In this section:
Application: Dulce Chocolates
States :
Chocolats Dulce, a company specializing in the production of artisanal chocolates, generates significant annual sales through several points of sale in France. In 2022, the company sold 200 units of its most popular chocolates. The unit purchase price (UP) from suppliers is €000 while the unit sale price (USP) is set at €2,50. The financial manager wants to determine the total gross margin for the year.
Work to do :
- Calculate the unit margin made on the sale of a chocolate.
- Determine the unit margin rate for each chocolate sold.
- Estimate the total annual gross margin for all sales.
- If the company aims to increase the unit margin rate to 60%, what should the new unit selling price be?
- Analyze the economic impact of reducing the unit selling price to €4,50 on the total gross margin.
Proposed correction:
- The unit margin is calculated by: PV HT – PA HT.
So, Unit Margin = €5,00 – €2,50 = €2,50.
The unit margin for each chocolate is €2,50. - The unit margin rate is calculated as follows: ((PV HT – PA HT) ÷ PA HT) x 100.
Substituting, Margin rate = ((€5,00 – €2,50) ÷ €2,50) x 100 = 100%.
Each chocolate sold generates a margin rate of 100%. - The total gross margin is calculated by multiplying the unit margin by the quantity sold: Unit margin x quantity sold.
Total gross margin = €2,50 x €200 = €000.
The annual gross margin is then €500.
- For a margin rate of 60%, the formula is: PV HT = PA HT x (1 + (Margin rate ÷ 100)).
By replacing, PV excluding tax = €2,50 x (1 + (60 ÷ 100)) = €4,00.
To achieve a 60% margin, the selling price must be €4,00 per chocolate. - If the PV excluding tax is reduced to €4,50 per chocolate, the new unit margin becomes:
Unit margin = €4,50 – €2,50 = €2,00.
Total gross margin = €2,00 x €200 = €000.
Reducing the selling price to €4,50 would result in a decrease in the total gross margin to €400.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Total gross margin | Unit margin x Quantity sold |
| Selling price for a margin rate | PA HT x (1 + (Margin rate ÷ 100)) |
Application: BioJus Santé
States :
BioJus Santé is a company that sells organic fruit juices. In 2022, the company sold 150 bottles. The purchase cost per bottle (PCB) is €000, and their unit selling price (USP) is €1,20. The manager would like to know how much margin his company was able to generate thanks to these sales.
Work to do :
- Calculate the unit margin for each bottle sold.
- Determine the unit markup rate for each bottle.
- Estimate the total annual gross margin.
- What unit selling price would achieve a margin rate of 150%?
- Discuss the financial implications if the sale price were lowered to €2,40.
Proposed correction:
- The unit margin is obtained by: PV HT – PA HT.
Unit margin = €3,00 – €1,20 = €1,80.
Each bottle thus generates a margin of €1,80. - The unit mark rate is calculated by: ((PV HT – PA HT) ÷ PV HT) x 100.
Markup rate = ((€3,00 – €1,20) ÷ €3,00) x 100 = 60%.
The unit mark rate is therefore 60%. - The total gross margin is the unit margin multiplied by the number of sales:
Total gross margin = €1,80 x €150 = €000.
The annual gross margin then amounts to €270.
- To obtain a margin rate of 150%, use the formula: PV HT = PA HT x (1 + (Margin rate ÷ 100)).
PV excluding tax = €1,20 x (1 + (150 ÷ 100)) = €3,00.
To achieve a 150% margin, the selling price must be €3,00 per bottle. - With a PV excluding tax of €2,40, the new unit margin would be:
Unit margin = €2,40 – €1,20 = €1,20.
Total gross margin = €1,20 x €150 = €000.
By lowering the selling price to €2,40, the total gross margin drops significantly to €180.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Total gross margin | Unit margin x Quantity sold |
| Selling price for a margin rate | PA HT x (1 + (Margin rate ÷ 100)) |
Application: ElectroDom Solutions
States :
ElectroDom Solutions, a specialist in household appliances, sold 10 units of a new dishwasher model in 000. The acquisition cost per unit (ACP excluding VAT) is €2022, and the unit selling price (USP excluding VAT) is €250. The CFO wants to evaluate the company's annual sales performance.
