Density functional theory is used for periodic models of monomeric vanadia species deposited on the CeO2(111) surface to study dissociative adsorption of methanol and its subsequent dehydrogenation to formaldehyde. Dispersion-corrected PBE+U calculations are performed and compared with HSE and B3LYP results. Dissociative adsorption of methanol at different sites on VO2·CeO2(111) is highly exothermic with adsorption energies of 1.8 to 1.9 eV (HSE+D). Two relevant pathways for desorption of formaldehyde are found with intrinsic barriers for the redox step of 1.0 and 1.4 eV (HSE+D). The calculated desorption temperatures (370 and 495 K) explain the peaks observed in temperature-programmed desorption experiments. Different sites of the supported catalyst system are involved in the two pathways: (i) methanol can chemisorb on the CeO2 surface filling a so-called pseudovacancy and the H atom is transferred to an V-O-Ce interphase bond or (ii) CH3OH may chemisorb at the V-O-Ce interphase bond and form a V-OCH3 species from which H is transferred to the ceria surface, providing evidence for true cooperativity. In both cases, ceria is directly involved in the redox process, as two electrons are accommodated in Ce f states forming two Ce(3+) ions whereas vanadium remains fully oxidized (V(5+)).