Say a U.S. company sells imported Scottish wool sweaters for $100. To keep things simple, no profit - the company simply buys them from a Scottish firm for $100 (and has no other expenses). Suppose the dollar and the Euro are in exact parity, so the Scottish firm gets €100.
Since the U.S. company has no profit, it doesn't have income tax liability. (Again, this is just to keep things simple.) But now Congress enacts a 20% destination-based corporate tax (DBCT). So amounts paid for imports are no longer deductible.
Now the U.S. company is going to have to pay $20 of tax upon selling the Scottish sweater for $100 to a U.S. consumer. So it is only willing to pay the Scottish firm $80.
No dice, so far as the Scottish firm is concerned, if it is selling as many sweaters as it likes on world markets for $100 = €100 and the dollar remains in parity with the Euro. But if the dollar appreciates against the Euro so that $80 = €100, everyone''s happy and it all works just as before.
Now let's add the export case. A U.S. firm was making cotton sweaters for $100 and selling them for $100, both at home and to EU firms. But now, under the 20% DBCT, it's going to exclude from "income" the amount that it gets from foreign purchasers, while still expensing the $100 that it spends. Now it only needs $80 from EU purchasers, rather than $100, to break even as it was before. And again this happens without any change if the dollar appreciates against the Euro so that $80 = €100.
Now, how does the currency shift happen? Ay, there's the rub, as they say, but now that supply and demand have changed as described above things should at some point get there, at least in the simple story. (Real world institutions and complications may have a huge interim effect, however.) Or to put it differently, there won't be a stable equilibrium until they get there, and until that moment shifts in supply and demand at the old exchange rate will be pushing in that direction. But how and when it gets there is actually, in my view, potentially quite disruptive in ways we might not like.
One last point about all this. The appreciation of the dollar against the Euro (etc.) would reduce the dollar value of Americans' foreign asset holdings, and increase the Euro (etc.) value of foreigners' U.S. asset holdings. As Alan Viard has noted:
“The wealth transfers could be quite large. Assume, for simplicity, that foreigners hold $10 trillion of American assets and that Americans hold the same amount of foreign assets. Adding a border adjustment to a 20 percent (tax-inclusive) VAT would increase foreigners’ wealth by $2 trillion and reduce Americans’ wealth by $2 trillion. Because cross-border holdings are balanced in this example, the border adjustment would not change the present discounted value of federal revenue, but it would cause $2 trillion of that revenue to be collected from Americans rather than from foreigners.”
What is more: “Because the United States is a net debtor country, the border adjustment would actually cause a net loss to the U.S. Treasury ... and foreign investors’ gains would exceed American investors’ losses.”