Summary
Application: Planet Fashion
States :
Planète Mode is an organic and ethical clothing store that wants to analyze the profitability of different items. You have received data regarding some of the items that need special attention in order to improve the pricing strategy.
Work to do :
- Calculate the selling price excluding VAT of a t-shirt if the purchase price excluding VAT is €20 and the desired markup rate is 40%.
- Determine the margin rate of a dress sold for €70 excluding tax, knowing that its purchase price excluding tax is €55.
- A pair of jeans costs €35 excluding VAT to buy and is sold for €60 excluding VAT. Find the brand rate.
- You need to lower the selling price of a dress by 15% to increase sales. The original selling price is €80. What will the new selling price be?
- How would the overall margin vary if the quantity of jackets sold is doubled (100 jackets) knowing that the unit margin excluding tax is €25?
Proposed correction:
-
To obtain a markup rate of 40%, we use the formula: PV HT = PA HT ÷ (1 – Markup rate).
Substituting, €20 ÷ (1 – 0,40) = €33,33.
The selling price excluding VAT should be €33,33 to achieve a mark-up rate of 40%. -
The margin rate is calculated as follows: ((PV HT – PA HT) ÷ PA HT) x 100.
Substituting, ((70 – 55) ÷ 55) x 100 = 27,27%.
The markup on the dress is 27,27%. -
The mark rate is given by: ((PV HT – PA HT) ÷ PV HT) x 100.
Applying the values, ((60 – 35) ÷ 60) x 100 = 41,67%.
So, the markup rate for jeans is 41,67%.
-
To decrease the price by 15%, we multiply the initial price by (1 – 0,15).
Replacing, €80 x (1 – 0,15) = €68.
The new selling price excluding VAT will be €68. -
The overall margin is: Unit margin x Quantity sold. If the quantity doubles, the new overall margin is: €25 x 100 = €2.
Thus, the doubled overall margin would amount to €2.
Formulas Used:
| Title | Formulas |
|---|---|
| Selling price excluding tax | PV HT = PA HT ÷ (1 – Mark rate) |
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Brand taxes | Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 |
| Price reduction | New PV HT = PV HT x (1 – Reduction %) |
| Overall margin | Overall margin = Unit margin x Quantity sold |
Application: Natural Health
States :
La Santé au Naturel is a company specializing in the sale of organic food supplements. The company wants to evaluate the financial performance of its flagship products to adjust its pricing strategy.
Work to do :
- Calculate the purchase price excluding VAT of a box of vitamins if the sale price is €40 excluding VAT with a margin rate of 25%.
- If an essential oil is sold for €24 excluding VAT with a mark-up rate of 30%, find the purchase price excluding VAT.
- You want to increase the selling price excluding VAT of a pack of tea by 10% to cope with the increase in costs. The initial price is €15 excluding VAT. What will the new price be?
- Determine the margin rate of a product purchased for €18 excluding tax and sold for €25 excluding tax.
- Consider the unit margin of a dietary supplement set at €5 and 200 units sold. What is the overall margin? If the quantity sold increases by 50%, how does the overall margin change?
Proposed correction:
-
The purchase price excluding tax is obtained by the formula: PA excluding tax = PV excluding tax ÷ (1 + Margin rate).
By replacing, €40 ÷ (1 + 0,25) = €32.
The purchase price excluding VAT of the box of vitamins is €32. -
The purchase price excluding tax is determined by: PA excluding tax = PV excluding tax x (1 – Markup rate).
Replacing, €24 x (1 – 0,30) = €16,80.
The purchase price excluding VAT of the essential oil is €16,80. -
The new selling price is: New PV HT = PV HT x (1 + Increase %).
By replacing, €15 x (1 + 0,10) = €16,50.
Therefore, the new selling price excluding VAT for the pack of tea will be €16,50.
-
The margin rate is calculated: ((PV HT – PA HT) ÷ PA HT) x 100.
Substituting, ((25 – 18) ÷ 18) x 100 = 38,89%.
