Understanding the Dollar Yield

This page explains one small portion of the process of calculating homestead property taxes in Vermont. To truly understand how education funding works you need to understand the Common Level of Appraisal (CLA), the Average Daily Membership (ADM), Equalized Pupils, other inputs to the Education Fund, Income Sensitivity and more. But for those who find the Dollar Yield particularly difficulty to understand, this document may help. You may want to read the Why so Complicated page to understand why the Dollar Yield is needed.

The Problem

The trick is to determine a method for filling the education fund, through property taxes, that allows for equal opportunity to access those funds. If you’re going to draw down $17,000 for each of your pupils, then you must pay a specific tax rate no matter if you live in a rich district or a poor district.

If Vermont was one school district with one budget funded by a statewide property tax, things would be simple. Assume the state has only five students and a state-wide vote determined that the majority wants to spend $1,000 for each student’s education. The state would need $5,000 in the education fund. If the state also had property that assessed at ten million dollars, the tax rate for everyone would be calculated as follows:

TaxRate=Budget / (PropertValue / 100)

The 100 is because the tax rate is on every $100 of property value.

The tax rate would be:

TaxRate=$5,000 / ($10,000,000/100)

The resulting .05 would mean that each tax payer would pay five cents for each $100 of their property value. The total taxes collected would be:

(Formula #1) TaxesCollected=TaxRate*(PropertValue / 100)

Which equals .05 * $100,000 or $5,000

The state would then send the one district a check for $5,000.

But we do not have a statewide school budget. Our school districts do not want the state dictating how much they spend on a student’s education. That’s local control. Districts vary considerably in size, wealth, income, and commitment to education. How do you take that into account and yet produce tax rates that give each students equal opportunity to access the Education Fund (a state resource)?

The Challenge

Understanding how this is solved means thinking in terms of Per Pupil Spending (PPS). That’s the amount being spent on each student’s education. One characteristic of our example statewide school district is that the PPS is the same for all students. The PPS is, after all, just the total budget divided by the number of students. In addition, the tax rate is the same for all taxpayers. So, one characteristic of a system that fulfills Vermont’s constitutional requirements is that districts with the same PPS must have the same tax rate.

On Town Meeting Day, when voters vote on their district school budget, they determine both their budget total and the PPS. Each can be determined from the other using the pupil count. After Town Meeting day the state can combine all district budgets and determine (roughly) how much money needs to be in the Education Fund. If every town approved their school district budget, the state would know exactly how much is needed.

The State can then determine how to fill that fund through property taxes.[1] What should the rate be for each district? Because the PPS is the best indicator of the amount of education benefit that each district wants to purchase for each student through taxes, it is the number that is used to set the local property tax rate.

The challenge is to determine a single state-wide number (the Dollar Yield) that is the amount of education benefit for a single pupil that one dollar of tax rate will fund. When applied to the PPS of each district, this will set that district’s tax rate. The PPS of the districts will vary, but any two towns with the same PPS will have the same tax rate, because that PPS is divided by the same state-wide number: the Dollar Yield.

Keep in mind that the number of students in each district is different and the taxable value of the property in districts varies. Yet a rich district with high property values and a low number of students with the same PPS as a poor district with lots of students must have the same tax rate. A dollar of tax rate must yield the same educational benefit in both rich and poor districts.

[1] In fact, there are many inputs to the Education Fund. Not just Homestead Property Taxes. But for the sake of simplicity we will assume all education costs are funded with this tax.

