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:

Code of Federal Regulations

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.

Code of Federal Regulations

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

Tips

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
Code of Federal Regulations 1032
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
Code of Federal Regulations 1033
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
Code of Federal Regulations 1034
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

CFR

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

Code of Federal Regulations

Code of Federal Regulations