commercial vat calculation | 9 Exercises

Application: Gourmet House

States :

Maison Gourmande is a pastry shop renowned for its delicious homemade cakes. Currently, they want to review their pricing policy by including taxes in an optimal way. Each sale includes an applicable VAT of 20% on the amount excluding VAT. You are responsible for helping Maison Gourmande better understand and manage the impacts of VAT on their prices. The following information is provided:

• Cost price excluding tax of a cake: €8
• Cost of making per cake: €5
• Selling price including tax for a cake: €15
• Annual quantity sold: 2500 cakes
• Total annual fixed cost: €10

Work to do :

1. What is the selling price excluding tax of a cake?
2. Calculate the unit margin made per cake.
3. Determine the overall margin made by the pastry shop over a year.
4. What is the markup on cakes?
5. Maison Gourmande is considering changing its prices, what would be the sales price excluding tax to reach a 30% markup rate?

Proposed correction:

1. To find the selling price excluding VAT, use the formula: PV excluding VAT = PV including VAT ÷ (1 + VAT).
   PV excluding tax = €15 ÷ (1 + 0,20) = €12,50.
   The selling price excluding tax of a cake is €12,50.

2. The unit margin is calculated by the difference between the selling price excluding tax and the manufacturing cost.
   Unit margin = PV excluding VAT – Cost price excluding VAT = €12,50 – €8 = €4,50.
   The unit margin made per cake is €4,50.

3. The overall margin is the unit margin multiplied by the quantity sold.

Overall margin = Unit margin x Quantity sold = €4,50 x 2500 = €11.
The overall margin achieved by Maison Gourmande over one year is €11.

4. The margin rate is given by the formula: ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€12,50 – €8) ÷ €8) x 100 = 56,25%.
   The margin rate on cakes is 56,25%.

5. To obtain a markup rate of 30%, we use the formula: PV HT = PA HT ÷ (1 – Markup rate).
   PV excluding tax = €8 ÷ (1 – 0,30) = €11,43.
   The selling price excluding VAT should be €11,43 to achieve a mark-up rate of 30%.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV HT = PV TTC ÷ (1 + VAT)
Unit margin	Unit margin = PV excluding VAT – Cost price excluding VAT
Overall margin	Overall margin = Unit margin x Quantity sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Selling price for markup rate	PV HT = PA HT ÷ (1 – Mark rate)

Application: EcoTech Services

States :

ÉcoTech Services is a company specializing in the maintenance of green IT equipment for businesses. In order to optimize their pricing with the changes in VAT, they need advice on the prices excluding and including VAT of their services. The following data is available:

• Maintenance rate per visit (excl. VAT): €120
• Average cost per visit: €75
• Current rate per visit (including tax): unknown
• Number of monthly visits: 300
• Applicable VAT: 20%

Work to do :

1. Calculate the maintenance rate per visit including tax.
2. What unit margin does the company make per visit?
3. Determine the total monthly margin achieved by ÉcoTech Services.
4. Calculate the current mark rate per visit.
5. ÉcoTech is considering offering a promotional rate including tax with a unit margin of €60. What would this new rate including tax be?

Proposed correction:

1. The all-inclusive rate is calculated as follows: PV including VAT = PV excluding VAT x (1 + VAT).
   PV including tax = €120 x (1 + 0,20) = €144.
   The maintenance rate per visit including tax is €144.

2. The unit margin is determined by subtracting the average cost per visit from the price excluding VAT.
   Unit margin = PV excluding tax – Average cost per visit = €120 – €75 = €45.
   The unit margin made per visit is €45.

3. The total monthly margin is calculated by the unit margin multiplied by the number of visits per month.

Total monthly margin = Unit margin x Number of visits = €45 x 300 = €13.
The total monthly margin achieved by ÉcoTech Services is €13.

4. The markup rate is given by the formula: ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((€120 – €75) ÷ €120) x 100 = 37,5%.
   The current mark rate per visit is 37,5%.

5. To obtain a unit margin of €60, we must solve the following formula: New HT + Unit margin = Average cost.
   PV excluding tax = €75 + €60 = €135.
   The promotional rate including tax would be: PV including tax = €135 x (1 + 0,20) = €162.
   The new all-inclusive rate would be €162 to achieve a unit margin of €60.

Formulas Used:

Title	Formulas
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT)
Unit margin	Unit margin = PV excluding tax – Average cost per visit
Total monthly margin	Total monthly margin = Unit margin x Number of visits
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New promotional rate	PV HT + Unit margin = Average cost per visit

Application: Studio Graphix

States :

Studio Graphix is ​​a creative studio specializing in the design of posters and displays for cultural events. They want to revise their pricing structure taking into account the variations in VAT to optimize their profitability. Here is the financial data provided:

• Sale price of a poster (excluding VAT): €30
• Production cost per poster: €18
• Annual quantity sold: 5000 posters
• Standard VAT rate applied: 20%
• Studio Graphix is ​​considering adding a premium range with a sales price including VAT of €50.

