If the current State Equalized Value or SEV (approximately 50% of the home's market value) and the Taxable Value (the current owners' tax basis) are the same, your taxes will probably not change much.
If there is a gap between the two, however, your taxes will adjust upward, and be based on the SEV.
Another factor is whether the property is your primary residence. A home purchased as a second residence or rental will have "non-homestead" taxes. In Ann Arbor, the non-homestead factor is currently .0592, so on a $240,000 property the taxes would be $120,000 x .0592, or $7,104. For an owner-occupied property, the taxes would be $5,640, based on a factor of .047 (Remember, these are approximations only).
To calculate the approximate taxes on a home you're considering purchasing in Michigan, you can use the Michigan Property Tax Estimator here.
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