When reading MBIA Inc.’s report for the second quarter, it makes sense to question how a company burning through more than $50 million in cash a week this year could have posted a profit.

The answer: a healthy slug of optimism.

The Armonk, N.Y.-based bond insurer surprised analysts by recording $894.7 million in profit during the second quarter.

This from a company that had lost a total of $4.3 billion the previous five quarters, and wiped out $9 billion in shareholder value since the beginning of 2007.

At first glance, the profit seems mathematically improbable.

Revenue plunged 70%. The company squirreled away $353.7 million to pay more claims on residential mortgage-backed securities it insures.

In a conference call with investors, chief financial officer Chuck Chaplin said the company expects claims on mortgage bonds “will remain elevated” for the rest of the year.

Overcoming the hits to the company’s balance sheet was a $1.1 billion assumption.

The assumption is that MBIA will be able to recover claims from mortgage lenders and servicers who allegedly tricked the company into insuring sketchy deals.

MBIA has been paying billions of dollars in claims on insured bonds secured by mortgages suffering from a blizzard of defaults.

The company has sued some of the lenders and servicers — most prominent among them Countrywide Financial and ResCap — that  constructed mortgage bonds MBIA insured.

The dispute concerns 24 deals comprising 496,917 home loans.

The allegations against these lenders go like this: with investors earlier this decade paying good money for mortgage bonds, the lenders abandoned their standards and piled as many shoddy home loans as they could fit into the trusts that eventually become residential mortgage-backed bonds.

In order to fool MBIA into insuring the deals, the lenders lied about such important details as borrowers’ credit scores and debt loads, and the value of the homes acting as collateral on the mortgages.

MBIA claims the lenders in the purchase agreements establishing the trusts swore by their underwriting criteria and promised to adhere to rigorous standards.

Now, here is the crux: in the purchase agreements, the lenders agreed to either replace any mortgage that did not comply with their standards, or buy it back from the trust, according to MBIA’s suit.

Further, if MBIA pays a claim on a defaulted loan later determined ineligible for the trust, the insurer gains the right to cash reimbursement for the claim when the lender repurchases the delinquent loan.

That is where the $1.1 billion MBIA tacked onto its assets comes in. It is a receivable from these servicers, assuming they will reimburse the company for claims paid on delinquent loans that should not have been in the bonds in the first place.

That receivable is an asset. An increase in assets without a corresponding reduction in liabilities is profit. Voila.

MBIA reviewed 23,765 loans — representing 27% of the defaulted loans in the 24 trusts under dispute — and concluded two-thirds of them “had serious breaches of representations and warranties.”

That is, they were ineligible for inclusion in the bonds based on the agreements with the servicers.

The breaches include things like breaking the requirement for debt-to-income and loan-to-value ratios and the like, or missing forms.

The $1.1 billion is the money the company expects to retrieve when the servicers ultimately honor or are legally forced to honor their commitments to repurchase the ineligible loans.

That sum is only from the 23,765 reviewed loans.

MBIA expects to record further gains once it reviews the remaining loans and uncovers more ineligible for the insured deals.

In fact, $1.1 billion represents “an enormous discount” to the figure ultimately to be recovered, MBIA reckons.

The insurer acknowledged it will take a while to collect this first round of remunerations, probably at least three years.

The $1.1 billion figure is the present value of the sum for the money it believes it is owed on the loans already determined to be ineligible, discounted over three years at a rate of 1.625%.

One might wonder, why recognize the gain now when the suit was filed almost a year ago? The company notes some encouraging developments.

For one thing, the New York State Supreme Court last month allowed MBIA’s fraud claims against Countrywide to proceed, for one.

Plus, in case anyone was worried about subprime mortgage lenders’ ability to raise enough cash to repurchase billions of dollars in bad loans, the financial conditions of some of the servicers MBIA accuses of fraud have been strengthened “due to mergers and acquisitions.” This is presumably referring to Countrywide’s acquisition by Bank of America, “and/or government assistance,” presumably referring to the federal government’s stake in ResCap’s parent, General Motors.

MBIA has yet to collect a material amount, and it does not expect to know more for at least a year and a half.

In fact, Countrywide has stonewalled MBIA at every step of this process, the insurer claims.

That did not stop MBIA from assuming it will prevail, spinning a period with more than $2 billion in lost revenue and $357.4 million in investment losses into a profitable quarter.

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