Advanced Taxation (UK) · Mitigation of tax by numerical analysis and reasoned argument

Quantifying Tax Savings Using Numerical Analysis in ATX

Updated 11 October 2026 · Fact-checked

Quantifying a tax saving means computing the total tax before a planning measure, computing it again after, and taking the difference. Then you deduct any extra costs to show the net saving. Use the rates and bands in the ACCA tax tables, and show every working so marks can be awarded.

Understand Quantifying Tax Savings Using Numerical Analysis

Tax planning advice is weak if it only says a step will save tax. The ATX examiner wants a number. You show what the client pays now, what they pay after the measure, and the gap between the two.

The method is a before and after comparison. Both computations must use the same facts, the same tax year and the same tables. Only the planning measure changes. If you change anything else, the saving is wrong.

The tax tables are your toolkit. The exam gives the income tax bands and rates, dividend rates, CGT rates and annual exempt amount, corporation tax rates and marginal relief, IHT nil rate bands and taper relief, and interest rates. The supplementary instructions say to assume the 2025/26 rates and allowances continue to apply unless told otherwise. Calculations are to the nearest £ and apportionments to the nearest month.

A saving in one tax can create a cost in another. Extra salary may bring NIC. A gift may remove the donor's CGT cost. So the net saving is the tax saved less any extra tax, costs or lost cash. Finish with a one-line conclusion the client can act on, and mention any risk or condition.

Key rules to remember

Tax saving: Saving = tax before the measure − tax after the measure; Use the same facts, tax year and tables in both computations.
Net saving: Net saving = tax saving − extra taxes − extra costs; Include any new NIC, other taxes triggered or fees. Say so if cash is lost, for example a pension contribution paid.
Corporation tax marginal relief: (Upper limit − Augmented profits) × Standard fraction × Taxable total profits ÷ Augmented profits; From the tax tables: lower limit £50,000, upper limit £250,000, standard fraction 3/200, main rate 25%, small profits rate 19%. Limits are reduced for associated companies and for short periods. Apply it when profits are between the limits.
Effective marginal rate of corporation tax: 25% + (3/200 × 100%) = 26.5%; Applies only where augmented profits equal taxable total profits and fall between £50,000 and £250,000, with no associated companies and a 12-month period.
Income tax rates (non-savings, non-dividend): 20% on £1 − £37,700; 40% on £37,701 − £125,140; 45% above £125,140; The bands apply to taxable income, after the personal allowance. Dividend rates are 8.75%, 33.75% and 39.35%, with a £500 dividend nil rate band.
CGT: Gain less annual exempt amount (£3,000), taxed at 18% within unused basic rate band and 24% above it; Business asset disposal relief and investors' relief give a 14% rate on qualifying gains up to the £1,000,000 lifetime limit.
IHT: Lifetime rate 20% and death rate 40% on the excess over the nil rate band of £325,000; Residence nil rate band £175,000. Taper relief reduces tax on gifts made more than three but less than seven years before death, in steps from 20% to 80%.

How to solve Quantifying Tax Savings Using Numerical Analysis questions

Use this order for any question that asks you to show how much a measure saves.

1Read the requirement. Note which taxpayer, which tax year and what exactly you must quantify.
2List the facts and the planning measure. Decide what changes and what stays fixed.
3Compute the tax position before the measure. Set it out as a clear working with the rates and bands from the tax tables.
4Compute the tax position after the measure on the same basis. Change only the items affected by the measure.
5Subtract to find the saving. Then deduct extra taxes or costs, such as NIC or cash paid out, to find the net saving.
6Check for knock-on effects, such as the effect on a band, a threshold or marginal relief, and on other taxes.
7State a conclusion and one or two conditions or risks, for example that the measure must be genuine and the client must be comfortable with the cash or control implications.

Quickest way: Compute only the difference

When to use it: Use when the measure only affects part of the computation and time is short. Do a full computation if you are unsure.

Identify the items that change, such as the income moved, the gain split or the profits reduced.
Work out the tax on just that slice before and after. Use the marginal rate for the band it falls in.
Watch for slices that cross a band boundary. Split them and apply each rate.
Check against the full before and after figures if time allows. Show enough to earn marks, because a bare answer may score nothing.

