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.
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
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)