Time Inc., the nation's largest magazine firm, has reported lower profits in the latest quarter and for 1980, reflecting the impact of recession on the publishing business.

For the final quarter of 1980, Time's profits fell to $39.2 million ($1.39 a share) from $43.1 million ($1.54) a year ago, although revenues rose to $818 million from $717 million.In the full year, Time earned $141.2 million ($5.02) compared with $143.9 million ($5.15) as revenues increased to $2.9 billion from $2.5 billion.

President J. Richard Munro said that, despite the economic slowdown, which "severely depressed" Time's lumber and building materials subsidiaries, other businesses did better than expected. He blamed the decline in profits on high interest costs; the launching of a new science magazine, Discover; and a restructuring of a film subsidiary.

He said profits increased at the Time-Life Books division in Alexandria; in paper operations; and at American Television and Communicatins Corp. and Home Box Office, Time subsidiaries engaged in cable television. Time's cable firms now serve 1.3 million subscribers through 125 cable TV systems.

The Time statement provided no information on 1980 operations of The Washington Star, which the New York-based publisher owns.