Enhancing Accuracy and Consistency in the Valuation of Plant and Equipment through Cubic Regression Models of Physical Deterioration

Abstract

The valuation of plant and equipment often involves valuers deducting physical, functional and economic depreciation from replacement cost estimates. These calculations have faced accuracy and consistency problems in the aspect of determining how much physical deterioration should be deducted. This study attempted to develop cubic regression models to resolve these accuracy and consistency problems in the basic metal, iron and steel and fabricated metal product sectors in Ogun state, Nigeria (Sango Ota and Agbara). Questionnaire surveys were administered on senior operators of plant and equipment in these sectors to draw information on the degree of physical deterioration of plant and equipment over service life, using expenditure on repairs as a proxy for physical deterioration. The questionnaire sought information on the service lives of plant and equipment, the pattern of physical depreciation over the service lives, and the degree to which the pattern is influenced by various operational factors. Data were analysed using means, standard deviations, multiple linear regressions and cubic regressions, to produce what could be the first potentially accurate and consistent valuation model of physical deterioration in Africa. The service lives of various plant and equipment were found to range at various times between 8 to 60 years. Cubic regression analyses showed that the pattern of the movement of transitions of expenditure on repairs (proxy for physical deterioration) over useful life of plant and equipment were not linear but cubic, and generally followed S-shaped patterns. Multiple regression analyses showed that the S-shaped patterns were in turn influenced by operational factors (such as intensity of use and power outages). The study concluded that valuers’ interests in accuracy and consistency in plant and equipment valuation were not served by any of the accounting methods hitherto used by valuers; accuracy in physical deterioration modelling follows an S-shaped transition over time.