commercial calculation exercises second bac pro | 9 Exercises

Application: Artisanal Biscuits

States :

Artisanal Biscuits, a small family business, manufactures high-end organic biscuits for specialist shops. The unit purchase price (PP) of a packet of biscuits is €3, while the sales price (SP) excluding tax is €5. The sales manager wants to understand the margins and profitability of his products in more detail.

Work to do :

1. Calculate the margin rate for each pack of biscuits sold.

2. Determine the markup rate for these cookies.

3. If the company wants to make a margin of €3,5 per pack, at what price excluding tax should it sell them?

4. Calculate the turnover excluding tax if the company sells 2000 packets of biscuits.

5. Analyze the impact of a 10% increase in purchasing cost on unit margin, without increasing the selling price.

Proposed correction:

1. To calculate the margin rate, we use the formula:
   Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
   Substituting, ((5 – 3) ÷ 3) x 100 = 66,67%
   The margin rate for each packet of biscuits sold is 66,67%.

2. For the markup rate, we use the formula:
   Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
   Substituting, ((5 – 3) ÷ 5) x 100 = 40%
   The markup rate for these biscuits is 40%.

3. The formula to obtain a specific margin is:

PV HT = PA HT + Desired margin
Replacing, 3 + 3,5 = €6,5
To obtain a margin of €3,5 per pack, the price excluding tax would have to be €6,5.

4. Net sales = Net sales x Quantity sold
   Replacing, 5 x 2000 = €10
   The turnover excluding tax would be €10 if the company sells 000 packs.

5. Increased purchase cost = PA HT x 1,10
   New PA = 3 x 1,10 = €3,30
   New unit margin = PV HT – New PA
   5 – 3,30 = 1,70 €
   A 10% increase in the purchase cost reduces the unit margin to €1,70 per pack.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
Calculation of PV HT	PA HT + Desired margin
Turnover excluding tax	PV HT x Quantity sold
Increase in purchase cost	PA HT x 1,10

Application: Futuristik lighting

States :

Luminaire Futuristik, a company specializing in innovative lighting accessories, sells LED lamps to DIY stores. The sales price excluding tax for a lamp is €90, and the purchase price is set at €50. The management team wants to analyze their financial performance and is considering increasing the price.

Work to do :

1. Determine the brand rate of the LED lamp.

2. Calculate the unit margin made by Luminaire Futuristik on each lamp sold.

3. If the company decides to apply a 15% increase on the selling price while keeping the same purchase cost, what will the new margin rate be?

4. Calculate the total profit on selling 400 LED lights.

5. Discuss the implications of a general increase in production costs on the overall profitability of the company.

Proposed correction:

1. Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
   Substituting, ((90 – 50) ÷ 90) x 100 = 44,44%
   The mark rate of LED lamp is 44,44%.

2. Unit margin = PV excluding tax – PA excluding tax
   Replacing, 90 – 50 = €40
   The unit margin made per lamp sold is €40.

3. New PV HT = PV HT x 1,15

Replacing, 90 x 1,15 = €103,50
New margin rate = ((103,50 – 50) ÷ 50) x 100 = 107%
The new margin rate after the increase would be 107%.

4. Total Profit = Unit Margin x Quantity Sold
   Replacing, 40 x 400 = €16
   The total profit on the sale of 400 LED lamps is €16.

5. A general increase in production costs would lead to a decrease in margins if sales prices are not adjusted. This could, in the long term, affect the overall profitability of the company if it fails to pass on these additional costs to its customers.

Formulas Used:

Title	Formulas
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
Unit margin	PV HT – PA HT
New PV HT calculation	PV HT x 1,15
New margin rate	((New PV HT – PA HT) ÷ PA HT) x 100
Total profit	Unit margin x Quantity sold

Application: Vertine Eco-Friendly Clothing

States :

Vertine, a company that makes clothing from organic materials, is looking to improve its price positioning. The cost of making a t-shirt is €15, and they currently sell it for €30 excluding tax. Faced with competition, they are considering revising their prices and margins.

