Warning, graphs ahead!
Update - this is no longer valid as of 2021
Laws, including the tax code, usually don’t contain mathematical functions. This is despite the fact that all taxation can best be described with mathematics. Politicians and media tend to describe this complex system using simplifications and examples based on averages or medians. Having never seen a complete picture describing the Czech income tax, I decided to investigate using tools like Wolfram Alpha. Here I would like to share my observations.
This article only covers a typical “Joe the Employee” and his desire to understand where all of this money goes. The information below is valid as of February 2016 with 2016 values for constants and all numbers in CZK.
First, some basic facts
There exists four different income taxes, two of which are referred to as compulsory insurance:
- Income tax (dan z prijmu)
- Health insurance (zdravotni pojisteni)
- Social security (socialni pojisteni)
- Solidarity tax (solidarni dan)
Social security is not called a tax, presumably because you receive benefits based on how much you pay into the system. With higher social security payments you get a bigger state pension and bigger support in case of job loss, more money during sick leave or maternity leave (the first 6 month only, after that you get flat support).
With higher
health insurance payments you don't get anything (so it is really a tax).
As a regular Joe the Employee you cannot decide how much you want to insure yourself, unlike those who are self-employed. In the analyses I do not account for the increase in benefits, and I treat both as taxes as a result of being mandatory. Those who are self-employed can choose how much insurance they wish to pay for, though they usually choose the minimal amount as the more you pay, the less you get for your money. Joe the Employee pays 4.5% of his gross salary for health insurance and 6.5% for social security. [2]
Super gross salary: you have permanent employment in the Czech Republic and make the rough national average[1] of 27,000 per month, then your monthly cost to your employer is actually 36,180. This increased amount is a result of them having to pay a larger part of your social (25%) and health (9%) insurance. Combined, this amounts to 34% on top of the gross salary - hence, “super gross” - specified in your contract. While many countries share this super gross approach, the Czech Republic has the second highest rate out of all OECD countries after France.
The
income tax itself is a simple, flat rate of 15% of your super gross salary, which equals 20.1% of your gross salary. Complexity arrives, however, once you begin accounting for various forms of tax relief, tax credits, tax base deductions, and the social security ceiling.
The
solidarity tax is 7% of your gross - not super gross - salary. It is only paid by people with
high income explained bellow.
Tax relief per taxpayer gets you a discount on the income tax you have to pay. It is 24,840 per year, which equals 2,070 per month. You can also get a similar discount for your spouse if they do not earn more than 68,000 in the calendar year. Tax relief can never yield a negative taxation value, so not everyone fully benefits from this. Additional forms of tax relief exist for students and those who are handicapped.
You can also get a
tax credit if you have kids. Unlike a tax discount, a tax credit can lower your income tax into negative values, yielding actual additional income.
- 1st child - 13,404 per year = 1,117 per month
- 2nd child - 15,804 per year = 1,317 per month
- every other child - 17,004 per year = 1,417 per month
Tax discounts can also lower your taxes. Unlike tax relief and tax credits they don't directly influence the taxes applied, but rather the base out of which the taxes are calculated. This allows you to use your money before taxes to purchase life insurance, donate to charities, cover your mortgage interest, or save up for a pension. Tax discounts don’t affect compulsory insurance nor the solidarity tax; they only affect the tax base for the income tax.
If your monthly salary reaches 108,024 - four times the national average[1] - you have reached the
high income tax bracket. There are two implications. You have reached the ceiling for social security, but now the solidarity tax kicks in at the same time.
As the minimum wage is 9,900 for 2016, we will only focus on salaries above that value in the charts below.
- The cost of work or just cost in the text refers to super gross salary
- Salary denotes the gross salary, the number that employees have in the contract. This number also includes any bonuses received.
- Income is the net income after taxes (including compulsory insurance) are subtracted. This is the amount the employee receives in their bank account.
Analyses
Now that we’ve gone through the basics, let’s see what we can learn by combining them and adding contex. As a first step, I will plot the each of the following on a simple graph:
- x axis is gross salary in CZK
- y axis is in CZK
- both axes use the same scale
- grey grid lines denote 10 000 CZK increments
- orange lines (from left to right):
- minimum wage (where the curves start)
- average salary (gross)
- denotes when the solidarity tax kicks in (high income)
- red line is super gross salary = cost of work
- green line is gross salary
- shades of blue lines show net income with 0, 1, and 2 children
- rest of the lines show taxation in parts and summed together
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| By gross salary |
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| By gross salary zoomed |
Observations
- We can see that the minimum wage of 9,900 results in a total cost of 13,266 for the employer, out of which the employee only gets 8,811. The state takes 4,455 which is more than half of the net income even without any income tax being paid.
- An average salary of 27,006 results in a total cost of 36,188 for employer, of which 3,358 is paid in taxes and 15,510 is paid to state in total, which leaves 20,667 for the employee.
- If you hit the high income level of 108,024 you cost your employer 144,752, pay 19,642 in income tax and 68,253 the to state in total, while getting 76,498 as net income.
- One interesting things happens at the higher income levels: due to the social security ceiling the super gross salary growth slows down, and employee and employer insurance drops down as well. The tax goes up because of the solidarity tax and so the net income maintains the same ratio to gross salary. This shows that income tax effectively replaces the social insurance (from the employee's point of view)
- You don't pay any income tax until your gross salary reaches 10,298 which is just four hundred CZK above minimum wage at the moment
- The blue curves are exactly parallel to each other, showing that in absolute value the tax bonus for children stays the same
- Your net salary can be higher than you gross salary.
