3.4: Sales Taxes

Introduction

On your recent cross-Canada road trip, you purchased from many different Tim Hortons’ stores. At each store, your products retailed for [latex]\$6.99[/latex]. When you review your credit card receipts after returning home from your trip, you notice that you paid different totals everywhere. In Alberta, they only added GST and your combo cost [latex]\$7.34[/latex]. In British Columbia, they added both PST and GST, resulting in total cost of [latex]\$7.83[/latex]. In Ontario, they added something called HST, resulting in a total cost of [latex]\$7.90[/latex]. You find it interesting that the same combo came to different totals as you travelled across Canada.

Three Sales Taxes

A sales tax is a percent fee levied by a government on the supply of products. In Canada, there are three types of sales taxes: the goods and services tax (GST), provincial sales tax (PST), and the harmonized sales tax (HST). In this section you will learn the characteristics of each of these taxes and then the mathematics for calculating any sales tax.

Goods & Services Tax (GST)

The goods and services tax, better known as GST, is a national federal tax of 5% that applies to the purchase of most goods and services in Canada. Every province and territory has GST. The consumer ultimately bears the burden of this sales tax.

Businesses must collect GST on most of their sales and pay GST on most purchases in the daily course of operations. However, when remitting these taxes, businesses claim a credit with the federal government to recover the GST they paid on eligible purchases. The net result is that businesses do not pay the GST on these eligible purchases. While this may outrage some people, the logic is simple. If a business pays the GST, it becomes a cost of the business, which is then passed on to consumers as it is incorporated into retail prices. When the consumer purchases the product, the consumer would be charged the GST again! In essence, a consumer would be double-taxed on all purchases if businesses paid the GST.

Some goods and services are exempt from GST. While there are many complexities and nuances to the exemptions, generally items that are deemed necessities (such as basic groceries), essential services (such as health, legal aid, and childcare), and charitable activities are nontaxable. You can find a complete listing of exemptions on the Canada Revenue Agency website at www.cra.gc.ca.

Provincial Sales Tax (PST)

Provincial sales taxes, or PST, are provincially administered sales taxes that are determined by each individual provincial or territorial government in Canada. The table here lists the current PST rates in Canada.

Similar to GST, PST applies to the purchase of most goods and services in the province, and consumers bear the burden. For the same reasons as with GST, businesses typically pay the PST on purchases for non-resale items (such as equipment and machinery) and do not pay the PST on resale items. Businesses are responsible for collecting PST on sales and remitting the tax to the provincial government. Individual provincial websites list the items and services that are exempt from PST.

Harmonized Sales Tax (HST)

The harmonized sales tax, or HST, is a combination of GST and PST into a single number. Since most goods and services are subjected to both taxes anyway, HST offers a simpler method of collecting and remitting the sales tax—a business has to collect and remit only one tax instead of two. Because there are pros and cons to HST, not all provinces use this method of collection, as summarized in the table below.

To understand HST you can separate it into its GST and PST components. For example, Ontario has an HST of [latex]13\%[/latex]. If GST is [latex]5\%[/latex] and the HST is [latex]13\%[/latex], then it is clear that the province has a PST of [latex]8\%[/latex]. HST operates mostly in the same manner as GST, in that consumers generally bear the burden for paying this tax, and businesses both collect and pay the HST but have the HST reimbursed on eligible purchases when remitting taxes to the government.

Calculating the Sales Tax Amount

With respect to sales taxes, you usually calculate two things:

1. The dollar amount of the sales tax.
2. The price of a product including the sales tax.

A sales tax is a percent rate calculated on the base selling price of the product. Therefore, if you are interested solely in the amount of the sales tax (the portion owing), applying Formula 3.1b on Rate, Portion, Base:

[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\hspace{1em}\rightarrow\hspace{1em}\text{Tax Rate}=\frac{\text{Tax Amount}}{\text{Price Before Taxes}}\end{align*}[/latex]

Rearranging this formula to solve for the tax amount gives the following:

[latex]\begin{align*}\text{Portion}&=\text{Rate}\times\text{Base}\\\text{(which is the same as Tax Amount}&=\text{Tax Rate}\times\text{Price Before Taxes)}\end{align*}[/latex]

This is not a new formula. It applies the existing formula from Chapter 3.

