Valuation of Machines with a Random Service Life Based on the System of National Accounts – 2008

We propose a mathematical model describing the decrease in the market value of machines (depreciation) with age in a situation where its service life is random and has a Weibull distribution. We measure the depreciation of a used machinery item using a goodness factor, that is, the ratio of its value to the value of a similar new machinery item. The model is based on the principle of anticipation of benefits adopted in the valuation theory and the discounting cash flows method. The model takes into account that machine’s technical and economic characteristics deteriorate with age and its benefits are reduced according to the hyperbolic dependence adopted in the system of national accounts SNA‑2008. We have built the dependences of average machine's goodness factor on its relative age (the ratio of the actual age to the average service life). Calculations show that the discount rate and average service life have little effect on these dependencies. This made it possible to divide the machines into three categories and propose for each of them its own dependence of the goodness factor on the relative age, which is convenient for practical use in appraisal activities.