Last week's private-equity buyout of Burger King (NYSE: BKC) is only the beginning.

It's an appetizer -- a slider if you will -- because sector consolidation will continue in the restaurant industry.

Investors looking to cash in on the shopping spree will probably be disappointed. The hot names won't be acquired. There is no reason for Chipotle Mexican Grill (NYSE: CMG) to burrito-roll its way to a suitor. The company's doing too well on its own, and the valuation also isn't for the squeamish. No one is going to buy McDonald's (NYSE: MCD). Beyond the fact that few could afford its $90 billion enterprise value, it would take a fat premium above that for Mickey D's to consider a sale.

In other words, investors will have to settle for the losers here. Because private equity is doing the buying, it's looking for broken companies that it can stash away for a couple of years, buff up, and take public at higher price points.

Burger King was the perfect example -- a meandering burger chain that everyone recognizes. Following that logic, let's go over a few potential candidates for acquisition.

  • Wendy's/Arby's Group (NYSE: WEN): The combination of Wendy's and Arby's has been a ho-hum disaster. The shares have been trading in the single digits for nearly three years. It's actually surprising that Burger King went before Wendy's.
  • AFC Enterprises (Nasdaq: AFCE): Most drumstick eaters have no idea that Popeyes is public. AFC Enterprises watches over the fried-chicken chain of nearly 2,000 outlets. The company is holding up OK. Sales, earnings, and same-store sales all inched higher in the latest quarter, and the company even increased its guidance for 2010 last month. Growing its presence has been the bigger problem for the chain that's second only to KFC in a specialty niche. Obviously, KFC isn't on the block, so Popeyes becomes that much more alluring as a privatization play.
  • Sonic (Nasdaq: SONC): The "drive-in" chain of burgers, slushies, and Frito pies has been in a rut for a few years. It wasn't a surprise to see a retiring board member replaced by a venture capitalist last month. The concept's retro charm makes it a natural candidate to follow the footsteps of Biglari Holdings' (NYSE: BH) Steak n Shake -- part of a larger company so that its cash flows can be used to grow in more appetizing areas.

The buyouts will continue, but investors need to be careful here. Buying into a company only because it's in a rut is a recipe for disaster. Make sure that the brands are strong, and that -- under the right circumstances -- the business can be made more valuable under the right managerial nudges.

You're looking for buyouts in fast food, not sellouts.

Which fast food chain do you think will go next? Share your thoughts in the comments box below.

Chipotle shares are recommended by Motley Fool Rule Breakers and Motley Fool Hidden Gems. The Fool owns shares of Biglari Holdings and Chipotle. Try any of our Foolish newsletter services free for 30 days. True to its name, The Motley Fool is made up of a motley assortment of writers and analysts, each with a unique perspective; sometimes we agree, sometimes we disagree, but we all believe in the power of learning from each other through our Foolish community.

Longtime Fool contributor Rick Munarriz does patronize Burger King often because it's a local company -- or at least used to be -- but he does not own shares in any of the companies in this story. He is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early. The Fool has a disclosure policy.