Summary
Application: The Pastry of Delights
States :
La Pâtisserie des Délices wants to improve its financial management by optimizing the valuation of its products. The company generates a turnover mainly through the sale of its famous macarons. Currently, each macaron is sold at €3,50 including tax, and the purchase cost excluding tax is €1,50 per macaron. The applicable VAT is 5,5%. They sell an average of 2 macarons per month. They want to evaluate the margin, the margin rate, the markup rate and other essential indicators to better manage their business.
Work to do :
- Calculate the sales price excluding tax (HT) of a macaron.
- Determine the amount of unit margin made on each macaron.
- Calculate the margin rate of the macaroons sold.
- Find the markup rate of the macarons sold.
- Estimate the overall margin made on the monthly sale of macarons.
Proposed correction:
-
The sales price including tax of a macaron is €3,50. To find the sales price excluding tax, we use the formula:
PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
Substituting, we have: €3,50 ÷ €1,055 = €3,32.
So, the tax-free selling price of a macaron is €3,32. -
The unit margin is calculated by subtracting the pre-tax purchase price from the pre-tax sale price, i.e.:
PV excluding VAT – PA excluding VAT = €3,32 – €1,50 = €1,82.
The unit margin made on each macaron is therefore €1,82. -
The margin rate represents the profitability compared to the purchase cost. The formula is:
((PV HT – PA HT) ÷ PA HT) x 100.
((€3,32 – €1,50) ÷ €1,50) x 100 = 121,33%.
The margin rate of the macaroons sold is 121,33%.
-
The markup rate indicates the profitability relative to the selling price. We use the formula:
((PV HT – PA HT) ÷ PV HT) x 100.
Replacing, ((€3,32 – €1,50) ÷ €3,32) x 100 = 54,82%.
The markup rate is therefore 54,82%. -
The overall margin is obtained by multiplying the unit margin by the quantity sold:
Unit margin x Quantity = €1,82 x 2 = €000.
So, the overall margin achieved monthly is €3.
Formulas Used:
| Title | Formulas |
|---|---|
| Sale price excl. VAT | PV incl. VAT ÷ (1 + VAT rate) |
| Unit Margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Overall Margin | Unit margin x Quantity sold |
Application: The Gadget Workshop
States :
L'Atelier des Gadgets is a start-up specializing in high-tech accessories. It recently launched a connected bracelet sold for €99 including tax. The cost price for each bracelet is €45 excluding tax. The applicable VAT is 20%. Each month, around 500 bracelets find buyers. The company wants to better understand certain management indicators in order to adjust its pricing strategy.
Work to do :
- Determine the selling price excluding tax of a bracelet.
- Calculate the amount of unit margin generated by the sale of a bracelet.
- Evaluate the margin rate of the bracelets.
- Find the markup rate for these bracelets.
- Calculate the overall monthly margin made from bracelet sales.
Proposed correction:
-
To obtain the sales price excluding VAT, we must subtract the VAT from the sales price including VAT:
PV excluding VAT = PV including VAT ÷ (1 + VAT rate).
99 € ÷ 1,20 = 82,50 €.
So, the selling price excluding tax of a bracelet is €82,50. -
The unit margin is the difference between the selling price excluding VAT and the purchase cost excluding VAT:
82,50 € – 45 € = 37,50 €.
Each bracelet sold generates a unit margin of €37,50. -
The margin rate is obtained by the following calculation:
((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€82,50 – €45) ÷ €45) x 100 = 83,33%.
The margin rate for bracelets is 83,33%.
-
To find the markup rate, we use this formula:
((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = ((€82,50 – €45) ÷ €82,50) x 100 = 45,45%.
The brand rate of the bracelets is therefore 45,45%. -
The overall margin is calculated by multiplying the unit margin by the number of bracelets sold:
€37,50 x 500 = €18.
The overall monthly margin amounts to €18.
Formulas Used:
| Title | Formulas |
|---|---|
| Sale price excl. VAT | PV incl. VAT ÷ (1 + VAT rate) |
| Unit Margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Overall Margin | Unit margin x Quantity sold |
Application: Modern Boilermaking
States :
Chaudronnerie Moderne, which specializes in the manufacture of metal parts, mass-produces ball bearings. These bearings are sold for €24 excluding VAT each, while their production cost is €18 excluding VAT. Since the market is competitive, the company sells an average of 1 bearings per month. The financial director wants to estimate the monthly financial performance of this product.
