Ab initio band structure calculations based on density functional theory were performed for NaCl, CdCl2, and the Suzuki phase Na6CdCl8. For Na6CdCl8 the structural parameters and physical properties, such as molar volume and the magnitude of the free internal coordinate and electric field gradients, together with their pressure dependence, were obtained. These results are compared to calculations for NaCl and CdCl2 to investigate the hypothesis that Na6CdCl8 can only exist as precipitates in a stabilizing surrounding NaCl matrix. From the present calculations it follows that the lattice parameters of NaCl and the Suzuki phase are identical within the accuracy of the calculations, and that therefore no "clamping" of the Suzuki phase occurs. However, it is found that Na6CdCl8 is only metastable with respect to the decomposition into solid sodium chloride and cadmium chloride. Calculations for NaCl were also used to evaluate the quality of different exchange-correlation functionals (LDA, GGA-PW91, GGA-PBE96), where the best results are obtained when the GGA-PBE96 is used. The NaCl calculations suggest that the bulk modulus of the B2 phase reported in the literature is too large, mainly due to a lack of data for the molar volume at ambient pressure.