Personal and Business Income Tax Simplification with 1-3 Slope Formulas for Many Countries
A. Tax Calculation Systems in Other Countries
B. Tax Calculation Simplification (Multi tax brackets (Problem #1: too many bracket numbers), xx formulas (Problem #2: too many
formulas), xx taxable income ranges (Problem #3: too many ranges with different numbers), and xx-page Withholding Tables
(Problem #4: too many pages and too complex) are matched/simplified by 2 or 1 simple and fair linear (slope) formula and
1 existing formula resulting in 75%-99% simplification and 15 benefits) to save significant time and costs
1. Existing and LG Simplification Tax Systems for Australian with 2 or 1 simple linea formula
2. Existing and LG Simplification Tax Systems for Canada with 1 simple linear formula
3. Existing and LG Simplification Tax Systems for China with 3 or 2 simple linear formulas
4. Existing and LG Simplification Tax Systems for India with 2 simple linear formula
5. Existing and LG Simplification Tax Systems for Japan with 3 or 2 simple linear formulas
6. Existing and LG Simplification Tax Systems for UK with 1 simple linear formula
* UK Corporate Tax Reform Draft with Smooth Tax Rate Changes and 2 Brackets According to Budget Balance
A. Tax Calculation systems in other countries
Comparing with many other countries, the U.S. has the most complex and detail national personal tax system with 7 tax brackets, 21-page Withholding Tables, 224 (7x4x8) and 12-page Tax Table. But more tax brackets also mean more time and cost involved, which can be matched and simplified with smooth tax rates and less tax brackets/ranges.
Many countries have flat tax rates for corporate tax systems such as Argentina (35%), Australia (30%), Brazil (34%), China (25%), Egypt (25%), France (33.33%), Greece (26%), Japan (25.5%), Mexico (30%), New Zealand (28%), Pakistan (35%), Russian (20%), South African (28%), Spain (28%), Thailand (20%) and U.K. (20%). A flat tax rate is too simple to cover different taxable incomes reasonably, which is not reasonable. In general speaking, large and strong companies need to have more social responsibilities. Flat tax rates are not reasonable for different taxable incomes. Few countries have tax rate ranges for corporate tax systems such as Germany has tax rate range 30-33%, India has 30-40%, Netherlands has 20-25%, Switzerland has 12.5-24% and the U.S. has 15-35% (before 2018). A nice business tax plan is to have relatively low bottom tax rate, which can encourage more people to start businesses. Small businesses hire many employees to meet social and economical needs for people and economical development. Then mid and large businesses are more stable and pay relatively higher tax rates. Two brackets for corporate tax calculation system are suggested.
Comparing with corporate tax systems, most countries usually do not use flat tax rates for their individual tax systems and also use multi tax brackets in tax systems to collect income taxes from individuals because flat tax rates are too simple to cover different taxable incomes, which are not reasonable. Such as Australia has 5 tax brackets, China has 7 tax brackets, Japan has 7 tax brackets and Singapore has 9 tax brackets. Many countries have relatively wide tax rate ranges such as Argentina (9-35%), Australia (17-45%), Brazil (7.5-27.5%), China (3-45%), Egypt (10-25%), France (5.5-41%), Germany (14-45%), Greece (0-42%), Japan (5-50%), Mexico (0-30%), New Zealand (0-39%), Pakistan (0-25%), Spain (24.75-52%), Thailand (5-37%), U.K. (0-45%) and Zambia (0-35%). Only very few countries such as Georgia, Libya and Russia have flat tax rates for individual tax systems. For wide tax rate ranges, smooth tax rate changes are very important. Multi or many tax brackets produce smooth tax rate changes. But more tax brackets make tax systems more complex with more time and costs to employers, individuals and governments.
B. Tax Calculation simplification (Multi tax brackets, xx formulas, xx taxable income ranges and xx-page Withholding Tables
are matched/simplified by 2-4 formulas/brackets) with 1-3 simple slope (linear) formulas
Effective slope (linear) and gradual (LG) tax system has been developed to simplify our existing individual and corporate tax systems with 2-4 tax rate ranges, which balances the number of tax brackets and simplicity. Few slope (linear) formulas (1-3) are introduced to match existing tax rates and taxes, which can replace existing multi tax brackets, xx-xxx withholding formulas for different filing periods (364, 52, 26, 24, 12, 4, 2 or 1), and x-xx page - withholding tables. Same formula for last tax brackets is converted from existing tax format to tax rate/tax format without any change for tax rates and taxes. Its tax rate changes are gradual without change comparing with prior situations. When a taxable income is increased more and more, tax rates approach to its top tax rate.
Then tax and tax rate calculations, analysis, modification, projection and reform can be done simply and reasonably with the LG tax system. Besides tax simplifications, the LG tax system can also offer many taxpayers with a one-income source and non-complex tax situations have the option to file simple tax returns or not file tax returns because accurate withholding income taxes are filed by employers. The LG tax simplification means to simplify tax rate/tax calculations, analysis, modification and projection without changing tax rates.
Methods: We have done our tax simplification research with 12 publications at http://taxsimplecenter.net/publication.html When 2 tax rates are set, simple effective (linear) tax rates between the two points with a straight line are fair and practical. Existing flat and curve or step tax rates with less or more tax brackets are unfair and complex. Then multi tax brackets, multi tax formulas and xx-page Withholding Tables can be matched/simplified by 2 or 3 simple brackets/formulas fairly*. Figure 1 / Comparison
* Fair tax rate changes: www.scitcentral.com/documents/be5648da4795008d9893b752b9226c8f.pdf (3. Tax Rate Change Speed, ......)
1. Existing and LG Simplification Tax Systems for Australian with 2 simple slope formulas
Table 1 shows the tax rates for Australian residents in 2015-2022. There are 5 flat tax rates of 0, 19%, 27%, 32.5% and 45% during the 5 tax brackets. The tax rate curves between taxable incomes from Table 1 are not smooth with steps and rough with changeable tax rate change slopes. Table 1 can be converted into Table 2 after deducting $18,200 from incomes to taxable incomes (TI). When the LG tax rate system is used, the tax rates can be simplified with the 3 taxable income ranges with simple taxable income ranges and smooth tax rate changes, which is shown in Table 3. Also the 3 tax rate range checks of 19%-28.23%-0.35%-45% are used for checking related calculations to avoid or reduce tax rate and tax calculations. The filing period factor (F), which is 52, 26, 24, 13, 12, 4 or 1 based on weekly, bi-weekly, semi-monthly, monthly, quarterly or annually basis, is used for employers to file tax withholding, which is simpler than existing tax system. There are multi-page withholding tables such as www.ato.gov.au/uploadedFiles/Content/MEI/downloads/Weekly-tax-table-from-13-October-2020.pdf (weekly) and
www.ato.gov.au/uploadedFiles/Content/MEI/downloads/Monthly-tax-table-2017-18.pdf (monthly).
Table 1 Australian Resident Tax Rates with Incomes
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Income Tax on this income Tax Computation
0 - $18,200 Nil 0
18,201-37,000 19c for each $1 over $18,200 0.19x(TI - 18,200)
37,001-80,000 $3,572 plus 32.5c for each $1 over $37,000 3,572+0.325x(TI-37,000)
80,001-180,000 $17,547 plus 37c for each $1 over $80,000 17,547+0.37x(TI-$80,000)
over 180,001 $54,547 plus 45c for each $1 over $180,000 54,547+0.45x(TI-180,000)
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A standard deduction, which may change over time, may be deducted from incomes into taxable incomes (TI): TI=Income-18,200 (or 18,000). The LG tax rate system can be used to design related tax software product for income tax calculation, payroll, withholding, analysis, inspection, reform and projection reasonably. Then related multi tax formulas and withholding tables can be eliminated/replaced by the 3 formulas simply.
