Inclusive and exclusive Tax rate

mathematically, 25% income tax out of $100 income yields same 33% sales tax on $75 purchase.

tax rates can presented differently due differing definitions of tax base, can make comparisons between tax systems confusing.

some tax systems include taxes owed in tax base (tax-inclusive, before tax), while other tax systems not include taxes owed part of base (tax-exclusive, after tax). in united states, sales taxes quoted exclusively , income taxes quoted inclusively. majority of europe, value added tax (vat) countries, include tax amount when quoting merchandise prices, including goods , services tax (gst) countries, such australia , new zealand. however, countries still define tax rates on tax exclusive basis.

for direct rate comparisons between exclusive , inclusive taxes, 1 rate must manipulated other. when tax system imposes taxes on income, tax base household s pre-tax income. appropriate income tax rate applied tax base calculate taxes owed. under formula, taxes paid included in base on tax rate imposed. if individual s gross income $100 , income tax rate 20%, taxes owed equals $20.

the income tax taken off top , individual left $80 in after-tax money. tax laws impose taxes on tax base equal pre-tax portion of s price. unlike income tax example above, these taxes not include actual taxes owed part of base. priced @ $80 25% exclusive sales tax rate yields $20 in taxes owed. since sales tax added on top , individual pays $20 of tax on $80 of pre-tax goods total cost of $100. in either case, tax base of $100 can treated 2 parts—$80 of after-tax spending money , $20 of taxes owed. 25% exclusive tax rate approximates 20% inclusive tax rate after adjustment. including taxes owed in tax base, exclusive tax rate can directly compared inclusive tax rate.

inclusive income tax rate comparison exclusive sales tax rate:


let



t


{\displaystyle t}

income tax rate. 20% rate,



t
=
0.20


{\displaystyle t=0.20}


let



a


{\displaystyle a}

rate in terms of sales tax.
let



p


{\displaystyle p}

price of (including tax).


the revenue go government:








t
×
p


{\displaystyle t\times p}






the revenue remaining seller of good:








p
−
t
×
p


{\displaystyle p-t\times p}






to convert tax, divide money going government money company nets:








a
=



t
×
p


p
−
t
×
p



=


t

1
−
t





{\displaystyle a={\frac {t\times p}{p-t\times p}}={\frac {t}{1-t}}}






therefore, adjust inclusive tax rate of exclusive tax rate, divide given rate 1 minus rate.


15% inclusive = 18% exclusive
20% inclusive = 25% exclusive
25% inclusive = 33% exclusive
33% inclusive = 50% exclusive
50% inclusive = 100% exclusive




^ bachman, paul; haughton, jonathan; kotlikoff, laurence j.; sanchez-penalver, alfonso; tuerck, david g. (november 2006). taxing sales under fairtax – rate works? (pdf). beacon hill institute. tax analysts. retrieved 2007-04-24.