In this section:
- Application: Gastronome Society
- Application: Supermarket Les Saveurs Fraîches
- App: Cookie Shop
- Application: Technovision Company
- Application: OxyGen Inc.
- Application: Maison Duval
- Application: Zephyr Company
- Application: Electron Company
- Application: Clothing store “Fashion Corner”
- Application: “La Belle Epoque” Company
- Application: MGC Electronics
Application: Gastronome Society
States :
La Société Gastronome is a small restaurant located in Paris. Recently, the manager decided to increase some menu prices and decrease others to attract more customers and increase turnover. The company also wants to introduce special offers for students, which involves analyzing and evaluating complex scenarios related to percentage increase, percentage decrease, proportion and percentage.
Work to do :
1. The lunch menu which initially cost €12 excluding tax has been increased by 15%. What is the new menu price?
2. The company plans to reduce the price of its dinner menu by 10%, which initially costs €20 excluding tax. What will be the new price of this menu?
3. The company plans to introduce a special offer for students which will represent 5% of all menus. If the restaurant serves an average of 150 menus per day, how many of these menus will be student specials?
4. If on student menus which cost €10 excluding VAT, the restaurant makes a margin of €2 per menu, what is the margin rate?
5. On a lunch menu for €14 excluding VAT (after the price increase), what would be the mark-up rate if the purchase cost is €8 excluding VAT?
Proposed correction:
1. To find the new lunch menu price, multiply the percentage increase by the original price and add the result to the original price:
New price = Original price + (Initial price x Percentage increase)
New price = €12 + (€12 x (15 ÷ 100)) = €12 + €1,80 = €13,80.
2. To find the new price of the dinner menu after reduction, multiply the percentage reduction by the original price and subtract the result from the original price:
New Price = Original Price – (Original Price x Discount Percentage)
New price = €20 – (€20 x (10 ÷ 100)) = €20 – €2 = €18.
3. To determine the number of special student menus, let's multiply the percentage of student offers by the total number of menus:
Number of special offers = Total number of menus x Percentage of student offers
Number of special offers = 150 x (5 ÷ 100) = 7,5? rounded up to 8 special student offers.
4. To calculate the margin rate, let's use the formula: Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Margin rate = ((€10 – €8) ÷ €8) x 100 = 25%
5. The brand rate is calculated by: Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100
Brand rate = ((€14 – €8) ÷ €14) x 100 = 43%
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| New price = Original price + (Initial price x Percentage increase) | Calculate a price after a percentage increase. |
| New Price = Original Price – (Original Price x Discount Percentage) | Calculate a price after a percentage discount. |
| Number of special offers = Total number of menus x Percentage of student offers | Calculate the proportion of a special offer. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Calculate the margin rate. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | Calculate the mark rate. |
Application: Supermarket Les Saveurs Fraîches
States :
In the Les Saveurs Fraîches supermarket, the administrator would like to evaluate certain financial transactions. Transactions include purchasing products, pricing products, and sales. Here are some details:
– The cost of purchasing a box of milk is €2.
– The administrator has set the selling price at €2,50 per box of milk.
– The quantity of boxes of milk sold during the month is 2000 boxes.
– Due to a special offer, the sale price of the milk box has been reduced by 15%.
– The VAT rate applied is 20%.
Work to do :
1. What is the unit margin in euros for the box of milk?
2. Calculate the overall margin in euros.
3. What is the new sales price excluding tax after the reduction?
4. What is the percentage increase in the purchase price compared to the new sales price excluding tax?
5. What is the proportion of the purchase price in the new sales price excluding tax?
Proposed correction:
1. The unit margin of the box of milk is obtained by subtracting the purchase cost from the selling price, i.e.: €2,50 – €2 = €0,50.
2. The overall margin is obtained by multiplying the unit margin by the quantity sold, i.e.: €0,50 x 2000 = €1000.
3. The new sales price excluding tax after the reduction is obtained by subtracting 15% from the sales price, i.e.: €2,50 – 15% x €2,50 = €2,125.
