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Benefit Plans and Other Postretirement Benefits (Tables) - Pension Benefits | 12 Months Ended
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Dec. 31, 2021
Defined Benefit Plan Disclosure |
Schedule of change in projected benefit obligation and plan assets | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | U.S. Plans | ​ | Foreign Plans | ​ | Total
​ | ​ | ​ | 2021 | ​ | ​ | 2020 | ​ | ​ | 2021 | ​ | ​ | 2020 | ​ | ​ | 2021 | ​ | ​ | 2020
Change in projected benefit obligation: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Projected benefit obligation at beginning of year | ​ | $ | 526.4 | ​ | $ | 496.5 | ​ | $ | 302.0 | ​ | $ | 261.4 | ​ | $ | 828.4 | ​ | $ | 757.9
Service cost | ​ |  | 4.2 | ​ |  | 4.5 | ​ |  | 3.3 | ​ |  | 3.0 | ​ |  | 7.5 | ​ |  | 7.5
Interest cost | ​ |  | 8.6 | ​ |  | 13.2 | ​ |  | 2.7 | ​ |  | 3.5 | ​ |  | 11.3 | ​ |  | 16.7
Plan amendments | ​ |  | 0.4 | ​ |  | — | ​ |  | — | ​ |  | 0.1 | ​ |  | 0.4 | ​ |  | 0.1
Actuarial (gain) loss | ​ |  | (16.9) | ​ |  | 38.5 | ​ |  | (20.4) | ​ |  | 24.1 | ​ |  | (37.3) | ​ |  | 62.6
Foreign exchange translation | ​ |  | — | ​ |  | — | ​ |  | (12.3) | ​ |  | 17.9 | ​ |  | (12.3) | ​ |  | 17.9
Benefits paid | ​ |  | (27.4) | ​ |  | (26.3) | ​ |  | (9.4) | ​ |  | (8.0) | ​ |  | (36.8) | ​ |  | (34.3)
Projected benefit obligation at end of year | ​ |  | 495.3 | ​ |  | 526.4 | ​ |  | 265.9 | ​ |  | 302.0 | ​ |  | 761.2 | ​ |  | 828.4
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Change in plan assets: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Fair value of plan assets at beginning of year | ​ |  | 515.7 | ​ |  | 473.2 | ​ |  | 116.6 | ​ |  | 107.8 | ​ |  | 632.3 | ​ |  | 581.0
Actual return on plan assets | ​ |  | 38.2 | ​ |  | 67.8 | ​ |  | 6.3 | ​ |  | 6.3 | ​ |  | 44.5 | ​ |  | 74.1
Employer contributions | ​ |  | 1.0 | ​ |  | 1.0 | ​ |  | 5.8 | ​ |  | 5.5 | ​ |  | 6.8 | ​ |  | 6.5
Foreign exchange translation | ​ |  | — | ​ |  | — | ​ |  | (2.8) | ​ |  | 5.0 | ​ |  | (2.8) | ​ |  | 5.0
Benefits paid | ​ |  | (27.4) | ​ |  | (26.3) | ​ |  | (9.4) | ​ |  | (8.0) | ​ |  | (36.8) | ​ |  | (34.3)
Fair value of plan assets at end of year | ​ |  | 527.5 | ​ |  | 515.7 | ​ |  | 116.5 | ​ |  | 116.6 | ​ |  | 644.0 | ​ |  | 632.3
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Over (under) funded status at end of year | ​ | $ | 32.2 | ​ | $ | (10.7) | ​ | $ | (149.4) | ​ | $ | (185.4) | ​ | $ | (117.2) | ​ | $ | (196.1)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Amounts recognized on the balance sheet as of December 31: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Other long-term assets | ​ | $ | 50.0 | ​ | $ | 7.8 | ​ | $ | 0.7 | ​ | $ | 0.3 | ​ | $ | 50.7 | ​ | $ | 8.1
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Other accrued expenses | ​ | ​ | 1.1 | ​ | ​ | 1.0 | ​ | ​ | 3.1 | ​ | ​ | 3.3 | ​ | ​ | 4.2 | ​ | ​ | 4.3
Accrued pension and postretirement benefit obligations | ​ | ​ | 16.7 | ​ | ​ | 17.5 | ​ | ​ | 147.0 | ​ | ​ | 182.4 | ​ | ​ | 163.7 | ​ | ​ | 199.9
