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Defined contribution and defined benefit retirement (Tables) | 12 Months Ended
--- | ---
Dec. 31, 2023
Defined Benefit Plan Disclosure [Line Items] |
Composition of Pension Plan Assets | The composition of our pension plan assets by asset category and fair value level at December 31, 2022 and 2023 is shown in the tables below.
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Fair Value Measurements at December 31, 2022
​ |  | ​ | ​ |  | Quoted |  | Significant |  | ​ | ​ |  | ​ | ​
​ | ​ | ​ | ​ | ​ | Prices in | ​ | Other | ​ | Significant | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | Active | ​ | Observable | ​ | Unobservable | ​ | Assets
​ | ​ | ​ | ​ | ​ | Markets | ​ | Inputs | ​ | Inputs | ​ | measured
​ | ​ | Total | ​ | (Level 1) | ​ | (Level 2) | ​ | (Level 3) | ​ | at NAV
​ | ​ | (In millions)
Germany | ​ | $ | 234.0 | ​ | $ | — | ​ | $ | — | ​ | $ | 234.0 | ​ | $ | —
Canada: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |
Local currency equities | ​ |  | .1 | ​ |  | .1 | ​ |  | — | ​ |  | — | ​ |  | —
Non local currency equities | ​ |  | 11.0 | ​ |  | 11.0 | ​ |  | — | ​ |  | — | ​ |  | —
Local currency fixed income | ​ |  | 72.9 | ​ |  | 72.9 | ​ |  | — | ​ |  | — | ​ |  | —
Cash and other | ​ |  | .6 | ​ |  | .6 | ​ |  | — | ​ |  | — | ​ |  | —
Norway: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |
Local currency equities | ​ |  | 2.3 | ​ |  | 2.3 | ​ |  | — | ​ |  | — | ​ |  | —
Non local currency equities | ​ |  | 4.7 | ​ |  | 4.7 | ​ |  | — | ​ |  | — | ​ |  | —
Local currency fixed income | ​ |  | 21.8 | ​ |  | 7.0 | ​ |  | 14.8 | ​ |  | — | ​ |  | —
Non local currency fixed income | ​ |  | 8.4 | ​ |  | 8.4 | ​ |  | — | ​ |  | — | ​ |  | —
Real estate | ​ |  | 7.8 | ​ |  | — | ​ |  | — | ​ |  | 7.8 | ​ |  | —
Cash and other | ​ |  | 2.7 | ​ |  | 2.4 | ​ |  | — | ​ |  | .3 | ​ |  | —
U.S.: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  | ​ | ​ |  |
Equities | ​ |  | 12.4 | ​ |  | 1.0 | ​ |  | — | ​ |  | — | ​ |  | 11.4
Fixed income | ​ |  | 22.9 | ​ |  | .2 | ​ |  | — | ​ |  | — | ​ |  | 22.7
Cash and other | ​ |  | 3.8 | ​ |  | 2.8 | ​ |  | — | ​ |  | — | ​ |  | 1.0
Other | ​ |  | 24.2 | ​ |  | 1.5 | ​ |  | — | ​ |  | 22.7 | ​ |  | —
Total | ​ | $ | 429.6 | ​ | $ | 114.9 | ​ | $ | 14.8 | ​ | $ | 264.8 | ​ | $ | 35.1
​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Fair Value Measurements at December 31, 2023
​ |  | ​ | ​ |  | Quoted |  | Significant |  | ​ | ​ |  | ​ | ​
​ | ​ | ​ | ​ | ​ | Prices in | ​ | Other | ​ | Significant | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | Active | ​ | Observable | ​ | Unobservable | ​ | Assets
​ | ​ | ​ | ​ | ​ | Markets | ​ | Inputs | ​ | Inputs | ​ | measured
​ | ​ | Total | ​ | (Level 1) | ​ | (Level 2) | ​ | (Level 3) | ​ | at NAV
​ | ​ | (In millions)
Germany | ​ | $ | 269.4 | ​ | $ | — | ​ | $ | — | ​ | $ | 269.4 | ​ | $ | —
