Valuation of used machinery based on the new model of its degradation

Abstract

We propose a new model of equipment degradation. In it, the machine is subjected to random latent failures, the danger of which depends on the equipment condition and after each failure the intensity of the equipment's benefits decreases by a random amount. Equipment that brings negative benefits is subject to decommissioning. The model parameters are found based on known information about the average value and the coefficient of variation of the equipment lifetime. Market value of equipment is determined by discounting the flow of benefits from its future use. This allows us to find the dependence of the equipment’s market value on the benefits it brings. Assessing the market value of new equipment is usually not difficult, but it is much more difficult to do this for used equipment items. Appraisers are usually unable to estimate the value of the work performed by equipment, and when valuing a used equipment, they have to rely on its age. To do this, the market value of a similar new equipment is usually reduced by a depreciation factor or multiplied by Percent Good Factor (PGF, relative value), depending on the age of equipment being valued. However, equipment of the same age may be in different conditions and, therefore, have a different market value. Therefore, such PGFs, in fact, relate to the average equipment that has survived to the appropriate age. Appraisers determine them by formulas or tables that are usually not supported by proper justifications. The proposed model makes it possible to build the dependence of the average PGF on age and calculate the market value of the work performed by machines, even if such works are not traded on the market. It turns out that it is possible to take into account the influence of the utilization cost of the machine and inflation in the model. The results of experimental calculations performed using the model (with calibration parameters selected appropriately) are in good agreement with the market prices of some types of construction equipment.