.0307
64.1	.0307
64.0	.0308
63.9	.0308
63.8	.0309
63.7	.0309
63.6	.0310
63.5	.0310
63.4	.0311
63.3	.0311
63.2	.0312
63.1	.0312
63.0	.0313
62.9	.0313
62.8	.0313
62.7	.0314
62.6	.0314
62.5	.0315
62.4	.0315
62.3	.0316
62.2	.0316
62.1	.0317
62.0	.0317
61.9	.0318
61.8	.0318
61.7	.0319
61.6	.0319
61.5	.0320
61.4	.0320
61.3	.0321
61.2	.0322
61.1	.0322
61.0	.0323
60.9	.0323
60.8	.0324
60.7	.0324
60.6	.0325
60.5	.0325
60.4	.0326
60.3	.0326
60.2	.0327
60.1	.0327
60.0	.0328
59.9	.0328
59.8	.0329
59.7	.0329
59.6	.0330
59.5	.0331
59.4	.0331
59.3	.0332
59.2	.0332
59.1	.0333
59.0	.0333
58.9	.0334
58.8	.0334
58.7	.0335
58.6	.0336
58.5	.0336
58.4	.0337
58.3	.0337
58.2	.0338
58.1	.0338
58.0	.0339
57.9	.0340
57.8	.0340
57.7	.0341
57.6	.0341
57.5	.0342
57.4	.0342
57.3	.0343
57.2	.0344
57.1	.0344
57.0	.0345
56.9	.0345
56.8	.0346
56.7	.0347
56.6	.0347
56.5	.0348
56.4	.0348
56.3	.0349
56.2	.0350
56.1	.0350
56.0	.0351
55.9	.0351
55.8	.0352
55.7	.0353
55.6	.0353
55.5	.0354
55.4	.0355
55.3	.0355
55.2	.0356
55.1	.0356
55.0	.0357
54.9	.0358
54.8	.0358
54.7	.0359
54.6	.0360
54.5	.0360
54.4	.0361
54.3	.0362
54.2	.0362
54.1	.0363
54.0	.0364
53.9	.0364
53.8	.0365
53.7	.0366
53.6	.0366
53.5	.0367
53.4	.0368
53.3	.0368
53.2	.0369
53.1	.0370
53.0	.0370
52.9	.0371
52.8	.0372
52.7	.0372
52.6	.0373
52.5	.0374
52.4	.0374
52.3	.0375
52.2	.0376
52.1	.0377
52.0	.0377
51.9	.0378
51.8	.0379
51.7	.0379
51.6	.0380
51.5	.0381
51.4	.0382
51.3	.0382
51.2	.0383
51.1	.0384
51.0	.0385
50.9	.0385
50.8	.0386
50.7	.0387
50.6	.0388
50.5	.0388
50.4	.0389
50.3	.0390
50.2	.0391
50.1	.0391
50.0	.0392
49.9	.0393
49.8	.0394
49.7	.0394
49.6	.0395
49.5	.0396
49.4	.0397
49.3	.0398
49.2	.0398
49.1	.0399
49.0	.0400
48.9	.0401
48.8	.0402
48.7	.0402
48.6	.0403
48.5	.0404
48.4	.0405
48.3	.0406
48.2	.0406
48.1	.0407
48.0	.0408
47.9	.0409
47.8	.0410
47.7	.0411
47.6	.0411
47.5	.0412
47.4	.0413
47.3	.0414
47.2	.0415
47.1	.0416
47.0	.0417
46.9	.0418
46.8	.0418
46.7	.0419
46.6	.0420
46.5	.0421
46.4	.0422
46.3	.0423
46.2	.0424
46.1	.0425
46.0	.0426
45.9	.0426
45.8	.0427
45.7	.0428
45.6	.0429
45.5	.0430
45.4	.0431
45.3	.0432
45.2	.0433
45.1	.0434
45.0	.0435
44.9	.0436
44.8	.0437
44.7	.0438
44.6	.0439
44.5	.0440
44.4	.0440
44.3	.0441
44.2	.0442
44.1	.0443
44.0	.0444
43.9	.0445
43.8	.0446
43.7	.0447
43.6	.0448
43.5	.0449
43.4	.0450
