Commercial Calculations BTS NDRC (11 corrected exos)

Welcome to this article on exercises on business calculations and more specifically on 11 commercial calculation exercises for BTS NDRC. 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.

Application: Fresh Grocery Store

States :

L'Epicerie Fraîcheur is a small retail business specializing in the sale of seasonal fruits and vegetables. The manager of the business wants to better understand the financial performance of his business. To do this, he needs to calculate the margin rate on the apples he sells in his store.

In order to calculate the margin rate, he needs to know the sales price excluding tax (SPT) as well as the purchase price excluding tax (PPT) of each of his products. Therefore, here is the information he has collected:

– Purchase price excluding tax for apples: €1,50/kg
– Sales price excluding tax for apples: €3,00/kg

Work to do :

1. What is a margin rate?
2. What is the formula for calculating the margin rate?
3. What is the gross margin for apples in the Fresh Grocery Store?
4. What is the margin rate for apples sold in the Fresh Grocery Store?
5. If the manager of the Epicerie Fraîcheur wants to increase his margin rate, what could he do?

Proposed correction:

1. Profit margin is an indicator used to measure the financial performance of a company. It allows us to know how much a company earns by selling its products or services once all expenses directly related to the production and sale of these products or services are deducted.

2. The formula for calculating the margin rate is: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100

3. The gross margin for apples in the Fresh Grocery Store is €3,00 – €1,50 = €1,50

4. To calculate the margin rate for apples sold in the Fresh Grocery Store, we use the formula: ((€3,00 – €1,50) ÷ €1,50) x 100 = 100%

5. To increase his margin rate, the manager of the Epicerie Fraîcheur could either increase the selling price of his apples or reduce his purchasing costs. However, he must be careful not to lose customers if the selling price is too high, and not to compromise the quality of his products if the purchasing cost is too low.

Summary of Formulas Used:

Financial indicators	Packages
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100

Application: The Cake House

States :

La Maison du Gâteau is a small business that makes and sells various types of cakes and pastries. By studying the balance sheet of this company, we obtained the following information:

– Purchase price excluding tax (PA HT) of a cake: €5.
– Sales price excluding tax (PV HT) of the same cake: €12.
– Quantity of cakes sold: 1000.

Work to do :

1. Calculate the unit margin of La Maison du Gâteau.
2. Calculate the overall margin.
3. Calculate the margin rate.
4. Estimate the markup rate.
5. What do these numbers represent for La Maison du Gâteau?

Proposed correction:

1. The unit margin is calculated by subtracting the HT PA from the HT PV. Therefore, Unit margin = HT PV – HT PA = €12 – €5 = €7.

2. The overall margin is obtained by multiplying the unit margin by the quantity sold. Therefore, Overall margin = Unit margin x Quantity sold = €7 x 1000 = €7.

3. The margin rate is the ratio between the unit margin and the HT PA, all multiplied by 100. Therefore, Margin rate = ((HT PV – HT PA) ÷ HT PA) x 100) = ((€12 – €5) ÷ €5) x 100 = 140%. La Maison du Gâteau thus achieves a margin of 140% on each cake sold.

4. The markup rate is the ratio between the unit margin and the HT PV, all multiplied by 100. Therefore, Markup rate = ((HT PV – HT PA) ÷ HT PV) x 100) = ((€12 – €5) ÷ €12) x 100 = 58.33%. Which means that 58,33% of the HT sales price is added as a margin.

5. These figures show that La Maison du Gâteau is able to generate a considerable margin on each cake sold. This is a good indicator of the financial health of the company.

Summary of Formulas Used:

Formulas	Explanation
Unit margin = PV excluding tax – PA excluding tax	Margin made on the sale of a unit of product
Overall margin = Unit margin x Quantity sold	Total margin made on all sales
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Proportion of margin to purchase price
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100	Proportion of margin to selling price

Application: The company “Les Delices de Mamie”

States :

The company "Les Delices de Mamie" sells bakery products with a good margin. For the sake of optimal management, the company wants to determine the margin rate of some of its products.