How it’s done

A State-wide District

The “single state-wide number” we’re looking for is called the Dollar Yield. If Vermont were a single district, it would be easy to calculate. Using the earlier single district numbers, the state-wide tax rate was $0.05 for each $100 of property value. If $0.05 (1 nickel) yielded $5,000 in total educational benefit, then a dollar of total educational benefit would cost twenty times $5,000 (because there are 20 nickels in a dollar) which equals $100,000. The word “total” is important. The Dollar Yield is, by definition, for a single student’s educational benefit. In order to determine the Dollar Yield in our single district we need to know the number of students. There were five students in our example. The Dollar Yield would be $100,000 / 5. A single dollar of tax rate would yield $20,000 of educational benefit for each student. That’s if the tax rate were a dollar. Our district’s tax rate is only a nickel. We want 1/20 of that amount for each student, that’s $1,000. With 5 students we would get $5,000 and the budget is satisfied,

The Dollar Yield is directly related to PPS because it is the amount for a single student’s educational benefit. The $DollarYield represents the following relationship

This can read that as: “One dollar is to the $DollarYield as $TaxRate is to $PerPupilSpending.” Or “A tax rate of $1.00 will generate a specific amount of Per Pupil Spending.” That specific amount is the same throughout the state.

Using the single district numbers this relationship would be:

A little algebra applied to that relationship produces two interesting equations:[2]

[2] To get the $DollarYield alone on one side of the equation, first multiple both sides by the $DollarYield, then multiply both sides by $PerPupleSpending/$TaxRate. To get the $TaxRate alone on one side of the equation, multiple each side by $PerPupilSpending.

In our single state-wide district example we have a tax rate of .05. The PPS is $5,000/5 or $1,000. The dollar yield would be $1,000 / .05 or $20,000. Each dollar of tax rate yields $20,000 in school spending for a single student.

The Dollar Yield can be used in the second equation to produce the tax rate: $1,000 / $20,000 equals .05.

If our state-wide school district had one landlord paying all the property taxes then s/he would pay five cents for each $100 in the total value of $10,000,000 of property values: .05 X ($10,000,000 / $100) = $5,000. That would fund the education of those five students. Everyone is happy.

More than one town. Now things get messy.

Because Vermont has more than one district things get messy when calculating the Dollar Yield.

Assume Vermont is a two-district state with property that is of very different value. The districts also have different numbers of pupils and different voter-approved budgets. After Town Meeting the State combines the approved budgets and determines how much money is needed in the Education Fund. The state must then collect enough money from both districts to fill that fund. The collected taxes brought in from both districts through the tax rate must be enough to fund the combined budgets.

This can be written mathematically as:

Because the taxes collected in each district can be calculated by multiplying the tax rate by the property value divided by 100, we can replace the TaxesCollected variables with a calculation (formula #1 above) and write the following:

Note that local property and tax rate values are used for district One and district Two.

Because, as shown earlier (formula #2 above), the Tax Rate is the same as the $PerPupilSpending / $DollarYield we can next replace that variable and make the formula even messier:

The Dollar Yield we’re looking for is a single number for both districts. It is not local. All the other values on the left side of that equation are district specific. But if we can solve that equation for the $DollarYield we will have a single number that can be applied to both districts to generate their tax rate. So, we now solve for the $DollarYield by multiplying each side by the $DollarYield and dividing by the $CombinedBudget. We get:

We have a complicated way to calculate the $DollarYield for our two districts. We can make this apply to all the school districts in Vermont. It would be a very long equation with each district’s PPS multiplied by the PropertyValue and added to the same value for the next district, all of which would be divided by the total budget amount needed. It’s messy, but it’s just plugging in numbers for each district. In this formula we have only two districts. The real calculation would have to be expanded to include all the school districts in Vermont. The following is the result with n being the number of school districts in Vermont.

Assuming there is only one type of education property in the grand list that is used to fund education and all education is funded by a single tax on that property, and each town is a school district the following formula works.

We now have a single number, the Dollar Yield, that can be used to calculate the local tax rates for all the districts in the formula:

Though our two districts may have very different property values, budgets and pupil counts, the result is a tax rate that, when applied to those property values, brings in enough money to fill the education fund. The state can send back enough money to fund each district’s budget.