Work to do :

1. Calculate Vertine's current margin rate for a t-shirt.

2. If Vertine wants a 50% markup rate, what should the new selling price excluding tax be?

3. What would be the impact on the unit margin if Vertine increased its selling price by €5 while keeping the purchase price constant?

4. Estimate the turnover needed to make a profit of €18, knowing that the unit margin is €000.

5. Analyze how a 10% downward price variation could affect customer perception of product quality.

Proposed correction:

1. Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
   Substituting, ((30 – 15) ÷ 15) x 100 = 100%
   Vertine's current margin rate for a t-shirt is 100%.

2. To obtain a markup rate of 50%, we use the formula:
   PV HT = PA HT ÷ (1 – Mark rate)
   By replacing, 15 ÷ (1 – 0,50) = €30
   For a markup rate of 50%, the selling price excluding tax should be €30.

3. New unit margin = (PV HT + 5) – PA HT

Replacing, (30 + 5) – 15 = €20
With an increase of €5, the unit margin would increase to €20.

4. Required turnover = Desired profit ÷ Unit margin
   Substituting, 18 ÷ 000 = 15 units
   Vertine would need to achieve a turnover of 1 units to sell to achieve this profit.

5. A 10% price cut could potentially reduce the perception of product quality, as customers might associate low cost with lower quality. However, a strategic price cut could also increase sales volumes.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Calculation for target mark rate	PA HT ÷ (1 – Mark rate)
New unit margin	(PV HT + Increase) – PA HT
Necessary turnover	Desired Profit ÷ Unit Margin

Application: SoinCap, Hair products

States :

SoinCap, a company specializing in high-end hair products, offers a range of shampoos at competitive prices. A bottle is sold at the price of €8 excluding VAT, while its manufacturing cost is €4,50. The company strives to maximize its profitability while maintaining its market share.

Work to do :

1. Calculate the profit margin (in euros) for each bottle sold.

2. Evaluate the company's current margin rate for this product.

3. If manufacturing costs increase by 10%, what will the new selling price have to be to maintain the same unit margin?

4. Calculate the sales volume in units needed to reach a turnover of €50.

5. Discuss the strategic implications if the company wants to enter new markets by charging lower prices.

Proposed correction:

1. Profit margin = PV excluding tax – Manufacturing cost
   Replacing, 8 – 4,50 = €3,50
   The profit margin per bottle is €3,50.

2. Margin rate = ((PV HT – Manufacturing cost) ÷ Manufacturing cost) x 100
   Substituting, ((8 – 4,50) ÷ 4,50) x 100 = 77,78%
   The current margin rate for this product is 77,78%.

3. New manufacturing cost = 4,50 x 1,10 = €4,95

New PV excluding tax to maintain the same margin = 4,95 + 3,50 = €8,45
The new selling price will have to be €8,45 to maintain the same margin.

4. Required sales volume = Target sales ÷ Unit sales price
   Substituting, 50,000 ÷ 8 = 6 units
   6 units will need to be sold to reach a turnover of €250.

5. Adopting a lower pricing policy could increase market share by attracting price-sensitive customers. However, it could also compromise profit margins. A well-planned strategy is essential to ensure successful penetration without harming profitability.

Formulas Used:

Title	Formulas
Profit margin	PV HT – Manufacturing cost
Margin rate	((PV HT – Manufacturing cost) ÷ Manufacturing cost) x 100
New manufacturing cost	Manufacturing cost x 1,10
Required sales volume	Target sales ÷ Unit sales price

Application: Gusto Italiano, Local Pizzeria

States :

Gusto Italiano, a popular local pizzeria, offers a Margherita pizza that costs €4 to produce. The company wants to keep prices attractive while ensuring adequate profitability.

Work to do :

1. Evaluate the margin rate if the pizza is sold at €8 excluding tax.

2. Calculate the difference in margin in euros if the sale price is reduced to €7 excluding VAT.

3. If monthly sales reach 1000 units, determine the net sales figure.

4. Propose a new selling price to achieve a 50% markup rate.

5. Analyze the effects of a margin reduction on customer loyalty.

Proposed correction:

1. Margin rate = ((PV HT – Production cost) ÷ Production cost) x 100
   Substituting, ((8 – 4) ÷ 4) x 100 = 100%
   The margin rate is 100%.

