Business calculations in Bac pro | 9 Exercises

Application: DistriMod

States :

DistriMod is a company specializing in the sale of fashionable clothing. It wants to optimize its pricing and marketing policy in order to increase its profitability. You are responsible for analyzing several financial aspects of this company to help it better manage its sales prices.

Work to do :

1. Calculate the sales price excluding tax (SPT) of a pair of trousers if the purchase price excluding tax (PPT) is €30 and the desired margin rate is 40%.

2. What is the overall margin achieved by DistriMod if it sells 500 pairs of trousers at a selling price excluding tax of €42?

3. The VAT rate for clothing is 20%. Calculate the sales price including VAT of a pair of trousers sold for €42 excluding VAT.

4. If the markup rate on a batch of shirts is 25%, what would be the purchase price excluding tax for a sale price excluding tax of €60?

5. Analyze the impact of a 10% discount on the €60 net selling price of a batch of shirts on the initially 25% markup rate.

Proposed correction:

1. The selling price excluding tax of a pair of trousers is calculated using the formula: PV excluding tax = PA excluding tax x (1 + Margin rate).
   By replacing, €30 x (1 + 0,40) = €42.
   The selling price excluding tax must therefore be €42.

2. The unit margin is €42 – €30 = €12.
   The overall margin is therefore €12 x €500 = €6.
   DistriMod achieves an overall margin of €6 on the sale of these pants.

3. To calculate the sales price including tax, we use the formula: PV including tax = PV excluding tax x (1 + VAT rate).

By replacing, €42 x (1 + 0,20) = €50,40.
The selling price including tax for a pair of trousers is therefore €50,40.

4. The purchase price excluding tax for a markup rate of 25% is calculated as follows: PA excluding tax = PV excluding tax x (1 – Markup rate).
   Replacing, €60 x (1 – 0,25) = €45.
   The purchase price excluding VAT of the shirts must be €45 to reach the 25% markup rate.

5. A 10% discount on the excluding VAT sale price of €60 gives a new sale price of €54.
   The initial markup rate was 25%.
   The new markup rate is calculated as follows: ((€54 – €45) ÷ €54) x 100 = 16,67%.
   Thus, the discount reduces the markup rate from 25% to 16,67%.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV excluding tax = PA excluding tax x (1 + Margin rate)
Unit margin	Unit margin = PV excluding tax – PA excluding tax
Overall margin	Overall margin = Unit margin x Quantity sold
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT rate)
Purchase price excluding tax	PA HT = PV HT x (1 – Mark rate)
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100

Application: TechNova

States :

TechNova, an innovative company in the electronic gadget sector, wants to understand the impact of its pricing choices on its profitability. You are responsible for analyzing various financial aspects of the company in order to improve its commercial performance.

Work to do :

1. Determine the selling price excluding tax of a gadget whose purchase price excluding tax is €150 with a target margin rate of 30%.

2. What is the overall margin for TechNova if it sells 1 gadgets at a selling price excluding VAT of €000?

3. Taking into account 20% VAT, calculate the selling price including VAT of a gadget sold for €195 excluding VAT.

4. If TechNova achieves a markup rate of 22% on a device sold at €120 excluding VAT, what is the purchase price excluding VAT?

5. Discuss the impact of a 15% promotion on the net selling price of €195 for the initial markup rate of 22%.

Proposed correction:

1. The selling price excluding tax of a gadget is calculated by: PV excluding tax = PA excluding tax x (1 + Margin rate).
   By replacing, €150 x (1 + 0,30) = €195.
   The selling price excluding tax must be €195 to reach the margin rate.

2. The unit margin is €195 – €150 = €45.
   The overall margin is €45 x €1 = €000.
   TechNova therefore achieves an overall margin of €45 on the sale of gadgets.

3. To calculate the sales price including tax, we use the formula: PV including tax = PV excluding tax x (1 + VAT rate).

By replacing, €195 x (1 + 0,20) = €234.
The selling price including tax of a gadget is therefore €234.

4. Let's calculate the purchase price excluding tax using: PA excluding tax = PV excluding tax x (1 – Markup rate).
   Replacing, €120 x (1 – 0,22) = €93,60.
   The purchase price excluding VAT must be €93,60.

