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A General Mathematical Theory of Depreciation
Journal of the American Statistical Association
Abstract
In the older treatments of depreciation the cost, or “theoretical selling price” of the product of a machine, was conceived of as determined causally by the addition of a number of items of which depreciation is one. In other words, depreciation was first computed by some rather arbitrary formula not involving the theoretical selling price, which was then found by the addition of depreciation to operating costs and division by quantity of output. It will be shown in this paper that depreciation and theoretical selling price must be computed simultaneously from a pair of equations which are frequently a bit complicated. The differences in the results obtained from the arbitrary and mathematical formulae are often very large.
... Ejemplos notables son Hotelling [6] y Ramsey [8] Todo esto ha cambiado abruptamente en el último decenio como resultado de un reavivamiento, o mejor de una reorientación, del cálculo de variaciones impulsado en gran medida por los requerimientos de la tecnología espacial 4 En su versión moderna, el cálculo de variaciones se conoce como teoría del control óptimo Se ha convertido, merecidamente, en el instrumento central de la teoría del capital, a la que le ha infundido un nuevo soplo de vida Como consecuencia de ello, la teoría del capital ha sido transformada tan profundamente que ha sido rebautizada como teoría del crecimiento, y se ha avenido con numerosas cuestiones importantes prácticas y teóricas que previamente ni siquiera pudieron formularse La principal tesis de este documento es que la teoría del control óptimo formalmente es idéntica a la teoría del capital, y que sus principales ideas se pueden lograr mediante el razonamiento económico estricto Dicha tesis se sostendrá al derivar el teorema principal de la teoría del control óptimo, llamado el principio del máximo, mediante el análisis económico ...
... lo que es simplemente la suma de la tasa a la cual se está obteniendo una ganancia en cualquier instante descontada a la fecha inicial (si se desea) y sumada para todos los instantes. 5 En esta notación x no denota un número ordinario sino la trayectoria temporal completa de la variable de decisión x desde la fecha inicial hasta T. Esta notación asegura que si la empresa empieza con una cantidad de capital inicial k 0 y luego sigue la política de decisión indicada por x , se obtendrá un resultado total W, el cual es la integral de los resultados obtenidos en cada instante; estos resultados a su los instantes 6 En esta notación x no denota un número ordinario sino la trayectoria temporal completa de la variable de decisión x desde la fecha inicial hasta T Esta notación asegura que si la empresa empieza con una cantidad de capital inicial k 0 y luego sigue la política de decisión indicada por x , se obtendrá un resultado total W, el cual es la integral de los resultados obtenidos en cada instante; estos resultados a su vez dependen de la fecha del instante pertinente, luego del nivel de capital y de la decisión aplicable a ese momento La empresa está en libertad, dentro de límites, para elegir la trayectoria temporal de la variable de decisión x pero no puede elegir independientemente la cantidad de capital en cada instante; esto es una consecuencia del capital en la fecha inicial y la trayectoria temporal elegida para la variable de decisión Esta restricción se expresa al decir que la tasa de cambio de las existencias de capital en cualquier momento es función de su situación presente, la fecha y las decisiones adoptadas Simbólicamente: 7 (1) ...
... Así, las decisiones tomadas en cualquier instante tienen dos efectos Influyen la tasa a la que las ganancias se obtienen en ese momento y también influyen la tasa a la cual las existencias de capital están cambiando, y por lo tanto el nivel de capital que estará disponible en instantes de tiempo subsiguientes Estas dos ecuaciones expresan la esencia del problema de tomar decisiones en un contexto dinámico El problema consiste en seleccionar la trayectoria temporal simbolizada por x de manera que se haga el valor total del resultado, W, tan grande como sea posible al tomar en cuenta el efecto de la elección de x tanto en la tasa instantánea de ganancias como de las existencias de capital que tienen que trasladarse al futuro Esto es en realidad un problema difícil, y no solamente para principiantes La dificultad esencial estriba en que se tiene que seleccionar una trayectoria temporal completa de alguna variable El cálculo elemental enseña cómo elegir el mejor número posible para asignarlo a una variable única o los mejores números para unas pocas variables mediante la diferenciación de alguna función y la igualación de las derivadas parciales a cero Pero el encontrar la mejor trayectoria temporal posible es un asunto totalmente diferente y conduce a ciertas matemáticas avanzadas La estrategia de la solución apunta a reducir el problema, el cual, como se presenta, nos requiere encontrar una trayectoria temporal completa para un problema que nos demanda determinar solamente un único número (unos pocos números), lo que es algo que se sabe cómo hacerlo con base en el cálculo ordinario Dicha transformación del problema se puede realizar de diversas formas Una de ellas, que data del siglo xviii, conduce al cálculo de variaciones clásico Otra, que se adoptará aquí, lleva al principio 6 El argumento t permite la introducción de cualquier ecuación de descuento que pueda ser apropiada 7 ...
Traducción del artículo Dorfman, Robert (1969) “An Economic Interpretation of Optimal Control Theory”, The American Economic Review, vol. lix, núm. 5, diciembre, pp. 817-831.
... Moreover, in the model, the distinction between capital-stock and commodity-flow approaches (Wei 2013) is moot. (3) A scooter on what Heal (2007: 7) calls a two-way street between resource economics and broader economics, the model is of particular interest because Hotelling (1925) also wrote on accounting for depreciation. While it is oversimplified, its specific analytic results render an intricate discussion of the following issues more manageable. ...
... The value of the stock (the wealth) remaining in the sector at time t >0 is Hotelling (1925) and Samuelson (1937) define depreciation as − dV dt = −V . Differentiating the sides of the first equality of Eq. (5) yields that ...
... Since Hotelling (1925) also wrote the seminal paper on economic depreciation, it is of more than historical interest to note that Hotelling (1931: 170) disagreed with recording the rent q as the depreciation and thereby rendering income equal to zero: "It has been said that if the value of ore removed from the ground could be claimed as a deduction from income, then a mining company having no income except from the sale of ore could escape payment of income tax entirely. The fallacy of this contention may be examined by considering the value of the mine at time t. . ...
