Welcome to this article dedicated to applications on business calculations and more specifically on the calculation of the commercial margin, VAT, the margin rate, the markup rate. You will find here no less than 11 applications of corrected and detailed commercial calculations of management on commercial calculations for Operational Management.
By the end of this article, you will know how to easily perform the 11 business calculation applications without any worries.
In this section:
- Application: EcoShop Supermarket
- Application: World Coffee
- Application: “Chez Grand Père” Supermarket
- Application: TechnoHigh Company
- Application: Self-Service
- Application: “Douce Maison” furniture store
- Application: Bakery “Au Petit Grain”
- Application: “DormEco” Bedding House
- Application: “Les Gourmands” Supermarket
- Application: Elisa Chocolate Factory
- Application: Chocolate House
Application: EcoShop Supermarket
States :
EcoShop supermarket has decided to offer its customers several promotions on certain products to increase its sales. To do this, they must calculate the different financial parameters such as VAT, margin rate, markup rate, sales price including VAT, margin, discounts and increases.
Here are the details for one of the products on which a promotion is being offered:
– Purchase price excluding tax (PA excluding tax): €100
– Margin rate usually applied: 30%
– Proposed reduction rate: 10%
– VAT rate: 20%
Work to do :
1. Calculate the sales price excluding tax (PV HT) by applying the usual margin rate.
2. Calculate the markup rate on the product.
3. Calculate the VAT to obtain the sales price including VAT.
4. How much is the overall margin if we sell 50 units of the product?
5. Calculate the new sales price including tax after applying the reduction.
Proposed correction:
1. The PV HT is calculated by applying the margin rate to the PA HT. Therefore, PV HT = PA HT + (Margin rate x PA HT). Here, PV HT = €100 + (0,30 x €100) = €130.
2. The markup rate is calculated as follows: ((PV HT – PA HT) ÷ PV HT) x 100. Here, ((130 € – 100 €) ÷ 130 €) x 100 = 23,08%.
3. VAT is calculated by multiplying the PV excluding VAT by the VAT rate, so VAT = PV excluding VAT x VAT rate. VAT = €130 x 0,20 = €26. This VAT is then added to the PV excluding VAT to obtain the PV including VAT, so PV including VAT = PV excluding VAT + VAT. PV including VAT = €130 + €26 = €156.
4. The overall margin is calculated using the formula Unit margin x quantity sold. Here, the unit margin is PV HT – PA HT = €130 – €100 = €30. If we sell 50 units, then the overall margin = €30 x 50 = €1500.
5. The discount is calculated by multiplying the VAT PV by the discount rate. Therefore, Discount = VAT PV x Discount rate. With a 10% discount, we have Discount = €156 x 0,10 = €15,6. We then subtract this discount from the VAT PV to obtain the new VAT PV, so New VAT PV = VAT PV – Discount. New VAT PV = €156 – €15,6 = €140,4.
Summary of Formulas Used:
| Item | Formula |
|---|---|
| PV HT | PA HT + (Margin rate x PA HT) |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| VAT | PV excluding VAT x VAT rate |
| PV including tax | PV excluding VAT + VAT |
| Overall margin | Unit margin x Quantity sold |
| Discount | PV incl. VAT x Reduction rate |
| New PV including VAT | PV TTC – Reduction |
Application: World Coffee
States :
Café du Monde, a small family business located in the center of Paris, is renowned for its selection of coffees from around the world. As part of their financial statement, they need to understand several aspects of their financial operation.
They buy a kilo of coffee beans at €10 excluding VAT from their supplier. After roasting, they sell the kilo of coffee at €16 excluding VAT. They want to know their margin and brand rate for this product.
In addition, Café du Monde has planned a 10% increase on the net selling price of coffee. They also want to offer a 15% discount on the new price for a promotional offer.
Café du Monde is subject to a VAT rate of 20% and they wish to calculate the sales price including VAT before and after the reduction.
Work to do :
1. Calculate Café du Monde’s margin rate on their coffee.
2. Calculate the markup rate of Café du Monde on their coffee.
3. Calculate the new selling price excluding VAT after the 10% increase.
4. Calculate the sales price including tax before the reduction.
5. Calculate the sales price including tax after the 15% reduction.
Proposed correction:
1. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((16 € – 10 €) ÷ 10 €) x 100 = 60%
2. Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((16 € – 10 €) ÷ 16 €) x 100 = 37,5%.
