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The cost of designing a logo depends on a multitude of factors, including, but not limited to, design expertise (credibility/skill of the designer), scope of work and hours required to complete the design. Logo’s can be designed for $10 per 15 minutes; however, we do not recommend this as a solution. This low cost for design will likely be through a contest or designed by artists all across the world who have no investment what so ever in your company. A much better solution, even though the cost will be higher is to invest in a company that is willing to invest the time to learn about your company and use that as their investment and commitment into your business. There is no real formula to determine the cost of a logo design, no more so than determining the cost of a painting by an artist like a Rembrandt or a Van Gough. Designers with real talent simply do not work on community sites where they only get paid by winning the contest.
If you want to learn more about the differences in Branding, Identity and Logo Design, this is a good article from an international designer, Jacob Cass. Just Creative: Brand, Identity and Logo Design Explained