11 Exercises Commercial Calculations Operational Management

Application: The Fantastic Chocolate Factory

States :

Chocolaterie Fantastique is a well-established company that produces and sells a variety of chocolate sweets. To best control its costs and optimize its profits, management needs to study its margins and rates on different products.

For the company's flagship product, the figures are as follows:
– Purchase price excluding tax (PA HT): €10 per unit
– Sales price excluding tax (PV HT): €15 per unit

Additionally, La Chocolaterie Fantastique sold 2000 units of this product in the last month.

Work to do :

1. Calculate the unit margin for this product.
2. Calculate the overall margin for this product.
3. Calculate the markup rate for this product.
4. Calculate the brand rate for this product.
5. Suppose that La Chocolaterie Fantastique plans to decrease the selling price by 10%. How would this affect the margin rate and the markup rate?

Proposed correction:

1. The unit margin is the difference between the sales price excluding tax and the purchase price excluding tax. In this case, the unit margin is €15 – €10 = €5.

2. The overall margin is the unit margin multiplied by the quantity sold. In this case, the overall margin is €5 x 2000 = €10.

3. The margin rate is ((PV HT – PA HT) ÷ PA HT) x 100. In this case, the margin rate is ((15 € – 10 €) ÷ 10 €) x 100 = 50%.

4. The markup rate is ((PV HT – PA HT) ÷ PV HT) x 100. In this case, the markup rate is ((15 € – 10 €) ÷ 15 €) x 100 = 33,33%.

5. If the selling price drops by 10%, the new selling price will be €15 – €1,5 = €13,5. The new margin rate will be ((€13,5 – €10) ÷ €10) x 100 = 35%. The new markup rate will be ((€13,5 – €10) ÷ €13,5) x 100 = 25,93%.

A 10% decrease in the selling price leads to a significant decrease in the margin rate and the markup rate, which can affect the profitability of the company.

Summary of Formulas Used:

Formulas	Explanation
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. It represents the profit made on a single unit of the product.
Overall margin = Unit margin x quantity sold	The overall margin represents the total profit made after selling all units of the product.
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	The margin rate is a measure of the profit made for each euro spent on the purchase of the product.
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100	The markup rate is a measure of the profit made for each euro received from the sale of the product.

Application: Divine Chocolate Factory

States :

Divine Chocolate Factory is a company that manufactures and sells high-quality artisanal chocolates. The company's management has asked you as a financial expert to analyze its profitability. It has provided the following information for one of its flagship products, pralines:

– Purchase price excluding VAT: €4,00;
– Quantity sold: 2500 units;
– Selling price excluding VAT: €10,00;

Work to do :

1. Calculate the overall margin in €.
2. Calculate the margin rate.
3. Calculate the mark rate.
4. If the VAT rate is 20%, what would the sales price including VAT be?
5. If the margin rate must be at least 60%, at what price should Chocolaterie Divine sell its pralines?

Proposed correction:

1. The unit margin is calculated by subtracting the purchase price excluding VAT from the sale price excluding VAT. In this case, this gives 10 – 4 = €6. The overall margin is then obtained by multiplying the unit margin by the quantity sold, i.e. 6 x 2500 = €15 for the period considered.

2. The margin rate is calculated by dividing the unit margin by the purchase price excluding VAT and multiplying the result by 100 to obtain a percentage. In our case, this gives ((10 – 4) ÷ 4) x 100 = 150%.

3. The markup rate is calculated by dividing the unit margin by the selling price excluding tax and multiplying the result by 100. Here, this gives ((10 – 4) ÷ 10) x 100 = 60%.

4. The sales price including VAT is determined by adding VAT to the price excluding VAT. Here, the VAT amount would be 10 x 20% = €2, so the sales price including VAT would be 10 + 2 = €12.

5. If Chocolaterie Divine wants a margin rate of 60%, the selling price excluding tax should be ((4 x 60%) + 4) = €6,4.

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
All taxes included price	PV excluding VAT + (PV excluding VAT x VAT rate)
Target PV HT to achieve a specified margin rate	(PA HT x Desired margin rate) + PA HT

Application: Organic Grocery Store

States :

Organic Grocery is a retail company selling organic food products. It has recently added a new variety of honey to its product catalog. Here is the relevant information:

– Cost of each jar of honey (Purchase Price Excluding Tax): €6.
– Quantity of honey pots sold: 1000.
– Sale price excluding tax (PV HT): €10.
– VAT rate: 20%.

