When McDonald’s CEO Jim Skinner retires this summer, he will be leaving behind a company that by all accounts has had a decade of successes. Newly anointed CEO Don Thompson has been a big part of that.

Thompson, for example, led the company’s foray into specialty coffee drinks and new menu offerings, helped it weather the recent economic downturn, oversaw redesigned stores and improved customer service (including double-lane drive-thrus), and pushed for greater international expansion, according to an article in The Wall Street Journal. Thompson is currently McDonald’s president and chief operating officer.

The question for Thompson is whether to stay the course — and hope that McDonald’s exceptional performance over the past decade won’t begin to lag — or try some new initiatives that could ensure even greater forward momentum.

Wharton management lecturer Adrian Tschoegl advises him to stay the course. “In terms of geographical expansion, McDonald’s is pretty much everywhere they want to be,” he says. They are absent in most of Africa, but “they have good reasons for not being there. One is that they would need to maintain the quality of the food they sell, and that can be difficult. It requires strong infrastructure, good storage facilities, reliable suppliers, well-functioning ports and so on. Plus there are issues around political risk.” Adding a store in China in a second-tier city “would probably mean more to the bottom line than adding stores in some capitals in Africa,” says Tschoegl.

In addition, the company “got into trouble overexpanding in some of their markets in both the U.S. and abroad,” Tschoegl notes. “That is what Skinner helped turn around in 2002 by focusing on two things: the mechanics of delivery, meaning operations, and upgraded product offerings.” McDonald’s has been abroad long enough that it now faces domestic fast food competitors — not just American firms like Burger King, Wendy’s and Domino’s Pizza, Tschoegl adds. “So they can no longer survive by being different and exotic. They have to be better. One way is through [maintaining] operational excellence, and they have done that.” 

He points to other McDonald’s initiatives already in the works, including McCafe, a competitor to Starbucks, that is being introduced in the U.S. and internationally. And in Europe, McDonalds is starting to move “just a tad up-budget. They are not planning to roll out tablecloths and candles, but some of the food offerings seem to be much more tailored” to that part of the world. “They even hired a chef in Europe to help them out.”

Indeed, an article in February in The Wall Street Journal noted that in France, McDonald’s is about to offer the McBaguette, a burger served on a baguette and topped with French-made cheese and mustard. The goal is to appeal to a slightly more affluent customer, one for whom high-quality bread is an important part of the menu.

Given all this activity, “my opinion is that Thompson could do worse than continue on with the current agenda,” says Tschoegl. “It has been working well for the last 10 years.”  

Others seem to agree. An article in Fortune posted on CNN.com suggested that “Thompson’s biggest challenge as CEO will be to maintain the momentum that took hold on Skinner’s watch,” and quoted the new CEO’s description of Skinner as “one of the strongest mentors I’ve ever had. He’s given me tremendous room in terms of the day-to-day business of McDonald’s.” The article also referred to an earlier profile of Skinner in which it described “his leadership as having brought on nothing short of a Golden Age for the Golden Arches.” Profits in 2011 were $5.5 billion, “more than double what they were in 2004, the year Skinner took over. The stock reached an all-time high of $102.22 on January 20.”