52 2013 ppg annual report and form 10-k repatriation of undistributed earnings of non-u.s . subsidiaries as of december 31 , 2013 and december 31 , 2012 would have resulted in a u.s . tax cost of approximately $ 250 million and $ 110 million , respectively . the company files federal , state and local income tax returns in numerous domestic and foreign jurisdictions . in most tax jurisdictions , returns are subject to examination by the relevant tax authorities for a number of years after the returns have been filed . the company is no longer subject to examinations by tax authorities in any major tax jurisdiction for years before 2006 . additionally , the internal revenue service has completed its examination of the company 2019s u.s . federal income tax returns filed for years through 2010 . the examination of the company 2019s u.s . federal income tax return for 2011 is currently underway and is expected to be finalized during 2014 . a reconciliation of the total amounts of unrecognized tax benefits ( excluding interest and penalties ) as of december 31 follows: .

Row 1: ( millions ), 2013, 2012, 2011
Row 2: balance at january 1, $ 82, $ 107, $ 111
Row 3: additions based on tax positions related to the current year, 12, 12, 15
Row 4: additions for tax positions of prior years, 9, 2, 17
Row 5: reductions for tax positions of prior years, -10 ( 10 ), -12 ( 12 ), -19 ( 19 )
Row 6: pre-acquisition unrecognized tax benefits, 2014, 2, 2014
Row 7: reductions for expiration of the applicable statute of limitations, -10 ( 10 ), -6 ( 6 ), -7 ( 7 )
Row 8: settlements, 2014, -23 ( 23 ), -8 ( 8 )
Row 9: foreign currency translation, 2, 2014, -2 ( 2 )
Row 10: balance at december 31, $ 85, $ 82, $ 107

the company expects that any reasonably possible change in the amount of unrecognized tax benefits in the next 12 months would not be significant . the total amount of unrecognized tax benefits that , if recognized , would affect the effective tax rate was $ 81 million as of december 31 , 2013 . the company recognizes accrued interest and penalties related to unrecognized tax benefits in income tax expense . as of december 31 , 2013 , 2012 and 2011 , the company had liabilities for estimated interest and penalties on unrecognized tax benefits of $ 9 million , $ 10 million and $ 15 million , respectively . the company recognized $ 2 million and $ 5 million of income in 2013 and 2012 , respectively , related to the reduction of estimated interest and penalties . the company recognized no income or expense for estimated interest and penalties during the year ended december 31 , 2011 . 13 . pensions and other postretirement benefits defined benefit plans ppg has defined benefit pension plans that cover certain employees worldwide . the principal defined benefit pension plans are those in the u.s. , canada , the netherlands and the u.k . which , in the aggregate represent approximately 91% ( 91 % ) of the projected benefit obligation at december 31 , 2013 , of which the u.s . defined benefit pension plans represent the majority . ppg also sponsors welfare benefit plans that provide postretirement medical and life insurance benefits for certain u.s . and canadian employees and their dependents . these programs require retiree contributions based on retiree-selected coverage levels for certain retirees and their dependents and provide for sharing of future benefit cost increases between ppg and participants based on management discretion . the company has the right to modify or terminate certain of these benefit plans in the future . salaried and certain hourly employees in the u.s . hired on or after october 1 , 2004 , or rehired on or after october 1 , 2012 are not eligible for postretirement medical benefits . salaried employees in the u.s . hired , rehired or transferred to salaried status on or after january 1 , 2006 , and certain u.s . hourly employees hired in 2006 or thereafter are eligible to participate in a defined contribution retirement plan . these employees are not eligible for defined benefit pension plan benefits . plan design changes in january 2011 , the company approved an amendment to one of its u.s . defined benefit pension plans that represented about 77% ( 77 % ) of the total u.s . projected benefit obligation at december 31 , 2011 . depending upon the affected employee's combined age and years of service to ppg , this change resulted in certain employees no longer accruing benefits under this plan as of december 31 , 2011 , while the remaining employees will no longer accrue benefits under this plan as of december 31 , 2020 . the affected employees will participate in the company 2019s defined contribution retirement plan from the date their benefit under the defined benefit plan is frozen . the company remeasured the projected benefit obligation of this amended plan , which lowered 2011 pension expense by approximately $ 12 million . the company made similar changes to certain other u.s . defined benefit pension plans in 2011 . the company recognized a curtailment loss and special termination benefits associated with these plan amendments of $ 5 million in 2011 . the company plans to continue reviewing and potentially changing other ppg defined benefit plans in the future . separation and merger of commodity chemicals business on january 28 , 2013 , ppg completed the separation of its commodity chemicals business and the merger of the subsidiary holding the ppg commodity chemicals business with a subsidiary of georgia gulf , as discussed in note 22 , 201cseparation and merger transaction . 201d ppg transferred the defined benefit pension plan and other postretirement benefit liabilities for the affected employees in the u.s. , canada , and taiwan in the separation resulting in a net partial settlement loss of $ 33 million notes to the consolidated financial statements .

Question: what is the average increase in the balance of unrecognized tax benefits from 2011 to 2013?
Program: divide(82, 107), divide(85, 82), add(#0, #1), divide(#2, const_2)
Answer: 0.90147