You need to first start off with deciding whether to charge by day or by hours (solely depends on you). In Texas, hours seem to be more common and I've seen rates ranging from $30-$80/hr.
It also depends if this guy is your buddy or not. You also have to consider whether the quality of your work is up to par with the industry quality in order to charge market prices.
Best of luck!
Real rates, IOW what you end up actually getting paid for your work can range from $1.00 (one dollar) per hour to several hundred. It depends completely on your skill level, your reputation, and the amount of time you waste in production.
The rates you use to estimate the cost have little basis in reality until you have enough experience to know that it will take you X amount of time to pull a clean key from Y type of footage and composite in Z number of layers. Until you've done a bunch of projects that are very similar to the project you are trying to bid on you have NO IDEA how long it will take you.
The rates you quote on the bid or contract should either represent the regional hourly rates or a fixed rate for your project with an additional fee required for more than, lets say, 3 revisions of the design.
You have to set up your contracts or letters if agreement in much the same way a contractor would write a contract to redo your kitchen. Time + Materials + contingency + change orders. If you don't learn how to write a contract, no matter how good you become, you will never make a living as a motion graphics designer or compositor, or film maker.
That said, first, ask your client what they had in mind for a budget, then ask them for a detailed description of what they expect you to deliver, then tell them that you will have to go and run some numbers and get back to them in a day or so.
Now go home, do as much research as you can, play around a little, pray if you have to - and that's not a bad idea on any creative project - then decide if you can work within the clients budget. If you get the job then don't waste any time, keep great records, even if they are only on a scrap of paper, and do the work. After you deliver the project, if the client has a big smile on his face ask to use the work in your demo reel (they bought it so they own it) and ask for an endorsement on your Linkedin page, add the project to your CV (look it up) and then, and only then, dig through your records and decide if you have made any money. If you did, do the same thing for the next job. If you did not, improve every part of your workflow until you are profitable.
The first part of what we are all trying to do with AE is Show, the second and most important word is Business.
Plenty of good info here already. I charge daily rates usually here in Albuquerque, NM, because the projects tend to last at least that long. A minute+ of animation can be a lot of work, depending on what you are doing.
When you're first starting out, daily and hour rates tend to be lower because of your (lack of) experience, but I wouldn't go lower than $250/day, even in a small market. Once you take out taxes (30%) and account for business expenses (another 25-35%), that only leaves you with around $125, and you can get that working at Starbucks (no offense).
$300-$500/day or $50-$80/hr is about average even for smaller markets, generally. But like it was mentioned in the other comments, you can't charge industry rates if you can't do industry quality work. If you feel confident about your work, charge full price and don't get talked down (i.e. don't subsidize another company's advertising budget ;-) . If you aren't confident, don't charge anything except maybe a lunch, and use it as real-world experience.
Hope that helps!
Thanks for all the great info. If it wouldn't be too much trouble, does anyone have a contract they could send me so I can see what they look like and what all needs to go in them?