Here is some data for three types of products (each sold in units):

1. Traditional baguette:
– Purchase price excluding tax (PA HT): €0,60
– Sale price excluding tax (PV HT): €0,90

2. Chocolate bread:
– PA HT: €0,45
– PV excluding tax: €0,80

3. Croissant:
– PA HT: €0,40
– PV excluding tax: €0,70

Work to do :

1. Calculate the margin rate for the traditional baguette.
2. Calculate the margin rate for the pain au chocolat.
3. Calculate the margin rate for the croissant.
4. In which product does the company make the highest percentage margin?
5. Which of these products is the least profitable in terms of margin rate?

Proposed correction:

1. Margin rate for traditional baguette = ((€0,90 – €0,60) ÷ €0,60) x 100 = 0,50 x 100 = 50%.
2. Margin rate for pain au chocolat = ((€0,80 – €0,45) ÷ €0,45) x 100 = 0,78 x 100 = 78%.
3. Margin rate for croissant = ((€0,70 – €0,40) ÷ €0,40) x 100 = 0,75 x 100 = 75%.
4. The company makes the highest percentage margin on pain au chocolat.
5. The least profitable product in terms of margin rate is the traditional baguette.

Summary of Formulas Used:

Margin rate ((PV HT – PA HT) ÷ PA HT) x 100

The margin rate is an indicator that allows you to evaluate the percentage of margin made on the purchase price excluding tax. It is expressed as a percentage. It should be noted that the product that generates the highest margin is not necessarily the most profitable, because the sales volume also influences the overall profit.

Application: “Fashion Style”

States :

Fashion Style is a high-end fashion company that sells clothing and accessories. In the last financial year, the company sold a total of 500 units of a specific leather jacket. The sales price excluding tax (SVP HT) of this jacket is €250. The company's purchase price excluding tax (PP HT) for the same jacket is €100.

Work to do :

1. Calculate the unit margin on the sale of the jacket.
2. Calculate the overall margin for all jackets sold.
3. Calculate the margin rate.
4. Calculate the mark rate.
5. Evaluate the effectiveness of the company's financial strategy in light of the financial results obtained.

Proposed correction:

1. The unit margin is calculated by subtracting the purchase price excluding tax from the sale price excluding tax. Unit margin = PV excluding tax – PA excluding tax. Unit margin = €250 – €100 = €150.

2. The overall margin is calculated by multiplying the unit margin by the quantity sold. Overall margin = Unit margin x quantity sold. Overall margin = €150 x €500 = €75.

3. The margin rate is calculated by dividing the unit margin by the purchase price excluding tax and multiplying the result by 100 to obtain a percentage. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100. Margin rate = ((€250 – €100) ÷ €100) x 100 = 150%.

4. The markup rate is calculated by dividing the unit margin by the sales price excluding tax and multiplying the result by 100 to obtain a percentage. Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100. Markup rate = ((€250 – €100) ÷ €250) x 100 = 60%.

5. The effectiveness of the company's financial strategy can be measured using the two financial ratios calculated. A markup ratio of 150% indicates that the company is making a significant margin on each unit sold, which is positive. However, the markup ratio of 60% is a bit low, which means that the company might consider increasing its prices to improve this ratio.

Summary of Formulas Used:

Concept	Formulas
Unit margin	PV HT – PA HT
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: TechnoWorld

States :

TechnoWorld is a company that sells technology products. It buys a model of mobile phone at €150 excluding VAT per unit and resells it at €200 excluding VAT. The company has a stock of 500 units of this model on its balance sheet. The goal is to understand and calculate the margin rate of this product.

Work to do :

1. What is the total purchase cost excluding VAT of the phones?

2. What is the gross margin per unit made on the sale of each phone?

3. How much did the company make in total gross margin?

4. What is TechnoWorld's unit margin rate on this product?

5. What is TechnoWorld's overall margin rate on this product?

Proposed correction:

1. Total pre-tax purchase cost = Unit pre-tax PA x quantity = €150 x 500 = €75

2. Gross unit margin = PV HT – PA HT = €200 – €150 = €50

3. Total gross margin = Unit gross margin x quantity sold = €50 x 500 = €25

4. Unit margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((200€ – 150€) ÷ 150€) x 100 = 33,33%

5. Overall margin rate = (total gross margin ÷ total pre-tax purchase cost) x 100 = (€25 ÷ €000) x 75 = 000%

Summary of Formulas Used:

Formulas	Description
Total purchase cost excluding tax = Unit cost excluding tax x quantity	To calculate the total purchase cost excluding tax, multiply the unit purchase price excluding tax by the quantity.
Unit gross margin = PV excluding tax – PA excluding tax	The unit gross margin is calculated by subtracting the purchase price excluding tax from the selling price excluding tax.
Total gross margin = Unit gross margin x quantity sold	To obtain the total gross margin, multiply the unit gross margin by the quantity sold.
Unit margin rate = ((PV HT – PA HT) ÷ PA HT) x 100	The unit margin rate formula is obtained by restoring the unit gross margin from the purchase price excluding tax, the whole multiplied by 100 to obtain a percentage.
Overall margin rate = (total gross margin ÷ total pre-tax purchase cost) x 100	To obtain the overall margin rate, divide the total gross margin by the total pre-tax purchase cost, all multiplied by 100 to obtain a percentage.

Application: Fresh Bread Bakery

States :

Le Pain Frais is a bakery located in the city center. It offers a variety of breads, pastries and cakes. You are the financial manager of this bakery and you are asked to analyze the financial performance of your store. You have decided to start by analyzing the margin rate.

Here is some information about the products sold:

– Pain au chocolat: Purchase Price excluding VAT (PAHT) = €0,30, Sale Price excluding VAT (PVHT) = €0,90, Quantity sold = 200
– Croissant: PAHT = €0,20, PVHT = €0,80, Quantity sold = 250
– Baguette: PAHT = €0,50, PVHT = €1,20, Quantity sold = 300

Work to do :

1. Calculate the margin rate for each product.
2. Which product has the highest margin rate?
3. Calculate the overall margin for each product.
4. What is the total overall margin for all products?
5. If you want to increase the margin rate of each product by 5%, how high should the new selling prices be excluding VAT?

Proposed correction:

1. Margin rate for each product:

– Pain au chocolat: ((€0,90 – €0,30) ÷ €0,30) x 100 = 200%
– Croissant: ((€0,80 – €0,20) ÷ €0,20) x 100 = 300%
– Baguette: ((€1,20 – €0,50) ÷ €0,50) x 100 = 140%

2. The product with the highest margin rate is the Croissant.

3. Overall margin for each product:

– Pain au chocolat: (€0,90 – €0,30) x 200 = €120
– Croissant: (€0,80 – €0,20) x 250 = €150
– Baguette: (€1,20 – €0,50) x 300 = €210

4. The total of the overall margin for all products is €480 (€120 + €150 + €210).

5. New sales prices excluding VAT after 5% increase in the margin rate:

– Pain au chocolat: €0,90 x 1,05 = €0,945
– Croissant: €0,80 x 1,05 = €0,84
– Baguette: €1,20 x 1,05 = €1,26

Summary of Formulas Used:

Concept	Formulas
Margin rate	((PV HT – PA HT) ÷ PV HT) x 100)
Overall Margin	Unit margin x quantity sold

Application: Dubois Company

States :

Dubois is a high-end clothing retailer. They have had a successful year with several successful new collection launches. Below we have some information on one of the best-selling collections of the year.

The purchase price excluding tax (PA HT) of each part upon purchase: €50.
The sales price excluding tax (PV HT) for each piece: €90.
Quantity sold during the year: 1000 pieces.

Work to do :

1. Calculate the unitary margin of the collection
2. Calculate the overall margin of the collection for the year
3. What is the Rate of Margin (ROM) for the collection?
4. What is the Rate of Mark (ROMK) for the collection?
5. If the company wants to increase its ROMK to 50%, what should the new PV HT be?

Proposed correction:

1. Unit margin = PV HT – PA HT = €90 – €50 = €40.

2. Overall margin = Unit margin x quantity sold = €40 x 1000 = €40.

3. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100)) = ((90 € – 50 €) ÷ 50 €) x 100 = 80%.

4. Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100)) = ((90 € – 50 €) ÷ 90 €) x 100 = 44,44% (rounded to the nearest hundredth).

5. To have a markup rate of 50%, we use the formula: PA HT = PV HT – (PV HT x markup rate / 100), or we can rearrange the formula for PV HT = PA HT / (1 – (markup rate / 100)). So, PV HT = €50 / (1 – (50 / 100)) = €100.