Canada: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |
Non local currency equities | ​ |  | 2.7 | ​ |  | 2.7 | ​ |  | — | ​ |  | — | ​ |  | —
Local currency fixed income | ​ |  | 86.2 | ​ |  | 86.2 | ​ |  | — | ​ |  | — | ​ |  | —
Cash and other | ​ |  | 1.1 | ​ |  | 1.1 | ​ |  | — | ​ |  | — | ​ |  | —
Norway: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |
Local currency equities | ​ |  | 2.4 | ​ |  | 2.4 | ​ |  | — | ​ |  | — | ​ |  | —
Non local currency equities | ​ |  | 7.2 | ​ |  | 7.2 | ​ |  | — | ​ |  | — | ​ |  | —
Local currency fixed income | ​ |  | 23.9 | ​ |  | 4.4 | ​ |  | 19.5 | ​ |  | — | ​ |  | —
Non local currency fixed income | ​ |  | 4.2 | ​ |  | 4.2 | ​ |  | — | ​ |  | — | ​ |  | —
Real estate | ​ |  | 6.6 | ​ |  | — | ​ |  | — | ​ |  | 6.6 | ​ |  | —
Cash and other | ​ |  | 3.0 | ​ |  | 2.8 | ​ |  | — | ​ |  | .2 | ​ |  | —
U.S.: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  | ​ | ​ |  |
Equities | ​ |  | 11.3 | ​ |  | — | ​ |  | — | ​ |  | — | ​ |  | 11.3
Fixed income | ​ |  | 27.1 | ​ |  | — | ​ |  | — | ​ |  | — | ​ |  | 27.1
Cash and other | ​ |  | 1.9 | ​ |  | .7 | ​ |  | — | ​ |  | — | ​ |  | 1.2
Other | ​ |  | 15.9 | ​ |  | — | ​ |  | — | ​ |  | 15.9 | ​ |  | —
Total | ​ | $ | 462.9 | ​ | $ | 111.7 | ​ | $ | 19.5 | ​ | $ | 292.1 | ​ | $ | 39.6
A rollforward of the change in fair value of Level 3 assets follows.
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31,
​ |  | 2022 |  | 2023
​ | ​ | (In millions)
Fair value at beginning of year | ​ | $ | 320.5 | ​ | $ | 264.8
Gain (loss) on assets held at end of year | ​ |  | (31.0) | ​ |  | 11.1
Gain (loss) on assets sold during the year | ​ |  | (3.6) | ​ |  | 14.4
Assets purchased | ​ |  | 13.8 | ​ |  | 1.7
Assets sold | ​ |  | (15.5) | ​ |  | (9.3)
Transfers out | ​ | ​ | (.1) | ​ | ​ | —
Currency exchange rate fluctuations | ​ |  | (19.3) | ​ |  | 9.4
Fair value at end of year | ​ | $ | 264.8 | ​ | $ | 292.1
​
Defined Benefit Pension Plans |
Defined Benefit Plan Disclosure [Line Items] |
Schedule of Changes in Plan Assets and Benefit Obligations Recognized in Other Comprehensive Income (Loss) | The table below details the changes in other comprehensive income (loss) during 2021, 2022 and 2023. ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | Years ended December 31,
​ | ​ | 2021 | ​ | 2022 | ​ | 2023
​ | (In millions)
Changes in plan assets and benefit obligations recognized in other comprehensive income (loss): |  | ​ |  |  | ​ |  |  | ​ |
Net actuarial gains (losses) | ​ | $ | 50.7 | ​ | $ | 134.1 | ​ | $ | (25.5)
Amortization of unrecognized: | ​ |  |  | ​ |  |  | ​ |  |
Net actuarial losses | ​ |  | 21.6 | ​ |  | 14.7 | ​ |  | 3.8
Prior service cost | ​ |  | .2 | ​ |  | .1 | ​ |  | —
Settlements | ​ |  | — | ​ |  | .4 | ​ |  | 6.5
Total | ​ | $ | 72.5 | ​ | $ | 149.3 | ​ | $ | (15.2)
Schedule of Rollforward of Change in Fair Value of Level 3 Assets | ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Fair Value Measurements at December 31, 2023