2. Margin difference = (Old PV HT – Production cost) – (New PV HT – Production cost)
   Substituting, (8 – 4) – (7 – 4) = €1
   The margin difference is €1 per pizza.

3. Net sales = Net sales x Quantity sold

Replacing, 8 x 1000 = €8
The monthly turnover excluding tax reached €8.

4. New PV HT for a markup rate of 50% = Production cost ÷ (1 – 0,50)
   Replacing, 4 ÷ 0,5 = €8
   For a 50% markup, the price should be €8.

5. A reduction in margin could make the product more accessible but could also affect perceptions of quality. However, by increasing loyalty, the company could compensate with increased sales volume.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – Production cost) ÷ Production cost) x 100
Margin difference	(Old PV HT – Production cost) – (New PV HT – Production cost)
Turnover excluding tax	PV HT x Quantity sold
Calculation for target mark rate	Production cost ÷ (1 – Markup rate)

Application: GreenTech Innovation

States :

GreenTech Innovation develops green technologies for eco-responsible companies. They sell a solar energy kit for €1 excluding taxes, while the cost price is €200. The company is considering new pricing strategies to increase its competitiveness.

Work to do :

1. Calculate the unit profit made on each kit sold.

2. What is the margin rate for this product?

3. If GreenTech Innovation decides to offer a 5% discount on the sale price, what will the new price excluding VAT be?

4. Compare the margin with and without discount, in euros.

5. Discuss how price attractiveness could influence competition in green technologies.

Proposed correction:

1. Unit profit = PV excluding tax – Cost price
   Replacing, 1 – 200 = €800
   The unit profit is €400.

2. Margin rate = ((PV HT – Cost price) ÷ Cost price) x 100
   Substituting, ((1 – 200) ÷ 800) x 800 = 100%
   The margin rate for this product is 50%.

3. New PV HT with discount = PV HT x (1 – Discount)

Substituting, 1 x (200 – 1) = €0,05
After a 5% discount, the new price excluding VAT will be €1.

4. Margin with discount = New PV excluding tax – Cost price
   Replacing, 1 – 140 = €800
   The margin with discount is €340, a difference of €60 compared to the initial margin.

5. An attractive pricing policy could attract more customers, but may also intensify competition in the green technology sector, forcing companies to engage in a price war.

Formulas Used:

Title	Formulas
Unit profit	PV HT – Cost price
Margin rate	((PV HT – Cost price) ÷ Cost price) x 100
Calculation with discount	PV HT x (1 – Discount)
Margin with discount	New PV HT – Cost price

Application: Elite Games

States :

Elite Games, a board game store, is selling a popular game listed at €50 excluding VAT. The retailer's purchase price is €30. With the game's growing popularity, the marketing team is considering the optimal pricing to maximize their profits while ensuring a high sales volume.

Work to do :

1. Determine the gross margin in euros for each unit sold.

2. Calculate the margin rate on this product.

3. What turnover would be achieved if Jeux Elite sells 500 games?

4. If a 10% discount is applied to the sale price, what would be the new price excluding VAT?

5. Analyze the potential impact of the price reduction on brand perception and sales.

Proposed correction:

1. Gross margin = PV HT – PA HT
   Replacing, 50 – 30 = €20
   The gross margin per game sold is €20.

2. Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
   Substituting, ((50 – 30) ÷ 30) x 100 = 66,67%
   The margin rate is 66,67%.

3. Turnover = PV HT x Quantity sold

Replacing, 50 x 500 = €25
The turnover achieved would be €25 for 000 games sold.

4. New price excluding VAT after reduction = PV excluding VAT x (1 – 0,10)
   Replacing, 50 x 0,90 = €45
   The new price excluding VAT applying a 10% reduction would be €45.