5. The promotion reduces the sale price to €195 x (1 – 0,15) = €165,75.
   The new markup rate is calculated as follows: ((€165,75 – €93,60) ÷ €165,75) x 100 = 43,53%.
   Promotion improves brand rate to 43,53% reduces turnover.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV excluding tax = PA excluding tax x (1 + Margin rate)
Unit margin	Unit margin = PV excluding tax – PA excluding tax
Overall margin	Overall margin = Unit margin x Quantity sold
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT rate)
Purchase price excluding tax	PA HT = PV HT x (1 – Mark rate)
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100

Application: GreenGrocers

States :

GreenGrocers, a specialty organic food store, is considering optimizing its margins by adjusting its prices. You are tasked with reviewing some of the financial aspects of its products to identify opportunities for improvement.

Work to do :

1. What selling price excluding tax should be set for a product with a purchase cost of €8 if we want to obtain a margin of 50%?

2. If GreenGrocers sells 200 units of a product with a net selling price of €12, what is the overall margin generated?

3. Calculate the sales price including tax of a product sold for €14,50 excluding tax by applying a VAT of 5,5%.

4. To obtain a markup rate of 35%, at what purchase price excluding tax should a product sold at €20 excluding tax be negotiated?

5. Evaluate the impact on turnover if a 5% reduction is applied to the net selling price of €12, knowing that 200 units have been sold.

Proposed correction:

1. The desired selling price excluding tax can be obtained using the formula: PV excluding tax = PA excluding tax x (1 + Margin rate).
   By replacing, €8 x (1 + 0,50) = €12.
   The selling price excluding tax must be set at €12.

2. The unit margin is €12 – €8 = €4.
   So the overall margin is €4 x €200 = €800.
   GreenGrocers makes an overall margin of €800 for this product.

3. The calculation of the sales price including tax is: PV including tax = PV excluding tax x (1 + VAT rate).

By replacing, €14,50 x (1 + 0,055) = €15,298.
The sales price including VAT is approximately €15,30.

4. The purchase price excluding VAT can be determined by: PA excluding VAT = PV excluding VAT x (1 – Markup rate).
   Replacing, €20 x (1 – 0,35) = €13.
   A purchase price excluding VAT of €13 is required for the desired markup rate.

5. The 5% reduction lowers the selling price excluding VAT to €12 x (1 – 0,05) = €11,40.
   The new turnover is €11,40 x 200 = €2.
   The reduction affects the turnover, lowering its total level to €2.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV excluding tax = PA excluding tax x (1 + Margin rate)
Unit margin	Unit margin = PV excluding tax – PA excluding tax
Overall margin	Overall margin = Unit margin x Quantity sold
Sales price including tax	PV including VAT = PV excluding VAT x (1 + VAT rate)
Purchase price excluding tax	PA HT = PV HT x (1 – Mark rate)

Application: BistroDeluxe

States :

BistroDeluxe, a high-end restaurant, must adjust its prices to maximize its margins while remaining competitive. You are responsible for analyzing the financial elements of its menu to optimize its pricing strategy.

Work to do :

1. Determine the selling price excluding tax of a dish offered at €50 including tax, knowing that the VAT applied is 5,5%.

2. If a dish costs €12 to produce and we want to apply a margin rate of 70%, what should the selling price excluding tax be?

3. What is the markup rate achieved if a dish is sold for €48 excluding VAT and its purchase price is €28 excluding VAT?

4. BistroDeluxe wants to increase its sales by applying a 15% discount on a dish currently at €48 excluding VAT. Calculate the new selling price excluding VAT.

5. Discuss the relevance of such a 15% reduction on a dish, taking into account a margin rate initially set at 70%.

Proposed correction:

1. The selling price excluding VAT is calculated using the formula: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €50 ÷ (1 + 0,055) = €47,39.
   The selling price excluding tax is therefore €47,39.

2. To set the selling price excluding tax, use: PV excluding tax = PA excluding tax x (1 + Margin rate).
   By replacing, €12 x (1 + 0,70) = €20,40.
   The selling price excluding tax must be €20,40 for the dish.

3. The mark rate is obtained with: Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Replacing, ((€48 – €28) ÷ €48) x 100 = 41,67%.
The mark rate achieved is 41,67%.

4. Applying a 15% discount on €48 excluding VAT gives: €48 x (1 – 0,15) = €40,80.
   The new selling price excluding tax for the dish will be €40,80.

5. A 70% markup ensures a comfortable margin. The discount lowers the price to €40,80, decreasing the available margin while potentially increasing demand.
   A strategic assessment is needed to determine whether the new margins will sustain the restaurant operation.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV HT = PV TTC ÷ (1 + VAT rate)
Selling price excluding tax	PV excluding tax = PA excluding tax x (1 + Margin rate)
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Price after reduction	PV after reduction = Initial PV x (1 – Reduction rate)

Application: HealthPlus

States :

SantéPlus, a medical equipment distribution center, wants to analyze its margins to better plan its product catalog. You are responsible for performing this financial analysis to help SantéPlus maintain its competitiveness in the market.