Work to do :

1. Calculate the overall margin from the sale of jars of honey.
2. Calculate the margin rate on the purchase price.
3. Calculate the markup rate on the selling price.
4. Calculate the sales price including all taxes.
5. What is the total amount of sales?

Proposed correction:

1. Overall margin = Unit margin x quantity sold = (PV HT – PA HT) x quantity sold = (10€ – 6€) x 1000 = 4000 €.

2. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100) = ((10€ – 6€) ÷ 6€) x 100 = 66.67%.

3. Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((10€ – 6€) ÷ 10€) x 100 = 40%.

4. Sales price including tax = PV excluding tax + (PV excluding tax x VAT rate / 100) = €10 + (€10 x 20% / 100) = €12.

5. The total amount of sales is therefore 1000 units x 12€ = 12,000€.

Summary of Formulas Used:

App: Epicure Gourmet Store

Epicure Gourmet Store is a company that specializes in selling artisanal and high-quality food products. Their assortments include a variety of cheeses, sausages, homemade jams, specialty cookies, etc.

States :

The company recently purchased a batch of cheese at a unit purchase cost of €15 excluding VAT and decided to resell it at €35 excluding VAT. During the first month, the company sold 150 units of cheese. The VAT rate applied is 20%.

Work to do :

1. What is the unit margin obtained by the cheese?
2. What is the cheese turnover excluding tax for the first month?
3. What is the cheese margin rate and what is the brand rate?
4. How much VAT is collected?
5. If the company wants to increase its margin rate by 10%, at what should it set the selling price excluding tax of the cheese?

Proposed correction:

1. The unit margin is obtained by subtracting the unit purchase cost from the unit selling price. That is: €35 – €15 = €20 unit margin.

2. The net sales figure is calculated by multiplying the net sales price by the quantity sold. That is: €35 x 150 = €5 net sales figure.

3. The margin rate is calculated as follows:
Margin rate = ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100
That is: ((€35 – €15) ÷ €15) x 100 = 133,33%. The margin rate is therefore 133,33%.
The markup rate is calculated as follows:
Brand rate = ((Sales price excluding tax – Purchase price excluding tax) ÷ Sales price excluding tax) x 100
That is: ((€35 – €15) ÷ €35) x 100 = 57,14%. The markup rate is therefore 57,14%.

4. The amount of VAT collected is calculated by multiplying the turnover excluding VAT by the VAT rate. That is: €5 x 250% = €20 VAT collected.

5. If the company wants to increase its margin rate by 10%, it will have to increase its selling price excluding tax in the following manner:
New Selling Price = Excl. VAT Purchase Price + (Excl. VAT Purchase Price x New Margin Rate)
That is: €15 + (€15 x (133,33% + 10%)) = €43. The company should therefore set the selling price excluding tax of the cheese at €43 to obtain the expected margin rate.

Summary of Formulas Used:

Unit margin	= Selling price excluding VAT – Purchase price excluding VAT
Turnover excluding tax	= Selling price excluding VAT x quantity sold
Margin rate	= ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100
Brand taxes	= ((Selling price excluding VAT – Purchase price excluding VAT) ÷ Selling price excluding VAT) x 100
VAT collected	= Turnover excluding VAT x VAT rate
New Selling Price excluding VAT	= Purchase price excluding VAT + (Purchase price excluding VAT x new margin rate)

Application: Company “Les Papillons d'Or”

States :

The company “Les Papillons d'Or” specializes in the sale of organic beauty products. It offers its customers a wide range of products: cosmetics, essential oils, soaps, and much more. Here are the details of one of their flagship products: organic argan oil.

The company purchases organic argan oil from a manufacturer at a purchase price excluding tax (PP excluding tax) of €12 per unit. The company decides to resell it at a sales price excluding tax (STP excluding tax) of €20 per unit. The VAT rate is 20%.

Work to do :

1. Calculate the unit margin.
2. Determine the margin rate.
3. Calculate the mark rate.
4. Find the sales price including all taxes (PV TTC).
5. Estimate the amount of VAT.

Proposed correction:

1. The unit margin is calculated using the following formula: Unit margin = PV HT – PA HT. Therefore, in our case: Unit margin = €20 – €12 = €8.

2. The margin rate is determined by the following formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100. Therefore, in our case, the margin rate is ((20 € – 12 €) ÷ 12 €) x 100 = 66,67%.

