commercial calculation exercises bac pro commerce pdf | 9 Exercises

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Application: At the Delights of the Gourmet

States :

The bakery-pastry shop "Aux Délices du Gourmet" wants to analyze its croissant sales. Each croissant has a retail price (excluding tax) of €1,50. The cost of goods sold (excluding tax) for making each croissant is €0,90. The bakery sells an average of 3,000 croissants per month.

Work to do :

1. Calculate the unit margin made on each croissant sold.
2. Determine the overall monthly margin achieved.
3. Find the margin rate of croissants.
4. Calculate the markup rate of croissants.
5. If the bakery wants to increase the unit margin by 10%, what should the new selling price excluding VAT be?

Proposed correction:

1. The unit margin is calculated by subtracting the purchase cost excluding tax (PA HT) from the sale price excluding tax (PV HT).
   So, Unit Margin = €1,50 – €0,90 = €0,60.
   Thus, the bakery makes a margin of €0,60 per croissant sold.

2. The monthly overall margin is obtained by multiplying the unit margin by the quantity sold monthly.
   Total margin = €0,60 x €3 = €000.
   The monthly margin made on the sale of croissants is €1.

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

Margin rate = ((€1,50 – €0,90) ÷ €0,90) x 100 = 66,67%.
The margin rate for croissants is 66,67%.

4. The markup rate is calculated using the formula ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((€1,50 – €0,90) ÷ €1,50) x 100 = 40%.
   The markup rate for croissants is therefore 40%.

5. To increase the unit margin by 10%, we need to add 10% to the current margin:
   New margin = €0,60 + (€0,60 x 0,10) = €0,66.
   New PV HT = PA HT + New margin = €0,90 + €0,66 = €1,56.
   The new selling price excluding VAT should be €1,56 to achieve this objective.

Formulas Used:

Application: Tech Innovate

States :

The company "Tech Innovate" sells smartphones. The retail price of a smartphone is €800 excluding tax, and the purchase cost excluding tax is €600. They sold 500 units last month. Tech Innovate wants to understand its financial indicators.

Work to do :

1. Calculate the unit margin for each smartphone sold.
2. Determine the overall margin for the last month.
3. Calculate the margin rate for smartphones.
4. Find the markup rate of smartphones.
5. What should the selling price be excluding tax to obtain a margin rate of 40%?

Proposed correction:

1. The unit margin is equal to the difference between the PV HT and the PA HT.
   Unit margin = €800 – €600 = €200.
   “Tech Innovate” makes a profit margin of €200 per smartphone.

2. The overall margin is found by multiplying the unit margin by the number of units sold:
   Overall margin = €200 x 500 = €100.
   The overall margin for the last month is €100.

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

Margin rate = ((€800 – €600) ÷ €600) x 100 = 33,33%.
The margin rate is 33,33%.

4. For the markup rate, the formula is ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((€800 – €600) ÷ €800) x 100 = 25%.
   The markup rate is 25%.

5. For a margin rate of 40%, we use the formula PV HT = PA HT x (1 + Target margin rate).
   PV excluding tax = €600 x (1 + 0,40) = €840.
   The selling price excluding tax should be €840 to achieve a margin rate of 40%.

Formulas Used:

Application: Fashion and Creation

States :

The "Fashion and Creation" boutique sells handbags at a retail price of €120 (excluding VAT) and acquires them at a purchase price of €75 (excluding VAT). During the last quarter, 200 bags were sold. Management wishes to adjust its sales strategies.

Work to do :

1. Calculate the unit margin of each handbag.
2. Determine the overall margin for the last quarter.
3. Calculate the margin rate of handbags.
4. What would the pre-tax selling price be if "Mode et Création" wanted to apply a 30% markup?
5. Analyze the impact of a 10% increase in purchasing cost on unit margin.

Proposed correction:

1. The unit margin is the difference between the PV HT and the PA HT.
   Unit margin = €120 – €75 = €45.
   Each bag sold generates a margin of €45.

2. The overall margin is calculated by multiplying the unit margin by the number sold.
   Overall margin = €45 x 200 = €9.
   In total, the margin achieved over the quarter is €9.

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

Margin rate = ((€120 – €75) ÷ €75) x 100 = 60%.
The margin rate applied is 60%.

4. To obtain a markup rate of 30%, we apply the formula PV HT = PA HT ÷ (1 – Markup rate).
   PV excluding tax = €75 ÷ (1 – 0,30) = €107,14.
   The selling price excluding tax must be €107,14.