Work to do :
- Calculate the unit margin on each bearing.
- Determine the bearing margin rate.
- Find the markup rate on all bearings.
- Calculate the overall margin for monthly sales.
- If Chaudronnerie Moderne increases its selling price excluding tax by 10%, what would the new unit margin be?
Proposed correction:
-
The unit margin is obtained by subtracting the pre-tax purchase cost from the pre-tax selling price:
24 € – 18 € = 6 €.
The unit margin on each bearing is therefore €6. -
The margin rate is calculated as follows:
((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€24 – €18) ÷ €18) x 100 = 33,33%.
The rolling margin rate is 33,33%. -
The markup rate is determined using the following formula:
((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = ((€24 – €18) ÷ €24) x 100 = 25%.
So the markup rate of bearings is 25%.
-
The overall margin is calculated as the unit margin multiplied by the number of bearings sold:
€6 x €1 = €200.
The overall margin for monthly sales therefore amounts to €7. -
If the selling price excluding tax increases by 10%, it will be:
€24 x 1,10 = €26,40.
The new unit margin would then be: €26,40 – €18 = €8,40.
The new unit margin after the price increase is therefore €8,40.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit Margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Overall Margin | Unit margin x Quantity sold |
| New PV HT | Old PV HT x (1 + increase rate) |
Application: Pauline's Flowers
States :
Les Fleurs de Pauline is a family business selling flowers online. Each bouquet sold on their site costs €45 including tax. The cost to compose each bouquet is €25 excluding tax. The applicable VAT is 5,5%. On average, 800 bouquets are sold each month. The company questions its performance indicators to make decisions on its pricing strategy.
Work to do :
- Calculate the selling price excluding tax of a bouquet.
- Determine the unit margin on the sale of a bouquet.
- Compare the margin rate to the markup rate.
- Evaluate the overall margin achieved within a month.
- If Pauline wants to reduce the sales price including tax by 10% to increase sales, what would the new sales price excluding tax be?
Proposed correction:
-
To determine the selling price excluding VAT, you must subtract the VAT from the selling price including VAT:
PV HT = PV TTC ÷ (1 + VAT rate) = €45 ÷ 1,055 = €42,70.
The selling price excluding tax of a bouquet is €42,70. -
The unit margin is calculated by taking the difference between the selling price excluding tax and the cost excluding tax:
42,70 € – 25 € = 17,70 €.
Each bouquet sold generates a unit margin of €17,70. -
Margin rate is different from markup rate. Let’s calculate them:
Margin Rate: ((PV HT – PA HT) ÷ PA HT) x 100 = ((€42,70 – €25) ÷ €25) x 100 = 70,80%.
Markup Rate: ((PV HT – PA HT) ÷ PV HT) x 100 = ((€42,70 – €25) ÷ €42,70) x 100 = 41,45%.
The margin rate is higher than the markup rate, indicating good control of purchasing costs.
-
The monthly overall margin is:
Unit margin x Quantity = €17,70 x 800 = €14.
The overall margin achieved monthly is €14. -
If Pauline applies a 10% reduction on the sales price including tax, it will become:
€45 x (1 – 0,10) = €40,50.
The selling price excluding VAT will correspond to: €40,50 ÷ 1,055 = €38,39.
Thus, the new selling price excluding tax would be €38,39.
Formulas Used:
| Title | Formulas |
|---|---|
| Sale price excl. VAT | PV incl. VAT ÷ (1 + VAT rate) |
| Unit Margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| New PV including VAT | Former PV including VAT x (1 – reduction rate) |
Application: Eco Cars
States :
Les Voitures Éco is a company that specializes in the sale of used electric cars. Each car is sold at a price of €15 including VAT. The reconditioning cost for each vehicle is €000 excluding VAT. The VAT applicable for this type of product is 12%. Each month, the company manages to sell 000 cars. The company wants to evaluate its margins and profitability.
Work to do :
- Calculate the selling price excluding tax of a car.
