Supervalu — not long ago the nation’s third largest supermarket operator — would shrink even further if its Save-A-Lot chain is successfully transformed into an independent publicly traded company.

From an investors’ perspective, that’s just fine: Supervalu’s announcement Tuesday that it aims to spin off Save-A-Lot, a national discount grocery chain, sent the company’s shares soaring 10 percent. A decent Supervalu earnings report Tuesday also helped the stock.

Save-A-Lot, with 1,300 stores nationwide though only one in Minnesota, has been seen as Supervalu’s crown jewel for years. Analysts have regarded it as Supervalu’s best bet for growth, but also as a potential sale or spinoff candidate.

“We have long been believers in the attractiveness of the Save-A-Lot’s hard discount concept and the potential value of separating it from (Supervalu),” John Heinbockel, a Guggenheim Securities analyst, wrote in a note Tuesday. “That said, what is this business worth?”

A spinoff of Save-A-Lot would “unlock value” in Supervalu’s stock, as analysts put it. Save-A-Lot, which Supervalu has owned for more than 20 years, is in one of the few parts of the grocery business that could be called fast-growing.

It’s an ultralow price chain, which relies heavily on private-label goods, and competes particularly with Aldi, Wal-Mart and dollar stores. Save-A-Lot, like Aldi, has small stores that are about 15,000 square feet — ­compared to 50,000 square feet or more for a ­conventional ­supermarket.

“A separation of Save-A-Lot could allow for greater management focus on each of our wholesale, retail food and Save-A-Lot business units,” Supervalu CEO Sam Duncan told stock analysts in a conference call.

Save-A-Lot comprised $4.6 billion of the company’s $17.8 billion in sales during its last fiscal year. Supervalu was doing about $36 million in revenue before 2013 when the ailing company dumped its four largest grocery chains for $3.3 billion.

Without Save-A-Lot, about 75 percent of Supervalu’s business would come from food wholesaling. The rest of its sales would stem from a ­collection of regional chains like Cub. In essence, Supervalu would be a small player in the rapidly consolidating U.S. retail grocery business.

Supervalu has set no timetable for the disposition of St. Louis-based Save-A-Lot, and the company noted in a press statement that there is no assurance a spin off will happen.

Supervalu’s shares, which had fallen nearly 40 percent from a peak of $11.90 in April, were up 18 percent earlier Tuesday before settling at $8.14 per share, up 10.6 percent, or 78 cents.

Back in early 2013, even Save-A-Lot was flailing as Supervalu was caught in an ugly spiral that led to the sale of its four largest supermarket chains to Cerberus Capital Management.

Duncan became CEO soon after the Cerberus deal, and one of his first major management moves was to hire a new CEO for Save-A-Lot. By the end of 2013, Save-A-Lot was posting positive same-store sales again for the first time in nine months. (Same-store sales, a key gauge in retail businesses, account for the opening and closing of stores.)

Supervalu has beefed up Save-A-Lot’s offerings, including an improved produce selection and rolling out full-scale meat counters. “We have repositioned the brand,” Duncan told stock analysts. Save-A-Lot’s leadership “has done a great job in turning the business around.”

The one Save-A-Lot store in Minnesota is in St. Cloud and is owned by Coborn’s Inc. Nationally, about 900 Save-A-Lots are owned by licensees like Coborn’s, while the rest are corporate-owned by Supervalu. Florida, Ohio, Kentucky and Tennessee all have more than 100 Save-A-Lot stores.

Supervalu posted a net profit of $65 million, or 23 cents per diluted share, for the quarter ending June 20, which includes a $2 million one-time charge. That tops last year’s first quarter adjusted net earnings of $48 million, or 18 cents per share.

Stock analysts polled by Thomson Reuters were looking for earnings of 20 cents per share and sales of $5.39 ­billion. Supervalu reported first quarter sales of $5.41 billion, up from $5.26 billion a year ago.

Save-A-Lot had sales of $1.41 billion, up 3.8 percent from a year ago. Still, same-store sales growth was only 0.6 percent, below analysts’ expectations.

Supervalu’s conventional grocery business, which includes Cub, saw same-store sales drop 0.3 percent, the first decline in five quarters. However, because of new store openings, overall sales rose from $1.43 billion a year earlier to $1.47 billion. Supervalu’s wholesale business posted $2.46 billion in sales, up from $2.42 billion a year earlier.