yield, fuel costs, labor costs and other relevant factors. If an impairment occurs, the impairment loss recognized is the amount by which the aircraft's carrying amount exceeds its estimated fair value. We estimate aircraft fair values using published sources, appraisals and bids received from third parties, as available.  

 

Income Tax Valuation Allowance  

 

We periodically assess whether it is more likely than not that we will generate sufficient taxable income to realize our deferred income tax assets. We establish valuation allowances if it is not likely we will realize our deferred income tax assets. In making this determination, we consider all available positive and negative evidence and make certain assumptions. We consider, among other things, our future projections of sustained profitability, deferred tax liabilities, the overall business environment, our historical financial results, our industry's historically cyclical financial results and potential current and future tax planning strategies.  

 

We recorded a full valuation allowance in 2004 due to our cumulative three year loss position at that time, compounded by the negative industrywide business trends and outlook. At December 31, 2012, we had an $11.0 billion valuation allowance established against our deferred income tax assets, which represents a full valuation allowance against our net deferred income tax asset.  

 

During the March 2012 quarter, we moved from a cumulative loss position over the previous three years to a cumulative income position for the first time since we established a full valuation allowance. We have concluded as of December 31, 2012 that the valuation allowance was still needed on our net deferred tax assets based upon the weight of the factors described above, especially considering the history of losses. We continue to evaluate our cumulative income position and income trend as well as our future projections of sustained profitability and whether this profitability trend constitutes sufficient positive evidence to support a reversal of our valuation allowance (in full or in part).  

 

Defined Benefit Pension Plans  

 

We sponsor defined benefit pension plans for eligible employees and retirees. These plans are closed to new entrants and frozen for future benefit accruals. As of December 31, 2012 , the unfunded benefit obligation for these plans recorded on our Consolidated Balance Sheet was $13.3 billion . 

During 2012 , we contributed $697 million to these plans and recorded $368 million of expense in salaries and related costs on our Consolidated Statement of Operations. In 2013, we estimate we will contribute approximately $675 million to these plans and that our expense will be approximately $350 million. The most critical assumptions impacting our defined benefit pension plan obligations and expenses are the discount rate and the expected long-term rate of return on the plan assets.  

 

Weighted Average Discount Rate. We determine our weighted average discount rate on our measurement date primarily by reference to annualized rates earned on high quality fixed income investments and yield-to-maturity analysis specific to our