4. The percentage increase in the purchase price compared to the new sales price excluding tax is calculated using the formula ((new sales price excluding tax – purchase price) ÷ purchase price) x 100. Thus, ((€2,125 – €2) ÷ €2) x 100 = 6,25%.
5. The proportion of the purchase price in the new sales price excluding tax is calculated using the formula (purchase price ÷ new sales price excluding tax) x 100. Thus, (€2 ÷ €2,125) x 100 = 94,12 .XNUMX%.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Unit margin = Sales price excluding tax – Purchase price excluding tax | Calculation of unit margin |
| Overall margin = Unit margin x Quantity sold | Calculation of the overall margin |
| New sales price excluding tax = Sales price excluding tax – (% reduction x Sales price excluding tax) | Calculation of the new sales price after reduction |
| Increase in % = ((New sales price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 | Calculation of the percentage increase in the Purchase Price compared to the New sales price excluding tax |
| Proportion = (Purchase price excluding tax ÷ New selling price excluding tax) x 100 | Calculation of the proportion of the Purchase Price in the New sales price excluding tax |
App: Cookie Shop
States :
The Cookie Shop is a company that sells cookies at retail. The company is very happy with its sales, but wants to better understand the dynamics of its business from a financial perspective. To do this, it provides the following information:
– Purchase price excluding taxes of a cookie: €1,00.
– Sales price excluding tax of a cookie: €2,00.
– Quantity of cookies sold: 2000 cookies.
– To boost its sales, the Cookie Shop decided to increase the selling price of its cookies by 10% and noted a decrease in sales of 15%.
Work to do :
1. What is the Cookie Shop’s unit gross margin in euros before the price increase?
2. What is the Cookie Shop’s margin rate before the price increase?
3. What is the new sales price excluding tax after the 10% increase?
4. How many cookies did the Cookie Shop sell after sales decreased by 15%?
5. What is the new overall margin in euros after the price increase and the decrease in sales?
Proposed correction:
1. The unit gross margin in euros of the Cookie Shop before the price increase is equal to €2,00 – €1,00 = €1,00.
2. The margin rate of the Cookie Shop before the price increase is equal to ((€2,00 – €1,00) ÷ €1,00) x 100 = 100%.
3. The new sales price excluding taxes after the 10% increase is equal to €2,00 x 1,10 = €2,20.
4. The number of cookies sold by the Cookie Shop after the 15% decrease in sales is equal to 2000 x (100% – 15%) = 1700 cookies.
5. The new overall margin in euros after the price increase and the decrease in sales is equal to (€2,20 – €1,00) x 1700 = €2.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Unit gross margin | Unit gross margin = PV excluding tax – PA excluding tax |
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Percent increase | Price after increase = Initial price x (1 + rate of increase) |
| Percentage decrease | Quantity after decrease = Initial quantity x (1 – rate of decrease) |
| Overall margin | Overall margin = Unit margin x quantity sold |
Application: Technovision Company
States :
Technovision is a company specializing in the sale of computer equipment. The company has had satisfactory sales over the past year, but the manager wants to optimize the company's performance. To do this, he asks you to analyze certain financial elements of the company.
Work to do :
1. The company's profits increased by 8% compared to the previous year. If profits from the previous year were €25, what is the increase in total profits for this year?
2. The cost of raw materials decreased by 12%. If the original raw material cost was €15, what is the new raw material cost?
3. If the company Technovision sold 500 units of a specific product and this figure represents 20% of its total sales, what is the total quantity of products sold by Technovision?
4. If the company was able to sell 75% of its total inventory, what percentage is the unsold inventory?
5. If Technovision wants to increase the selling price of its products by 5% and the current price is €100, what will the new selling price be?
Proposed correction:
1. The increase in total profits for this year can be calculated using the percentage increase formula: Increase = Percentage increase x original amount. So, Increase = 8% x €25 = €000. The profits for this year would therefore amount to €2 + €000 = €25.
2. The decrease in raw material cost can be found by using the percentage decrease formula: Decrease = Percentage Decrease x Original Amount. So, Decrease = 12% x €15 = €000. The new cost of raw materials would therefore be €1 – €800 = €15.
