Welcome to this article on exercises on business calculations and more specifically on 11 second year professional commercial calculation exercises. Here you will find no less than 11 detailed corrected management exercises on commercial calculations on Operational Management.
By the end of this article, you will know how to perform these 11 business calculation exercises without any worries.
In this section:
- Application: Gourmet Bakery
- Application: Glorious Jewels
- Application: Orleans Furniture Company
- Application: Happiness Company
- Application: Leather Goods Store
- Application: Dessert House
- Application: Green Store
- Application: Chocolaterie Delice
- Application: Electronix Company
- Application: Glamour Clothing Store
- Application: TechnoGuru Company
Application: Gourmet Bakery
States :
Boulangerie Gourmet is well known in its region for its delicious croissants and artisan breads. Here is some information on the purchase price excluding tax (PA HT) and other costs associated with some of their products:
– Purchase price excluding tax of croissants: €0,80 per unit
– Desired sale price: €1,20 per unit
– Their VAT rate is 5,5%
– They plan to sell 200 croissants per day
Work to do :
1. What is the sales price excluding tax (PV HT) of croissants in the bakery?
2. What is the margin rate for croissants?
3. What is the markup rate of croissants?
4. How much would the overall margin be if they sell their expected number of croissants per day?
5. If the bakery decides to increase the sales price including tax of croissants by 10%, what would the new sales price including tax be?
Proposed correction:
1. To calculate the PV excluding VAT, subtract the VAT amount from the VAT-inclusive sales price. Formula: PV including VAT – VAT amount = PV excluding VAT. First, calculate the VAT amount using the formula: [PV including VAT / (1 + VAT rate)] x VAT rate = VAT amount.
So, VAT = [€1,20 / (1 + 0,055)] x 0,055 = €0,062.
Then, we calculate the PV excluding tax: €1,20 – €0,062 = €1,138
2. To calculate the margin rate, we use the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
So, Margin rate = ((€1,138 – €0,80) ÷ €0,80) x 100 = 42,25%.
3. To calculate the markup rate, we use the formula: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100).
So, Markup Rate = ((€1,138 – €0,80) ÷ €1,138) x 100 = 29,70%.
4. The overall margin is calculated as follows: Overall margin = Unit margin x quantity sold.
Therefore, Unit Margin = PV HT – PA HT = €1,138 – €0,80 = €0,338.
Then, Overall Margin = €0,338 x 200 = €67,60.
5. To calculate the increase in the PV including tax, we use the formula: New PV including tax = PV including tax + (PV including tax x increase rate).
So, New PV including VAT = €1,20 + (€1,20 x 10/100) = €1,32.
Summary of Formulas Used:
| VAT : | [PV TTC / (1 + VAT rate)] x VAT rate = VAT amount |
| PV HT: | PV including tax – VAT amount = PV excluding tax |
| Margin rate: | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Mark rate: | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Overall margin: | Unit margin x quantity sold |
| PV increase including tax: | PV TTC + (PV TTC x increase rate) |
Application: Glorious Jewels
States :
Glorieux Bijoux is a company that sells jewelry online. The company buys a gold bracelet for €150 excluding tax from a supplier. It applies a markup rate of 50% to set the sales price excluding tax. The company applies a VAT rate of 20%.
To strengthen its customer base, the company decided to offer a 10% discount on this bracelet when it was launched.
However, once the promotion ends, the company is considering increasing the price of the bracelet by 5% to cover some unforeseen operational expenses.
Work to do :
1. Calculate the sales price excluding tax (SRP HT) of the bracelet.
2. Determine the selling price including all taxes (PV TTC) of the bracelet.
3. Calculate the amount of the discount when launching the bracelet.
4. Calculate the new sales price including all taxes (PV TTC) after the promotion.
5. Estimate the sales price including all taxes (PV TTC) after the 5% increase.
Proposed correction:
1. The formula for calculating the PV HT with a markup rate is: PV HT = PA HT / (1 – Markup rate). Here, PV HT = €150 / (1 – 0,5) = €300. Therefore, the sales price excluding tax of the bracelet is €300.
