#### § 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 |
| --- | --- | --- |
| 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.

| 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 |

Table I—Decimal Equivalents for Use of Sum of the Years-Digits Method, Based on Remaining Life

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* = 2*R* / (*W* + 2*F*)(*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.

| | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| | | | | | | | | | | | | | | |

Depreciation Computations on a Group Account Under Remaining Life Plan

| 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 |
| 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.