WHEN TO REPLACE individual units of durable equipment by similar or improved units is one of the main problems, upon which the success of industrial enterprise depends. Nevertheless, no unified presentation of its many aspects appears to have been published up to the present. The principal writers refer to replacement merely incidentally, when discussing the subject of depreciation. From the theoretical point of view, such an approach really amounts to putting the cart before the horse.' Replacement is the basic problem, because it actually affects the composition and productivity of a plant. Calculations of depreciation are mere figures entered into books, the significance of which depends entirely on the use to which they are put. The concept of depreciation does not enter into the theory of capital value at all. In practice, on the other hand, differences in depreciation methods do to some extent influence the judgment of traders in the negotiable symbols of composite capital goods. This anomaly is due partly to defective accounting methods. A study of the replacement problem by itself must precede attempts to correct the situation. The value aspect of replacement or arises from the familiar phenomenon that many types of machines outlive their usefulness. The income stream derived from their operation gradually declines, until a more attractive alternative becomes available. The theory that the economic life of a machine is a period which makes the unit cost (plus interest) of the product a minimum, appears to have been originated by Professor J. S. Taylor.2 His algebraic presentation was simplified and refined by Professor Harold Hotelling,3 who employs continuous functions for the purpose. The basic formula given by the latter writer is:4

IN A PREVIOUS article1 I made a brief and incomplete survey of the theory of depreciation. In the present paper I discuss its practice. One obstacle to practical progress in this field is that mathematically trained minds are seldom well informed on what accountants actually do. The latter are therefore more often criticized for methods which they are not using than for those which they are. Even otherwise valuable contributions thus elicit opposition quite unnecessarily. The inappropriate antithesis tends to discredit the rest of the argument and prompts general retorts, for instance that is a of . . . determined by the practices of men.-Where accounting treatment diverges from economic theory, a similar divergence is likely to be found between economic theory and practice.2 Such an attitude, in turn, is not very helpful or progressive, even if the dangerous phrase tool of business is interpreted only in its best possible sense. In the article cited, I probably added to the already existing confusion by calling sample methods by certain names without proper qualification, although the same names are commonly applied to substantially different methods. The truth is that the familiar singlemachine formulae permit of different interpretations. To clarify the situation, the present paper identifies a greater number of methods unequivocally by developing their basic many-machine equations and comparing the results. References to practice and to individual writers' ideas are made wherever possible, before choosing a method which appears best suited to the practical needs of large enterprises and the investing public.

Many accountants appear to have no very definite notion of what a balance sheet is. Forthright opinions on the subject are rare; by inference, however, two main trends of thought may be distinguished, one of which is based on the capital-value or property concept and the other on the investment or amount-of-money-advanced concept. The former is exemplified by the so-called fundamental equation: Assets minus liabilities equal net worth. Numerous remarks on the subject of accounting valuations clearly show that their authors were guided at least temporarily by the idea that a balance sheet is or ought to be a statement of the worth of the business. This comment applies to all who would write up good will not purchased or who hold that, if purchased, it need not be amortized until it is actually worth less than it cost. That patents need not be amortized, because they are, in time, supplanted by good will, and that if a company's stock is quoted at a discount, its balance sheet must be inflated, are further samples of the same trend of thought.

The article asserts that the general law governing the value of capital goods has been known for some time. It may be stated briefly by saying that any capital good may be bought or sold for the present value of all future services expected from it. This rule is continuously being applied in practice by bond-traders and all bond tables are based upon it. Nevertheless, apparently no one has made systematic use of it to explain the formation of common stock values. Discussions upon the subject are frequent, but they seldom clear the hurdle of terminological difficulties. To review this preliminary difficulty, the article discusses the behavior of fair market value and yield of common stock. It highlights that when the earning rate equals the money rate, the expansion rate and the horizon lose their significance. The fair market value of the investment will equal the book value and the yield will equal the money rate. Moreover, when the money rate is very low, the fair market value of investments is very high, and their yields correspond closely to their expansion rates.

The article focuses on defining the concept of goodwill. Initially goodwill was defined as nothing more than the probability of old customers returning to the old place. In one instance, goodwill has been defined as an intangible property which, in the nature of things, can have no existence apart from a business of some sort that has been established and carried on at a particular place. Goodwill is the favor which the management of a business wins from the public and the probability that all customers will continue their patronage. It is the general public patronage and encouragement which a business receives from its customers on account of its local position; that is the subject of value and price and of bargain and sale, though intangible. In this definition, the patronage concept is dominant, although its dependence upon location is still mentioned. In general, it may be stated that the emphasis upon the local aspect of goodwill has declined gradually, although there has been considerable overlapping of views in point of time.

The article focuses on taxation and the business year. The inequality of titration resulting from a difference in accounting periods may be illustrated by a simple although somewhat extreme example adapted from actual practice. Income tax regulations make no specific mention of the matter, but applications for change supported by the plea that the corporate taxpayer wanted to bring its books into agreement with its natural business year have been approved by the Commissioner of the U.S. Internal Revenue Service. The theoretical limits of the natural business year may now be examined from the viewpoint of taxation. The last old closing date will evidently be defined as that point in time, at which the present value of all future income tax payments is a minimum. In order to single out the problem of seasonal fluctuations, it is necessary to disregard changes in profit due to the business cycle, the general long-term trend and the individual trend of the business under consideration. To obtain the amount saved per annum, all that is necessary is to multiply the present value of the total savings by the interest rate.

Whereas the terminology of law or medicine is intended to serve primarily if not exclusively the members of those learned professions, the accountants' language must be understood by everybody who has occasion to refer to financial statements. Professional jargon is utterly out of place. Editors of accountants' dictionaries should have desired to make their publications as comprehensive as possible, including not only terms current in business life, but also miscellaneous additional information which might be useful to accountants and business men in general. British usage as well as all words used in their ordinary sense should be omitted or at most, listed with a reference to standard dictionaries. Commonly used terms, which differ from a defined term only by a self-explanatory adjective were also to he excluded. The terminology committee of the American Institute of Accountants has no higher goal than that negative recompense which, according to Dr. Johnson, is the only one that lexicographers can ever hope to attain, namely to escape reproach.