Right now I'm working on the concept of minimum viable design - what is truly needed to get your business going and to the next level. First – make sure you aren't designing for design's sake. Customer acquisition is numero uno and that usually doesn't take a lot of design out of the gates to start selling.

At any rate if you're not there yet – I've found paying for design always results in a better result than "equity". Your company isn't worth anything (yet) and as soon as something else comes along for your designer "partner" he could jump ship and you'll be hosed.

I've always found people work harder for money unless they are an original co-founder or partner.

Hope this helps!