  We have performed magneto-optical Kerr spectroscopy measurements on
intercalated transition-metal dichalcogenide Fe$_{0.25}$TaS$_{2}$ in the polar
Kerr geometry as a function of temperature, magnetic field, and wavelength. The
Kerr angle exhibits pronounced peaks at $\sim$775 nm (1.6 eV) and $\sim$515 nm
(2.4 eV), which we attribute to spin-dependent interband optical transitions
arising from states in the vicinity of the Fermi energy. Below the
ferromagnetic transition temperature (165 K), we observe strongly wavelength-
and magnetic-field-dependent Kerr signal. At a fixed wavelength, the
magnetic-field dependence of the Kerr angle shows a clear hysteresis loop, but
its shape sensitively changes with the wavelength. We propose a model that
takes into account contributions from domain walls, which allowed us to derive
a mathematical expression that successfully fits all the observed hysteresis
loops.
