Robert S. Noe is just one of 96 county executives in Virginia currently enmeshed in the annual budget battle. This year, Noe, Prince William County's top administrator, says he is struggling with the toughest fiscal problem of his career.

Inflation and the rising cost of living are two factors that Noe blamed for his decision to ask the Prince William County supervisors to approve a $147.3 million budget for fiscal 1982 -- $16.4 million more than last year's total of $130.9 million. The 1982 plans include the county schools' proposed budget of $102.3 million.

As a result of the proposed budget increases, Noe asked the supervisors to raise the Prince William property tax rate from $1.40 to $1.60.

But the supervisors, after receiving the fiscal plan earlier this month, immediately told Noe to cut $10 million from the budget and submit a proposal with a tax rate of no more than $1.45 for each $100 of assessed value.

Noe expects to submit an amended budget plan as soon as he receives similar revisions from the county school system. The supervisors have told Superintendent Richard Johnson that the school budget must be reduced by at least $3 million. School officials had asked the county for a 13 percent increase in this year's budget.

"This is the most difficult budget I've ever prepared because of the fiscal climate and the substantial increase in the school budget," said Noe, who is in his third year as the county's top administrator.

Noe said no decisions have been taken yet on where exact cuts will be made. However, county supervisor Donald White expects the cutbacks to come, in part, by allowing no increases in the size of county government.

"There are no clear winners and losers in this budget," said White, an accountant. "Everybody is going to have to bear some of the cuts. Things are getting out of hand. We're not like (the state). We don't have the luxury of a budget surplus, and when you don't there comes a day of reckoning."

One unknown quantity in the budget is the allocation to finance the county's share of the cost of building a new courthouse complex in Manassas. On March 31, voters will be asked to approve a bond referendum to finance the complex. The county's share of the $9.5 million project would be $6.9 million and, if the bond issue fails, Noe says the supervisors may have to consider other sources of financing. Manassas would contribute $1.9 million and Manassas Park, $350,000. The remaining $325,000 not covered by the bond referendum reprresents the cost of the land, which is already owned by the county.

"If the referendum fails, then the supervisors will have to do something," said Noe, who included the county's share of the courthouse bill in his budget proposal.

Despite the current budget crunch, White believes Prince William County is finally emerging from the financial crisis is faced five years ago.

"We were on the verge of going bankrupt," White says. "We were headed for insolvency."

White blames those problems on what he described as artificially low tax rates and a poor tax collections system.

Although, according to Noe, the county now spends $1.58 for every $1.40 it collects in property taxes, White says the county's financial picture is beginning to stabilize. Within five years, he says, the supervisors hope to have a balanced budget.