That's what I've been describing above. However, there are also sponsorships, where you might be compensated through further event promotion services rather than cash. This is called a Cross Promotion. There are some companies that will be able to provide you with value other than cash. This could be the case for print sponsorships, radio sponsorships or any company that has promotion value to offer.
All cross promotions are different.
Each company will evaluate the benefits that the other has to offer and decide on a reasonable barter. The first thing you should do is cut and paste all of the unique benefits that you had listed in your Sponsorship Profile. After you have one long list, you'll want to separate your benefits into categories. For a small cross promotion, you won't want to offer one of your strongest benefits. While the exact specifics of your final cross promotion my not be exactly what you have listed, it will be a good jumping off point for negotiations.