On the basis of density functional - pseudopotential calculations, we study structural, electronic, magnetic, and mechanical properties of the hypothetical CaC ionic compound in the rock-salt (RS), B2, zinc-blende (ZB), wurtzite (WZ), NiAs (NA), and anti-NiAs (NA*) structures. The results show that RS-CaC is the most stable system at equilibrium while applying negative hydrostatic pressures may stabilize the half-metallic WZ and ZB structures. The ferromagnetic equilibrium state observed in the RS, ZB, NA and WZ structures of CaC is attributed to the sharp partially filled p band of the carbon atom. It is argued that the ionic interaction increases the sharpness of the p band and hence enhances ferromagnetism while the covalent interaction increases the band dispersion and weakens magnetism. We investigate various properties of the exchange interaction in the ferromagnetic CaC structures. It is observed that the interatomic exchange interaction in these systems have consistent behavior with the spin splittings of the bond points. Comparing the structural properties in the ferromagnetic and nonmagnetic states. indicates a weak magneto-structural coupling in CaC. Applying non-local corrections to the exchange functional enhance the exchange splitting and hence give rise to a half-metallic electronic structure for the WZ, RS, and NA structures of CaC. In the framework of density functional perturbation theory, the phonon spectra of these systems are investigated and the observed dynamical instabilities in the NA* and B2 structures are attributed to the tendency of the carbon atoms toward dimerization. Various mechanical properties of the dynamically stable structures of CaC are determined from their phonon spectra.