Welcome to this article on exercises on business calculations and more specifically on how to calculate a reduction percentage. Here you will find 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 a discount percentage in business calculations without any worries.
In this section:
- Application: Chocolate Gourmet
- Application: The Chic Boutique
- Application: High-end clothing store “Fashion Elite”
- Application: La Belle Époque Shop
- Application: Good Deals Supermarket
- Application: “Aux Bonnes Affaires” Supermarket
- Application: “Trendy” clothing sales company
- Application: Trobico Company
- Application: SuperElectro10
- Application: JoliStyle Store
- Application: OptimalDiscount
Application: Chocolate Gourmet
| Formulas | Explanation |
|---|---|
| % Discount = (Original Price – Discounted Price) ÷ Original Price x 100 | This is the formula to calculate the percentage of the discount. |
| Original Price = Discounted Price ÷ (1 – % Discount ÷ 100) | This is the formula to calculate the original price before the discount, from the discounted price and the discount percentage. |
States :
You are the financial manager of Chocolaterie Gourmandise. Before Valentine's Day, one of the major events for the chocolate factory, you carry out price analyses on the various products to establish attractive offers. Product price list:
– Special Valentine’s Day box of chocolates: €50
– Assortment of homemade truffles: €35
– 70% dark chocolate bar: €15
– Milk chocolate bars: €20
– Homemade pralines: €40
Work to do :
1. If you decide to offer a 20% discount on the box of chocolates, what would its new price be?
2. If the homemade praline is on sale for €32, what is the percentage reduction applied?
3. If you want to offer a 15% discount on the truffle assortment, what would be its new price?
4. If the dark chocolate bar is on sale for €12, what percentage of the discount is applied?
5. If you want to offer a 30% discount on milk chocolate bars, what would their new price be?
Proposed correction:
1. The new price after a 20% discount on the box of chocolates would be: €50 x (1 – 20 ÷ 100) = €40.
2. The percentage discount on the praline would be: ((€40 – €32) ÷ €40) x 100 = 20%.
3. The new price after a 15% discount on the truffle assortment would be: €35 x (1 – 15 ÷ 100) = €29,75.
4. The percentage discount on the dark chocolate bar would be: ((€15 – €12) ÷ €15) x 100 = 20%.
5. The new price after a 30% discount on milk chocolate bars would be: €20 x (1 – 30 ÷ 100) = €14.
Summary of Formulas Used:
| % Discount = (Original Price – Discounted Price) ÷ Original Price x 100 | Original Price = Discounted Price ÷ (1 – % Discount ÷ 100) |
|---|---|
| This is the formula to calculate the discount percentage. | This is the formula to calculate the original price before the discount, from the reduced price and the discount percentage. |
Application: The Chic Boutique
States :
Boutique Chic, a luxury clothing store, has planned a big Black Friday sale with deep discounts on various items. To prepare for the sale, the store manager needs to determine the percentage off each item.
For this exercise we will use the following information:
– Initial price of an evening dress: €800
– Initial price of a suede jacket: €700
– Initial price of a pair of high heels: €500
After reduction, the prices are:
– Evening dress: €600
– Suede jacket: €560
– Pair of high heels: €400
Work to do :
1. What is the percentage discount on the evening dress?
2. What is the percentage discount on the suede jacket?
3. What is the percentage discount on the pair of heels?
4. Which product has the biggest percentage discount?
5. If a customer purchases these three items, what will be the overall discount percentage?
Proposed correction:
1. Percentage discount on evening dress:
Formula: Discount Percentage = ((Original Price – Price After Discount) ÷ Original Price) x 100)
Discount percentage = ((€800 – €600) ÷ €800) x 100 = 25%
2. Percentage discount on suede jacket:
Formula: Discount Percentage = ((Original Price – Price After Discount) ÷ Original Price) x 100)
Discount percentage = ((€700 – €560) ÷ €700) x 100 = 20%
3. Percentage discount on the pair of heels:
Formula: Discount Percentage = ((Original Price – Price After Discount) ÷ Original Price) x 100)
Discount percentage = ((€500 – €400) ÷ €500) x 100 = 20%
4. The evening dress has the biggest percentage discount at 25%.
5. The overall discount percentage is calculated as follows: Sum of initial prices – Sum of prices after discount) ÷ Sum of initial prices) x 100
Overall discount percentage = ((€2000 – €1560) ÷ €2000) x 100 = 22%
Summary of Formulas Used:
| Packages | Explanation |
|---|---|
| Discount percentage = ((Original price – Price after discount) ÷ Original price) x 100) | This allows you to calculate the proportion of money saved compared to the initial cost of the product. |
Application: High-end clothing store “Fashion Elite”
States :
The store "Fashion Elite" is planning to carry out a discount campaign on a selection of its products for the sales season. For this, the following details must be taken into account:
– A wool coat is sold at the initial price of €180 excluding VAT. The store wants to reduce the price and sell it at €126 excluding VAT.
