Commercial and financial calculations in professional baccalaureate | 9 Exercises

Application: Sophie's Delights

States :

Les Délices de Sophie is an artisanal pastry shop that sells various cakes and pastries. In order to improve profitability, the owner Sophie wants to analyze the performance of certain products. Considering a chocolate cake sold for €25 including tax, with a VAT rate of 5,5%, and a production cost of €18 excluding tax per unit, she decides to calculate different commercial and financial indicators.

Work to do :

1. Calculate the sales price excluding tax (HT) of the chocolate cake.
2. Determine the unit margin excluding tax for this product.
3. Calculate the margin rate for the chocolate cake.
4. Determine the net sales figure if Sophie sells 150 units of this cake.
5. Analyze the impact on profitability if the cost of production increases by 10%.

Proposed correction:

1. To calculate the sales price excluding VAT, we must remove the VAT from the price including VAT. The formula is: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €25 ÷ (1 + 0,055) = €23,70.
   The selling price excluding tax of the cake is therefore €23,70.

2. The HT unit margin is calculated using the formula: HT unit margin = HT PV – HT PA.
   As a replacement, €23,70 – €18 = €5,70.
   The unit margin excluding tax is €5,70.

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

Replacing, ((€23,70 – €18) ÷ €18) x 100 = 31,67%.
The margin rate for chocolate cake is 31,67%.

4. The net sales figure for 150 units is calculated by multiplying the net sales price by the quantity sold.
   Replacing, €23,70 x 150 = €3.
   The net turnover for the sale of 150 cakes is €3.

5. If the production cost increases by 10%, the new cost is: PA HT = €18 x (1 + 0,10) = €19,80.
   The new unit margin excluding tax would then be: €23,70 – €19,80 = €3,90.
   An increase in production cost reduces profitability, but the product remains profitable.

Formulas Used:

Title	Formulas
Sale price excl. VAT	PV HT = PV TTC ÷ (1 + VAT rate)
Unit margin excluding tax	Unit margin excluding tax = PV excluding tax – PA excluding tax
Margin rate	Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Turnover	CA HT = PV HT x Quantity sold
Adjusted production cost	New HT PA = HT PA x (1 + Cost increase rate)

Application: TechInno Solutions

States :

TechInno Solutions is an innovative company specializing in the sale of technological gadgets. A new model of smart sensor is launched on the market for €120 excluding VAT. The management is interested in its commercial performance after the sale of 500 units and wants to evaluate several key indicators.

Work to do :

1. Calculate the sales price including VAT of the sensor with a VAT rate of 20%.
2. Determine the overall margin achieved if the manufacturing cost per unit is €80 excluding VAT.
3. Calculate the sensor mark rate.
4. Find the turnover including tax generated by the sale of these 500 units.
5. Discuss the impact on the margin of changing the manufacturing cost to €90 excluding VAT per unit.

Proposed correction:

1. The sales price including tax is calculated using the formula: VAT inclusive price = VAT excluding tax x (1 + VAT rate).
   By replacing, €120 x (1 + 0,20) = €144.
   The sales price including tax of the sensor is therefore €144.

2. The overall margin is calculated by: Overall margin = (PV HT – PA HT) x Quantity sold.
   Replacing, (€120 – €80) x 500 = €20.
   The overall margin achieved is €20.

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

Replacing, ((€120 – €80) ÷ €120) x 100 = 33,33%.
The sensor mark rate is 33,33%.

4. The turnover including tax is given by: CA including tax = PV including tax x Quantity sold.
   Replacing, €144 x 500 = €72.
   The turnover including tax achieved with these 500 units is €72.

5. With a manufacturing cost of €90 excluding VAT, the new unit margin becomes: €120 – €90 = €30.
   The overall margin would then be: €30 x €500 = €15.
   Rising costs reduce overall margins, prompting repricing or improved manufacturing techniques.

Formulas Used:

Title	Formulas
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT rate)
Overall margin	Overall margin = (PV HT – PA HT) x Quantity sold
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Turnover including tax	CA incl. VAT = PV incl. VAT x Quantity sold
New Global Margin	New overall margin = (PV HT – New PA HT) x Quantity sold

Application: FashionFuture

States :

FashionFuture is a fashion start-up specializing in eco-friendly clothing. One of their best-sellers, a recycled denim jacket, sells for €90 including tax. With the VAT rate at 5,5%, and a production cost of €55 excluding tax per jacket, the company wants to analyze its pricing strategy.

