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The formation energies of CeFe$_{12}$ relative to the Ce$_{2}$Fe$_{17}$ + bcc-Fe phase and to the CeFe$_{2}$ + bcc-Fe phase are calculated with the assumptions of trivalency and tetravalency for Ce. Those values are compared with corresponding results in $R$Fe$_{12}$ for $R=$ Nd, Sm, and Zr. Our results suggest that the tetravalent Ce is a promising stabilizer of the ThMn$_{12}$ structure. 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