Summary
Application: The House of Delights
States :
Maison Délices is a pastry shop renowned for its artisanal cakes. It wants to optimize its profits and better understand its costs. You are responsible for carrying out several commercial calculations for various products in the shop.
Work to do :
- Calculate the sales price excluding tax (PV HT) of a cake, knowing that its purchase price excluding tax (PA HT) is €10 and that the desired margin rate is 50%.
- Determine the markup rate if the selling price excluding VAT of a cake is €20 and the purchasing price excluding VAT is €12.
- Find the unit margin made per cake sold, knowing that the selling price is €25 including tax.
- If the annual quantity sold is 5000 cakes, find the overall margin achieved.
- Analyse the implications for trade if the VAT rate falls from 20% to 5,5% for all its products.
Proposed correction:
-
To calculate the PV HT with a margin rate of 50%, use the formula: PV HT = PA HT x (1 + Margin rate ÷ 100).
Replacing, €10 x (1 + 50 ÷ 100) = €15.
The selling price excluding tax must therefore be €15. -
The markup rate is given by the formula: ((PV HT – PA HT) ÷ PV HT) x 100.
Replacing, ((€20 – €12) ÷ €20) x 100 = 40%.
Thus, the mark rate is 40%. -
The unit margin is calculated using the formula: PV HT – PA HT.
The selling price excluding VAT can be calculated by deducting the 20% VAT: 25 ÷ 1,20 = €20,83.
So, Unit Margin = €20,83 – €10 = €10,83.
The unit margin achieved is €10,83 per cake sold.
-
The overall margin is calculated with the formula: Unit margin x Quantity sold.
Replacing, €10,83 x 5000 = €54.
The overall margin achieved is €54 for the year. -
If the VAT rate drops from 20% to 5,5%, the sales price of a cake including VAT would decrease, which could attract more customers. However, this will also impact the sales price excluding VAT if costs remain constant, potentially increasing margins.
Formulas Used:
| Title | Formulas |
|---|---|
| PV HT | PA HT x (1 + Margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Unit margin | PV HT – PA HT |
| Overall margin | Unit margin x Quantity sold |
Application: Techno Innov
States :
Techno Innov, a startup in the technology gadget sector, is launching a new product on the market. You need to conduct financial analyses to better understand pricing strategies.
Work to do :
- Identify the purchase price excluding VAT if the sale price excluding VAT is €80 and the desired margin rate is 25%.
- Calculate the sales price including tax for a product with a purchase price excluding tax of €60 and a markup rate of 30%.
- Determine the overall margin if 2000 units of the product are sold at a selling price of €80 including tax.
- Estimate the break-even point in units if the company's annual fixed costs amount to €50 and the unit margin is €000 after VAT.
- Discuss the financial implications if the company benefits from a 5% tax reduction on the cost of its orders.
Proposed correction:
-
The PA HT is calculated by rearranging the margin rate formula: PA HT = PV HT ÷ (1 + Margin rate ÷ 100).
Substituting, €80 ÷ (1 + 25 ÷ 100) = €64.
The purchase price excluding VAT should be €64. -
First use the formula to find the PV HT: PV HT = PA HT ÷ (1 – Markup Rate ÷ 100).
Substituting, €60 ÷ (1 – 30 ÷ 100) = €85,71.
The sales price including tax is therefore calculated with 20% VAT: €85,71 x 1,20 = €102,85.
The sales price including VAT is €102,85. -
First, calculate the PV excluding VAT by deducting the VAT: 80 ÷ 1,20 = €66,67.
Then, the unit margin = €66,67 – €60 = €6,67.
The overall margin = €6,67 x 2000 = €13.
The overall margin achieved is €13.
-
The break-even point in units is given by the formula: Fixed costs ÷ Unit margin.
Replacing, €50 ÷ €000 = 25 units.
You need to sell 2000 units to reach break-even. -
A 5% tax reduction on the cost of orders would reduce the company's expenses and increase profitability significantly, because it would lower purchasing prices or allow reinvestment in new opportunities for the company.
