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The Poisson process of machinery degradation: Application to valuation

Author

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  • Smolyak, S.

    (Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia)

Abstract

The machinery degradation process is described by a random process in which failures occur with constant intensity, and with each failure the rate of benefits generated by the machinery item reduces by a random amount. If the machinery item begins to generate negative benefits, it is subject to decommissioning. We get explicit expressions for the average life of the machinery items and the coefficient of variation of the service life. Machine's value is determined by discounting the flow of benefits from its future use. This allows to link this value with the rate of benefits that the machinery item brings. In cases where there is no information on the amount of such benefits, appraisers rely on the machine's age. However, different machinery items of the same age may be found in a different condition and therefore are characterized by different values. We offer formulas for calculating the percent good factors reflecting the average decrease in the equipment's value with age. To take into account the effects of income tax, property tax and inflation, it suffices to adjust the discount rate in the constructed model. It has been verified that the proposed dependencies are in a fairly good agreement with market price data for two different types of construction equipment.

Suggested Citation

  • Smolyak, S., 2020. "The Poisson process of machinery degradation: Application to valuation," Journal of the New Economic Association, New Economic Association, vol. 48(4), pages 63-84.
    • Handle: RePEc:nea:journl:y:2020:i:48:p:63-84
    DOI: 10.31737/2221-2264-2020-48-4-3
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    References listed on IDEAS

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    1. Toshio Nakagawa, 2007. "Shock and Damage Models in Reliability Theory," Springer Series in Reliability Engineering, Springer, number 978-1-84628-442-7, December.
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    Cited by:

    1. Smolyak, Sergey, 2023. "Оценка Подержанных Машин На Основе Новой Модели Их Деградации [Valuation of used machinery based on the new model of its degradation]," MPRA Paper 119423, University Library of Munich, Germany, revised 15 Jun 2023.

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    More about this item

    Keywords

    machinery; market value; benefits; valuation; age; depreciation; percent good factors; degradation; failures; exponential failure distribution;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management

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