... A firm measures the value of an asset as the present value of the sum of its expected earnings from deployment. The factors that impact the asset's value are broadly divided into two groups: depreciation and revaluation (Hotelling, 1925;Hulten and Wykoff, 1981;Fraumeni, 1997). While depreciation is the change in value associated with aging, revaluation is the price fluctuation associated with the factors other than aging. ...
... Our study is related to several strands of literature. Specifically, our model critically examines the subtle disconnect in the prior collateral channel literature which does not explicitly recognize the price variability of some assets especially durable assets in the secondary asset market and the financial constraint of firms (Hotelling, 1925;Hulten and Wykoff, 1981;Hart and Moore, 1994;Fraumeni, 1997;Gan, 2007b;Chaney et al., 2012;Campello and Giambona, 2013;Cvijanović, 2014;Baldwin et al., 2015;Murfin and Pratt, 2019;Rampini, 2019;Demirci et al., 2019;Campello et al., 2021;Lanteri and Rampini, 2021;Gupta et al., 2022). While prior research identifies that a wedge exists between large down payment burden and enhanced debt capacity when collateralizing durable assets, the extant literature does not consider especially durable assets such as real estate that exhibit a persistent upward price momentum, which in turn enhances a firm's net worth through the collateral channel. ...
Firms acquiring durable assets face a lease-or-purchase decision. The collateral channel narrative argues that durability can facilitate (hinder) purchases by enhancing pledgeability (requiring large down payment). However, this prior research hasn't recognized that some durable assets (e.g. property) can appreciate at a rate that exceeds operational income growth. It also doesn't endogenize a firm's decision to lease assets. We show that when these considerations are explicitly incorporated into a firm's optimal investment decision-making calculus , financially constrained firms are incentivized to purchase durable assets. If leasing is feasible, firms revert to renting given the downpayment outlay.
... The transition probabilities can be deduced by dividing transition degrees by outgoing degrees of the graph vertex. Then, we jointly model the variable effects of liking old, pursuing new, and geographical restriction based on the mere exposure effect [24], depreciation theory [25], and Taylor's first law [21], respectively. We finally provide TOP-N POI recommendations. ...
... The memory of the user's access to the POI will affect the novelty of the subsequent POI, and the impact is related to the time interval. Like depreciation in economics, the residual value is smaller when the time is longer, and the possibility of purchasing new equipment is greater [25]. We assume that the POI currently checked in by the user will affect the utility of subsequent POIs, and this effect is related to the time interval. ...
The POI recommendation system has become an important means to help people discover attractive and interesting places. Based on our data analysis, we observe that users pay equal attention to conservatism and curiosity. In particular, adopting analysis corresponding to different time intervals, we find that users lean towards old POIs in the short term and look for new POIs with the increase of the time interval. However, existing approaches usually neglect users’ conservatism and curiosity preferences. Therefore, they are confronted with a bottleneck of depicting accurate user needs, making it difficult to improve the recommendation performance further. Besides, we further find that the number of user daily check-ins has uneven distribution, which is not conducive to capture the accurate transition patterns of user behaviors. In light of the above, we design a single POI sequential method. On this basis, we propose a recommendation method of the variable additive Markov chain. We consider the user sequential preferences, especially liking old and pursuing new features. In addition, our model exploits the geographical tendency of user behaviors. Finally, we conduct abundant experiments on four cities in the two real datasets, i.e., Foursquare and Jiepang. The experimental results show its superiority over other competitors.
... He was preparing a talk for the Mathematical Society Meeting in Chicago on December 26th, 1924. On that date, he had just submitted his paper on depreciation to the Journal of the American Statistical Association (Hotelling, 1925a). The talk consisted of a presentation of his first results on depreciation and showing the fecundity of the method he had applied to other economic problems, among them the theory of mining economics. ...
... 7 In Hotelling's early writings, it may also refer to an analogy with a natural force, suggesting an image of the interest rate as independent from anyone's will. 8 Secondly, Hotelling (1925a) stresses that economic theory should not consider depreciation as depending on the quantity of output alone, "the omnipresence of interest preventing this" (p. 353). ...
The paper focuses on Harold Hotelling's approach to time discounting in the context of the intertemporal allocation of exhaustible natural resources. In 1931, Hotelling introduces a positive discount rate when dealing with the “social value” or “total utility” derived from a resource. His position was in contrast with early economic literature on conservation, as well as with the point of view of Frank Ramsey, according to whom time discounting expressed an unjustified preference for the welfare of present generations over that of future ones. Hence, it has been argued that Hotelling dismissed ethical concerns. Using archival material, we find that, for Hotelling, economic questions should not be restricted to issues of economic efficiency; that his choice to discount utility – which he considered as analogous to a concrete benefit – at the interest rate is compatible with Ramsey's position; and, more broadly, that this choice does not preclude an ethical position on the desirable distribution of exhaustible resources through time. To Hotelling, ethics is implemented by politics, through fiscal corrections of the interest rate. Revisiting Hotelling on the articulation between ethics, allocative efficiency, and policies allows us to rethink the way we do that in current models using time discounting.
... An area of considerable interest among fleet managers and equipment maintenance managers has been determining the optimal level of equipment inventory and its maintenance (Hotelling, 1925;Taylor, 1923). Evaluating this tradeoff between inventory replenishment and CONTACT Kevin P. Scheibe kscheibe@iastate.edu ...
... Consequently, there is a point in the life of equipment where it is costlier to keep than to replace. Determining that exact replacement point has been the focus of academics and practitioners for nearly a century (Hotelling, 1925;Taylor, 1923). Many models have been created to recommend good replacement rules with various parameters (Hartman & Tan, 2014). ...
It is said that knowledge is power, yet often, decision makers ignore information that ought to be considered. The phenomenon known as Semmelweis reflex occurs when new knowledge is rejected because it contradicts established norms. The goal of evidence-based management (EBMgt) is to help overcome Semmelweis reflex by integrating evaluated external evidence with stakeholder preference, practitioner experiences, and context. This evaluated external evidence is the product of scientific research. In this paper, we demonstrate an EBMgt business analytics model that uses computer simulation to provide scientific evidence to help decision makers evaluate equipment replacement problems, specifically the parallel machine replacement problem. The business analytics application is demonstrated in the form of a fleet management problem for a state transportation agency. The resulting analysis uses real-world data allowing decision makers to unfreeze their current system, move to a new state, and re-freeze a new system.
