commercial calculations bac pro mcv | 9 Exercises

Application: Birch Delights

States :

Les Délices du Bouleau, a local pastry shop, is looking to expand its sales strategy for the holiday season. It currently sells a Yule log at a tax-free retail price of €25 and is considering lowering the retail price to boost sales. The tax-free purchase cost of this log is €15.

Work to do :

  1. Calculate the current margin rate.
  2. Determine the pre-tax sales price needed to achieve a 30% markup rate.
  3. Imagine that the selling price excluding tax is reduced to €22, describe the impact on the margin rate.
  4. If the company wants to sell 300 units this season, calculate the overall margin at the initial selling price of €25.
  5. Now consider a VAT of 5,5%, what will be the initial sales price including VAT of the log?

Proposed correction:

  1. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100).
    Here: ((25 – 15) ÷ 15) x 100 = 66,67%.
    The current margin rate is 66,67%.

  2. To obtain a markup rate of 30%, we use the formula: PV HT = PA HT ÷ (1 – Markup rate).
    Substituting, 15 ÷ (1 – 0,30) = €21,43.
    The selling price excluding VAT should be €21,43 to achieve a mark-up rate of 30%.

  3. New margin rate = ((PV HT – PA HT) ÷ PA HT) x 100).

That is: ((22 – 15) ÷ 15) x 100 = 46,67%.
The drop to €22 reduces the margin rate to 46,67%.

  1. Overall margin = Unit margin x quantity sold.
    Unit margin = PV HT – PA HT = 25 – 15 = 10 €.
    Overall margin = 10 x 300 = €3.
    The overall margin would be €3 for 000 units sold.

  2. Selling price including tax = PV excluding tax x (1 + VAT rate).
    That is: 25 x (1 + 0,055) = €26,38.
    The initial sales price including tax for the log is €26,38.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV HT for Brand Rate PA HT ÷ (1 – Mark rate)
Overall margin Unit margin x quantity sold
Sales price including tax PV excluding VAT x (1 + VAT rate)

Application: TechGénie

States :

TechGénie, a local distributor of technological gadgets, is questioning the profitability of its new flagship product, the TechX. This gadget has a sales price excluding tax of €120, while its purchase cost excluding tax amounts to €90.

Work to do :

  1. Calculate the current markup rate.
  2. For a desired margin rate of 40%, determine the ideal selling price excluding tax.
  3. If the selling price excluding tax is reduced by 10%, assess the new margin rate.
  4. Determine the overall margin if TechGénie sells 500 units at the initial selling price.
  5. Calculate the sales price including VAT with a VAT rate of 20%.

Proposed correction:

  1. Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100).
    That is: ((120 – 90) ÷ 120) x 100 = 25%.
    The current markup rate is 25%.

  2. For a margin rate of 40%, use: PV HT = PA HT x (1 + Margin rate).
    So: 90 x (1 + 0,40) = €126.
    The ideal selling price excluding tax would be €126.

  3. New PV excluding tax = 120 x (1 – 0,10) = €108.

New margin rate = ((108 – 90) ÷ 90) x 100 = 20%.
The 10% reduction in the net selling price reduces the margin rate to 20%.

  1. Unit margin = PV HT – PA HT = 120 – 90 = 30 €.
    Overall margin = 30 x 500 = €15.
    The overall margin would be €15 for 000 units sold.

  2. Selling price including tax = PV excluding tax x (1 + VAT rate).
    That is: 120 x (1 + 0,20) = €144.
    The sales price including VAT is €144.

Formulas Used:

Title Formulas
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
PV HT for Margin Rate PA HT x (1 + Margin rate)
Selling price after reduction PV HT x (1 – decrease in %)
Overall margin Unit margin x quantity sold
Sales price including tax PV excluding VAT x (1 + VAT rate)

Application: Page-Tournee Bookstore

States :

The Page-Tournée bookstore is organizing a special sale for rare manuscripts. It is offering a book at a sale price of €300 excluding VAT. The acquisition cost excluding VAT of each book is €200.

