We report the electronic structures and density of states (DOS) of perfect LiCAF and LiSAF crystals calculated from density functional theory (DFT) with local density approximation (LDA) using optimized lattice constants. DOS calculations reveal that the valence band is mainly derived from F 2p, thereby resulting to a very narrow valence band manifold. Meanwhile, the conduction band is mainly derived from Ca 4s or Sr 5s resulting to Sr having a broader band dispersion compared to Ca. Both fluoride compounds have indirect band gaps with LiCAF having a band gap of 8.02 eV and LiSAF a band gap of 7.92 eV. This is, to the best of our knowledge, the first report on the electronic structure of LiSAF calculated using DFT with LDA. Our results suggest that when doped with Ce3+, the shorter 5d-conduction band distance in Ce:LiSAF combined with the difficulty of growing high-purity crystals lead to the more pronounced excited state absorption (ESA) and solarization effect experimentally observed in Ce:LiSAF, limiting its potential as a laser material compared with Ce:LiCAF.