First-principles calculations are performed to investigate in detail the electronic structure of ultrathin Ag films deposited on V(001). Quantum-well states in the Ag films show the typical dispersion with film thickness, but their spectral densities differ significantly from those model systems. Ab initio claculations for several systems (bulk, surfaces, interfaces, and thin films) reveal as origins band-structure effects and hybridization between Ag and V states. Quantization effects show up as intensity oscillations in the constant-initial-state mode of photoelectron spectroscopy. Earlier experimental investigations, which reported inconsistencies with typical manifestations of quantization effects, are discussed.