3. The total quantity of products sold by Technovision can be found using the proportion formula: Total = Share / Percentage. So, Total = 500 units / 20% = 2 units.
4. If the company managed to sell 75% of its total inventory, the percentage of unsold inventory would be 100% – 75% = 25%.
5. Product sales price increase can be calculated using the percentage increase formula: Increase = Percentage increase x original amount. So, Increase = 5% x €100 = €5. The new selling price would therefore be €100 + €5 = €105.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Increase = Percentage increase x original amount | To calculate the amount of a percentage increase. |
| Decrease = Percentage decrease x original amount | To calculate the amount of a percentage decrease. |
| Total = Share / Percentage | To find a total when we know a proportion. |
| Unsold stock = 100% – Percentage sold | To find the percentage of unsold inventory. |
| Increase = Percentage increase x original amount | To calculate the increase in the selling price. |
Application: OxyGen Inc.
States :
OxyGen Inc., is a company specializing in the manufacturing of oxygenated products for different industries. Their flagship product is an industrial oxygen generator. The company has entered into a major deal with a foreign company that will significantly increase its sales and require the purchase of additional equipment.
Work to do :
1. If OxyGen Inc., sold 100 oxygen generators this month for a total of €50, what is the unit sales price?
2. If the average purchase price is €350 per generator, what is the margin rate achieved if the VAT rate is 20%?
3. A major contract requires the purchase of equipment for a total cost of €60. The VAT on this purchase is 000%. What is the total cost of the purchase, VAT included?
4. If the contract increases sales by 30%, how many generators will the company sell the following month?
5. If the cost of the material decreases by 15% the following month, what will be the new cost of purchasing this material?
Proposed correction:
1. To find the unit price, we need to divide the total sales by the number of products sold. So €50 ÷ 000 = €100 per generator.
2. For the margin rate, we use the formula ((Selling Price excluding tax – Purchase Price excluding tax) ÷ Purchase Price excluding tax) x 100. The selling price excluding tax is 500 ÷ 1,2 = €416,67 . The margin rate is therefore ((€416,67 – €350) ÷ €350) x 100 = 19,05%
3. For the total cost of the purchase, VAT included, we add 20% of the purchase cost to the latter. So €60 x 000 = €1,2
4. To find the number of generators sold after a 30% increase, we add 30% to the initial number. So, 100 x 1,3 = 130 generators.
5. For the new purchase cost after a 15% decrease, we subtract 15% from the original purchase cost. So €60 x 000 = €0,85
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Unit Sales Price = Total sales ÷ Number of items sold | Calculation of sales price per unit |
| Margin rate = ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 | Calculation of the margin rate on sales |
| Total cost of purchase with VAT = Purchase cost x (1 + VAT rate) | Calculation of the total cost of the purchase, VAT included |
| Number of items sold after an increase = Initial number x (1 + Increase rate) | Calculating the number of items sold following an increase |
| New purchase cost after reduction = Initial purchase cost x (1 – Rate of reduction) | Calculation of the purchase cost following a reduction |
Application: Maison Duval
States :
The Maison Duval company is a company specializing in the marketing of high-end decorative items. Its manager, Mr. Duval, wishes to review his pricing policy on certain items to maximize his profits. It has the following information:
– Article A: Purchase price excluding taxes (PA excluding tax) = €40, Selling price excluding taxes (PV excluding tax) = €80.
– Article B: Purchase price excluding tax (PA excluding tax) = €50, Selling price excluding tax (PV excluding tax) = €100.
– Article C: Pa excluding tax = €60, PV excluding tax = €120.
– Sales from the previous year break down as follows: Item A: 1000 units, Item B: 800 units, Item C: 700 units.
Work to do :
1. Calculate the value margin and the purchase cost margin rate for each item.
2. Calculate the company’s overall margin.
3. Mr. Duval is considering a 10% increase in the sales price excluding tax of item A. What would be the new sales price excluding tax and the new unit margin?
4. If the quantity sold of item A decreased by 20% following the price increase, what would be the company's new overall margin?
