Garfinckel, Brooks Brothers, Miller and Rhoades Inc. yesterday reported its annual profits increased 16 percent in 1977, while sales climbed 11.2 percent.

The Washington retailing company said its sales of $330 million produced earnings of $11.2 million ($2.61 a share) compared with 1976 sales of $296 million and profits of $9.6 million ($2.25).

Garfinckel Chairman and President David R. Waters noted that the company increased its profit margin from 3 percent of sales to 3.4 percent.

For the fourth quarter, ended Jan. 28, the company's sales grew from $99.4 million to $116.2 million and net income rose from $6.4 million ($1.60) to $6.8 million ($1.60).

Waters said, "The upward trend in sales, earnings and gross margins that began in the second quarter accelerated through the remainder of the year."

The company does not break down sales or earnings by division, but Waters said the Brooks Brothers men's wear stores "achieved significant sales and earnings gains over outstanding 1976 performance."

The Garfinckel' stores in the Washington area "had good results in the second half of the year despite a sharp increase in retail competition."

Because the acquisition was not completed until late in the year, the purchase of the Ann Taylor chain contributed little to the company's 1977 sales and earnings. It is expected to add significantly" to the 1978 growth, Waters said.

He said the company spent $2.8 million on new stores and remodeling last year an will boost that outlay to $10 million this year.

Waters said the 1977 results "put the company well on the road to accomplishing the five-year goal" of doubling sales to $600 million by 1981 and increasing profits at least that much.