Table 2 Australian Resident Tax Rates with Taxable Incomes
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Taxable Income (TI) Tax on this income Tax/Bracket Tax Computation
0-19,000 19c for each $1 3,610 0.19*TI
19,000-62,000 32.5c for each $1 from 19,000 to 62,000 13,975 3,610+0.325x(TI-19,000)
62,001-162,000 37c for each $1 from 62,001 to 162,000 37,000 17,585+0.37x(TI-$62,000)
over 162,000 45c for each $1 over $162,000 54,585+0.45x(TI-162,000)
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Table 3 LG Tax Rate System for Matching Australian Resident Tax Rates
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S Yearly TI TI Tax rate and tax formula Tax rate Range check Tax
Not over 60,000xS (YTI/650,054/S+0.19)xTI 0.19-0.2823
(60,000-180,000)xS (YTI/1,772,526/S+0.24845)xTI 0.2823-0.35
Over 180,000xS (0.45-18,000*S/YTI)xTI 0.35-0.45
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YTI=TI*F. YTI is yearly taxable income, TI is taxable income and F is filing period # (1, 2, 4, 12, 26, 52 or 365 on different filing period). 650,054 is from 60,000 / (0.2823-0.19). 1,772,526 is from (180,000-60,000) / (0.35-0.2823). 18,000 is from 180,000 x (0.45-0.35). Total tax calculation, analysis and projection are:
Total Tax(S=1) = ∑(YTIm/650,054/S+0.190) YTIm + ∑(YTIn/1,772,526/S+0.24845) YTIn) + ∑(0.45-18,000*S/YTIo) YTIo)
For over $162,000, existing 54,585+0.45*(YTI-162,000)=0.45 YTI - 18,315=0.45-18,315/YTI) x YTI, which is converted to (0.45 - 18,000*S/YTI) x TI
Example: Monthly income is 5,000.55, TI=5,000-18,200/12=3,483.33
Then tax rate and tax=(3,483.33*12/650,054/S+0.19)x3,483.33=0.2543x3,483.33=885.82 (tax rate: 25.43%)
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
There is no tax filing status difference, which means no difference between such as married filing jointly, married filing separately, single or head of household, which may be too simple. Two or three tax filing statuses with married filing jointly, married filing separately, single and head of household are suggested to cover different social statuses reasonably by such as S=1, 1.5 or 2.
Conclusion: The 5 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 3 simple brackets/formulas fairly.
2. Existing and LG Simplification Tax Systems for Canada with 1 simple slope formula
Canadian federal tax rates for 2016 - 2020 on yearly basis are shown in Table 1. There are 5 tax brackets or steps at 15%, 20.5%, 26%, 29% and 33%. From 2016 to 2020, yearly taxable income (YTI) ranges are changed unregularly. Income withholding taxes need to be divided with more withholding tables and computations with different filing periods. There are withholding tables at www.canada.ca/content/dam/cra-arc/formspubs/pub/t4127-jan/t4127-01-20e.pdf (8 pages). Existing tax system with more formulas and multi-page withholding tables are complex.
Table 1 Canadian Federal Tax Rates for 2016 - 2020 (Yearly Taxable income = YTI)
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Federal tax rates for 2020: Federal tax rates for 2018: Federal tax rates for 2016:
15% Not over $48,535 Not over $46,605 of yearly taxable income (0.15*YTI) Not over $45,282
20.5% $48,535 - $97,069 $46,605 - $93,208 (6,991+0.205 (TI-46,605)) $45,282 - $90,563
26% $97,069 - $150,473 $93,208 - $144,489 (16,544+0.26 (TI-93,208)) $90,563 - $140,388
29% $150,473 - $214,368 $144,489 - $205,842 (29,877+0.29 (TI-144,489) $140,388 - $200,000
33% Over $214,368 Over $205,842 (47,670+0.33 (TI-205,842)) Over $200,000
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For yearly taxable income (YTI) at $100,000 in 2018, its tax rate is 18.31% (16,544+0.26 (100,000-93,208))/100,000 or 18.53% ((0.15x45,282+0.205x45,281(9282.605)+0.26x9,437)/100,000) in 2016. There are slight tax rate changes. Tax rate at YTI=200,000 is 22.99% ((29,877+0.29(200,000-144,489))/200,000) in 2018, which is simplified to 23%.
The LG tax system introduces filing period (F) # (F is 1, 2, 4, 12, 26, 52 or 365 on different filing period) into smooth tax rate formulas from unsmooth (step and curve) tax rates, which is shown in Table 2 to simplify existing Canadian tax system without withholding and tax tables. F=1 is for tax returns. Yearly taxable income (YTI) and taxable incomes ranges are often changed, which affect tax rates. Tax status # (S) may be considered for such as 1 for Married Filing Separately, 1 for Single, 2 for Married Filing Jointly or 1.5 for Head of Household. There is no difference currently (S=1 for all tax statuses).
Table 2 LG Tax System for Matching the Existing Canadian Federal Tax Rates (2018)
YTI is yearly taxable Income and TI is taxable income (YTI=TI*F). Filing period (F) is 365, 52, 26, 24, 12, 4, 2
or 1 on daily, weekly, bi-weekly, semi-monthly, monthly, quarterly, semi-yearly or yearly basis.
________________________________________________________________________________________
S Yearly TI TI Tax rate and tax formula Tax rate check Tax Rate Tax (TI*rate)
Not over 100,000xS (YTI/1,204,819/S+0.15)xTI 0.15-0.183
(100,000-200,000)xS (YTI/2,127,660/S+0.136)xTI 0.183-0.23
Over 200,000xS (0.33-20,000*S/YTI)xTI 0.23-0.33
________________________________________________________________________________________
For over $200,000, existing (47,670+0.33 (TI-205,842))=0.33 YTI - 20,258=0.33-20,258/YTI) x YTI, which is converted to (0.33 - 20,000*S/YTI) x TI
Total tax (S=1) =0.15∑YTIa+∑(YTIxYTI)a/1,204,819+0.136∑YTIb+∑(YTIxYTI)b/2,127,660+0.33∑YTIc-20,000*C
Proposal of Tax Simplification Draft: 218_canada_tax_simplification_1.pdf
Table 2 can be also further simplified to two tax brackets/ranges from 0-$200,000 and over $200,000.
Table 3 LG Tax System for Matching the Existing Canadian Federal Tax Rates (2018) (2 brackets)
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Yearly TI TI Tax rate and tax formula Tax rate check Tax Rate Tax (TI*rate)
Not over 200,000xS (YTI/2,500,000/S+0.15)xTI 0.15-0.23
Over 200,000xS (0.33-20,000*S/YTI)xTI 0.23-0.33
____________________________________________________________________________________________
2,500,000 is from 200,000 / (0.23-0.15). 20,000 is from 200,000 x (0.33-0.23).
Example: Biweekly taxable income is 5,000,
Then tax rate and tax=(5,000x26/2,500,000/1+0.15)x5,000=0.202x5,000=1,010.00 (tax rate: 20.2%)
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
Total tax (S=1) =∑(YTIa/2,500,000/S + 0.15) YTIa + ∑(0.33-20,000*S/YTIb) YTIb)
Conclusion: The 5 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 2 simple brackets/formulas fairly.
