3.5: Property Taxes
Symbol & Formula Hub
For this section you will need the following:
Symbols Used
- [latex]\sum=[/latex] summation symbol
- [latex]\%C=[/latex] percent change
- [latex]V_\textrm{i}=[/latex] initial value
- [latex]V_\textrm{f}=[/latex] final value
- [latex]\text{AV}=[/latex] assessed value
- [latex]\text{PTR}=[/latex] property tax rate
Formulas Used
-
Formula 3.2a – Percent Change
[latex]\begin{align*}\%C=\frac{V_\textrm{f}-V_\textrm{i}}{V_\textrm{i}}\times 100\end{align*}[/latex]
-
Formula 3.5 – Property Taxes
[latex]\text{Property Tax}=\sum\left(\text{AV}\times\text{PTR}\right)[/latex]
Introduction
As you drive through your neighbourhood, you pass a city crew repairing the potholes in the road. Hearing sirens, you check your rear-view mirror and pull to the side of the road as a police car and fire engine race by, heading toward some emergency. Pulling back out, you drive slowly through a public school zone, where you smile as you watch children playing on the gigantic play structure. A city worker mows the lawn.
Where does the municipality get the money to pay for all you have seen? No one owns the roads, schools are free, fire crews and police do not charge for their services, play structures have no admission, and parks are open to everyone. These are just some examples of what your municipality does with the money it raises through property taxes.
Property Taxation
Property taxes are annual taxes paid by real estate owners to local levying authorities to pay for services such as roads, water, sewers, public schools, policing, fire departments, and other community services. Every individual and every business pays property taxes. Even if you don’t own property, you pay property taxes that are included in your rental and leasing rates from your landlord.
Property taxes are imposed on real estate owners by their municipal government along with any other bodies authorized to levy taxes. For example, in Manitoba each divisional school board is authorized to levy property taxes within its local school division boundaries.
Since property taxes are administered at the municipal level and every municipality has different financial needs, there are a variety of ways to calculate a total property tax bill. Formula 3.5 is designed to be flexible to meet the varying needs of municipal tax calculations throughout Canada.
[latex]\boxed{3.5}[/latex] Property Taxes
[latex]{\color{red}{\text{Property Tax}}}\text{ is Property Tax Amount:}[/latex] The amount of property taxes that are owing represents the total of all property taxes from all taxable services. For example, your property tax bill could consist of a municipal tax, a public school tax, a water tax, and a sewer/sanitation tax. Each of these taxes is levied at a specific rate. Therefore, the formula is designed to sum all applicable taxes, as represented by the summation symbol ([latex]{\color{blue}{\sum}}[/latex]) on the right-hand side of the equation.
[latex]{\color{green}{\text{AV}}}\text{ is Assessed Value of Property:}[/latex] Every piece of real estate has two valuations: the market value and the assessed value. Only the assessed value is relevant when computing property taxes.
- The market value of a property is a snapshot of the estimated selling price of your property. It is what you might have been able to sell your property for at a certain time period. For example, the City of Winnipeg updates the market value of all property in the city every two years.
- The assessed value of a property is the portion of the market value that is subjected to the property tax rate. It is calculated by taking the market value and multiplying it by a percentage determined by the municipality’s tax policy:
[latex]\text{Market Value}\times\text{Tax Policy}=\text{Assessed Value}[/latex]
In some municipalities, the tax policy is to tax [latex]100\%[/latex] of the market value. In others, the tax policy can be substantially less. Continuing with the example, the tax policy for Winnipeg is to tax [latex]45\%[/latex] of the market value. Therefore, a [latex]\$200,000[/latex] market value home in Winnipeg has a [latex]\$90,000[/latex] assessed value. This [latex]\$90,000[/latex] is the base for the tax.
[latex]{\color{purple}{\text{PTR}}}\text{ is Property Tax Rate:}[/latex] Two methods commonly express how assessed value is taxed, a tax rate and a mill rate.
