METHODS OF DETERMINING THE AMOUNT OF DEPRECIATION 1. Sinking-fund method.—The system of providing for depreciation which is known as the sinking-fund method, derives its name from the fact that the prin ciple employed is the same as that used in building up a sinking fund, altho those who use this method do not contemplate the establishment of an actual fund of cash or securities. A sinking fund is used for the purpose of paying a debt at its maturity. Certain regular instalments of cash are paid at periodic inter vals to a trustee who invests the cash in interest-bear ing securities ; the interest on the investment is col lected by the trustee and goes to increase the fund. Thus the fund is augmented by these regular pay ments, plus the interest on the investment of all pre vious instalments and interest.
Suppose a certain machine is purchased for $1,000, and that it has an estimated life of five years, and that it will have a scrap value at the end of that period of $25. This means that in five years $975 must be al lowed for depreciation. The problem is to find what annual sum must be set aside and accumulated at compound interest, at an assumed rate per cent which will amount to $975 at the end of the estimated life.
Let it be assumed that the rate is six per cent per annum. Reference to a compound-interest table will show that the amount of an annuity of one dollar at the end of the fifth period is $5.63709296; if $975 is divided by this amount, the quotient will be the an nual amount which, theoretically at least, is to be set aside and compounded at six per cent. The following tabulation shows the allowances that would be made during the several years, and how they are derived from the base or the quotient, $172.96, found as de scribed above.
The amount to be set aside each year for deprecia tion is found in the column headed "allowance for year." 2. Significance of the sinking-fund method.—It will be seen that according to this method the depre ciation allowances increase by accelerating amounts as the asset grows older; but to say that there are in creases in the values of services means either that the value of a unit of service increases as time elapses, or that the machine has been judged capable of rendering an increasing amount of service—i.e., increasing effi
ciency—as it grows older. The latter is extremely un likely, and it is only a little less probable that unit values should increase. Therefore the allocited cost principle does not justify the sinking-fund method.
3. Significance under value-shrinkage principle.— According to the value-shrinkage principle, the sink ing fund Method implies that the operating efficiency of the instrument is constant during its life. This im plication is illustrated in the following table in which it is shown that a constant annual rental value of $232.96 is implied by the assumption that an asset which costs $1,000 will have a scrap value of $25 at the end of five years, and shrinks in recapitalized value as a result of the sinking-fund method, interest being computed at six per cent per annum.
This rental value is ascertained by subtracting from cost, $1,000, the present worth of the estimated scrap value of $25, which present worth is $18.68 -F, and dividing the remainder by the present worth of a five year sinking fund or annuity of one dollar, which is $4.212364.
The value-shrinkages for the successive years are shown on the last line. Comparison of these with the allowances shown in the preceding table show them to be identical except for two discrepancies of one cent each, which are due to the rounding off of decimals. It should be noted that even according to the value shrinkage theory, uniform efficiency of the instrument does not usually imply depreciation in accordance with the sinking-fund method. This method would apply only in the rare case when the cost of the instrument, estimated rental and scrap values, and rates of inter est bear to one another the relationship expressed above.