Welcome to this article on exercises on business calculations and more specifically on 11 commercial calculation exercises Bac Pro Vente. You will find here no less than 11 detailed corrected management exercises on commercial calculations for Operational Management.
At the end of this article, you will know how to calculate brand rates, margin rates, sales prices excluding tax or tax without any worries.
In this section:
- Application: TopChauss
- Application: The Winning Business Store
- Application: The Enchanted Shop
- Application: The Market Grocery Store
- Application: “The good deals corner” store
- Application: The Wines of the Valley
- Application: ElectroMax Company
- Application: Stylado Clothing Company
- Application: Multi-Product Company
- Application: “The Magic Screen” Store
- Summary of Formulas Used:
- Application: LeBonFromage Company
Application: TopChauss
States :
The company TopChauss is a shoe store that offers products from different brands. The manager recently ordered a batch of Premium brand sports shoes at a unit purchase price excluding tax (excluding taxes) of €40.
He decided to offer these shoes for sale in his shop at a Selling Price excluding VAT of €80 per pair. To set this price, he took into account a VAT rate of 20%.
The manager wants to have better visibility on his commercial calculations linked to this purchase and sale.
Work to do :
1. Assuming that the manager sold 100 pairs of these shoes, calculate the overall margin.
2. What is the manager's margin rate on this product?
3. What is the markup rate of this product?
4. What is the selling price including tax for each pair of shoes?
5. Shudit, the new salesman, sold 30 pairs of these shoes last month. How much did he contribute to the company's overall margin?
Proposed correction:
1. The overall margin is calculated by multiplying the unit margin (PV HT – PA HT) by the quantity sold. That is: (€80 – €40) x 100 = €4000.
2. The margin rate is calculated using the formula: ((PV HT – PA HT) ÷ PA HT) x 100. That is: ((80 € – 40 €) ÷ 40 €) x 100 = 100%.
3. The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100. That is: ((80 € – 40 €) ÷ 80 €) x 100 = 50%.
4. The sales price including tax is calculated by adding the VAT rate to the sales price excluding tax. That is: €80 + (€80 x 20%) = €96.
5. Shudit contributed to the company's overall margin by selling 30 pairs of shoes. That is (€80 – €40) x 30 = €1200.
Summary of Formulas Used:
– Overall margin = Unit margin x quantity sold
– Unit margin = PV HT – PA HT
– Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100
– Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100
– Selling price including tax = VAT excluding tax + (VAT excluding tax x VAT rate)
Application: The Winning Business Store
States :
Pascal Piquion is the manager of the clothing store "Les Affaires Gagnantes". His store mainly sells branded products. Pascal recently received a new brand of premium jeans and wants to make sure that his selling price is set correctly. He bought each pair of jeans for €85 excluding VAT and he wants to make a margin of 40%. The applicable VAT rate is 20%.
Work to do :
1. Calculate the sales price excluding tax (SRP HT) of the jeans.
2. Calculate the sales price including all taxes (SRP TTC) of the jeans.
3. Calculate the VAT amount.
4. Calculate Pascal's margin rate.
5. Calculate Pascal's mark rate.
Proposed correction:
1. To calculate the sales price excluding tax (SVP HT), we use the formula: SVP HT = PA HT + (PA HT x %Margin). Thus, SVP HT = €85 + (€85 x 0,40) = €119.
2. To calculate the sales price including all taxes (PV TTC), we use the formula: PV TTC = PV HT + (PV HT x % VAT). Thus, PV TTC = €119 + (€119 x 0,20) = €142,80.
3. To calculate the amount of VAT, we use the formula: VAT = PV incl. VAT – PV excl. VAT. Thus, VAT = €142,80 – €119 = €23,80.
4. To calculate the margin rate, we use the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100. Thus, the margin rate = ((119 € – 85 €) ÷ 85 €) x 100 = 40%, which proves that Pascal has achieved his objective.
5. To calculate the markup rate, we use the formula: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100. Thus, the markup rate = ((119 € – 85 €) ÷ 119 €) x 100 = 28,57%.
