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Table VI on page 199 shows the financial condition of the property for each year of its life. Column 1 shows the years from the original construction of the plant, figure unknown at the time of an appraisal and introduced here simply to show the amount that should actually be in the reserve fund to preserve the value of the investment intact. The reserve funds, which should be in hand at the end of each year, are shown in column 4. At the time of an appraisal the cost-new, the mean age and the amount in reserve would be known. From the mean age the years of remaining life, column 5, are known. The undertaking will obtain the interest compounding at 3 per cent on the reserves during each of the remaining years of life, column 6, and an annuity of $8,723.06 and interest accumulations during the same period, column 7. At the end of the life of the property, the amount in hand will be the sum of these two figures, -column 6 plus column 7,shown in column 8.

To take an example: cost-new, $100,000, mean age 6 years, and depreciation reserves $56,424.32. There are therefore 4 years of remaining life. $56,424 at compound interest at 3 per cent for 4 years will amount to $63,506. There will be an annuity $8,723 for 4 years and with its interest accretions it will amount to $36,494. The sum of these two figures, $63,506 and $36,494, will be the present value of the property, in this case equal to the cost-new.

The second typical normal case which will be considered will be that of a plant which has been growing and the additions have been paid for by the stockholders. As an example of this case, the conditions considered in section 137 will be taken. It will be assumed, therefore, that a plant originally costing $100,000 had been increased by ten per cent of the cost-new at the end of each year. Ample reserves had been made each year and held in a

sinking fund upon which interest at three per cent was obtained.

TABLE VII

EXAMPLE OF CALCULATION OF VALUE OF PROPERTY CONSISTING OF PLANT AND RESERVES

All Reserves Properly Made and Held in 3% Sinking Fund

As will be seen from the above table, the undertaking having made proper reserves for depreciation will have in hand, at the periods noted, the funds shown in column 4 as well as perishable property of costs-new, at the same times, of the values given in column 2. The undertaking will obtain compound interest on the reserves during the remaining years of life. The amount of the reserves, shown in column 4, when placed at compound interest for the remaining life of the plant in each case is given in column 6. Moreover, the undertaking can obtain an annuity, figured at current rates of interest, upon the cost-new of the perishable property. The aggregates of these annuities and interest for each value of the plantnew at the end of the life of the property are shown in column 7. The sum of the reserve fund in hand at the time of valuation plus interest accretions (column 6) and

the annuity plus interest (column 7) gives column 8, and shows that at the end of the life of the plant there will be a sufficient reserve in hand to replace the property which has become unserviceable. It follows from this that the full value of the investment in perishable property has been maintained throughout the life of the plant and, consequently, that its present value is, at all times within that period, equal to the cost-new. In other words, the investment has suffered no loss in value and, consequently, has suffered no depreciation.

As an illustration the case can be taken of a property having a pseudo mean age of 4.96 years and consisting of a plant of which the cost-new is $194,872, and of depreciation reserves amounting to $89,579. The remaining life of the plant is approximately 5.03 years and, in consequence, the $89,579 will obtain compound interest during that time. $89,579 plus the compound interest will amount to $103,952. The cost-new of the plant is $194,872 and necessarily is independent of the cost of any additions or extensions that may be made at a later date. The annuity which the undertaking will receive during the remaining 5.03 years of life is approximately $17,000. These annuities plus the interest upon them will aggregate $90,920. $103,952 plus $90,920 equals $194,872, - the cost-new of the perishable property at the time of the appraisal.

142. Loss in value of property consisting of plant, built partly with reserves, and of reserves. The case of a property consisting of plant and reserves but wherein a portion of the plant has been built with some of the reserves is more usual than the cases described in the previous section. The method of calculating the present value of the property as a whole will be the same, for the reason that injustice in some cases might be done to the undertaking if this method were not employed. As the illustration given below will show, reserves which are

made on the sinking fund method presuppose that the amounts set aside are to obtain the benefit of interest accumulations. If sums are taken from the reserves, - which have been obtained on the sinking fund basis and, consequently, are less than the cost-new divided by the life,-for the purpose of paying for plant extensions, the undertaking suffers a loss. If reserves are to be used for enlargements of plant, as in many cases it is wise to do, then the reserves should be made on a straight line basis even though at the time of an appraisal it may be shown that there is a greater value in the property than its actual cost-new.

This is well illustrated by the following example. For this case let it be assumed that original cost of the plant was $100,000; that it had a ten-year life; that reserves had been made on a sinking fund basis; but that at the end of two years $15,000 was taken from the reserve funds to pay for needed extensions of the plant.

The following table illustrates the changes in the value of the property under the assumed conditions:

TABLE VIII

EXAMPLE OF CALCULATION OF VALUE OF PROPERTY CONSISTING OF PLANT AND RESERVES

Portion of Reserves, Made on Sinking Fund Basis, Invested in Plant

3

95,856

115,000 2.74 12,821 7.25 15,886 79,970 4 115,000 3.74 23,237 6.25 27,955 67,901 95,856

This example need not be carried farther. It shows that, although reserves had been made in amounts suffi

ciently large to recover the cost-new of the property by the end of its life on a sinking fund basis, the removal of $15,000 from the reserves for depreciation had reduced the value of the property. The present value of the property, as shown by column 8, is $95,856, which shows that the undertaking's investment of $100,000 has diminished in value by $4,144, which means that the undertaking by investing this sum in plant rather than by holding it in reserves has lost the compound interest on $15,000 for more than eight years.

143. General consideration of loss in value due to age. -The above cases sufficiently illustrate the methods to be used in calculations of the loss in value of investments in perishable property or, as it is more frequently called, of the depreciation in the value of property. In the last case it was assumed that a portion of the reserve funds had been used for the purchase of new plant. The method of treatment would have been the same if the reserves in the earlier years had been inadequate or if the $15,000 had been paid outright to the stockholders. The loss in the value of the property would have been, however, much greater. In such a case the cost-new would have been found to be only $100,000 and, in consequence, the annuity on a sinking fund basis could have been only $8,723. The mean life at the period chosen would have been two years. The $2,708 at compound interest for eight years would have been $3,430, and the amount of the annuity and interest at the end of eight years would have been $77,568. The sum of these two figures is $80,998, which shows a depreciation of $19,002.

The above consideration of depreciation presents methods which, as far as general rules are concerned, are fair and equitable to both the undertaking and the public in questions concerning rates and to both buyer and seller as well as to the public in cases of condemnation or sale.