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.
(a) Straight Line Method
The straight line method is, first of all, simple in application and can easily be adapted to any asset under almost any conditions. Partly because of the ease of calculation and application, it has been designated as an official method by many regulatory boards. Its basis is a time basis and it spreads the charge evenly over the periods of the service life of the asset. Accordingly, where the time elements of depreciation, viz., decrepitude, inadequacy, or obsolescence, control and where the output does not fluctuate much from period to period, the straight line method should give satisfactory results for its intended purpose, i.e., for allocating the real depreciation charge.
Its effect, however, must be considered also in conjunction with the distribution of the other costs connected with the asset. Many engineers maintain that repairs are light during the early life of an asset and heavy during the later years. If this is true and these costs are charged to the period in which they are incurred, the combined depreciation and up-keep costs place an unjustly heavy burden on the output of the later years. Almost equally good authority maintains that the cost of repairs is in no sense uniformly graduated as implied above but can be counted upon in practice to be extremely irregular. If this is true and up-keep costs are charged as above, then many periods are apt to be underburdened and others loaded too heavily.
While, however, these considerations must be given weight when a single asset is under view, in a large plant after operation has continued to the point where a normal and fairly regular cost of up-keep has become established, the inequalities of the individual up-keep charges may merge into fairly equal charges for the up-keep of the plant as a whole. This the law of averages accomplishes to a greater or less degree. But in a small plant with few assets subject to depreciation, the equality of the whole might not result from the individual inequalities. After all, this magic rule of averages which is invoked to cover up many troublesome and embarrassing situations is obnoxious to scientific accounting; it is a makeshift which carries with it a shiftless trust in the happy outcome of things—a trust which has been so often betrayed as to carry little weight.
If depreciation costs can be predetermined with a satisfactory degree of accuracy—and an estimate of them is all that can ever be made—with equal accuracy and satisfaction can up-keep costs be predetermined. The one is no more difficult than the other and equal reason exists for predetermination in both cases, viz., the securing of an equitable distribution of costs. With both estimates made at the beginning of the service life of the asset, all costs in connection with the asset can thus be prorated over the years of its service life.
If, as stated above, the output is fairly regular as between periods, fair and equitable results will be obtained. If the output fluctuates violently, unsatisfactory costs and an inequitable burdening of product will be the result. The proper treatment of overtime and “beyond-capacity” work, i.e., abnormal operations, requires care. It is expected that such work will have a higher unit cost than normal output, and it is proper that a sliding scale of depreciation be applied in such a case.
(b) Working Hours Method
Most of the considerations taken into account for the straight line method are equally applicable to the working hours method. Here, with the service life expressed in terms of working hours instead of fiscal periods, a far step has been made towards securing an equitable distribution of depreciation costs over product. The rate per working hour can in this way be applied directly to the product. The machine-hour and sold-hour methods of costing distribute the depreciation along with all other costs on this basis of “rate per working hour.”
Where a machine or other asset is limited in its use to a few operations equally wearing in their effect, this method should give satisfactory results. Where, however, one asset can be used for many different processes, involving inequalities in wear and tear, if the service rendered is the controlling factor, an inequitable distribution will result. Similarly, beyond-capacity operation, i.e., operation beyond the normal speed at which depreciation cost has been predetermined, will not be taken care of automatically by this method. Adjustment is necessary and, though arbitrarily made, must be attempted. Thus, ten articles might be turned out in one working hour, whereas an estimated output of six formed the basis for determining the rate of depreciation per working hour. As with the straight line method, so here equal care must be exercised in securing an equitable distribution of up-keep costs.
(c) Composite Life Method
This is not a working method for estimating individual depreciation costs, but rather a method of proof or check, which proves very valuable in some cases. The method is discussed in detail on page 197 where the uses to which it may be turned are pointed out.
(d) Service Output Method
The service output method bases the depreciation cost not on years of life nor on life in terms of working hours of service. Here an attempt is made to predetermine the output of the asset in terms of units of product, and so burden every unit with its fair share of depreciation. To secure full equality of charges, up-keep costs must be reckoned on the same basis, rather than on a time basis of service hours or length of life. If conditions are uniform and normal, this method, where applicable, secures perhaps the most satisfactory of all allocations of depreciation costs. To an individual machine performing several different processes the method would scarcely be applicable. To a group or battery of machines, turning out a uniform product in finished form or in the same degree of partly finished condition, the method could be well applied. The estimated total output of the group would then be taken as the basis for calculating the service output of each machine in the group. When calculating service life in whatever units, that speed of operation which secures the highest efficiency is taken as the figure of normal operation.
From the foregoing it follows that the service output method of calculating the depreciation charge per unit of output is well adapted to an inherently wasting asset, such as a mine, a quarry, and timber lands, and is almost invariably applied in such cases.
