billion benefit in our provision for income taxes, primarily related to the valuation allowance release.  

 

At the end of 2014 our net deferred tax asset balance was $7.6 billion , against which we maintained a $46 million valuation allowance, primarily related to state net operating losses with 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, 2014 , the unfunded benefit obligation for these plans recorded on our Consolidated Balance Sheet was $12.5 billion . During 2014 , we contributed $917 million to these plans and recorded $233 million of expense in salaries and related costs on our Consolidated Statement of Operations. In 2015, we estimate we will contribute at least $950 million to these plans, including $340 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 yield-to-maturity analysis specific to our estimated future benefit payments. We used a weighted average discount rate to value the obligations of 4.14% and 5.01% at December 31, 2014 and 2013 , respectively. Our weighted average discount rate for net periodic pension benefit cost in each of the past three years has varied from the rate selected on our measurement date, ranging from 4.10% to 4.99% between 2014 and 2012 .  

 

Expected Long-Term Rate of Return. Our expected long-term rate of return on plan assets is based primarily on plan-specific investment studies using historical market return and volatility data. Modest excess return expectations versus some public market indices are incorporated into the return projections based on the actively managed structure of the investment programs and their records of achieving such returns historically. We also expect to receive a premium for investing in less liquid private markets. We review our rate of return on plan asset assumptions annually. Our annual investment performance for one particular year does not, by itself, significantly influence our evaluation. Our actual historical annualized three and five year rate of return on plan assets for our defined benefit pension plans was approximately 11% and 9% , respectively, as of December 31, 2014 . The investment strategy for our defined benefit pension plan assets is to earn a long-term return that meets or exceeds our annualized return target while taking an acceptable level of risk and maintaining sufficient liquidity to pay current benefits and other cash obligations of the plan. This is achieved by investing in a globally diversified mix of public and private equity, fixed income, real assets, hedge funds, and