... The collection center is not only important for storing the biomass, but it also provides employment to local people. The employment rate increases by the introduction of the upstream of supply chain (Hotelling, 1925;Huamao and Fengqi, 2007). ...
Waste handling is one of the biggest problems across the globe. An additional challenge of mitigating climate change also arises during the burning of fossil fuel. The fossil fuel-based transportation system in India that gives rise to air pollution has a worse impact on people. To overcome these problems, a sustainability assessment framework is introduced in this study. Ethanol, a member of the biofuel family, is one of the cleanest and most sustainable forms of energy sources. The purpose of this research is to develop a sustainability assessment framework to investigate the environmental feasibility of a supply chain system that provides an end-to-end solution and how it would benefit the transportation sector. A second-generation (2G) ethanol-based supply chain is envisaged, and agro-waste such as corncobs and paddy straw are considered in this study. The assessment is carried out using a heuristic-based method, known as particle swarm optimization (PSO) technique, within the framework of circular economy. The results show that the biomass collection in the proposed area produces 2.5 tons of CO 2 per hectare area on average, which is much lower in comparison to 996.6 tons of CO 2 per hectare in the Middle East, the main source of fossil fuel. In the future, this research would benefit the enterprises and government organizations that establish 2G ethanol plants.
... The time series depreciation measures depreciation as the rate of change in the individual asset's value over time. The underlying economic theory of time series depreciation is traced to the work of Hotelling (1925), who viewed depreciation as the rate at which an asset decreases in value concerning time. The cross-section depreciation (CSD) estimates depreciation according to vintage, similar to the vintage capital model. ...
In this book, circularity is introduced and discussed as a driver of the
UN Sustainable Development Goals (SDGs) and its progress in emerging
and developing countries. As we move forward, we want to capture the
realities of the circular economy concept as much as possible by moving
quickly to the fascinating theoretical and practical progress across various
sectors in these economies. The circular economy approach is inherently
accompanied by a wide range of other issues, which one must address
while exploring its progress path: early in the book, a state-of-the-art
review provides a theoretical framework for mapping the subtle characteristics, scope, and progress of emerging and developing economies, while
the diverse case studies provide insight into the real stories—the progress
and challenges.
This book was written to help students at universities, and other
institutions of higher education find empirical case studies on circular
economy from emerging and developing countries. It is also intended for
people pursuing a professional career in sustainability and readers with
a general interest in circular economy and the SDGs. At an advanced
level, this text can also be used as a handbook, providing an overview
of current theoretical and empirical debates and controversies regarding
circular strategies and SDGs. As well as providing a non-technical entry
point towards circular economy strategies in emerging and developing
economies, the book provides a broader perspective on circular economy
as an emerging field.
This indispensable reference is written by a team of international
scholars from a variety of disciplines, including development, education,
business, ecology, geography, and planning, and presents the current state
of circular economy research within emerging and developing economies.
... For short-run decisions, for instance, managerial accounting textbooks recommend the use of incremental costs rather than full cost measures, due to the fact that full cost measures generally include sunk costs. For long-run decisions, most managerial accounting textbooks do not point to a single unit cost measure, but instead recommend a corporate finance approach that focuses on the discounted stream of future cash flows (Hotelling 1925;Schneider 1961;Mahlert 1976;Swoboda 1979;Luhmer 1980;Kistner and Luhmer 1981;Küpper 1984;Schweitzer et al. 2015;Datar and Rajan 2018). In contrast, Mahlert (1976) and Swoboda (1979) advocate for the use of unit cost measures that are consistent with a corporate finance approach seeking to maximize the net present value of the long-run decision under consideration. ...
Levelized cost is a life-cycle cost measure that aggregates investment expenditures and operating costs into a unit cost figure. So far, most applications of this concept have originated in relation to energy technologies. This paper describes the role of the levelized cost concept in cost accounting and synthesizes multiple research streams in connection with electricity, energy storage, hydrogen and carbon capture. Finally, we sketch multiple potential future applications of the levelized cost concept.
... El modelo puro, si considera también como unit of account al ente en su conjunto, debería reconocer la llave de negocio autogenerada. 17 An early seminal work in this field is provided byHotelling (1925), who defines economic depreciation to be determined by changes in market value from period to period(Staehle, M., & Lampenius, N. 2011, p 8). Depreciation is defined simply as rate of decrease of value... Now the value of a machine is the sum of the anticipated rentals which it will yield, each multiplied by a discount factor to allow for interest, plus the scrap or salvage value, also discounted(Hotteling, 1925, pp. 341 y 342) ...
El trabajo intenta comprender la relación de las ramas contables tradicionales con la noción de valor económico reconociendo que, según los diferentes contenidos concretos que asumamos, los modelos contables pueden arrojar resultados diferentes. Se intentan caracterizar dos modelos extremos en la forma de reflejar el valor económico en el campo contable tradicional, discerniendo sobre la ingente cantidad de posibilidades intermedias que en la realidad pueden observarse para los sistemas concretos. Se concluye respecto de la importancia que la integración de los informes de sostenibilidad con los estados financieros tradicionales tendrá en la conformación de futuros modelos contables relacionados siempre con el concepto de valor.
... Други разработки на Хотелинг също оказват съществено влияние върху развитието на икономическата теория. Още през 1925 г., едновременно със своята дисертация по математика, той публикува статия относно загубата на стойност на активите (Hotelling, 1925). Опирайки се на изследванията на Ървинг Фишер (вж. ...
Резюме: Харолд Хотелинг е влиятелен учен-статистик, работил в началото на 20-и век, включително в областта на кономическата теория. Трудовете му имат основополагаща роля за съвременната икономика и отварят пътя за нови изследователски въпроси в стопанската наука. Най-известна е работата му върху решението на проблема с изчерпаемите ресур-
си. Хотелинг поставя начало на изследванията в областта на пространствената икономика и анализа на продуктовото ди-
ференциране чрез решението на позиционния проблем на фирмите в дуопол. По-малкопознати, но съществени, са риносите му за развитието на съвременната неокласи ческа микроикономическа теория. Хотелинг е един от учените, които през 50-те години на миналия век налагат математическия подход в икономическите изследвания. Настоящата статия предлага въведение в ключовите му приноси.
