Optimal replacement interval and depreciation method of a combine on a representative dryland grain farm in northcentral Montana

Abstract

Economic uncertainty is one of the foremost problems in agriculture and introduces many complexities into the decision making process. To account for these risks and uncertainties in the replacement problem, a model is formulated within a dynamic programming framework and applied to a typical cash grain farm in northcentral Montana. The decision criterion used under conditions of risk is the minimization of costs associated with each asset through the firm's planning horizon. The asset under study is a combine and the optimal replacement decision regarding this asset is based on the stochastic nature of winter wheat prices. Transition probabilities for price changes are calculated from a single equation price prediction model. The other state variables are deterministic and include fifteen asset ages and sixteen tax conditions. Together, they completely summarize the costs associated with the combine. The optimal decision minimizes the expected immediate costs and those from the n-1 stage process which are a function of the state variables and decision alternative selected. Besides being able to keep or replace, the decision variable for replacement also includes all the possible depreciation schedules and investment incentives which can be used on the new asset. The optimal policy selected is dependent upon the state of the process. The accelerated cost recovery system is used in high income years after five years of service and a longer recovery period when returns are very low. The evidence also indicates the value of investment tax credit. The practical and wide ranging results obtained through the use of stochastic dynamic programming contributes to the body of theoretical knowledge on replacement analysis.