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IRVING, Texas—Companies rarely boast about cutting the shareholders’ dividend, so it was noteworthy this week when officials at Electronic Data Systems Corp. alerted reporters to one paragraph in a 27-page filing in which the company suggested it may do just that. These, however, are not ordinary times at EDS.

Chairman and chief executive Michael H. Jordan acknowledged Tuesday that the company has lost “a couple” competitions for new work because the customers were worried about EDS’ financial health.

EDS, a pioneer in making a business of running other people’s computers, is one year into a turnaround bid. It is trying to dig out from money-losing contracts and fending off questions about an ongoing investigation by the Securities and Exchange Commission.

EDS also is fighting to prevent ratings agencies from downgrading its debt to junk status, and that’s where the dividend cut comes in.

The company announced Monday that it may cut its quarterly dividend from 15 cents per share to as little as 5 cents per share, which would save up to $192 million. EDS said it may also raise more than $1 billion by issuing new stock or stock-based securities.

Jordan said the company would decide the dividend and stock issues in the next several weeks.

Joseph Vafi, an analyst with Jefferies & Co., estimated that issuing $1 billion in new stock would dilute the value of current shares by 10 percent to 12 percent.

“I don’t believe they would be talking about it if they weren’t going to do it,” Vafi added. “It’s not the kind of thing you bring up if you’re not going to follow through.”

EDS announced the possible dividend cut and stock issue after the market closed Monday. In trading Tuesday, EDS shares dropped $1.03, or 5.9 percent, to close at $16.48 on the New York Stock Exchange.

The announcement of a possible dividend cut and issue of new stock was a signal to the three major ratings agencies that are reviewing EDS’ investment-grade status. A spokesman said the company tipped off reporters so it wouldn’t look like EDS was burying bad news in a long SEC filing.

Company officials have long maintained that a downgrade wouldn’t add much to interest costs—analysts estimate about $5 million, compared to EDS’ annual revenue of $21.5 billion.

But analysts say a downgrade could frighten away customers worried about EDS’ longevity. They noted that several of EDS’ top competitors, including IBM Corp. and Computer Services Corp., have far-superior credit ratings.

Jordan declined to identify the companies who rejected EDS bids because of a possible downgrade and wouldn’t estimate the value of the lost work. He said that current customers are standing by EDS.

“We don’t lose our existing customers, but we want to make sure we’re absolutely 120 percent competitive for new projects,” Jordan said in an interview after a company event at the site of this week’s EDS Byron Nelson Championship professional golf tournament. “Any kind of negative about the company makes it difficult to win new clients.”

EDS reported $2 billion in cash and investments as of March 31, and Jordan said the company would double that by year end. The company is selling assets to raise cash.

Ratings agencies have been alarmed as EDS has cut its estimate of cash flow, largely because of problems with big contracts, especially an $8.8 billion deal to build a communications network for the Navy and Marine Corps.

In the first quarter, EDS lost $145 million—more than expected—on the Navy deal, and $94 million on another contract that analysts say is with Dow Chemical Co.

EDS is counting on an improving economy to lift corporate purchases of technology services. That appears to be happening, according to three other CEOs, including Michael S. Dell of Dell Inc., who appeared with Jordan at an EDS-sponsored symposium on leadership.

Dell said the economy is improving, “so companies are switching from a kind of cost orientation, cost control, to growth and productivity and remembering why we were supposed to be investing in IT (information technology) to begin with.”