  We compute the $\beta$-decay $ft$-values within the frameworks of the energy
density functional (EDF) and the interacting boson model (IBM). Based on the
constrained mean-field calculation with the Gogny-D1M EDF, the IBM Hamiltonian
for an even-even nucleus and essential ingredients of the interacting
boson-fermion-fermion model (IBFFM) for describing the neighboring odd-odd
nucleus are determined in a microscopic way. Only the boson-fermion and
residual neutron-proton interaction strengths are determined empirically. The
Gamow-Teller (GT) and Fermi (F) transition rates needed to compute the
$\beta$-decay $ft$-values are obtained without any additional parameter or
quenching of the $g_A$ factor. The observed $\ft$ values for the $\beta^+$
decays of the even-even Ba into odd-odd Cs nuclei, and of the odd-odd Cs to the
even-even Xe nuclei, with mass $A\approx 130$ are reasonably well described.
The predicted GT and F transition rates represent a sensitive test of the
quality of the IBM and IBFFM wave functions.
