Kroger (NYSE:KR) stock is finally showing some signs of life. In the aftermath of Amazon's Whole Foods acquisition announcement, shares of the company have underperformed the broader market, including a 9% decline on the day of the announcement itself.

Kroger's stock has finally halted its slide, mostly on the back of a ground-breaking deal with British online grocer Ocado to address its online order and delivery deficiencies. Kroger needed to show a strong quarter to change its narrative, and it did just that with its first-quarter earnings report.

Woman shopping in a grocery store/

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Strong earnings report set the table for investors

Kroger beat analyst estimates on both the top and bottom lines this quarter by reporting revenue of $37.5 billion and adjusted EPS of $0.73, versus consensus figures of $37.3 billion and $0.63. The EPS estimate was aided by a precipitous decline in the shares outstanding figure (more on this later), along with tax benefits.

However, what really drove the stock higher was management's guidance. Kroger expects same-store sales (excluding fuel) to grow 2.25% at the midpoint, higher than the consensus of 1.9%. Shares closed 10% higher on the announcement.

Are the bears right?

The bearish thesis against Kroger is that the Amazon/Whole Foods combination will eventually disrupt the grocery industry like Amazon has many other terrestrial retailers. Although I'm an Amazon bull, here's why the argument against Kroger could be overstated -- or at least premature:

Biased sample sizes: Stock-pickers/analysts tend to be a well-compensated group of people with well-compensated friends, so food prices are less important to them than the median grocery shopper. While Amazon has lowered prices at Whole Foods somewhat, it's still outside of many shoppers' budgets at this time. As a result, it's likely Wall Street analysts have been overly bearish on Kroger and its value proposition, making the stock cheap on a relative basis.

Assumption that grocery is like other retailers: Groceries -- particularly perishable items like fruits, vegetables, and meats -- are different from other goods. While I believe online shopping and delivery will comprise a larger portion of grocery sales going forward, most food shoppers will continue to do shop for groceries through traditional means. As such, e-commerce will most likely have a more muted effect on the industry than an industry like electronics or apparel.

Locations are an asset: As the largest U.S grocery chain, many analysts view Kroger as more susceptible to disruption via e-commerce. However, I feel it's as likely to be an asset, as digital shoppers will most likely shop at a grocer with a local presence. And with nearly 2800 stores, Kroger has more geographical/demographic reach than Whole Foods and its 465-store total.

It's true Kroger will most likely have to be more effective in monitoring its store portfolio and closing underperforming locations. But this is no different than any time since its founding.

Kroger thinks it's undervalued

Even with the recent rebound, shares of the company still appear valued for a day of reckoning that may never come. Shares trade at 13 times forward earnings, versus the greater S&P 500's valuation of 17 times.

The company has taken full advantage of its cheap valuation. In April the company announced a $1.2 billion share buyback authorization; this was on top of the $1 billion total already outstanding. At the time, $2.2 billion was 10% of the company's market cap.

In the first fiscal quarter Kroger used a significant portion of that total, buying $1.8 billion in shares to take advantage of the cheap valuation. As a result, the company has lowered its diluted shares outstanding 8.5% from the prior year.

Bagging it up

Just so we're clear, the grocery industry may be the toughest operationally. The margins are razor-thin, and generally only the better operators can make any profit via scale. Additionally, I feel Amazon will eventually make major headways into the market and ultimately be successful -- after all, it's Amazon.

However, at $600 billon-plus, the U.S. grocery market is more than ample enough to support multiple operators. While it's difficult to recommend any grocer as a lifetime holding (see prior paragraph), analysts' assumptions are keeping Kroger cheap, and providing an opportunity for value-oriented investors.

John Mackey, CEO of Whole Foods Market, an Amazon subsidiary, is a member of The Motley Fool's board of directors. Jamal Carnette, CFA owns shares of Amazon. The Motley Fool owns shares of and recommends Amazon. The Motley Fool has a disclosure policy.