3. The markup rate is found using the following formula: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100. In our case, the markup rate is: ((20 € – 12 €) ÷ 20 €) x 100 = 40%.

4. The sales price including all taxes (PV TTC) is found with the formula: PV TTC = PV HT x (1 + VAT rate/100). Thus, the PV TTC is €20 x (1 + 20/100) = €24.

5. The amount of VAT is calculated using the formula: VAT = PV incl. VAT – PV excl. VAT. In our case, the amount of VAT is therefore €24 – €20 = €4.

Summary of Formulas Used:

• Unit margin = PV excluding tax – PA excluding tax
• Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
• Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
• PV incl. VAT = PV excl. VAT x (1 + VAT rate/100)
• VAT = PV including VAT – PV excluding VAT

Application: Divine Chocolate Factory

States :

Chocolaterie Divine is a small business that produces and markets a variety of artisanal chocolates. The company purchases raw chocolate, which it then transforms into different products. It is currently doing an analysis of its financial performance for the past year.

Here is some information provided by the company's accounting department:

– Cost price of raw material (raw chocolate): €10 per kg.
– Quantity of raw chocolate purchased: 1000 kg.
– Selling price of finished chocolates: €30 per kg.
– Quantity sold: 800 kg.
– Applicable VAT: 20%.

Work to do :

1. Calculate the unit margin on each kg of chocolate sold.
2. Calculate the overall margin achieved during the year.
3. Calculate the margin rate.
4. Calculate the mark rate.
5. Calculate the amount of VAT to be paid.

Proposed correction:

1. The unit margin is the difference between the selling price excluding VAT (PV HT) and the cost price, which is also the purchasing price excluding VAT (PA HT). In our case, it is €30 – €10 = €20 per kg.

2. The overall margin is the unit margin multiplied by the quantity sold, i.e. €20 x 800 = €16.

3. The margin rate is calculated using the formula ((PV HT – PA HT) ÷ PA HT) x 100). Here, this gives ((€30 – €10) ÷ €10) x 100 = 200%.

4. The markup rate, for its part, is calculated by following the formula ((PV HT – PA HT) ÷ PV HT) x 100). This gives ((€30 – €10) ÷ €30) x 100 = 66,67%.

5. The amount of VAT to be paid is calculated by multiplying the total sales excluding VAT by the VAT rate. That is (€30 x 800) x 20% = €4.

Summary of Formulas Used:

Formulas	Meaning
Unit margin = PV excluding tax – PA excluding tax	Calculation of unit margin.
Overall margin = Unit margin x quantity sold	Calculation of the overall margin.
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Calculation of the margin rate.
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100	Calculation of the markup rate.
VAT payable = Selling price excluding VAT x VAT rate	Calculation of VAT to be paid.

Application: The Green Grocery Store

States :

L'Épicerie Vertes is a local business that mainly sells organic products and local produce. The grocery store manager is questioning its commercial and financial performance regarding some of its products.

For example, he sells a batch of 10 kg of organic apples for €25 excluding VAT. The cost of purchasing this batch from his supplier is €15 excluding VAT. He applies VAT at a rate of 5,5%.

Work to do :

1. What is the grocery store's gross margin per unit on a 10 kg batch of organic apples?
2. What is the margin rate?
3. What is the markup rate?
4. What is the selling price including tax for a batch of 10 kg of organic apples?
5. What is the net profit after deducting VAT?

Proposed correction:

1. The gross margin per unit is calculated by subtracting the purchase price excluding tax (PA excluding tax) from the sale price excluding tax (PV excluding tax). In our case, this gives: Gross margin per unit = PV excluding tax – PA excluding tax = €25 – €15 = €10.

2. The margin rate is calculated by dividing the gross margin per unit by the purchase price excluding tax (PA excluding tax) and then multiplying the result by 100 to obtain a percentage. In our case, this gives: Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€25 – €15) ÷ €15) x 100 = 66,67%.

3. The markup rate is calculated in the same way as the margin rate, except that the gross margin per unit is divided by the selling price excluding tax (STP excluding tax) and the result is multiplied by 100. In our case, this gives: Markup rate = ((STP excluding tax – STP excluding tax) ÷ STP excluding tax) x 100 = ((€25 – €15) ÷ €25) x 100 = 40%.

