With a deal in place to acquire Burger King (NYSE: BKC) for a tidy $24 a share, investors are handed the opportunity to quickly assess how its rivals are valued. Any rivals selling at a sharp discount to Burger King’s price are likely to see renewed investor interest as the M&A action heats up in the sector.

[Read: How Investors Should Handle the M&A Frenzy]

Private equity (PE) firms like to buy underperforming companies. In recent years, Burger King has seen McDonald’s (NYSE: MCD) and Yum Brands (NYSE: YUM) pull away in terms of same-store sales growth and sharply rising cash flow. Those companies are likely too large and too healthy to be of real interest to these turnaround specialists. For that matter, Chipotle Mexican Grill (NYSE: CMG) is far too healthy — and richly valued — to hold any appeal. [More on Chipotle — and why you should short it]

So I decided to take a look at three major chains that are underperforming and have major room for improvement.

A fair deal
Burger King is being acquired for about 11 times trailing cash flow — a fair multiple when you offset the company’s strong brand, yet slightly weaker operating metrics than rival McDonald’s, which trades for about 13 times trailing cash flow. The buyout is a bit unusual in that Burger King is not in distress and performing only slightly below expectations.

Rival Wendy’s/Arby’s Group (NYSE: WEN) has often been considered the most logical buyout candidate, thanks to its very weak results in terms of gross and operating profit margins. Wendy’s has been a moderate underperformer while Arby’s has been a severe underperformer. Presumably, a PE firm could come in and shake things up to bring the Wendy’s and Arby’s chains up to snuff. The trouble with that logic is that Nelson Peltz, a major shareholder, has already been working diligently to improve results without any success. PE firms may question whether they can do any better.

But if Wendy’s/Arby’s could once again operate as well as its peers, then shares would be quite undervalued at these levels. As the table below notes, Wendy’s enterprise value is less than its annual sales (or said another way, the shares have an EV/sales ratio below one), while McDonald’s trades for more than four times sales and Burger King trades for about 1.5 times sales. That gap is explained away by profit margins. If Wendy’s/Arby’s could boost margins up to the peer group, then every dollar of sales it generates would be more highly valued by investors (pushing up the EV/sales ratio).

The cheapest stock in the group

Perhaps the real bargain for PE firms would be Denny’s (Nasdaq: DENN), which I recently recommended. [Read: Five Beaten-Down Stocks with +100% Upside Potential]

Shares are out of favor right now thanks to a severe contraction in sales. Sales should stabilize by year-end, but even at these depressed levels, Denny’s profit metrics appear solid. Gross and operating profit margins are on par with Burger King and would likely be nicely higher if and when sales rebound. Most importantly, shares trade for less than seven times EBITDA, on an enterprise value basis. PE firms can presume that EBITDA can rise sharply as the economy improves, so they can offer to pay up to nine or 10 times trailing EBITDA under the assumption that the forward EBITDA multiples would be well lower.

#-ad_banner-#As I noted in my recommendation of Denny’s a few weeks ago, shares likely have significant upside down the road, so it’s unclear that a PE firm would be able to get shares below $4. Then again, they may not be inclined to pay above that figure in light of the still-slumping sales. So Denny’s may not come into play until results start to stabilize and turn up.

A turnaround play
DineEquity (NYSE: DIN), which operate the Applebee’s and International House of Pancakes (IHOP) franchises, is not seen as a clear rival to the burger chains. But like Burger King, it is seen as a typical PE target and that’s helping push shares up +7% on Thursday. DineEquity throws off large amounts of cash flow, which PE firms love to see when they look to load up their targets with debt.

The company is already sitting on more than $1.6 billion in debt, so there are limits to how much more debt it can take on, but annual free cash flow of more than $100 million compared to a market value of around $600 million implies that a PE firm could pay a +20% to +30% premium for DineEquity, keep it private for three or four years while paying off some debt with that free cash flow and then bring those restaurant chains public again once sales are on the upswing and investors see them as growth vehicles.

Action to Take –> Wendy’s/Arby’s has acknowledged receiving buyout interest in the recent past, though it’s unclear that any PE firm could swoop in while Nelson Peltz is in control. If there is a PE value to be unlocked, he’s got first dibs, though he has yet to make any such move in that direction. Denny’s looks like the most clear-cut acquisition candidate, and as soon as sales stabilize, perhaps in a quarter or two, then shares could heat up.