3. Existing and LG Simplification Tax Systems for China with 2 or 3 simple slope formulas
China has 7 tax brackets with tax rates 3-45% currently, which is shown in Table 1 with 7 tax brackets on monthly basis. China had 9 tax brackets (tax rates: 5-45%) in 2007. There is no tax filing status difference, which means no difference between such as married filing jointly, married filing separately, single or head of household, which may be too simple. The curves between taxable incomes and tax rates from Table 1 are not smooth with changeable tax rate change slopes. When the LG tax rate system is used, the tax rates can be simplified to the 4 tax brackets (43% reduction), simple taxable income ranges and smooth tax rate changes, which are shown in Table 4. Different filing periods (F) with corresponding taxable incomes are considered, which is such as 1, 2, 3, 6 or 12 on monthly, bi-monthly, quarterly, semi-yearly or yearly basis, may be used for withholding taxes by employers and Chinese government.
Table 1 Existing Chinese Individual Tax Rates (Monthly)
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# Taxable income Tax Rate Tax Computation
1 not over 1,500 3% 0.03xTI
2 1,500-4,500 10% 0.03x1500+0.1x(TI-1500) = 0.1xTI-105
3 4,500-9,000 20% 45+0.1x3000+0.2x(TI-4500) = 0.2xTI-555
4 9,000-35,000 25% 45+300+0.2x4500+0.25x(TI-9000)=0.25xTI-1,005
5 35,000-55,000 30% 345+900+0.25x26000+0.3x(TI-35000)=0.3xTI-2,755
6 55,000-80,000 35% 7745+0.3x20000+0.35x(TI-55000)=0.35xTI-5,505
7 over 80,000 45% 13745+0.35x25000+0.45x(TI-80000)=0.45xTI-13,505
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Table 1 can be simplified by the LG tax rate system (Table 2) with no or minor tax rate differences. It is good to simplify the existing 7 marginal tax rates of 3%, 10%, 20%, 25%, 30%, 35% and 45% and complex tax system into the 4 tax rate ranges and simple taxable income ranges. The tax rate range check is used for checking purpose to avoid or reduce calculation mistakes. A payroll-withholding software program may be designed for employers to use.
Table 2 LG Tax Rate System for Matching Chinese Individual Tax Rates
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Monthly TI TI Tax rate formula Tax rate Range check Tax
Not over 0,000xS 0.03+TIxF/83,333.3/S 0.03-0.15
(10,000-50,000)xS 0.12625+TIxF/421,052.6/S 0.15-0.245
(50,000-100,000)xS 0.175+TIxF/714,285.7/S 0.245-0.315
Over100,000 0.45 – 13,500xS/TI/F 0.315-0.45
_____________________________________________________________________________
Total Tax=0.03∑TIm+∑(TI2)m/83,333+0.12625∑TIn+∑(TI2)n/421,052+0.175∑TIo+∑(TI2)o/714,286+0.45∑TIp–13,500 p
The 4 brackets may be further reduced to 3 brackets (Table 3). Two or three tax filing statuses with married filing jointly, married filing separately and single may be suggested to cover different tax statuses reasonably by such as S=2 or 1. Besides standard deduction, education, child credit, and elder care credit deductions are suggested to have a fair and simple tax system. Simplification Summary
Table 3 LG Tax Rate System for Matching Chinese Individual Tax Rates (3 brackets)
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Yearly TI TI Tax rate and tax formula Tax rate Range check Tax
Not over 120,000xS (TIxF/1,000,000/S+0.03)xTI 0.03-0.15
(120,000-960,000)xS (TIxF/6,353,636/S+0.131143)xTI 0.15-0.282
Over 960,000xS (0.45 – 161,280xS/TI/F)xTI 0.282-0.45
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For over $80,000x12, existing 0.45xTIx12-13,505x12=0.45 YTI - 162,060=(0.45-162,060/YTI) x YTI, which is converted to (0.45 - 161,280xS/YTI) x TI
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
Total Tax=∑(YTIm/1,000,000/S+0.03) YTIm)+∑(YTIn/6,353,636/S+0.131143) YTIn)+∑(0.45–161,280xS/YTIo) YTIo)
1,000,000 is from 120,000 / (0.15-0.03). 6,353,636 is from (960,000-120,000) / (0.282-0.15). 161,280 is from 960,000 x (0.45-0.282).
Conclusion: The 7 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 3 simple brackets/formulas fairly.
4. Existing and LG Simplification Tax Systems for India with 1 simple linear formula
India has 6 tax brackets at 0, 5%, 10%, 15%, 20% and 30% with tax rates 3-45%, which is shown in Table 1.
https://taxsummaries.pwc.com/india/individual/taxes-on-personal-income
Table 1 Existing India Personal Tax Rates
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# Taxable income Tax Rate
1 not over 300,000 0
2 300,000-600,000 5%
3 600,000-900,000 10%
4 900,000-1,200,000 15%
5 1,200,000-1,500,000 20%
6 Over 1,500,000 30%
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Table 1 can be simplified by the LG tax rate system (Table 2) with no or minor tax rate differences. It is good to simplify the existing 6 marginal tax rates into the 2 tax rate ranges and simple taxable income ranges. The tax rate range check is used for checking purpose to avoid or reduce calculation mistakes. A payroll-withholding software program may be designed for employers to use. Tax status (S) may be used wiith such as 1 or 2.
Table 2 LG Tax Rate System for Matching India Individual Tax Rates
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Yearly TI TI Tax and rate formula Tax rate Range check Tax
(0 - 1,500,000)xS (TI x F / 10,000,000 / S)xTI 0 - 0.15
Over 1,500,000)xS (0.3 - 225,000xS/TI/F)xTI 0.15 - 0.3
_______________________________________________________________________________________
Total Tax=∑(TI2)m/10,000,000/S+0.3∑TIn–2,250,000xS n
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
10,000 is from 1,500,000 / (0.15-0) and 225,000 is from 1,500,000 x (0.3 - 0.15).
Conclusion: The 6 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 2 simple brackets/formulas fairly.
5. Existing and LG Simplification Tax Systems for Japan with 2 or 3 simple slope formulas
Japan has 7 tax brackets with tax rate range 5%-45% in 2015 with the 7 marginal tax rates of 5%, 10%, 20%, 23%, 33%, 40% and 45%. Tax base are very large, which may cause calculation mistakes easily. The curves between taxable incomes and tax rates from Table 1 are not smooth with changeable tax rate change slopes. When the LG tax rate system is used, the tax rates can be simplified to the 4 or 3 tax brackets, simple taxable income ranges and smooth tax rate changes, which is shown in Table 2 or 3. The filing period factor, which is 365, 52, 26, 24, 13, 12, 4 or 1 based on daily, weekly, bi-weekly, semi-monthly, monthly, quarterly or annually basis, is used for employers to file tax withholding, which is simpler than existing tax system for employers and Japanese government.
Table 1 Existing Japan Individual Income Tax Rates
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# Tax Base (Yen)(TB) Tax Tax Computation
1 1-1,950,000 5% 0.05xTB
2 1,950,000-3,300,000 10% 0.05x1,950,000+0.1x(TB-1,950,000)
3 3,300,000-6,950,000 20% 232,500+0.2*(TB-3,300,000)
4 6,950,000-9,000,000 23% 23% of base exceeding 6,950,000
5 9,000,000-18,000,000 33% 33% of base exceeding 9,000,000
6 18,000,000-40,000,000 40% 40% of base exceeding 18,000,000
7 over 40,000,000 45% 45% of base exceeding 40,000,000
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Table 2 LG Tax Rate System for Matching Japan Individual Tax Rates (4 brackets)
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Yearly TB TB Tax rate and tax formula Tax rate Range check Tax
Not over 10 millionxS (TBxF/73,529,412/S+0.05)xTI 0.05-0.186
(10-20 million)xS (TBxF/126,582,278/S+0.107)xTI 0.186-0.265
(20-40 million)xS (TBxF/294,117,647/S+0.197)xTI 0.265-0.333
Over 40 millionxS (0.45 - 4,680,000xS/TBxF)xTI 0.333-0.45
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Table 3 LG Tax Rate System for Matching Japan Individual Tax Rates (3 brackets)
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Yearly TB TB Tax rate and tax formula Tax rate Range check Tax
Not over10 millionxS (TBxF/73,529,412/S+0.05)xTI 0.05-0.186
(10-40 million)xS (TBxF/204,081,633/S+0.137)xTI 0.186-0.333
Over 40 millionxS (0.45 - 4,680,000xS/TB*F)xTI 0.333-0.45
_____________________________________________________________________________________
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
Total Tax=∑((YTIm/73,529,412/S+0.05) YTIm) + ∑((YTIn/204,081,633/S+0.137) YTIn) + ∑ (0.45 - 4,680xS/YTIo) YTIo)
73,529,412 is from 10,000,000 / (0.186-0.05). 204,081,633 is from (40-10)x1,000,000 / (0.333-0.186). 4,680,000 is from 40 million x (0.45-0.333).