The margin rate for this product is 38,89%. -
The initial overall margin is: €5 x 200 = €1. With a 000% increase, the quantity is 50 units and therefore: €300 x 5 = €300.
The overall margin would increase to €1.
Formulas Used:
| Title | Formulas |
|---|---|
| Purchase price excluding tax | PA HT = PV HT ÷ (1 + Margin rate) |
| Purchase price (markup rate) | PA HT = PV HT x (1 – Mark rate) |
| Price increase | New PV HT = PV HT x (1 + Increase %) |
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Overall margin | Overall margin = Unit margin x Quantity sold |
Application: TechnoGreen
States :
TechnoGreen is an innovative company in renewable energy technologies. It sells solar batteries and wants to optimize its margins to increase its profits while maintaining its market share against the competition.
Work to do :
- Determine the mark-up rate of a battery sold at €500 excluding VAT knowing that its purchase price is €350 excluding VAT.
- Calculate the selling price excluding tax of a solar panel if the purchase price excluding tax is €1 and the desired margin rate is 200%.
- You anticipate a 12% drop in the initial prices of wind turbines offered at €2 excluding VAT. What will the new selling price excluding VAT be?
- With a unit margin of €150 for 50 batteries sold, what is the overall margin? If sales increase by 20%, what is the new overall margin?
- For a charging system offered at €400 excluding VAT and a brand rate of 25%, what is its purchase price excluding VAT?
Proposed correction:
-
The markup rate is calculated as follows: ((PV HT – PA HT) ÷ PV HT) x 100.
Substituting, ((500 – 350) ÷ 500) x 100 = 30%.
So the battery mark rate is 30%. -
The selling price excluding tax is given by: PV excluding tax = PA excluding tax x (1 + Margin rate).
Substituting, €1 x (200 + 1) = €0,30.
Therefore, the solar panel must be sold for €1 excluding VAT to obtain a 560% margin. -
The reduced price is calculated by: New PV excluding VAT = PV excluding VAT x (1 – Reduction %).
Substituting, €2 x (000 – 1) = €0,12.
The new selling price excluding tax for the wind turbines will be €1.
-
Initial overall margin = Unit margin x Quantity = €150 x 50 = €7.
If sales increase by 20%, quantity = 60 then,
New overall margin = €150 x 60 = €9.
The new overall margin would be €9. -
The purchase price is determined by: PA HT = PV HT x (1 – Markup rate).
Replacing, €400 x (1 – 0,25) = €300.
The purchase price excluding VAT of the charging system is €300.
Formulas Used:
| Title | Formulas |
|---|---|
| Brand taxes | Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 |
| Selling price excluding tax | PV excluding tax = PA excluding tax x (1 + Margin rate) |
| Discount | New PV HT = PV HT x (1 – Reduction %) |
| Overall margin | Overall margin = Unit margin x Quantity sold |
| Purchase price (markup rate) | PA HT = PV HT x (1 – Mark rate) |
Application: Culinary Arts
States :
Art Culinaires is a high-end gourmet food company. It wants to maximize its profits while expanding its business internationally. Let’s analyze the financial impacts of price changes.
Work to do :
- For an olive oil sold for €15 excluding VAT with a purchase cost of €10 excluding VAT, find the margin rate.
- Calculate the selling price excluding tax of a box of chocolates if the purchase price excluding tax is €25 with a desired mark-up rate of 50%.
- The selling price excluding VAT of a batch of jams worth €30 must be increased by 8%. What will the new price excluding VAT be?
- What is the overall margin if 500 bottles of wine are sold with a unit margin of €7? If sales increase by 25%, what will be the total overall margin?
- If a terrine is purchased for €12 excluding VAT and sold with a mark-up rate of 20%, how much is it sold for excluding VAT?
Proposed correction:
-
The margin rate is calculated by: ((PV HT – PA HT) ÷ PA HT) x 100.
Substituting, ((15 – 10) ÷ 10) x 100 = 50%.
The margin for olive oil is 50%. -
The selling price is: PV HT = PA HT ÷ (1 – Markup rate).
