Employee benefit plans (Tables)
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12 Months Ended |
Dec. 31, 2025 |
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| Employee benefit plans |
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| Schedule of defined benefit pension plans |
| | | | | Benefit obligation for defined benefit plans | | | | | in € K | | | | | | | 2025 | | 2024 | Partially funded obligations | | | | | U.S. plan | | 304,184 | | 338,757 | French plan | | 5,639 | | 5,780 | | | | | | Funded obligations by insurance contracts | | | | | German plan | | — | | 4,137 | | | | | | Unfunded obligations | | | | | German plan | | 498,282 | | 557,185 | French plans | | 10,232 | | 11,212 | | | | | | Total benefit obligations | | 818,337 | | 917,071 |
| | | | | Net pension liability | in € K | | | 2025 | | 2024 | Change in benefit obligation: | | | | | Benefit obligation at beginning of year | | 917,071 | | 890,025 | Foreign currency translation (gains) losses | | (39,423) | | 20,472 | Current service cost | | 23,755 | | 28,748 | Past service cost | | (1,678) | | (481) | Interest cost | | 37,980 | | 37,304 | (Gains) losses from settlement | | 216 | | — | Transfer of plan participants | | (1,063) | | 18 | Actuarial (gains) losses arising from changes in financial assumptions | | (75,217) | | (19,944) | Actuarial (gains) losses arising from changes in demographic assumptions | | 5 | | 17 | Actuarial (gains) losses arising from experience adjustments | | (1,572) | | (185) | Remeasurements | | (76,784) | | (20,112) | Benefits paid | | (36,899) | | (38,903) | Settlements paid | | (4,838) | | — | | | | | | Benefit obligation at end of year | | 818,337 | | 917,071 | | | | | | Change in plan assets: | | | | | Fair value of plan assets at beginning of year | | 259,832 | | 255,772 | Foreign currency translation gains (losses) | | (31,103) | | 15,547 | Interest income from plan assets | | 13,135 | | 13,169 | Actuarial gains (losses) arising from experience adjustments | | (4,322) | | (4,122) | Actual return on plan assets | | 8,813 | | 9,047 | Employer contributions | | 55,746 | | 7,968 | Benefits paid | | (25,059) | | (28,502) | Settlements paid | | (4,622) | | — | Fair value of plan assets at end of year | | 263,607 | | 259,832 | Net funded position at end of year | | 554,730 | | 657,239 | Benefit plans offered by other subsidiaries | | 35,954 | | 35,399 | Net pension liability at end of year | | 590,684 | | 692,638 |
| | | | | Pension plan assets and liabilities | | | | | in € K | | | | | | | 2025 | | 2024 | Pension plan liabilities | | | | | U.S. plan | | 40,650 | | 83,148 | German plan | | 498,282 | | 557,185 | French plans | | 15,798 | | 16,906 | Total | | 554,730 | | 657,239 | Thereof current(1) | | 15,096 | | 12,876 | Thereof non-current(2) | | 539,634 | | 644,363 | | | | | | Benefit plans offered by other subsidiaries | | | | | Pension assets (3) | | (1,143) | | (531) | Current pension liabilities(1) | | 1,924 | | 1,620 | Non-current pension liabilities(2) | | 35,173 | | 34,310 | Total other pension liabilities, net | | 35,954 | | 35,399 |
| (1) | Recorded in the line item “Current provisions and other current liabilities” in the consolidated balance sheets. |
| (2) | Recorded in non-current liabilities as “Pension liabilities” in the consolidated balance sheets. |
| (3) | Recorded as “Other non-current assets” in the consolidated balance sheets. |
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| Schedule of weighted-average assumptions utilized in determining benefit obligations |
| | | | | Weighted average assumptions | in % | | | 2025 | | 2024 | | | | | | Discount rate | | 4.85 | | 4.39 | Rate of compensation increase | | 3.18 | | 3.18 | Rate of pension increase | | 2.00 | | 2.00 |
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| Schedule of sensitivity analysis |
| | | | | Sensitivity analysis | in € K | | | 0.5% increase | | 0.5% decrease | | | | | | Discount rate | | (54,284) | | 61,260 | Rate of compensation increase | | 7,985 | | (7,825) | Rate of pension increase | | 31,332 | | (28,619) |
An increase of the mortality rate of 10% would reduce the pension liability by €18,686, while a decrease of 10% would increase the pension liability by €20,864 as of December 31, 2025.