3. New PV HT = Old PV HT + (10% of the old PV HT) = €16 + (10% of €16) = €16 + €1,60 = €17,60.
4. PV including tax before reduction = New PV excluding tax x (1 + VAT rate) = €17,60 x (1 + 20%) = €21,12.
5. PV including tax after reduction = PV including tax before reduction – 15% of PV including tax before reduction = €21,12 – 15% of €21,12 = €17,95.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | This formula is used to calculate the margin rate. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | This formula calculates the markup rate. |
| PV including VAT = PV excluding VAT x (1 + VAT rate) | This formula calculates the sales price including tax. |
| Price after reduction or increase = Initial price x (1 ± percentage reduction or increase) | This formula is used to calculate the price after a reduction or increase. |
Application: “Chez Grand Père” Supermarket
The supermarket “Chez Grand Père” is a well-established food distribution company in the city of Nantes in France. The company’s management is planning to introduce a new product into their store: “Marie Jeanne organic orange juice”. They have purchased this product from a local supplier at a purchase price excluding tax (PA HT) of €2,00 per bottle. The management plans to sell each bottle at a sales price excluding tax (PV HT) of €3,00.
States :
The company “Chez Grand Père” is seeking your expertise in financial management to better understand and interpret different aspects of its pricing policy.
Work to do :
1. Calculate the unit margin of “Marie Jeanne organic orange juice”.
2. Determine the margin rate and the markup rate of this product.
3. Calculate the sales price including all taxes (PV TTC) by adding VAT at the standard rate of 20%.
4. Calculate the new overall margin if the company decides to increase the quantity sold of this product by 1000 units.
5. Evaluate the effects of a 20% reduction in the selling price on the margin rate, the markup rate and the overall margin.
Proposed correction:
1. The unit margin is the difference between the sales price excluding tax (SPT) and the purchase price excluding tax (PP). In this case, the unit margin would be €3,00 – €2,00 = €1,00.
2. The margin rate is calculated by dividing the unit margin by the purchase price excluding tax and multiplying the result by 100. Here, the margin rate would be ((€3,00 – €2,00) ÷ €2,00) x 100 = 50%. On the other hand, the markup rate is obtained by dividing the unit margin by the sale price excluding tax and multiplying the result by 100. The markup rate in this case would therefore be ((€3,00 – €2,00) ÷ €3,00) x 100 = 33,33%.
3. The sales price including all taxes (PV TTC) is obtained by adding VAT (20% of the sales price excluding taxes) to the sales price excluding taxes. Thus, the PV TTC would be €3,00 + (20% of €3,00) = €3,60.
4. The overall margin is obtained by multiplying the unit margin by the quantity sold. If the company decides to increase the quantity sold of this product by 1000 units, the new overall margin would be €1,00 x 1000 = €1000,00.
5. A 20% reduction in the sales price would affect the margin rate, the mark-up rate as well as the overall margin. The new PV excluding tax after reduction would be €3,00 – (20% of €3,00) = €2,40.
The new margin rate would be ((€2,40 – €2,00) ÷ €2,00) x 100 = 20% and the new markup rate would be ((€2,40 – €2,00) ÷ €2,40) x 100 = 16,67%. The overall margin would also decrease because it is directly proportional to the selling price. Thus, the new overall margin would be €0,40 x 1000 = €400,00.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Unit margin = PV excluding tax – PA excluding tax | Calculation of the unit margin of a product. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Calculation of the margin rate of a product. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | Calculating the markup rate of a product. |
| PV including tax = PV excluding tax + (VAT% of PV excluding tax) | Calculation of the sales price including all taxes (PV TTC). |
| Overall margin = Unit margin x Quantity sold | Calculation of the overall margin made on a product. |
| PV HT after reduction = PV HT – (Reduction% of PV HT) | Calculation of the sales price excluding tax after a reduction. |
Application: TechnoHigh Company
TechnoHigh is a company specializing in the sale of electronic equipment. It recently launched a new product, a tablet specially designed for technology professionals. It sold this product at a unit sales price excluding VAT of €500 and purchased it at a unit purchase price excluding VAT of €300. VAT is 20%. The company has sold 1000 units of this tablet so far.
