While you already have received some good advice, let me try and add further. The right answer to your question depends upon the nature of your business and its dependency on having a designer onboard. If your business, by any chance, is related to offering designing service then you can consider exploring the goodness of fit. But, if it's something different then it doesn't makes any sense trying to fit sheep with lions.

However, trading equity for cash may not be a bright idea as long as everyone with equity in hand doesn't share similar vision, intent, integrity, and values. The white- collared-weekend-party crowd has created a sort of love affair for equity option, and wannabe entrepreneurs with no sense of entrepreneurship finds them appealing, even if that holds no value. Ask your designer why he/she is willing to get compensated in equity? He may be looking at it wearing glorified goggles than true one.

Some obvious pitfalls in equity sharing is as follows:

1. It requires a lot of record keeping and absence of proper paperwork may crop up issues down the road.

2. Paying in equity isn't just compensating but, diluting your business. The equity may become worth many in near future.

3. If you're too short on cash and anticipate availing the designers service for times to come then, make your agreement terminable at will. That way if you find the individual isn't adding much value then you compensate him/her and save your equity. Otherwise, there's no harm in retaining an exceptional individual with impeccable skills.

4. If your business is S Corporation then you would need to verify the IRS rules.

Hope this helps. All the best!!