Welcome to this article on exercises on business calculations and more specifically on 11 basic business calculation exercises. Here you will find no less than 11 detailed corrected management exercises on business 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: L'Éclat de Diamant Jewelry
- Application: SuperMark
- Application: JustNails Company
- Application: Fashionable clothing store
- Application: Gourmet Sweets
- Application: The House of Chocolate
- Application: The Golden Attic
- Application: ModeChic
- Application: The Aurore Boutique
- Application: Pulsar Supermarket
- Application: The Delight Pastry
Application: L'Éclat de Diamant Jewelry
States :
The L'Éclat de Diamant jewelry store sells a multitude of jewelry of all kinds. Today, it sold 50 gold rings at €200 excluding tax each. The purchase price excluding tax of these rings is €100 each. The applicable VAT rate is 20%.
Work to do :
1. Calculate the unit margin.
2. Calculate the overall margin.
3. Calculate the margin rate.
4. Calculate the mark rate.
5. Calculate the sales price including all taxes (TTC) of a ring.
Proposed correction:
1. The unit margin is calculated by taking the difference between the sales price excluding tax (SPT) and the purchase price excluding tax (PP): Unit margin = SPT – PP = €200 – €100 = €100.
2. The overall margin is calculated by multiplying the unit margin by the quantity sold: Overall margin = Unit margin x quantity sold = €100 x 50 = €5000.
3. The margin rate is obtained by calculating the ratio between the unit margin and the purchase price excluding tax (PA HT), all multiplied by 100 to obtain a percentage: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((€200 – €100) ÷ €100) x 100 = 100%.
4. The markup rate is calculated by taking the ratio between the unit margin and the sales price excluding tax (SVP HT), the whole multiplied by 100 to obtain a percentage: Markup rate = ((SVP HT – PA HT) ÷ SVP HT) x 100 = ((€200 – €100) ÷ €200) x 100 = 50%.
5. The sales price including all taxes (TTC) is obtained by adding the amount of VAT (which is 20% of the price excluding taxes) to the sales price excluding taxes (PV HT): Price including taxes = PV HT + (PV HT x VAT rate) = €200 + (€200 x 20%) = €200 + €40 = €240.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| VAT rate = 20% | 5,5% | The VAT rate is the percentage of the price excluding tax that is added to the total amount to obtain the price including all taxes. |
| Overall margin = Unit margin x quantity sold | The overall margin is the product of the unit margin (difference between the selling price excluding tax and the purchase price excluding tax) by the quantity sold. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | The margin rate is the percentage representing the portion of the pre-tax sales price that is margin, compared to the pre-tax purchase price. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | The markup rate is the percentage representing the portion of the pre-tax selling price that is margin, compared to the pre-tax selling price. |
Application: SuperMark
States :
SuperMark is a supermarket chain offering consumer goods. You are hired as a financial expert to analyze and evaluate their financial situation. They have sold 1 units of a product with a unit purchase price excluding tax of €200 and a sales price excluding tax of €15 per unit. The applicable VAT rate is 30%.
Work to do :
1. Calculate the overall margin.
2. What is the margin rate?
3. What is the markup rate?
4. Calculate the total amount of VAT.
5. What will be the sales price including tax for the product?
Proposed correction:
1. To calculate the overall margin, we use the formula Overall margin = Unit margin x quantity sold. Here, the unit margin is PV HT – PA HT or €30 – €15 = €15. Therefore, Overall margin = €15 x 1200 = €18.
2. The margin rate is calculated using the formula Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100. Which gives ((€30 – €15) ÷ €15) x 100 = 100%.
3. The markup rate, which is calculated using the formula Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100, is therefore ((€30 – €15) ÷ €30) x 100 = 50%.
4. For the total amount of VAT, we multiply the sales price excluding tax by the VAT rate and the quantity sold, i.e. 1200 x €30 x 20% = €7.
5. To find the sales price including tax for the product, add the sales price excluding tax and the VAT amount, i.e. €30 + (€30 x 20%) = €36.
Summary of Formulas Used:
| Packages | Description |
|---|---|
| VAT rate = 20% | 5,5% | VAT rate which can be 20% or 5,5% |
| Overall margin = Unit margin x quantity sold | The formula calculates the overall margin from multiplying the unit margin by the quantity sold. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | The formula calculates the margin rate. We subtract the purchase price excluding tax (PA HT) from the sale price excluding tax (PV HT), then divide the total by the PA HT and multiply by 100 to obtain the percentage |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | The formula calculates the markup rate, which is very useful for knowing the profitability of a product. We subtract the HT PA from the HT PV, then divide the total by the HT PV and multiply by 100 to obtain the percentage |
Application: JustNails Company
States :
JustNails is a distributor of nail salon products. Among its many products, it sells a premium nail polish.
