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General Mills is buying its way into the natural and organic food market as it wrestles with stagnating demand for its traditional packaged items.

The company said Monday that it has agreed to purchase Annie’s Inc., the firm known for its natural macaroni and cheese, for $820 million. The deal is the largest to date in a series of natural and organic acquisitions for General Mills.

The company that sells Lucky Charms, Toaster Strudel and Totino’s pizza rolls will pay $46 per share, a 37 percent premium on Annie’s closing price of $33.51 on Monday. The price reflects how important it is for the Golden Valley-based packaged food giant to gain a better foothold in the natural and organic market.

“Annie’s is one of the leaders in the natural and organic space. That’s where consumers are moving, and Mills wants to be better represented there,” said Jack Russo, an analyst with Edward Jones in St. Louis. “For these little growth companies that can boost your presence in an area that you want to have a bigger presence in, you’ve got to pay for it.”

Annie’s annual sales of $204 million would bring General Mills’ natural and organic sales to about 3 percent of total revenue. The company’s previous natural and organic acquisitions include Cascadian Farm, Larabar and Food Should Taste Good. Together those brands account for $330 million of the company’s $17.9 billion in annual sales.

Erin Lash, an analyst with Morningstar in Chicago , said that with Annie’s representing a relatively small piece of General Mills’ overall business, the purchase price “strikes us as quite rich at first blush,” said. She said the deal highlights the “muted growth prospects within the packaged good landscape.”

Given the growth prospects for natural and organic food, however, Lash views the purchase as a positive for General Mills.

“We also think the added distribution channels through which Annie’s products are sold could open new doors for General Mills,” she wrote in a note to investors. “Management has proved to be prudent acquirers in the past, and we don’t expect this deal to be any different.”

Headquartered in Berkeley, Calif., Annie’s Inc. is named after Annie Withey, who created an upmarket popcorn in her Boston kitchen in the 1980s called Smartfood. The popcorn was later acquired by Frito-Lay, and Withey and then-husband Andrew Martin went on to start Annie’s Homegrown in 1989.

They marketed her macaroni and cheese as natural, with no preservatives or dyes. In the early days she answered letters from customers and handed out cups of white cheddar macaroni at ski lodges in New England.

The company was acquired by investors in 1999 and now markets more than 145 products in more than 35,000 retail locations in the United States and Canada. Withey, who still lives in Connecticut, retains the title “inspirational president.”