- A tax rate is a tax per [latex]\$100[/latex] of assessed value. Most municipalities in Ontario and further east use this system. The mathematical expression for the tax rate is:
[latex]\begin{align*}\frac{\text{Tax Rate}}{100}\end{align*}[/latex]
- A mill rate is a tax per [latex]\$1,000[/latex] of assessed value. Most municipalities in Manitoba and further west use this system. The mathematical expression for the mill rate is:
[latex]\begin{align*}\frac{\text{Mill Rate}}{1,000}\end{align*}[/latex]
HOW TO
Work with Property Taxes
Follow these steps when working with calculations involving property taxes:
Step 1: Identify all known variables. This includes the market value, tax policy, assessed value, all property tax rates, and the total property taxes.
Step 2: If you know the assessed value, skip this step. Otherwise, calculate the assessed value of the property by multiplying the market value and the tax policy.
Step 3: Calculate either the tax amount for each property tax levy or the grand total of all property taxes by applying Formula 3.5[latex]\text{Property Tax}=\sum\left(\text{AV}\times\text{PTR}\right)[/latex][latex]\text{Property Tax}=\sum\left(\text{AV}\times\text{PTR}\right)[/latex].
Continuing with the Winnipeg example in which a home has a market value of [latex]\$200,000[/latex], the tax policy of Winnipeg is to tax [latex]45\%[/latex] of the market value. A Winnipegger receives a property tax levy from both the City of Winnipeg itself and the local school board. The mill rates are set at [latex]14.6[/latex] and [latex]16.724[/latex], respectively. Calculate the total property tax bill.
Step 1: The known variables are:
[latex]\begin{align*}\text{Market Value}&=\$200,000\\\text{Tax Policy}&=45\%\\\text{City of Winnipeg Mill Rate}&=14.6\\\text{School Board Mill Rate}&=16.724\end{align*}[/latex]
Step 2: Calculate the assessed value by taking the market value of [latex]\$200,000[/latex] and multiplying by the tax policy of [latex]45\%[/latex], or
[latex]\begin{align*}\text{Assessed Value}&=\$200,000\times 45\%\\\text{Assessed Value}&=\$90,000\end{align*}[/latex]
Step 3: To calculate each property tax, apply Formula 3.5[latex]\text{Property Tax}=\sum\left(\text{AV}\times\text{PTR}\right)[/latex][latex]\text{Property Tax}=\sum\left(\text{AV}\times\text{PTR}\right)[/latex]
[latex]\begin{align*}\text{City of Winnipeg Property Tax}&=\$90,000\times\frac{14.6}{1,000}\\\text{City of Winnipeg Property Tax}&=\$1,314\end{align*}[/latex]
[latex]\begin{align*}\text{School Board Property Tax}&=\$90,000\times\frac{16.724}{1,000}\\\text{School Board Property Tax}&=\$1,505.16\end{align*}[/latex]
Add these separate taxes together to arrive at Total Property Tax.
[latex]\begin{align*}\text{Total Property Tax}&=\$1,314+\$1,505.16\\\text{Total Property Tax}&=\$2,819.16\end{align*}[/latex]
Key Takeaways
Mill rates are commonly expressed with four decimals and tax rates are expressed with six decimals. Although some municipalities use other standards, this text uses these common formats in its rounding rules. In addition, each property tax levied against the property owner is a separate tax. Therefore, you must round each property tax to two decimals before summing the grand total property tax.
Things To Watch Out For
The most common mistake is to use the wrong denominator in the tax calculation. Ensure that you read the question accurately, noting which term it uses, tax rate or mill rate. If neither appears, remember that Ontario eastward uses tax rates and Manitoba westward uses mill rates.
A second common mistake is to add multiple property tax rates together when the assessed value remains constant across all taxable elements. For example, if the assessed value of [latex]\$250,000[/latex] is used for two tax rates of [latex]2.168975[/latex] and [latex]1.015566[/latex], you may be tempted to sum the rates, which would yield a rate of [latex]3.184541[/latex]. This does not always work and may produce a small error (a penny or two) since each tax is itemized on a tax bill. You must round each individual tax to two decimals before summing to the total property tax.
Example 3.5.1
A residence has a market value of [latex]\$340,000[/latex]. The municipality’s tax policy is set at [latex]70\%[/latex]. Real estate owners have to pay three separate taxes: the municipality tax, a library tax, and an education tax. The tax rates for each are set at [latex]1.311666[/latex], [latex]0.007383[/latex], and [latex]0.842988[/latex], respectively. Calculate the total property tax bill for the residence.