Work to do :

1. Calculate the selling price including tax of a standard poster.
2. What is the unit margin achieved by standard poster?
3. Determine the overall annual margin for standard posters.
4. Calculate the margin rate for a standard poster.
5. For the premium range, calculate the selling price excluding VAT.

Proposed correction:

1. Use the formula: PV incl. VAT = PV excl. VAT x (1 + VAT).
   PV including tax = €30 x (1 + 0,20) = €36.
   The sales price including tax for a standard poster is €36.

2. The unit margin is calculated as follows: Unit margin = PV excluding tax – Production cost.
   Unit margin = €30 – €18 = €12.
   The unit margin achieved by standard poster is €12.

3. The annual overall margin is calculated by: Overall margin = Unit margin x Quantity sold.

Overall margin = €12 x 5000 = €60.
The overall annual margin for standard posters is €60.

4. The margin rate is determined by the formula: ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€30 – €18) ÷ €18) x 100 = 66,67%.
   The margin rate for a standard poster is 66,67%.

5. For the premium range with PV including tax = €50, calculate PV excluding tax: PV excluding tax = PV including tax ÷ (1 + VAT).
   PV excluding tax = €50 ÷ (1 + 0,20) = €41,67.
   The selling price excluding VAT for the premium range will be €41,67.

Formulas Used:

Title	Formulas
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT)
Unit margin	Unit margin = PV HT – Production cost
Annual overall margin	Overall margin = Unit margin x Quantity sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Selling price excluding tax	PV HT = PV TTC ÷ (1 + VAT)

Application: Elegant Shop

States :

Boutique ÉléGant is a ready-to-wear company that wants to analyze the impact of VAT on the profitability of its spring collections. Considering current trends, the store offers three types of clothing with specific pricing policies. Here are the details about one of their star products:

• Cost price excluding tax of a dress: €40
• Current selling price excluding VAT of a dress: €75
• Quantity sold in one season: 600 dresses
• The standard VAT rate is 20%.

Work to do :

1. Determine the selling price including tax of a dress.
2. Calculate the unit gross margin per dress.
3. What is the net turnover achieved in one season?
4. Calculate the margin rate per dress.
5. Boutique ÉléGant wants to apply a 40% markup rate for its dresses in its next collection. What would be the new selling price excluding VAT?

Proposed correction:

1. Use the formula: PV incl. VAT = PV excl. VAT x (1 + VAT).
   PV including tax = €75 x (1 + 0,20) = €90.
   The selling price including tax for a dress is €90.

2. The unit gross margin is calculated by: Unit gross margin = PV excluding VAT – Cost price excluding VAT.
   Gross margin per unit = €75 – €40 = €35.
   The gross margin per dress is €35.

3. The net sales figure is given by: Net sales figure = Net sales figure x Quantity sold.

Turnover excluding tax = €75 x 600 = €45.
The net turnover achieved in one season is €45.

4. The margin rate is determined by the formula: ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€75 – €40) ÷ €40) x 100 = 87,5%.
   The margin rate per dress is 87,5%.

5. To obtain a markup rate of 40%, use: PV HT = PA HT ÷ (1 – Markup rate).
   PV excluding tax = €40 ÷ (1 – 0,40) = €66,67.
   The new selling price excluding VAT for the next collection would be €66,67.

Formulas Used:

Title	Formulas
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT)
Unit gross margin	Gross unit margin = PV excluding VAT – Cost price excluding VAT
Turnover excluding tax	Net sales = Net sales x Quantity sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
New selling price excluding VAT	PV HT = PA HT ÷ (1 – Mark rate)

Application: Garden of Delights

States :

Jardin Délices is a company that produces and sells organic fruit wholesale for markets and specialty stores. In order to adapt to taxation and maximize its profits, it wants to review its prices while taking into account the applicable VAT. Here are the details of the operations concerning one of their flagship products, the organic apple:

• Production cost per kilo (excluding VAT): €1,20
• Selling price excluding tax for a kilo of apples: €2,50
• Total sales amount in kilos: 10 kilos
• VAT applicable on the sale of fruit: 5,5%

Work to do :

1. What is the selling price including tax for a kilo of apples?
2. What gross margin do you make per kilo of apples?
3. Determine the total margin for all apple sales.
4. Calculate the margin rate on these apple sales.
5. If Jardin Délices wants to offer a promotional discount that reduces the price including tax by 10%, what would be the new sales price including tax?

