Fast food CEO: McDonald's has problems. We don't

Cheaper gas, a rosier jobs picture and charbroiled burgers: this is the recipe for strong sales at CKE Restaurants, the privately held parent company of fast food chains Carl's Jr. and Hardee's.

"I won't give you exact numbers, but our sales have been very good since about the middle of June," CEO Andy Puzder told CNBC in a phone interview.

CKE went private in mid-2010 after affiliates of private equity firm Apollo Management bought the chain. Before the takeover, its sales were shrinking. An affiliate of private equity firm Roark Capital Group acquired it in 2013.

Not everyone in the fast-food landscape is delivering good numbers. Burger behemoth McDonald's recently reported its worst U.S. monthly sales in more than a decade. As part of its domestic turnaround strategy, it plans to pare down its menu, increase customization and give local operators more autonomy.

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Overall though, the fast-food category is growing, albeit tepidly in part due to McDonald's woes. For the year ending October 2014, fast food visits were flat while spending rose 3 percent, according to market research firm NPD Group.

Despite trouble at the Golden Arches, Puzder says other competitors aren't in the same boat.

"The tendency is to look at McDonald's," Puzder said. "I speak to some of the other CEOs in the industry, and most of the rest of us aren't seeing the problems that McDonald's is seeing."

During the third quarter, Burger King's comparable sales rose 3.6 percent in the U.S. and Canada while Wendy's saw its North America company-operated same-restaurant sales increase 2 percent and franchise sales rise 0.5 percent.

Drive-in restaurant Sonic reported system same-store sales jumped 4.6 percent during its fiscal fourth quarter.

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Rather, Puzder sees most of McDonald's problems as endemic to the chain.

"In fact, I think most people are experiencing the benefits of lower gas prices, which is putting more cash in people's pockets," he said.

Part of Carl's Jr. and Hardee's strategy in staying relevant to consumers, particularly to millennials, is delivering new items, like the "natural" burger that Carl's Jr. will debut Wednesday. The burger represents the first all-natural grass-fed, free-range beef patty without added hormones, antibiotics or steroids from a major fast food company.

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In testing, the burger ranked tops in overall opinion of the burgers Puzder has tested in his tenure at the helm. With a $4.69 price tag, it's roughly comparable to the price of Carl's Jr.'s premium Black Angus Third Pounder.

The company balances its menu with more indulgent items like its half-pound mile high cheeseburgers to cater to its core audience—what Puzder describes as "young, hungry guys."

"We do make products that meet consumer desire to eat more healthily as well as products that are just plain good," he said.