14. "Arithmetic progression," method and value shrinkage principle.—According to the value-shrink age principle, deterioration, as it is shown in the arithmetic progression method, implies that the service value of the instrument decreases rapidly at first, and more slowly with advancing age, but by an amount that is never less than the depreciation al lowance of the period immediately preceding. Thus for the thousand-dollar machine—prospective life, five years; scrap value, $25, estimated on a six per cent discount basis—the implied service-values range from $385 down to $69.40. The higher the discount basis, the more rapid the implied decrease in operating effi ciency.
15. Best depreciation method for practical pur poses.—When the chief thing to be considered is either a single instrument, so constructed that the whole wears out and has to be discarded, or individual parts, the method chosen should be one which allows for more depreciation in the earlier periods than in the later period. This is because the service-value, or operating efficiency, of the instrument rarely in creases with age. Frequently it remains constant, as in the case of a house with a well-constructed roof. Often it is less during the first few months than later, because of the time lost while the instrument is under going the necessary adjustment. But whether the operating efficiency remains constant or diminishes, the allocated-cost principle, which we hold to be true, operates to diminish depreciation allowances. The amount of depreciation per period for the whole mechanism becomes fairly constant, however, when one figures it not for one part, but for several, which together constitute a whole organized mechanism. This is true, however, only when the mechanism, as a whole, is so old that it is composed of parts of all ages, from those that are perfectly new, to those that are about to fail and be replaced. But even in such a
case the principle of diminishing depreciation still holds as regards each separate part.
For practical purposes, therefore, we recommend the level-depreciation method, notwithstanding the fact that theoretically it does not hold for the first part of a machine's life. We recommend it not only be cause it is logically applicable during the instrument's later life, but because it is the simplest from a prac tical standpoint. In a factory where depreciation or repair allowances enter into the cost-accounting sys tem, the adoption of this method does not make it necessary to revise the cost rates month by month, as would be necessary under any other method of com putation.
16. Appraisal method.—Another method that is sometimes used is the appraisal. The value of the de preciating asset is estimated from time to time by ex pert appraisers, and the difference between the suc cessive appraised valuations is called the depreciation for that period. This system simply shifts the re sponsibility from the owner to the appraisers; for the latter must have some method by which they arrive at the valuations they place upon assets. Seem ingly, this would consist either of judging directly the amount that could be realized on an asset, were it to be sold at the time, or else of arriving at a valua tion of the article when new, and then making a valua tion of the asset as it actually stands. We have al ready taken the position that the salable value of an article of equipment which is being used as an in tegral part of a going business, has nothing to do with the problem of its depreciation, which is simply a question of cost-apportionment.