A method recently proposed to calculate by computer simulation the relative free energy between two conformational states of a polyelectrolyte is used for the case of the salt induced B- to Z-DNA transition. In this method, the calculation of the free energy may be split in two steps, one corresponding to the setup of the uncharged conformer in solution while the other one is the charging process of such a structure. Following the description of the method, simulations are reported to compute the free energy difference between the above mentioned DNA conformers in presence of monovalent added salt. We use a simple DNA solution model-the DNA is represented by charged spheres at the canonical positions of the phosphate groups, water by a dielectric continuum of appropriate permittivity and counterions and colons are modeled as soft spheres of equal ionic radius-for which theoretical approximations have been proposed. It is seen that the charging term is much more important than the setup contribution at any of the investigated salt concentrations. The variation of the free energy of each conformer as a function of the added NaCl concentration has been calculated. Both the B and Z conformers increase noticeably their stabilities with higher salt concentrations but the effect is more pronounced for the latter. As a consequence, the relative population of B-DNA, which is clearly prevalent at moderate ionic strengths, decreases with the addition of salt. However, up to 4.3 M NaCl a B-->Z transition is not predicted for this DNA solution model. Additionally, the theoretical calculations are checked for the first time against computer simulation results. In particular, we have tried to assess the foundations and predictive ability of (especially) the Soumpasis potential of mean force theory and, in a lesser extent, the counterion condensation theory of Manning and the polymer reference interaction site model theory of Hirata and Levy.