Magnetic materials have many applications in technology. The magnetic properties of materials are therefore important to catalogue for future use. In this project, the magnetic properties of thin films of permalloy are investigated. Specifically, the goal is to find the perpendicular magnetic anisotropy energy (PMAE) of thin film geometries of permalloy of varying film thickness. The PMAE is computed with powerful parallel computers using density functional theory (DFT) as implemented in the open-source DFT package OpenMX. The project consists of two parts: Computations on the bulk system and computations on six thin film systems of varying thickness. The thin films are periodic in the basal plane (the permalloy has a tetragonal crystal structure). The easy axis of magnetization was found to be along the c-axis of the tetragonal structure, both for bulk and thin film geometries. For the thin film geometries, this corresponds to an out-of-plane easy axis. The PMAE of the thinnest thin film geometries (4-5 atomic layers) were several times greater than that of the bulk system. Thin films with one more layer of Fe than Ni have especially great PMAE. When comparing the results to another study, the magnetocrystalline anisotropy as computed in this project turned out to be more than two orders of magnitude greater than in the previous study. It is hypothesised that this is because of the differing crystal structure of permalloy used in the study.