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Goodwill and Other Intangible Assets | 12 Months Ended
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Dec. 31, 2022
Goodwill and Intangible Assets Disclosure [Abstract] |
Goodwill and Other Intangible Assets | Goodwill and Other Intangible Assets White Mountains accounts for business combinations 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. Goodwill represents the excess of the amount paid to acquire subsidiaries over the fair value of identifiable net assets at the date of acquisition. 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 company as of December 31, 2022 and 2021:
$ in Millions |  | Weighted Average Economic Life (in years) |  | December 31, 2022 |  | December 31, 2021
| Acquisition Date Fair Value |  | Accumulated Amortization |  |  |  | Net Carrying Value |  | Acquisition Date Fair Value |  | Accumulated Amortization |  |  |  | Net Carrying Value
Goodwill: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ark |  | N/A |  | $ | 116.8 |  |  | $ | — |  |  |  |  | $ | 116.8 |  |  | $ | 116.8 |  |  | $ | — |  |  |  |  | $ | 116.8 |
Kudu |  | N/A |  | 7.6 |  |  | — |  |  |  |  | 7.6 |  |  | 7.6 |  |  | — |  |  |  |  | 7.6 |
Other Operations |  | N/A |  | 52.1 |  |  | — |  |  |  |  | 52.1 |  |  | 17.9 |  |  | — |  |  |  |  | 17.9 |
Total goodwill |  |  |  | 176.5 |  |  | — |  |  |  |  | 176.5 |  |  | 142.3 |  |  | — |  |  |  |  | 142.3 |
Other intangible assets: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Ark |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Underwriting capacity |  | N/A |  | 175.7 |  |  | — |  |  |  |  | 175.7 |  |  | 175.7 |  |  | — |  |  |  |  | 175.7 |
Kudu |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Trade names |  | 7 |  | 2.2 |  |  | 1.2 |  |  |  |  | 1.0 |  |  | 2.2 |  |  | .9 |  |  |  |  | 1.3 |
Other Operations |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
Trade names |  | 15.9 |  | 17.9 |  |  | 3.0 |  |  |  |  | 14.9 |  |  | 8.2 |  |  | 1.5 |  |  |  |  | 6.7 |
Customer relationships |  | 12.4 |  | 29.5 |  |  | 7.5 |  |  |  |  | 22.0 |  |  | 18.8 |  |  | 4.5 |  |  |  |  | 14.3 |
Other |  | 12.1 |  | 2.8 |  |  | .5 |  |  |  |  | 2.3 |  |  | .3 |  |  | .1 |  |  |  |  | .2 |
Subtotal | 50.2 |  |  | 11.0 |  |  |  |  | 39.2 |  |  | 27.3 |  |  | 6.1 |  |  |  |  | 21.2 |
Total other intangible assets | 228.1 |  |  | 12.2 |  |  |  |  | 215.9 |  |  | 205.2 |  |  | 7.0 |  |  |  |  | 198.2 |
Total goodwill and other intangible assets | $ | 404.6 |  |  | $ | 12.2 |  |  |  |  | 392.4 |  |  | $ | 347.5 |  |  | 7.0 |  |  |  |  | 340.5 |
Goodwill and other intangible assets attributed to non-controlling interests | (102.7) |  |  |  |  |  |  |  |  | (91.8) |
Goodwill and other intangible assets included in White Mountains’s common shareholders’ equity |  | $ | 289.7 |  |  |  |  |  |  |  |  | $ | 248.7 |
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. 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. Goodwill and Other Intangible Asset Rollforward The following table presents the change in goodwill and other intangible assets:
|  | December 31, 2022 |  | December 31, 2021
Millions |  | Goodwill |  | Other Intangible Assets |  | Total Goodwill and Other Intangible Assets |  | Goodwill |  | Other Intangible Assets |  | Total Goodwill and Other Intangible Assets
Beginning balance |  | $ | 142.3 |  |  | $ | 198.2 |  |  | $ | 340.5 |  |  | $ | 19.2 |  |  | $ | 26.4 |  |  | $ | 45.6 |
Acquisition of businesses (1) |  | 59.5 |  |  | — |  |  | 59.5 |  |  | 15.8 |  |  | — |  |  | 15.8 |
Ark Transaction |  | — |  |  | — |  |  | — |  |  | 116.8 |  |  | 175.7 |  |  | 292.5 |
Attribution of acquisition date fair value estimates between goodwill and other intangible assets |  | (22.9) |  |  | 22.9 |  |  | — |  |  | (9.3) |  |  | 9.3 |  |  | — |
Measurement period adjustments (2) |  | (2.4) |  |  | — |  |  | (2.4) |  |  | (.2) |  |  | — |  |  | (.2) |
Assets held for sale (3) |  | — |  |  | — |  |  | — |  |  | — |  |  | (8.6) |  |  | (8.6) |
Amortization |  | — |  |  | (5.2) |  |  | (5.2) |  |  | — |  |  | (4.6) |  |  | (4.6) |
Ending balance |  | $ | 176.5 |  |  | $ | 215.9 |  |  | $ | 392.4 |  |  | $ | 142.3 |  |  | $ | 198.2 |  |  | $ | 340.5 |
(1) Relates to acquisitions within Other Operations. (2) Measurement period adjustments relate to updated information about acquisition date fair values of assets acquired and liabilities assumed. During 2022 and 2021, adjustments relate to acquisitions within Other Operations. (3) As of December 31, 2021, White Mountains has classified one of its Other Operating Businesses as held for sale, which includes of $8.6 of insurance licenses. See Note. 21 — “Held for Sale and Discontinued Operations.” During the years ended December 31, 2022 and 2021, White Mountains did not recognize any impairments to goodwill and other intangible assets. Amortization of Other Intangible Assets Amortization expense was $5.2 million, $4.6 million and $1.6 million for the years ended December 31, 2022, 2021 and 2020. White Mountains expects to recognize amortization expense in each of the next five years as the following table presents:
Millions |  | Amortization Expense
2023 |  | $ | 7.1 |
2024 |  | 6.6 |
2025 |  | 5.7 |
2026 |  | 4.8 |
2027 and years after |  | 16.0 |
Total (1) |  | $ | 40.2 |
(1) Excludes Ark’s indefinite-lived intangible assets of $175.7.

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- Definition The entire disclosure for goodwill and intangible assets. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Publisher FASB -Name Accounting Standards Codification -Topic 350 -URI https://asc.fasb.org/topic&trid=2144416 + Details
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