- Determine the unit margin for each car sold.
- What is the margin rate on car sales?
- Calculate the markup rate for these sales.
- If Les Voitures Éco wants to reduce its reconditioning cost to €11 excluding VAT, what would the new unit margin be?
Proposed correction:
-
The selling price excluding VAT is calculated by removing VAT from the selling price including VAT:
PV excluding VAT = PV including VAT ÷ (1 + VAT rate) = €15 ÷ 000 = €1,20.
So, the selling price excluding tax of a car is €12. -
The unit margin is the difference between the selling price excluding VAT and the cost excluding VAT:
€12 – €500 = €12.
The unit margin per car sold is therefore €500. -
The margin rate is calculated using the formula:
((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€12 – €500) ÷ €12) x 000 = 12%.
The margin rate on cars sold is 4,17%.
-
The markup rate is established as follows:
((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = ((€12 – €500) ÷ €12) x 000 = 12%.
The markup rate for selling cars is therefore 4%. -
If the reconditioning cost drops to €11 excluding VAT, the new unit margin will be:
€12 – €500 = €11.
The new unit margin would be €1.
Formulas Used:
| Title | Formulas |
|---|---|
| Sale price excl. VAT | PV incl. VAT ÷ (1 + VAT rate) |
| Unit Margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
Application: Elegance Jewelry
States :
Bijoux Élégance is an online store specializing in the sale of handcrafted necklaces. Each necklace is sold at €120 including tax. The production cost of a necklace is €75 excluding tax. The VAT to be applied is 20%. On average, 100 necklaces are sold each month. The company wants to analyze its profitability to improve its business strategy.
Work to do :
- What is the value of the selling price excluding tax for each necklace?
- Calculate the unit margin amount for a necklace.
- What is the margin rate for Bijoux Élégance?
- Find the markup rate applied to the necklaces.
- If the store wants to increase VAT to 25% in anticipation of a reform, what would be the new sales price including tax without changing the sales price excluding tax?
Proposed correction:
-
The selling price excluding tax is calculated using the formula:
PV HT = PV TTC ÷ (1 + VAT rate) = €120 ÷ 1,20 = €100.
So, the selling price excluding tax of a necklace is €100. -
The unit margin is found by subtracting the cost excluding tax from the selling price excluding tax:
100 € – 75 € = 25 €.
The unit margin for each necklace is therefore €25. -
The margin rate is obtained by the following calculation:
((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€100 – €75) ÷ €75) x 100 = 33,33%.
Bijoux Élégance’s margin rate is 33,33%.
-
To calculate the markup rate:
((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = ((€100 – €75) ÷ €100) x 100 = 25%.
The applied markup rate is 25%. -
If VAT rises to 25%, the calculation remains PV including VAT with the constant sales price excluding VAT:
New VAT-inclusive PV = VAT-exclusive PV x (1 + new VAT rate) = €100 x 1,25 = €125.
The new sales price including VAT, increased VAT, is €125.
Formulas Used:
| Title | Formulas |
|---|---|
| Sale price excl. VAT | PV incl. VAT ÷ (1 + VAT rate) |
| Unit Margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| New PV including VAT | PV HT x (1 + new VAT rate) |
Application: Sacha's Notebooks
States :
Les Cahiers de Sacha is an online stationery store that sells creative notebook sets. A complete set is offered at €28 including tax. The purchase cost of the stationery set is €12 excluding tax. VAT is 5,5%. The company sells about 300 sets per month. They want to refine their profitability analysis to optimize their margins.
Work to do :
- Calculate the price excluding VAT of a set of notebooks.
- What would be the unit margin amount per set sold?
- Determine the margin rate achieved by Les Cahiers de Sacha.
- What is the markup rate applied?
- Consider an increase in the purchase cost to €15 excluding VAT; redetermine the unit margin.
Proposed correction:
-
To obtain the selling price excluding VAT:
PV HT = PV TTC ÷ (1 + VAT rate) = €28 ÷ 1,055 = €26,54.
The selling price excluding VAT of a set is €26,54. -
The unit margin is the difference between the selling price excluding VAT and the purchase cost excluding VAT:
26,54 € – 12 € = 14,54 €.