Abstract: Harold Hotelling is an influential statistician working in the field of economic theory at the beginning of the 20th century. His contributions to economics are trailblazing and open new topics for economic and business analysis. His best-known work is his solution to the problem of exhaustible resources. He also triggered the exploration of spatial economics and the analysis of product differentiation through his solution of the optimal location of producers in a duopoly. Less known, but important, are his
contributions to the development of modern neoclassical microeconomic theory. Hotelling is also one of the scientists who initiated the turn towards mathematical economics in the 1950s. In this paper we provide an introduction of his groundbreaking work on
economic theory.
... Freeman's description implies there is some 'correct' value of depreciation. Hotelling (1925) in setting out a general mathematical theory of depreciation noted that for the accountant to properly determine how much of the cost of a machine to allocate to each period, the accountant had to have regard to the value of the output (he assumed the machine operated at full capacity). Only by doing so would the right decisions on profitability be made. ...
A survey of the theory and practice of economic regulation of distribution networks in Australia
... At the beginning of the 1930s, he taught not only his own economics but also that of classic authors in mathematical economics (Cournot, Léon Walras, Vilfredo Pareto, Bowley, Jules Dupuit). His knowledge of the literature had improved, which allowed him to specify the characteristics of his own research, compared to Roos's, Evans's, or Roy G. D. Allen's for instance (e.g., Hotelling 1931aHotelling , 1935Hotelling , 1939see Darnell 1990a). ...
Harold Hotelling’s (1895–1973) articles in mathematical economics from the 1930s are classics. Some are keystones of entire sub-disciplines of economic theory such as location economics [Hotelling (1929). Stability in cCompetition. The Economic Journal, 39(153), 41–57] and natural resource economics [Hotelling (1931). Review of Review of mathematical introduction to economics, by Griffith C. Evans. The American Mathematical Monthly, 38(2), 101–103. https://doi.org/10.2307/2301858]; others are associated with significant theoretical results [Hotelling (1932). Edgeworth’s Taxation Paradox and the Nature of Demand and Supply functions. Journal of Political Economy, 40(5), 577–616; (1938). The general welfare in relation to Problems of Taxation and of Railway and Utility rates. Econometrica, 6(3), 242–269]. Yet, Hotelling’s place in the rising of mathematical economics is mostly a black hole in the history of economic thought. The present paper aims to provide a better understanding of Hotelling’s part in the history of mathematical economics. Using published as well as archival materials, it traces Hotelling’s itinerary in mathematical economics, observes Hotelling using mathematics and scrutinizes Hotelling’s methodological writings to capture the meaning of his models and concepts, in particular his concept of utility as a monetary surplus.
... To see why, note that the value implicitly determined by the IRR, C t ðrÞ, is such that C 0 ðrÞ ¼ ÀFCF 0 , C n ðrÞ ¼ 0 and, for 1 t n À 1, Hazen, 2003;Teichroew et al., 1965aTeichroew et al., , 1965b. This value is sometimes called Hotelling value (Hotelling, 1925). 8 It may be negative in some periods and positive in some other periods, in which case the project has a mixed nature. ...
We propose a genuinely internal approach to project valuation and decision based on the average Return On Investment (ROI), obtained as the ratio of total operating profit (NOPAT) to total invested capital or, equivalently, as the ratio of net cash flow to total invested capital. The approach presented enables decomposing the economic value created into the project scale (total capital invested) and the economic efficiency, obtained as the difference between average ROI and a suitably adjusted weighted average cost of capital (WACC). We show that a project’s average ROI is equal to the weighted mean of the average Return On Equity (ROE) (total net income divided by total equity capital) and the average Return On Debt (ROD) (total interest expenses to total debt outstanding) and show that the average ROE itself correctly measures shareholder value creation when compared with a suitably adjusted cost of equity. We show that the internal average-based approach presented is also valid under the more general assumption of time-varying cost of capital.
... O conceito de Substituição de Equipamentos (SE) tem origem nos primórdios da Administração Científica. Os trabalhos pioneiros de Taylor (1923) e Hotelling (1925) utilizam como objetivo principal a maximização do Valor Presente de um único equipamento. Para isto, analisa-se o ciclo de vida do mesmo e determina-se a Vida Econômica -o ponto ótimo de substituição no período. ...
O uso eficiente dos ativos fixos é um dos principais objetivos na administração de empresas do setor de transporte urbano. Os veículos de transporte determinam o nível de serviço oferecido e impactam significativamente na eficiência dos inputs envolvidos no seu uso. O administrador pode otimizar a rentabilidade e o nível de serviço oferecido através da escolha do veículo apropriado e da definição da taxa de substituição do equipamento no tempo. Este artigo apresenta uma metodologia para a substituição de frotas de ônibus por meio da integração de critérios econômicos e não-econômicos. Aspectos econômicos são contemplados por indicadores econômicos e fluxo de caixa, utilizando custos de aquisição e manutenção da frota, entre outros. Aspectos não-econômicos são representados por decisões estratégicas e de gestão, sendo avaliados por intermédio de ferramentas de decisão múltipla. A metodologia proposta possibilitou avaliação detalhada do desempenho dos ônibus atuais frente a potenciais substitutos, viabilizando constante monitoramento dos ativos da empresa e assegurando elevados níveis de serviço ao cliente. A metodologia é ilustrada em uma empresa pública de transporte urbano.
... Matheson (1910;91) used the term "diminishing value" to describe the method. Hotelling (1925;350) used the term "the reducing balance method" while Canning (1929;276) used the term the "declining balance formula". For a modern exposition of the geometric model of depreciation, see Jorgenson (1989). ...
How can a commercial property price index (CPPI) be defined and constructed? And what kind of relationship does the measurement of commercial property’s value have to the System of National Accounts and to concerns about national financial sectors? In order to answer such questions, this paper aims to outline the concepts that can be used to define and measure the value of commercial property, and to clarify the relationship of such measurement to the System of National Accounts and to the financial system.
