You are asking a very complicated tax and business question and also in relation an act that has not passed. First you need to understand current nexus law. I won't even begin to explain this as there are so many issues. You can get a slight idea of the complications by reading this http://www.steptoe.com/assets/attachments/1571.pdf.
This is something that needs to be determined by speaking with an experienced accountant or tax attorney after the act actually passes (assuming it does).
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Mr. Cappuccio has given you good advice. If you are a U.S. citizen you are taxed on your worldwide income. So moving the business to the Dominican Republic will not, by itself, eliminate the need to pay income tax. I doubt that it will help with sales tax because the states will probably view you as doing business in their states. In any event, the residents of the states buying from you will probably be required to pay a use tax. This is not something for which you will be able to get a reliable answer over the internet. You are going to have to go to a tax lawyer and write a check for a couple of thousand dollars to get advice.
As already mentioned, this is an area where you must be very cautious and must have a competent advisor. Usually, one of the main reasons companies move offshore is to eliminate or defer U.S. taxes on foreign earnings. If there is no international component to the business, you might not see many benefits. U.S. citizens are taxed on their worldwide income and renouncing citizenship to avoid taxes (if that is what you are thinking) may trigger the expatriation provisions of Internal Revenue Code Sections 877 and 877A. If you remain a U.S. citizen, your federal tax return will become more complicate because of the additional reporting requirements when you have interests in foreign entities and bank accounts. If you try to move your business offshore, Section 367 may treat the transfer as a taxable sale. You might also trigger various tax withholding obligations depending on the entity structure. These are only a few of the federal income tax issues. It is also possible that the expatriation will not reduce your exposure to sales taxes because these depends on the individual state laws, or the provisions of the Marketplace Fairness Act if it is enacted. I have not studied this proposed Act very closely, but I did not see an exemption for foreign sellers. You also need to factor in the cost of establishing your offshore legal structure. You might find that after weighing all of the costs, you would be better off developing a solution to your sales tax compliance issues. DISCLAIMER: These are just some general comments regarding issues you may wish to consider and must not be treated as legal or tax advice.
At first blush, if your goal is to save state income tax and use tax collection responsibilities, then I would say relocating can greatly reduce those burdens on your company. As the other responders point out, there will be other tax complications with this manuever on the federal and international level that may or may not offset your savings. This is a question to pose to an international tax lawyer with good sales and use tax knowledge.
This being said, I would caution you that dropshipments from US based wholesalers may complicate your scenario greatly. If the customer's state has jurisdction over the wholesaler, then, the wholesaler may have to collect tax either on the price you pay or, believe it or not, on the prie you charge your customer.
No matter what - you need to engage a good tax attorney to review the issues.
I hope this answer helps.