Consider the rules of thumb.
When determining a graphic design budget, a good place to start is to know how much revenue you’d like to make over the course of a year. Balance that number with your business goals and immediate financial capabilities. Budget 5-10% of that toward your marketing efforts (includes graphic design budget, website, copy-writing, advertising, etc). Common rules of thumb are: 10% for growth, 5% to maintain. So, if you want to make $100k your first year, consider budgeting $10k toward your marketing efforts. Allot that, as you determine is appropriate, between your hired talent and actual avenues for advertising.
Ultimately, your graphic design budget will determine how much focus a designer can give you. I might be a little biased in this matter, but anyone’s visual brand really deserves a lot of attention. This is where the essence of your business plan becomes manifest in the eyes of your prospects. I get passionate about it for that very reason. Otherwise, you may see failed advertising efforts because of an amateur visual brand. I recommend at least half of the 5 or 10% for your graphic design budget, but again, that number is up to you and your goals. Present that number to your graphic designer and he or she can help you determine how that can be broken down into specific project needs or campaign scopes.
If you cannot determine your graphic design budget, you can still move forward.
I will acknowledge this: Sometimes all we need is a vision and the faith to inspire us to take some solid baby steps. I have gladly worked with folks before who have been a little unclear about their plan. They went ahead with small steps (logo design, landing page, social media headers, etc). Creating the face of their brand gets them excited and eager to make it work. If this is you, then I will gladly take this approach with you, but custom graphic design is not a commodity. It helps to know what you can budget, even if it’s just to get started.