Work to do :

  1. Evaluate the current margin rate of this work.
  2. Calculate the selling price excluding VAT if the desired markup rate is 35%.
  3. If the selling price is increased by 15%, determine the new impact on the margin rate.
  4. If 50 books are sold at the original price, calculate the overall margin.
  5. Calculate the amount of the price including VAT with a VAT of 5,5%.

Proposed correction:

  1. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100).
    Here: ((300 – 200) ÷ 200) x 100 = 50%.
    The current margin rate is 50%.

  2. For a markup rate of 35%: PV HT = PA HT ÷ (1 – Markup rate).
    So: 200 ÷ (1 – 0,35) = €307,69.
    The selling price excluding VAT for a markup rate of 35% is €307,69.

  3. New PV excluding tax = 300 x (1 + 0,15) = €345.

New margin rate = ((345 – 200) ÷ 200) x 100 = 72,5%.
The 15% price increase pushes the margin rate up to 72,5%.

  1. Unit margin = PV HT – PA HT = 300 – 200 = 100 €.
    Overall margin = 100 x 50 = €5.
    The overall margin for 50 works sold is €5.

  2. Selling price including tax = PV excluding tax x (1 + VAT rate).
    That is: 300 x (1 + 0,055) = €316,50.
    The sales price including VAT is €316,50.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV HT for Brand Rate PA HT ÷ (1 – Mark rate)
Selling price after increase PV HT x (1 + increase in %)
Overall margin Unit margin x quantity sold
Sales price including tax PV excluding VAT x (1 + VAT rate)

Application: The Green Shop

States :

L'Échoppe Verte, an eco-friendly products store, sells reusable bottles at a retail price of €10 excluding VAT, each with a purchase cost of €7 excluding VAT.

Work to do :

  1. Calculate the current sales rate for these bottles.
  2. Find the selling price excluding tax to maintain a margin rate of 20%.
  3. If the selling price drops by €2, what will the new margin rate be?
  4. Assuming 2000 bottles are sold at this price, deduct the overall margin.
  5. By adding 20% ​​VAT, determine the price including VAT.

Proposed correction:

  1. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100).
    That is: ((10 – 7) ÷ 7) x 100 = 42,86%.
    The current margin rate is 42,86%.

  2. PV HT for a margin rate of 20% = PA HT x (1 + Margin rate).
    So: 7 x (1 + 0,20) = €8,40.
    The selling price excluding tax would be €8,40 for a margin of 20%.

  3. New PV excluding tax = 10 – 2 = 8 €.

New margin rate = ((8 – 7) ÷ 7) x 100 = 14,29%.
The €2 drop reduces the margin rate to 14,29%.

  1. Unit margin = 10 – 7 = €3.
    Overall margin = 3 x 2000 = €6.
    The overall margin for 2000 bottles is €6.

  2. Selling price including tax = PV excluding tax x (1 + VAT rate).
    That is: 10 x (1 + 0,20) = €12.
    The selling price including tax for a bottle is €12.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV HT for Margin Rate PA HT x (1 + Margin rate)
New sale price PV HT – drop
Overall margin Unit margin x quantity sold
Sales price including tax PV excluding VAT x (1 + VAT rate)

Application: Fashionnova

States :

Fashionnova, a clothing brand, sells jeans with a retail price excluding VAT of €50, while the purchase cost is €30.

Work to do :

  1. Determine the current markup rate for jeans.
  2. Identify the ideal selling price excluding tax for a margin rate of 60%.
  3. If the selling price increases by €5, what will the new margin rate be?
  4. Calculate the overall margin if 1000 units are sold at the original price.
  5. Applying 20% ​​VAT, find the sales price including VAT.

Proposed correction:

  1. Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100).
    That is: ((50 – 30) ÷ 50) x 100 = 40%.
    The current markup rate is 40%.