... 22 Crew and Kleindorfer (1992) noted that in the presence of emerging technology there is limited time for regulators to take remedial action and that exposed assets can adopt more accurate depreciation methods. Depreciation methods have long been of interest to economists, dating at least as far back as Hotelling (1925). Under rate of return regulation, choice of depreciation method represents a key input to regulated prices and has a circular reasoning which materially affects how capital costs are recovered (Schmalensee, 1989;Burness and Patrick, 1992). ...
From 2004 to 2018 the Regulatory Asset Base (RAB) of electricity networks across Australia’s National Electricity Market tripled in value, from 93 billion. The run-up in the capital stock was driven by forecast demand growth and a tightening of reliability standards. But demand contracted from 2010-2015. With a rising RAB, contracting demand and a regulated revenue constraint, an adverse cycle of sharply rising tariffs and falling demand appeared to be emerging. Some networks were characterised by significant investment mistakes in retrospect, and perhaps unsurprisingly, various consumer groups and regulatory bodies argued assets should be stranded or written-off completely and network tariffs reduced. From 2015-2018, energy demand increased once again. In this article we present a method for dealing with stranded assets under uncertainty; rather than permanently stranding assets that fail a used and useful test, we reorganise the financial and economic affairs of a template network utility and “Park” excess capacity, issue credit-wrapped bonds to temporarily finance the stranded capital stock, then re-test the Parked Assets at the end of each five-year regulatory determination. Parked Assets can then be “Un-Parked” and returned-to-service in line with connections growth, load growth, or both. The most interesting result is the immediate reduction in network tariffs, and a more stable trajectory under our generalised assumptions.
... The depreciation in the value of capital has been studied extensively since the fundamental work of Hotelling (1925). Following Hotelling, depreciation is commonly modelled as a continuous function of building age, for instance in the seminal paper by Hulten & Wykoff (1981) who found an approximately geometric pattern of depreciation. ...
The durability of real estate is closely related to physical deterioration and functional
obsolescence. Aging effects appear to be particularly relevant for industrial real estate, where structures are often designed for specific production processes, and office buildings where outward appearance, which is often related to characteristics that are specific for a building’s construction period, is related to the reputation of the user. These phenomena contribute to the dynamics of property prices and therefore to the returns on investment in real estate. In this paper, we examine the depreciation of commercial real estate values, for properties of different market segments and construction periods. We do so by estimating hedonic models, using rich information on transactions of commercial real estate in the Netherlands. We find that aging effects are heterogeneous over segments and construction periods, and that pre-WWII offices and industrial properties can experience increase of value with age, or “vintage” effects.
... Thus, maintenance planning has been the subject of a large number of classical studies, and preventive maintenance and investment planning have also been widely researched (Hotelling, 1925;Taylor, 1923;Roos, 1928;Preinreich, 1940;Terborgh, 1949Terborgh, , 1958Lutz and Lutz, 1951;Alchian, 1952;Smith, 1957Smith, , 1961Näslund, 1966;Rapp, 1974). Some of the studies' models are large and complicated, featuring limited interaction between the analysis and the decision makers. ...
There is a lack of models that could improve the understanding of
the underlying dimensions of maintenance. Many models are also large and complicated, and thus limiting the interaction between the analysis and the decision maker. Although a scheduled maintenance and reinvestment policy may reduce the number of failures, the cost of the scheduled maintenance may not reduce state costs. This paper develops a general framework and principles for maintenance and reinvestment decisions. The model in this study integrates four important dimensions: i) state of the facility; ii) maintenance; iii) reinvestment; iv) salvage value. The financial dimension is also included in the model (a fixed budget per period). The structure of the
model is to support the operative management of maintenance and reinvestment in the long run, i.e., timing of maintenance and reinvestment tasks. Four different maintenance and reinvestment policies are also developed.
Environmental Economics explores the ways in which economic theory and its applications, as practised and taught today, must be modified to explicitly accommodate the goal of sustainability and the vital role played by environmental capital.
Pivoting around the first and second laws of thermodynamics, as well as the principles of ecological resilience, this book is divided into five key parts, which include extensive coverage of environmental microeconomics and macroeconomics. It drills down into issues and challenges including consumer demand; production and supply; market organisation; renewable and non-renewable resources; environmental valuation; macroeconomic stabilisation and international trade and globalisation. Drawing on case studies from forestry, water, soil, air quality and mining, this book will equip readers with skills that enable the analyses of environmental and economic policy issues with a specific focus on the sustainability of the economy. This new edition has been updated throughout and provides further coverage on topics such as energy transition, market organisation and the role of environmental economics in regulatory decision-making including critiques of contemporary policy directives like tradable pollution permits and net zero emissions. Challenges to achieving stabilisation and emission reduction have been expanded to include wars and conflicts such as those in the Middle East and the Russian invasion of Ukraine. This book further reinforces the premise that there are clear limits to growth and that modesty and moderation are superior alternatives.
Rich in pedagogical features, including key concept boxes and review questions at the end of each chapter, this book will be a vital resource for upper-level undergraduate and postgraduate students studying not only environmental economics/ecological economics but also economics in general.
The State Transport Company, like any business organizations main aim is to minimum operational cost and maximum profit. However, the Company is faces with the problem of how long it buses should be on the road before it is replaced. The aim of this paper is therefore to determine a schedule of disposals and replacements of the higher bus, taking into account the revenue generated, operating cost and the salvage values, such that the total cost of these activities is minimized. Data was collected from the State Transport Company Office in Kumasi on the revenue generated, operating cost, and the salvage values on the bus with time. The problem was solved by using dynamic programming. It was found out that the company should always dispose its buses when they are two years old.
