ACCA Taxation (TX-UK) · Lesson 1 of 10
The income tax computation
Income tax is charged band by band on taxable income. Taxable income is net income less the personal allowance, and with a salary alone net income equals total income. At the end of this lesson you can compute the tax on any salary to the pound.
An example lesson built by Chalkwork Labs from public sources, to show the shapes. Your course is drafted from your material and checked by you.
1. The shape of the computation
Every income tax computation has the same three moves. First, add up the income. Second, take off the tax-free allowance. Third, tax what is left in bands, from the bottom up. Learn the shape before the numbers.
- A tax year is the twelve months that income tax is computed for. This lesson uses the [[meta.tax_year]] tax year: [[meta.tax_year_start|date]] to [[meta.tax_year_end|date]]. All rates come from GOV.UK for that year.
- Total income is all the taxable income of the tax year, added together. In this lesson it is one salary and nothing else.
- Net income is total income less reliefs such as qualifying loan interest. In this lesson there are no reliefs, so net income equals total income. The exam answer still shows the line.
- The personal allowance is the income a person can have before they pay any tax. It is [[income_tax.personal_allowance|gbp]].
- Taxable income is net income less the personal allowance. It cannot go below zero.
- A band is a slice of taxable income with its own tax rate. The bands fill in order, like buckets. The next one only fills when the one before is full.
The exam wants the computation in a fixed layout. That layout is a pro-forma: a list of lines in a fixed order. Here it is in words.
| Line | What it holds |
|---|---|
| Total income | Every source of income, added together |
| Net income | Total income less reliefs. With a salary alone, the same figure |
| Less personal allowance | The tax-free amount |
| Taxable income | Net income less the allowance |
| Tax, band by band | Each slice of taxable income times its rate |
| Income tax liability | The slices of tax, added together |
This lesson uses the bands for England, Wales and Northern Ireland. Scotland has its own bands. The TX-UK exam does not examine them.
2. Watch the bands fill
There are three bands. Each one is measured on taxable income, not on salary.
- The basic rate band is the first [[income_tax.basic_rate_limit|gbp]] of taxable income. It is taxed at [[income_tax.rates.basic|pct]].
- The higher rate of [[income_tax.rates.higher|pct]] applies to taxable income above that, up to [[income_tax.higher_rate_limit|gbp]].
- The additional rate of [[income_tax.rates.additional|pct]] applies to taxable income above [[income_tax.higher_rate_limit|gbp]].
Move the salary slider. The chart splits every pound of salary into the band it lands in. The tax line shows the total tax. Watch the tax-free layer shrink above [[income_tax.pa_income_limit|gbp]].
Two rates describe a tax charge. The marginal rate is the tax on the next pound of income, as a percentage. The effective rate is total tax divided by total income. It is the average rate on all of the income.
With the full allowance, the higher rate starts at a salary of [[V.higher_starts_salary|gbp]]: [[income_tax.personal_allowance|gbp]] of allowance plus the [[income_tax.basic_rate_limit|gbp]] band. A higher rate taxpayer still pays only [[income_tax.rates.basic|pct]] on the first slice.
3. The computation, line by line
This is the layout the exam expects. It follows the slider above. Move the slider and watch each line change. Lines for an empty band are left out, as they would be in an answer.
| Line | £ |
|---|---|
| Employment income | |
| Net income | |
| Adjusted net income over [[income_tax.pa_income_limit|num]] | |
| Allowance reduction: excess ÷ [[income_tax.pa_taper_divisor]] | |
| Less personal allowance | |
| Taxable income | |
| Income tax liability |
Worked example 1: a basic and higher rate taxpayer
Salary [[examples.we1.salary|gbp]], no other income. The allowance is in full, because the income is below [[income_tax.pa_income_limit|gbp]]. Taxable income is [[examples.we1.salary|num]] − [[examples.we1.personal_allowance|num]] = [[examples.we1.taxable|gbp]]. The first [[examples.we1.basic_slice|gbp]] is taxed at [[income_tax.rates.basic|pct]], which is [[examples.we1.tax_basic|gbp]]. The remaining [[examples.we1.higher_slice|gbp]] is taxed at [[income_tax.rates.higher|pct]], which is [[examples.we1.tax_higher|gbp]]. The liability is [[examples.we1.liability|gbp]].
