(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:

(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.

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

(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.

(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.