# 5.2 Property Taxes

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 watch, in amusement, at the children playing in the enormous city-built 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.

### The Property Tax Formula

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. The formula below is designed to be flexible to meet the varying needs of municipal tax calculations throughout Canada.

$\text{property tax}=\sum(\text{assessed property value})\cdot(\text{property tax rate})$

Property tax: 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 (Σ) on the right-hand side of the equation.

Assessed property value: 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: Market Value × Tax Policy = Assessed Value
In some municipalities, the tax policy is to tax 100% 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 45% of the market value. Therefore, a $200,000 market value home in Winnipeg has a$90,000 assessed value. This $90,000 is the base for the tax. Property tax rate: Two methods commonly express how assessed value is taxed, a tax rate and a mill rate. • A tax rate is a tax per$100 of assessed value. Most municipalities in Ontario and further east use this system. The mathematical expression for the tax rate is $\frac{\text{tax rate}}{100}$
• A mill rate is a tax per $1,000 of assessed value. Most municipalities in Manitoba and further west use this system. The mathematical expression for the mill rate is $\frac{\text{mill rate}}{1,000}$ Continuing with the Winnipeg example in which a home has a market value of$200,000, the tax policy of Winnipeg is to tax 45% 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 14.6 and 16.724, respectively. Calculate the total property tax bill.

Solution: total property tax amount = ?

\begin{align*} &\text{total property tax}= \text{city tax} + \text{school board tax}\\ \\ &=(\text{assessed value})\cdot\frac{\text{city m.r.}}{1000}+(\text{assessed value})\cdot\frac{\text{school board m.r.}}{1000}\\ \\ &=(\text{assessed value})\cdot\left(\frac{\text{city m.r.}}{1000}+\frac{\text{school board m.r.}}{1000}\right)\\ \\ &=(\text{market value})(\text{tax policy})\left(\frac{\text{city m.r.}}{1000}+\frac{\text{school board m.r.}}{1000}\right)\\ \\ &=(200000)(0.45)\left(\frac{14.6}{1000}+\frac{16.724}{1000}\right)\\ \\ &=\2,819.16 \end{align*}

##### Important Notes

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 $250,000 is used for two tax rates of 2.168975 and 1.015566, you may be tempted to sum the rates, which would yield a rate of 3.184541. 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 amount to two decimals before summing to the total property tax. #### Example 5.2A Calculating Property Taxes A residence has a market value of$340,000. The municipality’s tax policy is set at 70%. 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 1.311666, 0.007383, and 0.842988, respectively. Calculate the total property tax bill for the residence.

Answer: total property tax = ?

total property tax = municipal tax + library tax + education tax

Since

$\text{tax amount} = (\text{market value})(\text{tax policy})\left(\frac{\text{ tax rate}}{100}\right)$

we have:

$\text{municipal tax}=340000\cdot 0.7\cdot \frac{{1.311666}}{{100}}= \3,121.77$

$\text{library tax} = 340000\cdot 0.7\cdot \frac{{0.007383}}{{100}}= \17.57$

$\text{education tax} = 340000\cdot 0.7\cdot \frac{{0.842988}}{{100}}= \2,006.31$

Therefore,

$\text{property tax} = 3,121.77 + 17.57 + 2,006.31 = \5,145.65$

### 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 1,000 real estate owners each paying $2,000 in property tax, the municipality’s operating income from property taxes is$2,000 × 1,000 = $2,000,000. 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 5.2B Setting a New Mill Rate A school board is determining next year’s operating budget and calculates that it needs an additional$5 million. Properties in its municipality have an assessed value of $8.455 billion. The current mill rate for the school board is set at 6.1998. If the assessed property values are forecasted to rise by 3% next year, what mill rate should the school set? Answer: new mill rate = ? What do we know about the new mill rate? We know that, in general, the property tax is calculated using mill rate by $\text{property tax amount} =\left(d\frac{\text{mill rate}}{1000}\right)(\text{property value assessment})$ Since the new budget comes from the property tax with the new mill rate, it will therefore be calculated by $\text{new budget} = \left(d\frac{\text{new mill rate}}{1000}\right)(\text{new property value assessment})$ And so, by rearranging for the new mill rate, we have $\text{new mill rate} =\left(d\frac{\overset{?}{\text{new budget}}}{\overset{?}{\text{new property value assessment}}}\right)\cdot 1000$ So to find the new mill rate, we have to find out the value of the new budget and the new property value assessment. What do we know about the new budget? Condition(s): School board needs$5,000,000 more next year. So,

