The effect of tax depreciation on the stochastic replacement policy

• Published in: European journal of operational research Vol. 229; no. 1; pp. 155 - 164
• Main Authors: Adkins, Roger, Paxson, Dean
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.08.2013; Elsevier; Elsevier Sequoia S.A
• Subjects: Capital budgeting; Corporate taxes; Depreciation; Equipment replacement; Mathematical models; Operating costs; Operations research; Quasi-analytical solution; Studies; Tax depreciation; Tax rates; Uncertainty modelling; Capital budgeting; Tax depreciation; Quasi-analytical solution; Equipment replacement; Uncertainty modelling
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2013.01.050

► Replacement for equipment with a stochastic deteriorating operating cost is analyzed for three different tax depreciation schedules. ► The optimal policy is determined as the threshold boundary from a real option model. ► The effect of the tax shield is to lower the cost threshold, but positive tax changes do not universally lead to an earlier replacement. ► The cost threshold is less for younger than older assets. ► Accelerated depreciation does not necessarily justify an earlier replacement policy. The optimal replacement policy for an asset subject to a stochastic deteriorating operating cost is determined for three different tax depreciation schedules and a known re-investment cost, as the solution to a two-factor model using a quasi-analytical method. We find that tax depreciation exerts a critical influence over the replacement policy by lowering the operating cost thresholds. Although typically a decline in the corporate tax rate, increase in any initial capital allowance, or decrease in the depreciation lifetime (increase in depreciation rate) results in a lower operating cost threshold which justifies replacing older equipment, these results are not universal, and indeed for younger age assets the result may be the opposite. An accelerating depreciation schedule may incentivize early replacement in a deterministic context, but not necessarily for an environment of uncertainty.