Harold Hotelling (1895–1973) was a major contributor to twentieth-century American economics. The overall thrust of his research, and his view of the role of mathematics in the discipline, have so far received little attention. Based on an unprecedented examination of his work and professional archives, this article provides a thorough analysis of Hotelling’s background and contribution to economics. A self-taught economist in the 1920s, Hotelling built a research program that, despite apparently being highly technical, was primarily conceived as applied science to solve concrete social and economic issues, from spatial competition to natural resource exhaustion and public utility regulation. Although Hotelling’s research was not exempt from criticism, it remains profoundly inspiring for the twenty-first century, from both a theoretical and epistemological point of view. When we remember that he trained the greatest, from Kenneth J. Arrow to William Vickrey, his career and ideas are all the more worthy of consideration. (JEL B21, B23, B31) | ***Just click on 'Request full text' and we will send you the PDF.***
El objetivo de este artículo es visibilizar la realidad sobre el tema de la sustentabilidad. No se basa en la declaratoria de los Objetivos del Desarrollo Sostenible, ni en que se alcancen los 17 objetivos. Se hace un recuento de los hechos históricos desde el descubrimiento de América y la invasión a este territorio, a traves de la revisión documental y bibliográfica de estos hechos para llevar un hilo de los aspectos más trascendentales en América Latina, sobre este avance civilizatorio, después de la conquista y los movimientos de independencia, qué, aunque sucedieron, se sigue replicando el modo de explotación, de saqueo y de gobierno que heredaron los países hegemónicos que nos invadieron. Se llega a la reflexión y comprensión, que es mera simulación la promesa de los ODS, porque, para lograr al menos un objetivo de los 17, se necesita sacar el ente, la sombra, el país extranjero que está en la industria establecida en territorio latinoamericano. Es decir, seguir el discurso de la sustentabilidad, supone poner acciones reales para el cuidado y mejoramiento del medio ambiente, pero no se logra si persiste la fuente de contaminación, y esa es la sombra de los países invasores.
Sustainable development is increasingly decisive, making inroads in almost everyday decisions, including entities’ future direction. Within the business context, business sustainability focuses on growth, stability, and development and the revitalisation of enterprises. In this, maintaining capital and assets is critical in shifting from traditional based view to sustainable capital maintenance. Depreciation accounting is traditionally seen as the tool to achieve capital maintenance, however, evidence has shown that at best the current accounting rubrics run parallel to physical capital maintenance making it difficult to meet the requirements of capital sustainability. This chapter proposes a new model of capital maintenance ‘Sustainable Capital Maintenance Model’ by emphasising full convergence of depreciation accounting and capital maintenance. The evaluative analyses of the proposed model reveal its relevance and extended implications for circularity accounting through asset improvements and restoration. This chapter, therefore, presents a convergence model of depreciation accounting and capital maintenance to achieve sustainable capital maintenance and circular accounting.
In this intellectual memoir, Professor Lai describes how martingales came into his world of mathematical statistics, first in sequential tests and confidence intervals, then in time series, stochastic approximation, sequential design of experiments, and stochastic optimization. He sketches the trajectories of many other statisticians that he met along the way. He emphasizes the roles of Harold Hotelling, Abraham Wald, and Herbert Robbins in their creation of the environment for the study of martingales at Columbia University and then his own subsequent work at Stanford University. At Stanford, he came to see stochastic optimization as a unifying theme for the use of martingales in statistical modeling. In conclusion, he describes the multifaceted applications of martingales to statistics and stochastic optimization in the BigData and MultiCloud era.
Policy makers offer fiscal incentives to encourage companies to invest in renewable technologies. This work considers generation companies that take advantage of fiscal incentives to minimize income tax. Thus, a novel mixed-integer linear optimization model that minimizes total tax payments of a company owning a portfolio of energy projects is designed. The model strategically manages depreciation, tax loss carryforward, and tax incentive use for minimizing discounted income tax. A set of revenue scenarios was employed to analyze model results. The proposed model yields tax savings between 8.2% and 19.2% of the company’s taxes. Tax savings are significantly larger for companies with a large generation portfolio; which represents a clear advantage over small generation companies. The proposed model can also be employed by policy makers to adjust future ITA policies by taking advantage of the anticipative knowledge of the optimal tax strategies implemented by generation companies.
In green accounting, it is seldom checked that depreciation must sum to original value. A re-examination of green accounting under this condition finds that, in a non-autonomous program, income should include capital gains. Subtle questions respecting the role and treatment of capital gains are brought to light through six models in exhaustible-resource economics. It is likely that there are sources of non-autonomy when a problem is not optimal or when there are non-priced assets—in practice, always. Accordingly, the questions raised strongly influence accounting method.
This paper revisits capital measurement through a microeconomic analysis of a simple project consisting of diverse types of irreversibly invested capital. Capital is aggregated using the numeraire. Thus, the proposed method of measurement is a form of accounting. It associates all types of capital in a common framework. Under certainty, user cost and depreciation take internal accounting values that obey three axioms that comprise five conditions. The accounting values proliferate, but they have only a limited relation to market prices or shadow prices. Each type of capital earns the market rate of interest. In practice, under uncertainty, calculation of the accounting values would require projections of basic data, and would be hard to comprehend, especially for outsiders, and would leave room for moral hazard. Because of these obstacles, accounting practice departs from the ideal based on cash flows and strictly limits choice by using prescribed schedules of depreciation. These schedules are interpreted from an economic perspective.
In 1933, Ragnar Frisch introduced a distinction between microdynamics and macrodynamics. His claim that he proposed the first macrodynamic analysis and that microdynamic schemes were limited to single markets or individual behaviours influenced the subsequent development of economic models. But the division was above all between tools: maximisation at the individual level, and dynamic analysis at the aggregate level. What was at stake was the question of economic rationality and whether it could be extended to an aggregate system. This paper reconstructs the different research programs to give a new picture of the development of early mathematical models in economics.
La règle de Hotelling, décrivant la trajectoire optimale de long terme du prix d’un actif épuisable, est utilisée de longue date en économie des ressources naturelles. Elle est aujourd’hui également centrale en économie du climat pour l’estimation de ce que serait un prix optimal du carbone. Cette règle, énoncée par Harold Hotelling en 1931, est jugée utile pour dépassionner les débats et fournir une base objective aux arbitrages inter-temporels. Sur la base de matériaux d’archives, cet article propose de revenir aux sources, à savoir l’élaboration de la règle et la conception qu’en avait Hotelling afin de questionner son statut et ses usages aujourd’hui. Nous concluons en particulier que Hotelling ne considérait pas son outil comme neutre face aux enjeux de justice sociale, intra et intergénérationnelle. Délibération collective et action publique étaient au cœur de ses préoccupations, ce qui nous invite à appréhender sous un nouveau jour la fixation des prix du carbone au XXIe siècle.
