4. Miscellaneous Methods

Other methods of calculating the depreciation charge are used, but they cannot be classified under any of the three groups discussed so far. They are a miscellaneous, mongrel breed, scarcely to be dignified in some instances as methods. Among these may be mentioned the following:

(a) Maintenance Method

In this case a periodic charge for depreciation is made, equal in amount to the cost of maintenance of the asset for the period. It is thus a definite but variable amount, depending upon the maintenance policy.

(b) Replacement Method

This is hardly a method of calculating the depreciation charge, but rather of recognizing the fact of depreciation by charging all renewals and replacements to revenue. It is argued that in a large, widely extended plant after depreciation has reached the point where renewals are necessary, the charging of all renewals and replacements as expenses will take care of all accruing depreciation and secure a fairly uniform charge to product from period to period. Under this plan depreciation as such does not appear on the books but is taken care of under other titles.

(c) The Fifty Per Cent Method

This is somewhat similar to the replacement method in that it is applicable only after depreciation has reached the renewals stage. It is claimed for it that, in a property or class of asset consisting of many similar parts, as railroad ties, for example, after the stage of normal repairs has been reached so that the parts are in all degrees of repair from 0% to 100%, the normal maintenance and renewals policy will maintain the property or asset always in about 50% condition. Therefore the total depreciation for the asset or class is the other 50%, which never reaches a larger amount because of a constant renewal of parts. This 50% depreciation may or may not be carried on the books but it exists nevertheless. For the conditions under which it is applicable as above, the law of averages doubtless applies and makes the estimate a fairly good one.

(d) Appraisal Method

Here a physical appraisal of the asset or property is taken at the close of every fiscal period. The difference in value between the two appraisals for successive fiscal periods represents the depreciation for the period and would be brought on the books as such.

(e) Insurance Method

This is applicable only to large properties with assets widely distributed. Its operation “involves the actuarial principles of ordinary insurance. This means that the fund accumulated by depreciation charges should not be reserved as an accumulation until it can be spent for the purpose of replacing the identical property upon which the fund accumulated when such property is abandoned; and furthermore, that this fund should be expended, in whole or in part, during the year in which it is created, in the replacement of equipment.”

(f) Gross Earnings Method

Here the depreciation estimate is based on the gross earnings for the period. This does not necessarily mean that the depreciation estimate will be large when profits are large, and small or nothing when profits are small, although it may be made to apply in that way in individual cases. The policy of making ample reserves for depreciation in good years and scant reserves in poor years is not to be wholly condemned. Depreciation, however, has no relation to, or dependence upon, profits. Rather, profits depend on depreciation in the sense that they cannot exist until after charges for depreciation have been taken care of. Depreciation considered as a fixed per cent of gross earnings is almost the same in effect as the service output method, and has much to commend it.

Condition Per Cent

Before leaving the topic of method, it may be well to explain a term used in connection with the depreciation estimate, viz., condition per cent. The condition per cent of an asset is found by subtracting from 100%, the fraction which represents the ratio of the present accumulated depreciation to the total estimated depreciation. Thus, if an asset has depreciated in value one-quarter, its condition per cent is said to be 75 (100%-25%). Hence, condition per cent is easily calculated if depreciation has been estimated by any of the proportional methods. If, in addition to the standard notation used, we assume that:

then, in general, condition per cent may be expressed by the formula:

100% - Dₘ
D

Evidently, therefore,

Vₘ = V 100% - Dₘ
D

Under the proportional methods Dₘ/D = nd. Therefore, condition per cent is 100%-nd.

Under the sinking fund method, the calculation is more complex. Dₘ, the total amount of depreciation accumulated to date, i.e., after m periods, is the amount of the annuity A for m periods. From formula (3), [Chapter XV, page 272], the amount of an annuity A is seen to be

A(Rⁿ - 1)
r

Therefore,

Therefore, Dₘ = A(Rᵐ - 1)
r
and, D = A(Rⁿ - 1)
r

from which the ratio

= A(Rᵐ - 1) =
DₘrRᵐ - 1
D A(Rⁿ - 1)Rⁿ - 1
r

Accordingly, condition per cent under the sinking fund method is:

100% - Rᵐ - 1
Rⁿ - 1

CHAPTER X
DEPRECIATION—APPRAISEMENT
OF THE VARIOUS METHODS

General Considerations

No method of estimating depreciation will ever be devised which will be applicable under all conditions and to all kinds of property. Such a panacea for the ills of wasting assets can obviously never be found, for the very good reason that the same medicine will not suit all patients. What gives good results in one case may not be applicable or not equally so, in another case. In discussing the relative merits of the various methods, therefore, no dogmatic rules for their use can be laid down; furthermore, without a detailed knowledge of operating conditions, only their main points of strength and weakness can be pointed out, and this is all that will be attempted here.

In a critical discussion of methods and their effects, the fact of depreciation may be considered from either the viewpoint of time or service. Depreciation when viewed from the aspect of time may be said to be due to:

1. Decrepitude, which is merely the lapse of time.

2. Inadequacy, which is lack of capacity to do the work which increasing markets demand (a condition the essence of which is also time).

3. Obsolescence, which represents the inability to perform efficiently as compared with the service secured from more modern equipment, and which may be a condition brought about by lapse of time and the developments of an art or science.

When viewed from the aspect of service, depreciation may be due primarily to wear and tear, which is a condition directly dependent upon the service rendered.

It has been pointed out that these elements of depreciation, viz., wear and tear, inadequacy, obsolescence, etc., are single and isolated in their action and not cumulative. One of them, therefore, is the controlling element in any estimate of depreciation. Accordingly, in judging the merits of a method the kind of depreciation must be taken into account; i.e., depreciation must be viewed from a time and service standpoint.

Ideal Basis for Distribution of Depreciation Charge

Regardless of the actual progress of depreciation, the theoretically ideal method of distributing the charge, from the standpoint of a going concern, is so that each unit of output shall bear its just proportion of the burden. Any other attitude is inconsistent. Thus, assuming that actual depreciation does not progress uniformly, that, as some maintain, the rate of depreciation is heaviest towards the end of the service life of an asset, it would not be equitable to charge the product of those years with a much higher burden than that of the earlier years. Just as it is a misfortune to be born under some conditions, so here it would be a misfortune to a commodity to be produced during the latter years of the service life of an asset. The life-period of an asset must be viewed as a whole and its total depreciation should be distributed evenly over its output, if equity is to be secured—other conditions, of course, remaining the same. This principle does not apply alone to the depreciation charge but equally to all other charges in connection with the asset, such as repairs, maintenance, etc. The author does not believe that these other costs should include a charge for an assumed rate of interest on the money invested in the asset. For a full consideration of the question of interest on capital as an item of cost of production, the student is referred to [Chapter XXVI]. Any method of distributing the depreciation cost must take cognizance of the other costs as well.