commercial-calculations-formula-bac-pro-commerce

commercial calculation formula bac pro commerce | 9 Exercises

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Application: Suzanne's Pastry Shop

States :

Patisserie Suzanne is looking to optimize its price management for its popular fruit tarts. Each tart has a tax-free purchase price of €8 and a tax-free sales price of €12,5.

Work to do :

  1. Calculate the unit margin.
  2. Determine the margin rate.
  3. Evaluate the markup rate.
  4. If Suzanne wants to increase the selling price to achieve a 30% markup, what should the new selling price excluding tax be?
  5. Analyze the impact on sales if the price increases significantly.

Proposed correction:

  1. The unit margin is the difference between the selling price excluding VAT and the purchasing price excluding VAT:
    12,5 € – 8 € = 4,5 €.
    The unit margin is therefore €4,5 per tart.

  2. The margin rate is calculated as follows: ((PV HT – PA HT) ÷ PA HT) x 100.
    Replacing, ((€12,5 – €8) ÷ €8) x 100 = 56,25%.
    The margin rate is 56,25%.

  3. The markup rate is calculated as: ((PV HT – PA HT) ÷ PV HT) x 100.

Replacing, ((€12,5 – €8) ÷ €12,5) x 100 = 36%.
The markup rate is 36%.

  1. To obtain a markup rate of 30%, we use the formula: PV HT = PA HT ÷ (1 – Markup rate).
    Substituting, €8 ÷ (1 – 0,3) = €11,43.
    The new selling price excluding VAT should be €11,43 to achieve a mark-up rate of 30%.

  2. A price increase may reduce demand, especially if customers are price sensitive. Competitor analysis and market research would be necessary to anticipate the precise impact.

Formulas Used:

Title Formulas
Unit Margin PV HT – PA HT
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
New PV HT PA HT ÷ (1 – Mark rate)

Application: Modern Electronics

States :

Modern Electronics, a store specializing in high-tech gadgets, offers a smartphone model with a purchase price of €350 excluding VAT and they sell it for €500 excluding VAT.

Work to do :

  1. Calculate the unit margin on the smartphone.
  2. Determine the margin rate achieved by the company.
  3. Calculate the markup rate.
  4. If the company wants to apply a sales price with a unit margin of €200, what will the new sales price excluding tax be?
  5. Interpret the effect of such a unit margin on the product's brand image.

Proposed correction:

  1. The unit margin is the difference between the selling price excluding VAT and the purchasing price excluding VAT:
    500 € – 350 € = 150 €.
    The unit margin is €150 per smartphone.

  2. The margin rate is calculated by: ((PV HT – PA HT) ÷ PA HT) x 100.
    Replacing, ((€500 – €350) ÷ €350) x 100 = 42,86%.
    The margin rate is 42,86%.

  3. The markup rate is determined by the formula: ((PV HT – PA HT) ÷ PV HT) x 100.

Replacing, ((€500 – €350) ÷ €500) x 100 = 30%.
The markup rate is 30%.

  1. For a unit margin of €200, the calculation of the new PV excluding tax would be: PA excluding tax + Unit margin.
    By replacing, €350 + €200 = €550.
    The new selling price excluding VAT would be €550.

  2. An increase in the unit margin to €200 could position the product as more premium, but it could also become less competitive in terms of price.

Formulas Used:

Title Formulas
Unit Margin PV HT – PA HT
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
New PV HT (margin) PA excluding tax + Unit margin

Application: Escape Mode

States :

Mode Évasion, a clothing retailer, is selling a leather jacket with a purchase price of €70 excluding VAT and a sale price of €120 excluding VAT.

Work to do :

  1. Calculate the unit margin for each jacket sold.
  2. Determine the margin rate.
  3. Calculate the markup rate.
  4. If Mode Évasion wants to offer a 15% discount on the sale price, what will the new sale price excluding tax be?
  5. Discuss the potential impact of this discount on sales and customer retention.

Proposed correction:

  1. The unit margin is obtained by the difference between the selling price excluding tax and the purchase price excluding tax:
    120 € – 70 € = 50 €.
    The unit margin is €50 per jacket.

  2. The margin rate is calculated as follows: ((PV HT – PA HT) ÷ PA HT) x 100.
    ((€120 – €70) ÷ €70) x 100 = 71,43%.
    The margin rate is 71,43%.

  3. The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100.

((€120 – €70) ÷ €120) x 100 = 41,67%.
The markup rate is 41,67%.

