Welcome to this article on exercises on business calculations and more precisely on 11 exercises corrected on percentages. 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 perfectly master these corrected exercises on percentages without any worries.
In this section:
- Application: Les Délices du Terroir grocery store
- Application: Boutique Belle Allure
- Application: La Chocolaterie Gourmande
- Application: Commercial strategy of Société DesJardins
- Application: “Graine de Savoir” bookstore
- Application: ChloéAroma Company
- Application: Megastore
- Application: “FashionTrends” clothing store
- Application: Fashion 365 ready-to-wear house
- Application: Chauss'Fast Boutique
Application: Les Délices du Terroir grocery store
States :
The grocery store “Les Délices du Terroir” has decided to revise its prices on a range of its products. Following changes in suppliers and a high purchasing cost, it will have to increase certain prices while the promotion on other items will lead it to reduce their prices.
Here are some things you should consider:
1. The initial selling price of artisanal mountain honey is €15 per jar.
2. The cost of purchasing the Honey Jar has increased by 20%.
3. The grocery store has decided to maintain a margin rate of 30% on this product.
4. Another product, local red wine, has an initial selling price of €10 per bottle.
5. The bottle of wine is on sale with a 15% reduction.
Work to do :
1. Calculate the new cost of purchasing the jar of honey.
2. Calculate the new selling price of honey.
3. What is the percentage increase in the selling price of honey?
4. Calculate the new price of red wine.
5. What is the percentage decrease in the price of red wine?
Proposed correction:
1. The new cost of purchasing the jar of honey = €15 + (€15 x 20/100) = €18.
2. The new selling price of honey = Purchase price + (Purchase price x Margin rate) = €18 + (€18 x 30/100) = €23,4.
3. The percentage increase in the selling price of honey = ((€23,4 – €15) ÷ €15) x 100 = 56%.
4. The new price of red wine = €10 – (€10 x 15/100) = €8,5.
5. The percentage of the reduction in the price of red wine = ((€10 – €8,5) ÷ €10) x 100 = 15%.
Summary of Formulas Used:
| Formula to calculate a percentage: | (Specific number ÷ Total numbers) x 100 |
| Formula for calculating an increase: | Initial sales price + (Initial sales price x Rate of increase) |
| Formula to calculate a decrease: | Initial Sales Price – (Initial Sales Price x Decline Rate) |
| Formula for finding a proportional value: | (Value ÷ Set) x desired set |
Application: Boutique Belle Allure
States :
The Belle Allure company is a boutique specializing in the sale of evening dresses. At the start of the fiscal year, management set the following financial goals: increase sales by 15%, increase margins by 10% and decrease costs by 5%. A dress is currently sold for €200 and it costs €120 at Belle Allure.
Work to do :
1. What would be the projected selling price of the dress if Belle Allure achieves its sales and margin objectives?
2. What is the percentage of the initial margin made by Belle Allure on this dress?
3. What would be the projected cost of this dress if Belle Allure achieves its cost reduction goal?
4. What would be the percentage of the forecast margin on this dress after achieving the objectives?
5. What would be the forecast mark rate on this dress after reaching the objectives?
Proposed correction:
1. The forecast selling price of the dress is calculated by increasing the current price by 15%. Thus, the forecast price is €200 x 1,15 = €230.
2. The percentage of the initial margin is calculated using the formula: ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100. Thus, the initial margin rate is ((200 € – €120) ÷ €120) x 100 = 66,67%.
3. The forecast cost of this dress is calculated by reducing the current cost by 5%. Thus, the forecast cost is €120 x (1 – 0,05) = €114.
4. The percentage of the forecast margin is calculated as follows: ((Forecast selling price – Forecast cost) ÷ Forecast cost) x 100. Thus, the forecast margin rate is ((€230 – €114) ÷ €114 ) x 100 = 101,75%.
5. The forecast mark-up rate is calculated as follows: ((Forecast sales price – Forecast cost) ÷ Forecast sales price) x 100. Thus, the forecast mark-up rate is ((€230 – €114) ÷ 230 €) x 100 = 50,43%.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Forecast sales price | Current selling price x (1 + rate of increase) |
| Initial margin rate | ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 |
| Forecast cost | Current cost x (1 – rate of decrease) |
| Forecast margin rate | ((Forecast sales price – Forecast cost) ÷ Forecast cost) x 100 |
| Forecast brand rate | ((Forecast sales price – Forecast cost) ÷ Forecast sales price) x 100 |
Application: La Chocolaterie Gourmande
States :
La Chocolaterie Gourmande is a company renowned for its artisanal chocolate. It plans for the following year to modify the price of its products following market studies. The following information was collected:
– Current price of a chocolate bar: €6
– Dark chocolate represents 30% of their total sales.
