## Valuation for a Tax Abatement

Fair Warning – This is strictly for nerds!

The problem to be solved is to establish the fair assessment of a property based on its net operating income. The property owner thinks the assessment and resultant taxes are too high. The calculation problem is with the property taxes. You are deducting taxes that the owner thinks are too high, which lowers the NOI, which in turn lowers the value and lowers the taxes you just used. The circle can go on forever. Here is the solution:

FMV is Fair Market Value

AV is Assessed Value

EQR is Equalization Ratio; this is set by the State each year for each municipality. It is the ratio of Assessed Value divided by Fair Market Value

TF is Tax Factor

MR is Mil Rate; expressed as dollars of taxes per \$1,000 of AV

ExpOrd is Ordinary expenses excluding property taxes

CR is Cap Rate; this is a market-derived ratio of NOI ÷FMV

NOI is Net Operating Income; this is Income – Expenses, where expenses do not include non-operating items like interest or depreciation.

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NOI = Income – Expenses

EQR = AV ÷ FMV or better stated as Assessment = EQR x FMV

TF = MR x EQR

Tax Expense = TF x FMV = MR x EQR x FMV

Expenses = OrdExp + Tax Expense

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FMV = NOI ÷ CR = (Income – OrdExp – Tax Expense) ÷ CR

FMV = (Income – OrdExp – TF x FMV) ÷ CR

FMV x CR = Income – OrdExp – TF x FMV

FMV x CR + (TF x FMV) = Income – OrdExp

FMV x (CR + TF) = Income – OrdExp

FMV x (CR + TF) = (Income – Ord Exp)

FMV = (Income – Ord Exp) ÷ (CR + TF)

Thus you can use Expenses without taxes if you add the tax factor to the Cap Rate to get to FMV.

It follows that If you have NNN tenants and tenants are paying taxes, you use TF x (1-vacancy rate)