Stack gains on taxable income when splitting the higher and additional CGT bands

[vahid-ahmadi]

Fixes #2432

What and why

capital_gains_tax split gains above the basic rate band between the higher and additional CGT bands using the whole higher band (higher_rate_limit - basic_rate_limit, £87,440 in 2025-26) for every gainer. It never subtracted taxable income already above the basic rate limit, so a reform that sets the CGT higher and additional rates apart charged someone with £200,000 of income at the higher rate on their gains.

Gains are the top slice of income (TCGA 1992 ss. 1H(3), 1I). In law CGT has only two rates, 18% and 24%, and the model's additional_rate parameters exist only so reforms can mirror the income tax additional-rate band. For that split to mirror income tax, the gains above the basic rate band start at taxable income or the basic rate limit, whichever is higher:

remaining_higher_rate_band = max_(
    higher_rate_limit - max_(taxable_income, basic_rate_limit), 0
)

The main, residential property, carried interest and relief schedules share one higher-band loop, so the fix covers all four. No values are hard-coded.

£200,000 of earnings and £50,000 of gains, 2025-26:

Reform	Main	This branch
Current law	£11,280	£11,280
CGT additional rate 45%	£11,280	£21,150
CGT higher rate 45%	£21,150	£11,280

Current law

The higher and additional CGT rates are equal at every date, so current-law CGT is unchanged apart from float32 rounding where gains now straddle the moved split point. Two frozen expectations were updated for this:

• test_gift_aid.py::test_zero_gift_preserves_main_outputs_bit_for_bit: one row (£101,000 earnings, £40,000 gains) moves from 8880 to 8879.9990234375.
• test_capital_gains_tax_components.py::legacy_capital_gains_tax: the reference formula behind the bit-identity tests now uses the stacked higher band, so it still matches the new formula bit for bit.

TestEqualisationReforms hard-coded the buggy figure (£39,278: 87,440 at 40% and 9,560 at 45% on £87,430 of taxable income). Its expectation is now £41,764.50: 37,710 at 40% and 59,290 at 45%.

Interaction with #2419

#2419 (default CGT realisation response) answers the rate on the last pound of gains, so the wrong band also drives the wrong response there. Its docs example (£100,000 earnings, £200,000 gains, higher rate raised to 45%) quotes tax rising from £47,280 to £65,642 with no response. After this fix it rises to about £55,199: 37,710 at 45% and 159,290 at 24%. Its other example, with both rates at 45%, does not change.

Test plan

• New capital_gains_tax_rate_bands.yaml (10 cases, hand-computed): income below the basic rate limit, between the limits and above the higher rate limit under an additional-rate reform; higher-rate reforms; residential property and carried interest additional-rate reforms; current law; and the earnings-based example above. 7 fail on main and all pass here. The 3 that pass on main are the two current-law cases and the below-basic-limit case, where the whole band is correctly left.
• policyengine-core test policyengine_uk/tests/policy: 3,444 passed.
• pytest test_capital_gains_tax_components.py test_capital_gains_responses.py test_capital_gains_projection.py test_gift_aid.py and the other tests that touch CGT: pass.
• Full pytest -n 8 policyengine_uk/tests: 5,966 passed, 102 skipped, 1 xfailed.
• ruff format --check and ruff check: clean.
• Changelog fragment in changelog.d/

Reproducer

Reproducer: policyengine_uk/tests/policy/baseline/gov/hmrc/capital_gains_tax/capital_gains_tax_rate_bands.yaml, policyengine_uk/tests/test_capital_gains_tax_components.py::TestEqualisationReforms::test_main_rate_reform_leaves_the_other_schedules_at_current_law

axiom: n/a: the additional CGT band is a model-only reform hook; TCGA 1992 ss. 1H-1I as enacted have two rates (18% and 24%) and the higher and additional parameters are equal at every date, so no encoded rule or current-law result changes

🤖 Generated with Claude Code

[juaristi22]

Reviewed 54fa62d64d28a976df2ac6cc3ce5e79a38d53a5d. The new remaining-band expression matches the declared third-band reform convention in isolation, but it exposes one material interaction with the annual exemption.

C1 — Allocate the exemption at the rates actually reached after stacking. At capital_gains_tax.py:75–77 (consumed at line 179), the higher-band capacity becomes zero for a person already above the higher limit. The unchanged exemption ordering at lines 141–151 still compares only each schedule’s higher_rate, so it can exempt the wrong gains.

Reproducer: one adult aged 45 in 2025, employment income £200,000, total gains £50,000, of which residential-property gains are £25,000; reform only gov.hmrc.cgt.additional_rate to 0.45. No intermediate tax, allowance or eligibility inputs are supplied, and behavioural elasticities retain their zero defaults.

Head charges £16,530 CGT. It assigns the £3,000 exemption to residential gains at 24%, while the remaining main gains are now charged at 45%. Assigning the exemption to main gains instead gives £15,900: £25,000 × 24% + £22,000 × 45%. The resulting £630 excess reaches household tax and net income. An independent same-head simulation using only the exact captured-base CGT formula gives £11,280: under the old whole-higher-band allocation all £47,000 taxable gains in this case remained at 24%, so exemption placement was immaterial. This demonstrates why the changed split exposes the interaction.

TCGA 1992 s.1K(5) preserves the most-beneficial exemption allocation, irrespective of the otherwise applicable rate. The third rate remains a hypothetical reform hook; this finding does not claim it is an enacted general CGT rate. Please preserve beneficial exemption allocation under the new stacked bands and add a mixed-schedule regression. The new YAML cases each use only one taxable gain schedule.

Validation: 243 repository checks and 11 independent diagnostics passed; the added mixed-gain exemption regression failed at £16,530 versus £15,900. One private microsimulation test was deselected. Independent boundary, Gift Aid/pension extension, four-schedule conservation and final household-income checks passed. A 384-household synthetic current-law comparison against the captured-base formula found only float32 rounding differences (maximum CGT £0.0078125, household tax £0.015625; final net income unchanged). Nine official source originals checked. The Axiom n/a explanation and required reproducers/changelog are adequate.

At capture and the mid-review check, four hosted Python shards were still running; other reported checks passed. Review status: COMPLETE. Review severity: REQUEST_CHANGES. Confirmed critical count: 1.