2. To determine the VAT-inclusive sales price, we add the VAT to the VAT-exclusive sales price. The formula is: VAT-inclusive sales price = VAT-exclusive sales price + (VAT-exclusive sales price x VAT rate). Here, VAT-inclusive sales price = €300 + (€300 x 20/100) = €360. Therefore, the all-tax sales price of the bracelet is €360.
3. The discount is calculated on the PV including tax. The formula is: Discount = PV including tax x Discount rate. Here, Discount = €360 x 10 / 100 = €36. Therefore, the discount amount when the bracelet is launched is €36.
4. After the discount, the VAT-inclusive sales price is calculated as follows: VAT-inclusive sales price after discount = VAT-inclusive sales price – Discount. Here, VAT-inclusive sales price after discount = €360 – €36 = €324. Therefore, the new all-tax sales price of the bracelet after the promotion is €324.
5. After the promotion, if the price of the bracelet increases by 5%, the new VAT PV is calculated as follows: New VAT PV = VAT PV after reduction + (VAT PV after reduction x Increase rate). Here, New VAT PV = €324 + (€324 x 5 / 100) = €340,20. Therefore, the all-tax sales price of the bracelet after the 5% increase is €340,20.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Sale price excluding tax (PV HT) | PV HT = PA HT / (1 – Mark rate) |
| Sales price all taxes included (PV including tax) | PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate) |
| Discount | Reduction = PV incl. VAT x Reduction rate |
| Sales price including VAT after reduction | PV including tax after reduction = PV including tax – Reduction |
| New sales price including VAT | New PV including tax = PV including tax after reduction + (PV including tax after reduction x Increase rate) |
Application: Orleans Furniture Company
States :
La Compagnie du Meuble d'Orléans (CMO), a major player in the furniture market in the Centre region, operates a wide range of furniture including vintage chests of drawers. The company purchases these chests of drawers from a foreign manufacturer for a purchase price excluding tax (PA HT) of €180 per unit. CMO sells these chests of drawers for a sales price excluding tax (PV HT) of €300. The VAT rate applied is 20%.
For the month of June, CMO announces 30% off vintage dressers to boost sales. However, to compensate for this reduction, the company decides to increase the selling price excluding VAT by 10%.
Work to do :
1. Calculate the unit margin on each vintage dresser sold by CMO.
2. Calculate the margin rate on these dressers.
3. What is the sales price including tax (PV TTC) of a chest of drawers before the reduction?
4. What will be the new selling price excluding VAT after the 10% increase applied by CMO?
5. What will be the final sales price including VAT of a chest of drawers after the reduction announcement?
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). Thus, the unit margin = PV excluding tax – PA excluding tax = €300 – €180 = €120. The unit margin on each chest of drawers sold by CMO is therefore €120.
2. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100. In our case, Margin rate = ((300 € – 180 €) ÷ 180 €) x 100 = 66,67%.
3. The sales price including tax (STP TTC) is obtained by adding VAT to the sales price excluding tax (STP HT). In our example, STP TTC = STP HT + VAT = €300 + (€300 x 20%) = €360
4. To obtain the new selling price excluding tax after the 10% increase, we carry out: New PV excluding tax = PV excluding tax + (PV excluding tax x 10%) = €300 + (€300 x 10%) = €330.
5. The final sales price including VAT of a chest of drawers after the announcement of the reduction is calculated by subtracting the reduction from the new Sales Price including VAT. Final price = New PV including VAT – (New PV including VAT x 30%) = €396 – (€396 x 30%) = €277,20.
