MovieTexture is finally deprecated after Unity 5.6.0b1 release and new API that plays video on both Desktop and Mobile devices is now released.
VideoPlayer and Video
Similar to what the other answers have been saying. You could use callbacks for when preparing and end of video states. Rather than using coroutines and yield return.
videoPlayer.loopPointReached += EndReached;
videoPlayer.prepareCompleted += PrepareCompleted;
void PrepareCompleted(VideoPlayer vp) {
vp.Play();
}
void EndReached(VideoPlayer vp) {
// do something
}