Formulas Used:
| Title | Formulas |
|---|---|
| PA HT | PV HT ÷ (1 + Margin rate ÷ 100) |
| PV HT | PA HT ÷ (1 – Mark rate ÷ 100) |
| Unit margin | PV HT – PA HT |
| Overall margin | Unit margin x Quantity sold |
| Neutral | Fixed charges ÷ Unit margin |
Application: Chic Fashion
States :
Mode Chic is a high-end clothing company looking to adjust its pricing strategy for its luxury coats. You need to do some math to optimize the financial results.
Work to do :
- Determine the selling price excluding tax of a coat if the purchase price excluding tax is €150 to obtain a margin rate of 40%.
- What is the markup rate if the selling price excluding tax is set at €250 and the purchase price excluding tax is €200?
- Calculate the unit margin on a coat sold at €300 including tax.
- Find the overall margin knowing that 300 coats are sold during the year.
- Analyze the impact of a 15% VAT increase on sales figures.
Proposed correction:
-
The formula for calculating the PV HT with a margin rate is: PV HT = PA HT x (1 + Margin rate ÷ 100).
Replacing, €150 x (1 + 40 ÷ 100) = €210.
The selling price excluding VAT must be €210. -
The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100.
Replacing, ((€250 – €200) ÷ €250) x 100 = 20%.
The markup rate is 20%. -
Let's first calculate the PV excluding tax: 300 ÷ 1,20 = €250.
Unit margin = €250 – €200 = €50.
The unit margin achieved is €50 per coat.
-
For the overall margin: Unit margin x Quantity sold.
Replacing, €50 x 300 = €15.
The overall margin is €15. -
An increase in VAT to 15% could reduce consumers' purchasing power, potentially impacting demand for these high-end products and requiring a strategic review of sales prices or even supply.
Formulas Used:
| Title | Formulas |
|---|---|
| PV HT | PA HT x (1 + Margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Unit margin | PV HT – PA HT |
| Overall margin | Unit margin x Quantity sold |
Application: Bio Health
States :
Bio Santé, a company specializing in natural food supplements, wants to analyze its cost structure for one of its flagship products. You are responsible for conducting a study on their pricing policy to understand the potential impacts of market changes.
Work to do :
- Identify the required net selling price for a food supplement if the net purchase price is €20 and the target markup rate is 40%.
- Find the margin rate obtained if the product is sold at €30 excluding VAT, for a purchase price excluding VAT of €18.
- Calculate the unit margin knowing that the product is sold for €36 including tax.
- Estimate the overall margin if the company sells 1500 units of this product per year.
- Discuss the potential impacts of reducing VAT from 20% to a reduced rate of 10% on sales.
Proposed correction:
-
To find the PV HT, use: PV HT = PA HT ÷ (1 – Mark rate ÷ 100).
Substituting, €20 ÷ (1 – 40 ÷ 100) = €33,33.
The required selling price excluding VAT is €33,33. -
The margin rate is: ((PV HT – PA HT) ÷ PA HT) x 100.
Replacing, ((€30 – €18) ÷ €18) x 100 = 66,67%.
The margin rate obtained is 66,67%. -
The PV excluding tax is: 36 ÷ 1,20 = €30.
The unit margin is therefore: €30 – €18 = €12.
The unit margin achieved is €12 per unit.
-
The overall margin is: Unit margin x Quantity sold.
Replacing, €12 x 1500 = €18.
The overall margin is €18. -
A VAT cut could potentially reduce the inclusive price for consumers, boosting sales, but would also require a reassessment of pricing strategy to maintain expected margins.
Formulas Used:
| Title | Formulas |
|---|---|
| PV HT | PA HT ÷ (1 – Mark rate ÷ 100) |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Unit margin | PV HT – PA HT |
| Overall margin | Unit margin x Quantity sold |
Application: Clean Energy
States :
Clean Energy, a growing company in the renewable energy sector, wants to assess its margins to better manage its profitability. You need to conduct financial calculations regarding its latest wind turbine model.
Work to do :
- Calculate the selling price excluding tax of a wind turbine knowing that the purchase price excluding tax is €5000 and that the expected margin rate must be 30%.
- Evaluate the markup rate if the selling price excluding tax is €7500, for a purchase price excluding tax of €5850.
- Determine the unit margin knowing that the wind turbine is sold at the price of €9000 including tax.