5. What would be the percentage rate of decrease in the company's overall margin, compared to the initial situation?
Proposed correction:
1. Unit margin = PV excluding tax – PA excluding tax. Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
Article A: Unit margin = €80 – €40 = €40, Margin rate = ((€80 – €40) ÷ €40) x 100 = 100%.
Article B: Unit margin = €100 – €50 = €50, Margin rate = ((€100 – €50) ÷ €50) x 100 = 100%.
Article C: Unit margin = €120 – €60 = €60, Margin rate = ((€120 – €60) ÷ €60) x 100 = 100%.
2. Overall margin = Sum (unit margin x quantity sold) = €40 x 1000 + €50 x 800 + €60 x 700 = €107.
3. New PV excluding VAT (item A) = Old PV excluding VAT x (1 + 10% increase) = €80 x (1 + 10%) = €88.
New unit margin (item A) = New PV excluding tax – PA excluding tax = €88 – €40 = €48.
4. New overall margin = Sum (new unit margin x new quantity sold) = €48 x (1000 – 20%) + €50 x 800 + €60 x 700 = €102
5. Rate of decrease in overall margin = ((€107 – €000) ÷ 102) x 400 = 107%.
Summary of Formulas Used:
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Overall margin | Sum (unit margin x quantity sold) |
| New PV HT | Old HT PV x (1 + rate of increase) |
| New unit margin | New PV HT – PA HT |
| New overall margin | Sum (new unit margin x new quantity sold) |
| Rate of decrease in overall margin | ((overall margin before – overall margin after) ÷ overall margin before) x 100 |
Application: Zephyr Company
States :
The Zephyr company is a sports shoe manufacturing company. It uses different raw materials to manufacture its products. Recently, the price of some raw materials increased by 5%, while others decreased by 10%. The manager wants to analyze the impact of these price variations on the manufacturing cost.
1. The leather used to make the shoes cost €15 per meter. What is the new price after the 5% increase?
2. Rubber cost €10 per kg, how much does it cost now after the 10% reduction?
3. If the company uses 5 meters of leather and 3 kg of rubber to make a pair of shoes, what was the original cost and what is the new manufacturing cost with the new values?
4. What is the percentage increase between the two manufacturing prices?
5. If the company wants to keep its purchase of leather at 50% of its total cost, how many meters of leather can it purchase now?
Work to do :
1. Calculate the new price of leather after increasing it by 5%
2. Calculate the new price of rubber after a 10% decrease
3. Calculate the old and new cost of manufacturing a pair of shoes
4. Determine the percentage increase between the old and new manufacturing costs
5. Determine the quantity of leather she can purchase by keeping her purchase at 50%
Proposed correction:
1. The new price of leather after a 5% increase would be: €15 x (1 + 5/100) = €15,75
2. The new price of rubber after a 10% decrease would be: €10 x (1 – 10/100) = €9
3. The old manufacturing cost: (5 meters of leather x €15) + (3 kg of rubber x €10) = €75 + €30 = €105
The new manufacturing cost: (5 meters of leather x €15,75) + (3 kg of rubber x €9) = €78,75 + €27 = €105,75
4. The percentage increase would be: ((€105,75 – €105) ÷ €105) x 100 = 0,71%
5. If the purchase of leather is to represent 50% of the total cost, then the quantity of leather she can purchase would be: €105,75 x 50/100 ÷ €15,75 = 3,35 meters
Summary of Formulas Used:
| Expression | Formulas |
|---|---|
| Percent increase | Initial price x (1 + Percentage increase/100) |
| Percentage decrease | Initial price x (1 – Percentage reduction/100) |
| Proportion | Total cost x Proportion ÷ Unit price |
| Percentage increase | ((New price – Old price) ÷ Old price) x 100 |
Application: Electron Company
States :
The Electron company is a company specializing in the sale of electronic devices. In September 2021, the company achieved a turnover of €10. In October, turnover increased to €000. In November, turnover decreased to €12.
In addition, the company sold 500 smartphones in September for a total of €15. Smartphones therefore represented a certain proportion of the total turnover during this period.
