Kroger's (NYSE:KR) solid first-quarter results earlier this month made it clear Amazon.com isn't slowing the grocer down, despite worries that the e-commerce giant's acquisition of Whole Foods would take a toll on traditional grocers, Kroger's quarterly comparable-store sales growth rates have been trending upward over the past year. And Kroger's higher-than-expected revenue and earnings per share in its first quarter reaffirmed the company is not only holding its own but growing nicely.

Kroger's 3.4% revenue growth, 1.4% same-store sales growth, and 26% adjusted earnings-per-share growth in its first quarter undoubtedly speak to the company's resilience amid a changing retail landscape. But for investors who want to go a little deeper and learn about what's going on behind the headline numbers, Kroger's first-quarter earnings call featured some interesting takeaways.

Here are several key excerpts from Kroger's first-quarter earnings call.

A woman using her smartphone while shopping for groceries

Image source: Getty Images.

Private-label brands are crushing it

One area Kroger has been seeing outsize growth is with its own brands. Kroger CEO Rodney McMullen put the company's success with its private-label brands into perspective:

Kroger customers choose to put more of our brands in their baskets and pantries every day. Our brands grew faster than the national brands in nearly every department and gained significant share overall. In the first quarter, our brands made up 28.7% of unit sales and 26.7% of sales dollars. In fact, our brand set the record for the highest ever retail dollar share in our history.

Overall, Kroger's private-label brands saw a 5.1% year-over-year increase in sales and 3.4% increase in unit growth. This was notably driven by a standout performance from Kroger's Simple Truth and Simple Truth Organic lines, which saw "double-digit growth again," said McMullen.

Don't overlook this upcoming tailwind

Kroger's late-2017 launched Restock Kroger initiative, which is essentially a strategy to improve its stores' operations and the customer experience, is off to a great start, according to management. But it will take some time for some of the Restock Kroger's strategies to begin paying off. One good example is the company's efforts to better utilize the space in its stores. While it has optimized 30% of the 600 stores it plans to optimize in 2018, management says space optimization will be a headwind before it is a tailwind, since the process of shifting items around can deter shoppers.

But investors won't have to wait long for Kroger to benefit from space optimization strategies, explained Kroger CFO Mike Schlotman.

[A]s we continue to execute our space optimization strategy, that certainly creates a headwind [for same-store sales growth] today. We think that headwind will continue to mitigate throughout the second quarter, it'll continue to be headwind. And, by the time we get to late third quarter, we would expect that to be a tailwind...

McMullen also commented on how space optimization will morph into a tailwind, noting, "By [late in the third quarter], we will have more stores completed and maturing than in process or not yet started, which is why it'll start to be a benefit to sales later in the year."

Kroger's top- and bottom-line growth recently are certainly encouraging. But Kroger's solid execution is evident elsewhere, too -- namely its strong digital sales growth, promising performance fro its private-label brands, and its efforts related to its Restock Kroger initiative.

John Mackey, CEO of Whole Foods Market, an Amazon subsidiary, is a member of The Motley Fool's board of directors. Daniel Sparks has no position in any of the stocks mentioned. The Motley Fool owns shares of and recommends Amazon. The Motley Fool has a disclosure policy.