Summary of Formulas Used:
| Packages | Meaning |
|---|---|
| PV HT = PA HT + (PA HT x %Margin) | Sale price excluding tax |
| PV including VAT = PV excluding VAT + (PV excluding VAT x %VAT) | Selling price including all taxes |
| VAT = PV including VAT – PV excluding VAT | VAT amount |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Margin rate |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | Brand taxes |
Application: The Enchanted Shop
States :
The Enchanted Boutique is a clothing store for women and children. The manager, Mrs. Mirabelle, has just purchased a new collection of women's tops. She purchased 200 pieces at a purchase price excluding tax (PA HT) of €15 per piece. She wants to sell each top at a sales price excluding tax (PV HT) of €30.
The VAT applicable on these items is 20%.
Work to do :
1. Calculate the overall margin for the new collection.
2. Calculate the margin rate.
3. Calculate the mark rate.
4. Calculate the sales price all taxes included (PV including tax).
5. What is the total VAT amount for the sale of the entire collection?
Proposed correction:
1. Overall margin = Unit margin x quantity sold. Here, the unit margin is PV HT – PA HT = €30 – €15 = €15. Therefore, the overall margin is €15 x 200 = €3000.
2. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100). Here, this gives ((€30 – €15) ÷ €15) x 100 = 100%. Madame Mirabelle therefore makes a margin of 100% on each top sold.
3. Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100). Here, this gives ((€30 – €15) ÷ €30) x 100 = 50%. The markup rate of the tops sold is 50%.
4. PV TTC = PV HT x (1 + (VAT rate ÷ 100)). Here, PV TTC = €30 x (1 + (20 ÷ 100)) = €30 x 1,2 = €36.
5. Total amount of VAT for the sale of the entire collection = Unit VAT x Quantity sold = (PV inc. VAT – PV excl. VAT) x Quantity sold = (€36 – €30) x 200 = €6 x 200 = €1200.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Overall margin = Unit margin x quantity sold | Calculates the total margin made on all sales |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Calculates the percentage of margin made on the purchase price excluding taxes |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | Calculates the percentage of margin made on the sales price excluding taxes |
| PV including VAT = PV excluding VAT x (1 + (VAT rate ÷ 100)) | Calculates the sales price including all taxes |
| Total VAT amount for the sale of the entire collection = Unit VAT x Quantity sold | Calculates the total amount of VAT to be paid for the sale of the entire collection |
Application: The Market Grocery Store
States :
L'Épicerie du Marché is a small business that sells a range of local and organic products. The featured products are baskets of locally grown fruits and vegetables. Here is the financial information for the top-selling item, a fruit basket:
– Purchase price excluding tax (PA HT): €10
– Quantity sold: 150 baskets per week
– Sales price excluding tax (PV HT): €20
Work to do :
1. Calculate the overall margin over a week.
2. Find the margin rate as a percentage.
3. Find the markup rate as a percentage.
4. Calculate the amount of VAT for one week assuming a VAT rate of 20%.
5. Find the sales price including all taxes (PV TTC) for a basket.
Correction Proposal:
1. The overall margin is calculated by multiplying the difference between the sales price excluding tax and the purchase price excluding tax by the quantity sold.
Overall margin = (PV HT – PA HT) x Quantity sold = (€20 – €10) x 150 = €1
2. The margin rate is calculated by dividing the difference between the sales price excluding tax and the purchase price excluding tax by the purchase price excluding tax, then multiplying the result by 100 to obtain a percentage.
Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((20€ – 10€) ÷ 10€) x 100 = 100%
3. The markup rate is calculated by dividing the difference between the sales price excluding tax and the purchase price excluding tax by the sales price excluding tax, then multiplying the result by 100 to obtain a percentage.
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = ((€20 – €10) ÷ €20) x 100 = 50%
4. The amount of VAT is calculated by multiplying the sales price excluding tax by the VAT rate.
Amount of VAT per week = PV excluding VAT x Quantity sold x VAT rate = €20 x 150 x 20% = €600
5. The sales price including all taxes is calculated by adding the amount of VAT to the sales price excluding taxes.
PV including tax for a basket = PV excluding tax + VAT = €20 + (€20 x 20%) = €24
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Overall margin = (PV HT – PA HT) x Quantity sold | Calculating the total margin over a given period |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Calculation of the percentage of margin made on each unit sold |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | Calculation of the percentage of the margin in relation to the sale price |
| VAT amount = PV excluding VAT x VAT rate | Calculation of the amount of value added tax |
| PV including VAT = PV excluding VAT + VAT | Calculation of the sales price all taxes included |
Application: “The good deals corner” store
States :
At the end of 2020, the company "Le coin des bonnes affaires", specializing in the sale of high-tech products, wishes to evaluate its financial management. You work in the financial department.
