I am in possession of a license for version 11.1 for Intel® Parallel Studio XE Composer Edition for Fortran Windows.
I now need to upgrade to the 2015 or 2016 compiler. Does my license allow me to use that software? It was purchased as a CD-ROM installation if that is relevant.
Probably not. When you buy a license, you can download, install and use any update or version released in the following 12 months. For 13 months after support expiration, you can renew at a discount, but after that the discount is no longer available.
See https://software.intel.com/en-us/faq/purchasing-renewing-upgrading for more information.