– An evening dress is sold at the initial price of €220 excluding VAT. The store wants to offer it with a 30% discount.
– A batch of scarves is sold at the initial price of €80 excluding VAT per unit. The store wants to sell them at €60 excluding VAT per unit after a reduction.
Work to do :
1. Calculate the percentage discount applied to the wool coat.
2. Calculate the new price excluding VAT of the evening dress after the reduction.
3. Determine the percentage reduction applied to the batch of scarves.
4. Consider whether the overall margins obtained from sale items are sufficient to cover the operating costs of the store.
5. Evaluate the potential impacts on sales of other products that are not on sale.
Proposed correction:
1. The percentage discount on the wool coat is calculated using the formula: Percentage discount = [(Initial price excluding VAT – Price after discount) ÷ Initial price excluding VAT] x 100.
In this case: [(180 – 126) ÷ 180] x 100 = 30%. So the coat has undergone a reduction of 30%.
2. The price excluding VAT of the evening dress after the reduction is calculated using the formula: Price after reduction = Initial price excluding VAT – (Initial price excluding VAT x Reduction rate).
In this case: 220 – (220 x 30÷100) = €154 excluding VAT. So the evening dress will be sold at €154 excluding VAT after the reduction.
3. The percentage discount applied to the lot of scarves is obtained with the same formula as before: [(80 – 60) ÷ 80] x 100 = 25%. So the scarves have been reduced by 25%.
4. Assessing overall margins after discounts is a complex task that requires a more detailed analysis of the store's operating costs and the expected margins for each product. It is important to maintain an overall margin sufficient to cover operating costs and to make a profit. This question involves a thorough understanding of the company's cost structure.
5. The impact of discounts on sales of other products will depend on several factors, such as price flexibility, the attractiveness of the products on sale compared to other products, and consumer behavior towards discounts. This question requires a thorough knowledge of consumer behavior and the "Fashion Elite" market.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Discount percentage = [(Initial price excluding VAT – Price after discount) ÷ Initial price excluding VAT] x 100 | Formula for calculating the reduction rate |
| Price after reduction = Initial price excluding VAT – (Initial price excluding VAT x Reduction rate) | Formula for calculating the price after reduction |
Application: La Belle Époque Shop
States :
The Boutique La Belle Époque, specialized in vintage clothing, has decided to organize a promotional sale on a selection of its products. As part of this, they decide to offer percentage discounts on the initial prices of their items.
For all items, the initial price is €80. The discount provided for each item is shown in the following table:
– Article 1: 20%
– Article 2: 25%
– Article 3: 30%
– Article 4: 35%
– Article 5: 40%
Work to do :
1. What is the price of each item after discount?
2. How much is the discount for each item?
3. For article 3, what is the amount of the discount in euros?
4. For article 5, what is the amount of the discount in euros?
5. Which item received the largest reduction in absolute value?
Proposed correction:
1. To calculate the price of each item after discount, we use the formula: Initial Price – (Initial Price x Discount Percentage ÷ 100). This gives:
– Item 1: 80€ – (80€ x 20 ÷ 100) = 64€
– Item 2: 80€ – (80€ x 25 ÷ 100) = 60€
– Item 3: 80€ – (80€ x 30 ÷ 100) = 56€
– Item 4: 80€ – (80€ x 35 ÷ 100) = 52€
– Item 5: 80€ – (80€ x 40 ÷ 100) = 48€
2. The discount amount for each item is calculated as follows: Original price x Discount percentage ÷ 100. We obtain:
– Item 1: 80€ x 20 ÷ 100 = 16€
– Item 2: 80€ x 25 ÷ 100 = 20€
– Item 3: 80€ x 30 ÷ 100 = 24€
– Item 4: 80€ x 35 ÷ 100 = 28€
– Item 5: 80€ x 40 ÷ 100 = 32€
3. The discount amount for item 3 is €24.
4. The discount amount for item 5 is €32.
5. Article 5 benefited from the largest reduction in absolute value, namely €32.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Original Price – (Original Price x Discount Percentage ÷ 100) | Calculation of the price after reduction |
| Initial price x Discount percentage ÷ 100 | Calculation of the reduction amount |
Application: Good Deals Supermarket
For these exercises, we will base ourselves on the supermarket “Les Bonnes Affaires”, which regularly offers its customers various types of discounts on its products.
