May Department Stores Co. yesterday reported its 11th consecutive year of record sales and earnings, and increased its annual dividend.

In addition, the company declared a 2-for-1 stock split, subject to shareholder approval.

Earnings for the year ended Feb. 1 increased 10 percent to $235.4 million ($5.38 a share) from $214.1 million ($4.96) in 1984. Sales in 1985 were $5.03 billion, a 9.4 percent increase from the previous year.

Company directors increased by 10.6 percent the annual common stock dividend rate to $2.08 a share from $1.88. May Co., parent of The Hecht Co., said the stock split would be the second in two years.

Fourth-quarter earnings increased 9 percent to $119.9 million ($2.76 a share) from $110 million ($2.55) in the same period of 1984.

Quarterly sales were a record $1.65 billion, up 7.3 percent.

May operates 146 department stores, 62 discount stores and 1,874 shoe stores.

*Toys "R" Us Inc. increased its earnings by 7 1/2 percent in its 1986 fiscal year compared with fiscal 1985, with most of the growth coming from sales at new stores, the company reported yesterday.

Net income for the 52 weeks that ended Feb. 2 was $119.77 million compared with $111.42 million the previous year. Earnings per share for 1986 were $1.39, up 6.5 percent from $1.30 in 1985.

Sales for the year increased 16 percent to $1.976 billion from $1.701 billion. Fourth-quarter sales, which always are the largest in the retail-toy industry because of the Christmas season, increased 10 percent to $924.04 million from $838.75 million.

Sales rose just 2.4 percent in its existing stores, said Michael Goldstein, the company's chief financial officer. Most of our growth came from the new stores," Goldstein said. "Last year, there was a lack of exciting new product. The year before, we had Cabbage Patch dolls and Trivial Pursuit."

Fourth-quarter earnings increased more than 10 percent over the previous year, from $79.91 million to $88.11 million. Earnings per share for the quarter increased 9.7 percent, from 93 cents to $1.03.