Valuation of machines at the random process of their degradation and premature sales

Smolyak S.A.
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The model of the process of using machinery and equipment is considered, which takes into account the probabilistic nature of the process of their operation and sale. It takes into account the possibility of random hidden failures, after which the condition of the machine deteriorates abruptly, as well as the randomly arising need for premature (before the end of its service life) sale of the machine, which requires, generally speaking, random time. The model is focused on assessing the market value and service life of machines in accordance with International Valuation Standards. Strictly speaking, the market value of a used machine depends on its technical condition, but in practice, appraisers only take into account its age, since generally accepted measures of the technical condition of machines do not yet exist. As a result, the market value of a used machine is assumed to be equal to the average market value of similar machines of the corresponding age. For these purposes, appraisers use coefficients that reflect the influence of the age of machines on their market value. Such coefficients are not always justified and do not take into account either the degradation of the machine or the probabilistic nature of the process of its use. The proposed model is based on the anticipation of benefits principle. In it, we characterize the state of the machine by the intensity of the benefits it brings. The machine is subjected to a complex Poisson failure process, and after failure its condition abruptly worsens and may even reach its limit. Situations also arise that preclude further use of the machine by its owner. In such situations, the owner puts the machine up for sale before the end of its service life (prematurely), and the sale requires a random timing. The model allows us to take into account the influence of such situations and construct an analytical relationship linking the market value of a machine with its condition, and calculate the average coefficients of change in the market value of machines with age. At the same time, it is also possible to take into account the influence of inflation and the scrap cost of the machine. We have found that the rate of prematurely sales has a significant impact on the cost of new and used machines. The model also allows us to take into account the influence of inflation and the scrap value of the machine. We have found that the rate of premature sales has a significant impact on the service life and market value of new and used machines. At the same time, the dependence of the market value of machines on age is largely determined by the coefficient of variation of the service life of the machines. The results obtained allow us to obtain more reasonable estimates of the market value of machines, including for the purposes of the system of national accounts.

Keywords: machinery and equipment, the Poisson process, degradation, market value, anticipation of benefits principle, service life, tenure, premature sale, inflation
Citation in English: Smolyak S.A. Valuation of machines at the random process of their degradation and premature sales // Computer Research and Modeling, 2024, vol. 16, no. 3, pp. 797-815
Citation in English: Smolyak S.A. Valuation of machines at the random process of their degradation and premature sales // Computer Research and Modeling, 2024, vol. 16, no. 3, pp. 797-815
DOI: 10.20537/2076-7633-2024-16-3-797-815
URL: http://crm-en.ics.org.ru/journal/article/3493/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

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