Profits fell sharply at the New York Times Co. last year due to the long strike of its flagship newspaper in New York, while earnings rose modestly to record levels at CBS Inc., whose principal subsidiary is a television network that is fighting for viewers with industry leader ANC.

The New York Times was closed by an 88-day pressmen's strike from August to November last year, leading to a decline in 1978 profits to $15.6 million ($1.32 a share) from $26.1 million ($2.27) in 1977. The Times Co. estimated the strike cost $1.30 a share.

In the fourth quarter alone, Times Co. earnings plummeted to $2.5 million (21 cents a share) from $7.9 million (69 cents) in the same 1977 period. Revenues for the year declined to $492 million from $511 million and, for the quarter, fell to $115 million from $143 million.

Chairman Arthur Ochs Sulzberger was upbeat in his assessment yesterday, stating that The Times newspaper had become one of the most automated in the nation as a result of union settlements last year.

"With labor peace restored, and with manning reductions and technology serving to cut The Times' expenses, we have every reason to expect the company's steady upward profit trend to resume," he said.

Sulzberger, who also is publisher of The Times, said combined operating profits of magazines, broadcast stations, small-city papers and other subsidiaries had jumped 25 percent last year, providing evidence of "fundamental strength and growth potential" despite the New York newspaper situation; The Times itself posted a loss of $12.6 million for the year on revenues of $266 million.

Circulation of the daily newspaper has rebounded strongly, in contrast with some dire forecasts about New York newspaper readership. Sulzberger said daily sales will be at comparable 1978 levels this spring, with Sunday circulation back to its previous levels later in the year.

One factor leading to slower Sunday sales growth was a Jan. 7 boost in newsstand prices in the New York area to 85 cents from 75 cents.

CBS Inc. posted record earnings of $198 million ($7.15 a share) in 1978 compared with $182 million ($6.50), an increase of 9 percent. Revenues were up 16 percent to $3.2 billion. For the final quarter, CBS earned $56 million ($2.04 a share), up 12 percent from $50 million ($1.82), and sales jumped 17 percent to $987 million.

Chairman William Paley and President John Backe said all major divisions posted record revenues and profitability, although CBS-TV earnings gains were "modest as a result of continued substantial investments in television programming and program development designed to improve its competitive position." Overall broadcast division earnings were paced by company-owned stations.

Publishing contributed most of the CBS profit growth last year (up 45 percent), while CBS records gained 12 percent.

Associated Press also reported the following :

Warner Communications Inc. posted a 39 percent gain in fourth-quarter earnings, announced a 33 1/3 percent dividend boost and said it is splitting its common stock 4 for 3.

The new stock will be distributed on the basis of one share for every three shares currently held. While the number of shares is increasing by one-third, Warner Communications will continue to pay a 25-cents-a-share common stock dividend, the company said.

Warner's split is effective March 30 for shareholders of record on March 9; its new dividend is payable May 15 to shareholders of record April 16.

In the fourth quarter, Warner earned $27.5 million ($1.88 a share), up from $19.9 million ($1.48) a year before. Revenues for the quarter rose from $398 million in 1977 to $405 million in 1978.

For the year, the company recorded a profit of $87.1 million ($6.11), up from 1977 earnings of $70.8 million ($5.30). Revenues rose from $1.1 billion to $1.3 billion.