Using the density functional theory, we have investigated the effect of Ni doping on the Fe(111) surface in two reactions involving CO2: its dissociation to CO and O, and the formation of HCOO. These competitive reactions are of great interest because they are the first ones occurring during CO2 hydrogenation reactions to obtain hydrocarbons. Three bimetallic surfaces were considered: Ni as a substituent in the first layer (Ni1L), in the second layer (Ni2L), and as an adatom (Niad). In all the cases, the presence of Ni inhibits CO2 adsorption in comparison with Fe(111). For Fe(111) and Ni1L-Fe(111), we have obtained an adsorption state where the CO2 molecule is particularly activated, being this configuration different from the most stable adsorption mode. On these surfaces, a two-step reaction was proposed; first, the migration from the most stable state to the activated geometry, and then its dissociation. On Fe(111), the two-step dissociation was found to be kinetically more favored than the direct mechanism. Among the bimetallic surfaces, only Niad-Fe(111) is more favorable kinetically for CO2 dissociation in comparison with Fe(111). Concerning the hydrogenation process to form HCOO, it was found that the reaction is inhibited on mixed Ni-Fe sites.