– La Chocolaterie Gourmande plans to increase the price of its chocolate bars by 15%.
– Following the price increase, sales forecasts for dark chocolates decreased by 25%.
Work to do :
1. What will the new price of a chocolate bar be after the increase?
2. If Chocolaterie Gourmande sells a total of 1200 chocolate bars each month, how many dark chocolate bars did they sell before the price increase?
3. How many dark chocolate bars do they plan to sell after the expected decline in dark chocolate sales?
4. What will be the change in turnover generated by the sale of dark chocolates following these changes?
5. What would be the percentage rate of decrease in turnover generated by the sale of dark chocolates following these changes?
Proposed correction:
1. The new price of a chocolate bar will be calculated as follows: Initial price x (1 + percentage increase/100) = €6 x (1 + 15/100) = €6 x 1,15 = 6,90, €6,90. So the new price of the chocolate bar will be €XNUMX.
2. The number of dark chocolate bars sold before the price increase is calculated as follows: total quantity sold x proportion of dark chocolate sales = 1200 x 30/100 = 360 bars. So, they were selling 360 dark chocolate bars per month before the price increase.
3. The number of dark chocolate bars they expect to sell after the expected decrease in sales is calculated as follows: quantity sold before the decrease x (1 – percentage decrease/100) = 360 x (1 – 25/100 ) = 360 x 0,75 = 270 tablets. So, they plan to sell 270 dark chocolate bars per month after the price increase.
4. The variation in turnover generated by the sale of dark chocolates will be calculated as follows: (Expected turnover – Initial turnover) = (Price after increase x quantity sold after decrease) – (Price initial x initial quantity sold) = (€6,90 x 270) – (€6 x 360) = €1 – €863 = -€2. Therefore, the change in turnover generated by the sale of dark chocolates following these changes will be -€160, which indicates a decrease in turnover.
5. The percentage rate of decrease in turnover generated by the sale of dark chocolates following these changes will be calculated as follows: (Variation in turnover / Initial turnover) x 100 = (- €297 / €2) x 160 = -100%. Therefore, there would be a 13,75% decrease in turnover generated by the sale of dark chocolates.
Summary of Formulas Used:
| Calculation of an increase: | Initial price x (1 + percentage increase/100) |
| Calculating a proportion: | total quantity x percentage/100 |
| Calculation of a decrease: | quantity before reduction x (1 – percentage of reduction/100) |
| Calculation of the variation in turnover: | (Forecast revenue – Initial revenue) |
| Calculation of the rate of change: | (Variation in turnover / Initial turnover) x 100 |
Application: Commercial strategy of Société DesJardins
States :
Société DesJardins is a company specializing in the trade of horticultural products. During 2020, despite the crisis, the company managed to maintain its sales level. The company noticed that the sale of certain products even increased. As part of its business strategy for 2021, the company decided to carry out an analysis of its financial results from the previous year.
• In 2020, the company sold a total of €1 worth of products. Seed sales represented 200% of total sales.
• During 2020, Société DesJardins increased the price of its fertilizers by 15%.
• Conversely, to encourage the sale of certain products, the company decided to reduce the price of flower pots by 10%.
Work to do :
1. Calculate the amount of seed sales for the year 2020.
2. A bag of fertilizer cost €20 in 2019. What was its price in 2020 following the increase?
3. A flower pot cost €15 in 2019. What was its price in 2020 following the reduction?
4. What is the proportion of total sales of products other than seeds?
5. If seed sales increase by 10% in 2021, what will be the new seed sales amount?
Proposed correction:
1. To obtain this amount, we multiply the total sales by the percentage corresponding to the seeds: €1 * 200% = €000. Seed sales for the year 25 therefore amount to €300.
2. The increase in the price of the bag of fertilizer is 15% compared to the initial price. So, the new price is: €20 + (€20 * 15/100) = €23.
3. The reduction in the price of the flower pot is 10% compared to the initial price. So, the new price is: €15 – (€15 * 10/100) = €13,50.
