I agree with @dougcollins here. I think this trend of having designers do exercises to get hired is a slippery slope to begin with, and when it veers into "here's actual work for an actual client," that's a red flag in my book. That's spec work, and it's something I am 1000% against. Do not ever work for free unless the client is a charity organization (and sometimes not even then).
Your time is your value, and you deserve to be compensated for that. Charging a nominal fee to keep them honest (e.g. $45/hr) makes sense to me, and I think that anyone who balks at that is someone you don't want to work for in the first place — because they have every intention of exploiting you, intentionally or otherwise.