5. With a 10% increase in the PA HT:
   New PA excluding tax = €75 + (€75 x 0,10) = €82,50.
   New unit margin = €120 – €82,50 = €37,50.
   The increase in cost reduces the unit margin to €37,50.

Formulas Used:

Application: EcoVoyages

States :

The travel agency "EcoVoyages" offers luxury vacation packages for a list price of €3,500 (excluding VAT). The direct cost of a trip is €2,500. They sold 50 trips this quarter. The agency wants to analyze its financial performance to optimize its profitability.

Work to do :

1. Calculate the unit margin per stay sold.
2. Estimate the overall margin for the quarter.
3. Determine the margin rate of the stays.
4. Calculate the markup rate of stays.
5. If the goal is to achieve an overall margin of €60, how many stays will they have to sell?

Proposed correction:

1. The unit margin is calculated by subtracting the cost of a stay from the selling price:
   Unit margin = €3 – €500 = €2.
   The agency makes a margin of €1 for each stay.

2. The overall margin is obtained by multiplying the unit margin by the number of stays sold:
   Overall margin = €1 x 000 = €50.
   For this quarter, the overall margin is therefore €50.

3. The margin rate is given by ((PV HT – PA HT) ÷ PA HT) x 100.

Margin rate = ((€3 – €500) ÷ €2) x 500 = 2%.
The margin rate on stays is 40%.

4. The markup rate is calculated with ((PV HT – PA HT) ÷ PV HT) x 100.
   Markup rate = ((€3 – €500) ÷ €2) x 500 = 3%.
   Therefore, the markup rate is 28,57%.

5. To obtain an overall margin of €60, we use the formula Number of stays = Target margin ÷ Unit margin.
   Number of stays = €60 ÷ €000 = 1.
   The agency must sell 60 stays to reach this margin target.

Formulas Used:

Application: BioSanté Plus

States :

BioSanté Plus sells dietary supplements. Each bottle has a retail price of €60 (excluding VAT) and a purchase cost of €40 (excluding VAT). In one month, they sold 800 bottles. The company is looking to refine its sales strategies.

Work to do :

1. Calculate the unit margin per bottle of supplement sold.
2. Determine the overall monthly margin.
3. Calculate the margin rate for these bottles.
4. Calculate the required selling price excluding tax for a markup rate of 35%.
5. What variation in the net selling price is necessary to increase the unit margin by 25%?

Proposed correction:

1. The unit margin is calculated as follows: PV HT – PA HT.
   Unit margin = €60 – €40 = €20.
   The unit margin is therefore €20 per bottle.

2. The overall monthly margin is obtained by multiplying the unit margin by the number of bottles sold:
   Overall margin = €20 x 800 = €16.
   Thus, the overall monthly margin amounts to €16.

3. To calculate the margin rate: ((PV HT – PA HT) ÷ PA HT) x 100.

Margin rate = ((€60 – €40) ÷ €40) x 100 = 50%.
The margin rate on bottles is 50%.

4. To obtain a markup rate of 35%, use the formula PV HT = PA HT ÷ (1 – Markup rate).
   PV excluding tax = €40 ÷ (1 – 0,35) = €61,54.
   The required selling price excluding VAT is €61,54.

5. To increase the unit margin by 25%: New Margin = Current Margin x (1 + 0,25).
   New margin = €20 x 1,25 = €25.
   New PV HT = PA HT + New margin = €40 + €25 = €65.
   The selling price must increase to €65 to achieve this 25% increased margin.

Formulas Used:

Application: Green Wheels

States :

Green Wheels is a company specializing in the sale of electric bicycles. A bicycle is sold for €1,200 excluding VAT, with a purchase cost of €800 excluding VAT. It sold 150 bicycles during the last six months. The company is considering revising its pricing strategy.

Work to do :

1. Calculate the unit margin for each bike sold.
2. Determine the overall margin over the semester.
3. Calculate the margin rate applied.
4. What would be the new selling price excluding tax to obtain an overall margin of €70?
5. Analyze the strategic impact of a 5% reduction in the net selling price on the unit margin.

Proposed correction:

1. Unit margin = PV HT – PA HT.
   Unit margin = €1 – €200 = €800.
   Each bike generates a margin of €400.

2. Overall margin = Unit margin x quantity sold.
   Overall margin = €400 x 150 = €60.
   The overall margin achieved during the semester is €60.

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

Margin rate = ((€1 – €200) ÷ €800) x 800 = 100%.
The margin rate is 50%.

