Home Sharing only shows library from purchases made on iPhone; not from library on iMac

I've just purchased the newest Apple TV and want to use it to access and play tunes from my iTunes library. I have a 2009 iMac (OSX Yosemite 10.10.5) that has a large library on iTunes. I also have an iPhone 6 that has the same library (from a synch with the iMac), though a few songs were purchased directly with the iPhone from iTunes. I am signed into both the iPhone and iMac with the same Apple ID and have Home Sharing authorized on both devices. When I access my music on Apple TV, it only shows a few songs that I happened to have purchased through iTunes on the iPhone; none of the songs/albums which were uploaded from CDs to the iMac or purchased using the iMac show up on Apple TV. Although I have two different Apple IDs (and it's possible that the CDs were uploaded to the iMac when I was signed in to the other Apple ID), all the songs show up on the iMac when I sign into the same Apple ID that Apple TV is using. So, I'm not sure what I am doing wrong here and how I can get the same library that is on my iMac to show up on Apple TV. Any help would be greatly appreciated!