Summary of Formulas Used:
- Unit margin = Sales price excluding tax – Purchase price excluding tax
- Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
- PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate)
- New PV HT = PV HT + (PV HT x Percentage increase)
- Final price = New PV including tax – (New PV including tax x Reduction percentage)
Application: Happiness Company
States :
L'Entreprise du Bonheur is a jewelry store. We give you the purchase price excluding tax (PA HT) of a bracelet at €80. The bracelet is sold at a sales price excluding tax (PV HT) of €120. The quantity sold is 50 units. The VAT rate is 20%.
Work to do :
1. Calculate the Selling Price including VAT of the bracelet.
2. Calculate the unit margin.
3. Calculate the margin rate.
4. Calculate the mark rate.
5. The bracelet is on sale and has a 10% reduction. What is the new sales price including VAT?
6. After the sales period, the price of the bracelet is increased by 15%. What is the new sales price including VAT?
Proposed correction:
1. PV incl. tax = PV excl. tax + (PV excl. tax x VAT rate) = €120 + (20% x €120) = €144.
2. Unit margin = PV HT – PA HT = €120 – €80 = €40.
3. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100) = ((120 € – 80 €) ÷ 80 €) x 100 = 50%.
4. Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100) = ((120 € – 80 €) ÷ 120 €) x 100 = 33,3%.
5. Discount = Old Price – (Old Price x % discount) = €144 – (10% x €144) = €129,6.
6. Increase = Old Price + (Old Price x % increase) = €129,6 + (15% x €129,6) = €149,04.
Summary of Formulas Used:
| Enumeration of formulas | Packages |
|---|---|
| Calculation of the Sales Price including tax | PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate) |
| Calculation of the overall margin | Overall margin = Unit margin x quantity sold |
| Calculation of Margin Rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Calculation of the Markup Rate | Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 |
| Calculation of the Reduction | Discount = Old Price – New Price |
| Calculation of the Increase | Increase = New Price – Old Price |
Application: Leather Goods Store
States :
You work in the Leather Goods leather goods store, known for its high-quality craftsmanship and attention to detail. You are responsible for the financial management of the company and must deal with varied and complex situations.
Here are some situations:
1. You buy a product at a purchase price excluding VAT of €100, you want to generate an overall margin rate of 50%, the product is subject to a VAT rate of 20%.
2. During the sales, you offer a 15% discount on all your products. A bag initially costing €150 including tax is included in this offer.
3. After an increase in production costs, your bags cost 10% more to produce. The bags were initially sold at €200 including VAT with a VAT rate of 20%.
4. During a promotional campaign, you reduce the price of a bag by 20%. The bag originally cost €120 including VAT. After the promotion, you want to know the margin and brand rate.
5. Faced with an increase in demand, you decide to increase the selling price excluding VAT of your products by 7%. A bag was initially sold for €80 excluding VAT. What will its new selling price including VAT be with a VAT rate of 5,5%?
Work to do :
1. Calculate the selling price excluding tax (PV excluding tax) for the product in order to generate an overall margin of 50%.
2. Calculate the new price of the bag after the 15% discount.
3. What is the new selling price of bags after a 10% increase in production?
4. What is the margin and markup rate after the 20% discount?
5. What will be the new sales price including tax of the bag after a 7% increase in the sales price excluding tax?
Proposed correction:
1. To calculate the selling price excluding tax, we use the formula: PV excluding tax = PA excluding tax + (PA excluding tax x Margin rate). We obtain: PV excluding tax = €100 + (€100 x 0,5) = €150
2. To calculate the new price of the bag after the reduction, subtract the amount of the reduction (in €) from the initial price. We obtain: Price after reduction = €150 – (€150 x 0,15) = €127,5 incl. VAT
3. After a 10% increase in production costs, the increase in production costs will be reflected in the sales price, i.e. €200 including tax + (€200 x 0,1) = €220 including tax
4. To know the margin and markup rate, we must first calculate the selling price excluding VAT and the purchase cost excluding VAT after the promotion.