There is no tax filing status difference currently. There is no difference between such as married filing jointly, married filing separately, single or head of household, which may be too simple. Two or three tax filing statuses with married filing jointly, married filing separately, single and head of household may be suggested to cover different social statuses reasonably by such as S=2, 1 or 1.3-1.5.
Conclusion: The 7 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 4 or 3 simple brackets/formulas.
6. Existing and LG Simplification Tax Systems for UK with 1 simple slope formula
UK has unsmooth tax rates with 4 tax rates at 0%, 20%, 40% and 45%, which are shown in Table 1. There are 25-pages Taxable Pay Tables (TPT) at
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/878997/Tax-Tables-B-D_04-20.pdf and related formulas, which are complex.
Table 1 UK Tax Rates for 2018-2020 (Yearly Taxable income = YTI)
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Income for 2018/19: Tax formula: Income for 2019/20: Tax formula:
0% Not over 11,850 0 Not over 12,500 0
20% 11,850 - 46,350 0.2x(YTI-11,850) 12,500 - 50,000 0.2x(YTI-12,500)
40% 46,350 - 150,000 6,900+0.4x(YTI-46,350) 50,000 - 150,000 7,500+0.4x(YTI-50,000)
45% Over 150,000 48,360+0.45x(YTI-150,000) Over 150,000 47,500+0.45x(YTI-150,000)
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There is a "jump" problem when income after 12,500 or 50,000 because there are high tax rate speeds and then the speeds are reduced, which have been discussed at www.scitcentral.com/documents/be5648da4795008d9893b752b9226c8f.pdf (research paper). Their tax rate changes are not smooth. The LG tax system introduces smooth tax rate changes for taxable incomes not over such as 120,000 and filing period # (F is 1, 2, 4, 12, 26, 52 or 365 on different filing period) into smooth tax rate formulas from the above unsmooth (step and curve) tax rates, which is shown in Table 2 to simplify existing UK tax system without withholding tables (Taxable Pay Tables). F=1 is for tax returns. Yearly taxable income (YTI) and taxable incomes ranges are often changed, which affect tax rates. Tax status # (S) may be considered for such as 1 for Married Filing Separately, 1 for Single, 2 for Married Filing Jointly or 1.5 for Head of Household. There is no difference currently (S=1 for all tax statuses). Table 1 is converted to Table 2 with Standard Deduction 12,500 in 2019/20. Fiscal note is evaluated to adjust tax rate ranges for neutral tax revenue change.
Table 2 LG Tax System for Matching the Existing UK Federal Tax Rates (2019/20)
YTI is yearly taxable Income. TI is taxable income (YTI=TI*F). Filing period (F) is 365, 52, 26, 24, 12, 4, 2 or 1
on daily, weekly, bi-weekly, semi-monthly, monthly, quarterly, semi-yearly or yearly basis.
________________________________Option #1 (0%-29%-45%)_________ ______ Option #2 (0%-28%-44%)__________
Yearly TI ÷ S TI Tax rate and tax formula Tax rate check Tax rate and tax formula Tax rate check
Not over 120,000xS (YTI÷413,793÷S) x TI 0-0.29 (YTI ÷ 428,571÷S) x TI 0-0.28
Over 120,000xS (0.45-19,200xS÷YTI) x TI 0.29-0.45 (0.44 - 19,200xS÷YTI) x TI 0.28-0.44
_______________________________________________________________________________________________________
Total tax (S=1) = ∑((YTIa÷428,571÷S) YTI) + ∑((0.44 - 19,200xS ÷ YTIb) YTIb)
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
413,793 is from 120,000 / (0.29-0) and 19,200 is from 120,000 x (0.45 - 0.29).
Conclusion: The 4 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified with the 2 simple brackets/formulas.
* UK Corporate Tax Reform Proposal with Smooth Tax Rate Changes and 2 Brackets
UK has a simple flat corporate tax rate at 19%. USA had 8 tax brackets (15-35%) before 2018, which were too complex, and then has a flat tax rate at 21%, which is too simple and unreasonable. A flat tax rate is very simple. But a flat rate can not cover different taxable incomes and small and large companies reasonably. A nice business tax plan is to have a relatively low bottom tax rate, which can encourage more people to start businesses. Small businesses hire many employees to meet social and economic needs for people and economic development. Then mid and large businesses are more stable and pay relatively higher tax rates. UK corporate tax situations are:
Corporation tax rates:
Financial year 2020-21 Financial year 2021-22 Financial year 2022-23 Financial year 2023-24
Main rate 19% 19% 19% 25%
Small profits rate N/A N/A N/A 19%
Lower threshold N/A N/A N/A £50,000
Upper threshold N/A N/A N/A £250,000
Published 3 March 2021 from www.gov.uk/guidance/corporate-tax
When taxable incomes change from 250,000 to 250,001, tax difference will be 15,000 (250,000 (0.25-0.19)). The £1 can cause £15,000 difference, which is totally unreasonable with "cliff" problem. Two brackets such as 15%-20%-25% with two formulas are suggested to have smooth tax rate change without the cliff problem. Tax rates can be reduced or increased according to budget balance.
Option #1 (17%-19%-22%) Option #2 (15%-20%-25%)
Taxable income (TI) The tax rate and tax Tax rate range The tax rate and tax Tax rate range
Not over $50,000 (YTI÷2,500,000+0.17)×TI 17%-19% (YTI÷1,000,000+0.15)×TI 15%-20%
Over $50,000 (0.22-1,500÷YTI)×TI 19%-22% (0.25-2,500÷YTI)×TI 20%-25%
_____________________________________________________________________________________________
Total tax (S=1) = ∑(YTIa÷2,500,000 + 0.17) YTIa) + ∑((0.22 - 1,500÷YTIb) YTIb)
When yearly taxable income is not over 50,000, tax rate is 19% (flat tax rate), which is kept the same. The bottom tax rate can be reduced to such as 17% or 18% to have no tax revenue change according to its fiscal note evaluation. 50,000÷(0.19-0.17) is 2,500,000. 50,000x(0.22-0.19) is 1,500.
When the upper threshold (250,000) in the above corporate tax rates is kept the same and a linear formula is used, the tax cliff from 250,000 to 250,001 can be resolved without the problem for £1 income difference to cause £15,000 tax difference unfairly. Then tax rate changes are smooth.
