Hank is a U$.$S$.$ citizen $($i$.$e$.,$ a U$.$S$.$ person$),$ who owns $100\%$ of a domestic S$-$Corporation which, in turn, owns $100\%$ of the stock of Cheers Ltd$.,$ a foreign corporation. Although Cheers Ltd$.$ has accumulated significant earnings and profits $($E&P$)$ since its inception in early $2018,$ including current year E&P of $$1,000,000,$ it has never paid a dividend and none of its income has been subject to the U$.$S$.$ anti$-$deferral rules. Furthermore, assume that Hank is in a $37\%$ individual income tax bracket in the United States.

a$.$ What is Hank's current year U$.$S$.$ income tax liability related to Cheers Ltd$.?$

b$.$ What is Hank's current year U$.$S$.$ income tax liability related to Cheers Ltd$.$ if Cheers Ltd$.$ distributes a $$500,000$ dividend and Cheers Ltd$.$ resides in a foreign country that has a comprehensive income tax treaty with the United Sates?

c$.$ What if Cheers Ltd$.$ does not reside in a foreign country that has a comprehensive income tax treaty with the United States?