Solution
Step 1: What are we looking for?
You need to calculate the total property tax for the residence by summing the assessed value multiplied by the respective tax rates.
Step 2: What do we already know?
The house, tax policy, and tax rates are known:
[latex]\begin{align*}\text{Market Value}&=\$340,000\\\text{Tax Policy}&=70\%\\\text{Municipal PTR}&=1.311666\\\text{Library PTR}&=0.007383\\\text{Education PTR}&=0.842988\end{align*}[/latex]
Step 3: Make substitutions using the information known above.
Calculate the assessed value ([latex]\text{AV}[/latex]) by taking the market value and multiplying by the tax policy.
[latex]\begin{align*}\text{AV}&=\$340,000\times 70\%\\\text{AV}&=\$340,000\times 0.7\\\text{AV}&=\$238,000\end{align*}[/latex]
Apply Formula 3.5[latex]\text{Property Tax}=\sum\left(\text{AV}\times\text{PTR}\right)[/latex][latex]\text{Property Tax}=\sum\left(\text{AV}\times\text{PTR}\right)[/latex]. Note that this municipality uses a tax rate, so the PTR is divided by [latex]100[/latex].
[latex]\begin{align*}\text{Municipal Tax}&=\$238,000\times 1.311666100\\\text{Municipal Tax}&=\$3,121.77\end{align*}[/latex]
[latex]\begin{align*}\text{Library Tax}&=\$238,000\times 0.007383100\\\text{Library Tax}&=\$17.57\end{align*}[/latex]
[latex]\begin{align*}\text{Education Tax}&=\$238,000\times 0.842988100\\\text{Education Tax}&=\$2,006.31\end{align*}[/latex]
[latex]\begin{align*}\text{Property Tax}&=\sum\left(\text{AV}\times\text{PTR}\right)\\\text{Property Tax}&=\$3,121.77+\$17.57+\$2,006.31\\\text{Property Tax}&=\$5,145.65\end{align*}[/latex]
Step 4: Provide the information in a worded statement.
The property owner owes the municipality [latex]\$3,121.77[/latex], the library [latex]\$17.57[/latex], and education [latex]\$2,006.31[/latex] for a total property tax bill of [latex]\$5,145.65[/latex].
Paths To Success
The collective property taxes paid by all of the property owners form either all or part of the operating budget for the municipality. Thus, if a municipality consisted of [latex]1,000[/latex] real estate owners each paying [latex]\$2,000[/latex] in property tax, the municipality’s operating income from property taxes is
[latex]\$2,000\times 1,000=\$2,000,000[/latex].
If the municipality needs a larger budget from property owners, either the assessed values, the mill/tax rate, or some combination of the two needs to increase.
Example 3.5.2
A school board is determining next year’s operating budget and calculates that it needs an additional [latex]\$5\;\text{million}[/latex]. Properties in its municipality have an assessed value of [latex]\$8.455\;\text{billion}[/latex]. The current mill rate for the school board is set at [latex]6.1998[/latex]. If the assessed property values are forecasted to rise by [latex]3\%[/latex] next year, what mill rate should the school set?
Solution
Step 1: What are we looking for?
Aim to calculate the new property tax rate ([latex]\text{PTR}[/latex]) for next year’s mill rate.
Step 2: What do we already know?
The information about the school board and its municipality are known:
[latex]\begin{align*}\text{AV}&=\$8.455\;\text{billion}\\\text{PTR (current mill rate)}&=6.1998\\\%C\text{ (to AV next year)}&=3\%\end{align*}[/latex]
Property tax increase needed is [latex]\$5\;\text{million}[/latex].
Step 3: Make substitutions using the information known above.
Calculate the school board’s current budget using Formula 3.5. The property tax collected is the board’s operating budget.
[latex]\begin{align*}\text{Property Tax}&=\sum\left(\text{AV}\times\text{PTR}\right)\\\text{Property Tax}&=\$8,455,000,000\times\frac{6.1998}{1,000}\\\text{Property Tax}&=\$52,419,309\end{align*}[/latex]
Increase the budget, or [latex]\text{Property Tax}[/latex], for next year.