For example, we obtain: PV excluding VAT after promotion = €120 including VAT – (€120 x 0,2) = €96 including VAT. To obtain the PV excluding VAT, we use the formula: PV excluding VAT = PV including VAT / (1 + VAT rate) => €96 / (1+ 0,2) = €80 excluding VAT. Let's imagine that the purchase cost of the bag is €50 excluding VAT. We obtain for the margin rate: ((€80 – €50) ÷ €50) x 100 = 60% and for the markup rate: ((€80 – €50) ÷ €80) x 100 = 37,5%
5. If the bag was initially sold for €80 excluding VAT and you increase the VAT sale price by 7%, the new VAT sale price will be €80 + (€80 x 0,07) = €85,6 excluding VAT. The VAT sale price will therefore be €85,6 x (1 + 0,055) = €90,31 including VAT.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Sales price excluding tax (PV excluding tax) | PV excluding tax = PA excluding tax + (PA excluding tax x Margin rate) |
| Price after reduction | Price after discount = Initial price – (Initial price x Discount rate) |
| Price after increase | Price after increase = Initial price + (Initial price x Rate of increase) |
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100) |
| Brand taxes | Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100) |
| Sales price including tax | Sales price including tax = Sales price excluding tax x (1 + VAT rate) |
Application: Dessert House
States :
La Maison des Desserts, a company specializing in the production and sale of pastries and cakes, presented the following data regarding one of its products, the Gâteau Royal:
Purchase price excluding VAT: €10
Selling price excluding VAT: €15
Quantity sold: 300 units
VAT rate: 20%
Work to do :
1. Calculate the selling price including tax of the Royal Cake.
2. What is the margin rate on the Royal Cake?
3. What is the markup rate for Royal Cake?
4. Calculate the overall margin obtained on the sale of 300 Royal Cake.
5. What will be the new selling price excluding tax of the Royal Cake if Maison des Desserts decides to increase its selling prices excluding tax by 5%?
Proposed correction:
1. The selling price including tax of the Royal Cake is: €15 x (1+ 20/100) = €18.
2. The margin rate on the Royal Cake is: ((€15 – €10) ÷ €10) x 100 = 50%.
3. The markup rate for the Royal Cake is: ((€15 – €10) ÷ €15) x 100 = 33,33%
4. The overall margin obtained on the sale of 300 Royal Cakes is: (15-10) € x 300 = 1500 €.
5. The new selling price excluding tax of the Royal Cake if Maison des Desserts increases its selling prices excluding tax by 5% will be: €15 + (€15 x 5/100) = €15,75.
Summary of Formulas Used:
| VAT | Price including tax = Price excluding tax x (1 + VAT rate/100) |
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Brand taxes | Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 |
| Margin | Overall margin = Unit margin x quantity sold |
| Increase | Price with increase = Price without increase + (Price without increase x increase rate) |
Application: Green Store
States :
Le Magasin Vert is a retail company that sells various products including household appliances. The company recently sold a washing machine for €500 including VAT. The VAT rate applicable to this product is 20% and the company purchased this washing machine for €300 excluding VAT. In addition, Le Magasin Vert plans to run a promotion on this product with a 10% discount. In order not to lose on its margin, the company plans to increase the initial price of the product after the promotion.
Work to do :
1. Determine the selling price excluding tax of the washing machine.
2. Calculate the margin made on the sale of this product.
3. Define the product margin rate.
4. If the company plans a 10% discount on the product, what will be its new sales price including tax?
5. What should be the new sales price including VAT of the washing machine after the promotion to maintain the same margin?
Proposed correction:
1. To determine the selling price excluding VAT of the washing machine, we must subtract the VAT from the price including VAT. The formula for this is: Price including VAT ÷ (1 + VAT rate). In this case, we have €500 ÷ (1 + 20%) = €416,67 excluding VAT.
2. The margin made on the sale of this product is determined by subtracting the purchase price excluding VAT from the sale price excluding VAT. Therefore, the margin is €416,67 – €300 = €116,67.