- If you have child kid this occurs for gross salaries up to 10,154.
- If you have two children this occurs for gross salary up to 14,482.
- Your net salary can never be higher than super gross salary, so you are always net positive for the government budget.
Gross salary is quite simple: it is the number that appears on your contract, but it does not tell you how much your employer actually pays for you nor how much you actually get. We can plot that by adjusting the x axis and aspect ratio to super gross salary (to get the employer point of view) and net salary (to get your bank account point of view). It is exactly the same data only displayed differently, with the varying slopes putting different perspectives on the situation:
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| By cost of work |
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| By net salary |
Those graphs show the absolute numbers, but let's take a look at ratios. If we divide the previous graphs by the value on the x axis, we can nicely observe the real tax rate. On the first graph we can see that the income tax rate (magenta) goes from 0 to nearly 20% of gross salary. Even though employee insurance is just above 10%, the total taxation rate ranges from 45% to ~63%, while the net salary goes from 90% - 100% - 113% (0 - 1 - 2 children) to 71% - 72% - 73%.
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| Ratios of the salary |
The total tax plus net salary without kids in the previous graph gives 134% - the super gross salary. To assess the tax ratio it is more fair to set the base (ratio 1) to the super gross salary as seen in the next graph:
 |
| Ratios of the cost of work |
This graph shows quite well the total
tax burden in yellow (VAT not included, plotted for no children) going from ~34% to ~48% due to
tax progression; the intent being that people with higher income should pay higher taxes. In the Czech tax system this is achieved by constant tax relief. Most of this progression happens at the bottom part of the income ladder. It goes from ~34% to ~43% between the minimum and average salary. Interestingly, the tax burden rate drops after hitting the high income level. If we plot it over larger incomes in the next graph (x axis shows gross income), we see that the total tax burden drops to ~36%. The income tax with the solidarity tax grows to ~20% quite progressively, the solidarity tax effectively replaces the social security on the employee side, but there is no additional social security on the employer side, which causes the drop.
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| Ratios of the cost of work - prolonged (x axis is gross salary) |
For the complete picture we also plot the ratios to net salary (with 0 - 1 - 2 kids). Here it shows that having two kids gets you nearly 30% more money if you make the minimum wage. It also shows the fact that the cost of work is 150% - 190% of the money the employee receives.
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| Ratios of net income - no child |
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| Ratios of net income - 1 child |
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| Ratios of net income - 2 children |
Another question one might ask is,
what happens if I get a raise of X crowns? This is best answered by first derivation of the first graphs.
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| Next crown in salary |
This graph shows what happens with each subsequent crown being added to your gross salary (or as a bonus).
- Obviously your gross salary increases by one crown (green)
- The cost of you work increases by 1.34 up to the high income level where afterwards it only increases by 1.09.
- In the gross salary range of 9,900 - 10,400 you get 0.9 of every crown, then 0.69 all the way up to the high income, after which you get 0.73.
- All 3 net income curves are the same, as the benefit is fixed and completely independent of your income.
- Income above the high limit is taxed at a much lower rate than other income, as most of the taxation (0.25 on crown) comes from the employer social security obligation which has the ceiling
Below I have also plotted what happens with each subsequent crown being added from the cost of work and net income perspectives. What these plots illustrate is that any money spent by an employer above the high income level results in better gross and net salaries for the employee compared to lower income levels.
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| Next crown in cost of work |
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| Next crown in income |
One may also ask,
what if I get an X% raise? We arrive at the answer by transforming the function f[x] into (f[100% +
X% x]-f[x])/f[x] which is very similar to derivation, but depends on the absolute value of f[x] at x. I have plotted a 1% and 10% raise, but you can see that the 10% is simply a rolling sum (average * 10) that smooths out the 1% graph a bit.
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| 1% salary increase |
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| 10% salary increase |
You can see that the tax curve goes from infinity because you don't pay any taxes with a gross salary lower than ~10,400. This is the same reason why raise of 1% (99) at minimum wage (9,900) gives you raise of 1% of net income 8,811 + 88 = 8,899. As soon as the income tax kicks in, however you get hit quite hard; you get less than a 9% net income increase for a 10% gross salary increase up to the average salary (which less than half of the work force gets). Interestingly after hitting the high income threshold your net income will grow slightly faster than your salary (in relative terms).
Due to the fixed nature of the bonus for children, you get smaller relative income increases as the number of children increases. You do, however, still have a higher income. The difference is 0.78% - 0.69% - 0.61% at the lower peak salary 10,400, 0.9% - 0.85% - 0.81% at the average salary (27,006) and the difference almost disappears at high income level 1.02% - 1.00% - 0.99% (percentage increase per 1% increase in salary).
To complete the picture we should also look at the cost of work point of view.
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| 1% cost increase |
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| 10% cost increase |
For reference again:
[1] - This is expected average salary for 2016. It is calculated as 2 year old value adjusted by a coefficient. This value is used for calculation of the high income. Latest numbers to compare are for 2014 where the expected average was 25,942 and the actual value 25,607
[2] - Social security and health insurance paragraphs were corrected to actual situation. I did merge together sickness insurance (nemocenské pojištění) (part of social security) with health insurance.