43.3	.0451
43.2	.0452
43.1	.0453
43.0	.0455
42.9	.0456
42.8	.0457
42.7	.0458
42.6	.0459
42.5	.0460
42.4	.0461
42.3	.0462
42.2	.0463
42.1	.0464
42.0	.0465
41.9	.0466
41.8	.0467
41.7	.0468
41.6	.0469
41.5	.0471
41.4	.0472
41.3	.0473
41.2	.0474
41.1	.0475
41.0	.0476
40.9	.0477
40.8	.0478
40.7	.0480
40.6	.0481
40.5	.0482
40.4	.0483
40.3	.0484
40.2	.0485
40.1	.0487
40.0	.0488
39.9	.0489
39.8	.0490
39.7	.0491
39.6	.0493
39.5	.0494
39.4	.0495
39.3	.0496
39.2	.0497
39.1	.0499
39.0	.0500
38.9	.0501
38.8	.0502
38.7	.0504
38.6	.0505
38.5	.0506
38.4	.0508
38.3	.0509
38.2	.0510
38.1	.0511
38.0	.0513
37.9	.0514
37.8	.0515
37.7	.0517
37.6	.0518
37.5	.0519
37.4	.0521
37.3	.0522
37.2	.0524
37.1	.0525
37.0	.0526
36.9	.0528
36.8	.0529
36.7	.0530
36.6	.0532
36.5	.0533
36.4	.0525
36.3	.0536
36.2	.0538
36.1	.0539
36.0	.0541
35.9	.0542
35.8	.0543
35.7	.0545
35.6	.0546
35.5	.0548
35.4	.0549
35.3	.0551
35.2	.0552
35.1	.0554
35.0	.0556
34.9	.0557
34.8	.0559
34.7	.0560
34.6	.0562
34.5	.0563
34.4	.0565
34.3	.0566
34.2	.0566
34.1	.0570
34.0	.0571
33.9	.0573
33.8	.0575
33.7	.0576
33.6	.0578
33.5	.0580
33.4	.0581
33.3	.0583
33.2	.0585
33.1	.0586
33.0	.0588
32.9	.0590
32.8	.0592
32.7	.0593
32.6	.0595
32.5	.0597
32.4	.0599
32.3	.0600
32.2	.0602
32.1	.0604
32.0	.0606
31.9	.0608
31.8	.0610
31.7	.0611
31.6	.0613
31.5	.0615
31.4	.0617
31.3	.0619
31.2	.0621
31.1	.0623
31.0	.0625
30.9	.0627
30.8	.0629
30.7	.0631
30.6	.0633
30.5	.0635
30.4	.0637
30.3	.0639
30.2	.0641
30.1	.0643
30.0	.0645
29.9	.0647
29.8	.0649
29.7	.0651
29.6	.0653
29.5	.0656
29.4	.0658
29.3	.0660
29.2	.0662
29.1	.0664
29.0	.0667
28.9	.0669
28.8	.0671
28.7	.0673
28.6	.0675
28.5	.0678
28.4	.0680
28.3	.0682
28.2	.0685
28.1	.0687
28.0	.0690
27.9	.0692
27.8	.0694
27.7	.0697
27.6	.0699
27.5	.0702
27.4	.0704
27.3	.0707
27.2	.0709
27.1	.0712
27.0	.0714
26.9	.0717
26.8	.0719
26.7	.0722
26.6	.0724
26.5	.0727
26.4	.0730
26.3	.0732
26.2	.0735
26.1	.0738
26.0	.0741
25.9	.0743
25.8	.0746
25.7	.0749
25.6	.0752
25.5	.0754
25.4	.0757
25.3	.0760
25.2	.0763
25.1	.0766
25.0	.0769
24.9	.0772
24.8	.0775
24.7	.0778
24.6	.0781
24.5	.0784
24.4	.0787
24.3	.0790
24.2	.0793
24.1	.0797
24.0	.0800
23.9	.0803
23.8	.0806
23.7	.0809
23.6	.0813
23.5	.0816
23.4	.0819
23.3	.0823
23.2	.0826
23.1	.0830
23.0	.0833
22.9	.0837
22.8	.0840
22.7	.0844
22.6	.0847