Option #3 (17%-25%)
Taxable income (TI) The tax rate and tax Tax rate range
Not over $250,000 (YTI÷3,125,000+0.17)×TI 17%-25%
Over $250,000 0.25 25%
______________________________________________________
B. Tax Calculation Simplification (Multi tax brackets (Problem #1: too many bracket numbers), xx formulas (Problem #2: too many
formulas), xx taxable income ranges (Problem #3: too many ranges with different numbers), and xx-page Withholding Tables
(Problem #4: too many pages and too complex) are matched/simplified by 2 or 1 simple and fair linear (slope) formula and
1 existing formula resulting in 75%-99% simplification and 15 benefits) to save significant time and costs
1. Existing and LG Simplification Tax Systems for Australian with 2 or 1 simple linea formula
2. Existing and LG Simplification Tax Systems for Canada with 1 simple linear formula
3. Existing and LG Simplification Tax Systems for China with 3 or 2 simple linear formulas
4. Existing and LG Simplification Tax Systems for India with 2 simple linear formula
5. Existing and LG Simplification Tax Systems for Japan with 3 or 2 simple linear formulas
6. Existing and LG Simplification Tax Systems for UK with 1 simple linear formula
* UK Corporate Tax Reform Draft with Smooth Tax Rate Changes and 2 Brackets According to Budget Balance
A. Tax Calculation systems in other countries
Comparing with many other countries, the U.S. has the most complex and detail national personal tax system with 7 tax brackets, 21-page Withholding Tables, 224 (7x4x8) and 12-page Tax Table. But more tax brackets also mean more time and cost involved, which can be matched and simplified with smooth tax rates and less tax brackets/ranges.
Many countries have flat tax rates for corporate tax systems such as Argentina (35%), Australia (30%), Brazil (34%), China (25%), Egypt (25%), France (33.33%), Greece (26%), Japan (25.5%), Mexico (30%), New Zealand (28%), Pakistan (35%), Russian (20%), South African (28%), Spain (28%), Thailand (20%) and U.K. (20%). A flat tax rate is too simple to cover different taxable incomes reasonably, which is not reasonable. In general speaking, large and strong companies need to have more social responsibilities. Flat tax rates are not reasonable for different taxable incomes. Few countries have tax rate ranges for corporate tax systems such as Germany has tax rate range 30-33%, India has 30-40%, Netherlands has 20-25%, Switzerland has 12.5-24% and the U.S. has 15-35% (before 2018). A nice business tax plan is to have relatively low bottom tax rate, which can encourage more people to start businesses. Small businesses hire many employees to meet social and economical needs for people and economical development. Then mid and large businesses are more stable and pay relatively higher tax rates. Two brackets for corporate tax calculation system are suggested.
Comparing with corporate tax systems, most countries usually do not use flat tax rates for their individual tax systems and also use multi tax brackets in tax systems to collect income taxes from individuals because flat tax rates are too simple to cover different taxable incomes, which are not reasonable. Such as Australia has 5 tax brackets, China has 7 tax brackets, Japan has 7 tax brackets and Singapore has 9 tax brackets. Many countries have relatively wide tax rate ranges such as Argentina (9-35%), Australia (17-45%), Brazil (7.5-27.5%), China (3-45%), Egypt (10-25%), France (5.5-41%), Germany (14-45%), Greece (0-42%), Japan (5-50%), Mexico (0-30%), New Zealand (0-39%), Pakistan (0-25%), Spain (24.75-52%), Thailand (5-37%), U.K. (0-45%) and Zambia (0-35%). Only very few countries such as Georgia, Libya and Russia have flat tax rates for individual tax systems. For wide tax rate ranges, smooth tax rate changes are very important. Multi or many tax brackets produce smooth tax rate changes. But more tax brackets make tax systems more complex with more time and costs to employers, individuals and governments.
B. Tax Calculation simplification (Multi tax brackets, xx formulas, xx taxable income ranges and xx-page Withholding Tables
are matched/simplified by 2-4 formulas/brackets) with 1-3 simple slope (linear) formulas
Effective slope (linear) and gradual (LG) tax system has been developed to simplify our existing individual and corporate tax systems with 2-4 tax rate ranges, which balances the number of tax brackets and simplicity. Few slope (linear) formulas (1-3) are introduced to match existing tax rates and taxes, which can replace existing multi tax brackets, xx-xxx withholding formulas for different filing periods (364, 52, 26, 24, 12, 4, 2 or 1), and x-xx page - withholding tables. Same formula for last tax brackets is converted from existing tax format to tax rate/tax format without any change for tax rates and taxes. Its tax rate changes are gradual without change comparing with prior situations. When a taxable income is increased more and more, tax rates approach to its top tax rate.
Then tax and tax rate calculations, analysis, modification, projection and reform can be done simply and reasonably with the LG tax system. Besides tax simplifications, the LG tax system can also offer many taxpayers with a one-income source and non-complex tax situations have the option to file simple tax returns or not file tax returns because accurate withholding income taxes are filed by employers. The LG tax simplification means to simplify tax rate/tax calculations, analysis, modification and projection without changing tax rates.
Methods: We have done our tax simplification research with 12 publications at http://taxsimplecenter.net/publication.html When 2 tax rates are set, simple effective (linear) tax rates between the two points with a straight line are fair and practical. Existing flat and curve or step tax rates with less or more tax brackets are unfair and complex. Then multi tax brackets, multi tax formulas and xx-page Withholding Tables can be matched/simplified by 2 or 3 simple brackets/formulas fairly*. Figure 1 / Comparison
* Fair tax rate changes: www.scitcentral.com/documents/be5648da4795008d9893b752b9226c8f.pdf (3. Tax Rate Change Speed, ......)
1. Existing and LG Simplification Tax Systems for Australian with 2 simple slope formulas
Table 1 shows the tax rates for Australian residents in 2015-2022. There are 5 flat tax rates of 0, 19%, 27%, 32.5% and 45% during the 5 tax brackets. The tax rate curves between taxable incomes from Table 1 are not smooth with steps and rough with changeable tax rate change slopes. Table 1 can be converted into Table 2 after deducting $18,200 from incomes to taxable incomes (TI). When the LG tax rate system is used, the tax rates can be simplified with the 3 taxable income ranges with simple taxable income ranges and smooth tax rate changes, which is shown in Table 3. Also the 3 tax rate range checks of 19%-28.23%-0.35%-45% are used for checking related calculations to avoid or reduce tax rate and tax calculations. The filing period factor (F), which is 52, 26, 24, 13, 12, 4 or 1 based on weekly, bi-weekly, semi-monthly, monthly, quarterly or annually basis, is used for employers to file tax withholding, which is simpler than existing tax system. There are multi-page withholding tables such as www.ato.gov.au/uploadedFiles/Content/MEI/downloads/Weekly-tax-table-from-13-October-2020.pdf (weekly) and
www.ato.gov.au/uploadedFiles/Content/MEI/downloads/Monthly-tax-table-2017-18.pdf (monthly).
Table 1 Australian Resident Tax Rates with Incomes
_____________________________________________________________________________
Income Tax on this income Tax Computation
0 - $18,200 Nil 0
18,201-37,000 19c for each $1 over $18,200 0.19x(TI - 18,200)
37,001-80,000 $3,572 plus 32.5c for each $1 over $37,000 3,572+0.325x(TI-37,000)
80,001-180,000 $17,547 plus 37c for each $1 over $80,000 17,547+0.37x(TI-$80,000)
over 180,001 $54,547 plus 45c for each $1 over $180,000 54,547+0.45x(TI-180,000)
_____________________________________________________________________________
A standard deduction, which may change over time, may be deducted from incomes into taxable incomes (TI): TI=Income-18,200 (or 18,000). The LG tax rate system can be used to design related tax software product for income tax calculation, payroll, withholding, analysis, inspection, reform and projection reasonably. Then related multi tax formulas and withholding tables can be eliminated/replaced by the 3 formulas simply.