Work to do :
1. How much did revenue increase as a percentage from September to October?
2. How much did revenue decrease as a percentage from October to November?
3. What proportion of turnover is linked to smartphone sales in September?
4. What percentage of revenue is linked to smartphone sales in September?
5. If the company expects a 15% increase in turnover in December compared to November, how much will this turnover be?
Proposed correction:
1. The increase in turnover from September to October can be calculated as follows: ((€12 – €000) / €10) x 000 = 10%.
2. The decrease in turnover from October to November can be calculated as follows: ((€12 – €000) / €11) x 000 = 12%.
3. The proportion of turnover linked to smartphone sales in September is: €5 / €000 = 10 or 000%.
4. The percentage of turnover linked to smartphone sales in September is: (€5 / €000) x 10 = 000%.
5. If the company expects a 15% increase in turnover in December compared to November, the turnover for December will be: €11 x 000 = €1,15.
Summary of Formulas Used:
| Packages | Used in exercise |
|---|---|
| Percentage increase = ((Final value – Initial value) / Initial value) x 100 | Question 1 |
| Percentage decrease = ((Initial value – Final value) / Initial value) x 100 | Question 2 |
| Proportion = Part / Total | Question 3 |
| Percentage = (Specific value / Total value) x 100 | Question 4 |
Application: Clothing store “Fashion Corner”
States :
The clothing store “Fashion Corner” is experiencing significant growth in sales. To examine this growth, here are some key insights:
– In 2020, “Fashion Corner” achieved a turnover of €50.
– In 2021, turnover increased by 25% compared to 2020.
– In 2022, “Fashion Corner” predicts a 15% decrease due to changing industry trends.
– Women’s clothing represents 45% of total sales.
– Men’s clothing represents 40% of total sales.
– Children’s clothing represents 15% of total sales.
Work to do :
1. What was the turnover of “Fashion Corner” in 2021?
2. What will be the expected turnover for 2022?
3. What is the total revenue generated from the sale of women's clothing?
4. What is the total revenue generated from the sale of men's clothing?
5. What is the total revenue generated from the sale of children's clothing?
Proposed correction:
1. The turnover of “Fashion Corner” in 2021 is €50 x (000 + 1/25) = €100.
2. The expected turnover for 2022 will be €62 x (500 – 1/15) = €100.
3. The total income generated from the sale of women's clothing is €62 x 500/45 = €100.
4. The total revenue generated from the sale of men's clothing is €62 x 500/40 = €100.
5. The total income generated from the sale of children's clothing is €62 x 500/15 = €100.
Summary of Formulas Used:
– Percentage increase: New amount = Old amount x (1 + Percentage increase/100)
– Percentage decrease: New amount = Old amount x (1 – Percentage decrease/100)
– Share of total: Share of total = Total x Percentage/100
| Formulas | Description |
| New amount = Old amount x (1 + Percentage increase/100) | Calculate a percentage increase |
| New amount = Old amount x (1 – Percentage decrease/100) | Calculate a percentage decrease |
| Share of total = Total x Percentage/100) | Determine a percentage of the total |
Application: “La Belle Epoque” Company
States :
The company “La Belle Epoque” is a pastry shop located in Lille, France. As part of its activity, it manages a varied range of products and must take into account the different variations in prices and quantities in order to optimize its financial management.
1. At the start of the year, the price of a strawberry tart was €12. This price was increased by 15% mid-year. What is the new price of strawberry pie?
2. Conversely, the price of chocolate éclairs, initially at €5, had to be reduced by 20% to encourage sales. What is the new price of éclair?
3. The company has a product mix including 200 strawberry tarts, 300 chocolate éclairs and 500 croissants. What is the proportion of each product in the mix?
4. The company is having a promotional sale, where it offers a 10% discount on each strawberry pie. What will the new price of the pie be after this reduction?
5. The company makes a 25% margin on each éclair sold. What is the purchase price excluding tax for the éclair if we know the sales price excluding tax?
Work to do :
Answer each of the questions asked.
