CPM - cost per thousand, btw.
Facebook ads can be very effective if done correctly. They can be almost as costly of a mistake as a Google ad if you aren't prepared for them (which are very powerful).
However, the R&B website is ranked as a brand new website, essentially. The Alexa rating suggests it's barely refreshed and, in general, is missing lots of SEO work. Even the cookie isn't storing data correctly (it's missing two tokens).
SEO will probably be more important than social hits from friends of friends merely visiting the site. That won't likely grow business unless, obviously, they're looking for used cars in that area. "Spreading the word" in an enclosed eco system like Facebook has its own challenges - ads are no different. Bringing SEO up to snuff would be first priority before you spend money on, hopefully, inbound traffic generated by PPC.
So, not to sound circular (even though it is) Facebook, Google Ads (which are really more about inbound ranking improvement than actual advertising) would be useless until SEO is robust and bringing in exactly the type of traffic you could already measure.
Sure, Facebook could be great for a car dealership! Don't let Facebook naysayers fool you! However, it's sooooooo finicky because weight of inbound links improves with more organic growth and sudden surges of traffic from FB tend to dull rankings unless some other form of inbound can be referenced. (Eg. Facebook shoots your site a ton of links at the same time a newspaper site running an article on you sends you a ton of links too).
Translated: Facebook traffic is more valuable as a way to improve search engines than to get someone to buy from you.
If it's just Facebook... the best you're going to get is untargetted traffic no better/worse than a local newspaper.
If you go THAT route, consider getting a direct response rate with the paper (even if you set up a PO Box in another town) or pay to place ads in the National section with the stipulation you pay "up to [x]" as you measure results. Newspapers running Direct Response rates understand you'll pay a basic rate but will be willing to pay more if you can prove their newspaper sent you much, much more results. I've placed DR ads nationally and came off cheaper than selling a bicycle in the local section of the small town newspaper.
If people "like" your FB page it's really hard to measure, right? The number of "likes" doesn't equal a certain dollar amount.
Do you have access to server logs? If so, THAT might be useful... you MAY find that untargeted traffic for free beats paying for untargeted traffic via FB ads. Plus, there's no chance of a FB ad running away with your money if it is unexpectedly successful. Don't jump on a FB (or Google) ad unless you've done small scale testing and know exactly the type of result you're going to get.
CPC is typically lower on FB than Google. However, using a fan page for something secondary to used cars might be more useful. You're right - who wants to friend up a car dealership? So, consider ways you might create an event, a figure/person/spokesperson, or similar to give people a reason to hook up on FB. (Eg. How many people friend up Candice Michelle or Danica Patrick because they're attractive GoDaddy women as opposed to friending up a boring old domain registry? (GoDaddy)).
It can be worth it but Facebook, being what it is, probably won't work in the direct route. As you said - selling cars is hard enough, who wants to be solicited for them via FB? You may need secondary reasons that draw the FB type crowd. Also, be careful as FB has been changing policies for solicitation a lot lately - you don't want to have the page shut down for violating TOS.
Perhaps separating the work that needs to be done on SEO from the Social Networking would work best? The two can be related but mostly are not. Social Networking for business works best when the site has all its ducks in a row, has a strong Google ranking to make the social traffic worthwhile, and as a destination is ready to receive all the traffic (and statistics) it can. Facebook is one of many tools for a site like that. It would just be a dart thrown at a board for a business still working on its online presence.