4. To reach an overall margin of €70, the selling price must be adjusted:
   Number of bikes x New margin = €70.
   New unit margin = €70 ÷ 000 = €150.
   New PV HT = PA HT + New unit margin = €800 + €466,67 = €1.
   The price should be €1.

5. Impact of a 5% reduction on the PV HT:
   New PV excluding tax = €1 x (200 – 1) = €0,05.
   New unit margin = €1 – €140 = €800.
   The unit margin decreases to €340.

Formulas Used:

Application: Chocolatey Sweetness

States :

The "Douceur Chocolatée" chocolate shop sells boxes of chocolates for €25 excluding VAT, with a production cost of €15 excluding VAT. In November, 400 boxes were sold. The chocolate shop is considering implementing a promotion.

Work to do :

1. Calculate the unit margin on each box of chocolate.
2. Determine the overall margin achieved in November.
3. What is the current margin rate for a box of chocolate?
4. What will be the promotional PV excluding tax to achieve a margin of €12 per box?
5. Discuss the impact this promotion might have on brand perception.

Proposed correction:

1. Unit margin = PV HT – PA HT.
   Unit margin = €25 – €15 = €10.
   Each box generates a margin of €10.

2. Overall margin = Unit margin x quantity sold.
   Overall margin = €10 x 400 = €4.
   The overall margin for November is €4.

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

Margin rate = ((€25 – €15) ÷ €15) x 100 = 66,67%.
The margin rate applied is 66,67%.

4. To obtain a margin of €12, the PV excluding tax must be adjusted:
   Promotional PV excluding VAT = Cost + Target margin = €15 + €12 = €27.
   The new sale price during the promotion should be €27.

5. A price-cutting promotion could increase accessibility, but it could also position the brand as a less premium option, reducing the perception of quality among discerning consumers. A careful strategy on perceived impact is crucial.

Formulas Used:

Application: InnovTech Solutions

States :

InnovTech Solutions sells professional software for €2,400 excluding VAT, with a development cost of €1,500. During this quarter, 80 licenses were sold. The company wishes to analyze its profitability.

Work to do :

1. Determine the unit margin for each software sold.
2. Evaluate the overall margin for the quarter.
3. Calculate the margin rate for software.
4. What would be the selling price excluding tax for a 20% improvement in the unit margin?
5. Analyze how this price increase may influence the position of "InnovTech Solutions" in the market.

Proposed correction:

1. Unit margin = PV HT – PA HT.
   Unit margin = €2 – €400 = €1.
   A margin of €900 per software is achieved.

2. Overall margin = Unit margin x quantity sold.
   Overall margin = €900 x 80 = €72.
   The overall margin for the quarter is €72.

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

Margin rate = ((€2 – €400) ÷ €1) x 500 = 1%.
The margin rate for software is 60%.

4. For a 20% increase in unit margin:
   New unit margin = €900 x 1,20 = €1.
   New PV excluding tax = Cost + New unit margin = €1 + €500 = €1.
   The PV excluding tax must be €2.

5. A price increase might initially increase margins, but it also risks slowing sales, especially when faced with competitors offering lower prices. InnovTech must therefore balance its strategy between brand image and accessibility to maximize its presence on the market.

Formulas Used:

Application: GymFit

States :

GymFit offers annual gym memberships for €700 excluding VAT, with an operating cost of €300 per client. Last year, 300 memberships were sold. The management team wants to adjust its prices.

Work to do :

1. Calculate the unit margin for each subscription.
2. Determine the overall margin achieved over the year.
3. Calculate the margin rate applied for each subscription.
4. What price changes can be considered to achieve a unit margin of €500?
5. Evaluate the impact of a 10% cost increase on the margin rate if the subscription price remains the same.

Proposed correction:

1. Unit margin = PV HT – PA HT.
   Unit margin = €700 – €300 = €400.
   A margin of €400 per subscription is obtained.

2. Overall margin = Unit margin x number of subscriptions.
   Overall margin = €400 x 300 = €120.
   Thus, GymFit made a margin of €120 this year.

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

Margin rate = ((€700 – €300) ÷ €300) x 100 = 133,33%.
The margin rate for each subscription is 133,33%.

4. For a unit margin of €500:
   New PA HT = Cost + Target margin = €300 + €500 = €800.
   The subscription price would need to be €800.

5. With a 10% increase in cost:
   New cost = €300 x 1,10 = €330.
   New margin rate = ((€700 – €330) ÷ €330) x 100 = 112,12%.
   With this increase, the margin rate drops to 112,12%.

Formulas Used:

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