Here are some details that are communicated to you:
– The purchase cost excluding tax (CA excluding tax) of each smartphone sold is €200.
– The retail price excluding tax (PV HT) of the smartphones is €400.
– A total of 1000 smartphones were sold during the year 2020.
– The applicable VAT rate is 20%.
Work to do :
1. Calculate the overall margin achieved for the year 2020.
2. Calculate the margin rate made on each smartphone sale.
3. Calculate the mark rate.
4. How much money did the company collect for the state in VAT?
5. What is the selling price including tax of each smartphone?
Proposed correction:
1. The overall margin is calculated using the formula: Unit margin x quantity sold. The unit margin is obtained by subtracting the unit purchase cost excluding tax from the unit selling price excluding tax, i.e. €400 – €200 = €200. Therefore the overall margin is €200 x 1000 = €200.
2. The margin rate is calculated using the formula: ((PV HT – PA HT) ÷ PA HT) x 100. Therefore, ((400 € – 200 €) ÷ 200 €) x 100 = 100%.
3. The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100. Therefore, ((€400 – €200) ÷ €400) x 100 = 50%.
4. The VAT collected is calculated using the formula: PV HT x VAT rate. Therefore, (€400 x 20%) x 1000 = €80.
5. The sales price including tax is calculated using the formula: PV HT x (1 + VAT rate). Therefore, €400 x (1 + 20%) = €480.
Summary of Formulas Used:
| 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 |
| VAT collected | PV HT x VAT rate |
| PV including tax | PV HT x (1 + VAT rate) |
Application: The Wines of the Valley
States :
The company “The Wines of the Valley” specializing in the wine trade has a diversified range of products. Recently, it has acquired a new wine brand "Pépite d'Or" whose details are as follows:
Purchase price excluding tax (PA HT): €6,00
Sales price excluding tax (PV HT): €10,00
Quantity sold: 5000 bottles
The VAT rate is 20%.
Work to do :
1. Calculate the unit margin of the “Pépite d'Or” bottle of wine.
2. Calculate the overall margin for the quantity sold of the bottle of “Pépite d'Or” wine.
3. Calculate the margin rate of the “Pépite d'Or” bottle of wine.
4. Calculate the markup rate of the “Pépite d'Or” bottle of wine.
5. Calculate the sales price including all taxes (PV TTC) of a bottle of “Pépite d'Or” wine.
Proposed correction:
1. The unit margin is the difference between the sales price excluding tax and the purchase price excluding tax. In this case, Unit margin = PV excluding tax – PA excluding tax = €10,00 – €6,00 = €4,00
2. The overall margin is the unit margin multiplied by the quantity sold, i.e. Overall margin = Unit margin x Quantity sold = €4,00 x 5000 = €20
3. The margin rate is the ratio of the margin to the purchase price excluding tax, multiplied by 100, i.e. Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = (€4,00 ÷ €6,00) x 100 = 66,67%
4. The markup rate is the ratio of the margin to the selling price excluding tax, multiplied by 100, i.e. Markup rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = (€4,00 ÷ €10,00) x 100 = 40,00%
5. The sales price including all taxes (PV TTC) is the sales price excluding tax plus VAT. Here, VAT = PV excluding tax x (VAT rate/100) = €10,00 x 20/100 = €2,00. Hence PV TTC = PV excluding tax + VAT = €10,00 + €2,00 = €12,00
Summary of Formulas Used:
| Formulas | Definition |
| Unit margin = PV excluding tax – PA excluding tax | The unit margin is the difference between the selling price excluding tax and the purchase price excluding tax. |
| Overall margin = Unit margin x Quantity sold | The overall margin is the total amount of margin generated for all products sold. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | The margin rate is the percentage that represents the margin compared to the purchase price excluding tax. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | The markup rate is the percentage that represents the margin compared to the sales price excluding tax. |
| PV including VAT = PV excluding VAT + VAT | The sales price including tax is the price that the consumer pays. It contains both the sales price excluding tax and the applicable taxes. |
Application: ElectroMax Company
States :
ElectroMax is a distributor of household appliances. It buys washing machines from its supplier at a price of €250 excluding VAT per unit.
1. It applies a markup rate of 130% to set its selling price.
2. Then, it applies the VAT rate of 20% to obtain its sales price including tax.
3. During a sales period, she decides to give a 15% discount on the sales price including tax.
4. We want to know the number of washing machines that she must sell to obtain an overall margin of €100 during this sales period.
