Be it further enacted, That all property within the corporate limits, real and personal, not exempted by general law, shall be assessed as of January 10 in each year, for taxation by the city. The city property tax rate shall also be levied on the capital stock of merchants in accordance with the law providing for such a tax by the state or county. The property valuations upon which payments in lieu of taxes are made by any department or agency of the federal, state, or local government shall be considered as a part of the total assessed valuation of property in the city for computing debt limitation and similar purposes.