Common mistakes in Quantifying Tax Savings Using Numerical Analysis

Changing more than one thing between the before and after computations.
Students rush and update figures that were not affected by the measure.
Fix: Write down what changes. Copy everything else unchanged from the before computation.
Forgetting the knock-on effect on bands, such as unused basic rate band for gains or marginal relief for companies.
The tax rate is applied without checking which band the income or gain falls in.
Fix: Work out the taxable income or profit first, then see how much band is left before applying 18% or 24%.
Stating the gross tax saving without deducting extra costs.
The question seems to ask only for tax, so costs are ignored.
Fix: Always ask what the client gives up or pays extra. Show net saving and say so in the conclusion.
Using the wrong rates, such as normal rates on dividends or the old CGT rates.
Students rely on memory instead of the tax tables in the exam.
Fix: Take every rate and limit from the tables provided and name the table line you use in your working.
Giving figures with no workings or explanation.
Students think the answer alone is enough.
Fix: Show each working, as the supplementary instructions require, and add one sentence on what the figure means for the client.
Ignoring the time limit on corporation tax periods and the small profits and upper limits for associated companies or short periods.
Students apply £50,000 and £250,000 automatically.
Fix: Check the length of the period and the number of associated companies before applying the limits.

Worked examples

Example 1

Anna has a gain of £43,000 on shares she plans to sell in 2025/26. Her taxable income is £45,000 after the personal allowance. Her husband Ben has no income and no other gains. Quantify the CGT saving if Anna first transfers half of the shares to Ben, who then sells his half. Ignore business asset disposal relief. Assume the annual exempt amount for each is available.

Show the solution

Before: Anna's gain is £43,000. Less annual exempt amount £3,000 = £40,000.
Her taxable income of £45,000 already exceeds the basic rate band of £37,700, so all the gain is taxed at 24%.
CGT before = £40,000 × 24% = £9,600.
After: a transfer between spouses living together is on a no gain, no loss basis, so no tax arises on the transfer.
Anna's share of the gain is £21,500. Less £3,000 = £18,500. Taxed at 24% = £4,440.
Ben's share of the gain is £21,500. Less £3,000 = £18,500. He has no taxable income, so the full £37,700 basic rate band is available. Tax at 18% = £3,330.
CGT after = £4,440 + £3,330 = £7,770.
Saving = £9,600 − £7,770 = £1,830. There are no extra costs, though the transfer must be a genuine, outright gift.

Answer: Transferring half of the shares to Ben saves £1,830 of CGT (£9,600 before, £7,770 after), as it uses Ben's annual exempt amount and his lower rate band.

Example 2

Delta Ltd has no associated companies and has taxable total profits of £240,000 before a proposed employer pension contribution of £30,000, for the 12 months to 31 March 2026. It has no dividend income. Quantify the corporation tax saving and the net cost of the contribution. Ignore NIC and any annual allowance issues.

Show the solution

Before: profits £240,000 lie between £50,000 and £250,000, so main rate 25% less marginal relief applies.
Tax at 25% = £60,000.
Marginal relief = (£250,000 − £240,000) × 3/200 × (£240,000 ÷ £240,000) = £10,000 × 0.015 = £150.
Corporation tax before = £60,000 − £150 = £59,850.
After: the contribution is a deductible trading expense if wholly and exclusively for the trade, so profits are £240,000 − £30,000 = £210,000.
Tax at 25% = £52,500.
Marginal relief = (£250,000 − £210,000) × 3/200 = £40,000 × 0.015 = £600.
Corporation tax after = £52,500 − £600 = £51,900.
Saving = £59,850 − £51,900 = £7,950, which is 26.5% of £30,000.
Net cost = £30,000 − £7,950 = £22,050.

Answer: The contribution saves £7,950 of corporation tax, so the net cost is £22,050. The relief is at the effective marginal rate of 26.5%.

Exam tips

Open the tax tables at the start and underline the rates you will need. Use them as written, not from memory.
Always label the two computations clearly as before and after. Then draw a separate line for the saving.
Round to the nearest £ and show every working, as the supplementary instructions require.
After the numbers, write the advice. The professional skills marks reward a clear conclusion, a comment on risks, and a recommendation the client can follow.
Check for hidden thresholds in the question, such as the upper limit for corporation tax, the basic rate band or the pension cap on reliefs, before you apply the rate.

Practice questions from Mitigation of tax by numerical analysis and reasoned argument

Quantifying Tax Savings Using Numerical Analysis: frequently asked questions

How do I calculate a tax saving from tax planning in ATX?

Compute the total tax before the measure and again after it, using the same facts and tables. The difference is the saving. Deduct any extra taxes or costs to show the net saving.

Where do I find the tax rates in the ATX exam?

The exam reproduces the tax rates and allowances, including income tax, CGT, IHT, corporation tax and interest rates. Use them directly and assume 2025/26 rates continue unless the question says otherwise.

How accurate do my figures need to be?

Work to the nearest £ and apportion to the nearest month, as the supplementary instructions say. Show all workings so marks can be given for method even if you make an arithmetic slip.

Do I need to comment on the numbers?

Yes. ATX awards professional skills marks for analysis, commercial awareness and clear communication. State the saving, the conditions that must be met, and any risks or cash effects.