Over (under) funded status at end of year | ​ | $ | 32.2 | ​ | $ | (10.7) | ​ | $ | (149.4) | ​ | $ | (185.4) | ​ | $ | (117.2) | ​ | $ | (196.1)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Accumulated other comprehensive loss, net | ​ | $ | (83.0) | ​ | $ | (118.2) | ​ | $ | (51.8) | ​ | $ | (74.3) | ​ | $ | (134.8) | ​ | $ | (192.5)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Weighted average assumptions used to determine projected benefit obligations: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Discount rate |  | ​ | 2.69 | % | ​ | 2.30 | % | ​ | 1.58 | % | ​ | 1.12 | % | ​ | ​ | ​ | ​ | ​
Rate of compensation increase |  | ​ | 2.40 | % | ​ | 2.40 | % | ​ | 1.75 | % | ​ | 1.75 | % | ​ | ​ | ​ | ​ | ​
Schedule of amounts recognized in the balance sheet | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | U.S. Plans | ​ | Foreign Plans | ​ | Total
​ | ​ | ​ | 2021 | ​ | ​ | 2020 | ​ | ​ | 2021 | ​ | ​ | 2020 | ​ | ​ | 2021 | ​ | ​ | 2020
Change in projected benefit obligation: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Projected benefit obligation at beginning of year | ​ | $ | 526.4 | ​ | $ | 496.5 | ​ | $ | 302.0 | ​ | $ | 261.4 | ​ | $ | 828.4 | ​ | $ | 757.9
Service cost | ​ |  | 4.2 | ​ |  | 4.5 | ​ |  | 3.3 | ​ |  | 3.0 | ​ |  | 7.5 | ​ |  | 7.5
Interest cost | ​ |  | 8.6 | ​ |  | 13.2 | ​ |  | 2.7 | ​ |  | 3.5 | ​ |  | 11.3 | ​ |  | 16.7
Plan amendments | ​ |  | 0.4 | ​ |  | — | ​ |  | — | ​ |  | 0.1 | ​ |  | 0.4 | ​ |  | 0.1
Actuarial (gain) loss | ​ |  | (16.9) | ​ |  | 38.5 | ​ |  | (20.4) | ​ |  | 24.1 | ​ |  | (37.3) | ​ |  | 62.6
Foreign exchange translation | ​ |  | — | ​ |  | — | ​ |  | (12.3) | ​ |  | 17.9 | ​ |  | (12.3) | ​ |  | 17.9
Benefits paid | ​ |  | (27.4) | ​ |  | (26.3) | ​ |  | (9.4) | ​ |  | (8.0) | ​ |  | (36.8) | ​ |  | (34.3)
Projected benefit obligation at end of year | ​ |  | 495.3 | ​ |  | 526.4 | ​ |  | 265.9 | ​ |  | 302.0 | ​ |  | 761.2 | ​ |  | 828.4
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Change in plan assets: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Fair value of plan assets at beginning of year | ​ |  | 515.7 | ​ |  | 473.2 | ​ |  | 116.6 | ​ |  | 107.8 | ​ |  | 632.3 | ​ |  | 581.0
Actual return on plan assets | ​ |  | 38.2 | ​ |  | 67.8 | ​ |  | 6.3 | ​ |  | 6.3 | ​ |  | 44.5 | ​ |  | 74.1
Employer contributions | ​ |  | 1.0 | ​ |  | 1.0 | ​ |  | 5.8 | ​ |  | 5.5 | ​ |  | 6.8 | ​ |  | 6.5
Foreign exchange translation | ​ |  | — | ​ |  | — | ​ |  | (2.8) | ​ |  | 5.0 | ​ |  | (2.8) | ​ |  | 5.0
Benefits paid | ​ |  | (27.4) | ​ |  | (26.3) | ​ |  | (9.4) | ​ |  | (8.0) | ​ |  | (36.8) | ​ |  | (34.3)
Fair value of plan assets at end of year | ​ |  | 527.5 | ​ |  | 515.7 | ​ |  | 116.5 | ​ |  | 116.6 | ​ |  | 644.0 | ​ |  | 632.3
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Over (under) funded status at end of year | ​ | $ | 32.2 | ​ | $ | (10.7) | ​ | $ | (149.4) | ​ | $ | (185.4) | ​ | $ | (117.2) | ​ | $ | (196.1)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Amounts recognized on the balance sheet as of December 31: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Other long-term assets | ​ | $ | 50.0 | ​ | $ | 7.8 | ​ | $ | 0.7 | ​ | $ | 0.3 | ​ | $ | 50.7 | ​ | $ | 8.1
