The Washington Post Co. projects that net income in 1980 will "be down somewhat from last year" when the company reported income prior to an accounting change of $43 million ($2.75 a share), according to Chairman and chief executive Katharine Graham.

Graham, interviewed in the offices of the company's Newsweek magazine, declined to comment on analysts' estimates that Post Co. 1980 earnings would be about $2.35 a share. "We're feeling the recession, but not unduly," Graham said. She added that the earnings decline "is mostly due to investments we're making in the future," including the launching of Inside Sports, a monthly magazine, and the company's 30 percent ownership of the Bear Island newsprint mill in Virginia.

Fourth-quarter earnings won't show the extreme variations of this year's third quarter, when net income dipped 5 percent, Graham said. While declining to make a specific projection for 1981, she said that "with any kind of economy next year, we ought to have a better year."

Losses of Inside Sports, which are expected to amount to nearly $12 million before taxes in 1980, will be "substantially less in 1981," she stated. Graham also said the company, which estimates a $4.5 million pretax loss this year from its share of the Bear Island mill, expects to make a "small profit on that investment next year, beginning perhaps in the 1981 first quarter."

Graham said that the problems with Inside Sports have "been more with process than with product, which I think is excellent." The sports magazine was launched last April "in the credit crunch, and that may have been the worst month in six years to launch a newsstand magazine," Graham said.

Inside Sports failed to meet its goal for newsstand circulation, so the Post Co. attempted to build circulation by soliciting a larger number of subscribers than anticipated, thus incurring extra expenses. Graham said the magazine's circulation in the six months ending Dec. 31 will average 500,000, and Inside Sports plans to add another 50,000 purchasers by April. Advertising in Inside Sports' December 1981 issue reached 38 pages, the largest amount since its launch issue, she said.

On other topics, Graham said:

The Post Co. continues "to search outside and inside the company" for a new president and chief operating officer, to succeed Mark Meagher, who has resigned effective the end of this month. Graham said her son, Donald E. Graham, was not being considered for the position. Donald Graham, who was named publisher of The Washington Post in January 1979, has "taken on a very big job which is fully occupying him at the moment," she said.

Plans for Newsweek Focus, a magazine that would provide comprehensive coverage of subjects in the news, are "on hold." Results of a test issue last May "were successful enough that we would have gone ahead in normal conditions but not during a recession," Graham said.

The Post Co. sees opportunities in providing programs for broadcasting, but the company believes it may have waited too long to become an owner of a cable television system.