- Estimate the overall margin assuming the company sells 50 wind turbines per year.
- Analyze the potential effects of a 10% increase in procurement spending on margins.
Proposed correction:
-
Use: PV HT = PA HT x (1 + Margin rate ÷ 100).
Replacing, €5000 x (1 + 30 ÷ 100) = €6500.
The selling price excluding VAT must be €6500. -
The mark rate is given by: ((PV HT – PA HT) ÷ PV HT) x 100.
Replacing, ((€7500 – €5850) ÷ €7500) x 100 = 22%.
The markup rate is 22%. -
Calculate the PV excluding tax: 9000 ÷ 1,20 = €7500.
So, Unit Margin = €7500 – €5850 = €1650.
The unit margin achieved is €1650.
-
The overall margin is calculated: Unit margin x Quantity sold.
Replacing, €1650 x 50 = €82.
The overall margin is €82. -
A 10% increase in expenses could reduce margins if the selling price remains unchanged. This would require considering a cost pass-through to sales prices to maintain the net margin.
Formulas Used:
| Title | Formulas |
|---|---|
| PV HT | PA HT x (1 + Margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Unit margin | PV HT – PA HT |
| Overall margin | Unit margin x Quantity sold |
Application: Studio Light
States :
Studio Lumière, an audiovisual production company, wants to calculate various margins for its video production services as part of a major project. Your task is to perform several strategic calculations to optimize finances.
Work to do :
- Calculate the selling price excluding tax of a service knowing that the cost excluding tax is €3000 and that the company is aiming for a margin rate of 25%.
- Determine the markup rate if the selling price excluding tax is €4500 and the cost excluding tax is €3600.
- Calculate the unit margin if the service is billed at €5400 including tax.
- Estimate the overall margin if the company performs 100 such services in the year.
- Discuss the implications if demand for services increases by 15%, but costs are increased by 10%.
Proposed correction:
-
Use the formula: PV HT = PA HT x (1 + Margin rate ÷ 100).
Replacing, €3000 x (1 + 25 ÷ 100) = €3750.
The selling price excluding VAT should be €3750. -
The mark rate is given by: ((PV HT – PA HT) ÷ PV HT) x 100.
Replacing, ((€4500 – €3600) ÷ €4500) x 100 = 20%.
The markup rate is 20%. -
To find the PV excluding VAT, divide by 1,2 to remove the VAT: 5400 ÷ 1,20 = €4500.
Unit margin = €4500 – €3600 = €900.
The unit margin is €900.
-
For the overall margin: Unit margin x Quantity sold.
Replacing, €900 x 100 = €90.
The overall margin is €90. -
A 15% increase in demand coupled with a 10% increase in costs would require a price adjustment or various strategies in order to preserve margins without compromising the relative competitiveness of Studio Lumière.
Formulas Used:
| Title | Formulas |
|---|---|
| PV HT | PA HT x (1 + Margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Unit margin | PV HT – PA HT |
| Overall margin | Unit margin x Quantity sold |
Application: Nature Escape
States :
Evasion Nature is a sports and leisure store offering a wide range of products related to outdoor activities. The company wants to optimize its sales while respecting its profitability objectives. You must carry out certain numerical analyses.
Work to do :
- Evaluate the selling price excluding tax of a product knowing that it was purchased for €80 excluding tax and that the expected margin rate is 35%.
- Estimate the markup rate if the selling price excluding tax is €120 and the cost excluding tax is €95.
- Calculate the unit margin of a tent sold for €144 including tax.
- Determine the overall margin if the store sells 800 tents per year.
- Analyze the impact of a 5% reduction in the cost of goods on the pricing strategy.
Proposed correction:
-
Use: PV HT = PA HT x (1 + Margin rate ÷ 100).
Replacing, €80 x (1 + 35 ÷ 100) = €108.
The selling price excluding VAT must be €108. -
The markup rate is: ((PV HT – PA HT) ÷ PV HT) x 100.
Replacing, ((€120 – €95) ÷ €120) x 100 = 20,83%.
The markup rate is 20,83%. -
Divide the price including tax by 1,20 to get the price excluding tax: 144 ÷ 1,20 = €120.
