Abstract. 

We propose a model of degradation of machines (deterioration of their technical and economic characteristics). In it, the failure rate increases with the deterioration of the state of the machine, and after each failure, the intensity of benefits brought by the machine decreases by a random value. A machine that brings negative benefits is subject to decommissioning. We obtain explicit expressions for the average value and the coefficient of variation of the random lifetime of machines. Machine’s value is determined by discounting the flow of benefits from its future use. This allows us to find the dependence of the market value of the machine on the intensity of the benefits it brings. Assessing the market value of new machines is usually not difficult, but it is much more difficult to do this for used machines. Appraisers are usually unable to estimate the value of the work performed by machines, and when valuing a used machine, they have to rely on its age. To do this, the market value of a similar new machine is usually reduced by a depreciation factor or multiplied by Percent Good Factor (relative value), depending on the age of the machine being valued. However, machines of the same age can be in different conditions and therefore have different market values. Therefore, here Percent Good Factors are of an averaged nature, i.e. essentially refer to the average machine that has survived to a certain age. We offer formulas to calculate these average Percent Good Factors reflecting the average decrease in the machine’s value with age. To take into account the effect of inflation, it is sufficient to adjust the discount rate in the constructed model. The verification shows that the proposed dependencies are in good agreement with market price data for two different types of construction equipment.

Keywords: 

machines, equipment, market value, benefits, valuation, age, depreciation, Percent Good Factors, degradation, failures

PP. 48-60.

DOI: 10.14357/20790279220105

 

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