If I should charge, how much would be good price? I think it will take my team a cumulative of 15 hours. The potential client has not paid anything yet. I know some people would do this job for free in hopes of getting the business but I don't want to work for free.
Defintely! This is your beta version . A proof of concept for the idea. This is what will make them see how the project flow goes.
Analysis and design is the core of any successful project. Why do you want to do it for free ?
Execution of the plan is not the issue.