This paper studies the effect of inflation on the return on investment (ROI) required from a project in its first year of operation. This is important because ROI is often used to evaluate the performance of a project once it has been started.
The paper shows that inflation has a marked influence on the required initial ROI of projects. The extent of this effect depends upon the type of assets (the ratios of current, depreciable and non-depreciable assets) and the life of depreciable assets employed.
The analysis shows that decision makers should, under inflation, require a higher initial ROI from projects employing current assets than from projects employing depreciable or non-depreciable assets. It also shows that they should generally require a higher initial ROI from projects employing short life depreciable assets than from projects employing depreciable assets with a longer life.
A la hora de plantear un libro dedicado a los proyectos de repoblaciones, resulta imprescindible comentar las principales herramientas del análisis económico y financiero que se deben incorporar a un proyecto de estas características. Este capítulo se centra fundamentalmente en estos instrumentos, planteándolos desde el punto de vista de un centro decisor que pretende obtener información bien sea sobre la rentabilidad de dicho proyecto, o sobre el turno óptimo que debería aplicar a estas plantaciones bajo una componente estrictamente económica, una vez que se tengan en cuenta los posibles outputs asociados a este proyecto. Por otro lado, creemos que la inclusión de un capítulo de estas características en un manual dedicado a las repoblaciones forestales constituye un acierto y, a la vez, una novedad en la literatura forestal española. El acierto se debe a que la decisión de proceder o no a una repoblación o a planificarla convenientemente presenta una componente económica que debe ser tenida en cuenta, como se ya enfatizaba hace más de un siglo en otros países (Trentham Law 1912). Sin embargo, este hecho ha sido tradicionalmente obviado en la literatura española al respecto. Así, obras emblemáticas como las de Ramos (1965), García Salmerón (1991) o Serrada (2000) no incluyen en sus manuales ningún capítulo específicamente dedicado a esta materia, aunque Ramos (1965) dedica un capítulo casi por completo a la determinación de los costes asociados a una repoblación, pero sin proponer ninguna técnica para evaluar financieramente estas repoblaciones. Sin embargo, obras de referencia dedicadas a algún género, como el caso de Eucalyptus (FAO 1981), sí que incluyen tanto un capítulo con algunos resultados sobre la rentabilidad de especies de este género en diferentes países, como un anexo con el cálculo del valor actual neto para tres casos distintos. Llegados a este punto, cabría preguntarse si existen estudios donde se indique, de forma tentativa, cuál es la rentabilidad media de un proyecto de
Harold Hotelling’s work, from natural resources economics to optimal taxation, and from spatial to welfare economics, was deeply influenced by his Georgist affiliation and by a Georgist game that we now call Monopoly, which at the time was known as the Landlord’s Game. We explore this influence, its history, and the role it played in Hotelling’s work and ideas. We show that political beliefs deeply shaped Hotelling’s approach to economics and that the rules of the Landlord’s Game helped him think about economic mechanisms.
This study examines how asset values by industry sectors are affected by different depreciation methods. We theoretically show that estimating depreciation rate by the Perpetual Inventory Method (PIM) contains more information than the method by Depreciation Expense as Accounting Item (DEAI), which are equivalent under certain conditions. Using data of 37 industrial sectors in China from 2001 to 2016, we estimate depreciation rates by sectors using both PIM and DEAI methods, which enable us to estimate capital stock and capital efficiency by sectors. By the panel estimation, depreciation rates estimated by both PIM and DEAI methods significantly increase with the enterprise's profits after tax defined by that profits before tax minus tax. Our result is consistent with the prediction of the economic depreciation hypothesis, implying that tax shield of depreciation that raises corporate after-tax cash flows to the firm could improve corporate investments for replacement by scrapping the old equipment.
Farm machinery managers often need to make complex economic decisions on machinery replacement. Repair and maintenance costs can have significant impacts on this economic decision. The farm manager must be able to predict farm machinery repair and maintenance costs. This study aimed to identify a regression model that can adequately represent the repair and maintenance costs in terms of machine age in cumulative hours of use. The regression model has the ability to predict the repair and maintenance costs for longer time periods. Therefore, it can be used for the estimation of the economic life. The study was conducted using field data collected from 11 John-Deer 955 combine harvesters used in several western provinces of Iran. It was found that power model has a better performance for the prediction of combine repair and maintenance costs. The results showed that the optimum replacement age of John-Deer 955 combine was 54300 cumulative hours.
This paper investigates the relationship between economic value added (EVA) and the net present value (NPV) of projects, and especially the extent to which this is influenced by arbitrary depreciation schedules. For any depreciation schedule, the discounted EVA of a project is identical to its NPV. In project evaluation, EVA therefore overcomes the differences between earnings and cash flow introduced by arbitrary depreciation schedules. The paper also investigates the relationship between the true return of a project or a firm and the EVA reported by a project once in operation or the EVA reported by a firm. In these applications, the distortions caused by arbitrary depreciation schedules remain. Standardised EVA equals the true excess return for a firm that charges economic depreciation, or for a firm that grows at its IRR. In other instances large discrepancies are possible, and the use of standardised EVA as an indication of true excess return is potentially misleading.
Harold Hotelling’s 1931 article on the economics of exhaustible resources is considered groundbreaking in the history of non-renewable resource analysis. Hotelling’s innovation has been characterized by comparing his work with other contributions dealing with conservation issues. It has also been connected to his earlier work on depreciation, published in 1925, for using the same kind of mathematical formalism. This paper further explores this second research direction on the basis of new archival materials, showing that Hotelling conceived his contributions on resources and depreciation as closely and substantially intertwined. It also suggests that Hotelling’s interest in exhaustible resources came from his earlier readings in accounting. These results shed new light on Hotelling’s early economic research, on our common understanding of his 1931 contribution, and on the origins of the connection between nature and capital in the history of environmental economics.
