Turnover was expected to have risen to between £555m and £560m by the end of the financial year, from £533m the previous year, he said.
Although the growth rate had almost halved since the year to May 2008, when it was 8.8%, Graves said he was more than happy with the current rate, which was close to its 5% target.
"How many companies are growing at the rate we are?" he said. "When we achieved 8% growth it was on a small number of stores and less turnover. If we can keep this up in the present climate I will be pleased."
The number of stores has increased from 1,542 to 1,657 since September 2007 following the appointment of a new team specialising in recruiting members.
Like-for-like sales growth was 3.4%, he said, adding that the recession would help the business grow as independent retailers sought the benefits a symbol group had to offer such as competitive prices, credit and advice.
Costcutter would continue to support members by offering promotions, he said, and would double its ad spend to £2m over the course of the year.