Substituting, €25 ÷ (1 – 0,50) = €50.
The selling price excluding tax of the chocolate must be €50. -
The new price is calculated as follows: New PV HT = PV HT x (1 + Increase %).
By replacing, €30 x (1 + 0,08) = €32,40.
The new price excluding tax for the batch of jams will be €32,40.
-
The overall margin is calculated as: €7 x 500 = €3.
With a 25% increase in sales, 625 bottles are sold,
New overall margin = €7 x 625 = €4.
The total overall margin becomes €4. -
The selling price excluding tax is obtained by: PV excluding tax = PA excluding tax ÷ (1 – Markup rate).
Substituting, €12 ÷ (1 – 0,20) = €15.
It is sold for €15 excluding VAT.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Selling price (markup rate) | PV HT = PA HT ÷ (1 – Mark rate) |
| Price increase | New PV HT = PV HT x (1 + Increase %) |
| Overall margin | Overall margin = Unit margin x Quantity sold |
Application: Advanced Digital Services
States :
Advanced Digital Services, a cloud solutions company, plans to review its pricing offerings to boost revenue growth. Evaluating their strategies is crucial to ensure their competitiveness in the market.
Work to do :
- Determine the percentage reduction if a service initially sold for €300 excluding VAT is now offered at €255 excluding VAT.
- Calculate the purchase price excluding tax of a service billed at €150 excluding tax with a margin rate of 35%.
- A cloud offer is proposed at €500 excluding VAT, you wish to increase it by 15% to cover additional costs. What will be the new price excluding VAT?
- A 10% increase in sales is anticipated for a service with a unit margin of €40, initially sold 100 units. What will the new overall margin be?
- Evaluate the markup rate for a maintenance contract sold for €800 excluding VAT, acquired for €600 excluding VAT.
Proposed correction:
-
The percentage discount is calculated by: ((Original Price – Discounted Price) ÷ Original Price) x 100.
Substituting, ((300 – 255) ÷ 300) x 100 = 15%.
The discount applied is 15%. -
The purchase price excluding tax is calculated by: PA excluding tax = PV excluding tax ÷ (1 + Margin rate).
By replacing, €150 ÷ (1 + 0,35) = €111,11.
The purchase price excluding VAT is €111,11. -
The new price after increase is: New PV HT = PV HT x (1 + Increase %).
By replacing, €500 x (1 + 0,15) = €575.
The new price excluding VAT will be €575.
-
The original overall margin is: €40 x 100 = €4. With a 000% increase, 10 units are sold, therefore,
New overall margin = €40 x 110 = €4.
The new overall margin is €4. -
The markup rate is calculated by: ((PV HT – PA HT) ÷ PV HT) x 100.
Calculating, ((800 – 600) ÷ 800) x 100 = 25%.
The markup rate for the contract is 25%.
Formulas Used:
| Title | Formulas |
|---|---|
| Percentage reduction | Discount % = ((Original Price – Discounted Price) ÷ Original Price) x 100 |
| Purchase price excluding tax | PA HT = PV HT ÷ (1 + Margin rate) |
| Price increase | New PV HT = PV HT x (1 + Increase %) |
| Overall margin | Overall margin = Unit margin x Quantity sold |
| Brand taxes | Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 |
Application: Sustainable Construction
States :
Constructions Durables develops innovative solutions in the green building sector. Wanting to rationalize its prices while maximizing its margins, the company needs to analyze some of its products.
Work to do :
- Calculate the margin rate of a solar window sold at €800 excluding tax with a manufacturing cost of €600 excluding tax.
- At what selling price excluding VAT should you sell an insulator with a cost price of €100 to obtain a mark-up rate of 40%?
- If the cost of manufacturing a green wall is €250 excluding VAT and its margin is €100, what is its selling price excluding VAT?
- The price excluding tax of a green roof is reduced by 10%, going from €1 excluding tax to how much?
- What would be the impact of a 15% increase in sales on the overall margin for a product with a unit margin of €50 sold in 1 units, currently?