  2. For a margin rate of 60%: PV HT = PA HT x (1 + Margin rate).
    So: 30 x (1 + 0,60) = €48.
    The ideal selling price excluding tax would be €48.

  3. New PV excluding tax = 50 + 5 = 55 €.

New margin rate = ((55 – 30) ÷ 30) x 100 = 83,33%.
The increase of €5 brings the margin rate to 83,33%.

  1. Unit margin = 50 – 30 = €20.
    Overall margin = 20 x 1000 = €20.
    The overall margin for 1000 jeans sold is €20.

  2. Selling price including tax = PV excluding tax x (1 + VAT rate).
    That is: 50 x (1 + 0,20) = €60.
    The retail price including tax for a pair of jeans is €60.

Formulas Used:

Title Formulas
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
PV HT for Margin Rate PA HT x (1 + Margin rate)
Selling price after increase PV HT + increase
Overall margin Unit margin x quantity sold
Sales price including tax PV excluding VAT x (1 + VAT rate)

Application: Golden Wheat Bakery

States :

Boulangerie Aux Blés d'Or sells specialty breads at a selling price excluding tax of €3,50, with a purchase cost excluding tax of €2,00 per loaf.

Work to do :

  1. Calculate the margin rate on bread sales.
  2. Describe the selling price excluding VAT required to obtain a markup rate of 40%.
  3. If the selling price is reduced by €0,50, what will the new margin rate be?
  4. Calculate the overall margin if 500 loaves are sold daily for a month (30 days).
  5. Add the 5,5% VAT to determine the sales price including VAT of the bread.

Proposed correction:

  1. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100).
    That is: ((3,50 – 2,00) ÷ 2,00) x 100 = 75%.
    The margin rate on bread sales is 75%.

  2. For a markup rate of 40%: PV HT = PA HT ÷ (1 – Markup rate).
    So: 2,00 ÷ (1 – 0,40) = €3,33.
    The required selling price excluding tax for a markup rate of 40% is €3,33.

  3. New PV excluding tax = 3,50 – 0,50 = 3,00 €.

New margin rate = ((3,00 – 2,00) ÷ 2,00) x 100 = 50%.
The reduction of €0,50 lowers the margin rate to 50%.

  1. Unit margin = 3,50 – 2,00 = €1,50.
    Overall margin = 1,50 x 500 x 30 = €22.
    The overall margin for a month of sales is €22.

  2. Selling price including tax = PV excluding tax x (1 + VAT rate).
    That is: 3,50 x (1 + 0,055) = €3,69.
    The selling price including tax per loaf is €3,69.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV HT for Brand Rate PA HT ÷ (1 – Mark rate)
New sale price PV HT – reduction
Overall margin Unit margin x quantity sold x days
Sales price including tax PV excluding VAT x (1 + VAT rate)

Application: Spark Flowers

States :

Les Fleurs d'Étincelle, a flower shop, is offering a special bouquet at a retail price excluding tax of €30, with a purchase cost excluding tax of €18.

Work to do :

  1. Deduct the current margin rate on this bouquet.
  2. Calculate the selling price excluding tax that you would establish for a markup rate of 25%.
  3. Analyze the new margin rate if the selling price increases by 10%.
  4. If 150 bouquets are sold at the initial rate, calculate the overall margin.
  5. With a VAT of 5,5%, determine the sales price including VAT of the bouquet.

Proposed correction:

  1. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100).
    That is: ((30 – 18) ÷ 18) x 100 = 66,67%.
    The current margin rate on the bouquet is 66,67%.

  2. For a markup rate of 25%: PV HT = PA HT ÷ (1 – Markup rate).
    So: 18 ÷ (1 – 0,25) = €24.
    The selling price excluding VAT for a markup rate of 25% is €24.

  3. New PV excluding tax = 30 x (1 + 0,10) = €33.

New margin rate = ((33 – 18) ÷ 18) x 100 = 83,33%.
A 10% increase raises the margin rate to 83,33%.

