Business calculations in second year of vocational baccalaureate | 9 Exercises

Application: BeauxMots Publishers

States :

BeauxMots Éditeurs is a company specializing in the publication of paperback books. With the literary rentrée, the company wants to analyze the potential profitability of several new works. You have the financial information concerning a bestseller in the making and must perform a series of calculations to guide business decisions.

Work to do :

1. Calculate the unit margin if the selling price excluding tax of a book is €12 and the purchase price excluding tax is €7.

2. Determine the sales price including VAT if the book is sold using a VAT rate of 5,5%.

3. Estimate the overall margin if 5 copies of the book are expected to be sold.

4. Find the margin rate using the given selling price and purchase price data.

5. Imagine that the cost of production drops by €2, calculate the new markup rate.

Proposed correction:

1. The unit margin is calculated by subtracting the pre-tax purchase price from the pre-tax sale price:
   Unit margin = PV excluding tax – PA excluding tax
   Unit margin = €12 – €7 = €5
   The unit margin is therefore €5.

2. The sales price including tax is calculated by adding VAT to the sales price excluding tax:
   PV including VAT = PV excluding VAT x (1 + VAT rate)
   PV including tax = €12 x (1 + 0,055) = €12 x 1,055 = €12,66
   The sales price including tax is therefore €12,66.

3. The overall margin is obtained by multiplying the unit margin by the quantity sold:

Overall margin = Unit margin x Quantity sold
Total margin = €5 x €5 = €000
The overall expected margin is €25.

4. The margin rate is calculated by dividing the unit margin by the pre-tax purchase price, then multiplying by 100:
   Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
   Margin rate = ((€12 – €7) ÷ €7) x 100 = (5 ÷ 7) x 100 = 71,43%
   The margin rate is 71,43%.

5. If the production cost decreases by €2, the new purchase price excluding VAT is €7 – €2 = €5.
   The markup rate is recalculated as follows:
   Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
   Markup rate = ((€12 – €5) ÷ €12) x 100 = (7 ÷ 12) x 100 = 58,33%
   The new markup rate would be 58,33%.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Sale price including VAT	PV HT x (1 + VAT rate)
Overall margin	Unit margin x Quantity sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: LuminoCare

States :

LuminoCare is a company specializing in medical lighting devices for operating rooms. The company wants to analyze the profitability of a new high-performance surgical lamp. The company plans to produce and distribute this new model and needs precise calculations to evaluate its pricing strategy.

Work to do :

1. Calculate the selling price excluding VAT, knowing that the target mark-up rate is 30% and that the manufacturing cost of a lamp is €150.

2. Determine the sales price including VAT if the applicable VAT rate is 20%.

3. Evaluate the margin rate if the selling price excluding tax of a lamp is finally set at €220.

4. LuminoCare expects to sell 1 units during the year. What would be the overall margin?

5. Analyze the impact on the unit margin if, in the future, the manufacturing cost increases by €15.

Proposed correction:

1. To obtain the selling price excluding tax with a mark-up rate of 30%, we apply:
   PV HT = PA HT ÷ (1 – Mark rate)
   PV excluding tax = €150 ÷ (1 – 0,30) = €150 ÷ 0,70 = €214,29
   The selling price excluding VAT should be €214,29.

2. The calculation for the sales price including tax is:
   PV including VAT = PV excluding VAT x (1 + VAT rate)
   PV including tax = €214,29 x (1 + 0,20) = €214,29 x 1,20 = €257,15
   The sales price including tax will be €257,15.

3. The margin rate is found by:

Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Margin rate = ((€220 – €150) ÷ €150) x 100 = (70 ÷ 150) x 100 = 46,67%
The margin rate is 46,67%.

4. To determine the overall margin:
   Unit margin = PV HT – PA HT = €220 – €150 = €70
   Overall margin = Unit margin x Quantity sold
   Total margin = €70 x €1 = €200
   The overall margin would be €84.

5. If the manufacturing cost increases by €15, the new cost is €150 + €15 = €165.
   The new unit margin is:
   Unit margin = PV HT – PA HT = €220 – €165 = €55
   The unit margin would drop to €55.

Formulas Used:

Title	Formulas
PV HT	PA HT ÷ (1 – Mark rate)
Sale price including VAT	PV HT x (1 + VAT rate)
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Overall margin	Unit margin x Quantity sold
Unit margin	PV HT – PA HT

Application: VentraTech

States :

VentraTech is an innovative company in the green ventilation technology sector for eco-responsible buildings. For the launch of a new range of solar fans, the company must optimize its business strategy and evaluate the financial perspectives.

