In this article the influence of a layer dependent second-order perpendicular anisotropy on higher-order anisotropies in thin films in the framework of a macrospin model is investigated. Second-order and fourth-order effective anisotropies are necessary to achieve a reasonable description of the micromagnetic results using the macrospin approximation. We found that the origin of the fourth-order anisotropy is linked to the layer-wise variation of magnetization direction in the structure leading to dependence on field strength and exchange stiffness. Our results show that the apparent fourth-order anisotropy increases with decrease in exchange stiffness and thereby decreasing exchange length. This observation has important implications for experimental investigations of the thickness dependence of the perpendicular anisotropy.