Work to do :

1. Calculate the selling price excluding tax of equipment sold for €240 including tax with a VAT of 20%.

2. If a product is purchased for €50 and the company aims for a margin rate of 60%, what should its selling price excluding tax be?

3. A medical detector is sold for €150 excluding VAT, and its purchase price is €90 excluding VAT. What is the mark-up rate achieved?

4. By applying a 10% discount on a detector previously sold for €150 excluding VAT, determine the new selling price excluding VAT.

5. Assess whether maintaining the 10% discount is viable for SantéPlus while maintaining a margin rate of 60% initially implemented.

Proposed correction:

1. Let’s use the formula: PV HT = PV TTC ÷ (1 + VAT rate).
   By replacing, €240 ÷ (1 + 0,20) = €200.
   The selling price excluding tax is therefore €200.

2. Let’s calculate: PV HT = PA HT x (1 + Margin rate).
   By replacing, €50 x (1 + 0,60) = €80.
   The selling price excluding VAT should be €80.

3. With the formula: Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Replacing, ((€150 – €90) ÷ €150) x 100 = 40%.
The mark rate achieved is 40%.

4. The 10% discount on a price of €150 excluding VAT is calculated as: €150 x (1 – 0,10) = €135.
   The new selling price excluding VAT is therefore €135.

5. Maintaining a discount may stimulate demand, but with the price lowered to €135, it is crucial to analyse whether reducing an initial margin rate still guarantees sufficient profitability.
   An assessment of costs and volumes is necessary for viability.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV HT = PV TTC ÷ (1 + VAT rate)
Selling price excluding tax	PV excluding tax = PA excluding tax x (1 + Margin rate)
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Price after discount	PV after reduction = Initial PV x (1 – Reduction rate)

Application: AutoPartsXpress

States :

AutoPartsXpress, a parts trading company, is looking to assess the profitability of its products in terms of margins and selling prices. You are assigned to analyze different products for better strategic decisions in the market.

Work to do :

1. What is the selling price excluding tax of an auto part displayed at €60 including tax, knowing that the VAT applied is 20%?

2. A product purchased for €20 must be resold with a desired margin rate of 50%. What will be the selling price excluding tax?

3. With a selling price excluding tax of €45 and a purchase price of €30 excluding tax, find the markup rate achieved.

4. If it is decided to lower the price by 10% on a component sold for €50 excluding VAT, what will the new selling price excluding VAT be?

5. Explain whether a 10% drop in component price could impact the financial viability of AutoPartsXpress, while maintaining a high target margin rate.

Proposed correction:

1. To calculate the selling price excluding VAT: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €60 ÷ (1 + 0,20) = €50.
   The selling price excluding tax is then €50.

2. Using the formula: PV HT = PA HT x (1 + Margin rate).
   By replacing, €20 x (1 + 0,50) = €30.
   The selling price excluding tax must be €30.

3. By applying: Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.

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

4. For a 10% reduction on €50 excluding VAT: €50 x (1 – 0,10) = €45.
   The new selling price excluding VAT is €45.

5. The price reduction to €45 may increase sales volumes, but reduces the unit margin.
   An analysis of the impact on sales volume and fixed costs is essential to ensure profitability.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV HT = PV TTC ÷ (1 + VAT rate)
Selling price excluding tax	PV excluding tax = PA excluding tax x (1 + Margin rate)
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Price after reduction	PV after reduction = Initial PV x (1 – Reduction rate)

Application: TechHub

States :

TechHub, a disruptive technology startup, must juggle high production costs and price competitiveness to optimize its margins. Your help is requested to provide accurate analyses of the critical financial aspects of their flagship products.

Work to do :

1. If an electronic device is sold for €200 including tax, calculate its selling price excluding tax, taking into account a VAT of 20%.

2. TechHub buys a 3D printer for €400 and wants a 25% margin. At what price should they sell it excluding taxes?

3. Determine the markup rate achieved by TechHub if a gadget is sold for €500 excluding VAT for a purchase cost of €350 excluding VAT.

4. A 12% discount strategy is applied to the €500 net selling price of a gadget. Calculate the new net selling price.

5. Evaluate the strategic and financial impact of applying a 12% discount on overall sales volumes and profit margin.

Proposed correction:

1. Use of the formula: PV HT = PV TTC ÷ (1 + VAT rate).
   By replacing, €200 ÷ (1 + 0,20) = €166,67.
   The selling price excluding tax is therefore €166,67.