An Example

The grid below shows an example with Property Value, Pupil Count and Budget in yellow. Those values are plugged into the formulas described in this document. They are:

When you combine the two approved budgets you have the total that is needed in the Education Fund. You can then determine the Dollar Yield and each of the tax rates. Next, you can calculate collected taxes for each district. Those collected taxes are dumped in the Education Fund. The amount for each district’s budget is then pulled out and sent to the districts as revenue or educational benefit. Everything balances.

The whole process is compliant with the Vermont Constitution because the Dollar Yield is a state-wide number that gives each student the same amount of educational benefit for each dollar of tax rate. It is important to understand that districts with the same PPS (and tax rate) will collect from their taxpayer different totals to be sent to the state. The amount per pupil that they collect from taxpayers may be very different, but the amount they receive back per pupil will be the same.

To the right is the same grid with both districts voting the same Per Pupil Spending: $15,000. Though both voted for that PPS, the poor district sends only $450 to the education fund. The rich district sends $449,550. Note that their tax rates are the same: 4.5 cents for every $100 of property value.

This also means that some districts may well be sending more to the Education Fund than they receive back to fund their schools. In the first example, the property-poor district sent $333 dollars to the Education Fund and received $250,000 back. The property-rich district sent $399,667 and received $150,000 back.

When you combine the two approved budgets you have the total that is needed in the Education Fund. You can then determine the Dollar Yield and each of the tax rates. Next, you can calculate collected taxes for each district. Those collected taxes are dumped in the Education Fund. The amount for each district’s budget is then pulled out and sent to the districts as revenue or educational benefit. Everything balances.

The whole process is compliant with the Vermont Constitution because the Dollar Yield is a state-wide number that gives each student the same amount of educational benefit for each dollar of tax rate. It is important to understand that districts with the same PPS (and tax rate) will collect from their taxpayer different totals to be sent to the state. The amount per pupil that they collect from taxpayers may be very different, but the amount they receive back per pupil will be the same.

To the right is the same grid with both districts voting the same Per Pupil Spending: $15,000. Though both voted for that PPS, the poor district sends only $450 to the education fund. The rich district sends $449,550. Note that their tax rates are the same: 4.5 cents for every $100 of property value.

This also means that some districts may well be sending more to the Education Fund than they receive back to fund their schools. In the first example, the property-poor district sent $333 dollars to the Education Fund and received $250,000 back. The property-rich district sent $399,667 and received $150,000 back.

Conclusion

The Dollar Yield is the amount of educational benefit, measured in dollars, that one student receives from the education fund if the tax rate is $1.00. It is consistent throughout the state. It is not a set price. Instead, it is the result of a fairly complex calculation dependent on several factors: 1) voter approved budget amounts, 2) the number of pupils in each district, 3) the property value in each district and 4) any other inputs to the education fund. The beauty of the dollar yield is that it satisfies the requirements of the state constitution. The price of that education unit is the same throughout Vermont. Each district’s budget determines how much of the benefit is bought.

But . . .

When I took my explanation of the Dollar Yield to the person who actually does the calculations to see if I was correct. She said, “Yes, but that’s not the way we do it.” Aaaagh!

The problem is that there are three different tax calculations: homestead property tax, non-homestead property tax, and income sensitivity tax rate. By policy, not by law, the increase in actual tax bills resulting from those three should be about the same, so all tax bills increase at roughly the same rate. My calculations do not take that into account.

But that changes things just a little. It means that this is an iterative process. Adjusting the non-homestead property tax rate changes the amount of the Education Fund that is filled by that rate and therefore the amount that is filled by the homestead rate. The value is raised or lowered with each test run until the resulting increase in calculated tax bills is about the same. To understand this you need to know how all the pieces fit together, not just how the dollar yield is calculated.

There are also towns without schools for all their students. They send students to another district, but the property in the sending town still gets taxed. In fact, a town may send students to several difference districts. Figure that out!

This correction does not change the meaning of the dollar yield, its basic method of calculation, and its implications.