Small and medium size enterprises (SMEs) are greatly affected by cost escalations and overruns Reliable cost factors estimation and management is a key for the success of Enterprise Resource Planning (ERP) systems adoptions in enterprises generally and SMEs specifically. This research area is still immature and needs a considerable amount of research to seek solid and realistic cost factors estimation. Majority of research in this area targets the enhancement of estimates calculated by COCOMO family models. This research is the beginning of a series of models that would try to replace COCOMO with other models that could be more adequate and focused on ERP adoptions. This paper introduces a feed-forward back propagation artificial neural network model for cost factors estimation. We comment on results, merits and limitations of the model proposed. Although the model addresses SMEs, however, it could be extended and applied in various environments and contexts.