5. A price reduction could temporarily increase sales volumes and attract new customers, however, it could potentially affect the premium brand image, leading to knock-on effects on customer loyalty.

Formulas Used:

Title	Formulas
Gross margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Turnover	PV HT x Quantity sold
New price after discount	PV HT x (1 – 0,10)

Application: MusicWave

States :

MusicWave, a company that manufactures headphones, offers a model at €150 excluding VAT, the production cost being €90. Wanting to increase its presence on the market, the company is considering promotional actions.

Work to do :

1. Calculate the unit margin in euros and the margin rate of the helmet model.

2. If a promotion offers a 20% discount on the sale price, what will the new price be excluding VAT?

3. Estimate the turnover generated by the sale of 1000 helmets during the promotional period.

4. Compare the total margin before and after the promotion for 1000 helmets sold.

5. Consider how the price reduction might affect MusicWave's positioning against its competitors.

Proposed correction:

1. Unit margin = PV HT – Production cost
   Replacing, 150 – 90 = €60
   The unit margin is €60.
   Margin rate = ((150 – 90) ÷ 90) x 100 = 66,67%
   The margin rate is 66,67%.

2. New price excluding VAT = PV excluding VAT x (1 – 0,20)
   Replacing, 150 x 0,80 = €120
   The new price after a 20% promotion is €120.

3. Promotional turnover = New price excluding VAT x 1000

Replacing, 120 x 1000 = €120
The turnover with promotion is €120 for 000 helmets.

4. Total margin without promotion = Unit margin x 1000
   Replacing, 60 x 1000 = €60
   Unit margin with promotion = New price excluding tax – Production cost
   120 – 90 = 30 €
   Total margin with promotion = 30 x 1000 = €30
   Before promotion, the total margin is €60, and after, it is €000.

5. A reduction could improve MusicWave's competitiveness against its competitors by increasing its sales volumes. However, it must be careful not to erode its margin significantly while maintaining a high-quality image.

Formulas Used:

Title	Formulas
Unit margin	PV HT – Production cost
Margin rate	((PV HT – Production cost) ÷ Production cost) x 100
New price after promotion	PV HT x (1 – 0,20)
Promotional turnover	New price excluding VAT x Quantity sold
Total margin	Unit margin x Quantity sold

Application: PureNature

States :

PureNature, a natural cosmetics brand, sells a moisturizer for €40 excluding VAT with a production cost of €25. The brand is exploring various strategies to increase its commercial attractiveness while maintaining a sufficient margin.

Work to do :

1. How much profit does PureNature make on each jar sold?

2. Calculate the margin rate for this moisturizer.

3. If the brand decides to increase its price by 10%, what will the new price excluding VAT be?

4. What is the difference in total profit on selling 500 jars with and without this increase?

5. Analyze the viability of the price increase in relation to current trends in the natural cosmetics market.

Proposed correction:

1. Profit per pot = PV HT – Production cost
   Replacing, 40 – 25 = €15
   The profit per pot is €15.

2. Margin rate = ((PV HT – Production cost) ÷ Production cost) x 100
   Substituting, ((40 – 25) ÷ 25) x 100 = 60%
   The margin rate is 60%.

3. New price excluding VAT = PV excluding VAT x 1,10

Replacing, 40 x 1,10 = €44
The new price excluding VAT after the increase is €44.

4. Total profit without increase = Profit per pot x 500
   Replacing, 15 x 500 = €7
   New profit per pot = New price excluding tax – Production cost
   44 – 25 = 19 €
   Total profit with increase = 19 x 500 = €9
   The total profit difference is €2 with the increase.

5. A price increase could improve margins, but it is crucial that it does not exceed market expectations, which are potentially biased towards affordable products. Understanding trends and customer perception of value is essential for a successful strategy.

Formulas Used:

Title	Formulas
Profit per pot	PV HT – Production cost
Margin rate	((PV HT – Production cost) ÷ Production cost) x 100
New price after increase	PV HT x 1,10
Total profit	Profit per jar x Quantity sold