Bulk alloys and thin films of Fe-substituted Ti3Co5B2 have been investigated by first-principle density-functional calculations. The series, which is of interest in the context of alnico magnetism and spin electronics, has been experimentally realized in nanostructures but not in the bulk. Our bulk calculations predict paramagnetism for Ti3Co5B2, Ti3Co4FeB2 and Ti3CoFe4B2, whereas Ti3Fe5B2 is predicted to be ferromagnetic. The thin films are all ferromagnetic, indicating that moment formation may be facilitated at nanostructural grain boundaries. One member of the thin-film series, namely Ti3CoFe4B2, is half-metallic and exhibits perpendicular easy-axis magnetic anisotropy. The half-metallicity reflects the hybridization of the Ti, Fe and Co 3d orbitals, which causes a band gap in minority spin channel, and the limited equilibrium solubility of Fe in bulk Ti3Co5B2 may be linked to the emerging half-metallicity due to Fe substitution.