Q: Getting iTunes rental movie to play on AppleTV

OUR HARDWARE:

Apple Airport Extreme base station, connected to Verizon DSL

MacBook Pro 13-inch

iMac 21-inch

iPad Mini (2013)

AppleTV (previous generation)

HDTV with HDMI port connected to AppleTV

A few weeks ago, our family rented a movie using iTunes on the MacBook Pro laptop. The movie would not play on the AppleTV via AirPlay. There was some wanting message about the connected display was not authorized. So we had to watch the movie on the laptop.

Now we want to rent another movie via iTunes. How do we do this and successfully play it on the TV set? What's the trick?

The AppleTV was purchased several months ago as a refurbished model. It is the previous generation (the one before the new voice-activated ones).