This paper presents the initial findings of an exploratory case study on the convertibility between IFPUG and COSMIC Function Points (FP). Even though a number of conversion approaches have been proposed in the literature, no single model has yet gained general acceptance by the software engineering community due to limits on model usage or other constraints. One major factor hindering the research in this area is the lack of available sizing data and thorough investigation of the factors affecting convertibility between the IFPUG and COSMIC FP. We conducted a case study in Cap Gemini UK Plc to explore these factors, seeking new insights and generating new hypothesis for further research. We found that 1) the proposed conversion approaches in the literature, which take transactional size as the input, did not work well for our case, 2) two significant determining factors appeared to be the existence of maximum limits on transaction complexity in the IFPUG method (which do not exist in the COSMIC method) and the differences between the rules of the methods when deciding whether a candidate entity would correspond to a logical file (in IFPUG) or a data group (in COSMIC).