Ubiquitous multimedia applications diffuse our everyday life activities which appreciate their significance about improving our experiences. Therefore, proliferation of the multimedia applications enhancing these experiences needs critical attention of the researchers. Considering this motivation, to overcome the possible barrier of the proliferation of the 3D video-related multimedia applications providing enhanced quality of experience (QoE) to the end users, an objective metric is proposed in this study. The proposed metric tackles the depth perception prediction part reflecting the most important aspect of the 3D video QoE from the user point of view. Considering that the no reference metric type is the most effective one compared to its counterparts, the proposed metric is developed based on this type. In the light of the envision that human visual system-related cues have critical importance on developing accurate metrics, the focus of the proposed metric is directed on the association of the z-direction motion and stereopsis depth cues in the metric development. These cues are derived from the depth map contents having stressed significant depth levels. In addition, the analysis results of the conducted subjective experiments which are currently the "gold standards" for the reliable depth perception prediction are incorporated with the proposed metric. Considering the effective correlation coefficient and root mean square error performance assessment results taken using the proposed metric in comparison to the widely exploited quality assessment metrics in literature, it can be clearly stated that the development of the improved 3D video multimedia applications can be accelerated using it.