In the present work, the impact of phosphorus impurities on the grain boundary strength of nickel has been investigated by means of density functional theory (DFT) modelling. Owing to different outcomes and trends previously reported in the literature, it is unclear whether P is strengthening or weakening the Ni grain boundary. To address this issue, we utilize three different DFT based methods: the excess-energy approach, rigid grain separation, and Rice-Wang's thermodynamic approach. The results show that the commonly used rigid model predicts P to have an increasing effect on the peak stress of Ni of up to 14%, as opposed to a reduction, which is indicated by the excess-energy approach. Employment of the Rice-Wang approach, on the other hand, displays a slight reduction in work of separation. The results show that the discrepancies between previous works can be attributed not so much to the physics of the system, but to the applied model, the partition scheme and the interpretation of the outcomes. This underlines the importance of a proper description of the fracture process, and shows that common simplifications can have a decisive impact on the observed trends.