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Other accrued expenses | ​ | ​ | 1.1 | ​ | ​ | 1.0 | ​ | ​ | 3.1 | ​ | ​ | 3.3 | ​ | ​ | 4.2 | ​ | ​ | 4.3
Accrued pension and postretirement benefit obligations | ​ | ​ | 16.7 | ​ | ​ | 17.5 | ​ | ​ | 147.0 | ​ | ​ | 182.4 | ​ | ​ | 163.7 | ​ | ​ | 199.9
Over (under) funded status at end of year | ​ | $ | 32.2 | ​ | $ | (10.7) | ​ | $ | (149.4) | ​ | $ | (185.4) | ​ | $ | (117.2) | ​ | $ | (196.1)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Accumulated other comprehensive loss, net | ​ | $ | (83.0) | ​ | $ | (118.2) | ​ | $ | (51.8) | ​ | $ | (74.3) | ​ | $ | (134.8) | ​ | $ | (192.5)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Weighted average assumptions used to determine projected benefit obligations: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Discount rate |  | ​ | 2.69 | % | ​ | 2.30 | % | ​ | 1.58 | % | ​ | 1.12 | % | ​ | ​ | ​ | ​ | ​
Rate of compensation increase |  | ​ | 2.40 | % | ​ | 2.40 | % | ​ | 1.75 | % | ​ | 1.75 | % | ​ | ​ | ​ | ​ | ​
Schedule of weighted average assumptions used to determine projected benefit obligations | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | U.S. Plans | ​ | Foreign Plans | ​ | Total
​ | ​ | ​ | 2021 | ​ | ​ | 2020 | ​ | ​ | 2021 | ​ | ​ | 2020 | ​ | ​ | 2021 | ​ | ​ | 2020
Change in projected benefit obligation: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Projected benefit obligation at beginning of year | ​ | $ | 526.4 | ​ | $ | 496.5 | ​ | $ | 302.0 | ​ | $ | 261.4 | ​ | $ | 828.4 | ​ | $ | 757.9
Service cost | ​ |  | 4.2 | ​ |  | 4.5 | ​ |  | 3.3 | ​ |  | 3.0 | ​ |  | 7.5 | ​ |  | 7.5
Interest cost | ​ |  | 8.6 | ​ |  | 13.2 | ​ |  | 2.7 | ​ |  | 3.5 | ​ |  | 11.3 | ​ |  | 16.7
Plan amendments | ​ |  | 0.4 | ​ |  | — | ​ |  | — | ​ |  | 0.1 | ​ |  | 0.4 | ​ |  | 0.1
Actuarial (gain) loss | ​ |  | (16.9) | ​ |  | 38.5 | ​ |  | (20.4) | ​ |  | 24.1 | ​ |  | (37.3) | ​ |  | 62.6
Foreign exchange translation | ​ |  | — | ​ |  | — | ​ |  | (12.3) | ​ |  | 17.9 | ​ |  | (12.3) | ​ |  | 17.9
Benefits paid | ​ |  | (27.4) | ​ |  | (26.3) | ​ |  | (9.4) | ​ |  | (8.0) | ​ |  | (36.8) | ​ |  | (34.3)
Projected benefit obligation at end of year | ​ |  | 495.3 | ​ |  | 526.4 | ​ |  | 265.9 | ​ |  | 302.0 | ​ |  | 761.2 | ​ |  | 828.4
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Change in plan assets: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Fair value of plan assets at beginning of year | ​ |  | 515.7 | ​ |  | 473.2 | ​ |  | 116.6 | ​ |  | 107.8 | ​ |  | 632.3 | ​ |  | 581.0
Actual return on plan assets | ​ |  | 38.2 | ​ |  | 67.8 | ​ |  | 6.3 | ​ |  | 6.3 | ​ |  | 44.5 | ​ |  | 74.1
Employer contributions | ​ |  | 1.0 | ​ |  | 1.0 | ​ |  | 5.8 | ​ |  | 5.5 | ​ |  | 6.8 | ​ |  | 6.5