States :
1. Calculate the VAT value for one unit of product.
2. Determine the sales price including tax for a unit of product.
3. Calculate the company's unit margin.
4. Determine the company's margin rate.
5. Calculate the company's overall margin.
Work to do :
1. Apply the VAT calculation formula.
2. Use the formula for the sales price including tax.
3. Apply the unit margin calculation formula.
4. Use the margin rate formula.
5. Apply the overall margin formula.
Proposed correction:
1. Unit VAT = Unit selling price excluding VAT x VAT rate = €500 x 20% = €100
2. Unit sales price including tax = Unit sales price excluding tax + unit VAT = €500 + €100 = €600
3. Unit margin = Unit selling price excluding VAT – Unit purchase price excluding VAT = €500 – €300 = €200
4. Margin rate = ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100 = ((€500 – €300) ÷ €300) x 100 = 66,67%
5. Overall margin = Unit margin x Quantity sold = €200 x 1000 = €200
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| VAT = Selling price excluding VAT x VAT rate | VAT calculation formula |
| Selling price including tax = Selling price excluding tax + VAT | Formula for calculating the sales price including tax |
| Unit margin = Sales price excluding tax – Purchase price excluding tax | Formula for calculating unit margin |
| Margin rate = ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 | Formula for calculating the margin rate |
| Overall margin = Unit margin x Quantity sold | Formula for calculating the overall margin |
Application: Self-Service
States :
LibreService is a supermarket chain that buys chocolate bars from a supplier at a price excluding VAT of €1,20. The applicable VAT rate is 20%. LibreService resells these chocolate bars to its customers by applying a margin of 30% on the purchase price excluding VAT.
During a promotional operation, LibreService decides to lower the selling price of these chocolate bars by 10%. After this operation, the company decides to increase the selling price of the bars by 10%.
Work to do :
1. Calculate the selling price excluding VAT and the mark-up rate of the chocolate bar.
2. Calculate the VAT, the sales price including VAT and the margin rate of the chocolate bar.
3. Calculate the amount of the discount during the promotional operation.
4. Calculate the new selling price after the discount.
5. Calculate the amount of the increase after the promotional operation.
Proposed correction:
1. PV HT = PA HT x (1 + Margin rate) = €1,20 x (1 + 30/100) = €1,56. The markup rate = ((PV HT – PA HT) ÷ PV HT) x 100) = ((€1,56 – €1,20) ÷ €1,56) x 100 = 23,08%.
2. VAT = PV HT × VAT rate = €1,56 x 20/100 = €0,31. PV TTC = PV HT + VAT = €1,56 + €0,31 = €1,87. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((€1,56 – €1,20) ÷ €1,20) x 100 = 30%.
3. Discount = Initial amount x Discount rate = €1,87 x 10/100 = €0,19.
4. New sale price after reduction = PV incl. VAT – Reduction = €1,87 – €0,19 = €1,68.
5. Increase = Amount after reduction x Increase rate = €1,68 x 10/100 = €0,17. New sale price after increase = Amount after reduction + Increase = €1,68 + €0,17 = €1,85.
Summary of Formulas Used:
| Packages | Explanation |
|---|---|
| VAT = Amount excluding VAT × VAT rate | Value Added Tax is calculated by applying the VAT rate to the amount excluding tax. |
| PV including VAT = PV excluding VAT + VAT | The sales price including all taxes is equal to the sales price excluding taxes increased by VAT. |
| Overall margin = Unit margin x quantity sold | The overall margin is the product of the unit margin and the quantity sold. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100) | The margin rate is the proportion of profit made per unit sold, in relation to the purchase cost excluding tax. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100) | The markup rate is the proportion of profit made per unit sold, reported to the selling price excluding tax. |
| Reduction = Initial Amount – Amount after reduction | Discount is the amount by which the price of a product decreases from its original price. |
| Increase = Amount after increase – Initial Amount | The increase is the amount by which the price of a product increases from its original price. |
Application: “Douce Maison” furniture store
States :
The furniture store "Douce Maison" offers a wide range of furniture items. These items are purchased at a purchase price and are then sold at a higher sale price to make a profit. The Store operates on two VAT rates at 20% and 5,5%.
1. The “Cottage” table is purchased at a purchase price excluding VAT of €350. It is then sold at a sale price excluding VAT of €500. What is the margin made on the sale of this table? What are the margin rate and the mark-up rate?
2. The “Cosy” chair is purchased at a purchase price excluding tax of €60. The margin rate that the store wishes to apply is 55%. Calculate its sales price excluding tax. What will then be the sales price including tax of this item if it is subject to a VAT rate of 20%?
3. The store wants to give a 15% discount on the sales price including tax of the “Rustique” chest of drawers initially sold at €1200 including tax. What will the new price be after the discount?