(a) Fixed Per Cent of Diminishing Value Method
The chief merit of the variable percentage methods, in the eyes of their advocates, is the way they are automatically adjusted to the up-keep charges. The reader should study the graphs of these various methods as a means of comparing results.
On the graph, page 158, it is shown that under the fixed per cent of diminishing value method the periodic depreciation charges are heavy in the beginning and decrease toward the end. It is argued that, inasmuch as up-keep costs increase as the depreciation charge decreases, this method automatically equalizes these two costs. This argument was examined in detail under the previous discussion of the straight line method. What was there set down applies equally here. The fixed per cent method is also based on service life by periods—a time basis rather than a service or output basis. Furthermore, it involves a complex calculation and is perhaps never applied with any degree of accuracy. Lawrence R. Dicksee prefers this method for handling depreciation on machinery.
(b) Sum of Expected Life-Periods Method
The objection of complexity of calculation to the method just discussed is overcome largely in the sum of expected life-periods method. Here the rate of decrease is more marked, but the method has the same general effect as the fixed per cent method. If the repair charges are handled, as suggested, by means, of pre-estimates, the results will not be equitable. If repairs increase with uniform regularity as the depreciation costs decrease, fair equality is secured. Otherwise the method has little to commend it.
(c, d) Arbitrary Methods
The two other methods under this main group, viz.: arbitrary with increasing amounts in the one case and decreasing amounts in the other, are not based on any orderly scheme of calculation and, having little logic behind them, are not to be relied upon. Ease of calculation is perhaps their only merit.
General Considerations
In a discussion of compound interest methods the basic feature, that of the compound interest principle, requires consideration. The thought of progression on a compound interest basis is fascinating to many. It is a powerful instrument of accumulation and its charm seems to lie in the fact that through its instrumentality small sums can be made to grow into large sums. Whether the principle is applied to the creation of a fund or simply as a method of calculating periodic amounts, the remarks of P. D. Leake,[36] an English authority, are equally appropriate. He says: “May I impress upon you that these devices are dangerous expedients in any but the most skillful hands.... It (the sinking fund) is apt to give a sense of false security, because its whole virtue depends upon its obligations being faithfully carried out over the whole period, and this condition is not always fulfilled.... It is probable that in many cases the use of a sinking fund is an altogether unwarrantable draft upon the future, because there is no reasonable certainty that the fund, whether it be state, municipal or commercial, will not be raided before it attains its object.”
Over short periods the difference between the periodic amounts under this method and the straight line method is slight, as will be apparent from a comparison of the two charts on pages 153 and 162, giving graphic illustration of the two methods. There the period is for five years. When the period is extended to, say, twenty or fifty years, the difference in burden, due to interest accumulations, between the early years and the later years is very marked. “Thus, a 10-year unit having no salvage value, loses half its value in 5 years under the straight line theory, regardless of the rate of interest, and at 5% under the compound interest theory it loses nearly as much—about 44% of its value in the same time; ... but a 50-year unit, losing half its value in 25 years, under the straight line theory, loses only 22.8% of its value, at 5%, under the compound interest theory.”
(a) Sinking Fund Method
The sinking fund method as an orderly scheme for estimating the periodic depreciation charge will make the estimate, and, if adhered to faithfully, the entire depreciation will be written off by the end of the service life of the asset. In this respect it is to be preferred to any arbitrary or haphazard method. That it secures an equitable distribution of depreciation costs over the product of the various periods, or that it effects a correct valuation of the asset at intermediate periods of its life is open to serious questioning. The periodic charge under the sinking fund method perhaps bears no relation to the fact of depreciation. The method is, at the best, simply a mathematical device for an orderly calculation of periodic amounts. In the valuation work of public service companies or in regulation work where, as in California, actual funds must be set aside to accumulate at compound interest, there is no serious objection to the method. Although it rests on false or doubtful assumptions of fact and results in an inequitable burden on the product as viewed from the standpoint of individual assets, these are minor considerations; for the method does by the end of its service life take care of the loss in value. Judged from the standpoint of its relation to up-keep costs, the method lays an increasingly heavy burden on the later years of the life of the asset.
(b) Annuity Method
All that has been said with regard to the sinking fund method applies with equal point to the annuity method. As previously indicated, in the explanation of its essential features, this method automatically secures a charge for interest on the investment as a part of the depreciation charge. Not only is the charging of interest of doubtful propriety in itself, but certainly its inclusion under the title of depreciation is misleading and indefensible. The courage of one’s convictions with regard to interest as a part of cost should not allow interest to shelter itself under the cloak of “depreciation.” By referring to the appraisal schedule and chart, it is seen that the real depreciation charge is exactly the same under the annuity as under the sinking fund method.
(c) Unit Cost Method
The unit cost method represents an attempt to secure an equal burdening of each unit of product with interest, depreciation, and operating costs. In the language of its proponents, “this theory is probably the soundest theory of depreciation, and when applied with intelligence, probably furnishes the truest measure of accrued depreciation.” While the end sought by the unit cost method is commendable, it is a compound interest method and it mixes interest, up-keep, and depreciation under the one title “depreciation.”
