Журнал «Труды Института системного анализа Российской академии наук» - S.A. Smolyak The generalized Lvov formula for equipment under degradation

For the valuation of machinery and equipment, the Lvov formula is sometimes used. This formula allows us to calculate the market value of machinery item based on the market value of its analogue, taking into account the differences in their productivity, operating costs and service lives. However, this formula is based on the assumption that the productivity and operating costs of machinery items do not change over their service lives. We propose a generalization of this formula to a more realistic situation where the use of machinery items is described by a random degradation process.

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10. Smolyak, S.A. 2008. Problemy i paradoxy otsenki mashin i oborudovaniya [Problems and paradoxes of machinery and equipment valuation]. Moskow, Russia: RIO MAOK Publ. (in Russian)

11. Smolyak, S.A. 2012. Models for estimating depreciation in plants, machinery and equipment: Analysis and proposals // Journal of Property Tax Assessment & Administration. Vol. 9, Issue 3: 47-86.

12. Smolyak S.A. 2018. O formule D.S. Lvova dlya otsenki mashin [About the D.S. Lvov formula for machinery and equipment valuation] // Imushchestvennye otnosheniya v Rossiyskoy Federatsii [Property Relations in the Russian Federation]. 10(205): 19-25. (in Russian)

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17. Smolyak, S.A. 2014. Zavisimost' stoimosti mashin ot vozrasta: problemy i modeli [Dependence of the value of machinery on age: problems and models] // Audit i finansovy analiz [Audit and financial analysis]. No 5: 138-150. (in Russian)

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24. Leifer, L.A., Kashnikova, P.M. 2008. Opredeleniye ostatochnogo sroka sluzhby mashin i oborudovaniya na osnove veroyatnostnykh modeley [Calculation of the residual life of machinery and equipment based on probabilistic models]. Imushchestvennye otnosheniya v Rossiyskoy Federatsii [Property Relations in the Russian Federation]. 1: 66-79. (in Russian)

25. Smolyak, S.A. 2020. O dinamike obestseneniya machin so sluchaynym srokom sluzhby [On the dynamics of depreciation of machines with a random service life] // Trudy Instituta sistemnogo analiza Rossiyskoy Academii nauk [Proceedings of the Institute of Systems Analysis of the Russian Academy of Sciences]. 1(66): 55-64. (in Russian)

26. Smolyak, S.A. 2017. O veroyatnostnykh modelyakh dla otsenki ostatochnogo sroka sluzhby i iznosa mashin i oborudovaniya [On probabilistic models for machinery and equipment residual life and depreciation estimation]. Imushchestvennye otnosheniya v Rossiyskoy Federatsii [Property Relations in the Russian Federation]. 2(185) : 75-87. (in Russian)