At least a sixth of TCW's profit stems from payments made by former unit EIG, which spun out of TCW in 2011, according to data in the document which was seen by Reuters.

TCW is a unit of French bank Societe Generale (SOGN.PA).

EIG is separately seeking to block Carlyle's acquisition of TCW in court. EIG's fund that makes these payments has been put into a special trust by a judge pending an arbitration hearing. This hearing is expected on January 30, according to a person familiar with the situation.

While it was known that EIG contributed profit to TCW, a highly rated Los Angeles, California-based fixed income fund manager with $135 billion assets under management, the extent of these payments had not been previously made public.

This revelation and the outcome of EIG's arbitration could upset the math that Carlyle, which is one of the world's most powerful private equity firms, carried out in agreeing to buy TCW in August.

The stakes are high for TCW too. The deal with Carlyle was expected to end uncertainty about its future as it strives to become a more formidable competitor against some of the largest bond managers.

"We are fully committed to seeing the transaction through to completion," a Carlyle spokesman said, declining to comment on the document, the financing arrangements, Carlyle's profitability on the deal, or provide any other detail.

A TCW spokesman said: "As we have said, and as Carlyle has said, this transaction is not predicated on a restructuring of any sort."

A Societe Generale spokeswoman declined to comment on whether there could be circumstances under which the bank would compensate Carlyle for the loss of EIG payments. EIG declined to comment.

BANK COMMITMENTS

To be sure, the arbitration can have several outcomes, including the judge siding with TCW. Another possibility, were EIG's payments to TCW to end, would be for some sort of compensation to be agreed.

The judge may also decide to set up a Chinese wall, which makes the EIG fund separate from what Carlyle buys, according to a person familiar with the details of the legal case.

EIG filed the suit against TCW just days after the Carlyle deal, claiming that it violated a stipulation of its agreement with TCW that TCW could not compete with EIG. Like EIG, Carlyle has energy-focused buyout funds.

Carlyle has agreed to pay $343 million in cash for a 60 percent stake in TCW, while TCW management and employees will roll over equity worth $114 million for a 40 percent stake on a fully diluted basis, the document shows. The deal is slated to close in the first quarter of 2013.

Commitments by banks towards $405 million of debt to finance the deal are due on Monday, according to the document, which is part of materials that were distributed to banks to invite them to participate in a debt deal administered by JPMorgan Chase & Co (JPM.N). A JPMorgan spokeswoman declined to comment.

The terms of the deal represent pro forma leverage of 2.9 times TCW's earnings before interest, tax, depreciation and amortization (EBITDA) in the 12 months through the end of September 2012, the document shows.

The document does not list EIG's contribution to TCW's EBITDA separately but refers to it alongside the sharing of management fee revenue by Crescent Capital Group, an alternative credit manager that also spun out of TCW in 2010.

EIG and Crescent, which have $8.6 billion and $7.6 billion in assets under management respectively, together accounted for $39 million of TCW's $123 million in EBITDA in the 12 months ending September 2012, according to data from the document.

The document shows the contribution of management fees originating from EIG and Crescent to TCW's EBITDA and excludes carried interest -- the slice of investment profit that goes to the fund manager. It allows an estimate of EIG's contribution to the EBITDA because it offers details on how fund fees are shared with TCW.

Had EIG payments not occurred in the 12 months ending September 2012, TCW's pro forma EBITDA of $123 million would have been slashed by at least a sixth, based on management fee sharing data in the document.

The document does not reference the legal dispute with EIG, but repeatedly states that leverage, a measure of debt and hence risk, under the deal is "conservative".

However, if EIG were to succeed in arbitration and payments were to stop, it would increase the risk that lenders would be taking to finance the deal, which in turn could affect the interest rates they charge to lend that money.

Moreover, although TCW has enough room to service the debt from the deal even without EIG's profit contributions, losing that income would undermine the price Carlyle is paying to acquire a majority stake.

COST CUTS

The row with EIG also threatens more headaches for TCW as it prepares to embark on a spate of cost cuts under Carlyle. The Washington, D.C.-based firm sees TCW's cash flow margins -- a measure of how well a company transforms sales into cash -- as 35 percent lower than the industry standard, according to the document.

Private equity is known for seeking to increase the value of its assets though cuts in expenses. It is unclear whether a possible slump in the cash flow as a result of the dispute with EIG would prompt Carlyle to seek even more cost savings from TCW.

TCW plans $14.6 million in cost cuts, including through fee-sharing, reductions in headcount, executive compensation and products, to increase its cash flow margins to 24 percent from 20 percent now, according the document. That is still below the 31 percent median cash flow margins of TCW's peers, the document adds.

TCW has already made $8.7 million in cost cuts, according to the document. The firm has long had a reputation for being "a bit bloated" in terms of overhead, said Eric Jacobson, a senior analyst at Morningstar Inc, who used to cover the firm's mutual funds.

"I have heard that there are a lot of wholesalers and distribution and just a lot more of extra bodies than they probably need," Jacobson said.

TCW also outlines in the document that four Carlyle executives will be joining TCW's board, including Christopher Dodds, who was chief financial officer of Charles Schwab Corp (SCHW.N) from 1999 through May 2007.

(Additional reporting by Jennifer Ablan in New York; Editing by Paritosh Bansal)

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