Project Nayuki

Guide to Canada income tax by successive approximation

The Canadian income tax system is too complicated to learn all at once. So instead we’ll borrow a technique from science, which is to build a basic model to explain the system, and progressively refine the model to match the behavior of system better and better. (But unlike natural sciences, the system we wish to understand is human-made and can be fully known in principle, though it’s not easy to find and assimilate all the information.) We will focus on understanding income taxes because there are more rules involved and every resident must file a tax return every year, whereas consumption taxes have simpler rules and the burden of the calculation falls on businesses.

Narrative examples are typeset in this style.

(0) No income tax

In a world without taxes, life is simple. You get paid without interference. There are no tax rules to understand and nothing to calculate.

Alice takes a job that is advertised to pay $40k per year. Because there are no taxes, this figure is exactly the amount of money she takes home.

But in a taxless community it’s difficult to get individuals to pay for shared goods and services like public roads and universal medical care, so this brings us to the next step.

(1) Flat income tax

To build a pool of funds to provide public goods and services, a simple solution is to charge a fixed percentage of every paycheck as tax. This is easy to calculate and easy to apply. (In fact this is precisely how consumption/sales taxes work.)

The income tax rate is 20%. Bob receives $500 from his job each week, of which $100 goes to the government and $400 he gets to keep for himself.

(2) Progressive tax (lump sum)

It can be argued that having a flat tax rate puts a higher burden on poor people than on richer people. Taxing the poor means taking money away from necessities such as food and shelter, whereas taxing the rich means taking away discretionary income for things like toys, vacations, and bigger houses. Moreover, increasing the tax rate on the rich will yield more government revenue than identically increasing the tax rate on the poor (e.g. a tax hike of 1 percentage point on the rich yields more money than the same 1 pp on the poor). Ignoring political arguments about whether progressive taxation is socially desirable or fair or not, let’s take a progressive income tax system for granted because it’s what Canada, the USA, and many other countries have.

A progressive tax system works by taking your total income within the calendar year and classifying the amounts into brackets. The first bracket has a certain tax rate and monetary limit, the second bracket has its own rate and limit, etc. You classify your money in the lowest bracket until it fills up, then you start filling the next bracket. Your taxes owed is the total of the taxes from each bracket.

The tax rate brackets are as follows: 0% on the first $10k of income, 15% on the next $30k, 20% on the next $60k, 30% on the next $200k, and 50% thereafter.
Carol earned $50k this year. So the first $10k is taxed at 0%, the next $30k is taxed at 15%, and the last $10k is taxed at 20%. Her total tax is $6.5k, and her personal average tax rate is 13%. (Note that she fills the first two tax brackets, partially fills the third, and leaves the remaining brackets empty.)

It’s possible to implement this system as follows: Assume that all paychecks have no taxes deducted (unlike part (1)). You or your employer(s) or the government keeps track of all your income received throughout the year. When the year ends, add up all the income and calculate the amount of taxes owed. You send a cheque to the government as soon as possible to pay that amount.

While this system works correctly in a mathematical sense, it has serious practical shortcomings. If we rely on people to keep track of their own income, they need to spend time, they make mistakes (data entry, misunderstanding rules, etc.), and they have an incentive to underreport their income. If we rely on the government to keep track of everyone’s income, then there’s still a lot of administrative effort involved. Furthermore, for those who are inclined to spend their entire paycheck every time, the lump-sum tax payment at the end of the year will disrupt their budgeting and put them into temporary but painful debt. So having progressive tax brackets along with a lump-sum tax payment is not what countries do in practice.

(3) Progressive tax (withheld)

Let’s try to combine the ideas of the flat tax and progressive tax. With each paycheck, the government will try to withhold approximately the correct amount of tax, so that when the taxpayer does the calculation at the end of the year, the difference between the taxes paid and the taxes owed will be reasonably small. The way the current system does this is to extrapolate the annual pay based on each paycheck by itself, and tax it by the same proportion. An advantage of this system is that even if the person runs away, the employer will have already withheld nearly the correct amount of tax, which gives a disincentive to evade paying income taxes.

Dave earns $1000 every 2 weeks steadily, hence earns $26000 for the whole year. Using the tax brackets in part (2), he owes $2400 in taxes at the end of the year, so his employer withholds $2400 ÷ 26 = $92.31 in taxes on each paycheck. At the end of the year, he will have paid the correct amount of tax already (except for a few cents of rounding error).

But under this scheme, if your income changes throughout the year then the taxes paid might not match the taxes owed. The reconciliation at the end of the year is necessary because it’s desirable to withhold taxes on each paycheck, but it’s what happened over the entire year that determines the actual taxes owed.

Eve earns $1000 every 2 weeks but only worked 8 weeks (4 pay periods) this year. Just like Dave, she had $92.31 deducted from each paycheck, so she had $92.31 × 4 = $369.24 of taxes withheld. But with an annual income of $4000 she actually owed no tax, thus she would get the $369.24 refunded from the government at the end of the year.

It should be emphasized that any tax withheld on a paycheck is tentative, and is only an approximation of the true amount of tax you owe. It is the year-end calculation that authoritatively determines how much tax you actually need to pay. Afterwards, the amount of taxes owed minus the amount already withheld determines how much more you need to pay or how much tax refund you get.

