The individual vehicle replacement problem typical for freight transportation companies is discussed in the paper. Two characteristic features of such problem are that transportation companies utilise vehicles with intensity decreasing with an age of vehicles and that managers of such companies first of all take into account economical criteria when planning vehicle replacements. The paper presents a single criterion, nonlinear, deterministic and discrete mathematical model of such a problem that minimises a total exploitation and ownership costs calculated per kilometre. The exact solution procedure is proposed here. The problem is solved as a real life case study. As a result, an average, economically optimal 5-year exploitation period of vehicles has been determined.