Information about this product is as follows:
– Purchase price excluding VAT: €3,50
– Quantity sold: 2 units
– The VAT rate applied is 20%
– The company wishes to achieve an overall margin of €3
– The manager wants to know the margin and brand rate of his product.
Work to do :
1. Calculate the selling price excluding VAT.
2. Calculate the sales price including tax.
3. Calculate the margin rate.
4. Calculate the mark rate.
5. Is the overall margin desired by the manager achievable?
Proposed correction:
1. The selling price excluding VAT is calculated by adding the purchase price excluding VAT and the desired unit margin. The calculation formula is PV excluding VAT = PA excluding VAT + unit margin. In our case, the unit margin is the overall margin divided by the quantity sold, i.e. €3 ÷ 000 units = €2. Therefore, the selling price excluding VAT will be €000 + €1,50 = €3,50.
2. The sales price including VAT is calculated by adding VAT (20%) to the sales price excluding VAT. The calculation formula is PV including VAT = PV excluding VAT + PV excluding VAT x (VAT/100). In our case, this will give €5 + €5 x (20/100) = €6.
3. The margin rate is calculated using the formula ((PV HT – PA HT) ÷ PA HT). The margin rate is therefore ((€5 – €3,50) ÷ €3,50) x 100 = 42,86%.
4. The markup rate is calculated using the formula ((PV HT – PA HT) ÷ PV HT). So the markup rate is ((€5 – €3,50) ÷ €5) x 100 = 30%.
5. The overall margin desired by the manager is achieved if the product is sold at a selling price excluding tax of €5 and the quantity sold is 2 units because the overall margin will be €000 x 5 units – €2 x 000 units = €3,50.
Summary of Formulas Used:
| Terms | Packages |
|---|---|
| Sale price excl. VAT | PV HT = PA HT + unit margin |
| Sales price including tax | PV including VAT = PV excluding VAT + PV excluding VAT x (VAT/100) |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
Application: Fashionable clothing store
States :
You work as a manager in a fashionable clothing store. Here are some figures regarding business operations for the last week:
– You bought a leather jacket for €80 excluding tax and sold it for €150 excluding tax.
– Applicable taxes are 20% for this item.
– In total, you sold 200 of these jackets.
Work to do :
1. Calculate the unit gross margin for this jacket.
2. Calculate the overall gross margin for these jackets.
3. What is the margin rate?
4. What is the markup rate?
5. What is the selling price including tax of the jacket?
Proposed correction:
1. The gross margin per unit is the sales price excluding tax minus the purchase price excluding tax. In this case, the gross margin per unit is €150 – €80 = €70.
2. The overall gross margin is the unit gross margin multiplied by the number of products sold. In this case, the overall gross margin is €70 x 200 = €14.
3. The margin rate is the ratio of the gross margin to the purchase price excluding taxes, multiplied by 100 to obtain a percentage. Here, the margin rate is therefore ((€150 – €80) ÷ €80) x 100 = 87,5%.
4. The markup rate is the ratio of the gross margin to the selling price excluding taxes, multiplied by 100 to obtain a percentage. Therefore, the markup rate is ((€150 – €80) ÷ €150) x 100 = 46,67%.
5. The sales price including tax is the sales price excluding tax plus the value of the tax on this price. In our case, the tax is 20% or 0,20 of the sales price excluding tax or 0,20 x €150 = €30. Therefore, the sales price including tax is €150 + €30 = €180.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Unit gross margin = PV excluding tax – PA excluding tax | Allows you to calculate the unit gross margin (the profit on one unit of the product) |
| Overall gross margin = Unit gross margin x Quantity sold | Allows you to calculate the overall gross margin (total profit) |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Allows you to calculate the margin rate (the proportion of profit compared to the purchase price) |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | Allows you to calculate the markup rate (the proportion of profit compared to the sale price) |
| Selling price including tax = PV excluding tax + (VAT x PV excluding tax) | Allows you to calculate the sales price including all taxes (the final price that the customer pays) |
Application: Gourmet Sweets
States :
The company "Les Douceurs Gourmandes", specializing in the sale of artisanal pastries, offers a wide range of sweet treats. The company sells in particular an apple pie that is very popular with its customers.
