Reconciliations of the changes in the carrying value of goodwill during 2020 and 2019 follows (in millions).

	December 31,
	2020			2019
Balance at beginning of year	$	81,882		$	81,025
Acquisitions of businesses		1,758			890
Impairment charges		(10,033	)		(90	)
Other, including foreign currency translation		127			57
Balance at end of year*	$	73,734		$	81,882

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

	December 31, 2020				December 31, 2019
	Gross carrying amount		Accumulated amortization		Gross carrying amount		Accumulated amortization
Insurance and other:
Customer relationships	$	27,374	$	5,756	$	27,943	$	5,025
Trademarks and trade names		5,206		779		5,286		759
Patents and technology		4,766		3,313		4,560		3,032
Other		3,339		1,375		3,364		1,286
	$	40,685	$	11,223	$	41,153	$	10,102
Railroad, utilities and energy:
Customer relationships	$	678	$	361	$	678	$	324
Trademarks, trade names and other		1,003		98		325		84
	$	1,681	$	459	$	1,003	$	408

Intangible asset amortization expense was $1,277 million in 2020, $1,317 million in 2019 and $1,393 million in 2018. Estimated amortization expense over the next five years is as follows (in millions): 2021 – $1,262; 2022 – $1,190; 2023 – $1,108; 2024 – $986 and 2025 – $906. Intangible assets with indefinite lives were $18.3 billion as of December 31, 2020 and $19.0 billion as of December 31, 2019 and primarily related to certain customer relationships and trademarks and trade names.

During 2020, we concluded it was necessary to reevaluate goodwill and indefinite-lived intangible assets of certain of our reporting units for impairment due to the disruptions arising from the COVID-19 pandemic. We believed that the most significant of these disruptions related to the air travel and commercial aerospace and supporting industries. We recorded pre-tax goodwill impairment charges of approximately $10 billion and pre-tax indefinite-lived intangible asset impairment charges of $638 million in the second quarter of 2020. Approximately $10 billion of these charges related to Precision Castparts Corp. (“PCC”), the largest business within Berkshire's manufacturing segment. The carrying value of PCC-related goodwill and indefinite-lived intangible assets prior to the impairment charges was 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 cash flows and earnings, actual results in the future may vary significantly from the forecasts.