Foreign exchange translation | ​ |  | — | ​ |  | — | ​ |  | (2.8) | ​ |  | 5.0 | ​ |  | (2.8) | ​ |  | 5.0
Benefits paid | ​ |  | (27.4) | ​ |  | (26.3) | ​ |  | (9.4) | ​ |  | (8.0) | ​ |  | (36.8) | ​ |  | (34.3)
Fair value of plan assets at end of year | ​ |  | 527.5 | ​ |  | 515.7 | ​ |  | 116.5 | ​ |  | 116.6 | ​ |  | 644.0 | ​ |  | 632.3
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Over (under) funded status at end of year | ​ | $ | 32.2 | ​ | $ | (10.7) | ​ | $ | (149.4) | ​ | $ | (185.4) | ​ | $ | (117.2) | ​ | $ | (196.1)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Amounts recognized on the balance sheet as of December 31: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Other long-term assets | ​ | $ | 50.0 | ​ | $ | 7.8 | ​ | $ | 0.7 | ​ | $ | 0.3 | ​ | $ | 50.7 | ​ | $ | 8.1
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Other accrued expenses | ​ | ​ | 1.1 | ​ | ​ | 1.0 | ​ | ​ | 3.1 | ​ | ​ | 3.3 | ​ | ​ | 4.2 | ​ | ​ | 4.3
Accrued pension and postretirement benefit obligations | ​ | ​ | 16.7 | ​ | ​ | 17.5 | ​ | ​ | 147.0 | ​ | ​ | 182.4 | ​ | ​ | 163.7 | ​ | ​ | 199.9
Over (under) funded status at end of year | ​ | $ | 32.2 | ​ | $ | (10.7) | ​ | $ | (149.4) | ​ | $ | (185.4) | ​ | $ | (117.2) | ​ | $ | (196.1)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Accumulated other comprehensive loss, net | ​ | $ | (83.0) | ​ | $ | (118.2) | ​ | $ | (51.8) | ​ | $ | (74.3) | ​ | $ | (134.8) | ​ | $ | (192.5)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Weighted average assumptions used to determine projected benefit obligations: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Discount rate |  | ​ | 2.69 | % | ​ | 2.30 | % | ​ | 1.58 | % | ​ | 1.12 | % | ​ | ​ | ​ | ​ | ​
Rate of compensation increase |  | ​ | 2.40 | % | ​ | 2.40 | % | ​ | 1.75 | % | ​ | 1.75 | % | ​ | ​ | ​ | ​ | ​
​
Pension plans with an accumulated benefit obligation in excess of plan assets | The following summarizes information for defined benefit plans with an accumulated benefit obligation in excess of plan assets as of December 31, 2021 and 2020: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | U.S. Plans | ​ | Foreign Plans
​ | ​ | ​ | 2021 | ​ |  | 2020 | ​ |  | 2021 | ​ | ​ | 2020
Accumulated benefit obligation | ​ | $ | 29.2 | ​ | $ | 29.8 | ​ | $ | 254.1 | ​ | $ | 287.6
Fair value of plan assets | ​ | ​ | 12.0 | ​ | ​ | 11.7 | ​ | ​ | 110.3 | ​ | ​ | 110.7
Pension plans with a projected benefit obligation in excess of plan assets | The following summarizes information for defined benefit plans with a projected benefit obligation in excess of plan assets as of December 31, 2021 and 2020:
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | U.S. Plans | ​ | Foreign Plans
​ | ​ | ​ | 2021 | ​ |  | 2020 | ​ |  | 2021 | ​ | ​ | 2020
Projected benefit obligation | ​ | $ | 29.6 | ​ | $ | 30.1 | ​ | $ | 260.6 | ​ | $ | 296.4
Fair value of plan assets | ​ | ​ | 12.0 | ​ | ​ | 11.7 | ​ | ​ | 110.3 | ​ | ​ | 110.7
