First-principles calculations for the potential photovoltaic material (CZTS) are presented using density functional theory and the Perdew-Burke-Ernzerhof exchange-correlation functional as well as using the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional. The HSE results compare very favorably to experimental data for the lattice constants and the band gap, as demonstrated for CZTS and selected ternary chalcopyrites such as , , , and . Furthermore the HSE band structure is validated using quasiparticle calculations. The valence band is found to be made up by an antibonding linear combination of states and states, whereas an isolated band made up by and states dominates the conduction band. In the visible wavelength, the optical properties are determined by transitions from the states into this conduction band. Comparison of the optical spectra calculated in the independent-particle approximation and using time-dependent hybrid functional theory indicates very small excitonic effects. For the structural properties, the kesterite-type structure of symmetry is predicted to be the most stable one, possibly along with cation disorder within the Cu-Zn layer. The energy differences between structural modifications are well approximated by a simple ionic model.