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Deductions & credits
@CNOakland I think you may have missed the application of a multiplier in your Line 18 worksheet: where you state "the value should be 41,168 - 29,821 = 11,347", I think you likely need to apply a 0.5946 multiplier to the 29,821 (assuming those dividends belong in the 15% dividends category, on line 8). So the math would become 41,168 - (29,821 * 0.5946) = 23,436, which won't be nearly so helpful.
Also, as others have pointed out, you can't do the Line 18 adjustment unless you also adjust line 1a in a similar fashion. So just like we removed 59.46% of the worldwide qualified dividends from line 18, we have to remove 59.46% of the foreign qualified dividends from line 1a. So we subtract (4,994 * 0.5946) from 5,313, leaving only 2,344 on line 1a.
If you think about the relative size of the changes to line 1a and line 18, you'll see the problem: 1a went down by a bigger percentage than 18. Since 1a feeds into the numerator and 18 is the denominator of the ratio that determines the maximum foreign tax credit, these changes are going to reduce the foreign tax credit rather than increase it. So I think you are going to be better off using the adjustment exception.
In general the adjustments help when your foreign income is taxed at a higher average rate than your US income. So for example if your foreign income is wage or pension income taxable at say 22%, while your US-sourced income is primarily dividends taxable at 15%, then you'll get a higher foreign tax credit after doing the adjustments. But its more common for US taxpayers to have their ordinary income be US-sourced, and their foreign income to consist primarily of low-tax dividends. In that situation, the adjustments reduce the tax credit, so it's helpful to have an exception available for foreign dividends less than $20,000.
btw... if you're wondering where that odd 59.46% adjustment factor comes from (like I did!) it's based on the ratio of the tax rates 15% and 37%. It's used to answer the question "How many dollars of ordinary income generate the same amount of tax as a dollar of dividend income". Example: you have $100 of dividends taxed at 15% so you pay $15 in tax. To generate the same $15 in tax from ordinary income at a 37% tax rate, you would need $100 * 15/37 = $40.54 of ordinary income, which is 59.46% less than $100. So the 59.46% haircut applied to dividend income is an attempt to make it equivalent to ordinary income, in terms of its associated tax liability. That's probably oversimplified, but I've found it a helpful way to think about why these adjustments are made.