Unit margin = €120 – €95 = €25.
The unit margin achieved is €25.
-
For overall margin: Unit margin x Quantity sold.
Replacing, €25 x 800 = €20.
The overall margin is €20. -
A 5% reduction in the cost of goods could significantly improve margins or provide pricing flexibility to lower selling prices to capture more market share.
Formulas Used:
| Title | Formulas |
|---|---|
| PV HT | PA HT x (1 + Margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Unit margin | PV HT – PA HT |
| Overall margin | Unit margin x Quantity sold |
Application: Gourmand Table
States :
Gourmand Table is a fine dining restaurant looking to improve its profitability by reviewing its prices. You are responsible for optimizing the pricing policy for the spring menu, taking into account costs and margin expectations.
Work to do :
- Determine the selling price excluding tax of a dish if the cost excluding tax is €25 and we want a markup rate of 60%.
- Calculate the margin rate if the dish is sold for €50 excluding VAT and the cost excluding VAT is €30.
- Estimate the unit margin if the dish is billed at €60 including tax.
- For 1000 dishes sold over a season, evaluate the overall margin obtained.
- Provide a critical analysis of the impact of a 10% price increase on demand.
Proposed correction:
-
The PV HT is calculated with: PV HT = PA HT ÷ (1 – Mark rate ÷ 100).
Substituting, €25 ÷ (1 – 60 ÷ 100) = €62,50.
The selling price excluding VAT must be €62,50. -
The margin rate is: ((PV HT – PA HT) ÷ PA HT) x 100.
Replacing, ((€50 – €30) ÷ €30) x 100 = 66,67%.
The margin rate is 66,67%. -
The PV excluding tax is: 60 ÷ 1,20 = €50.
The unit margin is therefore: €50 – €30 = €20.
The unit margin is €20 per dish.
-
Overall margin = Unit margin x Quantity sold.
Replacing, €20 x 1000 = €20.
The overall margin is €20 for the season. -
A 10% price increase could impact demand, especially if customers perceive a lower value than expected. It would be wise to reinforce the perceived value or target customers willing to pay this premium.
Formulas Used:
| Title | Formulas |
|---|---|
| PV HT | PA HT ÷ (1 – Mark rate ÷ 100) |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Unit margin | PV HT – PA HT |
| Overall margin | Unit margin x Quantity sold |
Application: The Book Workshop
States :
L'Atelier du Livre, an independent bookstore, seeks to optimize its book selection and sales prices to maximize profits in a constantly changing market. You are responsible for performing calculations to support these objectives with a particular focus on bestsellers.
Work to do :
- Calculate the selling price excluding tax of a book knowing that the purchase price excluding tax is €12 and that the bookstore wishes to achieve a margin rate of 45%.
- What is the markup rate if the selling price of a book excluding tax is €22 and the purchase price excluding tax is €16?
- Determine the unit margin knowing that this book is sold at €24 including tax.
- Estimate the overall margin if the bookstore sells 2000 copies per year.
- Discuss the potential impact on sales and margins if the discount on bestsellers is increased by 5%.
Proposed correction:
-
Use the formula: PV HT = PA HT x (1 + Margin rate ÷ 100).
Replacing, €12 x (1 + 45 ÷ 100) = €17,40.
The selling price excluding VAT must be €17,40. -
The markup rate is: ((PV HT – PA HT) ÷ PV HT) x 100.
Replacing, ((€22 – €16) ÷ €22) x 100 = 27,27%.
The markup rate is 27,27%. -
PV HT = 24 ÷ 1,20 = €20.
The unit margin is therefore: €20 – €16 = €4.
The unit margin achieved is €4 per book.
-
Overall margin = Unit margin x Quantity sold.
Replacing, €4 x 2000 = €8.
The overall margin is €8 per year. -
If the discount on bestsellers increases by 5%, this could increase sales by attractiveness to customers, but decrease the unit margin. It is crucial to compensate for this reduction rate by increasing sales volume or by price adjustments on other products.
Formulas Used:
| Title | Formulas |
|---|---|
| PV HT | PA HT x (1 + Margin rate ÷ 100) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Unit margin | PV HT – PA HT |
| Overall margin | Unit margin x Quantity sold |