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Goodwill and Other Intangible Assets
6 Months Ended
Jun. 30, 2022
Goodwill and Intangible Assets Disclosure [Abstract]  
Goodwill and Other Intangible Assets Goodwill and Other Intangible Assets
    White Mountains accounts for purchases of businesses using the acquisition method. Under the acquisition method, White Mountains recognizes and measures the assets acquired, liabilities assumed and any non-controlling interest in the acquired entities at their acquisition date fair values. The estimated acquisition date fair values, generally consisting of intangible assets and liabilities for contingent consideration, may be recorded at provisional amounts in circumstances where the information necessary to complete the acquisition accounting is not available at the reporting date. Any such provisional amounts are finalized as measurement period adjustments within one year of the acquisition date.
The following table presents the economic lives, acquisition date fair values, accumulated amortization and net carrying values for other intangible assets and goodwill, by reportable segment as of June 30, 2022 and December 31, 2021:
$ in MillionsWeighted Average Economic
 Life
(in years)
June 30, 2022December 31, 2021
Acquisition Date Fair ValueAccumulated AmortizationNet Carrying ValueAcquisition Date Fair ValueAccumulated AmortizationNet Carrying Value
Goodwill:
ArkN/A$116.8 $ $116.8 $116.8 $— $116.8 
KuduN/A7.6  7.6 7.6 7.6 
Other Operations (1)
N/A77.4  77.4 17.9 — 17.9 
Total goodwill201.8  201.8 142.3 — 142.3 
Other intangible assets:
Ark
Underwriting CapacityN/A175.7  175.7 175.7 — 175.7 
Kudu
   Trade names72.2 1.1 1.1 2.2 .9 1.3 
Other Operations
   Trade names17.58.2 2.0 6.2 8.2 1.5 6.7 
Customer relationships13.018.8 5.7 13.1 18.8 4.5 14.3 
Other5.3.3 .2 .1 .3 .1 .2 
       Subtotal27.3 7.9 19.4 27.3 6.1 21.2 
Total other intangible assets205.2 9.0 196.2 205.2 7.0 198.2 
Total goodwill and other intangible assets
$407.0 $9.0 398.0 $347.5 $7.0 340.5 
Goodwill and other intangible assets attributed to
   non-controlling interests
(103.4)(91.8)
Goodwill and other intangible assets included in White Mountains’s
   common shareholders’ equity
$294.6 $248.7 
(1) The relative fair values of goodwill and other intangible assets recognized in connection with recent acquisitions within Other Operations had not yet been finalized as of June 30, 2022.

Intangible Assets Valuation Methods

The goodwill recognized for the entities shown above is attributed to expected future cash flows. The acquisition date fair values of other intangible assets with finite lives are estimated using income approach techniques, which use future expected cash flows to develop a discounted present value amount.
The multi-period-excess-earnings method estimates fair value using the present value of the incremental after-tax cash flows attributable solely to the other intangible asset over its remaining life. This approach was used to estimate the fair value of other intangible assets associated with the underwriting capacity, trade names, customer relationships and contracts and information technology.
The relief-from-royalty method was used to estimate fair value for other intangible assets that relate to rights that could be obtained via a license from a third-party owner. Under this method, the fair value is estimated using the present value of license fees avoided by owning rather than leasing the asset. This technique was used to estimate the fair value of domain names, certain trademarks and brand names.
The with-or-without method estimates the fair value of other intangible assets that provide an incremental benefit. Under this method, the fair value of the other intangible asset is calculated by comparing the value of the entity with and without the other intangible asset. This approach was used to estimate the fair value of favorable lease terms.
On at least an annual basis beginning no later than the interim period included in the one-year anniversary of an acquisition, White Mountains evaluates goodwill and other intangible assets for potential impairment. Between annual evaluations, White Mountains considers changes in circumstances or events subsequent to the most recent evaluation that may indicate that an impairment may exist and, if necessary will perform an interim review for potential impairment.
The following table presents a summary of the acquisition date fair values of goodwill and other intangible assets for acquisitions completed from January 1, 2021 through June 30, 2022:
$ in Millions
Acquisition of subsidiary/ asset
Goodwill and
Other intangible asset (1)
Acquisition Date
Ark$292.5 January 1, 2021
Other Operations$90.5 Various
(1) Acquisition date fair values include the effect of adjustments during the measurement period and excludes the effect of foreign currency translation subsequent to the acquisition date.

The following tables present the change in goodwill and other intangible assets for the three and six months ended June 30, 2022 and 2021:
Three Months Ended June 30,
20222021
MillionsGoodwillOther Intangible AssetsTotal Goodwill and Other Intangible AssetsGoodwillOther Intangible AssetsTotal Goodwill and Other Intangible Assets
Beginning balance$142.3 $197.2 $339.5 $135.7 $201.6 $337.3 
Acquisition of businesses59.5 
(1)
 59.5 15.8 
(1)
— 15.8 
Amortization (1.0)(1.0)— (.5)(.5)
Ending balance$201.8 $196.2 $398.0 $151.5 $201.1 $352.6 
(1) The relative fair values of goodwill and other intangible assets recognized in connection with recent acquisitions within Other Operations had not yet been finalized.

Six Months Ended June 30,
20222021
MillionsGoodwillOther Intangible AssetsTotal Goodwill and Other Intangible AssetsGoodwillOther Intangible AssetsTotal Goodwill and Other Intangible Assets
Beginning balance$142.3 $198.2 $340.5 $19.2 $26.4 $45.6 
Ark Transaction   116.8 175.7 292.5 
Acquisition of businesses59.5 
(2)
 59.5 15.8 
(2)
— 15.8 
Measurement period adjustments (1)
   (.3).1 (.2)
Amortization (2.0)(2.0)— (1.1)(1.1)
Ending balance$201.8 $196.2 $398.0 $151.5 $201.1 $352.6 
(1) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During the six months ended June 30, 2021, adjustments primarily relate to goodwill and other intangible assets of $0.2 in connection with the acquisition in the Other Operations segment.
(2) The relative fair values of goodwill and other intangible assets recognized in connection with recent acquisitions within Other Operations had not yet been finalized.