Notwithstanding any other provision of law, special or general, to the contrary, the governing body of any county, city or town may by ordinance provide that taxes on real estate, tangible personal property and machinery and tools be levied and imposed on a fiscal year basis of July 1 to June 30. Such locality is authorized and empowered to change the rate of any such levy during any fiscal year. As to any locality which has adopted such ordinance all provisions of this Code specifying a date or month relative to the levy, payment or collection of such taxes shall be interpreted to specify the corresponding date or month of the fiscal year, except that all property shall be assessed as of January 1 prior to such fiscal year unless otherwise specifically provided under § 58.1-3011. In order to effect a change to a fiscal tax year pursuant to this section, any locality may have a short calendar year from January 1 through June 30, or a short fiscal year from January 1 through June 30. All provisions of law applicable to the assessment of property, levy, payment and collection of taxes for a calendar year shall apply to such short tax year. If such short year is a fiscal year, the locality may borrow beginning January 1 pursuant to §§ 15.2-2629 and 15.2-2631 as if it had been on such fiscal year from the prior July 1. If such short year is a calendar year, borrowing pursuant to §§ 15.2-2629 and 15.2-2631 must be repaid at the time specified in § 15.2-2631 for fiscal year borrowings. Any locality which levies taxes on a fiscal year basis, as authorized by general law or special act, shall exonerate or refund its personal property tax for that portion of the tax year for which the property was properly assessed by another jurisdiction in the Commonwealth and the tax paid.