Work to do :

1. Calculate the selling price excluding tax of the denim jacket.
2. Determine the unit margin excluding tax for this product.
3. What is the margin rate for the jacket?
4. If 200 jackets are sold, what is the net turnover achieved?
5. Evaluate the implications of a 10% price reduction on turnover including tax.

Proposed correction:

1. The selling price excluding VAT is calculated by: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €90 ÷ (1 + 0,055) = €85,26.
   The selling price excluding tax is therefore €85,26.

2. The HT unit margin is obtained by: HT unit margin = HT PV – HT PA.
   As a replacement, €85,26 – €55 = €30,26.
   The unit margin excluding tax is €30,26.

3. The margin rate is calculated with: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

Replacing, ((€85,26 – €55) ÷ €55) x 100 = 55,02%.
The margin rate for the jacket is 55,02%.

4. The net sales figure for 200 jackets is calculated by: net sales = net sales x quantity sold.
   Replacing, €85,26 x 200 = €17.
   The turnover excluding tax is €17.

5. A 10% price reduction brings the new VAT-inclusive PV to: €90 x (1 – 0,10) = €81.
   The new turnover including tax for 200 jackets is: €81 x 200 = €16.
   The price drop will reduce the turnover including tax, requiring a higher sales volume to compensate.

Formulas Used:

Title	Formulas
Sale price excl. VAT	PV HT = PV TTC ÷ (1 + VAT rate)
Unit margin excluding tax	Unit margin excluding tax = PV excluding tax – PA excluding tax
Margin rate	Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Turnover excluding tax	CA HT = PV HT x Quantity sold
New turnover including tax	New turnover including tax = New PV including tax x Quantity sold

Application: HealthPlus Well-being

States :

SantéPlus Bien-être, a company specializing in the production of food supplements, is offering a new ecological vitamin C available at €30 including tax. With a VAT rate of 5,5% and a production cost of €18 excluding tax per bottle, the company wants to evaluate its commercial performance.

Work to do :

1. What is the selling price excluding tax of the bottle of vitamin C?
2. Calculate the unit margin excluding tax.
3. What is the markup rate for this product?
4. If the company plans to sell 300 bottles, what will the net sales be?
5. How would profitability be affected if the production cost drops to €15 excluding VAT?

Proposed correction:

1. The selling price excluding VAT is calculated as follows: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €30 ÷ (1 + 0,055) = €28,44.
   The selling price excluding VAT of the bottle is €28,44.

2. The HT unit margin is given by: HT unit margin = HT PV – HT PA.
   As a replacement, €28,44 – €18 = €10,44.
   The unit margin excluding tax is €10,44.

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

Replacing, ((€28,44 – €18) ÷ €28,44) x 100 = 36,70%.
The markup rate for the bottle is 36,70%.

4. The net sales figure for 300 bottles is given by: Net sales = Net sales x Quantity sold.
   Replacing, €28,44 x 300 = €8.
   The turnover excluding tax will be €8.

5. With a production cost reduced to €15 excluding VAT, the unit margin becomes: €28,44 – €15 = €13,44.
   This cost reduction would improve unit profitability without adjusting the selling price.

Formulas Used:

Title	Formulas
Sale price excl. VAT	PV HT = PV TTC ÷ (1 + VAT rate)
Unit margin excluding tax	Unit margin excluding tax = PV excluding tax – PA excluding tax
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Turnover excluding tax	CA HT = PV HT x Quantity sold
New Unit Margin	New unit margin = PV HT – New PA HT

Application: EduTech Academy

States :

EduTech Academy, a company specializing in the manufacture of educational tablets, decides to launch a new model at a price of €200 including VAT with a VAT rate of 20%. The production cost per unit is €160 excluding VAT. They want to analyze the financial performance of this new product.

Work to do :

1. Calculate the selling price excluding VAT of the tablet.
2. Determine the unit margin excluding tax for this model.
3. Calculate the margin rate for the tablet.
4. If the company plans to sell 1 units, what will be the net sales?
5. Discuss the impact of an increase in the production cost to €170 excluding VAT on the unit margin.

Proposed correction:

1. For the selling price excluding VAT, we have: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €200 ÷ (1 + 0,20) = €166,67.
   The selling price of the tablet excluding VAT is €166,67.

