The turnaround at slimmed-down grocery purveyor Supervalu is chugging along nicely, particularly at the firm’s Save-A-Lot discount chain, where sales have perked up at a surprisingly high rate.

Eden Prairie-based Supervalu Inc., at a 40-year nadir a year ago, has also shown improvements at its traditional supermarket chains, which include Cub Foods, since new CEO Sam ­Duncan took charge in January.

But Supervalu still faces a challenge after years of losing out to the Wal-Marts and SuperTargets of the grocery world. Indeed, despite announcing rosy results for its second fiscal quarter Thursday, Supervalu’s same-store sales — a key financial gauge — remained negative, a long-standing problem.

“While our end goal won’t be achieved overnight, I am encouraged with our results this quarter,” Duncan said in a statement.

The company posted $40 million in net profit for the quarter compared to a net $111 million loss a year earlier. Its adjusted earnings per share of 13 cents topped the 11-cent consensus forecast of analysts polled by Thomson Reuters. Sales clocked in at $3.95 billion, also above analysts’ estimates of $3.88 billion.

Even so, Supervalu’s stock tumbled 33 cents, nearly 4 percent, to close Thursday at $8.07.

The drop seemed to be because of Supervalu’s decision to increase investments in its traditional supermarkets in order to get them up to speed with competitors. Those investments, Supervalu executives said during a conference call with analysts, will lead to a “modest” drop in operating profits. They didn’t say how much, and Wall Street isn’t fond of such uncertainties.

Supervalu earlier this year sold its five largest grocery chains, including Albertsons and Jewel-Osco, to Cerberus Capital to concentrate on its wholesale and distribution business, its five traditional, regional grocery chains and its national Save-A-Lot banner.

Save-A-Lot, which has more than 1,300 stores, is Supervalu’s crown jewel in terms of potential sales and profit growth. During the second quarter, same-store sales at company-owned Save-A-Lot outlets were up 4.6 percent over a year ago — “very strong” growth, according to a research report from Meredith Adler, a Barclays analyst.

Indeed, the second quarter marked the first such growth of any kind at company-owned Save-A-Lot stores in six quarters, Bruce Besanko, Supervalu’s chief financial officer, said during a conference call. Same-store sales account for newly opened and closed stores.

Including Save-A-Lot’s many licensees, the chain’s overall same-store sales were down 0.3 percent, still an improvement over recent quarters. At Supervalu’s traditional retail grocery chains, which include Cub, same-store sales were down 0.9 percent over a year ago. But that was better than analysts expected. And it marked a clear improvement, considering that same-store sales in the first quarter were down 3 percent over the same time a year ago.

Duncan noted that Supervalu invested more than it had originally expected in its traditional stores during the quarter. The investments, including “labor hours to better serve the customer” are aimed at raising the stores’ operating standards, Duncan said.

“Our aisles are easier to navigate and quite honestly the overall store base simply looks more inviting,” he said. But Besanko noted that operating profits for the rest of Supervalu’s fiscal year will be modestly lower, primarily because of investments to drive sales at traditional supermarkets.

In Supervalu’s third major business group, wholesale grocery, sales were $1.84 billion, down 1.6 percent. The downturn was primarily due to lower sales to existing supermarket customers, although the segment’s operating earnings were a bit above last year’s levels.