Show the working in code
Optional. The same calculation as Python you can step through.
Step through the same computation in code
The block below holds real Python that runs in this page. You will not write or edit it. Press Next step and compare each new variable with the table at [[examples.we1.salary|gbp]]. Three bits of syntax: min(a, b) gives the smaller number, max(0, x) stops a figure going below zero, and a // b divides and drops any fraction. IT["basic_rate_limit"] looks up a figure in the lesson data, so the code never types a rate.
Block 1: Trace worked example 1, band by band
Each step is one line of the pro-forma. Watch which variables appear and what they hold.
- The salary, which is also the income the taper is tested on.
- The allowance: start at the full amount, then take off half of any excess over the limit.
- Taxable income: salary less the allowance.
- Cut taxable income into the three slices. Each slice is capped at its band.
- Tax each slice at its own rate.
- The liability: the slices of tax added together.
The block printed a liability of [[examples.code.step_liability|gbp]]. Which statement about it is right?
4. The taper and the 60% rate
The allowance is not the same for everyone. It gets smaller when income is high. The income figure that decides this is adjusted net income: total income less gross pension contributions and gift aid. With a salary alone, adjusted net income equals the salary.
The taper is the cut. The allowance loses £1 for every £[[income_tax.pa_taper_divisor]] of adjusted net income above [[income_tax.pa_income_limit|gbp]]. So it reaches nil at [[income_tax.pa_nil_point|gbp]]: [[income_tax.pa_income_limit|num]] + [[income_tax.pa_taper_divisor]] × [[income_tax.personal_allowance|num]].
Worked example 2: inside the taper
Salary [[examples.we2.salary|gbp]], no other income. Adjusted net income is above [[income_tax.pa_income_limit|gbp]], so the allowance is cut first. The exam expects the two taper lines shown in grey.
| Line | £ |
|---|---|
| Employment income | [[examples.we2.salary|num]] |
| Net income | [[examples.we2.salary|num]] |
| Adjusted net income over [[income_tax.pa_income_limit|num]] | [[examples.we2.excess|num]] |
| Allowance reduction: [[examples.we2.excess|num]] ÷ [[income_tax.pa_taper_divisor]] | [[examples.we2.reduction|num]] |
| Less personal allowance: [[income_tax.personal_allowance|num]] − [[examples.we2.reduction|num]] | [[examples.we2.personal_allowance|neg]] |
| Taxable income | [[examples.we2.taxable|num]] |
| [[income_tax.basic_rate_limit|num]] × [[income_tax.rates.basic|pct]] | [[examples.we2.tax_basic|num]] |
| [[examples.we2.higher_slice|num]] × [[income_tax.rates.higher|pct]] | [[examples.we2.tax_higher|num]] |
| Income tax liability | [[examples.we2.liability|num]] |
At a salary of [[income_tax.pa_income_limit|gbp]] the liability is [[examples.we2.liability_at_limit|gbp]]. The extra [[examples.we2.extra_salary|gbp]] of salary cost [[examples.we2.extra_tax|gbp]] of extra tax. That is [[examples.we2.marginal_rate|pct]] of the extra salary. No band has a rate of [[examples.we2.marginal_rate|pct]]. Where does it come from?
Inside the taper, each extra £1 of salary is taxed at [[income_tax.rates.higher|pct]]. It also removes [[V.lost_pence|int]]p of allowance. That [[V.lost_pence|int]]p becomes taxable at [[income_tax.rates.higher|pct]] too. Together the marginal rate is [[V.taper_marginal|pct]].
The marginal rate climbs in steps: nil, [[income_tax.rates.basic|pct]], [[income_tax.rates.higher|pct]], [[V.taper_marginal|pct]], then [[income_tax.rates.additional|pct]]. It does not drop back to [[income_tax.rates.higher|pct]] after the taper. The allowance reaches nil at [[income_tax.pa_nil_point|gbp]], and that is also where taxable income reaches the [[income_tax.higher_rate_limit|gbp]] additional rate limit. The effective rate never jumps. It rises smoothly and stays below the marginal rate.