​ |  | ​ | ​ |  | Quoted |  | Significant |  | ​ | ​ |  | ​ | ​
​ | ​ | ​ | ​ | ​ | Prices in | ​ | Other | ​ | Significant | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | Active | ​ | Observable | ​ | Unobservable | ​ | Assets
​ | ​ | ​ | ​ | ​ | Markets | ​ | Inputs | ​ | Inputs | ​ | measured
​ | ​ | Total | ​ | (Level 1) | ​ | (Level 2) | ​ | (Level 3) | ​ | at NAV
​ | ​ | (In millions)
Germany | ​ | $ | 269.4 | ​ | $ | — | ​ | $ | — | ​ | $ | 269.4 | ​ | $ | —
Canada: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |
Non local currency equities | ​ |  | 2.7 | ​ |  | 2.7 | ​ |  | — | ​ |  | — | ​ |  | —
Local currency fixed income | ​ |  | 86.2 | ​ |  | 86.2 | ​ |  | — | ​ |  | — | ​ |  | —
Cash and other | ​ |  | 1.1 | ​ |  | 1.1 | ​ |  | — | ​ |  | — | ​ |  | —
Norway: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |
Local currency equities | ​ |  | 2.4 | ​ |  | 2.4 | ​ |  | — | ​ |  | — | ​ |  | —
Non local currency equities | ​ |  | 7.2 | ​ |  | 7.2 | ​ |  | — | ​ |  | — | ​ |  | —
Local currency fixed income | ​ |  | 23.9 | ​ |  | 4.4 | ​ |  | 19.5 | ​ |  | — | ​ |  | —
Non local currency fixed income | ​ |  | 4.2 | ​ |  | 4.2 | ​ |  | — | ​ |  | — | ​ |  | —
Real estate | ​ |  | 6.6 | ​ |  | — | ​ |  | — | ​ |  | 6.6 | ​ |  | —
Cash and other | ​ |  | 3.0 | ​ |  | 2.8 | ​ |  | — | ​ |  | .2 | ​ |  | —
U.S.: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  | ​ | ​ |  |
Equities | ​ |  | 11.3 | ​ |  | — | ​ |  | — | ​ |  | — | ​ |  | 11.3
Fixed income | ​ |  | 27.1 | ​ |  | — | ​ |  | — | ​ |  | — | ​ |  | 27.1
Cash and other | ​ |  | 1.9 | ​ |  | .7 | ​ |  | — | ​ |  | — | ​ |  | 1.2
Other | ​ |  | 15.9 | ​ |  | — | ​ |  | — | ​ |  | 15.9 | ​ |  | —
Total | ​ | $ | 462.9 | ​ | $ | 111.7 | ​ | $ | 19.5 | ​ | $ | 292.1 | ​ | $ | 39.6
A rollforward of the change in fair value of Level 3 assets follows.
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31,
​ |  | 2022 |  | 2023
​ | ​ | (In millions)
Fair value at beginning of year | ​ | $ | 320.5 | ​ | $ | 264.8
Gain (loss) on assets held at end of year | ​ |  | (31.0) | ​ |  | 11.1
Gain (loss) on assets sold during the year | ​ |  | (3.6) | ​ |  | 14.4
Assets purchased | ​ |  | 13.8 | ​ |  | 1.7
Assets sold | ​ |  | (15.5) | ​ |  | (9.3)
Transfers out | ​ | ​ | (.1) | ​ | ​ | —
Currency exchange rate fluctuations | ​ |  | (19.3) | ​ |  | 9.4
Fair value at end of year | ​ | $ | 264.8 | ​ | $ | 292.1
​
Defined Benefit Pension Plans | United States |
Defined Benefit Plan Disclosure [Line Items] |
Schedule of Defined Benefit Plan Expected Future Payments | ​
​ | ​ | ​ | ​
Years ending December 31, |  | Amount
​ | ​ | (In millions)
2024 | ​ | $ | 28.4
2025 | ​ |  | 28.3
2026 | ​ |  | 28.7
2027 | ​ | ​ | 31.6
2028 | ​ |  | 35.7
Next 5 years | ​ | ​ | 169.5
Schedule of Funded Status | The funded status of our U.S. defined benefit pension plans is presented in the table below.