Work to do :
- Calculate the unit margin for each dishwasher sold.
- Estimate the unit margin rate for these sales.
- Calculate the total gross margin achieved during the year.
- If the goal is to have a 55% markup rate, what would be an appropriate selling price?
- Analyze the financial impact if the purchase cost increased to €300.
Proposed correction:
- The unit margin is calculated by subtracting the HT PA from the HT PV.
Unit margin = €500 – €250 = €250.
Each sale generates a margin of €250. - The unit margin rate is defined as follows: ((PV HT – PA HT) ÷ PA HT) x 100.
Margin rate = ((€500 – €250) ÷ €250) x 100 = 100%.
The margin rate is 100% for each unit sold. - The total gross margin is obtained by: Unit margin x Quantity sold.
Total gross margin = €250 x 10 = €000.
The annual gross margin is therefore €2.
- For a markup rate of 55%, use: PV HT = PA HT ÷ (1 – (Markup rate ÷ 100)).
PV excluding tax = €250 ÷ (1 – (55 ÷ 100)) = €555,55.
A sale price of €555,55 would achieve the desired markup rate. - If the PA excluding tax increases to €300, the unit margin becomes:
Unit margin = €500 – €300 = €200.
Total gross margin = €200 x 10 = €000.
An increase in purchasing costs to €300 would result in a total gross margin reduced to €2.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Total gross margin | Unit margin x Quantity sold |
| Selling price for a mark rate | PA HT ÷ (1 – (Market rate ÷ 100)) |
Application: Lasting Style Clothing
States :
Lasting Style is a fashion clothing store that offers a limited collection of 500 dresses each year. The purchase price per dress (PA HT) is €30, and the unit selling price (PV HT) is set at €75. Management hopes to better understand the impact of this line on margins over the past year.
Work to do :
- Estimate the unit margin for each dress sold.
- Calculate the unit margin rate for each sale.
- What is the total gross margin for the year?
- How much would the selling price need to be set to achieve a 200% margin rate?
- Analyze the consequences if the purchase price were reduced to €25 per dress.
Proposed correction:
- The unit margin is obtained by: PV HT – PA HT.
Unit margin = €75 – €30 = €45.
Each dress sold brings a margin of €45. - For the margin rate, use: ((PV HT – PA HT) ÷ PA HT) x 100.
Margin rate = ((€75 – €30) ÷ €30) x 100 = 150%.
The unit margin rate is 150%. - The total gross margin is simply: Unit Margin x Quantity Sold.
Total gross margin = €45 x €500 = €22.
The gross margin for the year is €22.
- For a margin rate of 200%: PV HT = PA HT x (1 + (Margin rate ÷ 100)).
PV excluding tax = €30 x (1 + (200 ÷ 100)) = €90.
The selling price must be €90 to achieve this margin rate. - If the PA excluding tax falls to €25, the unit margin becomes:
Unit margin = €75 – €25 = €50.
Total gross margin = €50 x €500 = €25.
With a decrease in the purchase cost, the total gross margin would increase to €25.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Total gross margin | Unit margin x Quantity sold |
| Selling price for a margin rate | PA HT x (1 + (Margin rate ÷ 100)) |
Application: Zoé Nature Cosmetics
States :
Zoé Nature sells natural cosmetics online and sold 20 day creams in 000. These creams are purchased at €2022 each (PA excluding VAT) and resold at €5 (PV excluding VAT). The founder is looking to optimize her margins for 15 by building on the results of the previous year.
Work to do :
- Calculate the unit margin for each cream sold.
- Determine the unit margin rate for these sales.
- How much is the annual gross margin?
- What unit selling price would be required for a 70% markup?
- Evaluate the financial impact of increasing the purchase price to €6 per unit.
Proposed correction:
- The unit margin is given by: PV HT – PA HT.