States :
The supermarket "Les Bonnes Affaires" has decided to offer its customers a discount on some of its products. The products concerned and their original prices are as follows:
1. Shampoo: €6
2. Biscuits: €3
3. Fruit juice: €5
4. Soap: €4
5. Chips: €2,5
Here are the discount percentages applied:
1. Shampoo: 10%
2. Biscuits: 20%
3. Fruit juice: 15%
4. Soap: 5%
5. Chips: 25%
Work to do :
1. What is the price of the shampoo after discount?
2. What is the price of the cookies after discount?
3. What is the price of fruit juice after discount?
4. What is the price of the soap after discount?
5. What is the price of the chips after discount?
Proposed correction:
1. Shampoo price after discount = Original price – (Original price x discount rate)
= €6 – (€6 x 10 ÷ 100)
= €6 – €0,6
= 5,4 €
2. Price of cookies after discount = Original price – (Original price x discount rate)
= €3 – (€3 x 20 ÷ 100)
= €3 – €0,6
= 2,4 €
3. Price of fruit juice after discount = Original price – (Original price x discount rate)
= €5 – (€5 x 15 ÷ 100)
= €5 – €0,75
= 4,25 €
4. Price of soap after discount = Original price – (Original price x discount rate)
= €4 – (€4 x 5 ÷ 100)
= €4 – €0,2
= 3,8 €
5. Price of chips after discount = Original price – (Original price x discount rate)
= €2,5 – (€2,5 x 25 ÷ 100)
= €2,5 – €0,625
= 1,875 €
Summary of Formulas Used:
| Financial commitment | Formulas |
|---|---|
| Price after reduction | Original Price – (Original Price x Discount Rate) |
Application: “Aux Bonnes Affaires” Supermarket
States :
The company "Aux Bonnes Affaires" is a supermarket specializing in the sale of everyday consumer goods. As part of a promotional operation, the management decided to set up discounts on certain products.
The conditions for these reductions are as follows:
1. Product A has a 15% discount on its original retail price of €120.
2. Product B has a discount of €35, and its original sale price is €150.
3. Product C is sold at €85 after a 30% discount.
4. Product D with an initial sale price of €350 is now sold at €265.
5. Product E has a 25% discount, its new price is €90.
Work to do :
1. What is the new price of product A after the discount?
2. What is the percentage discount applied to product B?
3. What was the original price of product C before the discount?
4. What is the percentage discount applied to product D?
5. What was the original price of product E before the discount?
Proposed correction:
1. New price of product A = Initial price – (Initial price x Discount rate) = €120 – (€120 x 0,15) = €102.
2. Discount rate for product B = Discount amount ÷ Initial price x 100 = €35 ÷ €150 x 100 = 23,33%.
3. Initial price of product C = Price after discount ÷ (1 – Discount rate) = €85 ÷ (1 – 0,30) = €121,43.
4. Discount rate for product D = (Initial price – Price after discount) ÷ Initial price x 100 = (€350 – €265) ÷ €350 x 100 = 24,29%.
5. Initial price of product E = Price after discount ÷ (1 – Discount rate) = €90 ÷ (1 – 0,25) = €120.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| New price after discount | Initial Price – (Initial Price x Discount Rate) |
| Reduction rate | (Initial price – Price after discount) ÷ Initial price x 100 |
| Original price before discount | Price after discount ÷ (1 – Discount rate) |
Application: “Trendy” clothing sales company
As part of their end-of-season operations, "Trendy", a clothing retail company, decides to offer discounts on various items. These discounts depend on the type of item, the margin made on each item, and the company's willingness to clear out their inventory for the new collection.
The finance manager noted the following key information about a particular item:
Purchase price excluding VAT: €20
Initial sale price excluding VAT: €50
States :
Suppose you are the financial manager. You are responsible for making the necessary calculations to determine possible discounts on the item.
Work to do :
1. What is the margin rate of the item?
2. What would be the maximum possible reduction (in euros) for this item if “Trendy” wishes to maintain a margin rate of 50%?
