8. Value-shrinkage principle and the level-depre ciation method.—The value-shrinkage principle justi fies level depreciation only if the service-rendering ca pacity decreases in a certain-manner with age. Thus, in the illustration just referred to, if the probable service values are discounted at six per cent per an num, value-shrinkage will be constant if the annual rental values are $255, $243.30, $231.60, $229.90 and $218.20 respectively. This is made clear, by the form shown on page 320.
If no errors had been made in dropping fractional cents when the second decimals were rounded off, the values would have been such as to cause a uniform value-shrinkage of $195 per annum.
9. Proportional-depreciation method.—If the pro portional-depreciation method is used, the deprecia tion percentage chosen must be such that its successive application to the diminishing undistributed cost of the instrument will reduce its book value to its esti mated scrap value by the end of its estimated life. For assets having a short life, this means a very uneven depreciation allowance, beginning with a very large amount in the first year and rapidly diminishing to a very small amount in the last. The depreciation on the thousand-dollar machine, for each of six years, would be the following: 16. Significance of the proportional-depreciation method; allocated-cost principle.—If the allocated cost principle is applied, the proportional method im plies that as the instrument grows older, its service rendering capacity decreases almost in the ratio of the complement to the depreciation percentage. If it is true, as some claim, that when the efficiency of an instrument has deteriorated 25 or 30 per cent the instrument must be discarded, evidently the propor tional-depreciation method is not applicable.
11. Significance as related to prin depreciation, according to the value-shrinkage principle implies that the efficiency of the instrument decreases in exactly the same ratio as the book value. The following table shows the pro portional value shrinkage of the machine previously referred to.
Many favor proportional depreciation because it assigns more depreciation to the earlier part of an instrument's life than to the latter. They favor this method for the following reasons: (1) The efficiency of the instrument does decrease. (2) The shrinkage in selling value is more the first month than it is for several years afterward. (3) It is possible, by com
bining the constantly lessening depreciation allow ances and the increasing repair costs to make a fairly uniform total maintenance charge.
In most cases we must concede the first reason, altho there are exceptions ; however, a decrease in the efficiency of the instrument is implied in the level depreciation method also. We contend that the sec ond reason has nothing to do with the case. Con cerning the third, it has already been recommended in this Text that, in the case of machinery or com plicated mechanism the depreciation allowance should be replaced by two allowances: viz., an al lowance for repairs and an allowance for obsolescence of the type. Finally, it does not seem likely that the decrease is nearly so rapid and extensive as this method would imply.
12. Method of "diminishing arithmetic progres sion."—The method known as "diminishing arithmetic progression" can perhaps best be defined by means of an illustration. Suppose that a certain instrument will last five years, add the numbers 5, 4, 3, 2 and 1— the sum is 15. Then 5/15 of the total depreciable value-5 representing the estimated life including the year in question—is the depreciation of the first year; 4/15 is that of the second year, and so on. Thus, since the depreciable value of the thousand-dol lar machine was $975, the depreciation allowances would be respectively $325, $260, $195, $130 and $65.
This method, however, makes a very uneven dis tribution of the depreciable value of the instrument when the assumed life is short; tho the longer the assumed life, the more nearly uniform is the deprecia tion.
13. Significance of "arithmetic progression" method; allocated-cost principle.—If a discount basis of 6 per cent per annum is assumed, in the illustration just used, the service values imply a rapid deteriora tion in the efficiency of the machine, altho with a higher discount basis the implied deterioration is not so rapid. If a higher discount basis is taken, the im plication is that the operating efficiency increases dur ing the early part of the instrument's life, and then rapidly decreases. If the service life that is assumed is long enough, this peculiar implication pertains even in the case of any lower discount basis.