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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:
CategoryEstimated useful life
Brands20 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 millionsBrandsIntellectual propertyDeveloped technologyCustomer relationshipsOtherTotal
Cost
Balance at January 1, 202138.9 144.8 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, 202138.9 144.8 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, 202238.9 147.1 1,220.2 228.6 222.5 1,857.3 
 
Accumulated amortization
Balance at January 1, 202111.1 78.8 510.7 95.9 42.9 739.4 
Amortization1.9 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, 202113.0 87.2 594.0 108.6 67.6 870.4 
Amortization1.9 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, 202214.9 95.8 677.4 121.3 105.5 1,014.9 
 
Carrying amount
December 31, 202125.9 57.6 626.2 120.0 122.4 952.1 
December 31, 202224.0 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)202020212022
Cost of Sales101.8 107.8 105.9 
R&D Costs12.0 14.5 18.2 
SG&A9.7 10.7 11.0 
Total Amortization123.5 133.0 135.1 
Future Amortization Expenses
As of December 31, 2022, the estimated amortization expenses for intangible assets for the next five years and thereafter is as follows:
€, in millionsAmount
2023130.8 
2024124.8 
2025119.3 
2026113.0 
2027109.1 
Thereafter245.4 
Total842.4