Table 2 Australian Resident Tax Rates with Taxable Incomes
_________________________________________________________________________________________
Taxable Income (TI) Tax on this income Tax/Bracket Tax Computation
0-19,000 19c for each $1 3,610 0.19*TI
19,000-62,000 32.5c for each $1 from 19,000 to 62,000 13,975 3,610+0.325x(TI-19,000)
62,001-162,000 37c for each $1 from 62,001 to 162,000 37,000 17,585+0.37x(TI-$62,000)
over 162,000 45c for each $1 over $162,000 54,585+0.45x(TI-162,000)
_________________________________________________________________________________________
Table 3 LG Tax Rate System for Matching Australian Resident Tax Rates
___________________________________________________________________________________
S Yearly TI TI Tax rate and tax formula Tax rate Range check Tax
Not over 60,000xS (YTI/650,054/S+0.19)xTI 0.19-0.2823
(60,000-180,000)xS (YTI/1,772,526/S+0.24845)xTI 0.2823-0.35
Over 180,000xS (0.45-18,000*S/YTI)xTI 0.35-0.45
___________________________________________________________________________________
YTI=TI*F. YTI is yearly taxable income, TI is taxable income and F is filing period # (1, 2, 4, 12, 26, 52 or 365 on different filing period). 650,054 is from 60,000 / (0.2823-0.19). 1,772,526 is from (180,000-60,000) / (0.35-0.2823). 18,000 is from 180,000 x (0.45-0.35). Total tax calculation, analysis and projection are:
Total Tax(S=1) = ∑(YTIm/650,054/S+0.190) YTIm + ∑(YTIn/1,772,526/S+0.24845) YTIn) + ∑(0.45-18,000*S/YTIo) YTIo)
For over $162,000, existing 54,585+0.45*(YTI-162,000)=0.45 YTI - 18,315=0.45-18,315/YTI) x YTI, which is converted to (0.45 - 18,000*S/YTI) x TI
Example: Monthly income is 5,000.55, TI=5,000-18,200/12=3,483.33
Then tax rate and tax=(3,483.33*12/650,054/S+0.19)x3,483.33=0.2543x3,483.33=885.82 (tax rate: 25.43%)
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
There is no tax filing status difference, which means no difference between such as married filing jointly, married filing separately, single or head of household, which may be too simple. Two or three tax filing statuses with married filing jointly, married filing separately, single and head of household are suggested to cover different social statuses reasonably by such as S=1, 1.5 or 2.
Conclusion: The 5 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 3 simple brackets/formulas fairly.
2. Existing and LG Simplification Tax Systems for Canada with 1 simple slope formula
Canadian federal tax rates for 2016 - 2020 on yearly basis are shown in Table 1. There are 5 tax brackets or steps at 15%, 20.5%, 26%, 29% and 33%. From 2016 to 2020, yearly taxable income (YTI) ranges are changed unregularly. Income withholding taxes need to be divided with more withholding tables and computations with different filing periods. There are withholding tables at www.canada.ca/content/dam/cra-arc/formspubs/pub/t4127-jan/t4127-01-20e.pdf (8 pages). Existing tax system with more formulas and multi-page withholding tables are complex.
Table 1 Canadian Federal Tax Rates for 2016 - 2020 (Yearly Taxable income = YTI)
_________________________________________________________________________________________________________
Federal tax rates for 2020: Federal tax rates for 2018: Federal tax rates for 2016:
15% Not over $48,535 Not over $46,605 of yearly taxable income (0.15*YTI) Not over $45,282
20.5% $48,535 - $97,069 $46,605 - $93,208 (6,991+0.205 (TI-46,605)) $45,282 - $90,563
26% $97,069 - $150,473 $93,208 - $144,489 (16,544+0.26 (TI-93,208)) $90,563 - $140,388
29% $150,473 - $214,368 $144,489 - $205,842 (29,877+0.29 (TI-144,489) $140,388 - $200,000
33% Over $214,368 Over $205,842 (47,670+0.33 (TI-205,842)) Over $200,000
__________________________________________________________________________________________________________
For yearly taxable income (YTI) at $100,000 in 2018, its tax rate is 18.31% (16,544+0.26 (100,000-93,208))/100,000 or 18.53% ((0.15x45,282+0.205x45,281(9282.605)+0.26x9,437)/100,000) in 2016. There are slight tax rate changes. Tax rate at YTI=200,000 is 22.99% ((29,877+0.29(200,000-144,489))/200,000) in 2018, which is simplified to 23%.
The LG tax system introduces filing period (F) # (F is 1, 2, 4, 12, 26, 52 or 365 on different filing period) into smooth tax rate formulas from unsmooth (step and curve) tax rates, which is shown in Table 2 to simplify existing Canadian tax system without withholding and tax tables. F=1 is for tax returns. Yearly taxable income (YTI) and taxable incomes ranges are often changed, which affect tax rates. Tax status # (S) may be considered for such as 1 for Married Filing Separately, 1 for Single, 2 for Married Filing Jointly or 1.5 for Head of Household. There is no difference currently (S=1 for all tax statuses).
Table 2 LG Tax System for Matching the Existing Canadian Federal Tax Rates (2018)
YTI is yearly taxable Income and TI is taxable income (YTI=TI*F). Filing period (F) is 365, 52, 26, 24, 12, 4, 2
or 1 on daily, weekly, bi-weekly, semi-monthly, monthly, quarterly, semi-yearly or yearly basis.
________________________________________________________________________________________
S Yearly TI TI Tax rate and tax formula Tax rate check Tax Rate Tax (TI*rate)
Not over 100,000xS (YTI/1,204,819/S+0.15)xTI 0.15-0.183
(100,000-200,000)xS (YTI/2,127,660/S+0.136)xTI 0.183-0.23
Over 200,000xS (0.33-20,000*S/YTI)xTI 0.23-0.33
________________________________________________________________________________________
For over $200,000, existing (47,670+0.33 (TI-205,842))=0.33 YTI - 20,258=0.33-20,258/YTI) x YTI, which is converted to (0.33 - 20,000*S/YTI) x TI
Total tax (S=1) =0.15∑YTIa+∑(YTIxYTI)a/1,204,819+0.136∑YTIb+∑(YTIxYTI)b/2,127,660+0.33∑YTIc-20,000*C
Proposal of Tax Simplification Draft: 218_canada_tax_simplification_1.pdf
Table 2 can be also further simplified to two tax brackets/ranges from 0-$200,000 and over $200,000.
Table 3 LG Tax System for Matching the Existing Canadian Federal Tax Rates (2018) (2 brackets)
____________________________________________________________________________________________
Yearly TI TI Tax rate and tax formula Tax rate check Tax Rate Tax (TI*rate)
Not over 200,000xS (YTI/2,500,000/S+0.15)xTI 0.15-0.23
Over 200,000xS (0.33-20,000*S/YTI)xTI 0.23-0.33
____________________________________________________________________________________________
2,500,000 is from 200,000 / (0.23-0.15). 20,000 is from 200,000 x (0.33-0.23).
Example: Biweekly taxable income is 5,000,
Then tax rate and tax=(5,000x26/2,500,000/1+0.15)x5,000=0.202x5,000=1,010.00 (tax rate: 20.2%)
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
Total tax (S=1) =∑(YTIa/2,500,000/S + 0.15) YTIa + ∑(0.33-20,000*S/YTIb) YTIb)
Conclusion: The 5 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 2 simple brackets/formulas fairly.
3. Existing and LG Simplification Tax Systems for China with 2 or 3 simple slope formulas
China has 7 tax brackets with tax rates 3-45% currently, which is shown in Table 1 with 7 tax brackets on monthly basis. China had 9 tax brackets (tax rates: 5-45%) in 2007. There is no tax filing status difference, which means no difference between such as married filing jointly, married filing separately, single or head of household, which may be too simple. The curves between taxable incomes and tax rates from Table 1 are not smooth with changeable tax rate change slopes. When the LG tax rate system is used, the tax rates can be simplified to the 4 tax brackets (43% reduction), simple taxable income ranges and smooth tax rate changes, which are shown in Table 4. Different filing periods (F) with corresponding taxable incomes are considered, which is such as 1, 2, 3, 6 or 12 on monthly, bi-monthly, quarterly, semi-yearly or yearly basis, may be used for withholding taxes by employers and Chinese government.
