Halifax Engineering Inc., a professional services company based in Alexandria, has announced plans to acquire HSC Engineering Corp. of Towson, Md., a privately owned civil engineering and construction firm, for a price reported to be under $5 million.

Howard C. Mills, president of Halifax, said he wanted to acquire HSC because he foresaw "tremendous opportunity" in the highway and bridge construction business. HSC is engaged in civil engineering, architectural design, highway and bridge construction and general contracting, mostly for state highway departments in Maryland, Delaware, Virginia, West Virginia and other states. It had about $5 million in revenue last year.

Mills said he signed an acquisition agreement with Joseph C. Huang, president of HSC, who will continue to operate HSC and will join the Halifax board of directors. Halifax said it will pay with a mixture of cash, notes and stock from the Halifax treasury.

The merger comes as Halifax is taking a number of steps to shore up sagging profits.

The company, which saw sales and profits grow in fiscal 1981, 1982 and 1983, watched earnings fall off in 1984 and turn into losses in 1985, even though fiscal 1985 sales rose to a record $28.4 million. Mills said the HSC deal would significantly improve Halifax's future per-share income.

In a blunt 1985 annual report to stockholders, Mills said the company's losses had come about, in part, because of problems with its estimates and handling of various government contracts. As a result, Mills said, Halifax has revamped its planning and budgeting, cost-accounting and contract administration procedures. Employe bonuses have been tied to the company's profitability. The company also has been changing its management style.

Meanwhile, United Virginia Bank recently gave Halifax a $6 million line of credit and Halifax stock moved to the American Stock Exchange. Halifax first sold stock to the public in June 1983 at $10 a share. The stock, which has traded in a range of $3.63 to $10.75, now sells at about $5.

Finally, the company has expanded membership on its board of directors, which now includes Clifford M. Hardin, former U.S. secretary of Agriculture.

"We think of ourselves as a new Halifax," said Mills, who has been president for a year.

During the fiscal 1986 first quarter ended June 30, Halifax saw its revenue drop from $7.3 million to $6.7 million, but its profits rise to 16 cents a share from 12 cents a share compared with a year ago.

Before the HSC announcement last week,, John G. Crossman, a securities analyst with S. D. Cohn in New York, estimated Halifax's 1986 earnings at 65 cents a share and 1987 earnings at 80 cents a share. Halifax lost 36 cents a share in fiscal 1985. Crossman was not available for comment last week.

Halifax's primary business is operating and maintaining government facilities and installing communications equipment. Its biggest customer is the federal government.