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Some government agencies in Illinois are joining homeowners in the rush to refinance their debts at lower interest rates.

But instead of seeking new $100,000 mortgages, the government agencies are talking about refinancing hundreds of millions of dollars of outstanding debts.

With interest rates at an eight-year low, officials expect to save taxpayers millions of dollars by calling in their debts and reborrowing at rates a couple of percentage points lower.

On Tuesday, officials of the Chicago School Finance Authority proposed a bond refinancing plan that they said would save city taxpayers as much as $186 million in interest payments over the next 22 years.

Next month, the State of Illinois will refinance $200 million of its bonds with expectations of saving $20 million to $30 million in interest.

”All our advisers are telling us, `Don`t let this market get away from you,` ” said State Budget Director Robert Mandeville. ”We haven`t seen interest rates like this since the 1970s.”

Other government officials say they would like to take advantage of the bargain rates but are holding back because of uncertainty over pending federal legislation that could restrict the way they spend the money they borrow. Some of them refinanced their debts last year, before interest rates reached their current lows, just to avoid having to deal with the new law.

The school finance authority proposal was promptly approved by the Chicago City Council Finance Committee, and it will be considered by the full council Wednesday.

Under the plan, the authority would sell $350 million in new bonds at an 8.12 percent interest rate. The authority then intends to pay off the $350 million in bonds it sold in 1980 at a 10.25 percent interest rate.

”Overall net savings of $186 million could be attained,” Lawrence Block, secretary of the authority, told members of the council Finance Committee.

The total cost of the $350 million bond issue of 1980, including principal and interest, would be $830 million until the last bond is retired in 2009. But under the refinancing proposal, the total cost at the lower interest rate is estimated at $644 million, a savings of $186 million.

The finance authority`s property tax rate would be reduced, it is estimated, to 42.3 cents from 49.2 cents per $100 of assessed valuation. The owner of a house with a market value of $50,000 would save $8 a year on his tax bill, beginning in 1987.

The finance authority was created by the Illinois General Assembly in 1980 to oversee finances of the Chicago Board of Education and to issue bonds to rescue the financially troubled school system. The schools ran out of cash in November, 1979, and faced a shutdown without the rescue effort.

The finance authority was compelled to sell bonds in 1980 during a period of high interest rates. ”It was not an ideal time to sell bonds, but with the city`s schools facing closure, what had to be done, was done,” Block said.

When the authority issued the bonds, there was a provision allowing it to pay them off early.

The state hopes to get an interest rate of well below 8 percent when it resells $200 million of bonds, some of which now pay interest as high as 11.5 percent, according to Mandeville. The state sold $100 million in bonds on Jan. 28 at an interest rate of 7.6 percent.

Mandeville noted that bond underwriters and lawyers charge sizable fees for handling new bond issues. In addition, interest rates are dictated by the credit evaluation of the borrowers by Standard & Poor`s Corp. and Moody`s Investors Service, bond rating agencies.

”But it`s still a net savings to the taxpayer when interest rates are as low as they are now,” he said. He said the interest savings would not necessarily reduce state taxes, but they would make it easier for the state to meet unforeseen financial needs without raising taxes.

James McKinney, manager of William Blair & Co., a Chicago investment banking firm, said he expects many local governments to try to take advantage of low interest rates in coming months. But he said that ”it`s not as simple as it sounds” because of pending federal restrictions.

Harold Downs, treasurer of the Metropolitan Sanitary District, agreed. He noted that the district refinanced $330 million of bonds last year, reducing interest rates on some bonds from as high as 11.55 percent to as low as 8.19 percent. The City of Chicago refinanced $217 million of bonds last year and the Illinois Toll Highway Authority $157 million.

”But with the current tax legislation under consideration, there are too many potential problems involved to take any more action now,” Downs said.

Because interest income on state and local government bonds is exempt from federal income taxes, some members of Congress consider the bonds a drain on the federal Treasury.

So the House has approved a bill, now pending in the Senate, that places restrictions on the bonds. For example, the bill requires tax-exempt bonds to be used for ”essential government functions” and not for projects such as retail stores or sports stadiums that would ultimately result in profits for private developers.

There`s no guarantee that any new tax bill will pass both houses of Congress. But since the current bill is retroactive to Jan. 1, 1986, potential bond buyers are demanding that governments meet all the restrictions in the legislation. If they don`t, bondholders fear they might end up having to pay tax on their interest income.

”It`s taken specialists in municipal finance a lot of time to determine how to comply with the pending federal legislation,” said Bill Taylor, a lawyer with Chapman & Cutler, which specializes in municipal bonds. ”But with interest rates so low, I think you`ll soon see more governments moving to take advantage of them.”