$\text{new budget} =\overset{?}{\text{current budget}} + 5,000,000$

So we need to know the current budget. What do we know about the current budget? We know the current mill rate, the current property value assessment, and that we can calculate the current budget by

\begin{align*} \text{current budget}&= \left(\frac{\text{current mill rate}}{1000}\right)(\text{current property value assessment})\\ \\ &=\frac{6.1998}{1000}\cdot 8,455,000,000\\ \\ &=\52,419,309 \end{align*}

Hence

\begin{align*} \text{new budget} &=\text{current budget} + 5,000,000\\ &=52,419,309+5,000,000\\ &=57,419,309 \end{align*}

To calculate the new mill rate, we also need the new property value assessment. We know that the property values are forecasted to rise by 3% next year. So,

\begin{align*} \text{new property }&\text{value assessment}\\ \\ &=(\text{current property value assessment})(1+0.03)\\ \\ &=8\,455\,000\,000\cdot 1.03=\8\,708\,650\,000 \end{align*}

Therefore we have that

\begin{align*} \text{new mill rate }&=\left(\frac{\text{new budget}}{\text{new property value assessment}}\right)\cdot 1000\\ \\ &=\frac{57\,419\,309}{8\,708\,650\,000}\cdot 1000\\ \\ &=6.59336510251\approx 6.5934 \end{align*}

## 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

### Applications

1. A house with an assessed value of $375,000 is subject to a tax rate of 1.397645. What is the property tax? 2. If a commercial railway property has a property tax bill of$166,950 and the mill rate is 18.5500, what is the assessed value of the property?
3. A house in Calgary has a market value of $450,000. The tax policy is 100%. The property is subject to a 2.6402 mill rate from the City of Calgary and a 2.3599 mill rate from the province of Alberta. What are the total property taxes? 4. A residential property in Regina has a market value of$210,000. The Saskatchewan tax policy is 70%. The property is subject to three mill rates: 13.4420 in municipal taxes, 1.4967 in library taxes, and 10.0800 in school taxes. What amount of tax is collected for each, and what are the total property taxes?
5. A municipality needs to increase its operating budget. Currently, the assessed value of all properties in its municipality total $1.3555 billion and the tax rate is set at 0.976513. If the municipality needs an additional$1.8 million next year, what tax rate should it set assuming the assessed values remain constant?
6. A municipality set its new mill rate to 10.2967, which increased its total operating budget by $10 million on a constant assessed value of$7.67 billion. What was last year’s mill rate?

### Challenge, Critical Thinking, & Other Applications

1. A school board is determining the mill rate to set for next year. The assessed property values for next year total $5.782035 billion, representing an increase of 5% over the current year. If the school board needs an additional$5.4 million in funding next year, by what amount should it change its current year mill rate of 11.9985?
2. In the current year, the market value of properties totals $6.896 billion. The current tax policy is 85% and the current mill rate is 15.6712. If the municipality requires an additional$2 million in its operating budget next year, market values increase by 4%, and the tax policy changes to 90%, what mill rate should it set for next year?
3. A $600,000 market value property is assessed with a tax policy of 75% and subject to two mill rates. If the total property taxes are$6,766.67 and the second mill rate is half of the first tax rate, calculate each mill rate.
4. Two properties in different provinces pay the same property taxes of $2,840. One province uses a mill rate of 24.6119 with a 60% tax policy, while the other province uses a tax rate of 1.977442 with an 80% tax policy. Compute the market values for each of these properties. 5. A water utility funded through property taxes requires$900 million annually to operate. It has forecasted increases in its operating costs of 7% and 3.5% over the next two years. Currently, properties in its area have a market value of \$234.85 billion, with projected annual increases of 3% and 5% over the next two years. The provincial government has tabled a bill that might change the tax policy from 70% to 75% 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.