4. After an increase in production costs, the store is forced to increase the selling price excluding VAT of the “Modern Chic” sofa, initially sold at €800 excluding VAT, by 6%. What will the new selling price excluding VAT be?
5. The store sells 15 units of the “Traditional” cabinet per month at a unit price excluding tax of €700. What is the overall margin that the store makes on the sale of this product per month?
Work to do :
1. Calculate the margin, margin rate and markup rate on the “Cottage” table.
2. Determine the sales price excluding tax and then the sales price including tax of the “Cosy” chair.
3. Calculate the new sale price of the “Rustic” chest of drawers after reduction.
4. Determine the new selling price excluding tax of the “Modern Chic” sofa after the increase.
5. Calculate the overall margin on the monthly sale of the “Traditional” cabinet.
Proposed correction:
1. Margin = Selling price excluding VAT – Purchase price excluding VAT = €500 – €350 = €150.
Margin rate = ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100 = ((€500 – €350) ÷ €350) x 100 = 42,86%.
Markup rate = ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Sale price excluding VAT) x 100 = ((€500 – €350) ÷ €500) x 100 = 30%.
2. Selling price excluding VAT = Purchase price excluding VAT x (1 + (margin rate / 100)) = €60 x (1 + (55 / 100)) = €93.
Selling price including tax = Selling price excluding tax x (1 + VAT rate / 100) = €93 x (1 + 20 / 100) = €111,60.
3. Discount = Initial price x discount rate / 100 = €1200 x 15 / 100 = €180.
New price after reduction = Initial price – Reduction = €1200 – €180 = €1020.
4. Increase = Initial price x increase rate / 100 = €800 x 6 / 100 = €48.
New price after increase = Initial price + Increase = €800 + €48 = €848.
5. Unit margin = Selling price excluding VAT – Purchase price excluding VAT = €700 – Purchase price excluding VAT (Let’s assume for example €500) = €200.
Overall margin = Unit margin x Quantity sold = €200 x 15 = €3000.
Summary of Formulas Used:
| Formulas | Definition |
|---|---|
| VAT rate | 20% | 5,5% |
| Overall margin | Unit margin x quantity sold |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Sales price including tax | PV HT x (1 + VAT rate / 100) |
| Discount | Original price – Reduced price |
| Increase | Final price – Initial price |
Application: Bakery “Au Petit Grain”
States :
The bakery "Au Petit Grain" is a company known for its high-quality artisanal pastries. The owner wants to have better financial management of his company following recent changes concerning the taxation and structuring of the prices of his products. He consulted his accounting documents and noted the following figures:
– Purchase price excluding tax (PA HT) of a batch of bread dough: €80
– Sales price excluding tax (PV HT) of the same batch after processing: €120
– Quantity of bread sold per day: 200
– VAT rate applicable to its products: 5,5%
– It also plans to increase its sales prices by 2% following the increase in production costs
– Finally, it offers its regular customers a 5% discount on the sale price.
Work to do :
1. What is the unit margin that the owner makes on a batch of bread?
2. Calculate the margin rate and markup rate on a batch.
3. What is the selling price including tax (PV TTC) of a batch after the 2% increase?
4. If a regular customer buys a batch of bread, how much will he pay after the 5% discount?
5. How does VAT impact the overall margin of the bakery?
Proposed correction:
1. The unit margin is calculated by the difference between the PV excluding tax and the PA excluding tax. In our case, this gives €120 – €80 = €40. The owner therefore makes a unit margin of €40 on a batch of bread.
2. The margin rate is calculated using the formula: ((PV HT – PA HT) ÷ PA HT) x 100. This gives: ((120 € – 80 €) ÷ 80 €) x 100 = 50%. As for the markup rate, it is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100. This gives: ((120 € – 80 €) ÷ 120 €) x 100 = 33,33%.
3. The PV including tax after the 2% increase is calculated as follows: (PV HT x 1,02) x (1 + 0,055). This gives: (€120 x 1,02) x (1 + 0,055) = €130,26.
4. If a regular customer buys a batch of bread, after the 5% discount he will pay: €130,26 x (1 – 0,05) = €123,75.
5. VAT impacts the overall margin by increasing the sales price including VAT, which can decrease demand if customers are price sensitive. This could lead to a decrease in the overall margin if sales volume decreases. In addition, VAT is a non-recoverable cost for the customer, which reduces the perceived value of the offer.
