Mortgage finance giants Fannie Mae and Freddie Mac could cost the government $53 billion through 2020 or save the government as much as $44 billion, depending on the accounting principles used, the non-partisan Congressional Budget Office said on Thursday.

The alternative methods result in quite different estimates of the (government sponsored enterprises') impact on the federal budget, CBO Director Douglas Elmendorf said in a letter to House Financial Services Committee Chairman Barney Frank, who requested the different estimates.

CBO used three different methodologies to come up with its estimates: cash treatments, fair value, and principles used under the Federal Credit Reform Act, or FCRA.

Using fair value accounting, Fannie Mae and Freddie Mac would cost the government about $14 billion in fiscal 2011, which begins October 1, $9 billion the following year and smaller amounts in later years, to bring the 10-year total cost to $53 billion.

Using cash transaction accounting, the two entities would cost about $20 billion in the first year, $10 billion in fiscal 2012 and then begin to save the government single-digit billions starting in fiscal 2014 to total about $8 billion in net savings over the decade.

Cash transactions reflect the payments made between the entities and the federal government, not transactions between the GSEs and the private sector.

Using FCRA rules, the government would save single-digit billions in each of the 10 years for a combined savings of $44 billion.

Under FCRA, the net cost of a loan or loan guarantee is calculated as the net present value of expected cash flows over the life of the obligation.

The fair value treatment differs from FCRA because it includes the cost of financial market risk.

By incorporating a market-based risk premium associated with the GSEs credit guarantees, they reflect the fact that the government's assumption of financial risk is costly to taxpayers, Elmendorf wrote.

CBO uses fair value treatment for its baseline budget forecasts to provide the Congress with the most accurate information about the cost of supporting Fannie Mae and Freddie Mac under conservatorship.

The United States government seized the two firms in late 2008 at the height of the financial crisis. Since then, the two entities have taken about $150 billion in direct aid from the government.

(Editing by Andrea Ricci)

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