2. The HT unit margin is calculated as follows: HT unit margin = HT PV – HT PA.
   As a replacement, €166,67 – €160 = €6,67.
   The unit margin excluding tax is €6,67.

3. The margin rate is calculated with: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

Replacing, ((€166,67 – €160) ÷ €160) x 100 = 4,17%.
The margin rate for the tablet is 4,17%.

4. The net sales figure for 1 units is calculated as: Net sales = Net sales x Quantity sold.
   By replacing, €166,67 x €1 = €000.
   The turnover excluding tax will be €166.

5. With a production cost of €170 excluding VAT, the new unit margin becomes: €166,67 – €170 = -€3,33.
   This increase would result in a negative unit margin, losing money on each unit sold.

Formulas Used:

Title	Formulas
Sale price excl. VAT	PV HT = PV TTC ÷ (1 + VAT rate)
Unit margin excluding tax	Unit margin excluding tax = PV excluding tax – PA excluding tax
Margin rate	Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Turnover excluding tax	CA HT = PV HT x Quantity sold
New Unit Margin	New unit margin = PV HT – New PA HT

Application: VertVogue

States :

VertVogue, an innovative company in the sustainable fashion sector, is launching a new range of handbags made from recycled materials. Each bag is sold for €150 including VAT, with a VAT rate of 5,5%. The production cost is €95 excluding VAT per bag. The management wants to analyse the expected profitability of this range.

Work to do :

1. Calculate the selling price excluding VAT of the handbag.
2. Determine the unit margin excluding VAT.
3. What is the markup rate for this product?
4. If the company sells 400 bags, what is the total turnover excluding tax?
5. Analyze the effect of a reduction in the selling price to €140 including tax on the unit margin excluding tax.

Proposed correction:

1. The selling price excluding VAT is defined by: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €150 ÷ (1 + 0,055) = €142,18.
   The selling price excluding VAT is €142,18.

2. The HT unit margin is obtained by: HT unit margin = HT PV – HT PA.
   As a replacement, €142,18 – €95 = €47,18.
   The unit margin excluding tax is €47,18.

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

Replacing, ((€142,18 – €95) ÷ €142,18) x 100 = 33,20%.
The markup rate is 33,20%.

4. The net sales figure for 400 bags is: Net sales = Net sales x Quantity sold.
   Replacing, €142,18 x 400 = €56.
   The turnover excluding tax is €56.

5. A sale price of €140 including tax reduces the net sales price to: €140 ÷ (1 + 0,055) = €132,75.
   The new unit margin excluding tax becomes: €132,75 – €95 = €37,75.
   Although the unit margin is reducing, it remains positive but is decreasing in absolute value.

Formulas Used:

Title	Formulas
Sale price excl. VAT	PV HT = PV TTC ÷ (1 + VAT rate)
Unit margin excluding tax	Unit margin excluding tax = PV excluding tax – PA excluding tax
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Turnover excluding tax	CA HT = PV HT x Quantity sold
New Unit Margin excluding VAT	New Unit Margin excluding VAT = New PV excluding VAT – PA excluding VAT

Application: GreenTech Machines

States :

GreenTech Machines builds environmentally friendly electric lawnmowers and sells a model for €300 including VAT with a VAT of 20%. Production costs amount to €250 excluding VAT per unit. The company seeks to optimize its profitability by examining several financial aspects.

Work to do :

1. Calculate the selling price excluding VAT of the mower.
2. Determine the unit margin excluding VAT.
3. Calculate the margin rate for this model.
4. What is the net turnover of the company if it sells 250 lawnmowers?
5. Discuss the impact of increasing production costs to €270 excluding VAT on profitability.

Proposed correction:

1. The selling price excluding VAT is calculated as follows: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €300 ÷ (1 + 0,20) = €250.
   The selling price excluding tax is therefore €250.

2. The HT unit margin is calculated by: HT unit margin = HT PV – HT PA.
   As a replacement, €250 – €250 = €0.
   The unit margin excluding tax is €0, which means that there is no profit before cost increases.

3. The margin rate is: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

Replacing, ((€250 – €250) ÷ €250) x 100 = 0%.
The margin rate is 0% indicating no profit with no change.

4. The net sales figure for 250 lawnmowers is given by: Net sales = Net sales x Quantity sold.
   Replacing, €250 x 250 = €62.
   The turnover excluding tax is €62.