  1. For a 15% discount, the new selling price excluding VAT is: PV excluding VAT x (1 – discount).
    Replacing, €120 x (1 – 0,15) = €102.
    The new selling price excluding VAT after discount is €102.

  2. A 15% discount can spur a temporary increase in sales and build customer loyalty, but it's crucial to watch the profit margin.

Formulas Used:

Title Formulas
Unit Margin PV HT – PA HT
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
New PV HT (discount) PV HT x (1 – discount)

Application: Aesthetic Well-being

States :

Bien-être Esthétique receives regular orders for its high-end skin care products. Each treatment is purchased at €25 excluding VAT and sold at €50 excluding VAT in its salons.

Work to do :

  1. Determine the unit margin for a treatment.
  2. Calculate the margin rate offered by this product.
  3. Evaluate the markup rate.
  4. What is the total turnover excluding tax if Bien-être Esthétique sells 200 of these treatments?
  5. Consider the importance of unit margin in determining the positioning of care in the market.

Proposed correction:

  1. The unit margin is calculated by subtracting the pre-tax purchase price from the pre-tax sale price:
    50 € – 25 € = 25 €.
    The unit margin on each treatment is €25.

  2. The margin rate is calculated using the formula: ((PV HT – PA HT) ÷ PA HT) x 100.
    ((€50 – €25) ÷ €25) x 100 = 100%.
    The margin rate is 100%.

  3. The markup rate is calculated as follows: ((PV HT – PA HT) ÷ PV HT) x 100.

((€50 – €25) ÷ €50) x 100 = 50%.
The markup rate is 50%.

  1. The overall turnover excluding tax for 200 treatments is given by: PV excluding tax x quantity sold.
    €50 x 200 = €10.
    The total turnover excluding tax is €10.

  2. Having a good unit margin is crucial for premium positioning, allowing to cover the additional costs of marketing and distribution while delivering a high perceived quality.

Formulas Used:

Title Formulas
Unit Margin PV HT – PA HT
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
Turnover excluding tax PV HT x quantity sold

Application: Integral Sports

States :

Sportif Intégral, a distributor of sports equipment, is selling a pair of shoes for €80 excluding VAT with a purchase price of €50 excluding VAT.

Work to do :

  1. Calculate the unit margin on this pair of shoes.
  2. Determine the margin rate applied by Sportif Intégral.
  3. Evaluate the markup rate.
  4. If the company wants to limit the decline in sales by revising the price to €90 excluding VAT, what will the new unit margin be?
  5. Analyze the potential impact of such a price increase on overall sales.

Proposed correction:

  1. The unit margin is the difference between the selling price excluding VAT and the purchasing price excluding VAT:
    80 € – 50 € = 30 €.
    The unit margin is €30 per pair of shoes.

  2. The margin rate is given by the formula: ((PV HT – PA HT) ÷ PA HT) x 100.
    Applying, ((€80 – €50) ÷ €50) x 100 = 60%.
    The margin rate is 60%.

  3. The markup rate is calculated by: ((PV HT – PA HT) ÷ PV HT) x 100.

((€80 – €50) ÷ €80) x 100 = 37,5%.
The markup rate is 37,5%.

  1. For a new selling price of €90 excluding VAT, the new unit margin would be: €90 – €50 = €40.
    The new unit margin would therefore be €40.

  2. An increase in the selling price could lead to a decrease in sales if customers perceive the prices to be too high compared to the competition, especially if there are no perceived product improvements.

Formulas Used:

Title Formulas
Unit Margin PV HT – PA HT
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
New Unit Margin New PV HT – PA HT

Application: Universal Library

States :

The Librairie Universelle sells a book for €15 excluding VAT, while the purchase price is €9 excluding VAT. It plans to increase its sales as the start of the university year approaches.

Work to do :

  1. Calculate the unit margin made on the sale of each book.
  2. Determine the margin rate.
  3. Evaluate the markup rate.
  4. If the bookstore offers a 10% discount on the sale price, what will be the new sale price excluding tax?
  5. Discuss discount strategy as a way to increase back-to-school sales.

Proposed correction:

  1. The unit margin is the difference between the selling price excluding VAT and the purchasing price excluding VAT:
    15 € – 9 € = 6 €.
    So the unit margin is €6 per book.

  2. The margin rate is calculated as follows: ((PV HT – PA HT) ÷ PA HT) x 100.
    Replacing, ((€15 – €9) ÷ €9) x 100 = 66,67%.
    The margin rate is 66,67%.

  3. The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100.

((€15 – €9) ÷ €15) x 100 = 40%.
The markup rate is 40%.

