Intangible assets, net (Tables)

12 Months Ended

Dec. 31, 2023

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, 2023, 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, 2022	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
Additions	—	—	—	—	39.3	39.3
Disposals	—	—	—	—	(0.3)	(0.3)
Effect of changes in exchange rates	—	—	—	—	(1.4)	(1.4)
Balance at December 31, 2023	38.9	147.1	1,220.2	228.6	260.1	1,894.9
Accumulated amortization
Balance at January 1, 2022	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
Amortization	1.9	8.3	76.8	12.7	27.9	127.6
Impairment charges	—	—	—	—	11.1	11.1
Disposals	—	—	—	—	(0.3)	(0.3)
Effect of changes in exchange rates	—	—	—	—	(0.1)	(0.1)
Balance at December 31, 2023	16.8	104.1	754.2	134.0	144.1	1,153.2
Carrying amount
December 31, 2022	24.0	51.3	542.8	107.3	117.0	842.4
December 31, 2023	22.1	43.0	466.0	94.6	116.0	741.7

Finite-Lived Intangible Assets Amortization Expense

The Consolidated Statements of Operations include the following amortization charges:

Year ended December 31 (€, in millions)	2021	2022	2023
Cost of Sales	107.8	105.9	102.7
R&D Costs	14.5	18.2	19.5
SG&A	10.7	11.0	5.4
Total Amortization	133.0	135.1	127.6

Future Amortization Expenses

As of December 31, 2023, the estimated amortization expenses for intangible assets for the next five years and

thereafter is as follows:

€, in millions	Amount
2024	124.9
2025	122.8
2026	117.5
2027	114.3
2028	93.3
Thereafter	168.9
Total	741.7