2. With: PV HT = PA HT x (1 + Margin rate).
   By replacing, €400 x (1 + 0,25) = €500.
   The selling price excluding tax must be set at €500.

3. The formula to apply: Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.

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

4. The reduction is calculated as follows: €500 x (1 – 0,12) = €440.
   The new selling price excluding VAT is €440.

5. A 12% discount can potentially increase demand, expanding the market covered by TechHub.
   However, this requires an increase in sales sufficient to offset the reduction in unit margin, requiring in-depth strategic analysis.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV HT = PV TTC ÷ (1 + VAT rate)
Selling price excluding tax	PV excluding tax = PA excluding tax x (1 + Margin rate)
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Price after reduction	PV after reduction = Initial PV x (1 – Reduction rate)

Application: MaisonNature

States :

MaisonNature, a chain of organic stores, is looking to evaluate the prices of its products to maintain its competitiveness while optimizing its margins. You need to analyze some of the flagship products to evaluate the opportunities for financial optimization.

Work to do :

1. MaisonNature sells a gourmet basket for €30 including tax. What is its selling price excluding tax, taking into account a VAT of 5,5%?

2. If a bottle of organic juice is purchased for €3 with a margin target of 70%, what will its selling price excluding tax be?

3. The markup rate of an essential oil sold for €20 excluding VAT and purchased for €12 is requested. Calculate it.

4. A volume strategy wants to apply an 8% discount on a selling price excluding VAT of €25. What is the new price excluding VAT?

5. Analyze the effects of an 8% reduction on MaisonNature's profitability, taking into account a solid initial margin of 70%.

Proposed correction:

1. Use: PV HT = PV TTC ÷ (1 + VAT rate).
   By replacing, €30 ÷ (1 + 0,055) = €28,44.
   The selling price excluding tax is then €28,44.

2. By applying: PV HT = PA HT x (1 + Margin rate).
   By replacing, €3 x (1 + 0,70) = €5,10.
   The selling price excluding tax must therefore be €5,10.

3. With: Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Replacing, ((€20 – €12) ÷ €20) x 100 = 40%.
The markup rate is 40%.

4. The reduction results in: €25 x (1 – 0,08) = €23.
   So, the new selling price excluding VAT is €23.

5. An 8% reduction in price can increase demand and sales, especially with a strong initial margin, however, it is essential to ensure that the sales level adequately compensates for the price reduction to maintain profitability.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV HT = PV TTC ÷ (1 + VAT rate)
Selling price excluding tax	PV excluding tax = PA excluding tax x (1 + Margin rate)
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Price after reduction	PV after reduction = Initial PV x (1 – Reduction rate)

Application: EcoSchool

States :

EcoSchool, a provider of eco-friendly school supplies, aims to adjust its pricing and margin strategy to better serve its mission while remaining financially viable. You are invited to evaluate certain products and propose recommendations to this effect.

Work to do :

1. A kit of supplies is sold for €15 including VAT. Determine its selling price excluding VAT if the VAT is 20%.

2. If EcoSchool buys a range of pens at €2 and wants a margin rate of 65%, what selling price excluding tax should be set?

3. What is the markup rate for a calculator sold for €18 excluding VAT when its cost is €10 excluding VAT?

4. A 5% discount is being considered to boost sales of a kit initially sold at €10 excluding VAT. At what price excluding VAT will they be sold?

5. Consider a strategy where a 5% discount could positively impact sales while still keeping the margin level significantly positive.

Proposed correction:

1. The calculation of the PV excluding VAT gives: PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
   By replacing, €15 ÷ (1 + 0,20) = €12,50.
   Thus, the selling price excluding tax is €12,50.

2. Let us apply: PV HT = PA HT x (1 + Margin rate).
   By replacing, €2 x (1 + 0,65) = €3,30.
   The selling price excluding VAT should be €3,30.

3. Via the formula: Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Replacing, ((€18 – €10) ÷ €18) x 100 = 44,44%.
The markup rate is 44,44%.

4. A 5% reduction results in: €10 x (1 – 0,05) = €9,50.
   The new selling price excluding VAT will be €9,50.

5. A 5% discount can increase sales volume, helping EcoSchool reach a wider market with a potential positive effect on overall revenue, provided the volume increase remains strong.

Formulas Used:

Title	Formulas
Selling price excluding tax	PV HT = PV TTC ÷ (1 + VAT rate)
Selling price excluding tax	PV excluding tax = PA excluding tax x (1 + Margin rate)
Brand taxes	Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Price after reduction	PV after reduction = Initial PV x (1 – Reduction rate)