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| Schedule of components of net periodic benefit cost |
| | | | | | | Components of net periodic benefit cost | in € K | | | 2025 | | 2024 | | 2023 | | | | | | | | Service cost | | 23,755 | | 28,748 | | 32,399 | Net interest cost | | 24,845 | | 24,135 | | 23,721 | Prior service cost | | (1,678) | | (481) | | (538) | (Gains) losses from settlements | | 216 | | — | | — | Net periodic benefit costs | | 47,138 | | 52,402 | | 55,582 |
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| Schedule of weighted-average assumptions utilized in determining net periodic benefit cost |
| | | | | | | Weighted average assumptions | in % | | | 2025 | | 2024 | | 2023 | | | | | | | | Discount rate | | 4.39 | | 4.22 | | 4.86 | Rate of compensation increase | | 3.18 | | 3.18 | | 3.22 | Rate of pension increase | | 2.00 | | 2.00 | | 2.00 |
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| Schedule of expected benefit payments |
| | | | | Defined benefit pension plans: cash outflows | in € K | | | 2025 | | 2024 | | | | | | 1 year | | 37,456 | | 37,074 | 1 - 3 years | | 79,346 | | 82,307 | 3 - 5 years | | 85,408 | | 90,462 | 5 - 10 years | | 234,397 | | 249,343 | Total | | 436,607 | | 459,186 |
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| Schedule of pension plan assets |
| | | | | | | | | | | | | | | | | Fair values of plan assets | in € K | | | | | Quoted prices | | | | | | | | Quoted prices | | | | | | | | | in active | | | | | | | | in active | | | | | | | | | markets for | | Significant | | Significant | | | | markets for | | Significant | | Significant | | | | | identical | | observable | | unobservable | | | | identical | | observable | | unobservable | Asset category | | Total | | assets | | inputs | | inputs | | Total | | assets | | inputs | | inputs | | | | | (Level 1) | | (Level 2) | | (Level 3) | | | | (Level 1) | | (Level 2) | | (Level 3) | | | | | | 2025 | | | | 2024 | Equity investments | | | | | | | | | | | | | | | | | Index funds(1) | | — | | — | | — | | — | | 73,272 | | 9,570 | | 63,702 | | — | | | | | | | | | | | | | | | | | | Fixed income investments | | | | | | | | | | | | | | | | | Government securities(2) | | — | | — | | — | | — | | 190 | | 19 | | 171 | | — | Corporate bonds(3) | | — | | — | | — | | — | | 171,860 | | — | | 171,860 | | — | Other bonds(4) | | — | | — | | — | | — | | 6,668 | | — | | 331 | | 6,337 | U.S. treasury money market funds(5) | | 60,741 | | 60,741 | | — | | — | | 3,619 | | 3,619 | | — | | — | | | | | | | | | | | | | | | | | | Other types of investments | | | | | | | | | | | | | | | | | Cash, money market and mutual funds(6) | | 73 | | 73 | | — | | — | | 4,223 | | 86 | | 4,137 | | — | Annuity buy-in contract(7) | | 202,793 | | — | | — | | 202,793 | | — | | — | | — | | — | Total | | 263,607 | | 60,814 | | — | | 202,793 | | 259,832 | | 13,294 | | 240,201 | | 6,337 |
| (1) | This category comprises low-cost equity index funds not actively managed that track the S&P 500, S&P 400, Russell 2000, MSCI Emerging Markets Index, and the MSCI EAFE Index. |
| (2) | This category comprises fixed income investments by the U.S. government and government sponsored entities. |
| (3) | This category primarily represents investment grade bonds of U.S. issuers from diverse industries. |
| (4) | This category comprises private placement bonds as well as collateralized mortgage obligations. |
| (5) | This category represents funds that invest in U.S. treasury obligations directly or in U.S. treasury backed obligations. |
| (6) | This category represents cash, money market funds, and mutual funds comprised of high grade corporate bonds. |
| (7) | This category comprises an annuity buy-in insurance contract. |
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