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In the previous scenario, yes you would. The Taxable Value will rise by the inflationary increase. This figure multiplied by the local unit's millage rate will determine your new property tax liability.
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Unfortunately, there isn't a yes or no answer to that question. If you've owned your property for a significant amount of time, more than likely your State Equalized Value (SEV) far exceeds your Taxable Value. If this is the case, a decrease in valuation, caused by a cooling real estate market, will be reflected in the SEV. The Taxable Value is required by the Michigan Constitution to increase each year by the rate of inflation or 5%, whichever is lower. In the case of a longtime property owner, the SEV could decrease, while the Taxable Value will increase.
Proposal A allowed many residents to pay property taxes on less than half of their market value by "capping" the Taxable Value, while still allowing the assessor to determine the market value by adjusting the State Equalized Value (SEV). This has caused, for many property owners, a great disparity between the SEV figure and the Taxable Value figure. The assessor can reduce the SEV to reflect the change in property value, but if the Taxable Value is still well below the SEV, it will keep increasing until the two figures meet. Taxes are based on Taxable Value; therefore you will end up with a tax increase.
if a property's value decreases each year, the State Equalized Value (SEV) will eventually meet the Taxable Value. The Taxable Value cannot exceed the SEV. When this happens, decreases in SEV will cause decreases in Taxable Value, which will then lower your property tax liability. Due to the gap between the SEV and Taxable Value figures, it would take several years of depressed market conditions to make the SEV and Taxable Value equal. If you happen to be a property owner who purchased a property in the last few years and you have decreasing property value, the SEV and Taxable Value figures could meet sooner than someone who has owned the property for a long period of time.