Table 1 Existing Chinese Individual Tax Rates (Monthly)
_________________________________________________________________
# Taxable income Tax Rate Tax Computation
1 not over 1,500 3% 0.03xTI
2 1,500-4,500 10% 0.03x1500+0.1x(TI-1500) = 0.1xTI-105
3 4,500-9,000 20% 45+0.1x3000+0.2x(TI-4500) = 0.2xTI-555
4 9,000-35,000 25% 45+300+0.2x4500+0.25x(TI-9000)=0.25xTI-1,005
5 35,000-55,000 30% 345+900+0.25x26000+0.3x(TI-35000)=0.3xTI-2,755
6 55,000-80,000 35% 7745+0.3x20000+0.35x(TI-55000)=0.35xTI-5,505
7 over 80,000 45% 13745+0.35x25000+0.45x(TI-80000)=0.45xTI-13,505
_________________________________________________________________
Table 1 can be simplified by the LG tax rate system (Table 2) with no or minor tax rate differences. It is good to simplify the existing 7 marginal tax rates of 3%, 10%, 20%, 25%, 30%, 35% and 45% and complex tax system into the 4 tax rate ranges and simple taxable income ranges. The tax rate range check is used for checking purpose to avoid or reduce calculation mistakes. A payroll-withholding software program may be designed for employers to use.
Table 2 LG Tax Rate System for Matching Chinese Individual Tax Rates
_____________________________________________________________________________
Monthly TI TI Tax rate formula Tax rate Range check Tax
Not over 0,000xS 0.03+TIxF/83,333.3/S 0.03-0.15
(10,000-50,000)xS 0.12625+TIxF/421,052.6/S 0.15-0.245
(50,000-100,000)xS 0.175+TIxF/714,285.7/S 0.245-0.315
Over100,000 0.45 – 13,500xS/TI/F 0.315-0.45
_____________________________________________________________________________
Total Tax=0.03∑TIm+∑(TI2)m/83,333+0.12625∑TIn+∑(TI2)n/421,052+0.175∑TIo+∑(TI2)o/714,286+0.45∑TIp–13,500 p
The 4 brackets may be further reduced to 3 brackets (Table 3). Two or three tax filing statuses with married filing jointly, married filing separately and single may be suggested to cover different tax statuses reasonably by such as S=2 or 1. Besides standard deduction, education, child credit, and elder care credit deductions are suggested to have a fair and simple tax system. Simplification Summary
Table 3 LG Tax Rate System for Matching Chinese Individual Tax Rates (3 brackets)
____________________________________________________________________________________
Yearly TI TI Tax rate and tax formula Tax rate Range check Tax
Not over 120,000xS (TIxF/1,000,000/S+0.03)xTI 0.03-0.15
(120,000-960,000)xS (TIxF/6,353,636/S+0.131143)xTI 0.15-0.282
Over 960,000xS (0.45 – 161,280xS/TI/F)xTI 0.282-0.45
____________________________________________________________________________________
For over $80,000x12, existing 0.45xTIx12-13,505x12=0.45 YTI - 162,060=(0.45-162,060/YTI) x YTI, which is converted to (0.45 - 161,280xS/YTI) x TI
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
Total Tax=∑(YTIm/1,000,000/S+0.03) YTIm)+∑(YTIn/6,353,636/S+0.131143) YTIn)+∑(0.45–161,280xS/YTIo) YTIo)
1,000,000 is from 120,000 / (0.15-0.03). 6,353,636 is from (960,000-120,000) / (0.282-0.15). 161,280 is from 960,000 x (0.45-0.282).
Conclusion: The 7 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 3 simple brackets/formulas fairly.
4. Existing and LG Simplification Tax Systems for India with 1 simple linear formula
India has 6 tax brackets at 0, 5%, 10%, 15%, 20% and 30% with tax rates 3-45%, which is shown in Table 1.
https://taxsummaries.pwc.com/india/individual/taxes-on-personal-income
Table 1 Existing India Personal Tax Rates
______________________________________
# Taxable income Tax Rate
1 not over 300,000 0
2 300,000-600,000 5%
3 600,000-900,000 10%
4 900,000-1,200,000 15%
5 1,200,000-1,500,000 20%
6 Over 1,500,000 30%
_____________________________________
Table 1 can be simplified by the LG tax rate system (Table 2) with no or minor tax rate differences. It is good to simplify the existing 6 marginal tax rates into the 2 tax rate ranges and simple taxable income ranges. The tax rate range check is used for checking purpose to avoid or reduce calculation mistakes. A payroll-withholding software program may be designed for employers to use. Tax status (S) may be used wiith such as 1 or 2.
Table 2 LG Tax Rate System for Matching India Individual Tax Rates
_______________________________________________________________________________________
Yearly TI TI Tax and rate formula Tax rate Range check Tax
(0 - 1,500,000)xS (TI x F / 10,000,000 / S)xTI 0 - 0.15
Over 1,500,000)xS (0.3 - 225,000xS/TI/F)xTI 0.15 - 0.3
_______________________________________________________________________________________
Total Tax=∑(TI2)m/10,000,000/S+0.3∑TIn–2,250,000xS n
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
10,000 is from 1,500,000 / (0.15-0) and 225,000 is from 1,500,000 x (0.3 - 0.15).
Conclusion: The 6 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 2 simple brackets/formulas fairly.
5. Existing and LG Simplification Tax Systems for Japan with 2 or 3 simple slope formulas
Japan has 7 tax brackets with tax rate range 5%-45% in 2015 with the 7 marginal tax rates of 5%, 10%, 20%, 23%, 33%, 40% and 45%. Tax base are very large, which may cause calculation mistakes easily. The curves between taxable incomes and tax rates from Table 1 are not smooth with changeable tax rate change slopes. When the LG tax rate system is used, the tax rates can be simplified to the 4 or 3 tax brackets, simple taxable income ranges and smooth tax rate changes, which is shown in Table 2 or 3. The filing period factor, which is 365, 52, 26, 24, 13, 12, 4 or 1 based on daily, weekly, bi-weekly, semi-monthly, monthly, quarterly or annually basis, is used for employers to file tax withholding, which is simpler than existing tax system for employers and Japanese government.
Table 1 Existing Japan Individual Income Tax Rates
_________________________________________________________________
# Tax Base (Yen)(TB) Tax Tax Computation
1 1-1,950,000 5% 0.05xTB
2 1,950,000-3,300,000 10% 0.05x1,950,000+0.1x(TB-1,950,000)
3 3,300,000-6,950,000 20% 232,500+0.2*(TB-3,300,000)
4 6,950,000-9,000,000 23% 23% of base exceeding 6,950,000
5 9,000,000-18,000,000 33% 33% of base exceeding 9,000,000
6 18,000,000-40,000,000 40% 40% of base exceeding 18,000,000
7 over 40,000,000 45% 45% of base exceeding 40,000,000
_________________________________________________________________
Table 2 LG Tax Rate System for Matching Japan Individual Tax Rates (4 brackets)
_____________________________________________________________________________________
Yearly TB TB Tax rate and tax formula Tax rate Range check Tax
Not over 10 millionxS (TBxF/73,529,412/S+0.05)xTI 0.05-0.186
(10-20 million)xS (TBxF/126,582,278/S+0.107)xTI 0.186-0.265
(20-40 million)xS (TBxF/294,117,647/S+0.197)xTI 0.265-0.333
Over 40 millionxS (0.45 - 4,680,000xS/TBxF)xTI 0.333-0.45
_____________________________________________________________________________________
Table 3 LG Tax Rate System for Matching Japan Individual Tax Rates (3 brackets)
_____________________________________________________________________________________
Yearly TB TB Tax rate and tax formula Tax rate Range check Tax
Not over10 millionxS (TBxF/73,529,412/S+0.05)xTI 0.05-0.186
(10-40 million)xS (TBxF/204,081,633/S+0.137)xTI 0.186-0.333
Over 40 millionxS (0.45 - 4,680,000xS/TB*F)xTI 0.333-0.45
_____________________________________________________________________________________
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
Total Tax=∑((YTIm/73,529,412/S+0.05) YTIm) + ∑((YTIn/204,081,633/S+0.137) YTIn) + ∑ (0.45 - 4,680xS/YTIo) YTIo)
73,529,412 is from 10,000,000 / (0.186-0.05). 204,081,633 is from (40-10)x1,000,000 / (0.333-0.186). 4,680,000 is from 40 million x (0.45-0.333).