Calculating a Price Including Tax

When calculating a selling price including the tax, you take the regular selling price and increase it by the sales tax percentage. This is a percent change calculation using Formula 3.2a:

[latex]\begin{align*}\%C=\frac{V_\textrm{f}-V_\textrm{i}}{V_\textrm{i}}\times 100\end{align*}[/latex]

The [latex]V_\textrm{i}[/latex] price is the price before taxes, the [latex]\%C[/latex] is the sales tax percentage, and you need to calculate the [latex]V_\textrm{f}[/latex] price including the tax. Rearranging the formula for [latex]V_\textrm{f}[/latex], you have

[latex]\begin{align*}V_\textrm{f}=V_\textrm{i}+V_\textrm{i}\left(\frac{\%C}{100}\right)\end{align*}[/latex]

which you factor and rewrite as

[latex]\begin{align*}V_\textrm{f}=V_\textrm{i}\times\left(\frac{\%C}{100}\right)\hspace{3em}\textit{or}\hspace{3em}V_\textrm{f}=V_\textrm{i}+\left(V_\textrm{i}\times\frac{\%C}{100}\right)\end{align*}[/latex]

This is a widespread application of the percent change formula. Since it can be tedious to keep rearranging Formula 3.2a[latex]\begin{align*}\%C=\frac{V_\textrm{f}-V_\textrm{i}}{V_\textrm{i}}\times 100\end{align*}[/latex], Formula 3.4a expresses this relationship.

[latex]\boxed{3.4\text{a}}[/latex] Selling Price Including Tax

[latex]{\color{red}{S_\textrm{tax}}}\text{ is Selling Price Including Tax:}[/latex] A subscript is added to the regular symbol of [latex]S[/latex] for selling price to denote that this is the price that sums the selling price and sales tax amount together.

[latex]{\color{blue}{S}}\text{ is Selling Price Without Tax:}[/latex] The regular selling price before taxes.

[latex]{\color{green}{\text{Rate}}}\text{ is Tax Rate:}[/latex] This is the sales tax in any form of GST, HST, or PST expressed in its decimal format.

Round the result of ([latex]S\times\text{Rate}[/latex]) to two decimals. If two taxes are involved in the tax-inclusive price (such as GST and PST), you cannot combine the rates together into a single rate. For example, Manitoba has [latex]5\%[/latex] GST and 7% PST. This is not necessarily equivalent to [latex]12\%[/latex] tax since each tax is rounded to two decimals separately and then summed. If you use a single rate of [latex]12\%[/latex], you may miscalculate by a penny. Instead, expand the formula to include two separate ([latex]S\times\text{Rate}[/latex]) calculations:

[latex]S_\textrm{tax}=S+(S\times\text{GST Rate})+(S\times\text{PST Rate})[/latex]

Ensure that you round off each calculation in brackets to two decimals before adding.

Assume a [latex]\$549.99[/latex] product is sold in British Columbia. Calculate the amount of the sales taxes and the price including the sales taxes.

Step 1: The price before taxes is [latex]=\$549.99[/latex]. In British Columbia, GST is [latex]5\%[/latex] and PST is [latex]7\%[/latex] (from the PST Table).

Step 2: To calculate the price including the sales taxes, apply Formula 3.4a[latex]S_\textrm{tax}=S+\left(S\times\text{Rate}\right)[/latex]:

[latex]\begin{align*}S_\textrm{tax}&=S+(S\times\text{GST Rate})+(S\times\text{PST Rate})\\S_\textrm{tax}&=\$549.99+(\$549.99\times 5\%)+(\$549.99\times 7\%)\\S_\textrm{tax}&=\$615.99\end{align*}[/latex]

Step 3: Applying the rearranged Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex] for the GST, you calculate:

[latex]\begin{align*}\text{GST Tax Amount}&=\text{GST Rate}\times\text{Price Before Taxes)}\\\text{GST Tax Amount}&=5\%\times\$549.99\\\text{GST Tax Amount}&= \$27.50\end{align*}[/latex]

Applying the same formula for the PST, you calculate:

[latex]\begin{align*}\text{PST Tax Amount}&=\text{PST Rate}\times\text{Price Before Taxes)}\\\text{PST Tax Amount}&=7\%\times\$549.99\\\text{PST Tax Amount}&= \$38.50\end{align*}[/latex]

(Note: You may notice that you could just pull these amounts from the interim calculations in Step 2). Therefore, on a [latex]\$549.99[/latex] item in British Columbia, [latex]\$27.50[/latex] in GST and [latex]\$38.50[/latex] in PST are owing, resulting in a price including sales taxes of [latex]\$615.99[/latex].

