pre_text: republic services , inc . notes to consolidated financial statements 2014 ( continued ) changes in the deferred tax valuation allowance for the years ended december 31 , 2012 , 2011 and 2010 are as follows: .
post_text: in assessing the realizability of deferred tax assets , management considers whether it is more likely than not that some portion or all of the deferred tax assets will not be realized after the initial recognition of the deferred tax asset . we also provide valuation allowances , as needed , to offset portions of deferred tax assets due to uncertainty surrounding the future realization of such deferred tax assets . we adjust the valuation allowance in the period management determines it is more likely than not that deferred tax assets will or will not be realized . we have state net operating loss carryforwards with an estimated tax effect of $ 130.2 million available at december 31 , 2012 . these state net operating loss carryforwards expire at various times between 2013 and 2032 . we believe that it is more likely than not that the benefit from certain state net operating loss carryforwards will not be realized . in recognition of this risk , at december 31 , 2012 , we have provided a valuation allowance of $ 113.5 million for certain state net operating loss carryforwards . at december 31 , 2012 , we also have provided a valuation allowance of $ 11.3 million for certain other deferred tax assets . deferred income taxes have not been provided on the undistributed earnings of our puerto rican subsidiaries of approximately $ 40 million and $ 39 million as of december 31 , 2012 and 2011 , respectively , as such earnings are considered to be permanently invested in those subsidiaries . if such earnings were to be remitted to us as dividends , we would incur approximately $ 14 million of federal income taxes . we made income tax payments ( net of refunds received ) of approximately $ 185 million , $ 173 million and $ 418 million for 2012 , 2011 and 2010 , respectively . income taxes paid in 2012 and 2011 reflect the favorable tax depreciation provisions of the tax relief , unemployment insurance reauthorization , and job creation act of 2010 ( tax relief act ) that was signed into law in december 2010 . the tax relief act included 100% ( 100 % ) bonus depreciation for property placed in service after september 8 , 2010 and through december 31 , 2011 ( and for certain long-term construction projects to be placed in service in 2012 ) and 50% ( 50 % ) bonus depreciation for property placed in service in 2012 ( and for certain long-term construction projects to be placed in service in 2013 ) . income taxes paid in 2010 includes $ 111 million related to the settlement of certain tax liabilities regarding bfi risk management companies . we and our subsidiaries are subject to income tax in the u.s . and puerto rico , as well as income tax in multiple state jurisdictions . our compliance with income tax rules and regulations is periodically audited by tax authorities . these authorities may challenge the positions taken in our tax filings . thus , to provide for certain potential tax exposures , we maintain liabilities for uncertain tax positions for our estimate of the final outcome of the examinations. .
table: 2012 2011 2010
table: Valuation allowance, beginning of year $118.1 $120.1 $126.5
table: Additions charged to income 1.9 2.1 8.3
table: Usage (3.2) (4.3) (10.4)
table: Expirations of state net operating losses (0.3) (0.3) (0.3)
table: Other, net 8.3 0.5 (4.0)
table: Valuation allowance, end of year $124.8 $118.1 $120.1
question: Analyse this data from a financial earnings document. what was the average balance of the end of year valuation allowance from 2010-2012