  We describe the afterglows of the long gamma-ray-burst (GRB) 130427A within
the context of a binary-driven hypernova (BdHN). The afterglows originate from
the interaction between a newly born neutron star ($\nu$NS), created by an Ic
supernova (SN), and a mildly relativistic ejecta of a hypernova (HN). Such a HN
in turn results from the impact of the GRB on the original SN Ic. The mildly
relativistic expansion velocity of the afterglow ($\Gamma \sim 3$) is
determined, using our model independent approach, from the thermal emission
between $196$~s and $461$~s. The power-law in the optical and X-ray bands of
the afterglow is shown to arise from the synchrotron emission of relativistic
electrons in the expanding magnetized HN ejecta. Two components contribute to
the injected energy: the kinetic energy of the mildly relativistic expanding HN
and the rotational energy of the fast rotating highly magnetized $\nu$NS. We
reproduce the afterglow in all wavelengths from the optical ($10^{14}$~Hz) to
the X-ray band ($10^{19}$~Hz) over times from $604$~s to $5.18\times 10^6$~s
relative to the Fermi-GBM trigger. Initially, the emission is dominated by the
loss of kinetic energy of the HN component. After $10^5$~s the emission is
dominated by the loss of rotational energy of the $\nu$NS, for which we adopt
an initial rotation period of $2$~ms and a dipole plus quadrupole magnetic
field of $\lesssim \! 7\times 10^{12}$~G or $\sim \! 10^{14}$~G. This scenario
with a progenitor composed of a CO$_{\rm core}$ and a NS companion differs from
the traditional ultra-relativistic-jetted treatments of the afterglows
originating from a single black hole.
