Least upper bound of percent good factors of used machinery items

Abstract

We consider one of the problems of valuation of used machinery items. During operation, the technical and economic characteristics of the machinery item tend to deteriorate and the probability of its catastrophic (resource) failure changes. Accordingly, the market value of a used machinery item is reduced compared to a similar new one. The ratio of the market value of a used machinery item and a similar new one, expressed in a percentage (or as fractions of a unit) is called the percent good factor (goodness factor). In general, it depends on the technical condition of the machinery item. However, it is difficult to quantify and reliably estimate it in many cases (for example, in mass assessment), and appraisers are forced to rely only on the machine’s age. There are numerous articles containing recommended by the authors dependencies of goodness factors (or their additions to one, namely physical depreciation factors) on age. We present a model of the dependence of the machine’s market value on age, which allows us to establish the exact upper limit for its goodness factors. We show that a number of recommended dependencies do not satisfy the obtained restriction and therefore can lead to erroneous results.