Reconciliations of the changes in the carrying value of goodwill during 2021 and 2020 follow (in millions).

	December 31,
	2021			2020
Balance at beginning of year	$	73,734		$	81,882
Business acquisitions		353			1,758
Impairment charges		—			(10,033	)
Other, including foreign currency translation		(212	)		127
Balance at end of year*	$	73,875		$	73,734

During 2020, we reevaluated goodwill and indefinite-lived intangible assets of certain of our reporting units for impairment due to the disruptions arising from the COVID-19 pandemic, which we believed most significantly affected the air travel, commercial aerospace and supporting industries. We recorded goodwill impairment charges of approximately $10 billion and indefinite-lived intangible asset impairment charges of $638 million in the second quarter of 2020. Approximately $10 billion of these charges pertained to Precision Castparts Corp. (“PCC”), one of the largest businesses within Berkshire’s manufacturing segment. The carrying values of PCC-related goodwill and indefinite-lived intangible assets prior to the impairment charges were approximately $31 billion. The impairment charges were determined based on discounted cash flow methods and reflected our assessments of the risks and uncertainties associated with the aerospace industry. Significant judgment is required in estimating the fair value of a reporting unit and in performing impairment tests. Due to the inherent uncertainty in forecasting future cash flows and earnings, actual results in the future may vary significantly from the forecasts.

The gross carrying amounts and related accumulated amortization of other intangible assets are summarized as follows (in millions).

	December 31, 2021						December 31, 2020
	Gross carrying amount		Accumulated amortization		Net carrying value		Gross carrying amount		Accumulated amortization		Net carrying value
Insurance and other:
Customer relationships	$	27,335	$	6,450	$	20,885	$	27,374	$	5,756	$	21,618
Trademarks and trade names		5,176		802		4,374		5,206		779		4,427
Patents and technology		4,763		3,484		1,279		4,766		3,313		1,453
Other		3,390		1,442		1,948		3,339		1,375		1,964
	$	40,664	$	12,178	$	28,486	$	40,685	$	11,223	$	29,462
Railroad, utilities and energy:
Customer relationships	$	678	$	396	$	282	$	678	$	361	$	317
Trademarks, trade names and other		1,015		146		869		1,003		98		905
	$	1,693	$	542	$	1,151	$	1,681	$	459	$	1,222

Intangible asset amortization expense was $1,252 million in 2021, $1,277 million in 2020 and $1,317 million in 2019. Estimated amortization expense over the next five years is as follows (in millions): 2022 – $1,189; 2023 – $1,120; 2024 – $1,023; 2025 – $939 and 2026 – $846. Intangible assets with indefinite lives were $18.5 billion as of December 31, 2021 and $18.3 billion as of December 31, 2020 and primarily related to certain customer relationships and trademarks and trade names.