[latex]\begin{align*}\text{Next Year Property Tax}&=\$52,419,309+\$5,000,000\\\text{Next Year Property Tax}&=\$57,419,309\end{align*}[/latex]
Increase the current assessed value base by applying Formula 3.2a (percent change), rearranging to solve for [latex]V_\textrm{f}[/latex]. The current [latex]AV[/latex] is the [latex]V_\textrm{i}[/latex] value.
[latex]\begin{align*}\%C&=\frac{V_\textrm{f}-V_\textrm{i}}{V_\textrm{i}}\times 100\\[1ex]3\%&=\frac{V_\textrm{f}-\$8,455,000,000}{\$8,455,000,000}\times 100\\[1ex]\$253,650,000&=V_\textrm{f}−\$8,455,000,000\\\$8,708,650,000&=V_\textrm{f}\\\text{Next Year Assessed Value}&=\$8,708,650,000\end{align*}[/latex]
Recalculate the new mill rate using the Next Year Property Tax and Next Year Assessed Value. Apply Formula 3.5 and solve for the mill rate in the [latex]\text{PTR}[/latex].
[latex]\begin{align*}\text{Property Tax}&=\sum\left(\text{AV}\times\text{PTR}\right)\\\$57,419,309&=\$8,708,650,000\times\frac{\text{Mill Rate}}{1,000}\\6.5934&=\text{Mill Rate}\end{align*}[/latex]
Step 4: Provide the information in a worded statement.
The current budget for the school board is [latex]\$52,419,309[/latex], which will be increased to [latex]\$57,419,309[/latex] next year. After the board adjusts for the increased assessed values of the properties, it needs to set the mill rate at [latex]6.5934[/latex] next year, which is an increase of [latex]0.4736[/latex] mills.
Section 3.5 Exercises
Mechanics
For questions 1–4, solve for the unknown variables (identified with a ?) based on the information provided.
|
|
Market Value |
Tax Policy |
Assessed Value |
Rate |
Type of Rate |
Property Tax |
|
1. |
$320,000 |
55% |
? |
26.8145 |
Mill |
? |
|
2. |
? |
85% |
$136,000 |
1.984561 |
Tax |
? |
|
3. |
$500,000 |
? |
? |
9.1652 |
Mill |
$3,666.08 |
|
4. |
? |
50% |
$650,000 |
? |
Tax |
$4,392.91 |
Solutions
- [latex]\text{AV}=\$176,000[/latex]; [latex]\text{Property Tax}=\$4,719.35[/latex]
- [latex]\text{Market Value}=\$160,000[/latex]; [latex]\text{Property Tax}=\$2,699.00[/latex]
- [latex]\text{Assessed Value}=\$400,000[/latex]; [latex]\text{Tax Policy}=80\%[/latex]
- [latex]\text{Market Value}=\$1,300,000[/latex]; [latex]\text{Tax Rate}=0.675832[/latex]
Applications
- A house with an assessed value of [latex]\$375,000[/latex] is subject to a tax rate of [latex]1.397645[/latex]. What is the property tax?
- If a commercial railway property has a property tax bill of [latex]\$166,950[/latex] and the mill rate is [latex]18.5500[/latex], what is the assessed value of the property?
- A house in Calgary has a market value of [latex]\$450,000[/latex]. The tax policy is [latex]100\%[/latex]. The property is subject to a [latex]2.6402[/latex] mill rate from the City of Calgary and a [latex]2.3599[/latex] mill rate from the province of Alberta. What are the total property taxes?
- A residential property in Regina has a market value of [latex]\$210,000[/latex]. The Saskatchewan tax policy is [latex]70\%[/latex]. The property is subject to three mill rates: [latex]13.4420[/latex] in municipal taxes, [latex]1.4967[/latex] in library taxes, and [latex]10.0800[/latex] in school taxes. What amount of tax is collected for each, and what are the total property taxes?
- A municipality needs to increase its operating budget. Currently, the assessed value of all properties in its municipality total [latex]\$1.3555[/latex] billion and the tax rate is set at [latex]0.976513[/latex]. If the municipality needs an additional [latex]\$1.8[/latex] million next year, what tax rate should it set assuming the assessed values remain constant?