3. The margin rate is calculated by defining the unit margin as a proportion of the purchase price excluding VAT. The formula is ((Sale Price excluding VAT – Purchase Price excluding VAT) ÷ Purchase Price excluding VAT) × 100. Therefore, the margin rate is ((€416,67 – €300) ÷ €300) x 100 = 38,89%.
4. If the store offers a 10% discount on the product, the new sales price including VAT will be €500 – 10% of €500 = €450.
5. To maintain the same margin after the promotion, the new sales price including tax would be the initial sales price including tax plus the margin, i.e. €500 + 10% of €500 = €550.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Selling price excluding tax | Price including VAT ÷ (1 + VAT rate) |
| Margin achieved | Selling price excluding VAT – Purchase price excluding VAT |
| Margin rate | ((Sale Price excluding VAT – Purchase Price excluding VAT) ÷ Purchase Price excluding VAT) x 100 |
| Product discount | Price including tax – (Percentage discount x Price including tax) |
| Selling price including tax after promotion to maintain the same margin | Price including tax + (Percentage reduction x Price including tax) |
Application: Chocolaterie Delice
States :
Chocolaterie Delice is a company specializing in the manufacture of high-end chocolates. Their flagship product is the "Delice Royal", an assortment of fine chocolates sold at a price of €15 including tax per unit. The purchase cost excluding tax for this product for the company is €9. The VAT applied to this type of product is 20%.
Following an increase in raw material costs, Chocolaterie Delice is considering increasing the purchase price by 10%. At the same time, a promotional operation is planned with a 5% reduction on the sale price.
Work to do :
1. Calculate the sales price excluding tax of “Delice Royal”.
2. Calculate the value margin and the margin rate.
3. What will the new purchase price be if the company increases its costs by 10%?
4. Calculate the new margin rate after the increase in purchase cost.
5. Finally, after the 5% reduction in the selling price, what will be the new selling price and the new markup rate?
Proposed correction:
1. The sales price excluding tax (PV HT) is calculated by removing VAT from the sales price including tax. The formula is therefore: PV HT = PV TTC ÷ (1 + VAT rate). Here, we have: PV HT = €15 ÷ (1 + 20/100) = €12,5.
2. The value margin is calculated by subtracting the purchase price excluding VAT from the sale price excluding VAT. Therefore Margin = PV excluding VAT – PA excluding VAT, i.e. Margin = €12,5 – €9 = €3,5. The margin rate is calculated using the formula: Margin rate = ((PV excluding VAT – PA excluding VAT) ÷ PA excluding VAT) x 100), i.e. Margin rate = ((€12,5 – €9) ÷ €9) x 100 = 38,89%.
3. The new purchase price following the 10% increase in cost will be: New HT PA = Old HT PA x (1 + increase rate), i.e. New HT PA = €9 x (1 + 10/100) = €9,9.
4. The new margin rate after increasing the purchase cost is: ((PV HT – PA HT new) ÷ PA HT new) x 100 = ((12,5 € – 9,9 €) ÷ 9,9 €) x 100 = 26,26%.
5. After a 5% reduction in the sale price, the new sale price will be: New HT PV = Old HT PV x (1 – reduction rate), i.e. New HT PV = €12,5 x (1 – 5/100) = €11,88. The new markup rate will be: ((New HT PV – New HT PA) ÷ New HT PV) x 100 = 16,89%.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Sale price excluding tax (PV HT) | PV HT = PV TTC ÷ (1 + VAT rate) |
| Margin in value | Margin = PV excluding tax – PA excluding tax |
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| New purchase price with increase | New HT PA = Old HT PA x (1 + increase rate) |
| New sale price with discount | New HT PV = Old HT PV x (1 – reduction rate) |
| New mark rate after reduction | Brand rate = ((New PV HT – New PA HT) ÷ New PV HT) x 100 |
Application: Electronix Company
States :
The company Electronix specializes in the sale of electronic equipment. One of the company's flagship products is a laptop sold for a purchase price excluding tax (PA HT) of €500. The company applies a margin of 30% on the purchase price excluding tax, the VAT rate is 20%.
