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Intangible assets, net (Tables) | 12 Months Ended
--- | ---
Dec. 31, 2022
Goodwill and Intangible Assets Disclosure [Abstract] |
Finite-Lived Intangible Assets Useful Lives | The following table shows the respective useful lives for intangible assets:
Category | Estimated useful life
Brands | 20 years
Intellectual property | 3–10 years
Developed technology | 6–15 years
Customer relationships | 8–18 years
Other | 2–10 years
Finite-Lived Other Intangible Assets | As of December 31, 2022, intangible assets consist mainly of brands, intellectual property, developed technology and customer relationships obtained from the acquisitions of HMI (2016) and Cymer (2013):
€, in millions | Brands | Intellectual property | Developed technology | Customer relationships | Other | Total
Cost |  |  |  |  |  |
Balance at January 1, 2021 | 38.9 |  | 144.8 |  | 1,230.1 |  | 228.6 |  | 145.9 |  | 1,788.3 |
Additions | — |  | — |  | — |  | — |  | 45.6 |  | 45.6 |
Divestment | — |  | — |  | (9.9) |  | — |  | (0.8) |  | (10.7) |
Disposals | — |  | — |  | — |  | — |  | (0.5) |  | (0.5) |
Effect of changes in exchange rates | — |  | — |  | — |  | — |  | (0.2) |  | (0.2) |
Balance at December 31, 2021 | 38.9 |  | 144.8 |  | 1,220.2 |  | 228.6 |  | 190.0 |  | 1,822.5 |
Additions | — |  | 1.5 |  | — |  | — |  | 32.5 |  | 34.0 |
Disposals | — |  | — |  | — |  | — |  | (1.6) |  | (1.6) |
Effect of changes in exchange rates | — |  | 0.8 |  | — |  | — |  | 1.6 |  | 2.4 |
Balance at December 31, 2022 | 38.9 |  | 147.1 |  | 1,220.2 |  | 228.6 |  | 222.5 |  | 1,857.3 |
Accumulated amortization |  |  |  |  |  |
Balance at January 1, 2021 | 11.1 |  | 78.8 |  | 510.7 |  | 95.9 |  | 42.9 |  | 739.4 |
Amortization | 1.9 |  | 8.4 |  | 84.2 |  | 12.7 |  | 25.8 |  | 133.0 |
Divestment | — |  | — |  | (0.9) |  | — |  | (0.4) |  | (1.3) |
Disposals | — |  | — |  | — |  | — |  | (0.4) |  | (0.4) |
Effect of changes in exchange rates | — |  | — |  | — |  | — |  | (0.3) |  | (0.3) |
Balance at December 31, 2021 | 13.0 |  | 87.2 |  | 594.0 |  | 108.6 |  | 67.6 |  | 870.4 |
Amortization | 1.9 |  | 8.6 |  | 83.4 |  | 12.7 |  | 28.5 |  | 135.1 |
Impairment charges | — |  | — |  | — |  | — |  | 9.2 |  | 9.2 |
Disposals | — |  | — |  | — |  | — |  | (1.4) |  | (1.4) |
Effect of changes in exchange rates | — |  | — |  | — |  | — |  | 1.6 |  | 1.6 |
Balance at December 31, 2022 | 14.9 |  | 95.8 |  | 677.4 |  | 121.3 |  | 105.5 |  | 1,014.9 |
Carrying amount |  |  |  |  |  |
December 31, 2021 | 25.9 |  | 57.6 |  | 626.2 |  | 120.0 |  | 122.4 |  | 952.1 |
December 31, 2022 | 24.0 |  | 51.3 |  | 542.8 |  | 107.3 |  | 117.0 |  | 842.4 |
Finite-Lived Intangible Assets Amortization Expense | The Consolidated Statements of Operations include the following amortization charges:
Year ended December 31 (€, in millions) | 2020 | 2021 |  | 2022
Cost of Sales | 101.8 |  | 107.8 |  |  | 105.9 |
R&D Costs | 12.0 |  | 14.5 |  |  | 18.2 |
SG&A | 9.7 |  | 10.7 |  |  | 11.0 |
Total Amortization | 123.5 |  | 133.0 |  |  | 135.1 |
Future Amortization Expenses | As of December 31, 2022, the estimated amortization expenses for intangible assets for the next five years an d thereafter is as follows:
€, in millions | Amount
2023 | 130.8 |
2024 | 124.8 |
2025 | 119.3 |
2026 | 113.0 |
2027 | 109.1 |
Thereafter | 245.4 |
Total | 842.4 |

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