When the Torpedo Factory Art Center, which was refurbished with $3.1 million in publicly backed funds, opens on Alexandria's waterfront next month, the city will not own a single concrete slab in the $5.4 million structure.

By using a financing scheme made possible by a recent Reagan administration-sponsored federal tax law, Alexandria officials say, the city will save $1.2 million over 15 years by redeveloping the old factory, selling it to a group of private investors and then leasing the building back. After 15 years, the city has the option of buying back the building at its then market value.

The Economic Recovery Tax Act of 1982, which enables local governments to make such a deal, is designed to allow jurisdictions essentially to sell tax breaks not available to governments to private developers, thus passing on part of the cost of redevelopment to the federal treasury instead of local taxpayers or private investors, officials said.

The investors profit by taking advantage of income tax credits associated with the ownership and restoration of aging property and through standard depreciation tax credits--advantages not available for governments because they don't pay income taxes.

Here is how the Torpedo Factory Art Center deal works, according to Bradford Hammer, Alexandria's Deputy City Manager for Finance: The city sold about $2.4 million in public bonds and borrowed $700,000 to renovate the building.

The city, which is still negotiating the final details of its agreement, will sell the building for $5.4 million to Alexandria Arts Center Associates, a partnership of local investors and REALCO-Potomac, a West Orange, N.J., development company that is the primary partner in the surrounding $50 million redevelopment plan. Local investors are led by Charles R. Hooff III, whose grandmother was instrumental in the redevelopment of Old Town in the 1920s. Hooff said he is expecting six to 12 local investors whose names will be made public this month.

Of the $5.4 million, $3.7 million will be made available to the private investors through the sale of industrial revenue bonds at substantially below-market interest rates by the Alexandria Redevelopment and Housing Authority. The investors will be responsible for paying off the debt.

The investors will qualify for an income tax credit that permits them to deduct 20 percent of the building's $4 million renovation cost, which is $800,000. Along with depreciation tax credits and the city's monthly lease payments, the investors are expected make a $750,000 profit on the $5.4 million investment. Investors can chose to take advantage of the tax breaks or they can sell those breaks on the open market.

Alexandria then will lease exclusive use of the building for 20 years with an option to buy it back after 15 years. The lease payments are still undetermined, but the total of the payments will not exceed $5.4 million, excluding the cost of maintenance, custodial and utilities, which the city must pay.

The citywill invest a portion of the $5.4 million sale price and use it to help make the monthly lease payments. The rest of the money will be used to pay off the $3.1 million in debt it incurred to refurbish the Torpedo Factory Art Center.

"As long as the Internal Revenue Service doesn't crack down on the use of this," said Wesley C. Hough, of the non-profit Government Finance Research Center, which assisted Alexandria arrange the sale-leaseback, " . . . I think it will be the thing of the future."