Proposed correction:

1. Use of the formula: PV incl. VAT = PV excl. VAT x (1 + VAT).
   PV incl. VAT = €2,50 x (1 + 0,055) = €2,6375, rounded to €2,64.
   The selling price including tax for a kilo of apples is €2,64.

2. The gross margin per kilo is given by: Gross margin = PV excluding tax – Production cost.
   Gross margin = €2,50 – €1,20 = €1,30.
   The gross margin per kilo of apples is €1,30.

3. The total margin is calculated as: Total margin = Gross margin x Total quantity.

Total margin = €1,30 x 10 = €000.
The total margin for all apple sales is €13.

4. The margin rate is extracted from: ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€2,50 – €1,20) ÷ €1,20) x 100 = 108,33%.
   The margin rate for apple sales is 108,33%.

5. For a 10% discount on the price including tax: New PV including tax = PV including tax x (1 – Discount).
   New PV including VAT = €2,64 x (1 – 0,10) = €2,376, rounded to €2,38.
   The new sales price including VAT after the discount is €2,38.

Formulas Used:

Title	Formulas
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT)
Gross margin	Gross margin = PV excluding tax – Production cost
Total margin	Total Margin = Gross Margin x Total Quantity
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
New PV including tax with discount	New PV incl. VAT = PV incl. VAT x (1 – Discount)

Application: Fitness & Fun

States :

Fitness & Fun is a gym that offers standard and premium monthly memberships. With the evolution of tax practices, they want to adjust their pricing policy to optimize their profitability while complying with regulations. Here is the data regarding standard memberships:

• Monthly fee excluding tax for a standard subscription: €45
• Monthly operational cost per subscription: €20
• Number of active standard subscriptions: 200
• VAT rate applicable to sports services: 20%

Work to do :

1. What is the price of the standard subscription including tax?
2. What is the unit margin achieved by standard subscription?
3. Calculate the total monthly margin for standard subscriptions.
4. What is the markup rate for the standard subscription?
5. Fitness & Fun wants to introduce a 15% discount on standard subscriptions for a summer promotion. What would be the new price including VAT?

Proposed correction:

1. The price including tax is calculated with: PV including tax = PV excluding tax x (1 + VAT).
   PV including tax = €45 x (1 + 0,20) = €54.
   The price including tax for the standard subscription is €54.

2. The unit margin is found with: Unit margin = PV HT – Operating cost.
   Unit margin = €45 – €20 = €25.
   The unit margin achieved by standard subscription is €25.

3. The total monthly margin is found by: Total margin = Unit margin x Number of subscriptions.

Total margin = €25 x €200 = €5.
The total monthly margin for standard subscriptions is €5.

4. The markup rate is calculated by: ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((€45 – €20) ÷ €45) x 100 = 55,56%.
   The markup rate for the standard subscription is 55,56%.

5. For a 15% reduction on the price including tax: New PV including tax = PV including tax x (1 – Reduction).
   New PV including VAT = €54 x (1 – 0,15) = €45,90.
   The new price including VAT after the reduction is €45,90.

Formulas Used:

Title	Formulas
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT)
Unit margin	Unit margin = PV HT – Operating cost
Total monthly margin	Total Margin = Unit Margin x Number of Subscriptions
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New PV including VAT with reduction	New PV incl. VAT = PV incl. VAT x (1 – Reduction)

Application: Flavors from Elsewhere

States :

Saveurs d'Ailleurs is a caterer known for its exotic dishes presented at events. With the changes in VAT rates, the company wants to adjust its pricing to maximize its profits while remaining competitive. The following information concerns one of their popular menus:

• Preparation cost per menu excluding tax: €15
• Initial sale price excluding tax for this menu: €30
• VAT rate applied to hotels and restaurants: 10%
• Let’s eat: 50 events per year with an average of 60 menus per event

Work to do :

1. What is the selling price including tax of a menu?
2. What is the unit margin achieved per menu?
3. Calculate the total annual margin for the menu.
4. What would be the margin rate for this menu?
5. To increase its sales, Saveurs d'Ailleurs is considering increasing the markup rate to 50%. What should the new selling price excluding tax be?

Proposed correction:

1. The price including tax is determined by: PV including tax = PV excluding tax x (1 + VAT).
   PV including tax = €30 x (1 + 0,10) = €33.
   The selling price including tax for a menu is €33.

2. The unit margin is obtained by: Unit margin = PV excluding tax – Preparation cost.
   Unit margin = €30 – €15 = €15.
   The unit margin made per menu is €15.

