Woodward & Lothrop reported yesterday its profits plunged almost 80 percent in the first quarter because of weak sales and high interest costs.

Earnings for Washington's biggest department store dropped to $204,000 (8 cents a share) for the three months ended May 1 from $968,000 (39 cents) in the same period last year.

Sales climbed by 4.6 percent, to $75.2 million from $71.9 million, but were described by Chairman Edwin K. Hoffman as "very weak, particularly during the important Easter season."

The first quarter is always the slowest in the year for retailers, but "we view the balance of the year with extreme caution," added the chief executive of Woodies, which as the biggest D.C.-based retailer is considered the best indicator of local retail trends.

Added Hoffman: "A continuing weak economy and restrained consumer spending adversely affected sales. Sales in the Washington metro area have been particularly weak, in what had been perceived to be a recession-proof region. Current high unemployment levels and the reduction in government employment have had an adverse affect on sales."

The firm's interest expense for the quarter climbed to $2.7 million from $2.1 million a year ago.

Potomac Electric Power Co. reported modest gains in sales, profits and per-share earnings in the 12-month period that ended April 30.

Pepco said it had net income of $111.3 million for the year, compared with $106.3 million in the same period a year ago. Pepco's profit equaled $2.15 per share, up from $2.12 in the preceding year.

Pepco, which provides electricity to customers in the District, the Maryland suburbs and a small slice of Northern Virginia, reported operating income of $1.044 billion in the 12-month period.

In the 1981 calendar year, Pepco had per-share earnings of $2.14, one cent less than the figure for the year ended April 30. Pepco has 44.1 million shares of stock outstanding.

Its much larger counterpart in Virginia, the Virginia Electric and Power Co., reported net income for the year ended April 30 of $258.2 million, on operating revenues of $2.24 billion. Both figures represented increases over net income of $237.8 million on revenues of $2.1 billion reported in the same period a year ago.

On a per-share basis, earnings for the latest period were $1.92, up seven cents from a year earlier. Vepco's directors declared a quarterly dividend of 37 1/2 cents per share.