Aluminum Co. of America, citing rising costs, said yesterday its second-quarter earnings were 45 percent below profits in the same quarter last year.

The company said it earned $81.5 million ($1.09 a share) on sales of $1.305 billion in the quarter compared with profits of $148.8 million ($2.08) on sales of $1.299 billion. The 1980 second-quarter results included a gain of $27.9 million (39 cents) from the sale of real estate.

The the first six months, Alcoa's net income was $182.6 million ($2.46) compared with $292.3 million ($4.11) for the first half of 1980. Sales for the six months were $2.604 billion in 1981 and $2.593 billion in 1980.

Bank of America reported second-quarter net earnings of $122.5 million (83 cents a share) versus $174 million ($1.18) for the same period last year. The six-month net was $231 million ($1.57) compared with $308.2 million ($2.10) a year earlier.

CBS Inc. said yesterday its earnings in the second quarter fell 22.8 percent to $41.9 million, as it increased spending to develop cable television, home video and theatrical film operations.

CBS reported profits rose for its broadcasting operations, which include a television and radio network and a group of company-owned stations.

Earnings for the second quarter came to $1.50 a share on record revenues of $998.2 million, compared with earnings of $54.3 million ($1.94) on revenues of $971.8 million in the same 1980 period.

For the first six months of the year, CBS had profits of $56 million, down 16.8 percent from the $67.3 million reported in the first half of last year. Earnings slipped to $2 a share from $2.41, although revenues rose to $1.99 billion from $1.94 billion a year ago.