Depreciation of machinery and equipment during the complex Poisson process of their degradation

Machines undergoing degradation are widely studied in reliability theory. However, the constructed models of the degradation process cannot be applied to assess the market value of used equipment. We solve this problem using a new mathematical model of the degradation process. In this model, the condition of the machine is characterized by the intensity of variable benefits (the market value of the work performed in a small unit of time minus the variable part of the operating costs). The degradation of the machine is described by a complex Poisson process. During operation, the machine is subjected to hidden failures that occur with constant intensity. After failure, the operating characteristics of the machine are subjected to a deteriorating jump. In our model, it is assumed that in this case the intensity of the variable benefits is multiplied by a random decreasing coefficient having a power distribution. We specify the limit conditions of the machine in which it should be disposed of. We construct the dependence of the market value of the machine on its condition. It can be used if it is possible to measure the benefits of the machine, and the market value of the new machine and the scrap value of the machines are known. Much more often, the appraiser knows only about the age of used machine. In this case, he can use information about the average service life of the machines and the coefficient of variation of this service life. This information allows him to set the values of the main parameters of the model. However, machines of the same age may be in different states, and therefore it is only possible to offer formulas for estimating their average market value. The constructed model also makes it possible to take into account the impact of inflation by properly adjusting the discount rate.

1. Arkin V. I., Slastnikov A. D., Smolyak S. A. (2006). Valuation of property and business under uncertainty (problems of the “tail” and “beginning”). Audit and financial analysis. Application. Collection of scientific papers, no 1, pp. 81–92 (in Russian).

2. Asaul A. N., Starinskiy V. N., Bezdudnay A. G., Staroytov M. K. (2011). Evaluation of machines, equipment and vehicles. Saint Petersburg, IPER (in Russian).

3. Gokhberg I. I. (2008). Some aspects of equipment evaluation. Kiev (in Russian).

4. Kovalev A. P., Belenicheva A. A. (2008). Features of the valuation of severely worn-out machines and equipment. Otsenochnaya Deyatelnost, no. 2, pp. 45–51 (in Russian).

5. Leifer L. A. (2008). [Determination of the remaining service life of machinery and equipment based on probabilistic models. Property Relations in the Russian Federation, no. 1 (76), pp. 66–79 (in Russian).

6. Leifer L. A. (ed). (2023). Handbook of appraiser of machinery and equipment. Correction factors and characteristics of the market of machinery and equipment. 3rd ed. N. Novgorod: Volga Center for Methodological and Informational Evaluation. 320 p. (in Russian).

7. Ostreykovsky V. A. (2003). Reliability Theory. Text-book. Moscow, Higher School (in Russian).

8. Smolyak S. A. (2016). Machinery and equipment valuation. Moscow, Option Publishing House (in Russian).

9. Smolyak S. A. (2017). On probabilistic models for assessing the residual life and wear of machinery and equipment. Property relations in the Russian Federation, no. 2 (185), pp. 75–87 (in Russian).

10. Smolyak S. A. (2020). The Poisson process of machinery degradation: Application to valuation. Journal of the New Economic Association, no. 4 (48), pp. 63–84 (in Russian).

11. Smolyak S. A. (2021). Assessment of machinery and equipment depreciation using the method used in the systems of national accounts. Proceedings of the Institute of the Systems Analyses of the Russian academy of sciences, no. 1, pp. 44–54 (in Russian).

12. Fedotova M., Kovalev A. P., Kushel A.A. et al. (2017). Machinery and Equipment Valuation: textbook. 2nd ed. Moscow, INFRA-M (in Russian).

13. Barth N., Cappelen Åd., Skjerpen T. et al. (2016). Expected service lives and depreciation profile for capital assets: Evidence based on a survey of Norwegian firms. Journal of Economic and Social Measurement, vol. 41, pp. 329–369.

14. Erumban A. A. (2008). Lifetimes of machinery and equipment: Evidence from Dutch manufacturing. Review of Income and Wealth, series 54, no. 2, pp. 237–268.

15. IVS (2022). Effective 31 January 2022. International Valuation Standards Council.

16. RICS Valuation – ​Global Standards. Effective from 31 January 2022. Published by the Royal Institution of Chartered Surveyors (RICS).

17. Nomura K., Suga Y. (2018). Measurement of depreciation rates using microdata from disposal survey of Japan. The 35th IARIW General Conference. Copenhagen, Denmark.

18.