As moondog says, there's absolutely no reason to hire a tour guide for a day trip to the Great Wall from Beijing, as nowhere within typical day trip distance is really dangerous or remote enough to warrant one; this is very much on the beaten path.

I would recommend heading for Mutianyu; it's less crowded and less of a tourist trap than Badaling. Take bus 936 from Beijing Dongzhimen bus station (there's two early-morning departures last I checked, at 0730 and 0830), and return in the afternoon. The bus should come in under ¥50 per person altogether; entrance is another ¥50 or so.