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Income taxes | 9 Months Ended
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Sep. 30, 2025
Income taxes |
Income taxes | Note 13 – Income taxes: ​
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Three months ended | ​ | Nine months ended
​ | ​ | September 30, | ​ | September 30,
​ |  | 2024 |  | 2025 |  | 2024 |  | 2025
​ | ​ | (In thousands)
Expected tax expense (benefit), at U.S. federal statutory income tax rate of 21% | ​ | $ | 9,425 | ​ | $ | (1,726) | ​ | $ | 13,217 | ​ | $ | (1,241)
Rate differences on equity in earnings (losses) of Kronos, net of dividends | ​ |  | (954) | ​ |  | 856 | ​ |  | (2,512) | ​ |  | 262
U.S. state income taxes and other, net | ​ |  | 37 | ​ |  | 16 | ​ |  | 93 | ​ |  | 59
Income tax expense (benefit) | ​ | $ | 8,508 | ​ | $ | (854) | ​ | $ | 10,798 | ​ | $ | (920)
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
Comprehensive provision (benefit) for income taxes allocable to: | ​ |  |  | ​ |  |  | ​ |  |  | ​ |  |
Net income (loss) | ​ | $ | 8,508 | ​ | $ | (854) | ​ | $ | 10,798 | ​ | $ | (920)
Additional paid-in capital | ​ | ​ | — | ​ | ​ | — | ​ | ​ | 8 | ​ | ​ | 8
Other comprehensive income (loss): | ​ |  |  | ​ |  | ​ | ​ |  |  | ​ |  |
Currency translation | ​ |  | 404 | ​ |  | 8 | ​ |  | (792) | ​ |  | 2,034
Pension plans | ​ |  | 99 | ​ |  | 87 | ​ |  | 301 | ​ |  | 257
Other | ​ |  | (14) | ​ |  | (7) | ​ |  | (33) | ​ |  | (25)
Total | ​ | $ | 8,997 | ​ | $ | (766) | ​ | $ | 10,282 | ​ | $ | 1,354
​ In accordance with GAAP, we recognize deferred income taxes on our undistributed equity in earnings of Kronos. Because we and Kronos are part of the same U.S. federal income tax group, any dividends we receive from Kronos are nontaxable to us. Accordingly, we do not recognize and we are not required to pay income taxes on dividends from Kronos. We received aggregate dividends from Kronos of $15.1 million and $5.3 million in the first nine months of 2024 and 2025, respectively. The amounts shown in the above table of our income tax rate reconciliation for rate differences on equity in earnings (losses) of Kronos, net of dividends, represent the income tax expense (benefit) associated with the nontaxable dividends we received from Kronos compared to the amount of deferred income taxes we recognized on our equity in earnings (losses) of Kronos. On July 4, 2025, the One Big Beautiful Bill Act (“OBBBA”) was signed into law in the United States. The OBBBA, among other provisions, provides for bonus depreciation of qualified property, permanently modifies the interest expense deduction to use an adjusted taxable income based on a calculation similar to EBITDA, and makes changes to international tax provisions including Foreign-Derived Intangible Income (“FDII”) (renamed Foreign-derived Deduction Eligible Income (FDDEI)). The legislation has multiple effective dates, with certain provisions effective in 2025 and others implemented through 2027. The OBBBA did not have a material impact on our 2025 consolidated financial statements, and we are in the process of evaluating the impact to future years as additional provisions take effect. ​ Income tax matters related to Kronos ​ On July 18, 2025, Germany enacted legislation which includes, among other provisions, an additional depreciation allowance for certain fixed assets, improvements to the research and development tax allowance and, starting in 2028, a reduction of the 15% corporate tax rate by one percentage point annually for five years reaching 10% in 2032. Kronos recorded a non-cash deferred income tax expense of $19.3 million in the third quarter to reduce their net German deferred tax asset as a result of the reduction of the German corporate tax rate. .

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