4. The sales price including tax for a batch of 10 kg of organic apples is calculated by adding VAT to the sales price excluding tax. In our case, this gives: Sales price including tax = PV excluding tax + (PV excluding tax x VAT rate) = €25 + (€25 x 5,5%) = €26,38.

5. Net profit after deducting VAT is simply the gross margin per unit minus VAT. In our case, this gives: Net profit = Gross margin per unit – VAT = €10 – (€25 x 5,5%) = €8,63.

Summary of Formulas Used:

Packages	Explanations
Unit gross margin = PV excluding tax – PA excluding tax	Calculates the difference between the sales price excluding tax and the purchase price excluding tax.
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Calculates the ratio of gross margin to the purchase price excluding taxes expressed as a percentage.
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100	Calculates the ratio of gross margin to the selling price excluding tax expressed as a percentage.
Selling price including tax = PV excluding tax + (PV excluding tax x VAT rate)	Adds VAT to the sales price excluding tax.
Net profit = Gross margin per unit – VAT	Calculation of final profit after deduction of VAT.

Application: The Flower Garden

States :

Le Jardin des Fleurs is a direct sales company of plants and flowers. It has a wide variety of plants and wants to improve its operational management.
The company purchases a batch of red roses at a price of €0,75 per unit excluding tax (HT) and plans to sell them at a price of €1,50 per unit excluding tax. Note that the applicable VAT rate is 20%.

Work to do :

1. Calculate the unit margin of these roses in euros and give the calculation formula.

2. Calculate the overall margin if 200 roses are sold and give the calculation formula.

3. Calculate the margin rate of these roses in percentage and give the calculation formula.

4. Calculate the markup rate of these roses in percentage and give the calculation formula.

5. Calculate the sales price including all taxes (TTC) of a rose and give the calculation formula.

Proposed correction:

1. The unit margin is calculated by subtracting the purchase price of roses excluding tax (PA excluding tax) from the sale price of roses excluding tax (PV excluding tax). Unit margin = PV excluding tax – PA excluding tax = €1,50 – €0,75 = €0,75

2. The overall margin is obtained by multiplying the unit margin by the number of roses sold. Overall margin = Unit margin x quantity sold = €0,75 x 200 = €150

3. The margin rate is calculated by dividing the unit margin by the purchase price excluding VAT, then multiplying the result by 100. Margin rate = ((PV excluding VAT – PA excluding VAT) ÷ PA excluding VAT) x 100 = ((€1,50 – €0,75) ÷ €0,75) x 100 = 100%

4. The markup rate is obtained by dividing the unit margin by the selling price excluding tax, then multiplying the result by 100. Markup rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 = ((€1,50 – €0,75) ÷ €1,50) x 100 = 50%

5. The sales price including tax is calculated by adding the sales price excluding tax with the VAT amount. Price including tax = PV excluding tax + (PV excluding tax x VAT rate) = €1,50 + (€1,50 x 20%) = €1,80

Summary of Formulas Used:

Formulas	Description
Unit margin = PV excluding tax – PA excluding tax	Calculation of unit margin
Overall margin = Unit margin x quantity sold	Calculation of the overall margin
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Calculation of the margin rate
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100	Calculation of the mark rate
Price including tax = PV excluding tax + (PV excluding tax x VAT rate)	Calculation of the sales price including tax

Application: Gourmet Candies

States :

The company “Les Bonbons Gourmands” specializes in the sale of candy. It recently purchased a batch of candy at a purchase price of €1000,00 excluding VAT. The company decided to sell each candy individually at a price of €2,00 excluding VAT and a VAT rate of 20%.

The lot contains 1000 candies.

Work to do :

1. Calculate the overall margin on the sale of the entire lot.
2. Calculate the margin rate on the sale of a candy.
3. Calculate the markup rate on the sale of a candy.
4. If the VAT rate increases to 5,5%, calculate the new sales price including VAT of a candy.
5. Calculate the new overall margin if the entire lot is sold with the new VAT rate.

Proposed correction:

1. To calculate the overall margin on the sale of the lot, we use the formula: Overall Margin = Unit Margin x Quantity Sold. Here, the Unit Margin is (Sale Price excluding VAT – Purchase Price excluding VAT) or (€2,00 – €1,00) = €1,00. Therefore, the Overall Margin is €1,00 x 1000 = €1000,00.

2. To calculate the margin rate on the sale of a candy, we use the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100. Here, this gives ((€2,00 – €1,00) ÷ 1,00) x 100 = 100%.