3. At what selling price excluding VAT should this item be sold to maintain a margin rate of 50%?
4. What percentage discount does this represent from the original price?
5. If a 20% discount is applied instead of the percentage calculated in question 4, what will the new margin rate be?
Proposed correction:
1) To calculate the margin rate, we use the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100
So the margin rate is ((€50 - €20) ÷ €20) x 100 = 150%
2) To determine the maximum possible reduction, we first calculate the new purchase price with a margin rate of 50% using the formula: PA HT = PV HT ÷ (1 + Margin rate).
So, PA HT = €50 ÷ (1 + 50/100) = €33,33. The maximum reduction is then €50 – €33,33 = €16,67
3) The selling price at a margin rate of 50% is €33,33
4) The discount percentage is the discount in euros divided by the original price, multiplied by 100%. So, using a discount of €16,67 and a price of €50, we get (€16,67 ÷ €50) x 100 = 33,34%
5) If a 20% discount is applied, the new selling price excluding VAT is 80% of the initial price, i.e. 0,80 x €50 = €40. Using the margin rate formula, we find a new margin rate of ((€40 – €20) ÷ €20) x 100 = 100%.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Maximum reduction (€) | PV HT – PA HT after margin |
| Selling price at a specific margin rate (€) | PA HT = PV HT ÷ (1 + Margin rate) |
| Percent reduction | (Reduction € ÷ Original price excluding VAT) x 100 |
| Margin rate after reduction applied | ((PV reduced excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
For example, let's try to gain a more in-depth understanding with an application exercise.
Summary of Formulas Used:
| Packages | Explanations |
|---|---|
| Discount Amount = (Discount Percentage x Original Price) ÷ 100 | Allows you to calculate the amount of the discount. |
| Discounted Price = Original Price – Discount Amount | Allows you to calculate the price after applying the discount. |
| Discount Percentage = (Discount Amount ÷ Original Price) x 100 | Allows you to calculate the discount percentage based on the discount amount and the original price. |
Application: Trobico Company
States :
Trobico wants to apply a discount on some of its products to stimulate sales. It has decided to implement a 15% discount on the initial price of its products with an initial price of €120.
Work to do :
1. How much is the discount applied by the Trobico company?
2. What will the new selling price be after applying the discount?
3. If the company decides to give a discount of 24€ on the product, what is the discount percentage applied?
4. How can the company increase its profit after applying the discount?
5. After analyzing the effectiveness of the discount, the company found a 5% increase in sales. What is the impact on the company's turnover?
Proposed correction:
1. The discount amount is calculated as follows: (15 x 120) ÷ 100 = €18. Therefore, Trobico company applied a discount amount of €18.
2. The new selling price after the discount is: €120 (original price) – €18 (discount amount) = €102. Therefore, the new selling price after applying the discount is €102.
3. The discount percentage is calculated as follows: (24€ ÷ 120€) x 100 = 20%. Therefore, the company has applied a 20% discount percentage on the product.
4. To increase its profit, the company can either increase the number of sales by doing more marketing to attract more customers, or increase the price of products on which the discount is less significant. It is up to the company to analyze the sales data and make a decision.
5. A 5% increase in sales means that for every €100 of initial sales, the company now makes an additional €5. Therefore, this increase translates into an increase in the company's turnover.
Summary of Formulas Used:
| Packages | Explanations |
|---|---|
| Discount Amount = (Discount Percentage x Original Price) ÷ 100 | Used to calculate the discount amount. |
| Discounted Price = Original Price – Discount Amount | Used to calculate the price after the discount. |
| Discount Percentage = (Discount Amount ÷ Original Price) x 100 | Used to calculate the discount percentage. |
Application: SuperElectro10
States :
SuperElectro10 is a company specializing in the sale of electronic equipment. It wants to launch a discount campaign to boost its sales. To maintain good financial management, it must establish an appropriate method for calculating the discount percentage.
It is your responsibility to find the best discount rate that keeps the business profitable while attracting consumers.
The company's overall margin for the last year was €1. The quantity of products sold was 200. Each product was sold at a sales price excluding tax of €100 and the purchase price excluding tax was €20. SuperElectro12 offers a discount of €10 per product sold.
