You better see Article 7 of DTAAwith the other country. Usually they state that Business income of an enterprise in a contracting state can be taxed only in that state and can be taxed in the other source state only if they have a PE in the source state and that too to the extent of income deemed to accrue to the PE.
For professional incomes the situation is different:-
Section 9 of our Income Tax Act States that even if the entity of the other country does not have PE in India, 20% TDS has to be deducted fr Professional & Technical (incl. Managerial) services.
In the DTAA India signs with other country, There is an article that handles payment of Royalties and Technical Services (Incl. Managerial Services) and another article that handles Professional and Included Independent Personal Services (Lawyers, Accountants, Doctors, Teachers etc.).
In both these articles, it is usually mentioned that both states have the right to tax this income and in some of thse agreements there is a limit fixed on how much of the gross amount a source scountry can tax. If this is lower than 20%, you can take cognizance of the DTAA and deduct lower tax provided after 1/10/2009 a PAN number should be given. Otherwise 20%.
In this same DTAA, the last section indicates how the credit of the tax is to be given to avoid double taxation. Normally it is in the form of a relief.
Say you paid professional fee of $10,000. The tax deducted is $2000. The foreign country will compute the tax in their jurisdiction on the $10,000 income. If it works out to more than the tax suffered in India ($2,000), then they have to pay the difference to their Government. If it works out to less than or equal to the tax suffered in India, they will not have to pay anything to their Government but they get no refund from their government.
Therefore you give the copy of DTAA to the foreigner and ask him to comply with the provisions and seek relief (not refund) from his jurisdiction. he cannot adjust the Indian Tax on his tax on income accruing to him in his country. He can adjust the Indian Tax only on the Indian Income on which he is liable to tax in his country on account of being resident.
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