Unit margin = €15 – €5 = €10.
Each cream generates a margin of €10. - The unit margin rate is calculated as follows: ((PV HT – PA HT) ÷ PA HT) x 100.
Margin rate = ((€15 – €5) ÷ €5) x 100 = 200%.
The margin rate is 200% for each cream. - For total gross margin, use: Unit Margin x Quantity Sold.
Total gross margin = €10 x €20 = €000.
The gross margin for the year is €200.
- For a markup rate of 70%, use: PV HT = PA HT ÷ (1 – (Markup rate ÷ 100)).
PV excluding tax = €5 ÷ (1 – (70 ÷ 100)) = €16,67.
The sale price must be €16,67 to reach this markup rate. - If the PA excluding tax increases to €6, the new unit margin becomes:
Unit margin = €15 – €6 = €9.
Total gross margin = €9 x €20 = €000.
An increase in the purchase price to €6 would reduce the gross margin to €180.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Total gross margin | Unit margin x Quantity sold |
| Selling price for a mark rate | PA HT ÷ (1 – (Market rate ÷ 100)) |
Application: Biking Pro
States :
Biking Pro is a high-end bicycle specialist store that sold 1 units of its flagship model in 000. Each bike is purchased at €2022 (PA excluding VAT) and sold at €800 (PV excluding VAT). The manager wants to evaluate the performance of this reference in terms of gross margin.
Work to do :
- Determine the unit margin for each bicycle sold.
- Evaluate the margin rate for these bikes.
- Calculate the annual gross margin for these sales.
- What should the selling price be to obtain a margin rate of 120%?
- Discuss the consequences of lowering the selling price to €1 per unit.
Proposed correction:
- The unit margin is obtained by: PV HT – PA HT.
Unit margin = €1 – €500 = €800.
Each bike sold generates a margin of €700. - For the margin rate, the formula is: ((PV HT – PA HT) ÷ PA HT) x 100.
Margin rate = ((€1 – €500) ÷ €800) x 800 = 100%.
The margin rate for each bike is 87,5%. - The total gross margin is calculated as: Unit margin x Quantity sold.
Total gross margin = €700 x €1 = €000.
The annual gross margin amounts to €700.
- For a margin rate of 120%, use: PV HT = PA HT x (1 + (Margin rate ÷ 100)).
PV excluding tax = €800 x (1 + (120 ÷ 100)) = €1.
A sale price of €1 would allow a margin rate of 760% to be achieved. - If the PV excluding tax is reduced to €1, the unit margin becomes:
Unit margin = €1 – €300 = €800.
Total gross margin = €500 x €1 = €000.
A decrease in the selling price to €1 would reduce the total gross margin to €300.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Total gross margin | Unit margin x Quantity sold |
| Selling price for a margin rate | PA HT x (1 + (Margin rate ÷ 100)) |
Application: Gourmet Espresso
States :
The company Gourmet Espresso sells high-end coffee machines. In 2022, it sold 8 units of a new machine. The purchase cost is €000 per unit (PA excluding VAT) and the unit selling price is €100 (PV excluding VAT). The CEO wants to evaluate the profitability of these sales.
Work to do :
- Calculate the unit margin for each machine sold.
- Determine the unit markup rate for these machines.
- Calculate the total gross margin for the year.
- What unit selling price would determine an 80% margin rate?
- Evaluate the consequences of a purchase cost increased to €120.
Proposed correction:
- The unit margin is calculated by: PV HT – PA HT.
Unit margin = €250 – €100 = €150.
Each machine allows a margin of €150 to be made. - The unit mark rate is given by: ((PV HT – PA HT) ÷ PV HT) x 100.
Markup rate = ((€250 – €100) ÷ €250) x 100 = 60%.
The unit markup rate is 60%. - Total gross margin is calculated by unit margin multiplied by sales.
Total gross margin = €150 x 8 = €000.
The gross margin for the year therefore amounts to €1.
- To achieve a margin rate of 80%, use the formula: PV HT = PA HT x (1 + (Margin rate ÷ 100)).