There is no tax filing status difference currently. There is no difference between such as married filing jointly, married filing separately, single or head of household, which may be too simple. Two or three tax filing statuses with married filing jointly, married filing separately, single and head of household may be suggested to cover different social statuses reasonably by such as S=2, 1 or 1.3-1.5.
Conclusion: The 7 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified by the 4 or 3 simple brackets/formulas.
6. Existing and LG Simplification Tax Systems for UK with 1 simple slope formula
UK has unsmooth tax rates with 4 tax rates at 0%, 20%, 40% and 45%, which are shown in Table 1. There are 25-pages Taxable Pay Tables (TPT) at
https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/878997/Tax-Tables-B-D_04-20.pdf and related formulas, which are complex.
Table 1 UK Tax Rates for 2018-2020 (Yearly Taxable income = YTI)
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Income for 2018/19: Tax formula: Income for 2019/20: Tax formula:
0% Not over 11,850 0 Not over 12,500 0
20% 11,850 - 46,350 0.2x(YTI-11,850) 12,500 - 50,000 0.2x(YTI-12,500)
40% 46,350 - 150,000 6,900+0.4x(YTI-46,350) 50,000 - 150,000 7,500+0.4x(YTI-50,000)
45% Over 150,000 48,360+0.45x(YTI-150,000) Over 150,000 47,500+0.45x(YTI-150,000)
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There is a "jump" problem when income after 12,500 or 50,000 because there are high tax rate speeds and then the speeds are reduced, which have been discussed at www.scitcentral.com/documents/be5648da4795008d9893b752b9226c8f.pdf (research paper). Their tax rate changes are not smooth. The LG tax system introduces smooth tax rate changes for taxable incomes not over such as 120,000 and filing period # (F is 1, 2, 4, 12, 26, 52 or 365 on different filing period) into smooth tax rate formulas from the above unsmooth (step and curve) tax rates, which is shown in Table 2 to simplify existing UK tax system without withholding tables (Taxable Pay Tables). F=1 is for tax returns. Yearly taxable income (YTI) and taxable incomes ranges are often changed, which affect tax rates. Tax status # (S) may be considered for such as 1 for Married Filing Separately, 1 for Single, 2 for Married Filing Jointly or 1.5 for Head of Household. There is no difference currently (S=1 for all tax statuses). Table 1 is converted to Table 2 with Standard Deduction 12,500 in 2019/20. Fiscal note is evaluated to adjust tax rate ranges for neutral tax revenue change.
Table 2 LG Tax System for Matching the Existing UK Federal Tax Rates (2019/20)
YTI is yearly taxable Income. TI is taxable income (YTI=TI*F). Filing period (F) is 365, 52, 26, 24, 12, 4, 2 or 1
on daily, weekly, bi-weekly, semi-monthly, monthly, quarterly, semi-yearly or yearly basis.
________________________________Option #1 (0%-29%-45%)_________ ______ Option #2 (0%-28%-44%)__________
Yearly TI ÷ S TI Tax rate and tax formula Tax rate check Tax rate and tax formula Tax rate check
Not over 120,000xS (YTI÷413,793÷S) x TI 0-0.29 (YTI ÷ 428,571÷S) x TI 0-0.28
Over 120,000xS (0.45-19,200xS÷YTI) x TI 0.29-0.45 (0.44 - 19,200xS÷YTI) x TI 0.28-0.44
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Total tax (S=1) = ∑((YTIa÷428,571÷S) YTI) + ∑((0.44 - 19,200xS ÷ YTIb) YTIb)
Withholding/Income tax=(Incomes-/+Adjustments-(Deductions+Exemptions)/F)xTax rate-Tax credits/F
413,793 is from 120,000 / (0.29-0) and 19,200 is from 120,000 x (0.45 - 0.29).
Conclusion: The 4 tax brackets, multi tax formulas and xx-page withholding tables can be matched/simplified with the 2 simple brackets/formulas.
* UK Corporate Tax Reform Proposal with Smooth Tax Rate Changes and 2 Brackets
UK has a simple flat corporate tax rate at 19%. USA had 8 tax brackets (15-35%) before 2018, which were too complex, and then has a flat tax rate at 21%, which is too simple and unreasonable. A flat tax rate is very simple. But a flat rate can not cover different taxable incomes and small and large companies reasonably. A nice business tax plan is to have a relatively low bottom tax rate, which can encourage more people to start businesses. Small businesses hire many employees to meet social and economic needs for people and economic development. Then mid and large businesses are more stable and pay relatively higher tax rates. UK corporate tax situations are:
Corporation tax rates:
Financial year 2020-21 Financial year 2021-22 Financial year 2022-23 Financial year 2023-24
Main rate 19% 19% 19% 25%
Small profits rate N/A N/A N/A 19%
Lower threshold N/A N/A N/A £50,000
Upper threshold N/A N/A N/A £250,000
Published 3 March 2021 from www.gov.uk/guidance/corporate-tax
When taxable incomes change from 250,000 to 250,001, tax difference will be 15,000 (250,000 (0.25-0.19)). The £1 can cause £15,000 difference, which is totally unreasonable with "cliff" problem. Two brackets such as 15%-20%-25% with two formulas are suggested to have smooth tax rate change without the cliff problem. Tax rates can be reduced or increased according to budget balance.
Option #1 (17%-19%-22%) Option #2 (15%-20%-25%)
Taxable income (TI) The tax rate and tax Tax rate range The tax rate and tax Tax rate range
Not over $50,000 (YTI÷2,500,000+0.17)×TI 17%-19% (YTI÷1,000,000+0.15)×TI 15%-20%
Over $50,000 (0.22-1,500÷YTI)×TI 19%-22% (0.25-2,500÷YTI)×TI 20%-25%
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Total tax (S=1) = ∑(YTIa÷2,500,000 + 0.17) YTIa) + ∑((0.22 - 1,500÷YTIb) YTIb)
When yearly taxable income is not over 50,000, tax rate is 19% (flat tax rate), which is kept the same. The bottom tax rate can be reduced to such as 17% or 18% to have no tax revenue change according to its fiscal note evaluation. 50,000÷(0.19-0.17) is 2,500,000. 50,000x(0.22-0.19) is 1,500.
When the upper threshold (250,000) in the above corporate tax rates is kept the same and a linear formula is used, the tax cliff from 250,000 to 250,001 can be resolved without the problem for £1 income difference to cause £15,000 tax difference unfairly. Then tax rate changes are smooth.
Option #3 (17%-25%)
Taxable income (TI) The tax rate and tax Tax rate range
Not over $250,000 (YTI÷3,125,000+0.17)×TI 17%-25%
Over $250,000 0.25 25%
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