5. Two levers: salary and a pension contribution
A second input changes the computation in two places at once. Suppose the taxpayer pays into a personal pension under relief at source. They pay a net amount. The provider claims [[pensions.relief_at_source_rate|pct]] from HMRC and adds it. The gross contribution is the full amount that reaches the pension: the net amount divided by 0.8.
The gross contribution does two things in the computation:
- It extends the basic rate band by the gross amount. The higher rate limit moves up by the same amount. More income is taxed at [[income_tax.rates.basic|pct]] instead of [[income_tax.rates.higher|pct]].
- It comes off adjusted net income. Inside the taper that gives back some of the personal allowance.
Move both sliders. Compare the two bars. Start at [[examples.pension.salary|gbp]] with a net contribution of [[examples.pension.net|gbp]], then try the same contribution at [[examples.pension_low.salary|gbp]].
At [[examples.pension.salary|gbp]] a net contribution of [[examples.pension.net|gbp]] is a gross of [[examples.pension.gross|gbp]]. The provider adds [[examples.pension.added_by_provider|gbp]]. The basic rate limit becomes [[examples.pension.extended_limit|gbp]]. Adjusted net income falls to [[examples.pension.ani|gbp]], so the allowance rises from [[examples.pension.pa_without|gbp]] to [[examples.pension.pa_with|gbp]]. The liability falls from [[examples.pension.tax_without|gbp]] to [[examples.pension.tax_with|gbp]]. Total relief is [[examples.pension.total_relief|gbp]] on a gross of [[examples.pension.gross|gbp]]: [[examples.pension.relief_pct|pct]].
At [[examples.pension_low.salary|gbp]] the same contribution gives total relief of [[examples.pension_low.total_relief|gbp]], which is [[examples.pension_low.relief_pct|pct1]] of the gross. The taper is why the relief is larger at the higher salary. Each pound of allowance recovered is a pound taxed at nil instead of [[income_tax.rates.higher|pct]].
Scope. This model is the TX-UK one: relief at source, a gross contribution within the taxpayer's earnings, and no annual allowance charge. Occupational schemes that deduct contributions from pay before tax work differently. The sources below cover the rates; the two-step mechanism is the standard TX-UK treatment.
Quick check
1. At what adjusted net income does the personal allowance reach nil?
2. Taxable income after the personal allowance is [[examples.checks.q2_taxable|gbp]]. What is the income tax?
3. What is the marginal rate on salary between [[income_tax.pa_income_limit|gbp]] and [[income_tax.pa_nil_point|gbp]]?
4. A taxpayer pays [[examples.pension.net|gbp]] net into a personal pension under relief at source. What is the gross contribution?
What to remember
- Three moves: total income (shown again as net income when there are no reliefs), less the personal allowance, then tax in bands.
- The personal allowance is [[income_tax.personal_allowance|gbp]]. It is cut by £1 for every £[[income_tax.pa_taper_divisor]] of adjusted net income over [[income_tax.pa_income_limit|gbp]], and is nil from [[income_tax.pa_nil_point|gbp]].
- Bands are measured on taxable income: [[income_tax.rates.basic|pct]] on the first [[income_tax.basic_rate_limit|gbp]], [[income_tax.rates.higher|pct]] up to [[income_tax.higher_rate_limit|gbp]], [[income_tax.rates.additional|pct]] above.
- Only the slice in a band pays that band's rate. One rate on the whole income is the most common error.
- Inside the taper the marginal rate is [[V.taper_marginal|pct]]: [[income_tax.rates.higher|pct]] on the pound plus [[income_tax.rates.higher|pct]] on the allowance it removes.
- A relief-at-source pension contribution is grossed up (net ÷ 0.8). The gross extends the basic rate band and reduces adjusted net income.
- Show the taper lines in the pro-forma whenever adjusted net income is above [[income_tax.pa_income_limit|gbp]].
Sources
Rates and allowances are for the [[meta.tax_year]] tax year. [[meta.attribution]]