This method requires two steps: the determination of, first, the income to be capitalized, second, the rate of capitalization. The determination of the income to be capitalized is not very difficult, although it requires some modification from the "net earnings" as reported by the railroad companies, with which it should be identical. The difficulty arises from the variation in the methods of railroad companies, in keeping their accounts. The net earnings represent the difference between the gross earnings and the amount properly assignable to operating expenses. For the purpose of this investigation such taxes as are paid are allowed as operating expenses so that the remainder represents the total which can be applied as a return in whatever form to the capital which has been invested. The chief difficulty lies in the variation among railroad accountants in charging expenditures for permanent improvements. One company may purchase additional rolling-stock and charge the entire cost to operating expenses. Others will charge the entire sum to the capital account. If the new equipment is partially to replace old and antiquated equipment, some will adopt the plan of charging the value of the replaced cars or locomotives to operating expenses and charge the remainder to the capital account. The last method is undoubtedly the correct method to adopt, since any permanent addition to the equipment of the road should be charged to capital account and not to operating expenses. Assuming that we have the rate of capitalization, if we divide the net income of the road by this rate of capitalization it will then give a valuation of the property which represents its actual financial worth. The determination of the proper rate of capitalization is very difficult and must be determined according to some fixed rule rather than by assigning an arbitrary value. A minute difference in the rate of capitalization will produce a very large difference in the resulting value of the road. The method adopted by the United States Department of Commerce and Labor may be very briefly indicated as follows:
The market quotations on the securities of each railroad were studied for a period of over six months previous to a given date; even this period was extended in the case of abnormal fluctuations. The details of each issue of debt, the amount outstanding, the rate of interest, the dates of the payment of interest, and the date of maturity were determined. The effect of accrued interest and expected dividends on the prices of securities was allowed for. Since the record of sales only includes a very small proportion of the railroad securities in existence, even the bid and ask prices, which resulted in no sales, were considered. Under usual conditions the bid price represents the lower limit of the market value of the security. The ask price represents the upper limit and the difference represents the zone within which bargaining takes place. On the general principle of adopting a lower valuation in case of doubt, the bid price was used as the basis upon which to value the securities considered. The actual return to a bondholder on a bond which matures at a given time is a very complicated mathematical function of the annual interest rate and of the length of time still remaining for the bond to run. Sets of tables are published which give the average rate per cent in annual return on bonds purchased at various prices above or below par. The rate of annual return on bonds of the road, on the basis of their market price and the date of their maturity, was then figured for each issue of bonds. Multiplying this rate by the actual market value of the bonds gives the virtual annual return to the investor. Dividing the sum total of these annual returns by the sum total of the market values then gives the average rate of income on the bonds which were actually sold or on which bidding prices had been determined. The valuation of the funded debt, which was not quoted on the stock-market, was estimated by giving it a valuation corresponding with other similar securities. Multiplying these values by the same rate per cent per annum will give the annual return on the unlisted securities. We can then add up the values for the actual (or probable) market value of all the funded debt of the road and also the computed annual return to the investor and, by dividing the return by the total market value, we obtain the average annual return in rate per cent per annum. The market price of the stocks, together with their actual dividends, are similarly obtained, but there must be added to the market price of these stocks an estimate which will represent the undivided profits which have not been returned to the stockholders in the form of dividends. "No well-managed corporation divides at any one time among its stockholders the precise amount of its gain since its last preceding dividend. Such a proceeding is not only impractical but also impossible, for the reason that it is impossible to tell precisely what the corporation gains have been during such a period. . . .The physical property has, to at least some extent, changed its identity during the period; the credits and obligations of the corporation have probably changed; the general aspects of its business opportunities have almost certainly changed; and all of these together have correspondingly modified the value of its physical property." Some of these improvements can be definitely allowed for. For example, the average annual expenditures for permanent improvements which have been made during a period of say five years should be added as though it were a dividend, since it might be considered as a dividend paid to the stockholder and immediately reinvested by him in the capital stock of the road. Similarly, variations in the profit-and-loss account, as indicated by the general balance-sheet, can be allowed for by considering the average annual change in the profit-and-loss item for a period of years. Even if there had been a loss each year a steady reduction in that loss may be considered as an average increase in the profit account.
Another item to be added is due to the fact that the sum of the actual annual payments of interest and guaranteed dividends may amount to more than the computed annual return based on the market price of the bonds. This annual excess must be added in order to compute the actual annual return to the investors of the road. In fact the only object of computing the annual return, based on the market price and the time of maturity of the bonds, was that a proper average rate could be obtained on which to compute the return on the unquoted securities. There is still one other item which may need to be added: if the returns on the common stock are based on the present rate of dividends, but the dividends have varied during a period of say five years, which is the period adopted for the annual averages of betterment, etc., we must consider that a reduction in some rate of declared dividend means that so much money has been added to the profit-and-loss account of the road, and therefore the average amount of this difference, spread out during a period of say five years, represents the average addition (or deduction) which must be made to or from the average income of the road. Taking the summation of these average returns and dividing it. by the summation of the market (and computed) prices of all forms of the securities of the road, we determine the actual average annual return in rate per cent on those securities.
Dividing the net earnings of the road by this computed rate of capitalization then gives the valuation of the entire property.