The competitiveness of the sheep sector in East Europe has been decreasing from year to year. The value added in the sector is not generated in the countries as a high proportion of the lambs are exported. For example, in Hungary, 95% of the lambs, unnecessary for replacement, are sold at an average weight of 21 kg and are slaughtered abroad. A stochastic model was constructed to investigate the connections between the cycle phases of the mutton production. Three modules were distinguished, the lamb production, fattening and slaughtering-processing sub-modules. The aim of our study was to identify the gross value added generated in the three sub-modules and to analyse the main factors influencing its volume using the conditions in Hungary as an example. The major hypothesis of our research was that the profitability of the production chain is mainly determined by the breed. The results showed that, considering market prices, the gross value added in the processing module was mostly influenced by the number of lambs sold per ewe per year at the bottom level of the mutton product chain. The next most important factors were the weight gain in the lamb producing and fattening sub-modules and dressing percentage in slaughtering-processing sub-module. Contour plots were constructed which help to describe the relationship among analyzed factors. Using the contour plots, the gross value added for different combinations of these factors might be forecast.