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Goodwill, Customer Relationships and Other Intangible Assets
 12 Months Ended
Dec. 31, 2020
Goodwill and Intangible Assets Disclosure [Abstract]  
Goodwill, Customer Relationships and Other Intangible Assets Goodwill, Customer Relationships and Other Intangible Assets
Goodwill, customer relationships and other intangible assets consisted of the following:
As of December 31,
20202019
(Dollars in millions)
Goodwill$7,405 7,415 
Customer relationships, less accumulated amortization of $2,246 and $1,538
$6,156 6,865 
Capitalized software, less accumulated amortization of $256 and $146
401 395 
Trade names, less accumulated amortization of $83 and $57
48 74 
Total other intangible assets, net$6,605 7,334 

Our goodwill was derived from Lumen's acquisition of us where the purchase price exceeded the fair value of the net assets acquired.

We assess our goodwill for impairment annually, or, under certain circumstances, more frequently, such as when events or changes in circumstances indicate there may be impairment. We are required to write down the value of goodwill only when our assessment determines the carrying value of equity of our reporting unit exceeds its fair value. Our annual impairment assessment date for goodwill is October 31, at which date we assess goodwill at our reporting unit. In reviewing the criteria for reporting units, we have determined that we are one reporting unit.

At October 31, 2020, we estimated the fair value of equity by considering both a market approach and a discounted cash flow method. The market approach method includes the use of comparable multiples of publicly traded companies whose services are comparable to ours. The discounted cash flow method is based on the present value of projected cash flows and a terminal value equal to the present value of all normalized cash flows after the projection period. As of October 31, 2020, based on our assessment performed, the estimated fair value of our equity exceeded our carrying value of equity by approximately 17%. We concluded that the goodwill was not impaired as of October 31, 2020.

Because Lumen's low stock price was a trigger for impairment testing, we estimated the fair value of our operations using only the market approach in the quarter ended March 31, 2019. Applying this approach, we utilized company comparisons and analyst reports within the telecommunications industry, which have historically supported a range of fair values of annualized revenue and EBITDA multiples between 2.1x and 4.9x and 4.9x and 9.8x, respectively. We selected a revenue and EBITDA multiple within this range. As of March 31, 2019, based on our assessments performed as described above, we concluded that the estimated fair value of equity was less than our carrying value of equity as of the date of our triggering event during the first quarter. As a result, we recorded a non-cash, non-tax-deductible goodwill impairment charge of $3.7 billion in the quarter ended March 31, 2019.
The market multiples approach that we used in the quarter ended March 31, 2019 incorporated significant estimates and assumptions related to the forecasted results for the remainder of the year, including revenues, expenses, and the achievement of certain cost synergies. In developing the market multiple, we also considered observed trends of our industry participants. Our assessment included many qualitative factors that required significant judgment. Alternative interpretations of these factors could have resulted in different conclusions regarding the size of our impairments.

At October 31, 2019, we estimated the fair value of equity by considering both a market approach and a discounted cash flow method. As of October 31, 2019, based on our assessment performed, the estimated fair value of our equity exceeded our carrying value of equity by approximately 26%. We concluded that the goodwill was not impaired as of October 31, 2019.

The following table shows the rollforward of goodwill from December 31, 2018 through December 31, 2020:
(Dollars in millions)
As of December 31, 2018$11,119 
Goodwill Impairment(3,708)
Effect of foreign currency exchange rate changes and other4 
As of December 31, 2019 (1)
7,415 
Effect of foreign currency exchange rate changes and other(10)
As of December 31, 2020 (1)
$7,405 
_______________________________________________________________________________
(1)Goodwill at December 31, 2020 and December 31, 2019 is net of accumulated impairment loss of $3.7 billion.

Total amortization expense for intangible assets for the years ended December 31, 2020, 2019 and 2018 was $838 million, $809 million and $798 million, respectively. As of December 31, 2020, the gross carrying amount of goodwill, customer relationships, indefinite-life and other intangible assets was $16.6 billion. As of December 31, 2020, the weighted average remaining useful lives of our finite-lived intangible assets was approximately 9 years in total; 9 years for customer relationships, 2 years for trade names, and 4 years for developed technology.

We estimate that total amortization expense for intangible assets for the years ending 2021 through 2025 will be as follows:
(Dollars in millions)
2021$843 
2022783 
2023755 
2024743 
2025679