The grocery business is being disrupted, but you wouldn't know it from Kroger's (NYSE:KR) first-quarter report. The company managed to increase sales and profits, and it guided for solid sales growth throughout 2018. This is all despite an ongoing price war in the grocery industry, with Walmart, Target (NYSE:TGT), and Costco pushing prices down, as well as Amazon's (NASDAQ:AMZN) entry into the industry via its year-ago acquisition of Whole Foods.

Solid results

Kroger's first-quarter sales rose 3.4% year over year to $37.5 billion. Excluding fuel and the impact of the company's divestiture of its convenience store business, sales rose 2.8%. Most of this growth was driven by existing stores, with identical sales excluding fuel up 1.9%. Identical-supermarket sales, which exclude the specialty pharmacy and ship-to-home businesses, rose 1.4%. Given the pricing pressure in the industry, that's a good result.

A shopping cart in a grocery store.

Image source: Getty Images.

Kroger expects the rest of 2018 to look a lot like the first quarter. The company sees identical sales excluding fuel growing by 2% to 2.5% for the full year. Adjusted earnings per share shot up nearly 26% year over year in the first quarter, and the company raised its earnings guidance for the full year. Kroger now expects 2018 adjusted earnings per share between $2.00 and $2.15, up from a previous range of $1.95 to $2.15.

Kroger's digital initiatives are helping to drive some of its sales growth. The company's digital sales surged 66% year over year in the first quarter, although the size of that business is likely still small. Kroger's ClickList, an online grocery ordering and pickup service, is live at over 1,000 stores. This is similar to initiatives from other grocers, including Walmart's online grocery pickup service.

Kroger is also driving growth by pushing its own brands. The company's private-label brands achieved their highest-ever retail dollar share during the first quarter, with the Simple Truth and Simple Truth Organic brands growing by double-digit percentages. Private-label products often carry higher gross margins for retailers than national brands, so private-label sales growth can provide a nice boost to the bottom line.

What could go wrong

Kroger is holding its own in the grocery wars, if its first-quarter results are any indication. But the company is facing a slew of threats. Beyond the ongoing pricing pressure, aggressive initiatives from competitors could take a bite out of sales.

One example is Target's Restock service. Restock offers shoppers next-day delivery of home essentials, including non-perishable groceries. Target slashed the fee for Restock earlier this year, and it eliminated the fee for holders of its store credit and debit cards. The lower fees combined with Target's general shift toward lower prices makes Restock a potent threat.

Amazon's Whole Foods is also a threat, although the e-commerce giant hasn't yet done anything too drastic. Amazon has cut prices and started offering additional discounts to Prime members, but Whole Foods remains an expensive grocery option. The company has also been rolling out free grocery delivery for Prime members from some Whole Foods stores, but the chain's small footprint could hamper that effort.

Still, Amazon could be more aggressive in the future, cutting prices even more or buying up more grocery chains to expand its physical presence. Amazon appears dead-set on gaining share in the grocery space, and Kroger will need to fight hard to protect its business.

Kroger's own push into online grocery is helping the company grow its sales, but these types of services are quickly becoming table stakes in the grocery industry. Kroger will need to stay ahead of the competition to keep winning. Given its first-quarter results, Kroger is clearly doing something right. But the grocery wars are far from over.

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