Sales and profits rose substantially at Woodward & Lothrop department stores during the final quarter ended Feb. 3, contributing to a record performance for the full fiscal year, the Washington retailer reported yesterday.

After modest gains earlier in the year, fourth-quarter volume soared more than 16 percent to $92.4 million as profits increased 24 percent to $6.8 million ($2.81 a share) from $5.5 million ($2.28) in the same period a year earlier, which included 13 weeks compared with 14 in the recent quarter.

With this boost from holiday-season sales, profits for the full year rose 7 percent to a record $12.2 million ($5.04 a share) from $11.4 million ($4.72). Sales increased about 9 percent to a record $271 million.

Moreover, Woodies spent $20 million last year from its own funds on a new branch and on remodeling. Four floors of the flagship store in downtown Washington were remodeled as were two branches at Wheaton Plaza and Chevy Chase. The company's newest store, at Lake Forest Mall in Gaithersburg, opened last September.

Although interest costs and depreciation expenses rose significantly, Woodies benefited from a reduction in federal income taxes because of higher investment tax credits.

"Earnings for the year exceeded our plan," said Chairman Edwin K. Hoffmann. "Accelerated sales increases, particularly during the most important Christmas season, professionally administered expense controls, improved growth margin, plus a sizable reduction in inventory shortage (theft) contributed to the improvement in performance."

According to Robert Mulligan, senior vice president for finance, the theft losses were at the lowest level in 10 years.

Profits were 4.5 percent of sales during the year, and the return on shareholders' stock investment in the firm was 14.3 percent. Both of these figures are among the highest for the department store business, in which Woodies is one of the few remaining major independent companies.

The company had no comment on the current effort by the Retail Clerks International Union to organize Woodies employes. Further details of the fiscal year will be included in the annual report, to be mailed in mid-April.