Status quo is properly presumed in monetary proportions, et alia, both as the default assumption in economic analysis, and by virtue of the Fed's "stability" mandate. (It can be overridden by temporary directional policies which average to a norm.) Note also the Fed's status quo assumption, referenced in the last paragraphs of Part III.
 The money is routed through the Mint, which deducts its costs, to the Treasury's General Fund. See How the Costs and Earnings Associated with Producing Coins and Currency Are Budgeted and Accounted For (April 2004, GAO-04-283 , page 11):
"The Fed pays Treasury the full face value of coins that it buys, and Treasury then allocates the payments to the Mint"All Mint revenues are deposited into its Public Enterprise Fund, including receipts from the Fed from the sale of circulating coins at face value, and all expenses for making coins are paid out of the Public Enterprise Fund...At least once a year, any amount that is determined by the Mint to be in excess of the amount required by the Public Enterprise Fund is to be transferred to Treasury's general fund."
Besides avoiding this, it is easy to see from the cover page why this highly relevant report was not even cited in the 2011 report:
"However, the Mint is still not explicitly stating whether the retained amounts are in excess of the estimated operating costs for the following year and, if so, it is not explaining how the retained earnings will be used, as required by law."
In an attached letter, the Treasury tortuously disputed the requirement to say how its excess funds were spent (page 38):
"[T]he GAO is recommending that the Mint provide information on the specific purposes for which retained amounts of earnings will be used. The PEF legislation requires reporting if earnings are retained that exceed the following year's estimated operating costs (i.e., "the amount on deposit in the PEF at the end of the period covered by the report exceeds the estimated operating costs of the PEF for the 1-year period beginning at the end of such period"). 31 U.S.C. - 5134( c)( 5)(B)(ii)."
 A less conservative approach (resulting in a slightly higher recovery of interest relief per coin-swap) would adopt the overall or target reserve ratio, instead of this fraction. And this fraction itself could be better adjusted, e.g. 1990 data should be used. Whatever adjustment is optimal, the difference would not meaningfully alter the order-of-magnitude conclusion drawn.
 Financial Audit: Bureau of the Public Debt's Fiscal Years 2011 and 2010 Schedules of Federal Debit (November 2011, GAO-12-164). Pages 24, 25.