Schedule of amounts, before tax, included in Accumulated other comprehensive loss that have not yet been recognized as expense | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | U.S. Plans | ​ | Foreign Plans | ​ | Total
​ | ​ | 2021 | ​ | 2020 | ​ | 2021 | ​ | 2020 | ​ | 2021 | ​ | 2020
Actuarial losses, net | ​ | $ | 103.6 |  | $ | 148.9 |  | $ | 64.7 |  | $ | 98.8 |  | $ | 168.3 |  | $ | 247.7
Prior service cost | ​ | ​ | 5.1 | ​ | ​ | 6.6 | ​ | ​ | 0.7 | ​ | ​ | 0.8 | ​ | ​ | 5.8 | ​ | ​ | 7.4
Schedule of components of net pension expense | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | U.S. Plans | ​ | Foreign Plans | ​ | Total
​ |  | 2021 |  | 2020 |  | 2019 | ​ | 2021 |  | 2020 |  | 2019 | ​ | 2021 |  | 2020 |  | 2019
Components of net pension expense: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Service cost | ​ | $ | 4.2 | ​ | $ | 4.5 | ​ | $ | 5.4 | ​ | $ | 3.3 | ​ | $ | 3.0 | ​ | $ | 2.6 | ​ | $ | 7.5 | ​ | $ | 7.5 | ​ | $ | 8.0
Interest cost | ​ |  | 8.6 | ​ |  | 13.2 | ​ |  | 16.8 | ​ |  | 2.7 | ​ |  | 3.5 | ​ |  | 4.7 | ​ |  | 11.3 | ​ |  | 16.7 | ​ |  | 21.5
Expected return on plan assets | ​ |  | (28.1) | ​ |  | (33.8) | ​ |  | (33.2) | ​ |  | (3.1) | ​ |  | (3.4) | ​ |  | (3.7) | ​ |  | (31.2) | ​ |  | (37.2) | ​ |  | (36.9)
Amortization of prior service cost | ​ | ​ | 1.9 | ​ | ​ | 2.1 | ​ | ​ | 1.7 | ​ | ​ | 0.2 | ​ | ​ | — | ​ | ​ | 0.1 | ​ | ​ | 2.1 | ​ | ​ | 2.1 | ​ | ​ | 1.8
Amortization of actuarial losses | ​ |  | 17.8 | ​ |  | 19.8 | ​ |  | 14.4 | ​ |  | 7.0 | ​ |  | 5.4 | ​ |  | 4.1 | ​ |  | 24.8 | ​ |  | 25.2 | ​ |  | 18.5
Net pension expense | ​ | $ | 4.4 | ​ | $ | 5.8 | ​ | $ | 5.1 | ​ | $ | 10.1 | ​ | $ | 8.5 | ​ | $ | 7.8 | ​ | $ | 14.5 | ​ | $ | 14.3 | ​ | $ | 12.9
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Weighted average assumptions used to determine net periodic benefit cost: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Discount rate |  | ​ | 2.30 | % | ​ | 3.11 | % | ​ | 4.14 | % | ​ | 1.12 | % | ​ | 1.59 | % | ​ | 2.28 | % | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Expected long-term return on assets |  | ​ | 6.00 | % | ​ | 7.50 | % | ​ | 7.50 | % | ​ | 2.71 | % | ​ | 3.25 | % | ​ | 3.75 | % | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Rate of compensation increase |  | ​ | 2.40 | % | ​ | 2.60 | % | ​ | 3.00 | % | ​ | 1.75 | % | ​ | 1.78 | % | ​ | 1.77 | % | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Schedule of weighted average assumptions used to determine net benefit cost/expense | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | U.S. Plans | ​ | Foreign Plans | ​ | Total
​ |  | 2021 |  | 2020 |  | 2019 | ​ | 2021 |  | 2020 |  | 2019 | ​ | 2021 |  | 2020 |  | 2019
Components of net pension expense: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Service cost | ​ | $ | 4.2 | ​ | $ | 4.5 | ​ | $ | 5.4 | ​ | $ | 3.3 | ​ | $ | 3.0 | ​ | $ | 2.6 | ​ | $ | 7.5 | ​ | $ | 7.5 | ​ | $ | 8.0
Interest cost | ​ |  | 8.6 | ​ |  | 13.2 | ​ |  | 16.8 | ​ |  | 2.7 | ​ |  | 3.5 | ​ |  | 4.7 | ​ |  | 11.3 | ​ |  | 16.7 | ​ |  | 21.5