Work to do :

1. Calculate the unit margin if a fan sells for €300 excluding VAT and costs €180 excluding VAT to produce.

2. Find the sales price including VAT of a fan by applying a VAT of 5,5%.

3. If VentraTech plans to sell 2 ventilators, what would the overall margin be?

4. Determine the margin rate using the selling price and the cost of production.

5. Discuss the impact of the increase in the VAT rate from 5,5% to 20% on the sales price including VAT.

Proposed correction:

1. The unit margin is calculated by:
   Unit margin = PV excluding tax – PA excluding tax
   Unit margin = €300 – €180 = €120
   The unit margin is therefore €120.

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

3. The overall margin, with 2 fans sold, is:

Overall margin = Unit margin x Quantity sold
Total margin = €120 x €2 = €500
The overall margin would be €300.

4. The margin rate is calculated by:
   Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
   Margin rate = ((€300 – €180) ÷ €180) x 100 = (120 ÷ 180) x 100 = 66,67%
   The margin rate is 66,67%.

5. By increasing VAT from 5,5% to 20%, the new sales price including VAT is:
   PV including tax = €300 x (1 + 0,20) = €300 x 1,20 = €360
   The sales price including VAT would increase to €360, which could influence demand.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Sale price including VAT	PV HT x (1 + VAT rate)
Overall margin	Unit margin x Quantity sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100

Application: StyleInnov

States :

StyleInnov is a fashion atelier that designs unique garments using recycled materials. In order to promote its new fall-winter collection, the company seeks to identify optimal pricing strategies for its creations.

Work to do :

1. Calculate the selling price excluding tax of an item targeting a markup rate of 40%, knowing that the cost price is €60.

2. Establish the sales price including tax, taking into account a VAT of 5,5%.

3. Check the margin rate for an item whose manufacturing cost is €60 and the selling price excluding tax is €100.

4. If StyleInnov plans to sell 150 units of this model, what will the overall margin be?

5. Analyze how a 10% decrease in production costs would affect unit net margin.

Proposed correction:

1. For a markup rate of 40%, the formula is:
   PV HT = PA HT ÷ (1 – Mark rate)
   PV excluding tax = €60 ÷ (1 – 0,40) = €60 ÷ 0,60 = €100
   The selling price excluding VAT should be €100.

2. The sales price including tax, with a VAT of 5,5%, is calculated as follows:
   PV including VAT = PV excluding VAT x (1 + VAT rate)
   PV including tax = €100 x (1 + 0,055) = €100 x 1,055 = €105,50
   The sales price including VAT is €105,50.

3. The margin rate is calculated with:

Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Margin rate = ((€100 – €60) ÷ €60) x 100 = (40 ÷ 60) x 100 = 66,67%
The margin rate is 66,67%.

4. The overall margin for 150 units is:
   Unit margin = PV HT – PA HT = €100 – €60 = €40
   Overall margin = Unit margin x Quantity sold
   Overall margin = €40 x 150 = €6
   The overall margin would be €6.

5. In case of a 10% reduction in costs, the new cost is:
   New PA HT = €60 x 0,90 = €54
   The new unit margin becomes:
   Unit margin = €100 – €54 = €46
   A drop in costs increases the unit margin to €46.

Formulas Used:

Title	Formulas
PV HT	PA HT ÷ (1 – Mark rate)
Sale price including VAT	PV HT x (1 + VAT rate)
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Overall margin	Unit margin x Quantity sold
New PA HT	PA HT x (1 – 10%)

Application: GreenMobility

States :

GreenMobility is an innovative company that offers electric bicycle solutions to promote sustainable urban mobility. As part of the expansion of sales of its “eco-rider” range, the company must conduct a comprehensive pricing analysis.

Work to do :

1. Calculate the unit margin if a bicycle is sold for €1 excluding VAT and purchased for €200 excluding VAT.

2. Determine the sales price including tax by applying 20% ​​VAT.

3. Consider that production reaches 1 units. What would be the overall margin?

4. Estimate the margin rate based on the given costs and prices.

5. Discuss the potential effect of a 5% increase in the net selling price on the markup rate.

Proposed correction:

1. The unit margin is calculated as follows:
   Unit margin = PV excluding tax – PA excluding tax
   Unit margin = €1 – €200 = €850
   The unit margin is therefore €350.

2. The sales price including VAT, with 20% VAT, is:
   PV including VAT = PV excluding VAT x (1 + VAT rate)
   PV including tax = €1 x (200 + 1) = €0,20 x 1 = €200
   The sales price including tax is €1.

3. To determine the overall margin at 1 units, we use:

Overall margin = Unit margin x Quantity sold
Total margin = €350 x €1 = €000
The overall margin would reach €350.

