A new methodology of calculation of dispersion and damping of collective excitations from ab initio molecular dynamics (AIMD) of liquid metals is proposed. It is suggested to use for the analysis of AIMD-derived time correlation functions a thermo-viscoelastic dynamic model within an approach of the generalised collective modes. The proposed scheme, in which the viscoelastic matrix elements of the generalised hydrodynamic matrix are directly calculated from AIMD and the matrix elements requiring knowledge of energy density fluctuations in the system are treated as fitting parameters, allows to recover AIMD time correlation functions in a wide range of wave numbers. The dispersion and damping of collective excitations are obtained as a complex-conjugated pair of the generalised hydrodynamic matrix. An issue of sum rules in the proposed scheme is discussed. The methodology is applied for calculations of dispersion and damping of generalised acoustic modes in molten lithium.