Summary of Formulas Used:
| Concept | 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 |
| PV including tax after increase | (PV HT x increase %) x (1 + VAT) |
| Price after reduction | PV incl. VAT x (1 – reduction %) |
Application: “DormEco” Bedding House
States :
The bedding company "DormEco" specializes in the sale of high-end mattresses. The manager of this company, Mr. Lafond, wants to analyze the financial performance of his company and make pricing decisions based on various business scenarios. Based on a specific mattress that costs €500 to purchase (PA HT) and is sold at a sales price excluding taxes (PV HT) of €800, consider the following parameters: the VAT rate at 20% and possible price increases or reductions.
Work to do :
1. What is the selling price including tax of this mattress?
2. How much value added tax (VAT) is added to the selling price of the mattress?
3. If Mr. Lafond reduces the PV excluding tax to €750, how much unit margin does he lose and what will the new margin rate be?
4. If Mr. Lafond, for a special promotion, decides to make a 10% reduction on the sales price including tax, how much does the company lose for each mattress sold?
5. Finally, if Mr. Lafond decides to increase the PV excluding tax to €900, what will the new markup rate be?
Proposed correction:
1. The selling price including tax of the mattress is calculated by adding the VAT to the PV excluding tax, i.e. €800 + (800 x 20 ÷ 100) = €960.
2. The VAT added to the sale price of the mattress amounts to 800 x 20 ÷ 100 = €160.
3. If Mr. Lafond reduces the PV excluding tax to €750, the unit margin goes from €300 to €250. The margin rate is then ((750 – 500) ÷ 500) x 100 = 50%.
4. If Mr. Lafond makes a 10% reduction on the sales price including tax, the company loses 960 x 10 ÷ 100 = €96 for each mattress sold.
5. If Mr. Lafond increases the PV excluding tax to €900, the markup rate will be ((900 – 500) ÷ 900) x 100 = 44,44%.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| VAT | PV HT x VAT rate / 100 |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| PV including tax | PV excluding VAT + VAT |
| Margin | Unit margin x quantity sold |
| Reduction | Initial price – Final price |
| Increase | Final price – Initial price |
Application: “Les Gourmands” Supermarket
States :
The supermarket "Les Gourmands" is a leader in the food sector. They are preparing to place new product orders for the next quarter. They want to conduct an in-depth analysis of their financial performance to understand the profitability of certain product lines and to be able to negotiate new rates with suppliers.
For one of the company's flagship products, a jar of luxury strawberry jam, the information is as follows:
Purchase price excluding tax (PA HT): €2,50
Sales price excluding tax (PV HT): €3,50
Quantity sold: 10 units
VAT rate: 20%
Work to do :
1. Calculate the unit margin amount and the overall margin for this product.
2. Calculate the margin rate.
3. Calculate the mark rate.
4. Calculate the sales price including tax.
5. If the supermarket considers a 10% discount on the PV excluding VAT, what would be the new margin rate and the new brand rate?
Proposed correction:
1. Unit margin = PV HT – PA HT = €3,50 – €2,50 = €1
Overall margin = Unit margin x quantity sold = €1 x 10 = €000
2. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((€3,50 – €2,50) ÷ €2,50) x 100 = 40%
3. Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((€3,50 – €2,50) ÷ €3,50) x 100 = 28,57%
4. VAT = (VAT rate x PV excluding VAT) ÷ 100 = (20 x €3,50) ÷ 100 = €0,70
Selling price including tax = PV excluding tax + VAT = €3,50 + €0,70 = €4,20
5. New PV excluding VAT after reduction = PV excluding VAT – (10% of PV excluding VAT) = €3,50 – (10% of €3,50) = €3,15
New margin rate = ((New PV HT – PA HT) ÷ PA HT) x 100 = ((€3,15 – €2,50) ÷ €2,50) x 100 = 26%
New mark rate = ((New PV HT – PA HT) ÷ New PV HT) x 100 = ((€3,15 – €2,50) ÷ €3,15) x 100 = 20,63%
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| VAT | (VAT rate x tax base) ÷ 100 |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Sales price including tax | PV excluding VAT + VAT |
| Overall margin | Unit margin x quantity sold |
| Discount | Initial amount – (discount rate x initial amount) |
Application: Elisa Chocolate Factory
States :
Chocolaterie Elisa is an artisanal company specializing in the production and marketing of different types of chocolates. The company decides to evaluate its financial performance and determine the impact of various business strategies on its finances.
She buys cocoa beans at €5 excluding VAT per unit and transforms them into chocolates which she sells at a sales price excluding VAT (SVP excluding VAT) of €9. The VAT rate is 20%. The chocolate factory managed to sell 2000 units of chocolates during the year.
