Despite exceeding limits imposed by companies that have received government aid, the compensation packages for General Motor’s new chief financial officer and the new head of GMAC were approved by the government pay czar, the Associated Press reported.

Chris Liddel, who will leave his job at Microsoft on Dec. 31 to take up his new role as GM’s new CFO, is set to receive a salary of $750,000 next year. He also will get up to another $5.45 million worth of stock starting in 2012 if GM successfully sells shares to the public. GM said in a government filing that it had worked out an exemption with the government pay czar Kenneth Feinberg.

Feinberg also approved a compensation package for Michael Carpenter, the new head of GMAC. It will pay him a base salary of $950,000 and up to another $8.55 million worth of stock.

GM has received $52 billion in taxpayer assistance, much of which was converted into equity that gives the U.S. government a 60 percent stake in the company.

Under new pay rules established in October for companies that received substantial government aid, the base pay of General Motors’ top executives is capped at $500,000. However, a small number of exemptions to pay limits have been granted for other major recipients of government money, such as with the American International Group Inc. It was allowed to boost its pay package for an employee to be better aligned with other executives at the insurer.

As for GM, much of the compensation will be paid in company stock that cannot be redeemed until the beginning in 2011 or after GM starts repaying its government loans.

In the case of Liddell, he will receive $3.45 million in company stock over three years starting in 2010 in addition to his base salary. He will get another stock grant of $2 million that vests in three years and is payable in 25 percent installments for every 25 percent repayment of GM’s $6.7 billion in government loans.

In the case of Carpenter, Feinberg ruled that in addition to the executives $950,000 base salary, he is eligible for up to $8.55 million in stock, payable in installments over several years and tied to the performance of GMAC.

GMAC, which is viewed as a key component of the Obama administration’s rebuilding of the auto industry, has already received $13.5 billion in government aid and is 35 percent owned by the federal government. The government has also indicated it will provide an additional $6.5 billion to GMAC to boost its capital reserves.

Carpenter, who has served on GMAC’s board, was picked to succeed Alvaro de Molina after his departure in November.