Optimal Replacement Interval and Depreciation Method for a GrainCombine

A stochastic dynamic programming model is developed to determine optimal replacement intervals and depreciation schedules for a combine on a cash grain farm in north central Montana, where the optimal decision is based on the stochastic nature of winter wheat prices. Empirical results indicate that the decision varies widely depending on the states describing the conditions facing the farm firm. Under normal profitable conditions and ERTA81 tax legislation, suggested replacement is after five years of service, the new asset being depreciated under the accelerated cost recovery system and the investment credit option. Changes to the tax law would tend to smooth out and increase this replacement interval. Key words: depreciation, marginal tax rate, replacement, stochastic dynamic programming. The basic marginal principle of economic the-ory can dictate the optimal replacement age by comparing the costs incurred from keeping an asset for another time period with those which would be realized from a new asset dur-ing the same interval. The difficulty with using this criterion arises in the proper specification of relevant cost elements. Recent work has in-cluded components besides the traditional re-pair and acquisition costs which account for the impact of income taxes on replacement policy (Chisholm, Kay and Rister) along with parameters to account for inflation (Bates, Rayner, and Custance) and the assets ' true re-maining market value (Reid and Bradford). While these are determinants of cost, their impact on the firm's investment decision is influenced by the economic environment sur-rounding the enterprise. Tax liability is de-pendent upon the depreciation schedule and investment incentives used on the asset an