1. For a special promotion, the company Electronix has decided to offer a 15% discount on the sales price including VAT.
2. A few months later, the company experiences a 10% increase in production costs, which forces them to increase their selling price.
Work to do :
1. Calculate the sales price excluding tax (SVP HT), the sales price including tax, the margin in € and the margin rate.
2. Calculate the new sales price including VAT after the 15% reduction.
3. Calculate the purchase price excluding VAT after the increase in production costs.
4. Calculate the new sales price including VAT after the increase in production costs.
5. What is the new margin rate after the increase in production costs?
Proposed correction:
1. To calculate the selling price excluding VAT (PV excluding VAT), we use the formula: PV excluding VAT = PA excluding VAT + (PA excluding VAT x margin%). The selling price including VAT is calculated as follows: PV including VAT = PV excluding VAT + (PV excluding VAT X VAT%). The margin in € is obtained using the formula: Overall margin = Unit margin x quantity sold. Finally, the margin rate is calculated using: Margin rate = ((PV excluding VAT – PA excluding VAT) ÷ PA excluding VAT) x 100. We therefore obtain:
PV excluding tax = €500 + (€500 x 30%) = €650;
PV including tax = €650 + (€650 x 20%) = €780;
Margin = PV excluding tax – PA excluding tax = €650 – €500 = €150;
Margin rate = ((€650 – €500) ÷ €500) x 100 = 30%.
2. For the new sales price including tax after the reduction, we apply a subtraction of the percentage of the reduction. This gives: Reduced PV including tax = PV including tax – (PV including tax x reduction%) = €780 – (€780 x 15%) = €663.
3. The purchase price excluding tax after the increase in production costs is: PA excluding tax after increase = PA excluding tax + (PA excluding tax x increase%) = €500 + (€500 x 10%) = €550.
4. The new sales price including VAT after the increase in costs is calculated as follows: PV including VAT after increase = (PA excluding VAT after increase + (PA excluding VAT after increase x margin%)) + ((PA excluding VAT after increase + (PA excluding VAT after increase x margin%)) x VAT%) = (€550 + (€550 x 30%)) + ((€550 + (€550 x 30%)) x 20%) = €858.
5. The new margin rate after the increase in costs is: New margin rate = ((PV HT after increase – PA HT after increase) ÷ PA HT after increase) x 100 = ((715 € – 550 €) ÷ 550 €) x 100 = 30%.
Summary of Formulas Used:
| Packages | Explanations |
|---|---|
| PV excluding tax = PA excluding tax + (PA excluding tax x margin%) | Calculation of the sales price excluding tax |
| PV including VAT = PV excluding VAT + (PV excluding VAT X VAT%) | Calculation of the sales price all taxes included |
| Overall margin = Unit margin x quantity sold | Margin Calculation |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Calculation of the margin rate |
| Reduced VAT PV = VAT PV – (VAT PV x reduction%) | Calculation of the sale price including all taxes after reduction |
| PA HT after increase = PA HT + (PA HT x increase%) | Calculation of the purchase price excluding tax after increase |
| New margin rate = ((PV HT after increase – PA HT after increase) ÷ PA HT after increase) x 100 | Calculation of the new margin rate after increase |
Application: Glamour Clothing Store
States :
Glamour is a clothing store based in Paris. It wants to evaluate its performance and sales prices for better cash flow management.
The shop bought a dress for €50 excluding VAT which it sells for €85 excluding VAT. VAT is 20%. The dress was sold in a quantity of 1000 units.
Recently, Glamour increased its sale price to €100 excluding VAT and is offering a 10% discount on this new price for its loyal customers.
Work to do :
1. Calculate the sales price including tax of the dress?
2. What is the overall margin made by the store on the sale of these dresses?
3. Calculate the margin and brand rates for this dress?
4. What is the new sales price including VAT after the increase?
5. What is the sales price including tax after the discount given to loyal customers?
Proposed correction:
1. The sales price including tax is calculated using the formula: Price excluding tax x (1 + VAT rate), therefore €85 x (1 + 20%) = €102 including tax.
