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to take a lump sum payment at the end of their service. The total accumulated benefit obligation is equivalent to the total projected benefit obligation ("Benefit Obligation"). 

The following are assumptions related to the U.S. defined benefit pension plans: 

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At December 31, 2018 as compared with December 31, 2017, we increased our discount rate from 3.63% to 4.34% based on an analysis of publicly-traded investment grade U.S. corporate bonds, which had a higher yield due to current market conditions. In determining 2018 expense, the expected rate of return on U.S. plan assets remained constant at 6.00%, primarily based on our target allocations and expected long-term asset returns. The long-term rate of return assumption is calculated using a quantitative approach that utilizes unadjusted historical returns and asset allocation as inputs for the calculation. For all U.S. plans, we adopted the RP-2006 mortality tables and the MP-2018 improvement scale published in October 2018. We applied the RP-2006 tables based on the constituency of our plan population for union and non-union participants. We adjusted the improvement scale to utilize 75% of the ultimate improvement rate, consistent with assumptions adopted by the Social Security Administration trustees, based on long-term historical experience. Currently, we believe this approach provides the best estimate of our future obligation. Most plan participants elect to receive plan benefits as a lump sum at the end of service, rather than an annuity. As such, the updated mortality tables had an immaterial effect on our pension obligation. 

Net pension expense for the U.S. defined benefit pension plans (including both qualified and non-qualified plans) was: 

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The estimated prior service cost and the estimated net loss for the U.S. defined benefit pension plans that will be amortized from accumulated other comprehensive loss into pension expense in 2019 is $0.2 million and $3.5 million, respectively. We amortize estimated prior service benefits and estimated net losses over the remaining expected service period. 

The following summarizes the net pension (liability) asset for U.S. plans: 

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