1. FSBA Dues Spreadsheet Explanation

2. Problem
The way that dues were previously calculated was very unclear; there was no known formula and it did not follow any clear pattern; multiple counties paid the same amount of dues, suggesting some sort of grouping, but at the same time, the values were fairly similar to the ln of the enrollment
The costs were not distributed very fairly either, for example, Miami-Dade and Broward counties were paying $.07 and $.08 per student respectively, while Jefferson county was paying $11.55 per student
For political reasons, dues could not be too heavily shifted from smaller counties to larger ones, limiting the extent to which the cost per student dilemma could be remedied and eliminating some models

3. Solution
To more clearly define how dues are to be calculated and remedy the cost per student of the smaller counties some without putting too much of a burden on the larger ones, the new dues will be calculated based on the following formula:
Dues= (16*(“K”*LN(Enrollment))+3*(EBV)+2*(BBC))/21+“R”
Where EBV = Enrollment Based Value and BBC = Benefit Based Contribution
“R” is readjustment for any rounding errors and is just an even distribution of any difference between the total costs and the rest of the above formula
“R”= (Total Costs – ∑(16*(“K”*LN(Enrollment))+3*(EBV)+2*(BBC))/21)/Number of Counties

4. Explanation of “K”*LN(Enrollment)
The LN of a number is the “natural logarithm” or log base e of that number
e ≈
A logarithm is the inverse of an exponential function; for example, 2^3= 8, meaning the log base 2 of 8= 3
LN is used over a different logarithm because it is simpler in most circumstances and due to the properties of logarithms, any logarithm can be re-expressed as a Constant * LN
Logarithms are used because they increase at a decreasing rate for all values they are defined and they are also used in pH and the Richter Scale
“K” = Total Costs/∑(LN(Enrollment))

5. Enrollment Based Value (EBV)
Enrollment Based Value is the proportion of the enrollment of the county to the total enrollment multiplied by the total costs
Mathematically:
Enrollment Based Value = Total Costs*(Enrollment/Total Enrollment)
Enrollment Based Value is weighed in to help to balance out the cost per student in each county

6. Benefit Based Contribution (BBC)
Benefit Based Contribution = Total Costs*(Benefit Ratio/ Sum of the Benefit Ratios)
Benefit Ratio = District Budget*(Enrollment of County/ Total Population of County)
The Benefit Based Contribution is used to try to account for the ability of each county to pay and the amount each county benefits from FSBA’s services
The Taxable Value takes into account each county’s ability to pay, and the ratio of the enrollment in each county to the total population of the county is intended to gauge how much each county benefits from FSBA

7. Old Dues vs. Enrollment

8. New Dues vs. Enrollment

9. Old Dues vs. District Budget

10. New Dues vs. District Budget

11. Old Dues vs. Benefit Based Contribution

12. New Dues vs. Benefit Based Contribution