5. We also want to know the margin rate of the ElectroMax company on each washing machine it sells.
Work to do :
1. Calculate the selling price excluding VAT
2. Calculate the sales price including tax
3. Calculate the sales price including tax after the discount
4. Calculate the number of washing machines to sell to obtain an overall margin of €100
5. Calculate the margin rate on each washing machine sold
Proposed correction:
1. The selling price excluding VAT is calculated as follows: Purchase price excluding VAT x (1 + Markup rate). Here, this gives: €250 x (1 + 130/100) = €575
2. The sales price including VAT is obtained by adding VAT to the sales price excluding VAT. Therefore, €575 x (1+20/100) = €690
3. The sales price including VAT after the discount is: €690 x (1- 15/100) = €586,5
4. To find the number of washing machines to sell to obtain an overall margin of €100, we divide this overall margin by the unit margin. The unit margin is the difference between the sale price including tax after the discount and the purchase price excluding tax, i.e. €000 – €586,5 = €250. So, €336,5 / €100? 000 washing machines to sell.
5. The margin rate is given by the formula: ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100. That is ((€575 – €250) ÷ €250) x 100 = 130%
Summary of Formulas Used:
| Packages | Description |
|---|---|
| Selling price excluding tax = PA excluding tax x (1 + Markup rate) | To calculate the sales price excluding tax |
| Selling price including tax = PV excluding tax x (1 + VAT rate) | To calculate the sales price including all taxes |
| Price after discount = PV including tax x (1 – Discount rate) | To calculate the sales price including tax after a discount |
| Number of products to sell = Overall margin ÷ Unit margin | To calculate the number of products to sell to obtain a defined overall margin |
| Margin rate = ((PV HT – PA HT) ÷ PA HT) * 100 | To calculate the margin rate on each product sold |
Application: Stylado Clothing Company
States :
La Stylado is a company that specializes in selling high-end clothing. It recently acquired a new clothing line, the Chemise Royale, which is sold at a price of €120 including tax. The unit purchase of the product from its suppliers costs it €50 excluding tax. The company sold 100 pieces of Chemise Royale this month.
Work to do :
1. Calculate the overall margin made on this sale.
2. Calculate the margin rate of the Stylado company.
3. Calculate the mark rate.
4. Suppose the company has decided to increase its selling price by 15%, then calculate the new markup rate.
5. If the company decided to implement this new rate, how many shirts must it sell to maintain its original overall margin?
Proposed correction:
1. To calculate the overall margin, we use the formula: Overall margin = Unit margin x Quantity sold. For the product Chemise Royale, we then have: Unit margin = Selling price excluding tax (€120 / 1,20 = €100) – Purchase price excluding tax = €100 – €50 = €50. Thus, Overall margin = €50 x 100 = €5.
2. To calculate the margin rate, we use the formula: Margin rate = ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100. For the product Chemise royale, we then have: ((€100 – €50) ÷ €50) x 100 = 100%.
3. To calculate the markup rate, we use the formula: Markup rate = ((Selling price excluding VAT – Purchase price excluding VAT) ÷ Selling price excluding VAT) x 100. For the product Chemise Royale, we obtain: ((€100 – €50) ÷ €100) x 100 = 50%.
4. If the company increases its sales price by 15%, the new sales price excluding VAT will be: €100 x 1,15 = €115. The new markup rate will therefore be: ((€115 – €50) ÷ €115) x 100 = 56,52%.
5. To maintain the same overall margin, the company should sell: Overall margin / New unit margin = €5 / (€000 – €115) = approximately 50 shirts.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Overall margin = Unit margin x Quantity sold | Allows you to calculate the total margin on the sale of multiple units of a product. |
| Margin rate = ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 | Allows you to calculate the percentage of margin made on the purchase cost of a product. |
| Brand rate = ((Sales price excluding tax – Purchase price excluding tax) ÷ Sales price excluding tax) x 100 | This rate indicates the commercial margin as a percentage of the selling price excluding tax. |
Application: Multi-Product Company
States :
MultiProducts Company operates in the wholesale sector. It sells various products, including electrical gadgets, books and office supplies. The company recently purchased a batch of digital tablets at a unit cost of €200 excluding VAT. It plans to sell these tablets at €350 excluding VAT per unit. The quantity of tablets purchased is 500 units.