  1. Unit margin = 30 – 18 = €12.
    Overall margin = 12 x 150 = €1.
    The overall margin for 150 bouquets sold is €1.

  2. Selling price including tax = PV excluding tax x (1 + VAT rate).
    That is: 30 x (1 + 0,055) = €31,65.
    The sales price including tax for the bouquet is €31,65.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV HT for Brand Rate PA HT ÷ (1 – Mark rate)
Selling price after increase PV HT x (1 + increase in %)
Overall margin Unit margin x quantity sold
Sales price including tax PV excluding VAT x (1 + VAT rate)

Application: Restaurant Le Gourmet Moderne

States :

Le Gourmet Moderne offers a daily special with a cost price excluding tax of €5 and a selling price excluding tax of €12.

Work to do :

  1. What is the margin rate for this dish?
  2. Calculate the selling price excluding tax if the restaurant wants a 50% markup rate.
  3. Let's look at the impact if the selling price is reduced by 20%.
  4. Calculate the overall margin if the restaurant sells 1000 dishes at this initial selling price.
  5. Adding 10% VAT, what is the sales price including VAT?

Proposed correction:

  1. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100).
    So: ((12 – 5) ÷ 5) x 100 = 140%.
    The margin rate for this dish is 140%.

  2. For a markup rate of 50%: PV HT = PA HT ÷ (1 – Markup rate).
    So: 5 ÷ (1 – 0,50) = €10.
    The target selling price excluding VAT for a 50% markup rate is €10.

  3. New PV excluding tax after reduction: 12 x (1 – 0,20) = €9,60.

New margin rate = ((9,60 – 5) ÷ 5) x 100 = 92%.
Reducing it by 20% lowers the margin rate to 92%.

  1. Unit margin = 12 – 5 = €7.
    Overall margin = 7 x 1000 = €7.
    The overall margin for 1000 dishes is €7.

  2. Selling price including tax = PV excluding tax x (1 + VAT rate).
    That is: 12 x (1 + 0,10) = €13,20.
    The sales price including tax for this dish is €13,20.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV HT for Brand Rate PA HT ÷ (1 – Mark rate)
Sale price after reduction PV HT x (1 – reduction in %)
Overall margin Unit margin x quantity sold
Sales price including tax PV excluding VAT x (1 + VAT rate)

Application: FitSanté Clinic

States :

The FitSanté Clinic offers a medical consultation service with an operating cost excluding tax of €30 and a sales price excluding tax of €70.

Work to do :

  1. Calculate the margin rate for this consultation.
  2. Determine the selling price excluding tax to achieve a markup rate of 40%.
  3. If the selling price excluding tax is increased by 15%, what is the new margin rate?
  4. Considering 500 consultations carried out at this price, determine the overall margin.
  5. With a VAT of 20%, what will the sales price including VAT be?

Proposed correction:

  1. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100).
    So: ((70 – 30) ÷ 30) x 100 = 133,33%.
    The margin rate for this consultation is 133,33%.

  2. For a markup rate of 40%: PV HT = PA HT ÷ (1 – Markup rate).
    That is: 30 ÷ (1 – 0,40) = €50.
    The required selling price excluding tax for a markup rate of 40% is €50.

  3. New PV excluding tax = 70 x (1 + 0,15) = €80,50.

New margin rate = ((80,50 – 30) ÷ 30) x 100 = 168,33%.
The 15% increase results in a new margin rate of 168,33%.

  1. Unit margin = 70 – 30 = €40.
    Overall margin = 40 x 500 = €20.
    The overall margin for 500 consultations is €20.

  2. Selling price including tax = PV excluding tax x (1 + VAT rate).
    So: 70 x (1 + 0,20) = €84.
    The sales price including tax for the consultation is €84.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
PV HT for Brand Rate PA HT ÷ (1 – Mark rate)
Selling price after markup PV HT x (1 + increase in %)
Overall margin Unit margin x quantity sold
Sales price including tax PV excluding VAT x (1 + VAT rate)

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