5. If production costs increase to €270 excluding VAT, the new unit margin becomes: €250 – €270 = -€20.
   This increase results in a deficit of €20 per mower, requiring a strategy adjustment.

Formulas Used:

Title	Formulas
Sale price excl. VAT	PV HT = PV TTC ÷ (1 + VAT rate)
Unit margin excluding tax	Unit margin excluding tax = PV excluding tax – PA excluding tax
Margin rate	Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Turnover excluding tax	CA HT = PV HT x Quantity sold
New Unit Margin	New unit margin = PV HT – New PA HT

Application: Gourmet Express

States :

Gourmet Express, a gourmet meal delivery company, has set the selling price of a menu at €45 including tax with a VAT of 5,5%. The production cost of the menu is €30 excluding tax. The company seeks to inform its strategic decisions through a few financial indicators.

Work to do :

1. Calculate the menu's selling price excluding tax.
2. What is the unit margin excluding tax achieved?
3. Calculate the markup rate for this menu.
4. What is the net turnover if the company sells 600 menus?
5. Analyze how the unit margin would be impacted if the selling price increases to €50 including tax.

Proposed correction:

1. The selling price excluding VAT is calculated by: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €45 ÷ (1 + 0,055) = €42,66.
   The menu's selling price excluding tax is €42,66.

2. The HT unit margin is obtained by: HT unit margin = HT PV – HT PA.
   As a replacement, €42,66 – €30 = €12,66.
   The unit margin excluding tax is €12,66.

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

Replacing, ((€42,66 – €30) ÷ €42,66) x 100 = 29,68%.
The markup rate is 29,68%.

4. For 600 menus, the net turnover is calculated by: Net turnover = Net sales x Quantity sold.
   Replacing, €42,66 x 600 = €25.
   The turnover excluding tax is €25.

5. With a sale price of €50 including tax, the new PV excluding tax is: €50 ÷ (1 + 0,055) = €47,39.
   The new unit margin excluding tax becomes: €47,39 – €30 = €17,39.
   The increase in the selling price significantly increases unit profitability.

Formulas Used:

Title	Formulas
Sale price excl. VAT	PV HT = PV TTC ÷ (1 + VAT rate)
Unit margin excluding tax	Unit margin excluding tax = PV excluding tax – PA excluding tax
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Turnover excluding tax	CA HT = PV HT x Quantity sold
New Unit Margin excluding VAT	New Unit Margin excluding VAT = New PV excluding VAT – PA excluding VAT

Application: BioFresh Market

States :

BioFresh Market, an organic store, sells a selection of seasonal products. A basket of fruit is sold at €20 including VAT, including a VAT of 5,5%. The cost of purchasing the fruit is €12 excluding VAT per basket. The company wants to review its pricing strategies in the face of new market trends.

Work to do :

1. Calculate the selling price excluding tax of the fruit basket.
2. Determine the unit margin excluding VAT.
3. Identify the margin rate on these fruit baskets.
4. What would be the net turnover if the sale reached 500 baskets?
5. What would be the effects of a reduction in cost to €10 excluding VAT on the unit margin?

Proposed correction:

1. For the selling price excluding VAT, use: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €20 ÷ (1 + 0,055) = €18,96.
   The selling price excluding VAT is €18,96.

2. The HT unit margin is calculated by: HT unit margin = HT PV – HT PA.
   As a replacement, €18,96 – €12 = €6,96.
   The unit margin excluding tax is €6,96.

3. The margin rate is: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

Replacing, ((€18,96 – €12) ÷ €12) x 100 = 58%.
The margin rate is 58%.

4. The net sales figure for 500 baskets is calculated as: net sales = net sales x quantity sold.
   Replacing, €18,96 x 500 = €9.
   The net turnover reached €9.

5. If the cost drops to €10 excluding VAT, the unit margin becomes: €18,96 – €10 = €8,96.
   This cost reduction increases unit profitability, providing greater flexibility on prices.

Formulas Used:

Title	Formulas
Sale price excl. VAT	PV HT = PV TTC ÷ (1 + VAT rate)
Unit margin excluding tax	Unit margin excluding tax = PV excluding tax – PA excluding tax
Margin rate	Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Turnover excluding tax	CA HT = PV HT x Quantity sold
New Unit Margin excluding VAT	New Unit Margin excluding VAT = PV excluding VAT – New PA excluding VAT