In the beginning it sounded like a tasty equivalent of free lunch, but the Reagan administration's payment-in-kind (PIK) plan to reduce grain and cotton surpluses is shaping up as the most expensive farm program in U.S. history.

Some private assessments of the PIK program suggest that it could cost taxpayers as much as $12 billion when other federal payments to farmers, and possibly new support loans, are put into the equation.

Department of Agriculture officials dispute these admittedly iffy projections but agree that the market value of the surplus wheat, corn, rice and cotton to be given farmers for not planting could be as high as $9 billion.

As announced by Reagan in January and outlined later by Agriculture Secretary John R. Block, the PIK idea had almost instant appeal: it would reduce federal surpluses expensive to store; it would cut production and lessen the likelihood of more federal farm-loan costs, and it would bolster sagging farm income by pushing prices higher.

Most members of Congress rushed to support the idea, and farmers showed their enthusiasm by indicating that they would not plant 82 million acres, or about one of every three acres that would have been devoted this year to wheat, corn, sorghum, cotton and rice.

Now some Democratic legislators have begun to raise questions about the real cost of PIK. And conveniently for an economy-minded administration, the program's first big bite into tax dollars will not come until fiscal 1985 and later--after the 1984 election, when Reagan farm policy is likely to be under attack by opposition forces.

In recent appearances on Capitol Hill, Block and his top aides have insisted that potential overall costs of the PIK program are not available and cannot be calculated accurately. Congress has shown no signs of doing its own in-depth study of PIK's costs.

USDA, however, in a recently published economic assessment, estimated that commodities with a market value ranging between $7 billion and $9 billion would be given to farmers who have agreed not to plant this year. They can sell the grain or feed it to livestock.

Those figures, impossible to calculate more accurately because exact participation in PIK is not known, are based on the amount of loans made by USDA's Commodity Credit Corp. to acquire the grain and cotton over several years.

The commodities are carried on the CCC's books as assets, but as they are given to farmers, will be written off, and Congress will be asked to make up the losses with appropriations beginning in fiscal 1985.

Under the price-support program, a farmer can obtain a CCC loan for his corn, for example, if market prices are not attractive. If prices do not increase, the farmer forfeits the loan and the CCC keeps the corn for sale later. In effect, the CCC's books are balanced when and if it sells the grain. But with PIK, that asset will be given to farmers in the program, and Congress will have to make up the CCC's loss.

Block said in an interview recently that he thought estimates of $10 billion to $12 billion as the cost of PIK were "too high." But, like economists who work for him, he could not provide more precise calculations.

"To be fair," Block said, "those commodities don't have much value. They can't be given away in that volume. They can't be sold on the domestic market--if we did that, prices would plunge. And you have to discount from their original costs the government's interest and storage expenses."

Block's assistant secretary for economics, William G. Lesher, said there was no question about the original cost of the PIK commodities to the CCC; he agreed that "three years down the road, the CCC will have to ask Congress for money."

But, he added: "The key distinction is that these commodities are not worth much to the taxpayer without our PIK program . . . . If we didn't have PIK, and the overproduction continued, government loan and deficiency payment outlays would be enormous. By giving these commodities instead of cash back to the farmers, we save on deficiency payments, storage and interest costs, fewer loans over the next three years and possible deterioration that would lower their value."

In its current budget calculations, the administration has argued that, without the PIK program, federal farm income support costs will be about $20 billion in fiscal 1983, the highest level in history.

Some independent agricultural economists, however, think that the PIK program will cost taxpayers considerably more than USDA is suggesting. Their estimates are based on assumptions that they concede may not be fully accurate.

E.A. Jaenke, a former CCC vice president now in the consulting business here, calculated a PIK cost that could reach $11 billion.

"It is a complicated subject," Jaenke said, "but what USDA is arguing that in the end it is cheaper to give away these commodities . . . . We can't accept that.

"Those commodities do have value, the CCC book value has a price and at some point our tax money has to be appropriated to cover the losses. Congress is going to have to come up with a slug of dollars to pay for it," he said.

Lynn Daft, a Carter administration economist now with Schnittker Associates, said his calculations of PIK costs for corn and wheat alone showed "a kind of scary figure" of about $5.6 billion.

"We have made rough estimates, but I am not comfortable with them," Daft said. "USDA has discounted the value of the PIK commodities very heavily, but they don't say how much. But it's so complicated, I don't think anyone could prove or disprove any of the cost estimates you might hear."