So, there were 2 things going on in your plunker.
Firstly the btn-radio attribute doesn't need interpolation ({{}}) you can (and should) provide an expression directly. So just write btn-radio="company.id" instead of btn-radio="{{company.id}}".
Secondly, you must know that the ng-repeat directive creates a new scope. This is a very, very common conceptual issue people have with AngularJS so I would encourage you to read https://github.com/angular/angular.js/wiki/The-Nuances-of-Scope-Prototypal-Inheritance
Coming back to you particular problem you can either change you ng-model expression to point to a parent scope (ng-model="$parent.radioModel") or bind to an object property (ng-model="radioModel.id").
Here is a working plunk with the second approach:
http://plnkr.co/edit/uGAxaRlPFK6sD4tRjGXX?p=preview