Deterministic models for premature and postponed replacement

Abstract

We examine the possibilities of premature and postponed replacement in a deterministic infinite horizon model when there is technological progress. Both revenue and operating cost deteriorate with age, but at different rates. The optimal deterministic replacement time is an implicit solution from the timing boundary obtained for the equivalent real option model using a dynamic programming framework, and then by setting the underlying volatilities equal to zero. A step change improvement characterizing technological progress in the initial operating cost level for the successor occurring during the economic lifetime of the incumbent justifies premature replacement, compared to the traditional present value approach. This finding can be extended to step change improvements in the initial revenue level for the successor and for the re-investment cost. In contrast, if the technological progress can be characterized by a constant declining rate for the initial operating cost level for the successor, then the replacement is postponed for certain parameter values. This finding can be extended to different assumed improvement rates in the initial revenue level for the successor and for the re-investment cost.