I have to agree with Janet on this one. Asking for any actual work to be done pre-hire is unethical. If during the interview, they posed the question as to what you WOULD do if given this assignment, that is one thing, but to get you to actually design something is completely another. This is essentially a free demo for them.
If they want to see what you’re capable of they should be looking at work you have already accomplished. I assume you are presenting a portfolio to them, correct? If so, that should be sufficient. I would also state that you are uncomfortable providing them with work without having been paid for your services. I know you want a job, and a lot of times we will do whatever it takes to get hired, but that doesn’t mean we should sacrifice our principles to get one. (Trust me, after working for a company who convinced me to do that for 8 years, I’ll never do it again.)
You wouldn’t request a doctor to perform exploratory surgery on you for free, just to see if you like his technique, and so you shouldn’t be asking the same of a developer. That is what the 90 day window after hire is for. =/