4. The margin rate is calculated by:
   Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
   Margin rate = ((€1 – €200) ÷ €850) x 850 = (100 ÷ 350) x 850 = 100%
   The margin rate is 41,18%.

5. A 5% increase in the PV HT results in a new PV HT:
   New PV excluding tax = €1 x 200 = €1,05
   The recalculated markup rate becomes:
   Markup rate = ((€1 – €260) ÷ €850) x 1
   Markup rate = (410 ÷ 1) x 260 = 100%
   A 5% increase in the net selling price would increase the markup rate to 32,54%.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Sale price including VAT	PV HT x (1 + VAT rate)
Overall margin	Unit margin x Quantity sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
New PV HT	PV HT x 1,05
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: ArtisanBiens

States :

ArtisanBiens is a small craft business specializing in the manufacture of custom-made solid wood furniture. The company wants to optimize its pricing strategy for the new designer furniture recently launched, and therefore requests a set of calculations to improve its profitability.

Work to do :

1. Determine the selling price excluding tax if the desired margin rate is 50% and the cost price of a table is €400.

2. Calculate the sales price including VAT with an applicable VAT of 20%.

3. If ArtisanBiens estimates selling 80 tables, what would be the overall margin?

4. Get the mark rate with the information provided previously.

5. Consider a 15% reduction in the sales price excluding VAT. What would the new price including VAT be?

Proposed correction:

1. The calculation of the selling price excluding tax with a margin rate of 50% uses:
   PV excluding tax = PA excluding tax x (1 + Margin rate)
   PV excluding tax = €400 x (1 + 0,50) = €400 x 1,50 = €600
   The selling price excluding VAT must be €600.

2. The sales price including VAT with 20% VAT is:
   PV including VAT = PV excluding VAT x (1 + VAT rate)
   PV including tax = €600 x (1 + 0,20) = €600 x 1,20 = €720
   The sales price including VAT is €720.

3. The overall margin for 80 tables is:

Unit margin = PV HT – PA HT = €600 – €400 = €200
Overall margin = Unit margin x Quantity sold
Overall margin = €200 x 80 = €16
The overall margin would be €16.

4. The markup rate is:
   Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
   Markup rate = ((€600 – €400) ÷ €600) x 100 = (200 ÷ 600) x 100 = 33,33%
   The markup rate is 33,33%.

5. After a 15% reduction, the new PV HT is:
   New PV excluding tax = €600 x 0,85 = €510
   The new price including tax is:
   PV including tax = €510 x 1,20 = €612
   The new price including tax would be €612.

Formulas Used:

Title	Formulas
PV HT	PA HT x (1 + Margin rate)
Sale price including VAT	PV HT x (1 + VAT rate)
Overall margin	Unit margin x Quantity sold
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New PV HT	PV HT x 0,85

Application: EcoPlantes

States :

EcoPlantes is a company committed to promoting ecological gardening through the sale of organic growing kits. Faced with an increase in raw materials, the company must readjust its prices while maintaining its cost structure.

Work to do :

1. Calculate the current selling price excluding VAT if the target markup rate is 25% and the cost per kit is €40.

2. Find the sales price including VAT by adding 5,5% VAT.

3. Establish the margin rate if the decided selling price excluding tax is €65.

4. Imagine a sales strategy of 500 units; what would the overall margin be?

5. Analyze the change in the markup rate if the unit cost drops by €5.

Proposed correction:

1. The selling price excluding tax is obtained via:
   PV HT = PA HT ÷ (1 – Mark rate)
   PV excluding tax = €40 ÷ (1 – 0,25) = €40 ÷ 0,75 = €53,33
   The selling price excluding VAT must be €53,33.

2. The sales price including VAT, with 5,5% VAT, is:
   PV including VAT = PV excluding VAT x (1 + VAT rate)
   PV including tax = €53,33 x (1 + 0,055) = €53,33 x 1,055 = €56,25
   The sales price including tax would be €56,25.

3. The margin rate based on a price excluding tax of €65 is:

Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Margin rate = ((€65 – €40) ÷ €40) x 100 = (25 ÷ 40) x 100 = 62,50%
The margin rate is 62,50%.

4. As for the overall margin of 500 units:
   Unit margin = €65 – €40 = €25
   Overall margin = Unit margin x Quantity sold
   Overall margin = €25 x 500 = €12
   The overall expected margin is €12.

5. If the cost drops to €35, the new markup rate becomes:
   Brand rate = ((€65 – €35) ÷ €65) x 100
   Markup rate = (30 ÷ 65) x 100 = 46,15%
   The cost reduction would raise the markup rate to 46,15%.

