The Carter administration has devised an end-run around the current budget crunch to finance some $1.1 billion in lending commitments made by the Export-Import Bank.

The makeshift policy, worked out this summer by high administration officials at the Treasury Department, Office of Management and Budget and the Ex-Im Bank, will force the bank to go to the costly private money market to fullfill the $1.1 billion in commitments instead of relying on less expensive direct federal lending.

This move by the bank, a federally funded institution that lends money to foreign borrowers to buy American goods, could cost U.S. taxpayers $200 million.

The idea is to permit the bank, which already has gone through its fiscal 1980 budgetary allotment, to finance some of the billions of dollars in loan commitments it has outstanding before the fiscal year runs out at the end of this month -- without reflecting the outlay on the current budget.

It's a classic case of off-budget financing by the administration, a practice that President Carter has deplored and his administration publicly has sought to stop. The administration's push for off-budget lending authority from Congress came last summer after major U.S. exporters, which directly benefit from the bank's loose-lending policies, launched a high pressure lobbying campaign to get Ex-Im Bank additional funds.

The off-budget scheme has caused consternation among career staffers at the bank. Privately, they worry that this is just another example of the Carter administration's policy of using the bank's valuable capital to subsidize unrealistically low interest rates. They say that as a result, the bank has about $12 billion in direct laon commitments, but an annual budget of only about $4 billion in lendable funds.

As internal dissent has heightened at the bank, the politically appointed top management met with the career professionals. The careerists have been challenged on their figures, and have been advised that stories about the threat to the bank's capital are much exaggerated.

Under John L. Moore Jr., the Carter-appointed chairman, the Ex-Im Bank has aggressively financed billions of dollars in U.S. exports by lending to foreign buyers. Even as the prime rate has soared to as high as 20 percent this past spring, Moore and his fellow Ex-Im Bank board members have sought to spur exports by lending money at rates ranging between 7 3/4 and 8 3/4 percent.

The U.S. industry benefiting most from this liberal lending policy is aircraft manufacturing. During the Carter administration, foreign buyers of U.S. planes have found financing easy to come by, especially with the threat of sales competition from the wide-bodied A300 planes manufactured by Airbus Industrie, a European combine.

But according to many Ex-Im Bank staffers -- a group that historically has been expansionist on bank-lending policy -- the board finally has gone too far.

"The board doesn't know how to say 'no,' "observes one official. "They've forgotten they're public servants. They're too concerned with making corporations happy."

Moore gets most of the criticism for what some see as the bank's current rocky condition. An Atlanta lawyer and long-time Carter supporter who had little experience in the complexities of international finance before joining the bank, Moore has spent much of his time since his appointment in 1977 on the road visiting potential customers.

Last spring, Moore was under attack on Capitol Hill when he pushed through a $201 million loan at 8 percent to an airline half-owned by Austrailian financier Rupert Murdoch. What caused the controversy then was not the low interest rate but rather the scent of politics that surrounded the deal.

On Feb. 19, the day Murdoch was negotiating the loan, he dropped by the White House for lunch with President Carter. And two days later, Murdoch's New York Post endorsed Carter in the upcoming New York's primary.

At subsequent hearings on the Murdoch affair before the Senate Banking Committee, the senators were unable to show any direct political influence involved in the loan. But the lasting impression from the hearings was that Murdoch had stampeded the bank board into granting him the low-interest loan.

Critics say that these same easy-lending ways have forced the administration's to devise the $1.1 billion off-budget item. These critics say that the administration, facing unprecedented billions of dollars in commitments by Ex-Im Bank in fiscal 1981 and beyond, got Congress to agree to an additional appropriation amounting to about one-quarter of the bank's normal appropriations in the last few weeks of the 1980 fiscal year. Congress agreed after it was clear the $1.1 billion would not show up in the budget.

Among the administration officials who came up with the plan and sold it to Congress were Ex-Im Bank's Moore and Fred C. Bergsten, assistant Treasury secretary for international affairs, with officials of the budget office in agreement.

Most of the Ex-Im Bank's financial support to foreign borrowers is in the form of direct credits. These loans are financed by the Treasury, which sells federal securities to raise funds. The Treasury securities currently have a rate of about 11 1/2 percent, while the Ex-Im Bank is lending at under 9 percent.

What allows Ex-Im Bank to continue to lend at apparently money-losing interest rates is the bank's capital.

Back in 1945, when Ex-Im Bank was founded, the Treasury put in seed funds of $1 billion. Over the years, those funds have been carefully nurtured so that the bank's capital, or equity, has grown to over $3 billion. In addition, the bank also has about $9 billion in funds that were borrowed from the Treasury at interest rates significantly below today's level.

By blending the low-interest capital with freshly borrowed funds, the bank year after year has been able to lend funds at higher rates than its current borrowing. It also allows the bank to state that it is "self-sustaining."

Along with direct credits, the Ex-Im Bank also puts the name of the U.S. government behind guarantees to enable foreigners to borrow from private financial institutions. Ex-Im Bank usually collects about half of one percent for this service, and the foreign borrower uses the funds to buy U.S. exports.

But guarantees, unlike credits, are not reflected on the federal budget. So this summer, the administration went to Congress to get $1.1 billion in guarantees to finance some of its commitments, off-budget.

Once Congress voted through the additional funding in the form of guarantees in late August, Ex-Im Bank by law then had to send Congress descriptions of any commitment of $100 million or more it planned to fund with the guarantees.

On Aug. 27 and 29, the bank set up five separate commitments, and Congress has 25 days from then to raise questions about them.

What upsets Ex-Im Bank staffers is that the five commitments to foreign borrowers were almost all for direct credits, at a weighted average interest rate of 9 percent. The direct credits could have been funded through the Treasury, but now that they have been converted to guarantees to avoid the budget, the bank must go into the private market to raise money.

Not only does this mean higher interest rates, it also means that the bank must absorb the difference between the weighted average rate of just under 9 percent and whatever the private-market rate is at the time the $1.1 billion is raised.

According to several sources, this $1.1 billion in guarantees will cost the bank at least $200 million in interest payments over the 10-year life of the loans. And to finance the $200 million, the bank must dip into its valuable capital.

This is what most troubles critics of this off-budget, eleventh-hour effort by the administration to fund $1.1 billion of Ex-Im Bank's multibillions in commitments, along with the bank's unrealistically low lending rates.

Says one bank official: "What has happened over the past 35 years could be undone in one whack if this goddamned foolishness doesn't stop."