The unit margin per set sold is €14,54. -
The margin rate is calculated by:
((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€26,54 – €12) ÷ €12) x 100 = 121,17%.
The margin rate for Les Cahiers de Sacha is 121,17%.
-
The markup rate is determined as follows:
((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = ((€26,54 – €12) ÷ €26,54) x 100 = 54,79%.
The markup rate used by Les Cahiers de Sacha is therefore 54,79%. -
If the purchase cost rises to €15 excluding VAT, the new unit margin will be:
26,54 € – 15 € = 11,54 €.
The unit margin, with the increased cost, would then be €11,54.
Formulas Used:
| Title | Formulas |
|---|---|
| Sale price excl. VAT | PV incl. VAT ÷ (1 + VAT rate) |
| Unit Margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
Application: TechSonic
States :
TechSonic produces wireless headphones that are marketed at €110 including VAT. The production cost of a pair is €70 excluding VAT. The applicable VAT is 20%. The company sells approximately 1 pairs each month. TechSonic wants to understand the dynamics of its margins to better calibrate its production.
Work to do :
- What is the value of the selling price excluding VAT?
- Evaluate the unit margin on each pair sold.
- What is the margin rate of the headphones sold?
- Calculate TechSonic's markup rate.
- If TechSonic decides to reduce the production cost to €65 excluding VAT, what would the new unit margin be?
Proposed correction:
-
To determine the selling price excluding VAT:
PV HT = PV TTC ÷ (1 + VAT rate) = €110 ÷ 1,20 = €91,67.
The selling price excluding tax is therefore €91,67. -
The unit margin is calculated with the following formula:
91,67 € – 70 € = 21,67 €.
Thus, the unit margin per earphone sold amounts to €21,67. -
The margin rate is defined by:
((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€91,67 – €70) ÷ €70) x 100 = 31%.
The margin rate of the headphones is 31%.
-
The markup rate is calculated using this formula:
((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = ((€91,67 – €70) ÷ €91,67) x 100 = 23,63%.
The markup rate is 23,63%. -
If the production cost decreases to €65 excluding VAT, the new unit margin would be:
91,67 € – 65 € = 26,67 €.
This new unit margin would therefore be €26,67.
Formulas Used:
| Title | Formulas |
|---|---|
| Sale price excl. VAT | PV incl. VAT ÷ (1 + VAT rate) |
| Unit Margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
Application: Alpine Hiking Shoes
States :
Alpine Hiking Shoes offers sturdy shoes sold at €180 including VAT. The manufacturing cost of a pair is €120 excluding VAT. VAT is 20%. Each month, approximately 600 pairs are sold. The company wants to better understand its financial situation to optimize its product offering.
Work to do :
- Convert the sale price to a value excluding VAT.
- Determine how much each pair sold brings in unit margin.
- Analyze the margin rate of shoes.
- Calculate the markup rate achieved.
- Let's imagine that the sales price including tax is reduced by 5%, what would the new price excluding tax be?
Proposed correction:
-
The selling price excluding tax is obtained by:
PV HT = PV TTC ÷ (1 + VAT rate) = €180 ÷ 1,20 = €150.
The selling price excluding tax is therefore €150. -
The unit margin is calculated by deducting the cost excluding tax from the selling price excluding tax:
150 € – 120 € = 30 €.
Thus, each pair sold brings in a unit margin of €30. -
The margin rate is defined by:
((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€150 – €120) ÷ €120) x 100 = 25%.
The markup on shoes is 25%.
-
The mark rate is given by:
((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = ((€150 – €120) ÷ €150) x 100 = 20%.
The mark rate achieved is 20%. -
If the sales price including tax is reduced by 5%, the calculation is then:
New PV including tax = Old PV including tax x (1 – 0,05) = €180 x 0,95 = €171.
So, the new price excluding VAT becomes: €171 ÷ 1,20 = €142,50.
The new price excluding VAT, after this reduction, would be €142,50.
Formulas Used:
| Title | Formulas |
|---|---|
| Sale price excl. VAT | PV incl. VAT ÷ (1 + VAT rate) |
| Unit Margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| New PV including VAT | Former PV including VAT x (1 – reduction rate) |