- A municipality set its new mill rate to [latex]10.2967[/latex], which increased its total operating budget by [latex]\$10[/latex] million on a constant assessed value of [latex]\$7.67[/latex] billion. What was last year’s mill rate?
Solutions
- [latex]\text{Property Tax}=\$5,241.17[/latex]
- [latex]\text{AV}=\$9,000,000[/latex]
- [latex]\text{Property Tax}=\$2,250.05[/latex]
- [latex]\text{Municipal Property Tax}=\$1,975.97[/latex]; [latex]\text{Library Property Tax}=\$220.01[/latex]; [latex]\text{School Property Tax}=\$1,481.76[/latex]; [latex]\text{Total Property Tax}=\$3,677.74[/latex]
- [latex]\text{Tax Rate}=1.109305[/latex]
- [latex]\text{Mill Rate}=8.9929[/latex]
Challenge, Critical Thinking, & Other Applications
- A school board is determining the mill rate to set for next year. The assessed property values for next year total [latex]\$5.782035[/latex] billion, representing an increase of [latex]5\%[/latex] over the current year. If the school board needs an additional [latex]\$5.4[/latex] million in funding next year, by what amount should it change its current year mill rate of [latex]11.9985[/latex]?
- In the current year, the market value of properties totals [latex]\$6.896[/latex] billion. The current tax policy is [latex]85\%[/latex] and the current mill rate is [latex]15.6712[/latex]. If the municipality requires an additional [latex]\$2[/latex] million in its operating budget next year, market values increase by [latex]4\%[/latex], and the tax policy changes to [latex]90\%[/latex], what mill rate should it set for next year?
- A [latex]\$600,000[/latex] market value property is assessed with a tax policy of [latex]75\%[/latex] and subject to two mill rates. If the total property taxes are [latex]\$6,766.67[/latex] and the second mill rate is half of the first tax rate, calculate each mill rate.
- Two properties in different provinces pay the same property taxes of [latex]\$2,840[/latex]. One province uses a mill rate of [latex]24.6119[/latex] with a [latex]60\%[/latex] tax policy, while the other province uses a tax rate of [latex]1.977442[/latex] with an [latex]80\%[/latex] tax policy. Compute the market values for each of these properties.
- A water utility funded through property taxes requires [latex]\$900[/latex] million annually to operate. It has forecasted increases in its operating costs of [latex]7\%[/latex] and [latex]3.5\%[/latex] over the next two years. Currently, properties in its area have a market value of [latex]\$234.85[/latex] billion, with projected annual increases of [latex]3\%[/latex] and [latex]5\%[/latex] over the next two years. The provincial government has tabled a bill that might change the tax policy from [latex]70\%[/latex] to [latex]75\%[/latex] effective next year, but it is unclear if the bill will pass at this point. For planning purposes, the utility wants to forecast its new mill rates for the next two years under either tax policy. Perform the necessary calculations for the utility.
Solutions
- [latex]\text{Increase the mill rate by}\;0.3626[/latex]
- [latex]\text{Mill Rate}=14.5412[/latex]
- [latex]10.0247[/latex] and [latex]5.0124[/latex]
- [latex]\$192,318.90[/latex] and [latex]\$179,524.86[/latex]
- [latex]\text{Mill Rates Under}\;70\%\;\text{Policy:}\;5.6872\;\text{then}\;5.6060[/latex]; [latex]\text{Mill Rates Under}\;75\%\;\text{Policy:}\;5.3081\;\text{then}\;5.2322[/latex]
THE FOLLOWING LATEX CODE IS FOR FORMULA TOOLTIP ACCESSIBILITY. NEITHER THE CODE NOR THIS MESSAGE WILL DISPLAY IN BROWSER.[latex]\text{Property Tax}=\sum\left(\text{AV}\times\text{PTR}\right)[/latex][latex]\begin{align*}\%C=\frac{V_\textrm{f}-V_\textrm{i}}{V_\textrm{i}}\times 100\end{align*}[/latex]
Attribution
“7.2: Property Taxes” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.
