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: .

Table:
( millions ) | 2013 | 2012 | 2011
balance at january 1 | $ 82 | $ 107 | $ 111
additions based on tax positions related to the current year | 12 | 12 | 15
additions for tax positions of prior years | 9 | 2 | 17
reductions for tax positions of prior years | -10 ( 10 ) | -12 ( 12 ) | -19 ( 19 )
pre-acquisition unrecognized tax benefits | 2014 | 2 | 2014
reductions for expiration of the applicable statute of limitations | -10 ( 10 ) | -6 ( 6 ) | -7 ( 7 )
settlements | 2014 | -23 ( 23 ) | -8 ( 8 )
foreign currency translation | 2 | 2014 | -2 ( 2 )
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?
Answer: 90.5%
Calculation: divide(82, 107), divide(85, 82), add(#0, #1), divide(#2, const_2)