The Prince William County Board of Supervisors moved yesterday to sharply cut taxes for business, an action aimed at making the county competitive in the fight for industrial growth.

The board voted unanimously to direct its staff to draft ordinances that would cut taxes on machinery and tools and utility use and asked for further study of a proposed tax cut on business inventory.

County officials estimated that enactment of their tax package would cut revenues by slightly more than $1 million by 1984 under no-growth conditions.But they said they were confident that the reductions would create more than enough business and manufacturing growth to offset those losses.

The board asked for an ordinance that would cut the tax on machinery and tools from $3.15 per $100 of value to $2 per $100 this fall and to $1 the following year.

According to economic development director David Dodd and finance director Garnett Ball, the machinery tax rate in Northern Virginia ranges from Arlington County's high of $3.54 to $2.25 in Fairfax County, $1.18 in Loudoun and 50 cents in Stafford County.

The board also asked for an ordinance to cut utility taxes over a six-year period by imposing a tax ceiling that would drop from $2,500 a business in 1979 to $500 in 1984.

County estimates for annual utility taxes paid by manufacturing companies show a cost of $9700 in Prince William, $8,200 in Fairfax County, $2,900 in Loudoun County, $1,100 in Stafford County and zero in Spotsylvania.

Dodd and Ball also proposed elimination of a 70 cents per $100 of cost value on inventory. They proposed instead a business license tax based on fees ranging from about $50 to $1,000.

The board asked for further study of those proposals.

"Industrial tax reform is required of Prince William County if we are able to hope for much sucess in attracting prime manufacturing and heavy distribution projects," Dodd and Ball said in their presentation.

Dodd said the county was now seeing increased interest on the part of industries that in the past viewed Prince William as a hostile environment.

"The impression now is positive, but it hasn't been in the past," Dodd said. "Industry wants to see action now."