Of the nine articles reprinted in this volume originally published in 1984, those by Ladelle, Hotelling and Anton are recognized as being the classic articles on the depreciation of a single 'machine'. Each of these articles was published in a journal that is often not accessible and reprinted here has brought them together in one place. For many years accountants have dealt with depreciation and capital maintenance as a static problem. This volume recognizes its dynamic aspects.
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Yes, you can access Depreciation and Capital Maintenance (RLE Accounting) by Richard Brief in PDF and/or ePUB format, as well as other popular books in Business & Accounting. We have over one million books available in our catalogue for you to explore.
ONE of the most commonly used methods of depreciating capital goods is to write off their initial value in equal annual portions in the course of the estimated lifetime. When this lifetime is correctly estimated and when the depreciation fund is left idle its value (apart from price changes which will be left entirely out of account here) at the end of the lifetime will evidently be equal to the initial value of the capital good and will allow for the replacement of the worn-out item by an exactly identical new one.
In reality, this equality will very seldom be fulfilled. This is not only due to the fact that the individual lifetimes of identical capital goods will vary so that, at best, only a correct average can be used which could yield equality for very large values of the initial stock only, but still more because depreciation funds are usually reinvested in one way or another long before replacement has become necessary.
In particular, in dynamic processes replacement and depreciation may differ considerably. Already in 1953 E. Domar [2] has proved that in an exponentially growing economy, when depreciation funds are immediately reinvested, the method of constant depreciation over time will lead to an amount of depreciation Dt at time t bearing a constant ratio to the amount to be replaced Rt, given by:
Dt : Rt = (eγT - 1) : γT (1)
where γ is the rate of growth of the economy and T the average lifetime of the capital goods. For reasonable values of γ and T the ratio may differ greatly from one.
Dr. Horvat [3] studies the consequences of the method for a different kind of dynamic process. He considers a large stock of identical new capital goods K0 at t = 0. All items are assumed to have exactly the same lifetime, T. Hence, according to the method of constant depreciation over time, each year
of the capital stock at the beginning of the year is depreciated. Dr. Horvat now makes two assumptions: that the depreciation fund is immediately reinvested in identical new capital goods and that no other investment takes place. Under these circumstances, the time path of the capital stock is completely determined. At first it will be subject to heavy fluctuations but these tend to be dampened and by some experimentation with numerical data, Dr. Horvat makes it plausible that the capital stock Kt will approach a limiting value Kα. As the ratio M = Kx : K0 in the cases considered by him turns out to be larger than one, he introduces for M the term depreciation multiplier.
In this article, it will not only be proved that Dr. Horvat's conjectures are correct and that M depends on the value of n, but also that Kt approaches a limiting value for a much more general form of lifetime distribution of the capital goods. The multiplier then turns out to depend to the average, T, and the standard deviation, σ, of this distribution and moreover, for certain combinations of the two, M can even become less than one.
The techniques to be used are the familiar ones of renewal theory. They go back to work done by Lotka in 1939 [4]. Here, the discrete approach will be used. Reference may also be made to a book by Cox [1] which contains bibliographical material.
II The General Formula for the Depreciation Multiplier
The capital stock (m...
Table of contents
Cover
Title
Copyright
Original Title
Original Copyright
Contents
Introduction
Theory of Depreciation: Single Machine
Theory of Depreciation: Composite Plant
Depreciation Multiplier
Depreciation and Capital Maintenance: Hicks's Views
