projections of capacity, passenger mile yield, fuel costs, labor costs and other relevant factors. If an impairment occurs, the impairment loss recognized is the amount by which the fleet'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, projected future taxable income, scheduled reversals of deferred tax liabilities, the overall business environment, our historical financial results and tax planning strategies. In evaluating the likelihood of utilizing our net deferred income tax assets, the significant factors that we consider include (1) our recent history of profitability, (2) growth in the U.S. and global economies, (3) forecast of airline revenue trends, (4) estimate of future fuel prices and (5) future impact of taxable temporary differences.

We recorded a full valuation allowance in 2004 due to our cumulative loss position at that time. During 2013, after considering all positive and negative evidence, we concluded that our deferred income tax assets are more likely than not to be realized. Accordingly, we released substantially all of the valuation allowance against our net deferred income tax assets. We recognized an $8.0 billion benefit in our provision for income taxes, primarily related to the valuation allowance release.

At the end of 2015 our net deferred tax asset balance was $5.0 billion , against which we maintained a $56 million valuation allowance, primarily related to state net operating losses, state credits and unrealized losses on investments, which have limited expiration periods.

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, 2015 , the unfunded benefit obligation for these plans recorded on our Consolidated Balance Sheet was $11.2 billion . During 2015 , we contributed $1.2 billion to these plans and recorded $240 million of expense in salaries and related costs on our Consolidated Statement of Operations. In 2016, we estimate we will contribute at least $1.0 billion to these plans, including $500 million of contributions above the minimum funding requirements, and that our expense will be approximately $250 million. The most critical assumptions impacting our defined benefit pension plan obligations and expenses are the discount rate, the expected long-term rate of return on plan assets and life expectancy.

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