I would not trade equity for design work. Unless this person will actually become a part of your team and create enough value to warrant equity. Otherwise it is short sighted to trade equity for something you need very early on just to launch. I'm sure your design/brand will evolve over time and this person will have put in a minor amount of work compared to what it will take to launch and continue a successful company. Additionally, you may be putting too much weight on your brand and not enough on what you're actually selling? However it is hard to give a more detailed answer without knowing what exactly you are doing and how detailed and ongoing the design work is. I would love to help answer your question, but need a little more detail on what exactly it is you do and what type of design/branding work you need.