Criticisms of the miscellaneous theories can be brief.
(a) Maintenance Method
This method is irregular in its incidence, and under it the depreciation charge fluctuates violently between periods. Just as maintenance is subordinated to the requirements and demands of the trade, so also are depreciation costs made to depend on the same conditions. The charging of depreciation thus becomes a matter of business convenience instead of an inexorable fact of production. Just as repairs are postponed to a slack period during which maintenance charges are in consequence heavy, so does the depreciation charge increase even though actual wear and tear has decreased. Presumably the method makes charges light during the early years and heavy during the later years of the life of the asset. In a large plant with various kinds of assets, after a normal up-keep charge has been established, the maintenance method of estimating the periodic charge for depreciation for the plant as a whole may work out fairly well on the theory of averages or by accident; for maintenance is not a measure of depreciation.
(b) Replacement Method
This is not a method of measuring depreciation but rather of financing it, i.e., of making good the loss. It also is based on the law of averages, and in a large plant after the point of normal replacements has been reached it may prove a satisfactory method of accomplishing its purpose. It does not serve as a means whereby a periodic depreciation charge can be brought on the books. Furthermore, it disregards the depreciation accrued up to the point of normal replacements.
(c) Fifty Per Cent Method
This method is also based on the law of averages. Here the law is very apt to work out satisfactorily. When the point of normal replacement of the assets, to which the 50% method is applicable, has been reached, the amount of depreciation is approximately 50% of the original value of the group of assets. This amount may be booked at that time and will remain without change thereafter, for the assets are maintained constantly in that condition. As a means of valuation, the method may serve well; as a measure of periodic depreciation or as a means of distributing the depreciation cost over the product, it is inadequate.
(d) Appraisal Method
This method is also inadequate as a means of measuring the periodic cost of depreciation. The physical facts of depreciation are not usually discernible at such short intervals. A judgment of values must, therefore, almost invariably make use, consciously or unconsciously, of some of the other methods of estimating the amount of depreciation by periods. After all, all methods of measuring depreciation are appraisals. Under the appraisal method confusion between original cost and reproduction cost is almost certain to occur, for present market values usually control physical appraisals. A discussion of the relative merits of original cost and reproduction cost as a proper basis for estimating depreciation will be presented in Chapter XI.
(e) Insurance Method
This method of carrying the depreciation charge is analogous to the policy practiced by some concerns of taking care of their fire losses by carrying their own insurance. If physical conditions are such as to make such a policy advisable or prudent, it should work out satisfactorily. It should be noted, however, that the insurance method is a means of providing funds for financing replacements and renewals rather than a method of insuring an equitable distribution of the depreciation cost over the product. The method of providing funds does not need to be the same as the method of measuring the periodic cost of depreciation. The insurance method serves the former purpose but is not well adapted to the latter. Much of the criticism of the sinking fund method is here applicable.
(f) Percentage of Gross Earnings Method
Measuring periodic depreciation as a percentage of the period’s gross earnings is a convenient and fairly satisfactory method under some conditions. If the principal element is wear and tear—a service factor rather than a time factor—output may have a very direct relation to gross earnings. If the commodity dealt in is a standardized product and its price does not fluctuate to any extent or, better still, is fixed, gross earnings will be a very fair measure of output. It is true that the estimate is based on a sales valuation of output rather than its cost of manufacture, but under some conditions this is a good measure of relative output as between periods. A depreciation charge based on gross earnings may thus give an equitable distribution of the depreciation burden. In the case of public utilities, when the price of the commodity or service dealt in is fixed, an estimate based on gross earnings usually gives satisfactory results where used. In applying the method, the expected earnings during the composite life-period of the plant are estimated and depreciation costs are then prorated over periods on the basis of earnings for the period as compared with total earnings for the composite life-period; or more simply, a fixed percentage based on past experience can be applied to the earnings of each period. Some objections to the method, arising in some cases from a misunderstanding of its operation, were pointed out when an explanation of its working was given.
In some cases gross earnings bear no relation, or only the remotest, to the quantity of output or the units of service rendered. A depreciation estimate based on earnings would not in that case be logical and could not give satisfactory results.
From the above discussion of some of the merits and shortcomings of the various methods, the cogency of the introductory remarks, to the effect that no method of measuring depreciation can serve as a panacea, should be appreciated. Every depreciation problem is more or less an individual problem; sweeping generalities will not serve.
Effect on Return on Investment
Many interesting studies have been made of the effect of some of the above methods on stability of income as between periods and their effect on the return of the investment, using hypothetical data as to the earnings of the depreciating asset. Except for the purpose of fixing rates in the case of public service corporations, where the public has an interest because of the monopoly granted, stability of income should be subordinated to the fact of depreciation and not serve as a test of the merit or demerit of a method.