for all periods presented , a portion of the balance at end of year pertains to state tax liabilities , which are presented before any offset for federal tax benefits . the effect of unrecognized tax benefits , if recorded , that would impact the annual effective tax rate for 2015 , 2014 , and 2013 would be approximately 12% ( 12 % ) , 4% ( 4 % ) , and ( 1 ) % (  % ) , respectively , of pretax book income ( loss ) . alcoa does not anticipate that changes in its unrecognized tax benefits will have a material impact on the statement of consolidated operations during 2016 ( see other matters in note n for a matter for which no reserve has been recognized ) . it is alcoa 2019s policy to recognize interest and penalties related to income taxes as a component of the provision for income taxes on the accompanying statement of consolidated operations . in 2015 , 2014 , and 2013 , alcoa recognized $ 8 , $ 1 , and $ 2 , respectively , in interest and penalties . due to the expiration of the statute of limitations , settlements with tax authorities , and refunded overpayments , alcoa also recognized interest income of $ 2 , $ 5 , and $ 12 in 2015 , 2014 , and 2013 , respectively . as of december 31 , 2015 and 2014 , the amount accrued for the payment of interest and penalties was $ 9 . u . receivables sale of receivables programs alcoa has an arrangement with three financial institutions to sell certain customer receivables without recourse on a revolving basis . the sale of such receivables is completed through the use of a bankruptcy remote special purpose entity , which is a consolidated subsidiary of alcoa . this arrangement provides for minimum funding of $ 200 up to a maximum of $ 500 for receivables sold . on march 30 , 2012 , alcoa initially sold $ 304 of customer receivables in exchange for $ 50 in cash and $ 254 of deferred purchase price under this arrangement . alcoa has received additional net cash funding of $ 200 for receivables sold ( $ 1258 in draws and $ 1058 in repayments ) since the program 2019s inception ( no draws or repayments occurred in 2015 ) , including $ 40 ( $ 710 in draws and $ 670 in repayments ) in 2014 . as of december 31 , 2015 and 2014 , the deferred purchase price receivable was $ 249 and $ 356 , respectively , which was included in other receivables on the accompanying consolidated balance sheet . the deferred purchase price receivable is reduced as collections of the underlying receivables occur ; however , as this is a revolving program , the sale of new receivables will result in an increase in the deferred purchase price receivable . the net change in the deferred purchase price receivable was reflected in the decrease ( increase ) in receivables line item on the accompanying statement of consolidated cash flows . this activity is reflected as an operating cash flow because the related customer receivables are the result of an operating activity with an insignificant , short-term interest rate risk. .
alcoa and its subsidiaries file income tax returns in the u.s . federal jurisdiction and various states and foreign jurisdictions . with a few minor exceptions , alcoa is no longer subject to income tax examinations by tax authorities for years prior to 2006 . all u.s . tax years prior to 2015 have been audited by the internal revenue service . various state and foreign jurisdiction tax authorities are in the process of examining alcoa 2019s income tax returns for various tax years through 2014 . a reconciliation of the beginning and ending amount of unrecognized tax benefits ( excluding interest and penalties ) was as follows: .
what was the increase in the settlements with tax authorities as a percent of the tax liabilities observed during 2013 and 2014?
december 31 , the reductions for tax positions of prior years of 2015 is -2 ( 2 ) ; the reductions for tax positions of prior years of 2014 is -4 ( 4 ) ; the reductions for tax positions of prior years of 2013 is -2 ( 2 ) ; december 31 , the settlements with tax authorities of 2015 is -2 ( 2 ) ; the settlements with tax authorities of 2014 is -29 ( 29 ) ; the settlements with tax authorities of 2013 is -8 ( 8 ) ;
december 31, 2015 2014 2013
balance at beginning of year $ 35 $ 63 $ 66
additions for tax positions of the current year 2 2 2
additions for tax positions of prior years 15 5 11
reductions for tax positions of prior years -2 ( 2 ) -4 ( 4 ) -2 ( 2 )
settlements with tax authorities -2 ( 2 ) -29 ( 29 ) -8 ( 8 )
expiration of the statute of limitations -1 ( 1 ) - -2 ( 2 )
foreign currency translation -4 ( 4 ) -2 ( 2 ) -4 ( 4 )
balance at end of year $ 43 $ 35 $ 63