Expected return on plan assets | ​ |  | (28.1) | ​ |  | (33.8) | ​ |  | (33.2) | ​ |  | (3.1) | ​ |  | (3.4) | ​ |  | (3.7) | ​ |  | (31.2) | ​ |  | (37.2) | ​ |  | (36.9)
Amortization of prior service cost | ​ | ​ | 1.9 | ​ | ​ | 2.1 | ​ | ​ | 1.7 | ​ | ​ | 0.2 | ​ | ​ | — | ​ | ​ | 0.1 | ​ | ​ | 2.1 | ​ | ​ | 2.1 | ​ | ​ | 1.8
Amortization of actuarial losses | ​ |  | 17.8 | ​ |  | 19.8 | ​ |  | 14.4 | ​ |  | 7.0 | ​ |  | 5.4 | ​ |  | 4.1 | ​ |  | 24.8 | ​ |  | 25.2 | ​ |  | 18.5
Net pension expense | ​ | $ | 4.4 | ​ | $ | 5.8 | ​ | $ | 5.1 | ​ | $ | 10.1 | ​ | $ | 8.5 | ​ | $ | 7.8 | ​ | $ | 14.5 | ​ | $ | 14.3 | ​ | $ | 12.9
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Weighted average assumptions used to determine net periodic benefit cost: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Discount rate |  | ​ | 2.30 | % | ​ | 3.11 | % | ​ | 4.14 | % | ​ | 1.12 | % | ​ | 1.59 | % | ​ | 2.28 | % | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Expected long-term return on assets |  | ​ | 6.00 | % | ​ | 7.50 | % | ​ | 7.50 | % | ​ | 2.71 | % | ​ | 3.25 | % | ​ | 3.75 | % | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Rate of compensation increase |  | ​ | 2.40 | % | ​ | 2.60 | % | ​ | 3.00 | % | ​ | 1.75 | % | ​ | 1.78 | % | ​ | 1.77 | % | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Fair values of Company's pension plan assets by asset category |
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | Assets Measured at
Asset Category | ​ | Total | ​ | Level 1 | ​ | Level 2 | ​ | Level 3 | ​ | Net Asset Value (a)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
December 31, 2021 | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Equity securities: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
U.S. equities — large cap | ​ | $ | 62.7 | ​ | $ | 30.1 | ​ | $ | 32.6 | ​ | $ | — | ​ | $ | —
U.S. equities — small/mid cap and other | ​ |  | 15.9 | ​ |  | — | ​ |  | 15.9 | ​ |  | — | ​ |  | —
International equities — growth | ​ |  | 31.8 | ​ |  | 25.5 | ​ |  | 6.3 | ​ |  | — | ​ |  | —
International equities — other | ​ |  | 70.9 | ​ |  | — | ​ |  | 45.7 | ​ |  | — | ​ |  | 25.2
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Alternative investment funds | ​ | ​ | 25.5 | ​ | ​ | — | ​ | ​ | — | ​ | ​ | — | ​ | ​ | 25.5
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Fixed income securities: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
U.S. fixed income securities — intermediate term | ​ |  | 97.3 | ​ |  | — | ​ |  | 97.3 | ​ |  | — | ​ |  | —
U.S. fixed income securities — long term | ​ | ​ | 266.1 | ​ |  | — | ​ |  | 266.1 | ​ |  | — | ​ |  | —
International fixed income securities — other | ​ |  | 30.2 | ​ | ​ | — | ​ |  | 30.2 | ​ |  | — | ​ |  | —
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Insurance contracts | ​ |  | 34.1 | ​ |  | — | ​ |  | — | ​ |  | 34.1 | ​ |  | —
Cash and cash equivalents | ​ |  | 9.5 | ​ |  | 9.5 | ​ |  | — | ​ |  | — | ​ |  | —
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Total | ​ | $ | 644.0 | ​ | $ | 65.1 | ​ | $ | 494.1 | ​ | $ | 34.1 | ​ | $ | 50.7
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