2. The overall margin is calculated using the formula: Unit margin x Quantities sold, so the unit margin is (€85 – €50) = €35. So the overall margin is €35 x 1000 = €35.
3. The margin rate is calculated using the formula: ((PV HT – PA HT) ÷ PA HT) x 100), therefore ((85 € – 50 €) ÷ 50 €) x 100) = 70%.
The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100), therefore ((85 € – 50 €) ÷ 85 €) x 100) = 41.18%.
4. The new sales price including tax after the increase is calculated using the formula: Initial price x (1 + percentage increase), therefore €100 x (1 + 20%) = €120 including tax.
5. The sales price including VAT after the reduction is calculated using the formula: Initial price x (1 – reduction percentage), therefore €120 x (1 – 10%) = €108 including VAT.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Calculation of the price including tax | Price excluding VAT x (1 + VAT rate) |
| Calculating the overall margin | Unit margin x Quantities sold |
| Calculation of the margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Calculation of the mark rate | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Calculating an increase | Initial price x (1 + percentage increase) |
| Calculation of a reduction | Original price x (1 – discount percentage) |
Application: TechnoGuru Company
States :
TechnoGuru is a technology equipment sales company. It wants to establish its pricing strategy for the current year. To do this, it has collected the following information:
– The purchase price excluding tax (PA HT) of a laptop is €500.
– The company wants to achieve a margin of 30% on the purchase price excluding taxes.
– The company plans to sell 100 units of this computer.
In addition, the following elements should be taken into account:
– VAT is 20%
– The company plans to offer a 10% discount on the computer's retail price including VAT on Black Friday
– Following an expected increase in charges, the company plans to increase the selling price excluding tax by 5%.
Work to do :
1. Calculate the sales price excluding tax (PV HT).
2. Calculate the sales price including all taxes (PV TTC).
3. What will be the overall margin achieved on the sale of 100 units?
4. What is the new PV HT and PV TTC after the 5% increase?
5. What will be the selling price including VAT of the laptop on Black Friday?
Proposed correction:
1. The sales price excluding tax (PV HT) is calculated by adding to the purchase price excluding tax (PA HT) the unit margin which corresponds to the margin rate applied to the PA HT. Therefore PV HT = PA HT + (PA HT x Margin rate) = €500 + (€500 x 30%) = €650.
2. The sales price including all taxes (PV TTC) is calculated by adding to the PV excluding tax the amount of VAT, which corresponds to the VAT rate applied to the PV excluding tax. Therefore PV TTC = PV excluding tax + (PV excluding tax x VAT rate) = €650 + (€650 x 20%) = €780.
3. The overall margin is obtained by multiplying the unit margin by the number of products sold. Therefore, Overall margin = Unit margin x Quantity sold = (€650 – €500) x 100 = €15.
4. The new PV excluding VAT after the 5% increase is therefore €650 x 1,05 = €682,50 and the new PV including VAT is €682,50 x 1,20 = €819.
5. The sales price including tax of the laptop on Black Friday, after applying the 10% reduction, is therefore €819 x 0,90 = €737,10.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| PV excluding tax = PA excluding tax + (PA excluding tax x Margin rate) | Calculation of the sales price excluding taxes |
| VAT included = VAT excluded + (VAT excluded × VAT rate) | Calculation of the sales price all taxes included |
| Overall margin = Unit margin x Quantity sold | Calculation of the overall margin made on the sale of 100 units |
| New PV HT = PV HT x (1 + Increase rate) | Calculation of the new sales price excluding tax |
| New PV including VAT = PV excluding VAT x (1 + VAT rate) | Calculation of the new sales price including all taxes |
| Black Friday sales price including tax = PV including tax x (1 – Discount rate) | Calculation of the sales price including tax of a product during Black Friday after application of the reduction |