How much free advertising did Oprah Winfrey’s deal with Weight Watchers bring? More than 1 billion media impressions, the company said.

Following Winfrey’s agreement to invest in Weight Watchers International and endorse the program in October, the company got a surge of free publicity, according to a regulatory filing on Wednesday. Each impression represents a time that a viewer was exposed to a mention of Weight Watchers.

The company is counting on Winfrey to help turn around its ailing business, but it’s hard to gauge the deal’s financial impact so far. Weight Watchers posted a loss of 3 cents a share in the fourth quarter, excluding some items. The program’s active subscribers fell 4.8 percent in the period from a year earlier.

It could have cost Weight Watchers as much as $17.5 million to generate 1 billion media impressions, depending on where the advertisements were placed, according to calculations by Apex Marketing Group.

“She definitely has the Midas touch,” said Eric Smallwood, a managing partner at Apex.

As part of their agreement, Weight Watchers sold roughly a 10th of the company to Winfrey for about $43.2 million. The company also granted Winfrey the right to buy 3.5 million shares at a price of $6.97 apiece.

The stock rose 9.8 percent to $13.79 on Thursday, valuing her 10 percent stake at about $88 million. That means Winfrey has more than doubled her investment, not including the options.

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