There are several stability problems important for fullerenic species, namely relative populations of (i) isomeric endohedrals, (ii) non-isomeric metallofullerenes differing in the number of the encapsulated metal atoms placed in still isomeric carbon cages, and (iii) monometallofullerenes with different metals encapsulated in one selected carbon cage. The related computational approaches are illustrated on endohedrals with encapsulated La and its congeners, evaluated using various density-functional theory (DFT) treatments or the second order Moller-Plesset perturbation theory (MP2). One of the illustrative examples treats encapsulations in the T_d IPR C₇₆ cage using the metal series Al, Sc, Y, La, and Ac. Three formal reaction steps can be considered with the encapsulations: (i) double- (or triple-) ionization of the free metal, (ii) double (or triple-) charging of the empty cage, and (iii) placing the metal di- (or tri-) cation into the di- or (tri-) anionic cage. The (ii) energy change is identical for all members of the series, and the (iii) terms should be similar as they are controlled by electrostatics. Hence, only the (i) energy term comes as a differentiating factor. In other words, the free-metal ionization potentials should actually represent the critical yield-controlling parameter.The computed relative potential-energy changes upon encapsulation δE and the relative observed ionization potentials of the free atoms δIP should (according to the above three-step analysis) be correlated. Interestingly, Ac has the second best encapsulation energy after La in the series.