3. The total annual margin is: Total margin = Unit margin x Total number of menus.

Total margin = €15 x (50 x 60) = €45.
The total annual margin for the menu is €45.

4. The margin rate is given by: ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€30 – €15) ÷ €15) x 100 = 100%.
   The margin rate for this menu is 100%.

5. To achieve a 50% markup rate, use: PV HT = PA HT ÷ (1 – Markup Rate).
   PV excluding tax = €15 ÷ (1 – 0,50) = €30.
   But since the new markup rate is clear, the price remains fair at €30 for this case.

Formulas Used:

Title	Formulas
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT)
Unit margin	Unit margin = PV excluding tax – Preparation cost
Total annual margin	Total Margin = Unit Margin x Total Number of Menus
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
New selling price excluding VAT	PV HT = PA HT ÷ (1 – Mark rate)

Application: Botanical Elixir

States :

Elixir Botanique is a natural cosmetics company, renowned for its creams based on essential oils. The management wishes to review its current pricing policy in order to maximize both competitiveness and profitability. The objective is to optimize the prices excluding and including tax with respect to taxation. Here are the details:

• Cost of manufacturing a cream excluding tax: €10
• Initial sale price excluding tax of a cream: €25
• Annual sales: 15 creams
• VAT rate on cosmetics: 20%

Work to do :

1. What would be the sales prices including tax for the creams?
2. Determine the unit profit made per sale.
3. Calculate the total annual margin for the sale of creams.
4. What would be the markup rate applied?
5. Elixir Botanique wants to introduce a seasonal discount of 5% on the price including VAT. What would be the selling price after discount?

Proposed correction:

1. The sales price including VAT is calculated by: VAT inclusive = VAT exclusive x (1 + VAT).
   PV including tax = €25 x (1 + 0,20) = €30.
   The selling price of the creams including tax is €30.

2. The unit profit per sale is: Unit profit = PV excluding tax – Manufacturing cost.
   Unit profit = €25 – €10 = €15.
   The unit profit made per sale is €15.

3. The annual margin is calculated by: Total annual margin = Unit profit x Annual sales volume.

Total annual margin = €15 x €15 = €000.
The total annual margin for the sale of creams is €225.

4. The mark rate is extracted through: ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((€25 – €10) ÷ €25) x 100 = 60%.
   The applied markup rate is 60%.

5. In the event of a 5% discount on the price including tax, we calculate: New PV including tax = PV including tax x (1 – Discount).
   New PV including VAT = €30 x (1 – 0,05) = €28,50.
   The sale price after discount is €28,50.

Formulas Used:

Title	Formulas
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT)
Unit profit	Unit profit = PV excluding tax – Manufacturing cost
Total annual margin	Total Annual Margin = Unit Profit x Annual Sales Volume
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New PV including tax after discount	New PV incl. VAT = PV incl. VAT x (1 – Discount)

Application: VéloVif

States :

VéloVif is a bicycle repair and rental workshop. To better retain its customers, the company is working on a more attractive offer by taking into account regional VAT changes and maximizing its profitability. In particular, they offer a special revision with the following elements:

• Cost of the revision excluding tax: €50
• Initial sale price excluding VAT for the revision: €95
• Number of annual revisions: 1
• VAT rate applicable to mechanical services: 10%

Work to do :

1. Calculate the sales price including tax for this revision.
2. What is the profit per revision?
3. What is the total annual margin achieved for revision services?
4. Calculate the margin rate.
5. Considering a loyalty discount, what would be the sales price including tax if an 8% discount is applied?

Proposed correction:

1. Calculate the price including VAT: PV including VAT = PV excluding VAT x (1 + VAT).
   PV including tax = €95 x (1 + 0,10) = €104,50.
   The sales price including tax for this revision is €104,50.

2. The profit per revision is found by: Profit = PV excluding VAT – Cost excluding VAT.
   Profit = €95 – €50 = €45.
   The profit per revision is €45.

3. The total annual margin corresponds to: Total margin = Profit x Number of annual revisions.

Total margin = €45 x 1 = €200.
The total annual margin achieved for the revision services is €54.

4. The margin rate is given by the formula: ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€95 – €50) ÷ €50) x 100 = 90%.
   The margin rate is 90%.

5. For an 8% loyalty discount, calculate: New PV incl. VAT = PV incl. VAT x (1 – Discount).
   New PV including VAT = €104,50 x (1 – 0,08) = €96,14.
   The sales price including tax after discount is €96,14.

Formulas Used:

Title	Formulas
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT)
Profit	Profit = PV excluding VAT – Cost excluding VAT
Total annual margin	Total Margin = Profit x Number of Annual Revisions
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
New PV including tax after discount	New PV incl. VAT = PV incl. VAT x (1 – Discount)