Proposed correction:
1. The new price of the strawberry pie is calculated by adding 15% to the original price. So: Price after increase = Initial price + (Initial price x Rate of increase) = €12 + (€12 x 15%) = €12 + €1,80 = €13,80.
2. The new price of the chocolate éclair is calculated by subtracting 20% from the original price. So: Price after reduction = Initial price – (Initial price x Rate of reduction) = €5 – (€5 x 20%) = €5 – €1 = €4.
3. The proportion of each product in the mix is calculated by dividing the number of that product by the total number of products. So: Proportion of strawberry pies = 200 ÷ (200 + 300 + 500) = 0,20 (20%); Proportion of chocolate éclairs = 300 ÷ (200 + 300 + 500) = 0,30 (30%); Proportion of croissants = 500 ÷ (200 + 300 + 500) = 0,50 (50%).
4. The price of the strawberry pie after the 10% reduction is calculated by subtracting 10% from the current price: Price after reduction = Initial price – (Initial price x Discount rate) = €13,80 – (13,80 € x 10%) = €13,80 – €1,38 = €12,42.
5. The tax-free purchase price of the éclair is calculated using the given margin rate. If the margin is 25%, this means that 25% of the sales price represents the difference between the sales price excluding tax and the purchase price excluding tax. So: Purchase price excluding tax = Selling price excluding tax – (Selling price excluding tax x Margin rate) = €5 – (€5 x 25%) = €5 – €1,25 = €3,75.
Summary of Formulas Used:
| Formulas | Representation |
|---|---|
| Price after increase | Initial price + (Initial price x Rate of increase) |
| Price after reduction | Initial Price – (Initial Price x Decline Rate) |
| Proportion | Number of products ÷ Total number of products |
| Price after reduction | Initial Price – (Initial Price x Discount Rate) |
| Purchase price excluding tax | Sales price excluding tax – (Sales price excluding tax x Margin rate) |
Application: MGC Electronics
States :
MGC Electronics is a company that distributes computer equipment. In 2020, the company achieved a turnover of €250 excluding tax. In 000, it made a profit of €2021 excluding tax. The company applies a VAT rate of 320%. In addition, the company has decided to reduce the price of certain products in their stock by 000%.
Work to do :
1. What is the rate of increase in turnover between 2020 and 2021?
2. What is the amount of sales in 2021 including tax?
3. If MGC Electronics decides to reduce the price of certain products, what will be the new price of a product which initially cost €500 excluding tax?
4. What is the proportion of 2020 turnover compared to that of 2021?
5. What amount represents 18% of 2021 turnover?
Proposed correction:
1. To calculate the percentage increase, we use the formula: ((Final value – Initial value) ÷ Initial value) x 100. Here, ((€320 – €000) ÷ €250) x 000 = 250% . Turnover therefore increased by 000% between 100 and 28.
2. To find the value including tax, we add VAT, i.e. (€320 x 000) + €0,20 = €320 including tax. The amount of sales of MGC Electronics in 000 with VAT is €384 including tax.
3. To calculate a reduction percentage, we subtract from the old price the value of 15% of the old price. Which gives: €500 – (€500 x 15%) = €500 – €75 = €425 excluding tax. The new price of the product will therefore be €425 excluding tax.
4. The proportion of the turnover of the previous year to that of this year is obtained by dividing the turnover of 2020 by that of 2021 and multiplying by 100. Thus, we have: (250 € ÷ 000 320 €) x 000 = 100%. We can say that the turnover of 78,125 corresponds to 2020% of that of 78,125.
5. To find a percentage of the total value, multiply the total value by the percentage. Here, 18% of the 2021 turnover will be: €320 x 000% = €18. So, 57% of the 600 turnover corresponds to €18.
Summary of Formulas Used:
| Designation | Formulas |
|---|---|
| Calculating the percentage increase | ((Final value – Initial value) ÷ Initial value) x 100 |
| Calculation of percentage decrease | ((Initial value – Final value) ÷ Initial value) x 100 |
| Calculation of proportion | (Partial value ÷ Total value) x 100 |
| Percentage calculation | (Value ÷ 100) x Total |