Value Added Tax, VAT: Recalculate Gross Amounts and Prices (With Tax Included), From Original VAT Rates to New Ones. Calculate Net Amounts (Without Tax), the New Gross Amounts and the Values of VAT Tax

Gross Amount = Net Value × (1 + Tax%)

Net Amount = Gross Amount ÷ (1 + Tax%)

Step 1: Calculate the Net Amount (Without Tax)

• Initial Gross Amount = Net Amount + Initial Tax Amount
• Initial Tax Amount = Initial Tax% × Net Amount
• Initial Gross Amount = Net Amount + Initial Tax% × Net Amount = (1 + Initial Tax%) × Net Amount

• Initial Gross Amount = (1 + Initial Tax%) × Net Amount

  In conclusion:

  Net Amount = Initial Gross Amount ÷ (1 + Initial Tax%) =

Step 2: Add the New Tax Amount to the Net Amount

• New Gross Amount = Net Amount + New Tax Amount
• New Tax Amount = New Tax% × Net Amount
• New Gross Amount = Net Amount + New Tax% × Net Amount = (1 + New Tax%) × Net Amount
• In conclusion, New Gross Amount = (1 + New Tax%) × Net Amount = (1 + New Tax%) × Initial Gross Amount ÷ (1 + Initial Tax%) = ^{(1 + New Tax%)}/_{(1 + Initial Tax%)} × Initial Gross Amount

  New Gross Amount = ^{(1 + New Tax%)}/_{(1 + Initial Tax%)} × Initial Gross Amount

Examples of calculations:

• Case 1: Initial Tax Rate = 20%, New Tax Rate = 19%
  
  Step 1, Calculate Net Amount:
  (1 + Initial Tax%) = 1 + 20% = ¹⁰⁰/<sub>100 + ²⁰/100 = ¹²⁰/100 = 1.2 => Initial Gross Amount = 1.2 × Net Amount, and Net Amount = Initial Gross Amount ÷ 1.2
  
  Step 2, Add the New Tax Amount:
  New Gross Amount = (1 + New Tax%) × Net Amount = (1 + 19%) × Net Amount = (¹⁰⁰/100 + ¹⁹/100) × Net Amount = ¹¹⁹/100 × Net Amount = 1.19 × Net Amount = 1.19 × Initial Gross Amount ÷ 1.2 = ^1.19/1.2 × Initial Gross Amount
  Answer: New Gross Amount = (1.19 ÷ 1.2) × Initial Gross Amount</sub>
• Case 2: Initial Tax Rate = 20%, New Tax Rate = 5%
  
  Step 1, Calculate Net Amount:
  (1 + Initial Tax%) = 1 + 20% = ¹⁰⁰/₁₀₀ + ²⁰/₁₀₀ = ¹²⁰/₁₀₀ = 1.2 => Initial Gross Amount = 1.2 × Net Amount, and Net Amount = Initial Gross Amount ÷ 1.2
  
  Step 2, Add the New Tax Amount:
  New Gross Amount = (1 + New Tax%) × Net Amount = (1 + 5%) × Net Amount = (¹⁰⁰/₁₀₀ + ⁵/₁₀₀) × Net Amount = ¹⁰⁵/₁₀₀ × Net Amount = 1.05 × Net Amount = 1.05 × Initial Gross Amount ÷ 1.2 = ^1.05/_1.2 × Initial Gross Amount
  Answer: New Gross Amount = (1.05 ÷ 1.2) × Initial Gross Amount.