During Black Friday, the company offered a 10% discount on the sale price of all its chocolate varieties.
In addition, due to rising production costs, the company is considering increasing the prices of its products by 5%.
Work to do :
1. Calculate the margin rate.
2. Calculate the mark rate.
3. Calculate the PV including tax.
4. Calculate the overall margin during the year.
5. Calculate the new price after the reduction as well as the one after the increase.
Proposed correction:
1.
For the margin rate, the company has a PV HT of €9 and a PA HT of €5. Therefore, we use the formula [(PVHT – PAHT) ÷ PAHT] x 100.
The margin rate is therefore ((9 – 5) ÷ 5) x 100 = 80%.
2.
For the brand rate, we use the formula [(PVHT – PAHT) ÷ PVHT] x 100.
The markup rate is therefore ((9 – 5) ÷ 9) x 100 = 44,44%.
3.
The PV including tax is defined as the PV excluding tax to which VAT is added. In this case, PV including tax = PV excluding tax + (PV excluding tax x VAT rate).
So, PV including tax = 9 + (9 x 20%) = €10,8.
4.
The overall margin is calculated by multiplying the unit margin (PV HT – PA HT) by the quantity sold. Therefore, the overall margin is (9 – 5) x 2000 = €8000.
5.
The new price after reduction is PV incl. VAT – (PV incl. VAT x 10%) = 10,8 – (10,8 x 10%) = €9,72.
The new price after the increase is PV TTC + (PV TTC x 5%) = 10,8 + (10,8 x 5%) = 11,34 €.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Sales price including tax | PV excluding VAT + (PV excluding VAT x VAT rate) |
| Overall margin | Unit margin x quantity sold |
| After reduction | PV incl. tax – (PV incl. tax x reduction rate) |
| After increase | PV TTC + (PV TTC x increase rate) |
Application: Chocolate House
States :
La Maison du Chocolat is one of the most famous chocolate shops. In order to maximize their profit, they want to analyze their cost and price structure. They sell a box of chocolates for €50 including tax. The purchase price excluding tax of this box is €20. They plan to sell 1200 boxes this month. The VAT applied is 20%.
Work to do :
1. What is the selling price excluding tax of the box of chocolates?
2. What is the margin rate and the markup rate?
3. Calculate the overall margin for this month.
4. If Maison du Chocolat offers a 10% reduction on the selling price excluding VAT, what will the new selling price including VAT be?
5. If Maison du Chocolat increases the purchase price excluding tax by 15%, what will be the mark-up rate and the margin rate?
Proposed correction:
1. The selling price excluding VAT is calculated using the formula: Selling Price including VAT ÷ (1 + VAT rate/100). Therefore, the selling price excluding VAT of the box of chocolates is €50 ÷ (1 + 20/100) = €41,67.
2. The margin rate is calculated using the formula: ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100. Therefore, the margin rate is ((€41,67 – €20) ÷ €20) x 100 = 108,35%. The markup rate is calculated using the formula: ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Sale price excluding VAT) x 100. Therefore, the markup rate is ((€41,67 – €20) ÷ €41,67) x 100 = 52%.
3. The overall margin is calculated using the formula: Unit margin x quantity sold. Here, the unit margin is €41,67 – €20 = €21,67. So, the overall margin for this month is €21,67 x 1200 = €26.
4. If Maison du Chocolat offers a 10% discount on the net selling price, the new net selling price will be €41,67 – 10% of €41,67 = €37,50. To find the new net selling price, you need to calculate: Net Selling Price x (1 + VAT Rate/100) or €37,50 x (1 + 20/100) = €45.
5. If Maison du Chocolat increases the purchase price excluding VAT by 15%, the new purchase price excluding VAT will be €20 + 15% of €20 = €23. Using the same formulas for margin and markup: The margin rate will be ((€41,67 – €23) ÷ €23) x 100 = 81,17%. The markup rate will be ((€41,67 – €23) ÷ €41,67) x 100 = 44,77%.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Selling price excluding VAT = Selling price including VAT ÷ (1 + VAT rate/100) | Calculates the sales price excluding tax |
| Margin rate = ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 | Calculates the margin rate as a percentage |
| Brand rate = ((Sales price excluding tax – Purchase price excluding tax) ÷ Sales price excluding tax) x 100 | Calculates the markup rate as a percentage |
| Overall margin = Unit margin x quantity sold | Provides the total sales margin on all products |