The purchase price excluding VAT (Excluding Tax) of the apple pie for the company is €5,00 and its quantity sold is 100 units. The company resells it at a price of €8,00 excluding VAT. The VAT rate (Value Added Tax) applied is 5,5%.
Work to do :
1. Calculate the overall margin (excluding VAT) of the apple pie.
2. Calculate the margin rate.
3. Calculate the mark rate.
4. Calculate the selling price including all taxes (TTC) of the apple pie.
5. Calculate the company's turnover including tax for the apple pie.
Proposed correction:
1. Overall margin = Unit margin x quantity sold = (Selling price excluding VAT – Purchase price excluding VAT) x quantity sold = (€8,00 – €5,00) x 100 = €300,00
2. Margin rate = ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 = ((€8,00 – €5,00) ÷ €5,00) x 100 = 60%
3. Brand rate = ((Selling price excluding tax – Purchase price excluding tax) ÷ Sales price excluding tax) x 100 = ((€8,00 – €5,00) ÷ €8,00) x 100 = 37,5 .XNUMX%
4. Sales price including VAT = Sales price excluding VAT x (1 + (VAT rate ÷ 100)) = €8,00 x (1 + (5,5 ÷ 100)) = €8,44
5. Turnover including tax = Selling price including tax x quantity sold = €8,44 x 100 = €844,00
Summary of Formulas Used:
Total Margin Formula: Total Margin = Unit Margin x Quantity Sold = (Selling Price Excl. Tax - Purchase Price Excl. Tax) x Quantity Sold Margin Rate Formula: Margin Rate = ((Selling Price Excl. Tax - Purchase Price Excl. Tax) ÷ Purchase Price Excl. Tax) x 100 Markup Rate Formula: Markup Rate = ((Selling Price Excl. Tax - Purchase Price Excl. Tax) ÷ Sales Price Excl. Tax) x 100 Sales Price Incl. Tax Formula: Sales Price Incl. Tax = Sales Price Excl. Tax x (1 + (VAT Rate ÷ 100)) Sales Revenue Incl. Tax Formula: Sales Revenue Incl. Tax = Sales Price Incl. Tax x Quantity Sold
Application: The House of Chocolate
States :
La Maison du Chocolat is a well-established company in the confectionery sector. As a financial manager, you must perform certain business calculations.
Here is the basic data you have:
– The purchase price excluding tax (PA HT) of a box of chocolates is €8,40.
– The quantity of boxes of chocolates sold is 500.
– The sales price excluding tax (PV HT) is €16,20.
– The VAT rate is 20%.
Work to do :
1. Calculate the overall margin.
2. Determine the margin rate.
3. Estimate the markup rate.
4. Calculate the VAT amount.
5. Calculate the sales price all taxes included (PV including tax).
Proposed correction:
1. The overall margin is calculated by doing: unit margin x quantity sold.
The unit margin being the difference between the PV excluding tax and the PA excluding tax, i.e.: €16,20 – €8,40 = €7,80.
Multiplying by the quantity sold, we obtain: €7,80 x 500 = €3.
2. The margin rate is calculated using the formula ((PV HT – PA HT) ÷ PA HT) x 100.
So we have ((€16,20 – €8,40) ÷ €8,40) x 100 = 92,86%.
3. For the markup rate, the formula is ((PV HT – PA HT) ÷ PV HT) x 100).
In our case, this gives us: ((€16,20 – €8,40) ÷ €16,20) x 100 = 48,15%.
4. The amount of VAT is calculated by multiplying the sales price excluding tax by the VAT rate, i.e. €16,20 x 20/100 = €3,24.
5. The sales price including all taxes is obtained by adding the amount of VAT to the sales price excluding taxes, i.e. €16,20 + €3,24 = €19,44.
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 amount | PV excluding VAT x VAT rate |
| PV including tax | PV excluding tax + VAT amount |
Application: The Golden Attic
Summary of Formulas Used:
States :
The company "Le Grenier Doré", located in the heart of Paris, is a boutique specializing in the sale of vintage jewelry. Recently, the company added to its catalog a pearl necklace from the 70s that it buys for €45. It sells this necklace for €85 excluding tax. The jewelry in this range is in high demand, which allowed it to sell 150 units in one month.
Work to do :
1. Calculate the unit margin for each collar.
2. Calculate the overall margin for the month.
3. Calculate the margin rate.
4. Calculate the mark rate.
5. What is the amount of VAT for a sale, considering a rate of 20%?
Proposed correction:
1. The unit margin is the Selling Price excluding Tax (PV HT) minus the Purchase Price excluding Tax (PA HT), i.e. €85 – €45 = €40.
