Is there an additional charge for installing this app on another device?

As long as you're using the same Apple ID on all of your iOS devices, you can install the app on as many devices as you like, and all of your prior purchases will be restored.

If your purchases are not automatically restored at startup, go to Contacts Sync > More > Store > Restore Purchases.

Keep in mind, however, that the Mac and iOS versions of this app are separate purchases.