PV excluding tax = €100 x (1 + (80 ÷ 100)) = €180.
To get 80% margin, the selling price should be €180. - If the PA excluding tax changes to €120, the unit margin becomes:
Unit margin = €250 – €120 = €130.
Total gross margin = €130 x 8 = €000.
With a purchase cost of €120, the gross margin drops to €1.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Total gross margin | Unit margin x Quantity sold |
| Selling price for a margin rate | PA HT x (1 + (Margin rate ÷ 100)) |
Application: EcoHabitat Residences
States :
ÉcoHabitat Résidences focuses on selling development solutions for ecological residences. In 2022, the company sold 2 rainwater harvesting systems. The purchase cost is €500 per unit (PA excluding VAT) and the sale price is €400 (PV excluding VAT). The finance department wants to better understand the margins achieved.
Work to do :
- Calculate the unit margin for each system sold.
- Determine the unit margin rate achieved.
- Calculate the total annual gross margin.
- What unit selling price would increase the margin rate to 100%?
- Analyze the impact of a decrease in the selling price to €650 on the total gross margin.
Proposed correction:
- The unit margin is obtained by: PV HT – PA HT.
Unit margin = €700 – €400 = €300.
Each system generates a margin of €300. - The unit margin rate is calculated as follows: ((PV HT – PA HT) ÷ PA HT) x 100.
Margin rate = ((€700 – €400) ÷ €400) x 100 = 75%.
The unit margin rate is 75%. - Total gross margin is calculated by: Unit margin x Quantity sold.
Total gross margin = €300 x €2 = €500.
The annual gross margin is €750.
- To obtain a margin rate of 100%, use: PV HT = PA HT x (1 + (Margin rate ÷ 100)).
PV excluding tax = €400 x (1 + (100 ÷ 100)) = €800.
A sale price of €800 would allow a margin rate of 100% to be achieved. - If the PV excluding tax is reduced to €650, the unit margin becomes:
Unit margin = €650 – €400 = €250.
Total gross margin = €250 x €2 = €500.
A reduction of €650 in the selling price would bring the total gross margin down to €625.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Total gross margin | Unit margin x Quantity sold |
| Selling price for a margin rate | PA HT x (1 + (Margin rate ÷ 100)) |
Application: Technology Space
States :
Espace Technologie sells innovative tablets and sold 12 units in 000. They are purchased at €2022 (PA excluding VAT) and sold at €200 (PV excluding VAT). The accounting department wants to evaluate the financial results and margins associated with this product line.
Work to do :
- Calculate the unit margin for each tablet sold.
- Determine the markup rate for these sales.
- Estimate the total gross margin for the entire year.
- What should the selling price be to achieve a 40% markup rate?
- Consider the effect of a possible increase in purchasing costs to €250 on gross margin.
Proposed correction:
- The unit margin is calculated by: PV HT – PA HT.
Unit margin = €350 – €200 = €150.
Each tablet sold generates a margin of €150. - The markup rate is defined as follows: ((PV HT – PA HT) ÷ PV HT) x 100.
Markup rate = ((€350 – €200) ÷ €350) x 100 ? 42,86%.
The markup rate for each tablet is about 42,86%. - The total gross margin is calculated by: Unit margin x Quantity sold.
Total gross margin = €150 x 12 = €000.
The annual gross margin thus reaches €1.
- For a markup rate of 40%, use: PV HT = PA HT ÷ (1 – (Markup rate ÷ 100)).
PV excluding tax = €200 ÷ (1 – (40 ÷ 100)) = €333,33.
A sale price of €333,33 would achieve a markup rate of 40%. - If the PA excluding tax increases to €250, the unit margin becomes:
Unit margin = €350 – €250 = €100.
Total gross margin = €100 x 12 = €000.
An increase in purchasing costs to €250 would reduce the total gross margin to €1.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Total gross margin | Unit margin x Quantity sold |
| Selling price for a mark rate | PA HT ÷ (1 – (Market rate ÷ 100)) |