As customers flock back to stores for their espresso fix, Starbucks Corp. Chief Executive Howard Schultz seems confident the chain can navigate its latest challenges, such as the rising coffee-bean costs and stepped-up competition from lower-priced competitors.

After Starbucks’ rapid expansion a few years ago—to the detriment of customer service—the Seattle company retrenched. It closed hundreds of stores, pared suppliers and introduced more efficient ways to grind beans and pull espresso shots. The changes helped it turn the corner: Earnings rose 44% during the holiday quarter, with customer visits up 5% and average customer checks up 2% from a year earlier.

Mr. Schultz recently spoke about how the company— which is approaching its 40th birthday—is evolving, how it’s handling the volatility in commodities prices and whether McDonald’s Corp.’s coffee has made a dent in its business.

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