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While the offset mainly applies to residents, where the foreign income of a foreign non-resident is taxed in Australia, they may be able to claim an offset.
These circumstances apply where a foreign resident pays income tax in a foreign country on an amount that is included in their assessable income (under Australian tax law) and such tax is imposed because the income is sourced in that country. By contrast, where a foreign country imposes tax on the amount included in an entity's assessable income merely because it is a resident of that country (that is residence-based taxation), a foreign income tax offset entitlement does not arise if the tax is imposed on income from a source outside the foreign country.
XYZ PLC is a United Kingdom resident that carries on a business through a permanent establishment (PE) in Australia. In carrying on such activities, it derives US source income, which is subject to tax in that country. The US source income is derived in connection with the PE activity in Australia, and a combination of Articles 7 and 21 of the Australia-UK tax treaty permits Australia to tax the income and treat it as being derived from sources within Australia, and therefore subject to Australian tax. Given that the US source income is taxed in that country on a source basis, the US tax paid counts towards a tax offset in Australia.
If XYZ pays UK tax on the US source income that is attributable to the Australian PE activity, the tax would be imposed on a residence basis on the non-UK sourced income and would not count towards the taxpayer's tax offset.