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31,
​ |  | 2022 |  | 2023
​ | ​ | (In millions)
Change in projected benefit obligations (PBO): | ​ | ​ | ​ | ​ | ​ | ​
Balance at beginning of the year | ​ | $ | 58.0 | ​ | $ | 43.4
Interest cost | ​ |  | 1.4 | ​ |  | 2.2
Actuarial losses (gains) | ​ |  | (11.8) | ​ |  | 1.2
Benefits paid | ​ |  | (4.2) | ​ |  | (4.1)
Balance at end of the year | ​ | $ | 43.4 | ​ | $ | 42.7
​ | ​ | ​ | ​ | ​ | ​ | ​
Change in plan assets: | ​ | ​ | ​ | ​ | ​ | ​
Fair value at beginning of the year | ​ | $ | 52.4 | ​ | $ | 39.1
Actual return on plan assets | ​ |  | (10.7) | ​ |  | 3.7
Employer contributions | ​ |  | 1.6 | ​ |  | 1.6
Benefits paid | ​ |  | (4.2) | ​ |  | (4.1)
Fair value at end of the year | ​ | $ | 39.1 | ​ | $ | 40.3
Funded status | ​ | $ | (4.3) | ​ | $ | (2.4)
​ | ​ | ​ | ​ | ​ | ​ | ​
Amounts recognized in the Consolidated Balance Sheets: | ​ | ​ | ​ | ​ | ​ | ​
Accrued pension costs: | ​ | ​ | ​ | ​ | ​ | ​
Current | ​ | $ | (.1) | ​ | $ | —
Noncurrent | ​ |  | (4.2) | ​ |  | (2.4)
Total | ​ |  | (4.3) | ​ |  | (2.4)
Accumulated other comprehensive loss - actuarial losses | ​ |  | 32.2 | ​ |  | 30.3
Total | ​ | $ | 27.9 | ​ | $ | 27.9
Accumulated benefit obligations (ABO) | ​ | $ | 43.4 | ​ | $ | 42.7
Components of Net Periodic Defined Benefit Cost | The components of our net periodic defined benefit pension cost for U.S. plans are presented in the table below. The amounts shown below for the amortization of recognized actuarial losses for 2021, 2022 and 2023 were recognized as components of our accumulated other comprehensive income (loss) at December 31, 2020, 2021 and 2022, respectively, net of deferred income taxes and noncontrolling interest.
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31,
​ |  | 2021 |  | 2022 |  | 2023
​ | ​ | (In millions)
Net periodic pension cost for U.S. plans: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Interest cost | ​ | $ | 1.3 | ​ | $ | 1.4 | ​ | $ | 2.2
Expected return on plan assets | ​ |  | (2.1) | ​ |  | (2.0) | ​ |  | (1.9)
Recognized net actuarial losses | ​ |  | 2.1 | ​ |  | 1.9 | ​ |  | 2.0
Settlements | ​ | ​ | (.5) | ​ | ​ | — | ​ | ​ | —
Total | ​ | $ | .8 | ​ | $ | 1.3 | ​ | $ | 2.3
Schedule of Plans for which Accumulated Benefit Obligations Exceeds Plan Assets | Information concerning our U.S. defined benefit pension plans (for which the ABO of all of the plans exceeds the fair value of plan assets as of the indicated date) is presented in the table below.
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | December 31,
​ |  | 2022 |  | 2023
​ | ​ | (In millions)
Plans for which the ABO exceeds plan assets: | ​ | ​ | ​ | ​ | ​ | ​
Projected benefit obligations | ​ | $ | 43.4 | ​ | $ | 42.7
Accumulated benefit obligations | ​ |  | 43.4 | ​ |  | 42.7
Fair value of plan assets | ​ |  | 39.1 | ​ |  | 40.3
Summary of Actuarial Assumptions Used to Determine the Benefit Obligation and Net Benefit Cost | The weighted-average rate assumptions used in determining the net periodic pension cost for our U.S. defined benefit pension plans for 2021, 2022 and 2023 are presented in the table below. The impact of assumed increases in future compensation levels does not have an effect on the periodic pension cost as the plans are frozen with regards to compensation.
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31, |
​ |  | 2021 |  | 2022 |  | 2023 |
Discount rate |  | 2.2% | ​ | 2.6% | ​ | 5.3% | ​
Long-term return on plan assets |  | 4.0% | ​ | 4.0% | ​ | 5.0% | ​
Defined Benefit Pension Plans | Non U.S. |
Defined Benefit Plan Disclosure [Line Items] |
Schedule of Funded Status | The funded status of our non-U.S. defined benefit pension plans is presented in the table below.
