The potential energy surface corresponding to the reaction of the cobalt cation with ethane, which represents a prototype of the activation of C-C and C-H bonds in alkanes by transition metal cations, has been investigated by employing the recently suggested density functional theory/Hartree-Fock hybrid method B3LYP combined with reasonably large one-particle basis sets. The quality of this approach has been calibrated against experimentally known Co-R(+) binding energies of possible exit channels and against CCSD(T) energy calculations. The performance of the chosen model is satisyfing with respect to the description of relative energies, although some nonuniform deviations between calculated and experimental data have been found for absolute binding energies. The calculated barriers for the initial insertion steps of Co+ into C-C and C-H bonds are undoubtedly found to be considerably less energy demanding than the activation barriers connected with the reductive elimination of H-2 and CH4, respectively. The rate determining step for the C-C activation branch is a 1,3-H shift leading to a complex between Co(CH2)(+) and methane. Along the C-H activation reaction coordinate, a concerted saddle point connecting the C-H inserted species directly with a complex of Co+ with molecular hydrogen and ethylene has been identified as the energetic bottleneck. Despite of being often proposed, no inserted dihydrido species could be located.