  1. For a 10% discount, the new selling price excluding VAT is: €15 x (1 – 0,10) = €13,50.
    The new selling price excluding VAT after discount is €13,50.

  2. A discount strategy can be a powerful lever to attract more students, especially during periods of high demand such as the start of the university year, by stimulating sales and increasing the volume sold.

Formulas Used:

Title Formulas
Unit Margin PV HT – PA HT
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
New PV HT (discount) PV HT x (1 – discount)

Application: Gourmet Delights

States :

Délices Gourmands, a boutique selling artisanal chocolates, offers its ballotins at a purchase price excluding tax of €20 and a sale price excluding tax of €35. The boutique is considering diversifying its range.

Work to do :

  1. Calculate the unit margin on each ballotin sold.
  2. Determine the margin rate.
  3. Evaluate the markup rate.
  4. What would be the selling price excluding tax if the company aims for a unit margin of €20?
  5. Analyze the risks associated with product line diversification.

Proposed correction:

  1. The unit margin is calculated by the difference between the selling price excluding VAT and the purchase price excluding VAT:
    35 € – 20 € = 15 €.
    The unit margin is €15 per ballotin.

  2. The margin rate is given by: ((PV HT – PA HT) ÷ PA HT) x 100.
    ((€35 – €20) ÷ €20) x 100 = 75%.
    The margin rate is 75%.

  3. The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100.

((€35 – €20) ÷ €35) x 100 = 42,86%.
The markup rate is 42,86%.

  1. For a target unit margin of €20, the calculation of the net selling price would be: €20 + €20 = €40.
    The desired selling price excluding tax to achieve this margin is €40.

  2. Diversification can strengthen the offering and attract new customers, but it carries risks, including additional production and marketing costs, and can dilute brand image if not carefully planned.

Formulas Used:

Title Formulas
Unit Margin PV HT – PA HT
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
New PV HT (target) Target unit margin + PA HT

Application: Future Technology

States :

Technologie Futur is offering a new laptop with a purchase cost of €800 excluding VAT and a sale price of €1 excluding VAT.

Work to do :

  1. Calculate the unit margin.
  2. Determine the margin rate.
  3. Calculate the markup rate.
  4. What is the total cost price for Technologie Futur if the applicable VAT is 20%?
  5. Consider the effect that new technologies can have on reducing profit margins.

Proposed correction:

  1. The unit margin is: €1 – €200 = €800.
    The unit margin is €400 per computer.

  2. The margin rate is calculated: ((PV HT – PA HT) ÷ PA HT) x 100.
    ((€1 – €200) ÷ €800) x 800 = 100%.
    The margin rate is 50%.

  3. The markup rate is calculated: ((PV HT – PA HT) ÷ PV HT) x 100.

((€1 – €200) ÷ €800) x 1 = 200%.
The markup rate is 33,33%.

  1. The total cost price including VAT: PA HT x (1 + VAT).
    €800 x 1,20 = €960.
    The total cost price with VAT is €960.

  2. New technologies often lead to price reductions as competition increases and innovations become more accessible, which can significantly reduce profit margins.

Formulas Used:

Title Formulas
Unit Margin PV HT – PA HT
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
Cost price with VAT PA HT x (1 + VAT)

Application: Natural Gardens

States :

Jardins Naturels sells gardening kits at a retail price of €45 excluding VAT, with a purchase price excluding VAT of €30. The company wants to expand into the online market.

Work to do :

  1. Calculate the unit margin.
  2. Determine the margin rate.
  3. Calculate the markup rate.
  4. If the company offers a €5 discount on the sale price, what will the new sale price excluding VAT be?
  5. Analyze the challenges that Jardins Naturels might face when marketing its products online.

Proposed correction:

  1. The unit margin is calculated as follows: €45 – €30 = €15.
    The unit margin is €15 per kit.

  2. The margin rate is given by: ((PV HT – PA HT) ÷ PA HT) x 100.
    ((€45 – €30) ÷ €30) x 100 = 50%.
    The margin rate is 50%.

  3. The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100.

((€45 – €30) ÷ €45) x 100 = 33,33%.
The markup rate is 33,33%.

  1. By applying a reduction of €5, the new selling price excluding tax is: €45 – €5 = €40.
    The new selling price excluding VAT will be €40.

  2. Online, Jardins Naturels could face additional costs such as shipping costs, face increased competition, and have to invest in digital marketing to stand out.

Formulas Used:

Title Formulas
Unit Margin PV HT – PA HT
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
Reduced Sale Price PV HT – reduction

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