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31,
​ |  | 2022 |  | 2023
​ | ​ | (In millions)
Change in PBO: | ​ | ​ | ​ | ​ | ​ | ​
Balance at beginning of the year | ​ | $ | 758.1 | ​ | $ | 508.6
Service cost | ​ |  | 11.3 | ​ |  | 6.3
Interest cost | ​ |  | 10.6 | ​ |  | 19.8
Participants’ contributions | ​ |  | 1.7 | ​ |  | 1.8
Actuarial losses (gains) | ​ |  | (198.6) | ​ |  | 44.3
Settlements | ​ | ​ | (1.4) | ​ | ​ | (8.6)
Change in currency exchange rates | ​ |  | (51.2) | ​ |  | 14.1
Benefits paid | ​ |  | (21.9) | ​ |  | (22.6)
Balance at end of the year | ​ | $ | 508.6 | ​ | $ | 563.7
​ | ​ | ​ | ​ | ​ | ​ | ​
Change in plan assets: | ​ | ​ | ​ | ​ | ​ | ​
Fair value at beginning of the year | ​ | $ | 481.5 | ​ | $ | 390.5
Actual return on plan assets | ​ |  | (52.5) | ​ |  | 37.4
Employer contributions | ​ |  | 15.0 | ​ |  | 14.7
Participants' contributions | ​ |  | 1.7 | ​ |  | 1.8
Settlements | ​ | ​ | (1.2) | ​ | ​ | (8.6)
Change in currency exchange rates | ​ |  | (32.1) | ​ |  | 9.4
Benefits paid | ​ |  | (21.9) | ​ |  | (22.6)
Fair value at end of the year | ​ | $ | 390.5 | ​ | $ | 422.6
Funded status | ​ | $ | (118.1) | ​ | $ | (141.1)
​ | ​ | ​ | ​ | ​ | ​ | ​
Amounts recognized in the Consolidated Balance Sheets: | ​ | ​ | ​ | ​ | ​ | ​
Noncurrent pension asset | ​ | $ | 9.3 | ​ | $ | 8.1
Noncurrent accrued pension costs | ​ |  | (127.4) | ​ |  | (149.2)
Total | ​ |  | (118.1) | ​ |  | (141.1)
Accumulated other comprehensive loss: | ​ | ​ | ​ | ​ | ​ | ​
Actuarial losses | ​ |  | 90.0 | ​ |  | 106.8
Prior service cost | ​ |  | .4 | ​ |  | .3
Total | ​ |  | 90.4 | ​ |  | 107.1
Total | ​ | $ | (27.7) | ​ | $ | (34.0)
ABO | ​ | $ | 493.9 | ​ | $ | 549.8
Components of Net Periodic Defined Benefit Cost | The components of our net periodic pension benefit cost for our non-U.S. plans are presented in the table below. ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Years ended December 31,
​ |  | 2021 |  | 2022 |  | 2023
​ | ​ | (In millions)
Net periodic pension cost for non-U.S. plans: | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Service cost | ​ | $ | 14.7 | ​ | $ | 11.3 | ​ | $ | 6.3
Interest cost | ​ |  | 8.3 | ​ |  | 10.6 | ​ |  | 19.8
Expected return on plan assets | ​ |  | (11.4) | ​ |  | (11.1) | ​ |  | (18.3)
Recognized net actuarial losses | ​ |  | 19.5 | ​ |  | 12.8 | ​ |  | 1.8
Amortization of prior service cost | ​ |  | .2 | ​ |  | .1 | ​ |  | —
Settlements | ​ |  | — | ​ |  | .4 | ​ |  | 6.5
Total | ​ | $ | 31.3 | ​ | $ | 24.1 | ​ | $ | 16.1
Schedule of Plans for which Accumulated Benefit Obligations Exceeds Plan Assets | Information concerning certain of our non-U.S. defined benefit pension plans (for which the ABO exceeds the fair value of plan assets as of the indicated date) is presented in the table below.
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | December 31,
​ |  | 2022 |  | 2023
​ | ​ | (In millions)
Plans for which the ABO exceeds plan assets: | ​ | ​ | ​ | ​ | ​ | ​
Projected benefit obligations | ​ | $ | 403.5 | ​ | $ | 463.1
Accumulated benefit obligations | ​ |  | 392.4 | ​ |  | 452.9
Fair value of plan assets | ​ |  | 276.0 | ​ |  | 313.8
Summary of Actuarial Assumptions Used to Determine the Benefit Obligation and Net Benefit Cost | The key actuarial assumptions used to determine our non-U.S. benefit obligations as of December 31, 2022 and 2023 are as follows:
​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | December 31, |
​ | ​ |  | 2022 |  | 2023 |
Discount rate | ​ |  | 3.9% | ​ | 3.4% | ​
Increase in future compensation levels | ​ |  | 2.7% | ​ | 2.7% | ​
​ A summary of our key actuarial assumptions used to determine non-U.S. net periodic benefit cost for 2021, 2022 and 2023 are as follows:
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | Years ended December 31, |
​ | ​ |  | 2021 |  | 2022 | ​ | 2023 |
Discount rate | ​ |  | 1.0% | ​ | 1.5% | ​ | 3.9% | ​
Increase in future compensation levels | ​ |  | 2.6% | ​ | 2.6% | ​ | 2.7% | ​
Long-term return on plan assets | ​ |  | 2.4% | ​ | 2.5% | ​ | 4.6% | ​

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