22.5	.0851
22.4	.0854
22.3	.0858
22.2	.0862
22.1	.0866
22.0	.0870
21.9	.0873
21.8	.0877
21.7	.0881
21.6	.0885
21.5	.0888
21.4	.0892
21.3	.0896
21.2	.0901
21.1	.0905
21.0	.0909
20.9	.0913
20.8	.0917
20.7	.0921
20.6	.0925
20.5	.0930
20.4	.0934
20.3	.0939
20.2	.0943
20.1	.0948
20.0	.0952
19.9	.0957
19.8	.0961
19.7	.0966
19.6	.0970
19.5	.0975
19.4	.0980
19.3	.0985
19.2	.0990
19.1	.0995
19.0	.1000
18.9	.1005
18.8	.1010
18.7	.1015
18.6	.1020
18.5	.1025
18.4	.1030
18.3	.1036
18.2	.1041
18.1	.1047
18.0	.1053
17.9	.1058
17.8	.1063
17.7	.1069
17.6	.1074
17.5	.1080
17.4	.1086
17.3	.1092
17.2	.1098
17.1	.1105
17.0	.1111
16.9	.1117
16.8	.1123
16.7	.1129
16.6	.1135
16.5	.1142
16.4	.1148
16.3	.1155
16.2	.1162
16.1	.1169
16.0	.1176
15.9	.1183
15.8	.1190
15.7	.1197
15.6	.1204
15.5	.1211
15.4	.1218
15.3	.1226
15.2	.1234
15.1	.1242
15.0	.1250
14.9	.1257
14.8	.1265
14.7	.1273
14.6	.1281
14.5	.1289
14.4	.1297
14.3	.1306
14.2	.1315
14.1	.1324
14.0	.1333
13.9	.1342
13.8	.1350
13.7	.1359
13.6	.1368
13.5	.1378
13.4	.1387
13.3	.1397
13.2	.1407
13.1	.1418
13.0	.1429
12.9	.1438
12.8	.1448
12.7	.1458
12.6	.1469
12.5	.1479
12.4	.1490
12.3	.1502
12.2	.1514
12.1	.1526
12.0	.1538
11.9	.1549
11.8	.1561
11.7	.1573
11.6	.1585
11.5	.1597
11.4	.1610
11.3	.1624
11.2	.1637
11.1	.1652
11.0	.1667
10.9	.1680
10.8	.1693
10.7	.1707
10.6	.1721
10.5	.1736
10.4	.1751
10.3	.1767
10.2	.1783
10.1	.1800
10.0	.1818
9.9	.1833
9.8	.1849
9.7	.1865
9.6	.1882
9.5	.1900
9.4	.1918
9.3	.1938
9.2	.1957
9.1	.1978
9.0	.2000
8.9	.2018
8.8	.2037
8.7	.2057
8.6	.2077
8.5	.2099
8.4	.2121
8.3	.2145
8.2	.2169
8.1	.2195
8.0	.2222
7.9	.2244
7.8	.2267
7.7	.2292
7.6	.2317
7.5	.2344
7.4	.2372
7.3	.2401
7.2	.2432
7.1	.2465
7.0	.2500
6.9	.2527
6.8	.2556
6.7	.2587
6.6	.2619
6.5	.2653
6.4	.2689
6.3	.2727
6.2	.2768
6.1	.2811
6.0	.2857
5.9	.2892
5.8	.2929
5.7	.2969
5.6	.3011
5.5	.3056
5.4	.3103
5.3	.3155
5.2	.3210
5.1	.3269
5.0	.3333
4.9	.3379
4.8	.3429
4.7	.3481
4.6	.3538
4.5	.3600
4.4	.3667
4.3	.3739
4.2	.3818
4.1	.3905
4.0	.4000
3.9	.4063
3.8	.4130
3.7	.4205
3.6	.4286
3.5	.4375
3.4	.4474
3.3	.4583
3.2	.4706
3.1	.4844
3.0	.5000
2.9	.5088
2.8	.5185
2.7	.5294
2.6	.5417
2.5	.5556
2.4	.5714
2.3	.5897
2.2	.6111
2.1	.6364
2.0	.6667
1.9	.6786
1.8	.6923
1.7	.7083
1.6	.7273
1.5	.7500
1.4	.7778
1.3	.8125
1.2	.8571
1.1	.9167
1.0	1.0000