December 31, 2020 | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Equity securities: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
U.S. equities — large cap | ​ | $ | 124.9 | ​ | $ | 63.5 | ​ | $ | 61.4 | ​ | $ | — | ​ | $ | —
U.S. equities — small/mid cap and other | ​ |  | 37.7 | ​ |  | — | ​ |  | 37.7 | ​ |  | — | ​ |  | —
International equities — growth | ​ |  | 67.5 | ​ |  | 61.6 | ​ |  | 5.9 | ​ |  | — | ​ |  | —
International equities — other | ​ |  | 96.2 | ​ |  | — | ​ |  | 41.3 | ​ |  | — | ​ |  | 54.9
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Alternative investment funds | ​ | ​ | 22.4 | ​ | ​ | — | ​ | ​ | — | ​ | ​ | — | ​ | ​ | 22.4
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Fixed income securities: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
U.S. fixed income securities — intermediate term | ​ |  | 29.2 | ​ |  | 29.2 | ​ |  | — | ​ |  | — | ​ |  | —
U.S. fixed income securities — long term | ​ | ​ | 130.5 | ​ |  | — | ​ |  | 130.5 | ​ |  | — | ​ |  | —
U.S. fixed income securities — high yield | ​ |  | 15.5 | ​ |  | — | ​ |  | 15.5 | ​ |  | — | ​ |  | —
International fixed income securities — other | ​ |  | 49.5 | ​ | ​ | — | ​ |  | 49.5 | ​ |  | — | ​ |  | —
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Insurance contracts | ​ | ​ | 40.0 | ​ |  | — | ​ |  | — | ​ |  | 40.0 | ​ |  | —
Real estate funds | ​ |  | 10.8 | ​ |  | — | ​ |  | — | ​ |  | 10.8 | ​ |  | —
Cash and cash equivalents | ​ | ​ | 8.1 | ​ |  | 8.1 | ​ |  | — | ​ |  | — | ​ |  | —
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Total | ​ | $ | 632.3 | ​ | $ | 162.4 | ​ | $ | 341.8 | ​ | $ | 50.8 | ​ | $ | 77.3
​
(a) | Certain investments measured at fair value using the net asset value (NAV) practical expedient have been removed from the fair value hierarchy but included in the table above in order to permit the reconciliation of the fair value hierarchy to total plan assets.
Reconciliation of fair value measurements using significant unobservable inputs (Level 3) | ​
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | 2021 | ​ | ​ | 2020
Balance on January 1 | ​ | $ | 50.8 | ​ | $ | 47.7
Unrealized (losses) gains, net | ​ | ​ | (0.1) | ​ | ​ | 1.1
Purchases, sales and settlements, net | ​ | ​ | (14.2) | ​ | ​ | (1.0)
Foreign currency translation | ​ | ​ | (2.4) | ​ | ​ | 3.0
Balance on December 31 | ​ | $ | 34.1 | ​ | $ | 50.8
Benefit payments related to the pension plans, including amounts to be paid out of Company assets and reflecting future expected service | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | U.S. | ​ | Foreign | ​ | ​ |
Year | ​ | Plans | ​ | Plans | ​ | Total |
2022 |  | $ | 28.2 |  | $ | 8.9 |  | $ | 37.1 |
2023 | ​ |  | 29.0 | ​ |  | 8.5 | ​ |  | 37.5 | ​
2024 | ​ |  | 29.6 | ​ |  | 9.6 | ​ |  | 39.2 | ​
2025 | ​ |  | 30.0 | ​ |  | 9.6 | ​ |  | 39.6 | ​
2026 | ​ |  | 30.2 | ​ |  | 10.1 | ​ |  | 40.3 | ​
2027-2031 | ​ |  | 147.5 | ​ |  | 54.4 | ​ |  | 201.9 | ​

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