2. The overall margin is obtained by multiplying the unit margin by the quantity sold. In our case, this gives €40 x 150 = €6.
3. The margin rate is calculated using the formula ((PV HT – PA HT) ÷ PA HT) x 100. Therefore ((85 € – 45 €) ÷ 45 €) x 100 = 88,89%.
4. The markup rate, for its part, is given by the formula ((PV HT – PA HT) ÷ PV HT) x 100. Therefore ((85 € – 45 €) ÷ 85 €) x 100 = 47,06%.
5. The amount of VAT is calculated by multiplying the sales price excluding VAT by the VAT rate. In our case, €85 x 20% = €17.
Summary of Formulas Used:
| Packages | Descriptions |
| 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: ModeChic
States :
ModeChic is a ready-to-wear clothing business. One of their flagship products is a black dress that sold 300 units in the last financial year. The unit purchase cost of this dress excluding tax was €35 and it was sold at a sales price excluding tax of €70 per unit.
The VAT applied to this type of product in commerce is 20%. The head of the company wants to analyze the financial performance of this product.
Work to do :
1. Calculate the total purchase price excluding tax (TPP) of the black dress for the last financial year.
2. Calculate the total selling price excluding tax (PV HT) of the black dress for the last financial year.
3. Calculate the overall margin made on this product.
4. Calculate the margin rate of the black dress.
5. Calculate the markup rate of the black dress.
Proposed correction:
1. The total purchase price excluding tax (TPP HT) of the black dress is calculated by multiplying the unit purchase cost excluding tax by the number of units sold. Therefore, TP HT = Unit purchase cost excluding tax x Quantity sold = €35 x 300 = €10.
2. The total selling price excluding tax (SRP HT) of the black dress is calculated by multiplying the unit selling price excluding tax by the number of units sold. Therefore, SRP HT = Unit selling price excluding tax x Quantity sold = €70 x 300 = €21.
3. The overall margin is calculated by subtracting the total purchase price excluding taxes from the total sale price excluding taxes. Therefore, Overall margin = PV excluding taxes – PA excluding taxes = €21 – €000 = €10.
4. The margin rate is calculated by dividing the unit margin (i.e. the difference between the unit selling price excluding tax and the unit purchase cost excluding tax) by the unit purchase price excluding tax and multiplying the result by 100. Therefore, Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((70 € – 35 €) ÷ 35 €) x 100 = 100%.
5. The markup rate is calculated by taking the ratio between the unit margin and the unit selling price excluding tax, all multiplied by 100. Therefore, Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((70 € – 35 €) ÷ 70 €) x 100 = 50%.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| PA HT = Unit purchase cost HT x Quantity sold | Calculation of the total purchase price excluding taxes |
| PV HT = Unit selling price HT x Quantity sold | Calculation of the total sales price excluding taxes |
| Overall margin = PV HT – PA HT | Calculation of the overall margin |
| Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 | Calculation of the margin rate |
| Brand rate = ((PV HT – PA HT) ÷ PV HT) x 100 | Calculation of the mark rate |
Application: The Aurore Boutique
States :
Boutique Aurore is a women's clothing store. The owner recently purchased a new range of dresses for €50 each. He decides to sell each of these dresses for €70 excluding tax. The applicable taxes are at a rate of 20%.
Work to do :
1. What is the total cost of the dresses if the store purchased 30 units?
2. What is the unit margin per dress?
3. What is the markup for these dresses?
4. What is the markup rate for these dresses?
5. What will be the overall margin if the owner sells all the dresses?
Proposed correction:
1. Total Cost of Dresses = Unit Purchase Price x Quantity
Total cost of dresses = €50 x 30 = €1500
2. Unit margin = Selling price excluding VAT – Purchase price
Unit margin = €70 – €50 = €20
3. Margin rate = ((Selling price excluding VAT – Purchase price) ÷ Purchase price) x 100
Margin rate = ((€70 – €50) ÷ €50) x 100 = 40%
4. Markup rate = ((Selling price excluding VAT – Purchase price) ÷ Selling price excluding VAT) x 100
Markup rate = ((€70 – €50) ÷ €70) x 100 = 28,57%
5. Overall margin = Unit margin x Quantity sold
Total margin = €20 x 30 = €600
Summary of Formulas Used:
| Formulas | Definition |
|---|---|
| Total Cost of Dresses = Purchase Price x Quantity | The total cost corresponds to the overall expense incurred for the purchase of the dresses. |
| Unit margin = Selling price excluding VAT – Purchase price | The unit margin represents the difference between the sales price excluding taxes and the purchase price of each dress. |
| Margin rate = ((Selling price excluding VAT – Purchase price) ÷ Purchase price) x 100 | The margin rate is the percentage of margin made on the purchase price. |
| Markup rate = ((Selling price excluding VAT – Purchase price) ÷ Selling price excluding VAT) x 100 | The markup rate is the percentage of margin made on the sales price excluding tax. |
| Overall margin = Unit margin x Quantity | The overall margin is the total sum of the margins made on all the dresses sold. |
Application: Pulsar Supermarket
States :
Pulsar supermarket buys packs of mineral water at a price of €10 excluding tax. The supermarket sells these packs at a sales price excluding tax of €13. During one month, the supermarket sold 1000 packs of mineral water. The VAT rate applicable to this product category is 5,5%.
