By Allan Sloan
July 2, 2013

FORTUNE — Here’s how I calculated the value of the Treasury’s stake in Ally Financial, formerly GMAC, General Motors’ finance subsidiary. And how I calculated the value of the stake held by Cerberus Capital and its present (and possibly former) investors.

In late May, shortly after a tentative settlement of the bankruptcy of Ally’s Residential Capital subsidiary, Ally announced that it was taking a $1.55 billion charge for expenses connected with the bankruptcy. Previously, it had taken a charge for $750 million, the amount it offered ResCap creditors in May of 2012, when it put ResCap into bankruptcy.

Add $1.55 billion and $750 million, and you get $2.305 billion, which I’ve rounded to $2.3 billion, as the cash Ally will put up to settle its obligations to ResCap creditors ($2.1 billion) and to regulators (as yet undisclosed, but presumably about $200 million).

As of Mar. 31, 2013, the most recent number available, Ally’s stated net worth was $20.474 billion. But that included $5.938 billion of preferred stock held by the U.S. Treasury. It also didn’t include any provision for the $1.55 billion May charge, which is tax-deductible. Apply a 40% tax rate, and the after-tax cost of the settlement provision is $930 million. So I subtracted that amount from Ally’s March reported net worth, and then proceeded with my calculations.

All of this yields the following numbers, which I used to estimate the value of Ally’s stock, which isn’t publicly traded:

Ally net worth as of 3/31/13…………………………….$20,474 million

Less Treasury preferred…………………………………$5,938  million

Common stock net worth………………………………..$14,536  million

Less after-tax effect of $1.55B reserve…………….$930  million

Common stock net of reserve………………………….$13,606 million

Divide by Ally’s 1,330,970 shares

Net worth per share………………………………………..$10,223

Valuing Treasury’s stake

Treasury has 981,971 common shares of Ally, shares, so the value of its common stock is $10.038 billion.

We add back the Treasury preferred stock, $5.938 billion.

Total value of Treasury common and preferred is $15.976 billion.

Treasury’s original total investment in Ally was $17.2 billion.

In 2011, it realized $2.7 billion from selling part of its preferred stock holdings.

Thus, its total cost is $14.5 billion, roughly $1.5 billion less than the value of its common and preferred holding.

Valuing Cerberus’s stake

Holdings of Cerberus & Affiliates are 115,434 shares.

Holdings of unnamed “third party investors” total 101,285 shares. These shares were originally part of the 2006 Cerberus deal to buy 51% of what was then called GMAC, but were split off from the other Cerberus holdings for regulatory reasons when Ally Financial became a bank holding company. That 101,285 number is not disclosed by Ally: I derived it by taking Ally’s total common shares outstanding, 1,330,970; and subtracting the Treasury stake; General Motors’ stake, 132,280 shares; and Cerberus & Affiliates’ stake, the aforementioned 115,434 shares.

Some of those “third party” shares have probably changed hands, but I’m treating all of them as Cerberus-related, in order to calculate the value of the investment that Cerberus and its customers  made in Ally.

I don’t know how many of the shares involved stem from the original $7.4 billion Cerberus and its investors paid for their then-51% stake, and how many stem from the $750 million that Cerberus and some of its investors put into the company in 2009, alongside $1.25 billion from the Treasury.

Now, the math

Total Cerberus & Affiliates and “third party” shares: 216,789

Multiply by $10,223, and the book value of these shares is $2.215 billion.

Cerberus and its investors paid a total of $8.15 billion for their shares, giving them a loss of about $5.9 billion.

Sources: Fortune calculations, from public records

BACK TO: Uncle Sam ahead on the Ally bailout? Who’da thunk it?

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