Summary of Formulas Used:

Terms	Packages
Unit margin	PV HT – PA HT
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
PV HT for a defined mark rate	PA HT / (1 – (brand rate / 100))

Application: Bright Fabrics

States :

The company Les Tissus Éclatants markets various types of fabrics. It has just acquired a new range of silk fabrics for which it wishes to determine the pricing strategy.

You have access to the following information on the new range of fabrics:

– Purchase price excluding tax (PA HT): €15/m
– Fixed costs: €2000
– Quantity sold: 150 meters
– VAT: 20%

Work to do :

1. Calculate the selling price excluding tax (PV excluding tax) knowing that the company wishes to achieve a margin rate of 30%.
2. Calculate the sales price including tax (PV including tax).
3. Calculate the overall margin.
4. Calculate the profit.
5. What does the margin rate represent for the company?

Proposed correction:

1. The margin rate is calculated with the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100). To find the PV HT, we rearrange the formula: PV HT = PA HT x (1 + Margin rate/100) = €15 x (1 + 30/100) = €19,5.

2. The sales price including VAT is calculated by adding VAT to the sales price excluding VAT: Sales price including VAT = Sales price excluding VAT x (1 + VAT/100). Sales price including VAT = €19,5 x (1 + 20/100) = €23,4.

3. The overall margin is the unit margin multiplied by the quantity sold. Unit margin = PV HT – PA HT = €19,5 – €15 = €4,5. Overall margin = Unit margin x Quantity sold = €4,5 x 150 = €675.

4. Profit is the overall margin minus fixed costs: Profit = Overall margin – Fixed costs = €675 – €2000 = -€1325. The company is therefore in deficit.

5. The margin rate represents the share of the margin in the sales price excluding taxes. A margin rate of 30% means that for each sale made, 30% represents the company's margin.

Summary of Formulas Used:

Formulas	Description
PV HT = PA HT x (1 + Margin rate/100)	Sale price excluding tax
PV including VAT = PV excluding VAT x (1 + VAT/100)	Selling price including all taxes
Unit Margin = PV HT – PA HT	Margin made on the sale of a product
Overall margin = Unit margin x Quantity sold	Total margin made on the sale of all products
Profit = Overall margin – Fixed costs	Profit made after deduction of fixed costs

Application: English & co

States :

The company Anglais & co specializes in the sale of books in English. It buys a book at a purchase price excluding tax (PA HT) of €15 from its supplier. It then resells it to its customers for a sale price excluding tax (PV HT) of €25.

The company Anglais & co wants to know the margin rate it makes on the sale of this book. To this end, it has decided to use the margin rate formula which is: ((PV HT – PA HT) ÷ PV HT) x 100). The elements we have for the company Anglais & co are as follows:
– Purchase price excluding tax (PA HT) = €15
– Sales price excluding tax (PV HT) = €25

Work to do :

1. Calculate the margin rate of the company Anglais & co on the sale of this book.
2. If the company wants to increase its profit margin to 50%, how much should it sell the book for?
3. If the company reduces its selling price to €20, what will its new margin rate be?
4. If the company wants to maintain its initial margin rate with the new selling price of €20, how much should it buy the book from its supplier for?
5. Does a higher margin rate automatically mean higher profitability for the company?

Proposed correction:

1. The margin rate is calculated as follows: ((PV HT – PA HT) ÷ PV HT) x 100) = ((25 € – 15 €) ÷ 25 €) x 100) = 40%
2. To obtain a margin rate of 50%, the company should resell the book at: €15 ÷ (1 – 50/100) = €30
3. If the company reduces its selling price to €20, its new margin rate would be: ((€20 – €15) ÷ €20) x 100) = 25%
4. To maintain its initial margin rate of 40% with the new selling price of €20, the company should purchase the book from its supplier at: €20 x (1 – 40/100) = €12
5. A higher margin rate does not automatically mean higher profitability for the company. In fact, it is possible that increasing the selling price will lead to a decrease in sales volume, which could reduce the overall profitability of the company. In addition, a high margin rate can sometimes indicate that the company is not competitive in the market.