Formulas Used:

Title	Formulas
PV HT	PA HT ÷ (1 – Mark rate)
Sale price including VAT	PV HT x (1 + VAT rate)
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Overall margin	Unit margin x Quantity sold
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

App: SoundWave Innovations

States :

SoundWave Innovations is a growing company specializing in high-fidelity audio products. The company has just released a new hi-fi system and wants to adjust its pricing to maximize profitability, while taking into account market preferences.

Work to do :

1. Calculate the selling price excluding tax if the target markup rate is 35% and the production cost is €300.

2. Determine the sales price including tax, taking into account a VAT of 20%.

3. Evaluate the margin rate if the selling price excluding tax is set at €460.

4. Consider selling 300 units; what would the overall margin be?

5. Propose a new pricing strategy if a 10% cost increase is anticipated.

Proposed correction:

1. To obtain the selling price excluding tax with a mark-up rate of 35%, we apply:
   PV HT = PA HT ÷ (1 – Mark rate)
   PV excluding tax = €300 ÷ (1 – 0,35) = €300 ÷ 0,65 = €461,54
   The selling price excluding VAT should be €461,54.

2. The sales price including VAT of 20% is:
   PV including VAT = PV excluding VAT x (1 + VAT rate)
   PV including tax = €461,54 x (1 + 0,20) = €461,54 x 1,20 = €553,85
   The sales price including VAT is €553,85.

3. The margin rate, with a net selling price of €460, is:

Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Margin rate = ((€460 – €300) ÷ €300) x 100 = (160 ÷ 300) x 100 = 53,33%
The margin rate reaches 53,33%.

4. For 300 units sold, the overall margin is:
   Unit margin = €460 – €300 = €160
   Overall margin = Unit margin x Quantity sold
   Overall margin = €160 x 300 = €48
   The overall margin would be €48.

5. A 10% increase in costs increases the cost to:
   New cost = €300 x 1,10 = €330
   To maintain the initially targeted markup rate, the new excluding tax sale price becomes:
   PV excluding tax = €330 ÷ 0,65 = €507,69
   In order to maintain a markup rate of 35%, the PV excluding tax should increase to €507,69.

Formulas Used:

Title	Formulas
PV HT	PA HT ÷ (1 – Mark rate)
Sale price including VAT	PV HT x (1 + VAT rate)
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Overall margin	Unit margin x Quantity sold
New cost	PA HT x 1,10

Application: BioCompassion

States :

BioCompassion, an organic flower plantation, offers a range of environmentally friendly bouquets. To adapt to market expectations and fluctuations in supply, the company focuses on its margins and prices.

Work to do :

1. Calculate the selling price excluding VAT if the desired markup rate is 20% and the cost is €18 per bouquet.

2. Find the sales price including VAT if 5,5% VAT must be applied.

3. Calculate the margin rate if the net selling price ultimately reaches €24.

4. If the plantation plans to sell 700 bouquets, what would be the overall margin?

5. Evaluate the possibility of improving the markup rate, if the cost of producing flowers drops by €3.

Proposed correction:

1. The selling price excluding tax to reach a markup rate of 20% is obtained by:
   PV HT = PA HT ÷ (1 – Mark rate)
   PV excluding tax = €18 ÷ (1 – 0,20) = €18 ÷ 0,80 = €22,50
   The selling price excluding VAT must be €22,50.

2. The sales price including VAT, with 5,5% VAT, is:
   PV including VAT = PV excluding VAT x (1 + VAT rate)
   PV including tax = €22,50 x (1 + 0,055) = €22,50 x 1,055 = €23,74
   The sales price including VAT is €23,74.

3. The margin rate based on a net selling price of €24 is:

Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Margin rate = ((€24 – €18) ÷ €18) x 100 = (6 ÷ 18) x 100 = 33,33%
The margin rate reaches 33,33%.

4. The overall margin for the sale of 700 bouquets is:
   Unit margin = €24 – €18 = €6
   Overall margin = Unit margin x Quantity sold
   Overall margin = €6 x 700 = €4
   The overall margin would be €4.

5. If the cost of flowers decreases by €3, the new cost is €15. For the same PV excluding VAT:
   New markup rate = ((€24 – €15) ÷ €24) x 100
   New mark rate = (9 ÷ 24) x 100 = 37,50%
   The cost reduction would allow a markup rate of 37,50%.

Formulas Used:

Title	Formulas
PV HT	PA HT ÷ (1 – Mark rate)
Sale price including VAT	PV HT x (1 + VAT rate)
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Overall margin	Unit margin x Quantity sold
New mark rate	((PV HT – PA HT) ÷ PV HT) x 100