Proposed correction:
-
The margin rate is calculated by: ((PV HT – PA HT) ÷ PA HT) x 100.
Substituting, ((800 – 600) ÷ 600) x 100 = 33,33%.
The solar window margin rate is 33,33%. -
The selling price is given by: PV HT = PA HT ÷ (1 – Markup rate).
Substituting, €100 ÷ (1 – 0,40) = €166,67.
The insulation should be sold for €166,67 excluding VAT. -
The selling price excluding tax is: PV excluding tax = Manufacturing cost + Margin.
By replacing, €250 + €100 = €350.
The green wall is sold for €350 excluding tax.
-
The new price after reduction is: New PV HT = PV HT x (1 – Reduction %).
Replacing, €1 x (000 – 1) = €0,10.
The green roof will cost €900 excluding tax. -
The overall margin is calculated by: Unit margin x Quantity sold.
Initially: €50 x 1 = €000. With a 50% increase, quantity = 000 then,
New overall margin = €50 x €1 = €150.
The increase in sales brings the overall margin to €57.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Selling price excluding tax | PV HT = PA HT ÷ (1 – Mark rate) |
| Selling price (margin) | PV HT = Manufacturing cost + Margin |
| Discount | New PV HT = PV HT x (1 – Reduction %) |
| Overall margin | Overall margin = Unit margin x Quantity sold |
Application: The World of Toys
States :
The company Le Monde du Jouet distributes a varied range of games and toys for children. In order to optimize their pricing policy, the management would like to review some sales data from the current season.
Work to do :
- What is the margin rate for a wooden toy sold for €35 excluding VAT if the purchase price is €25 excluding VAT?
- If a puzzle is purchased for €8 and sold with a markup of 20%, what is its selling price excluding tax?
- A stuffed animal displayed at €50 excluding VAT is subject to a 20% promotion. What will its promotional price excluding VAT be?
- Selling 300 tops with a unit margin of €2, calculate the overall margin. What will the new overall margin be if sales increase by 50%?
- An educational game is offered at €100 excluding VAT. Determine its purchase price excluding VAT if its margin rate is 25%.
Proposed correction:
-
The margin rate is determined by: ((PV HT – PA HT) ÷ PA HT) x 100.
Substituting, ((35 – 25) ÷ 25) x 100 = 40%.
The margin rate for wooden toys is 40%. -
The selling price excluding tax is calculated: PV excluding tax = PA excluding tax ÷ (1 – Markup rate).
Substituting, €8 ÷ (1 – 0,20) = €10.
The puzzle must be sold for €10 excluding VAT. -
The price after promotion is: New PV excluding VAT = PV excluding VAT x (1 – Promotion %).
Replacing, €50 x (1 – 0,20) = €40.
The promotional price of the plush toy will be €40 excluding VAT.
-
The overall margin: Unit margin x Quantity sold = €2 x 300 = €600. With a 50% increase, the quantity is 450, therefore,
New overall margin = €2 x 450 = €900.
The new overall margin would amount to €900. -
The purchase price excluding tax is obtained by: PA excluding tax = PV excluding tax ÷ (1 + Margin rate).
By replacing, €100 ÷ (1 + 0,25) = €80.
The purchase price excluding VAT of the educational game is €80.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Selling price excluding tax | PV HT = PA HT ÷ (1 – Mark rate) |
| promotional price | New PV HT = PV HT x (1 – Promotion %) |
| Overall margin | Overall margin = Unit margin x Quantity sold |
| Purchase price excluding tax | PA HT = PV HT ÷ (1 + Margin rate) |
Application: Sports Team
States :
Équipe Sportive is a distributor of equipment for athletes and sports enthusiasts. The goal is to refine the pricing strategies of their flagship items to boost sales and ensure optimal profitability.
Work to do :
- Calculate the markup rate of a pair of sneakers sold for €60 excluding VAT with a purchase price of €45 excluding VAT.
- Determine the selling price excluding tax of a batch of balloons purchased for €100 excluding tax to obtain a margin of €30.