Summary of Formulas Used:

Indicators	Packages
Margin rate	((PV HT – PA HT) ÷ PV HT) x 100)
Selling price for a given margin rate	PA HT ÷ (1 – Margin rate / 100)
Purchase price for a given margin rate	PV HT x (1 – Margin rate / 100)

Application: NaturalBio

States :

NaturalBio is a small company specializing in the sale of organic products. The company seeks to optimize its financial management, in particular to calculate the margin rate of certain products in order to improve its commercial performance.

For an organic product, she buys a batch of 50 units at a price of €500 excluding tax and sells it at a unit price of €15 excluding tax.

Work to do :

1. What is the unit purchase price (PA) excluding VAT of this product?
2. What is the unit margin of this product?
3. Calculate the margin rate for this product.
4. What is the overall margin of this product?
5. Calculate the markup rate of this product.

Proposed correction:

1. The unit purchase price (PA) excluding VAT is calculated by dividing the total purchase price by the number of units in the lot. Here, the unit PA excluding VAT = €500 ÷ 50 = €10.

2. The unit margin is the difference between the unit selling price (SPP) excluding VAT and the unit selling price excluding VAT. Here, the unit margin = (€15 – €10) = €5.

3. The margin rate is calculated by dividing the margin by the purchase price excluding VAT and multiplying the result by 100. This gives: Margin rate = ((15 – 10) ÷ 10) x 100 = 50%.

4. The overall margin is equal to the unit margin multiplied by the quantity sold. Here, the overall margin = €5 x 50 = €250.

5. The markup rate is calculated by dividing the margin by the selling price excluding tax and multiplying the result by 100. This gives: Markup rate = ((€15 – €10) ÷ €15) x 100 = 33,33%.

Summary of Formulas Used:

Formulas	Explanation
Unitary HT PA = Total HT PA ÷ quantity	This formula is used to calculate the unit purchase price excluding tax.
Unit margin = PV excluding tax – PA excluding tax	This formula is used to calculate the unit margin.
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	This formula is used to calculate the margin rate.
Overall margin = Unit margin x quantity sold	This formula is used to calculate the overall margin.
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100	This formula is used to calculate the markup rate.

App: Olympic Sport Store

States :

The Olympic Sport Store company is looking to increase its margin on its products in order to achieve its financial objectives. The company mainly sells sports clothing and equipment.

Olympic Sport Store has purchased designer running sneakers. For this product the following information is available:
– Purchase price excluding tax (PA excluding tax): €50
– Expected sale price excluding VAT (PV excluding VAT): €100
– Quantity sold: 200 pairs of shoes

Work to do :

1. Calculate the unit margin for this product.
2. Determine the margin rate for this product.
3. Calculate the overall margin (total profit) of this product.
4. If Olympic Sport Store decides to increase the selling price to €110 excluding VAT, what will the new margin rate be?
5. If Olympic Sport Store wants to achieve a margin rate of 60%, at what level should the company set its selling price excluding VAT?

Proposed correction:

1. The unit margin is calculated by subtracting the purchase price excluding tax (PA excluding tax) from the sale price excluding tax (PV excluding tax).
Or Unit margin = PV HT – PA HT = €100 – €50 = €50

2. The margin rate is calculated by dividing the margin by the purchase price excluding VAT and multiplying by 100 to obtain a percentage.
Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((100 € – 50 €) ÷ 50 €) x 100 = 100%

3. The overall margin, which represents the total profit of this product, is obtained by multiplying the unit margin by the quantity sold.
Overall margin = Unit margin x Quantity sold = €50 x 200 = €10

4. If Olympic Sport Store increases the PV excluding tax to €110, the new margin rate would be:
Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((110 € – 50 €) ÷ 50 €) x 100 = 120%

5. To achieve a margin rate of 60%, we reorganize the margin rate formula to obtain the PV HT:
PV HT = ((Margin rate x PA HT) ÷ 100) + PA HT = ((60 x 50 €) ÷ 100) + 50 € = 80 €

Summary of Formulas Used:

Formulas	Description
Unit margin = PV excluding tax – PA excluding tax	This formula is used to calculate the unit margin.
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	This formula is used to determine the margin rate.
Overall margin = Unit margin x Quantity sold	This formula is used to calculate the overall margin.
PV HT = ((Margin rate x PA HT) ÷ 100) + PA HT	This formula is used to determine the net selling price required to obtain a given margin rate.