The Washington Post Co. intends to set a new earnings-per-share record this year, despite the effects of its $350 million purchase of 53 cable television systems, Post Chairman Katharine Graham told shareholders at the company's annual meeting yesterday.

"That is an extremely ambitious goal. It will be a real challenge to achieve it in today's difficult advertising environment," she said.

Last year, The Post earned $102 million, or $7.73 per share, excluding gains from the sale of some of its interests in the SportsChannel regional cable network and in cellular mobile telephone franchises. To exceed that earnings-per-share record, The Post Co. will have to offset the costs of the cable systems purchase, which are equivalent to a reduction in earnings of about $1.40 a share this year, Graham said.

Graham and Donald E. Graham, publisher of The Washington Post, faced an array of questions including inquiries about other media acquisitions, drug screening of employes and the company's attitude toward a possible stock split. Longtime critic Reed Irvine of the media watchdog group Accuracy in Media challenged The Post's coverage of national security issues.

In response to one question, Katharine Graham reiterated that The Post does not tolerate the use of drugs on the job and offers assistance to those who wish help with drug-related problems.

"We have considered and will continue to consider other measures that seem appropriate, including the possibility of drug screening tests on a pre-employment basis," she said. "In fact, such a pre-employment screening device has been implemented in one division, Post-Newsweek stations."

Although the price of Post stock is one of the highest on the American Stock Exchange, "we don't see any problem in the trading of the shares," she said. "So we aren't contemplating a split right now."

Asked about The Post's interest in bidding for the Louisville Courier-Journal, Katharine Graham said, "We are looking at it and appraising its value and are interested in it in a general way, as at least six or eight other papers are."

The Post added more than $400 million in debt in the past year to finance the cable systems purchase and other new businesses. The pace of acquisitions is expected to slow this year and next.

"We would contemplate another large newspaper somewhere, some time," she said. "While our company is willing to pay a very full price for a large newspaper someday, we are not willing to pay a price that would be unreasonable and too large for our shareholders from the point of view of returns. . . . There's always one person at every auction who will step up and bid as much as $40 million more than the rest of us, which happened in Des Moines.

Post shareholders elected three new directors: Barbara Scott Preiskel, the first black to serve on the board, who is a former senior vice president and general counsel for the Motion Picture Association of America; William J. Ruane, cofounder and chairman of Ruane, Cuniff & Co., an investment management firm, and George W. Wilson, publisher of the Concord (N.H.) Monitor and vice chairman of the American Newspaper Publishers Association.

Two Post directors did not stand for reelection: Warren E. Buffett, chairman of Berkshire Hathaway Inc., resigned in January when he became a director of Capital Cities/ABC Inc., and Richard M. Paget, president of the consulting firm Cresap, McCormick and Paget, became ineligible for renomination upon reaching 72 years of age.