In a second investment round, can the managing founder protect his equity in the company if he does not invest?

I am a manging founder and one of a group of first-round investors of a company building a restaurant chain. We are in the midst of raising capital for the first store. But if we need additional capital for a second store, I don't plan to invest again. Can I protect my equity or will it be diluted along with that of the other investors? If the second round investment is for a higher share value, is it common practice to give first-round investors a discount on reinvesting (besides their right to first refusal) or do they have to invest at the same value as the new investors?
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Depending on the term sheet you signed when you first invested in the company, you may have the right to invest in follow-on rounds without diluting your equity. However, if you choose not to invest in subsequent rounds, you may very well find yourself owning a smaller piece of the company than you do now. My advice is to check with your attorney and see what anti-dilution protections you were originally granted. If you decide to try to re-cut your deal with your partners, it's better to have that discussion sooner than later.