Communications Satellite Corp. yesterday reported a drop of 13.9 percent in second-quarter earnings. Bank of Virginia Co. and Avemco Insurance Co. also reported quarterly drops, but Virginia Electric & Power Co. profits increased during the latest 12 months.

Net income for Comsat during the quarter ended June 30 was $9.1 million ($1.14 a share), compared with $10.6 million ($1.32). Revenues were $72.2 million, up from $63.7 million.

"Among the significant factors in the decrease were planned increases in costs related to Satellite Business Systems, a decline in revenues from service to the U.S. Navy through the Marisat global maritime communications system and costs associated with new ventures including Comsat General TeleSystems Inc. and Satellite Television Corp.," the company said in a statement. Marisat, SBS and the telesystems and television companies are divisions of Comsat.

Comsat's first-half net income dropped to $19.0 million ($2.38) from $22.5 million ($2.81). Revenues were $142.2 million, up from $123.7 million.

Virginia Electric and Power Co. yesterday reported an increase in net income for the 12 months ended June 30 from $196.7 million ($1.70 a share) to $201 million ($1.60).

Vepco President William W. Berry attributed the company's drop in earnings per share to the increasing numbers of outstanding shares of common stock, substantial expenses from the upgrading of fossil plants and the lack of growth in sales experienced in the past. He added that the company's inability to operate certain nuclear units because of federal requirements "continues to have a substantial impact on earnings."

Revenues for the 12 months were $1.97 billion, compared with $1.52 billion for the previous 12 months.

Bank of Virginia Co. reported a drop in earnings for the second quarter from $3.5 million (69 cents a share fully diluted) to $3.6 million (62 cents). The earnings were affected by a $22,740 securities gain during the second quarter this year and a $326,202 securities loss last year.

The decline in earnings for the quarter "was caused by a net yield margin squeeze that began in the third quarter of 1979," the company said. "This squeeze occurred because of the failure of asset yields to keep pace with the rising cost of money and was due to the high proportion of earning assets such as investment securities, consumer loans and mortgage loans where yields were either contractually fixed or limited by usury law."

First-half earnings were $6.0 million ($1.04) after securities losses of $839,113, compared with $6.8 million ($1.35) after securities losses of $696,489. Assets on June 30 were $2.4 billion, up 8.3 percent from $2.2 billion last year. Total deposits were $1.7 billion, compared with $1.6 billion.

Avemco Insurance Co. of Bethesda reported second-quarter earnings of $619,000 (24 cents a share), compared with $1.0 million (42 cents) a year earlier. Revenues were $6.1 million, up from $4.8 million.

First-half earnings were $1.682 million (67 cents), up slightly from $1.679 million (67 cents). Revenues were $11.8 million, up from $9.0 million.