- A sports bag is offered at €80 excluding VAT, with a 25% discount. What is the price after the discount?
- A company sets a unit margin of €5 for 200 armbands. What is the overall margin? What would the new margin be if sales increase by 40%?
- What is the purchase price excluding VAT if a sweatshirt is sold at €50 excluding VAT with a margin rate of 40%?
Proposed correction:
-
The markup rate is calculated by: ((PV HT – PA HT) ÷ PV HT) x 100.
Substituting, ((60 – 45) ÷ 60) x 100 = 25%.
The markup rate of sneakers is 25%. -
The selling price excluding tax is: PV excluding tax = PA excluding tax + Margin.
By replacing, €100 + €30 = €130.
The batch of balloons should be sold for €130 excluding VAT. -
The new price is: New PV HT = PV HT x (1 – Reduction %).
Replacing, €80 x (1 – 0,25) = €60.
The price of the sports bag after reduction is €60 excluding VAT.
-
The overall margin: Unit margin x Quantity sold = €5 x 200 = €1. With a 000% increase, the quantity becomes 40, therefore,
New overall margin = €5 x 280 = €1.
So the new overall margin is €1. -
The purchase price excluding tax is given by: PA excluding tax = PV excluding tax ÷ (1 + Margin rate).
By replacing, €50 ÷ (1 + 0,40) = €35,71.
The purchase price excluding VAT for the sweatshirt is €35,71.
Formulas Used:
| Title | Formulas |
|---|---|
| Brand taxes | Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 |
| Selling price excluding tax | PV excluding tax = PA excluding tax + Margin |
| Price after reduction | New PV HT = PV HT x (1 – Reduction %) |
| Overall margin | Overall margin = Unit margin x Quantity sold |
| Purchase price excluding tax | PA HT = PV HT ÷ (1 + Margin rate) |
Application: Urban Flowers
States :
Les Fleurs Urbanes, specializing in urban floral decoration, is focusing its expansion on new product lines in order to vary its source of income while maximizing profit margins.
Work to do :
- What is the margin rate for a bouquet of flowers sold for €20 excluding VAT when it costs €12 excluding VAT?
- You want a 50% markdown on a floral crown with a cost price of €16. What is the selling price excluding VAT?
- A green plant initially offered at €30 excluding VAT is on sale with a 20% reduction. What is the sale price?
- For 400 decorative pots with a margin of €3 per unit, calculate the overall margin. What would it be if sales increased by 30%?
- If a floral arrangement is sold for €50 excluding VAT with a margin of €18, what is the purchase price excluding VAT?
Proposed correction:
-
The margin rate is given by: ((PV HT – PA HT) ÷ PA HT) x 100.
Substituting, ((20 – 12) ÷ 12) x 100 = 66,67%.
The margin rate for the bouquet of flowers is 66,67%. -
The selling price excluding tax to obtain a markup rate is: PV excluding tax = PA excluding tax ÷ (1 – Markup rate).
Substituting, €16 ÷ (1 – 0,50) = €32.
The floral crown must be sold for €32 excluding VAT. -
The sale price after reduction is: New PV excluding VAT = PV excluding VAT x (1 – Reduction %).
Replacing, €30 x (1 – 0,20) = €24.
The green plant on sale costs €24 excluding VAT.
-
The overall margin is: Unit margin x Quantity sold = €3 x 400 = €1. With a 200% increase, the quantity becomes 30, therefore,
New overall margin = €3 x 520 = €1.
The new overall margin will be €1. -
The purchase price excluding tax is calculated by: PA excluding tax = PV excluding tax – Margin.
As a replacement, €50 – €18 = €32.
The purchase price excluding VAT of the floral arrangement is €32.
Formulas Used:
| Title | Formulas |
|---|---|
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Selling price excluding tax | PV HT = PA HT ÷ (1 – Mark rate) |
| Sale price | New PV HT = PV HT x (1 – Reduction %) |
| Overall margin | Overall margin = Unit margin x Quantity sold |
| Purchase price excluding tax | PA HT = PV HT – Margin |