same total amount should be placed in reserve each year, but that there should be set aside a uniform percentage of the wearing value of the plant as it is found to be after additions to the plant or removals of abandoned plant have been properly entered as positive or negative factors in the plant account.

If the depreciation reserves are invested in outside securities, the interest on the reserve funds is paid not by the public but by those having the use of the money. Moreover, the amount paid by the public as an annuity to the reserves would be uniform and (if 8 per cent could be obtained for such money) would be the amount shown as the annuity in the above table.

Thus it is seen that, provided the straight line method is used when reserves are invested in plant and the sinking fund method when reserves are invested in outside securities, the percentage of the wearing value of the plant to be set aside each year is uniform in each method but that the annual payments to the fund for renewals are larger when the straight line method is used than when the sinking fund method is employed.

109. Reserves invested in plant. — It must not be inferred that, because the amount paid annually as a reserve for depreciation is less with the sinking fund method, when such funds are invested in outside securities, than with the straight line method, the sinking fund method is, consequently, more favorable to the public and that it is therefore the proper method to be adopted generally. A careful consideration of this question will show that the burden upon the public is less when the straight line method is employed than it would be with the sinking fund method, in all cases where the undertaking is in successful operation, is growing and, consequently, requires new money with which to carry out needed enlargements or extensions of the plant.

This economic question is of such fundamental importance that it will be discussed somewhat at length. The use of reserve funds for plant extensions necessarily indicates that the business is growing. If the plant is of sufficient size for all immediate needs, then, clearly, the sinking fund method is the only plan that should be used. But for a growing property the management has two alternatives, either to use the reserves to defray the cost of plant extensions, or to obtain new money from the stockholders for that purpose. In the latter case, the public will have to pay the full return upon the stockholders' investment; in the former case, the new plant would be provided from funds upon which the stockholders can obtain no return. Where reserves are invested in plant, the undertaking is not using its own money for such extensions, but money in which the public has an interest, and, consequently, the public becomes to a certain extent a partner in the operations of the undertaking. As a consequence of this the burden upon the public is somewhat less when the reserves are invested in plant than would be the case if the stockholders' money was used. This point can be illustrated quantitatively by a numerical example.

Let the cost of the plant be taken as $100,000, and let it be supposed that the plant has no salvage value. Let the rate of return to the stockholders of the undertaking owning the plant be 8 per cent and the life of the plant be ten years.

Let us take the case first of the yearly requirements when the reserves are invested in plant. At the end of the first year $10,000 will be required as a reserve for depreciation. With this $10,000 let it be supposed that new plant is immediately purchased. The new plant will have a life of ten years. At the end of the first year of its use, i.e., at the end of the second year of the exist

ence of the plant, a reserve must be set aside to cover the depreciation of the plant a year old as well as the second installment toward the depreciation reserve of the original plant. So that at the end of the second year $11,000 must be set aside, i.e., $100,000 ÷ 10 and $10,000 ÷ 10. This has been set out in the following table:

TABLE II

ILLUSTRATING ACCUMULATION OF DEPRECIATION RESERVES

Amount set aside each Year

End of

Year

1234567

$10000...

10000+1000

10000+1000+ 1100

10000+ 1000+ 1100 + 1210

10000+1000+ 1100 + 1210 + 1331

10000+1000+ 1100 + 1210 + 1331 + 1464

10000+1000+ 1100 + 1210 + 1331 +1464 +1610

$10000

11000

12100

13310

14641

16105

17715

It must be remembered that, in accordance with the assumptions of this example, the amounts set aside each year as depreciation reserves are invested in plant and, in consequence, the cost of the plant is constantly increasing by the increments given in the last column of Table II. The stockholders' original investment is only $100,000, but the cost of the property is constantly increasing with yearly increments of increasing size. This growth in cost of the plant is shown in column 2 of Table III, page 153. Column 3 shows the condition of the investment of the stockholders in the undertaking. The original investment made by them in the plant unit remains unchanged during the first ten years, but the total amount that has been invested increases rapidly owing to the reserves that must be made to maintain the investment intact. At the end of the ninth year there has been expended to make good the original invest

TABLE III

ILLUSTRATING RELATIVE INVESTMENTS OF STOCKHOLDERS AND OF DEPRECIATION RESERVES IN A RAPIDLY EXPANDING ENTERPRISE

ment, as well as the wasting investment in plant built with reserves, a total sum of approximately $235,795.00. In other words, the cost of plant built with the reserve funds exceeds the cost of the original plant built with stockholders' money by approximately $135,795.00. The

plant as a whole still has a depreciated value of $100,000.00, as there has been invested from reserves approximately $135,795.00 in plant which has itself depreciated about $35,795.00 at the end of the tenth year, the plant representing the original investment has become worn out. At this time the stockholders must invest $100,000.00 of new money to make good the original plant which has passed out of existence and each year thereafter money must be paid in to replace portions of the plant, originally built with reserves, which become yearly unserviceable. At the beginning of the nineteenth year the stockholders' investment has become about $314,359.00, while there has been invested in plant approximately $555,992.00. This shows that at this particular time the reserves for renewals are $241,633.00, approximately three-quarters of the stockholders' investment.

This study illustrates the principle of the operation of depreciation reserves when invested in plant and brings out clearly the important fact that very large reserves, under certain conditions, are essential to the security of the investment in wasting property.

The above table has been presented in an extended form in order to illustrate the fact already suggested in section 105, that, for every additional investment in perishable property, there is required each year in perpetuity a sum of money equal to a certain fraction of that investment to be set aside from income for the purpose of renewals. Clearly the same results can be obtained more simply by making a reserve each year equal to the cost-new of the property divided by the life. The above table is useful also to show how the succeeding table has been prepared, wherein it is shown by how much greater the burden is upon the public when extensions to plant are constructed by the use of new money, subscribed by the stockholders, than is the case when the money