Work to do :
1. What is the total cost excluding tax for the company of this purchase operation?
2. What is the expected turnover for the sale of these tablets?
3. What is the overall margin and margin rate expected for this batch of tablets?
4. What is the expected markup rate?
5. If the company decides to apply a VAT rate of 20%, what will be the sales price including VAT of each tablet?
Proposed correction:
1. The total cost excluding tax for the company of this purchase operation is €200 x €500 = €100.
2. The expected turnover for the sale of these tablets is €350 excluding tax x 500 = €175 excluding tax.
3. The overall margin is calculated by (Sale price excluding VAT – Purchase price excluding VAT) x Quantity sold. That is (€350 – €200) x 500 = €75. The margin rate is calculated by ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 000. That is ((€100 – €350) ÷ €200) x 200 = 100%.
4. The markup rate is calculated by ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Sale price excluding VAT) x 100. That is ((€350 – €200) ÷ €350) x 100 = 42.86%.
5. If the company applies a VAT rate of 20%, the sales price including VAT of each tablet will be €350 x (1 + 20/100) = €420.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Overall margin = Unit margin x quantity sold | Calculates the overall margin for a batch or multiple batches of a product |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100) | Calculates the margin rate based on the cost and the selling price excluding taxes |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100) | Calculates the markup rate based on the cost and the sales price excluding tax |
| Price including tax = Price excluding tax x (1 + VAT rate / 100) | Allows you to determine the price including tax from the price excluding tax and the VAT rate |
Application: “The Magic Screen” Store
States :
The store "L'écran Magique" sells televisions. The purchase price excluding tax (PA HT) of a television is €400. The store applies a margin of 30% on the purchase prices excluding tax to calculate the sales prices excluding tax (PV HT). The VAT rate applicable to this type of product is 20%.
Work to do :
1. Calculate the Sales Price excluding tax (SRP HT).
2. Calculate the sales price including all taxes (PV TTC)
3. Calculate the overall margin if we sell 100 televisions.
4. What is the margin rate?
5. What is the markup rate?
Proposed correction:
1. The sales price excluding tax is calculated as follows: PV excluding tax = PA excluding tax + (Margin in % x PA excluding tax) = €400 + (30% x €400) = €400 + €120 = €520
2. The sales price including all taxes is obtained by adding VAT to the PV excluding VAT: PV including tax = PV excluding VAT + (VAT in % x PV excluding VAT) = €520 + (20% x €520) = €520 + €104 = €624.
3. The overall margin results from multiplying the unit margin by the quantity sold: Overall margin = Unit margin x quantity sold = (PV HT – PA HT) x quantity sold = (€520 – €400) x 100 = €120 x 100 = €12.
4. The margin rate is calculated as follows: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((€520 – €400) ÷ €400) x 100 = 30%.
5. The markup rate is obtained using the following formula: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((€520 – €400) ÷ €520) x 100 = 23,07%.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| PV HT = PA HT + (Margin in % x PA HT) | To calculate the Sales Price excluding tax |
| PV including VAT = PV excluding VAT + (VAT in % x PV excluding VAT) | To obtain the sales price including all taxes |
| Overall margin = Unit margin x quantity sold | To determine the overall margin based on the number of products sold |
| Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 | To calculate the margin rate |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | To get the mark rate |
Summary of Formulas Used:
| Spas | Formula |
|---|---|
| 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) |
Application: LeBonFromage Company
States :
The company LeBonFromage, specialized in the sale of cheese, carried out the following transactions:
1. She sold 200 cheeses at €5 excluding tax each.
2. The VAT rate applied is 20%.
3. The purchase price of the cheese is €3 excluding VAT.
Work to do :
1. Calculate the total amount excluding tax of sales.
2. Calculate the total amount of VAT.
3. Calculate the sales price including tax of each cheese.
4. Calculate the unit margin.
5. When calculating the margin rate, post a comment on profitability.
Proposed correction:
1. The total amount excluding tax of sales is 200 x 5 = €1.
2. The total VAT amount is 1 x 000% = €20.
3. The sales price including tax of each cheese is 5 + (5 x 20%) = €6.
4. The unit margin is 5 – 3 = €2.
5. The margin rate is ((5 – 3) ÷ 3) x 100 = 66,67%. The profitability of the cheese is therefore very good, with a margin of €2, i.e. a rate of 66,67%.