(4) Capped taxes

An example of a capped tax is the Canadian Pension Plan contribution, where you pay 0% of your first $3500 of income, 4.95% on next $49000 of income, and 0% thereafter. This means 4.95% of each paycheck will be taxed, but you will be overpaying if you earned less than $3500 or over $52500 in the calendar year, so this needs to be reconciled at the end of the year.

Frank receives a biweekly paycheck of $3000 gross (before taxes). He pays 4.95% to CPP, which is $148.50; he pays $3861.00 in total in the year. But based on his income of $78000, he only owes $2425.50, so the CPP owes him a refund of $1435.50.

(5) Taxable benefits

Some companies offer benefits that are taxed as income. From a transactional point of view, these benefits are equivalent to paying you cash and forcing you to purchase a particular good or service. Some of these benefits are optional (e.g. stock purchases) while others are mandatory (e.g. medical insurance).

The company gives Greta the option to reimburse her public transit costs at $1k per year. If she accepts the benefit, she would receive no extra cash, her reported income would increase by $1k, and she would pay more in income taxes (at her marginal tax rate). (However, this is a net win because it’s far less expensive than rejecting the benefit and paying the entire cost of $1k.)

Harry’s employer gives him the opportunity to buy some stock at a 20% discount. He exercises the benefit and buys $10k worth of stock at a cost of $8k to him. The discount of $2k added to his income as a taxable benefit. (This is because the transaction is equivalent to receiving a $2k cash bonus and combining it with $8k of cash to buy the stock).

(6) Foreign tax credits

Income taxes paid to another country (e.g. USA) can sometimes be used to deduct the tax owed to Canada. These income taxes may be incurred in foreign investments and foreign employment income.

When a person works in one country but is a permanent resident of another country, he is usually liable for income taxes in both countries. The same goes for investments in foreign securities – a Canadian owning US stocks will need to pay tax to both countries on the stock dividends. However, many countries have tax treaties in place to prevent double-taxation for the same chunk of income. The way this works in practice is that the person pays the appropriate tax in the country (e.g. USA) where the income is incurred, and then this amount is used as a (non-refundable) tax credit in the country of residence. If the amount of income taxes owed in the country of residence is higher, then he has to pay only the difference. Otherwise if it’s lower, he pays nothing to the country of residence but does not receive a refund either. Either way, the total tax he pays is equal to the highest amount among the two countries.

Irene works in the USA but is a citizen of Canada. She earns $100k and pays $30k tax to the USA (federal, state, and others combined). (Assume that $1 USD = $1 CAD.) She calculates that with her $100k income, she owes $32k tax to Canada (federal plus provincial). However, she can use the $30k of taxes paid to the USA as a foreign tax credit to offset her Canadian taxes, hence she only needs to pay $2k to the Canadian government.

(7) Tax-deferred investments (RRSP)

The Canadian government encourages its residents to save their own money for retirement instead of relying on a public or private pension plan. The RRSP offers the advantage of “deferring” one’s income: You can deduct a certain amount of money from this year’s income and put it into an RRSP account for investment. All investment gains within the account have no tax applied within the account. When you withdraw money from the account at retirement (hopefully with big gains), those amounts are added to your income at the year of withdrawal and taxed accordingly.

The contribution room for a particular calendar year is defined as 18% of the earned income of the previous year (up to a certain maximum), plus all the unused contribution room from before.

The advantage of this scheme is that you can deduct your income when your marginal tax rate is high, and withdraw it when the marginal rate is low (especially when you have no other income at retirement). Plus the fact that investment gains within the account have no immediate tax, it means compounding works much more effectively.

(8) Tax-advantaged investments

Eligible dividends from Canadian companies undergo this procedure: For n amount of dividends received, g × n is added to your income (g is called the gross-up factor; g is about 1.4), and c × g × n is subtracted from your income tax (c is the dividend tax credit rate; c is about 0.15). The purpose of this calculation is to approximately eliminate the effect of the corporate income tax. The amount g × n is approximately what the company had to earn in order to pay you this chunk of dividends, and c × g × n is approximately the corporate income tax paid by the company. This calculation more or less nullifies the corporate income tax, but shifts the entire corporate pre-tax income into your hands.

Capital gains are added to income at a rate of only 50%. For example if you buy a stock at $100 and sell at $140, then you report $40 ÷ 2 = $20 as income. Furthermore, capital losses can be used to offset capital gains in the past or future (with certain limitations).

(9) Non-refundable tax credits

Certain activities will generate tax credits – for example, buying a public transit monthly pass (e.g. Metropass) will result in an income tax credit of 15% of the item’s cost. However, the credit is non-refundable in the sense that if you already owe $0 or less in taxes to the government for this year, then the credit will not increase your refund. I suppose the logic in this is to give benefits to people who earn a certain minimum amount of income rather than to everyone.

(10) More to explore

This guide-by-approximation will end here, but there’s no shortage of topics for further exploration:

  • Tax-advantaged accounts: TFSA, RESP
  • Income- and dependant-based grants: GST/HST credit, UCCB
  • Deductible expenses
  • Other taxes: Surtaxes, health premium
  • Interest charges on late income tax payments

More info