Work to do :
1. What is the margin on the tax-free retail price of Pulsar supermarket for a pack of mineral water?
2. What is Pulsar's margin rate for a pack of mineral water?
3. What is the Pulsar markup rate for a pack of mineral water?
4. What is the overall margin of Pulsar supermarket for all the packs of mineral water sold during a month?
5. Calculate the sales price including all taxes (TTC) of a pack of mineral water.
Proposed correction:
1. The margin on the tax-free retail price of the Pulsar supermarket for a pack of mineral water is €13 – €10 = €3.
2. Pulsar's margin rate for a pack of mineral water is calculated as follows: ((€13 – €10) ÷ €10) x 100 = 30%.
3. Pulsar's markup rate for a pack of mineral water is calculated as follows: ((€13 – €10) ÷ €13) x 100 = 23,08%.
4. The overall margin of the Pulsar supermarket for all the packs of mineral water sold during a month is €3 x 1000 = €3000.
5. The sales price including all taxes (TTC) of a pack of mineral water is calculated as follows: €13 + (€13 x 5,5%) = €13,715.
Summary of Formulas Used:
| Design | Formulas |
|---|---|
| Margin on the sales price excluding tax | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Overall margin | Unit margin x quantity sold |
| Sales price including tax | PV HT + (PV HT x VAT rate) |
Application: The Delight Pastry
States :
La Pâtisserie Délice is a business specializing in the sale of artisanal pastries. You work for this company as a management controller and you must analyze the financial performance of La Pâtisserie Délice over the past year. You have the following information for three of the brand's most popular products:
– Strawberry cake: Purchase price excluding tax (PA excluding tax): €4,00, Sale price excluding tax (PV excluding tax): €10,00, Quantity sold: 1000 units.
– Macarons: PA excluding tax: €2,00, PV excluding tax: €8,00, Quantity sold: 2000 units.
– Apple pie: HT PA: €3,00, HT PV: €6,00, Quantity sold: 1500 units.
Work to do :
1- Calculate the unit margin, the overall margin and the margin rate for each product.
2- Determine the markup rate for each product.
3- Calculate the total amount including tax for each product.
4- Analyze the financial performance of each product.
5- Evaluate the overall effectiveness of La Pâtisserie Délice’s pricing strategy.
Proposed correction:
1- The unit margin is the difference between the sales price excluding tax (STP) and the purchase price excluding tax (PP excluding tax). The margin rate is calculated by doing ((STP – PP excluding tax) ÷ PP excluding tax) x 100 and the overall margin is calculated by doing the unit margin x the quantity sold. So I will calculate this data for each product.
2- The markup rate is calculated by doing ((PV HT – PA HT) ÷ PV HT) x 100. I will therefore calculate this rate for each product.
3- Finally, to calculate the total amount including tax for each product, I will add the sales price excluding tax (SPT) with the value added tax (VAT), which is 20% (SPT x 20%) for this type of activity.
4- Analyzing the results, I can say that the most profitable product is strawberry cake, followed by macaroons and apple pie.
5- According to my calculations, La Pâtisserie Délice's pricing strategy appears to be effective since unit and overall margins are positive for all products, and the margin and brand rates are also quite high.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Unit margin = PV excluding tax – PA excluding tax | It is the difference between the sales price excluding tax and the purchase price excluding tax for a unit of product. |
| Overall margin = Unit margin x quantity sold | It is the overall difference made by the sale of all products between their purchase price and their sale price. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | It measures the profitability of each product in relation to its acquisition cost. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | It measures what part of each euro collected is margin |
| Total amount including tax = PV excluding tax x (1 + VAT rate) | This is the total price that the customer must pay, including tax, for the purchase of the product. |