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Goodwill, Customer Relationships and Other Intangible Assets
12 Months Ended
Dec. 31, 2021
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,
20212020
(Dollars in millions)
Goodwill$9,360 9,360 
Customer relationships, less accumulated amortization of $5,699 and $5,611
$— 88 
Other intangible assets, less accumulated amortization of $1,876 and $1,831
199 255 
Total other intangible assets, net$199 343 

As of December 31, 2021, the gross carrying amount of goodwill, customer relationships and other intangible assets was $17.1 billion.

Substantially, all of 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, 2021, 2020 and 2019, 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. Based on our assessment performed, the estimated fair value of our equity exceeded our carrying value of equity by approximately 42%, 48% and 65% at October 31, 2021, 2020 and 2019, respectively. We concluded that goodwill was not impaired as of October 31, 2021, 2020 and 2019.
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. 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. As of March 31, 2019, based on our assessments performed as described above, we concluded that our goodwill was not impaired.

Our fair value estimates for evaluating goodwill incorporated significant judgements and assumptions including forecast revenues and expenses, cost of capital, and control premiums. In developing market multiples, we also considered observed trends of our industry participants and other qualitative factors that required significant judgment. Alternative estimates, judgements, and interpretations of these factors could have resulted in different conclusions regarding the need for an impairment charge.

We annually review the estimated lives and methods used to amortize our other intangible assets. The actual amounts of amortization expense may differ materially from our estimates, depending on the results of our annual reviews. As of December 31, 2021, the weighted average remaining useful life was 2 years for capitalized software.

Total amortization expense for intangible assets for the years ended December 31, 2021, 2020 and 2019 was $176 million, $481 million and $533 million, respectively.

We estimate that total amortization expense for intangible assets for the years ending December 31, 2022 through 2026 will be as follows:
(Dollars in millions)
Year ending December 31,
2022$86 
202362 
202413 
202512 
2026