Federal Realty Investment Trust has reported record profits for 1977 and acquired full ownership of a shopping center in Elizabeth City, N.C.

Earnings for the year rose 48 percent to $1.76 million ($1.29 a share) compared with $1.19 million ($1.16, on fewer shares outstanding) in 1976. Total revenues rose 16 percent to $6.6 million.

In the fourth quarter, the Chevy Chase-based real estate investment trust posted profits of $590,136 (43 cents) compared with $434,000 (34 cents) in the 1976 period.

Federal Realty also purchased for $500,000 the remaining 25 percent interest in Southgate Mall, Elizabeth City, formerly owned by S.L. Nusbaum & Co., of Norfolk, giving The trust full ownership of the 225,000-square foot complex.

With assets of more than $31 million, Federal Realty owns 5 apartment projects in the D.C. area and 11 retail malls in Virginia, Maryland, Illinois, Michigan and North Carolina.

Trustees Samuel J. Gorlitz and Daniel M. Lyons attributed the 1977 gains to income from the malls.

Scope Inc., an electronic technology company in Reston, reported record sales and profits for the fourth quarter and all of 1977.

In the recent quarter, Scope earned $818,000 (67 cents a share), up 38 percent from $592,000 (49 cents) in the same period of 1976. Sales were up 40 percent to $12.6 million.

For the year, profits rose 24 percent to $2.7 million ($2.20 a share) compared with $2.1 million ($1.78) in the previous period. Sales increased by 25 percent to $42.5 million.

Chairman William C. Schaub said Scope boosted its outlays for research and development by 30 percent to $2.2 million in 1977. He attributed the firm's gains primarily to sales growth of distribution systems, mobile radios and material handling equipment.

Financial Security Group Inc., a property-casualty insurance holding company affiliated with International Bank, reported record profits in 1977 of $6.3 million ($2.10 a share) compared with $4.4 million ($1.48) in 1976, Fourth-quarter earnings were $2.2 million (74 cents) vs. $1.6 million (54 cents).

President Robert D. Edison said the 41 percent increase in earnings last year reflected record profits from underwriting insurance of $5.1 million, coupled with a 10 percent gain in writen premiums and an 11 percent gain in investment income.

Assets a year's end were up 13 percent from 1976 at $173.5 million. Financial Security owns Hawkeye-Security Insurance, Northeastern Insurance Co. of Hartford and United Security Insurance.

Washington Homes Inc., an Oxon Hill home builder, reported a loss of $87,000 in the six months ended Jan. 31 compared with profits of $851,992 (66 cents a share) in the comparable period a year ago. Sales dipped to $15.4 million from $17.6 million.

For the quarter ended Jan. 31, Washington Homes earned $16,194 (1 cent) vs. $261.473 (20 cents) as sales rose to $7.3 million from $6.8 million. Directors declared a dividend of 2.5 cents a share payable April 7 to stockholders of record March 10.

Kapok Tree Inns Corp., which owns the Peter Pan restaurant in Urbana, Md., reported earnings of $298,214 (10 cents a share) in the 16 weeks ended Jan. 15, compared with $260,980 (9 cents) in the same period a year earlier. Sales rose to $4.9 million from $4.3 million.

The company said it has donated 40 acres of land adjacent to a restaurant in Clearwater, Fla., to that city. An income tax benefit of $378.488 from the donation must be used by Kapok by Sept. 25, 1983, the firm stated.

Kay Corp., an international trading firm which owns the Kay Jewelry stores, reported record profits from continuing operations in 1977 of $5 million ($1.39 a share) compared with $4.3 million (72 cents) in 1976. Revenues rose to $522 million from $361 million.

President Anthonie C. vanEkris said the Kay stores, the third largest U.S. jewelry chain, reported a 41 percent increase in profits on a 31 percent increase in revenues. Kay completed the year with 193 stores and plans to open 24 units in 1978.

Noland Co., a wholesale distributor of mechanical equipment in Newport News, reported a 20 percent increase in profits last year to $3.47 million ($1.41 a share) compared with $2.9 million ($1.17) in 1976. Sales rose nearly 15 percent to $240 million.

Doughtie's Foods Inc., of Portsmouth, reported record profits of $591,000 (95 cents a share) in 1977, compared with $372,000 (60 cents) the previous year. The 59 percent jump in earnings came on an increase of 12 percent in sales to $28 million, also a record.

TransTechnology Corp. reported a 42 percent increase in sales for the nine monthsended Dec. 31 to $21 million. But disappointing earnings in the third quarter reduced nine-month profits to $451,250 (25 cents) vs $727,547 (42 cents).