China, currently one of the world's most booming economies, has achieved great success in its economic growth since the start of economic reforms in the late 1970s. However, little attention has been paid to its environmental problems. Constrained by limited natural resources, China's losses in the environment could offset its economic growth despite the apparently relatively high growth rate. This research project discusses the theoretical foundations for deriving the "green" Net National Product (gNNP). Empirically it applies the net price approach, the total rent approach and the user cost approach in order to examine how environmental degradation affects sustainable development. The contents of measuring gNNP consist of the following studies: 1. The thesis illustrates the economic reforms and growth in China and points out environmental degradation and natural resource depletion problems there. The procedure for data collection is presented. 2. The research focuses mainly on assessing resource rents in deriving gNNP. The economic valuation of environmental depreciation and degradation in the national accounts is investigated and modelled. And the theoretical exploration relationship between gNNP and economic growth is addressed. A brief overview of models of gNNP is presented with special evaluation of the Hartwick rent. The research sets up the theoretical framework for the thesis by extending and applying the net price approach, the total rent approach and the user cost approach. 3. Assessment of environmental degradation in China. The situation of deforestation is reviewed, and the economic loss resulting from deforestation in China is measured. By using the net price approach and the user cost approach, economic loss from deforestation in China is derived in forest accounts. 4. Measuring energy resource depletion: coal and oil. The status of China's coal and oil situation is discussed. Pricing constraints and subsidies on coal and oil are illustrated. Adjustments to GNP are shown by deriving gNNP by applying the net price approach, the total rent approach and the user cost approach. 5. Major factors leading to air pollution. The status of Air Pollution in China and present pollution control are discussed. Health damage from small particulate matter is derived and economic loss in terms of GNP is computed. 6. Overall evaluation of environmental degradation in China. The overall economic loss from forestry, coal, oil and air pollution is evaluated by adjusting GNP to gNNP. Several aspects of the causes of environmental degradation are studied: population, pricing policies and property rights. Policies and ways to sustainable development are considered. Finally the thesis summarises the research as a whole and highlights a framework for future research.
This paper examines the theoretical properties of full-cost transfer prices in multidivisional firms. In our model, divisional managers are responsible for the initial acquisition of productive capacity and the utilization of that capacity in subsequent periods, once operational uncertainty has been resolved. We examine alternative variants of full-cost transfer pricing with the property that the discounted sum of transfer payments is equal to the initial capacity acquisition cost and the present value of all subsequent variable costs of output supplied to a division. Our analysis identifies environments where particular variants of full-cost transfer pricing induce efficiency in both the initial investments and the subsequent output levels. Our findings highlight the need for a proper integration of intracompany pricing rules and divisional control rights over capacity assets.
This paper was accepted by Suraj Srinivasan, accounting.
We present the well-known Internal Rate of Return, and show that it suffers from many pitfalls and bears no direct relationship to the business transactions underlying the project’s activities (and, therefore, no relationship to the capital actually employed). Therefore, we advise practitioners to dispense with. We present two related approaches, the Modified-Internal-Rate-of-Return approach and Teichroew-Robichek-Montalbano model, discussing pros and cons, and concluding that all these metrics have serious drawbacks which are overcome by the AIRR approach presented in Chapter 8.
When a durable good (other than housing) is purchased by a consumer, national Consumer Price Indexes typically attribute all of that expenditure to the period of purchase, even though the use of the good extends beyond the period of purchase.
Harold Hotelling's 1931 contribution is known for providing a basic principle—the Hotelling rule—to the economics of non‐renewable resources. Nearly 90 years later, empirical tests conclude the rule lacks empirical validity, requiring strong amendments to describe the long‐term, aggregate behaviour of its target object. On the basis of Hotelling's unpublished archival material, this paper revisits the place given to the Hotelling rule in non‐renewable resource economics. Our reconstruction shows that Hotelling's 1931 paper has been misinterpreted: from the outset, the Hotelling rule was not valid for mineral resources. In contrast, the consideration of two inherent geological constraints, alongside exhaustibility, offered the opportunity for an alternative basic framework, capable to generate bell‐shaped and U‐shaped equilibrium trajectories for supplies and prices, respectively. Inspired by this unknown aspect of Hotelling's work brought to light by our archival investigation, we sketch this alternative basic model, enabling non‐renewable resource economics to circumvent the empirical shortfalls of the Hotelling rule.
Ramsey’s 1928 paper on saving and Hotelling’s 1931 article on exhaustible resources are considered to be two seminal contributions in economic dynamics. They have been associated because of their temporal proximity, use of the calculus of variations, and because of Hotelling’s citation of Ramsey. This connection however needs to be precisely investigated and characterized. On the basis of archival material, this paper shows that, on the interpersonal and theoretical ground, the connection is quite thin, but that significant parallels are found in Ramsey’s and Hotelling’s expectations with mathematical economics for the progress of science and for informing public decision.
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The ability of a project's IRR to quantify its economic return has been questioned by many scholars over the past 60 years, most recently by Magni (2010 Magni, C.A. (2010) Average Internal Rate of Return and Investment Decisions: A New Perspective. The Engineering Economist, 55(2), 150–180.[Taylor & Francis Online], [Web of Science ®] [Google Scholar], 2013 Magni, C. A. (2013) The Internal-rate-of-return Approach and the AIRR Paradigm: A Refutation and a Corroboration. The Engineering Economist, 58(2), 73–111.[Taylor & Francis Online], [Web of Science ®] [Google Scholar]). Although IRR is a plausible—albeit imperfect—measure of a project's economic return when the cash flow stream is conventional, IRR can be an untenable measure of an unconventional project's economic return. The goal of this article is to identify a simple, intuitive explanation of IRR, one that can be applied to any cash flow pattern. To do this, the article shows how a project's IRR(s) systematically change when it first crosses from the conventional into the unconventional realm (i.e., a small cash outflow is appended to a conventional cash flow stream), and then as it becomes progressively more unconventional. This process reveals that the most robust economic interpretation of IRR—for both conventional and unconventional projects—is that a project's IRRs are external benchmarks which divide the set of all plausible discount rates into positive and negative NPV ranges, rather than internally generated returns. Because it can be difficult to estimate a project's cost of capital with precision, this information can help guide the sensitivity analysis of a project.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3046803
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