Woodward & Lothrop, the Washington based department store company, yesterday reported a 20 per cent rise in profits for the year ended Jan. 29.

Sales and profits during the full year were at record high levels for the retail firm and profits in the fourth quarter alone soared 33 per cent, president Edwin K. Hoffman said.

Earnings for the fiscal year totaled $11.7 million ($4.89 a share) compared with $9.8 million ($4.10) in the previous 12 months as sales increased 10.5 per cent to $241 million.

The sales volume was in line with an earlier projection by Hoffman, in an interview, but the profits were substantially higher than forecast by some securities analysts who follow Woodies. Ferris & Co., Inc., for example, last month predicted annual earnings of the retailer at $4.30 a share.

In part, the earnings growth for the full year reflected an unusually strong final quarter, as profits surged to $5.8 million ($22.43 a share) from $4.7 million ($1.83) in the same period a year ago. Fourth-quarter sales were up 9.6 per cent to $76.4 million - a rate of growth in volume that exceeded average retail sales expansion in metropolitan Washington.

Among earnings reports from other major retailers over the past week. Sears, Roebuck & Co. annual profits were up 30 per cent and the fourth-quarter gain was 33 per cent; May Department Stores reported a 1.4 per cent decline for the final-quarter and a 4.1 per cent gain for the full year. Federated Department Stores was up 7.6 per cent in the final quarter but down 1 per cent for the year; and Garfinckel, Brook's Brothers, Miller & Rhoads was up 15.3 per cent in the last quarter and 2.3 per cent for the year.

Woodies president Hoffman said yesterday his company's new store at Montgomery Mall, which opened a year ago, "exceeded our expectations in both sales and profits."

Higher gross profit margins and "effective expense controls contributed significantly to the results of the fourth quarter and the year," he added.

In an interview, Hoffman said a change in the merchandise mix at Woodies stores, with an emphasis on soft goods and better merchandise with higher profit margins, contributed to the record performance.

He noted that Woodies last year interviewed 1,000 customers for an hour and a half each, to determine preferences in shopping. Acting on results of those surveys, Woodies has reorganized its stores and its emphasis on different lines of goods.

Hoffman also said sales at his firm's downtown Washington store were at a record high level last year, with some of the gain attributed to a subway stop below the big unit. Officers of the company met yesterday to work on plans for a complete rehabilitation of the downtown store, to be completed by 1980.

As reported earlier, Woodies is about to begin a five-year, $20 million modernization of all its stores.

In February and March the first two months of the new fiscal year, sales have been ahead of expectations and "we anticipate a good spring season," Hoffman asserted. Woodies said its annual report will be mailed to stockholders in mid-April. The annual meeting has been scheduled for May 16 at the Shoreham Americana hotel.