The stock of MCI Communications Corp., a darling of investors for the past several years, has dropped by as much as $10 a share in recent weeks largely as a result of cuts in earnings projections by Wall Street analysts.

Although the stock joined a broad market rise to gain 2 1/8 today and close at 36 1/8, it had sold for as much as 45 3/4 as recently as Dec. 8.

A major Federal Communications Commission decision on Dec. 22 revised the methods companies use to pay for access to local telephone systems, a move read almost universally by analysts as negative for MCI. The company disputes that.

Bradford Peery of Paine Webber Mitchell Hutchins removed MCI from his firm's buy list after the FCC decision, and he is now neutral on MCI. Peery said that AT&T will cut its rates by 7 percent once the decision goes into effect Jan. 1, 1984, and MCI's costs will rise 3 percent.

"We think the decision has been misunderstood by some people who are trading and analyzing it," said William E. Conway Jr., an MCI vice president and treasurer.

Many analysts are predicting that AT&T will cut rates after the FCC decision is implemented next year. If AT&T were to cut rates sharply, it would diminish MCI's competitive advantage in long-distance business and residential calling.

MCI officials question that assertion, too. "AT&T is not earning its allowed rate of return," Conway said. "Number two, from the standpoint of its own costs, it has considerable problems ahead. It will need earnings from long distance to make up for the tough competition American Bell and Western Electric face."

Even one of MCI's most enthusiastic backers, Steven Chrust, analyst at Sanford C. Bernstein & Co., cut his estimate from $3.10 a share for the year ending March 31, 1984, to between $2.90 and $3.

On the other hand, the drop in the over-the-counter market value of MCI stock has encouraged some analysts, such as Harry Edelson of First Boston Corp., who were not touting MCI stock to reconsider that position. Edelson, according to a memo he is sending to clients tomorrow, "believes the stock is getting into buying range again."

Yesterday, the company announced it will move its international unit's headquarters from Manhattan to Westchester County, N.Y.