3. To calculate the markup rate on the sale of a candy, we use the formula: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100. Here, this gives ((€2,00 – €1,00) ÷ 2,00) x 100 = 50%.

4. If the VAT rate increases to 5,5%, the new sales price including VAT of a candy would be Sales Price excluding VAT x (1 + VAT rate / 100) or €2,00 x (1 + 5,5/100) = €2,11.

5. To calculate the new overall margin if the entire lot is sold with the new VAT rate, we use the formula Overall Margin = Unit Margin x Quantity Sold. With a decrease in the VAT rate, the Selling Price excluding VAT remains at €2,00 while the Purchase Price excluding VAT is still at €1,00. Therefore the new Unit Margin remains at €1,00 and the new Overall Margin is therefore €1,00 x 1000 = €1000,00.

Summary of Formulas Used:

Packages	Description
VAT rate = 20% | 5,5%	Current VAT rates
Overall Margin = Unit Margin x Quantity Sold	Global Margin Formula
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Margin Rate Formula
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100)	Markup Rate Formula

Application: Corner Grocery Store

States :

You are the manager of the Corner Grocery Store. You need to calculate the profitability of some of the products you sell. Here are some details for product A that you sell:

Purchase price (excl. VAT): €10
Sale price (excluding VAT): €20
Quantity sold: 50 units

Work to do :

1. What is the unit margin of your product A?
2. What is the overall margin of your product A?
3. What is the margin rate on the purchase cost of your product A?
4. What is the markup rate of your product A?
5. Calculate the sales price including tax.

Proposed correction:

1. The unit margin is calculated as the difference between the selling price and the purchase price. In this case, we have: Unit margin = PV HT – PA HT = €20 – €10 = €10

2. The overall margin being the multiplication of the unit margin by the quantity sold. Here it is therefore: Overall margin = Unit margin x quantity sold = €10 x 50 = €500

3. The margin rate is calculated by dividing the unit margin by the purchase price and multiplying this ratio by 100 to obtain a percentage. So we have: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100) = ((20 € – 10 €) ÷ 10 €) x 100 = 100%

4. Similarly, the markup rate is determined by dividing the unit margin by the selling price and multiplying this ratio by 100. We therefore obtain: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100) = ((20 € – 10 €) ÷ 20 €) x 100 = 50%

5. To calculate the sales price including tax, we use the VAT rate of 20%. In France, we obtain this price by multiplying the price excluding tax by (1 + VAT rate). So here: Sales price including tax = PV excluding tax x (1 + 20/100) = €20 x 1.2 = €24

Summary of Formulas Used:

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
Sales price including tax	PV HT x (1 + VAT rate)

Application: ArtDecoStyle Company

States :

ArtDecoStyle, a specialist retailer of high-end decorative items, wants to perform key business calculations on one of its flagship products: a magnificent glazed stoneware vase. The following data was collected:

– Purchase Price Excluding Tax (PA HT) of the vase: €60
– Quantity sold: 120 units
– Sale Price excluding Tax (PV HT): €120

Work to do :

1. Calculate the margin rate.
2. Calculate the mark rate.
3. Calculate the unit margin.
4. Calculate the overall margin.
5. Apply the VAT rate to this product to obtain the sales price including VAT.

Proposed correction:

1. The margin rate is calculated using the formula: ((PV HT – PA HT) ÷ PA HT) x 100). Here, this gives: ((120 € – 60 €) ÷ 60 €) x 100 = 100%.

2. The markup rate is calculated as follows: ((PV HT – PA HT) ÷ PV HT) x 100). We therefore have: ((120 € – 60 €) ÷ 120 €) x 100 = 50%.

3. The unit margin corresponds to the difference between the sale price and the purchase price, i.e. for this situation: €120 – €60 = €60.

4. The overall margin is obtained by multiplying the unit margin by the quantity sold: €60 x 120 = €7200.

5. To get the sales price including tax, you have to add VAT (which is 20% in our case) to the sales price excluding tax. Therefore, the sales price including tax would be: €120 + (€120 x (20 ÷ 100)) = €144.

Summary of Formulas Used:

Formulas	Description
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100)
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100)
Unit margin	PV HT – PA HT
Overall margin	Unit margin x quantity sold
VAT Incl.	PV excluding tax + (PV excluding tax x (VAT ÷ 100))