In this work we combine theory and experiment to study transient magnetic circular dichroism (TRMCD) in the extreme ultraviolet spectral range in bulk Co and CoPt. We use the ab initio method of real-time time-dependent density functional theory to simulate the magnetization dynamics in the presence of short laser pulses. From this we demonstrate how TRMCD may be calculated using an approximation to the excited-state linear response. We apply this approximation to Co and CoPt and show computationally that element-specific dynamics of the local spin moments can be extracted from the TRMCD in the extreme ultraviolet energy range, as is commonly assumed. We then compare our theoretical prediction for the TRMCD for CoPt with experimental measurement and find excellent agreement at many different frequencies including the M₂₃ edge of Co and N₆₇ and O₂₃ edges of Pt.