Paths To Success

You will often need to manipulate Formula 3.4a[latex]S_\textrm{tax}=S+\left(S\times\text{Rate}\right)[/latex]. Most of the time, prices are advertised without taxes and you need to calculate the price including the taxes. However, sometimes prices are advertised including the taxes and you must calculate the original price of the product before taxes. When only one tax is involved, this poses no problem, but when two taxes are involved (GST and PST), combine the taxes into a single amount before you solve for [latex]S[/latex].

The GST/HST Remittance

When a business collects sales taxes, it is a go-between in the transaction. These sales tax monies do not belong to the business. On a regular basis, the business must forward this money to the government. This payment is known as a tax remittance.

Generally speaking, a business does not pay sales taxes. As a result, the government permits a business to take all eligible sales taxes that it paid through its acquisitions and net them against all sales taxes collected from sales. The end result is that the business is reimbursed for any eligible out-of-pocket sales tax that it paid. Formula 3.4b expresses this relationship.

[latex]\boxed{3.4\text{b}}[/latex] GST/HST Remittance

[latex]{\color{red}{\text{Remit}}}\text{ is GST/HST Remittance:}[/latex] This is the dollar amount of the remittance.

• If this amount is positive, it means that the business collected more tax than it paid out; the
  company must remit this balance to the government.
• If this amount is negative, it means that the business paid out more taxes than it collected; the
  government must refund this balance to the company.

[latex]{\color{blue}{\text{Tax Collected}}}\text{ and }{\color{green}{\text{Tax Paid}}}\text{:}[/latex] Both of these parts of the formula apply Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex], representing the total amount of sales tax ([latex]\text{Portion}[/latex]) from all taxable amounts ([latex]\text{Base}[/latex]) at the appropriate sales tax rate ([latex]\text{Rate}[/latex]). The taxes collected are based on total tax-eligible revenues. The taxes paid are based on the total tax-eligible acquisitions.

Assume a business has paid GST on purchases of [latex]\$153,000[/latex]. It has also collected GST on sales of [latex]\$358,440[/latex]. Calculate the GST remittance.

Step 1: Identifying the variables, you have:

[latex]\begin{align*}\text{Total Revenue}&=\$358,440\\\text{Total Acquisitions}&=\$153,000\\\text{GST Rate}&=5\%\end{align*}[/latex]

Step 2: Calculate taxes collected by applying Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex], where:

[latex]\begin{align*}\text{GST collected}&=5\%\times\$358,440\\\text{GST collected}&=\$17,922\end{align*}[/latex]

Step 3: Calculate taxes paid by applying Formula 3.1b[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex], where:

[latex]\begin{align*}\text{GST paid}&=5\%\times\$153,000\\\text{GST paid}&=\$7,650\end{align*}[/latex]

Step 4: To calculate the remittance, apply Formula 3.4b[latex]\text{Remit}=\text{Tax Collected}-\text{Tax Paid}[/latex] and calculate:

[latex]\begin{align*}\text{Remit}&=\$17,922−\$7,650\\\text{Remit}&=\$10,272\end{align*}[/latex]

The business should remit a cheque for [latex]\$10,272[/latex] to the government.

Paths To Success

A shortcut can help you calculate the GST/HST Remittance using Formula 3.4b[latex]\text{Remit}=\text{Tax Collected}-\text{Tax Paid}[/latex]. If you do not need to know the actual amounts of the tax paid and collected, you can net GST/HST–eligible revenues minus acquisitions and multiply the difference by the tax rate:

[latex]\text{Remit}=(\text{Revenues}−\text{Acquisitions})\times\text{Rate}[/latex]

In the example above,

[latex]\begin{align*}\text{Remit}&=(\$358,440\;–\$153,000)\times 5\%\\\text{Remit}&=\$10,272\end{align*}[/latex]

If this calculation produces a negative number, then the business receives a refund instead of making a remittance.

Section 3.4 Exercises

THE FOLLOWING LATEX CODE IS FOR FORMULA TOOLTIP ACCESSIBILITY. NEITHER THE CODE NOR THIS MESSAGE WILL DISPLAY IN BROWSER.[latex]\begin{align*}\text{Rate}=\frac{\text{Portion}}{\text{Base}}\end{align*}[/latex][latex]S_\textrm{tax}=S+\left(S\times\text{Rate}\right)[/latex][latex]\begin{align*}\%C=\frac{V_\textrm{f}-V_\textrm{i}}{V_\textrm{i}}\times 100\end{align*}[/latex][latex]\text{Remit}=\text{Tax Collected}-\text{Tax Paid}[/latex]

Attribution

“7.1: Sales 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.