Note:

For determination of decimal equivalents of remaining lives falling between those shown in the above table, the taxpayer may use the next longest life shown in the table, interpolate from the table, or use the following formula from which the table was derived.

D = 2R / (W + 2F)(W + 1)

where:

D = Decimal equivalent. R = Remaining life. W = Whole number of years in remaining life. F = Fractional part of a year in remaining life. If the taxpayer desires to carry his calculations of decimal equivalents to a greater number of decimal places than is provided in the table, he may use the formula. The procedure adopted must be consistently followed thereafter.

(b) Applied to group, classified, or composite accounts—(1) General rule. The sum of the years-digits method may be applied to group, classified, or composite accounts in accordance with the plan described in subparagraph (2) of this paragraph or in accordance with other plans as explained in subparagraph (3) of this paragraph.

(2) Remaining life plan. The remaining life plan as applied to a single asset is described in paragraph (a)(2) of this section. This plan may also be applied to group, classified, or composite accounts. Under this plan the allowance for depreciation is computed by applying changing fractions to the unrecovered cost or other basis of the account reduced by estimated salvage. The numerator of the fraction changes each year to a number which corresponds to the remaining useful life of the account (including the year for which the allowance is being computed), and the denominator changes each year to a number which represents the sum of the years digits corresponding to the years of estimated remaining useful life of the account. Decimal equivalents of such fractions can be obtained by use of Table I under paragraph (a)(2)(ii) of this section. The proper application of this method requires that the estimated remaining useful life of the account be determined each year. This determination, of course, may be made each year by analysis, i.e., by determining the remaining lives for each of the components in the account, and averaging them. The estimated remaining life of any account, however, may also be determined arithmetically. For example, it may be computed by dividing the unrecovered cost or other basis of the account, as computed by straight line depreciation, by the gross cost or other basis of the account, and multiplying the result by the average life of the assets in the account. Salvage value is not a factor for the purpose of determining remaining life. Thus, if a group account with an average life of ten years had at January 1, 1958, a gross asset balance of $12,600 and a depreciation reserve computed on the straight line method of $9,450, the remaining life of the account at January 1, 1958, would be computed as follows:

$12,600−$9,450 ÷ $12,600 × 10 years equals 2.50 years. Example.The use of the sum of the years-digits method with group, classified, or composite accounts under the remaining life plan is illustrated by the following example: A calendar year taxpayer maintains a group account to which a five-year life is applicable. Original investment, additions, retirements, and salvage recoveries are the same as those set forth in example (3) of paragraph (b) of § 1.167(b)-1.

Depreciation Computations on a Group Account Under Remaining Life Plan
	1	2	3	4	5	6	7	8	9	10	11	12	13	14

Year	Asset balance Jan. 1	Current additions	Current retirements	Average asset balance	Straight line amount	Straight line reserve	Remaining life	Asset balance reduced by salvage	Current additions reduced by salvage	Salvage realized	Sum of the years digits depreciation
					Col. (4) ÷ life	Col. (5)− Col. (3) accumulated Jan. 1	[Col. (1)− Col. (6) ÷ Col. (1)] × average service life	Col. (1) × (100%− 6.67%)	Col (2) × (100%− 6.67%)		Accumulated reserve Jan. 1	Unrecovered Jan. 1	Rate based on Col. (7) from Table 1	Allowable depreciation
					Col. (4) ÷ life	Col. (5)− Col. (3) accumulated Jan. 1	[Col. (1)− Col. (6) ÷ Col. (1)] × average service life	Col. (1) × (100%− 6.67%)	Col (2) × (100%− 6.67%)		Prior reserve + Col. (14) + Col. (10)− Col. (3)	Col. (8)− Col. (11)		Col. (12) × Col. (13) + ¹⁄₂ Col. (9) × F²
1954		$12,000		$6,000	¹ $1,200		5.00		$11,200				0.3333	$1,866
1955	$12,000			12,000	2,400	$1,200	4.50	$11,200			$1,866	$9,334	.3600	3,360
1956	12,000			12,000	2,400	3,600	3.50	11,200			5,226	5,974	.4375	2,614
1957	12,000		$2,000	11,000	2,200	6,000	2.50	11,200		$200	7,840	3,360	.5556	1,867
1958	10,000		2,000	9,000	1,800	6,200	1.90	9,333		200	7,907	1,426	.6786	968
1959	8,000	10,000	4,000	11,000	2,200	6,000	1.25	7,466	9,333	400	7,075	391	.8125	1,874
1960	14,000		2,000	13,000	2,600	4,200	3.50	13,066			5,349	7,717	.4375	3,376
1961	12,000		2,000	11,000	2,200	4,800	3.00	11,200			6,725	4,475	.5000	2,238
1962						5,000					6,963
¹ ¹⁄₂ year's amount.
² F = Rate based on average service life (0.3333 in this example).

(3) Other plans for application of the sum of the years-digits method. Taxpayers who wish to use the sum of the years-digits method in computing depreciation for group, classified, or composite accounts in accordance with a sum of the years digits plan other than the remaining life plan described herein may do so only with the consent of the Commissioner. Request for permission to use plans other than that described shall be addressed to the Commissioner of Internal Revenue, Washington, D.C. 20224.