Work to do :
1. Calculate the margin rate.
2. Calculate the mark rate.
3. How much does the company lose in reduction?
4. Calculate the new margin rate after the reduction.
5. What is the percentage discount applied by the item?
Proposed correction:
1. The margin rate is calculated with the formula: ((PV HT – PA HT) ÷ PA HT) x 100. Therefore, the margin rate = ((20 – 12) ÷ 12) x 100 = 66,67%.
2. The markup rate is calculated with the formula: ((PV HT – PA HT) ÷ PV HT) x 100. Therefore, the markup rate = ((20 – 12) ÷ 20) x 100 = 40%.
3. The company loses €3 per product sold. Therefore, it loses 3 x 100 = €300 on 100 products.
4. We obtain the new selling price by subtracting the reduction from the original selling price: 20 – 3 = €17. The new margin rate is therefore ((17 – 12) ÷ 12) x 100 = 41,67%.
5. The discount percentage is calculated using the formula: Discount ÷ Original price × 100 : 3 ÷ 20 × 100 = 15%.
Summary of Formulas Used:
| Formula name | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Total lost through reduction | Discount x Quantity sold |
| New margin rate after reduction | ((New PV HT – PA HT) ÷ PA HT) x 100 |
| Percent reduction | Discount ÷ Original price × 100 |
Application: JoliStyle Store
States :
JoliStyle is a clothing store that offers discounts on its items. For its latest sale, the company wants to offer attractive discounts to its customers and needs your financial management knowledge to determine the discount percentages for its products.
Work to do :
1. The price of a t-shirt is initially €20. After a discount, its price is €14. What is the percentage discount applied to the t-shirt?
2. A pair of jeans was on sale for €60. Now they are on sale for €45. What is the discount percentage?
3. A handbag has been reduced from €120 to €90. Calculate the percentage of the reduction.
4. A dress was sold for €80, but is now €60. What is the discount rate?
5. A coat was sold for €150. After the reduction, it is €120. What is the percentage of the reduction?
Proposed correction:
1. The discount percentage for the t-shirt is: ((€20 – €14) ÷ €20) x 100 = 30%.
2. The discount percentage for jeans is: ((€60 – €45) ÷ €60) x 100 = 25%.
3. The handbag discount percentage is: ((€120 – €90) ÷ €120) x 100 = 25%.
4. The percentage discount on the dress is: ((€80 – €60) ÷ €80) x 100 = 25%.
5. The percentage reduction of the coat is: ((150 € – 120 €) ÷ 150 €) x 100 = 20%.
Summary of Formulas Used:
| Packages | Description |
|---|---|
| Discount percentage = ((original price – price after discount) ÷ original price) x 100 | Used to calculate the percentage discount on products in a retail context. |
Application: OptimalDiscount
| Terms | Packages |
|---|---|
| Percent reduction | (Original Price – Discounted Price) ÷ Original Price x 100 |
States :
OptimalDiscount is a company that specializes in clearance of high-end fashion items. The company regularly offers discounts on different items to encourage customers to buy. As a financial manager, you are responsible for calculating the discount percentage on different items.
For this exercise, we will consider the following data:
1. Item A: Initial price of €60, Reduced price to €45.
2. Article B: Initial price of €500, Price reduced to €375.
3. Article C: Initial price of €120, Price reduced to €90.
4. Article D: Initial price of €150, Price reduced to €90.
5. Article E: Initial price of €250, Reduced price to €175.
Work to do :
1. What is the discount percentage for item A?
2. What is the discount percentage for item B?
3. What is the discount percentage for item C?
4. What is the discount percentage for item D?
5. What is the discount percentage for item E?
Proposed correction:
1. For item A, the discount percentage is: (€60 – €45) ÷ €60 x 100 = 25%.
2. For item B, the discount percentage is: (€500 – €375) ÷ €500 x 100 = 25%.
3. For item C, the discount percentage is: (€120 – €90) ÷ €120 x 100 = 25%.
4. For item D, the discount percentage is: (€150 – €90) ÷ €150 x 100 = 40%.
5. For item E, the discount percentage is: (€250 – €175) ÷ €250 x 100 = 30%.
After calculation, we see that OptimalDiscount items benefit from discounts ranging from 25% to 40%.
Summary of the formulas used:
| Terms | Packages |
|---|---|
| Percent reduction | (Original Price – Discounted Price) ÷ Original Price x 100 |
The exercise allowed us to practice the percentage calculation formula to determine the level of discount offered for each item. As a financial manager, it is important to understand how these discounts can affect the profitability and sales of the company.