4. To answer this question, we need to subtract the percentage of total sales represented by seeds, from 100%. So, the proportion of other products is: 100% – 25% = 75%.
5. If seed sales increase by 10% in 2021, the new seed sales amount will be: €300 + (€000 * 300/000) = €10.
Summary of Formulas Used:
1. Percentage: (Part/Total) x 100
2. Proportion: Part/Total
3. Increase: (Final Value – Initial Value) x 100 / Initial Value
4. Decrease: (Initial Value – Final Value) x 100 / Initial Value
| Formulas | Description |
|---|---|
| (Part/Total) x 100 | Percentage Calculation |
| Part/Total | Proportion Calculation |
| (Final Value – Initial Value) x 100 / Initial Value | Calculation of the Increase |
| (Initial Value – Final Value) x 100 / Initial Value | Calculation of the Decrease |
Application: “Graine de Savoir” bookstore
States :
The “Graine de Savoir” bookstore is located in the city center. It offers different categories of books to its customers. Following the analysis of its sales over the past year, the bookstore plans to adjust its prices. Science fiction books which were sold at €15 will see their prices increased by 20%, and historical novels, formerly sold at €22, will see their prices reduced by 15%.
Work to do :
1. What will be the new price of Science fiction books?
2. What will be the new price for historical novels?
3. If the Bookstore sells 200 Science Fiction books, what will be the overall margin?
4. If the cost of purchasing a science fiction book is €10, what is the mark-up rate?
5. If the cost of purchasing a historical novel is €16, what is the mark-up rate?
Proposed correction:
1. The new price of Science fiction books will be: €15 x (1 + 20/100) = €18.
2. The new price for historical novels will be: €22 x (1 – 15/100) = €18,70.
3. If 200 Science Fiction books are sold at €18, then the overall margin will be: €18 x 200 = €3600.
4. The margin rate is calculated as follows: Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100). If the purchase cost of a science fiction book is €10 and its sale price €18, the margin rate is therefore ((€18 – €10) ÷ €10) x 100 = 80%.
5. The brand rate is calculated as follows: Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100). If the purchase cost of a historical novel is €16 and its sale price is €18.70, the brand rate is therefore ((€18.70 – €16) ÷ €18.70) x 100 = 14.44%.
Summary of Formulas Used:
| Formulas | Meaning |
| Price after increase = Initial price x (1 + percentage increase /100) | This is the formula that allows you to calculate the new price after an increase. |
| Price after reduction = Initial price x (1 – reduction percentage /100) | This is the formula that allows you to calculate the new price after a decrease. |
| Overall margin = Unit margin x quantity sold | This is the formula that allows you to calculate the overall margin. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | This is the formula that allows you to calculate the margin rate. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | This is the formula that allows you to calculate the mark rate. |
Application: ChloéAroma Company
States :
The ChloéAroma company is a distributor of high-end perfumes. It has a well-defined pricing and discount policy. Your job as a junior financial manager will be to evaluate the financial impact of several transactions.
1. The “Odyssée de Fleurs” perfume normally costs €90 to purchase. During a special discount, the company gets 25% off. What is the new purchase price (PA) (excluding tax) of this perfume after the discount?
2. ChloéAroma has decided to sell the perfume “Odyssée de Fleurs” for €150. Calculate the gross margin (MB) made by the company on each sale (excluding tax).
3. What is the margin rate (TM) made on each sale of the “Odyssée de Fleurs” perfume (excluding tax)?
4. Based on the initial selling price (PV), ChloéAroma has decided to increase the price by 10%. What is the new price after increase?
5. The company then decided to lower this new price by 15%. What then is the new price after the decrease?
Work to do :
Solve questions 1-5 above.
Proposed correction:
1. To determine the new PA after the 25% discount, we use the formula: new PA = old PA – (old PA x discount percentage). So the new AP is €90 – (€90 x 25%) = €67,5.
2. To calculate the gross margin, we use the formula: gross margin = PV (sales price) – PA (new purchase price). So, the gross margin is €150 – €67,5 = €82,5.
3. The margin rate is calculated with the formula: TaM = (MB ÷ PA) x 100. Therefore, the margin rate is (82,5 ÷ 67,5) x 100 = 122,22%.
4. To determine the new PV, we use the formula: new PV = old PV + (old PV x rate of increase). So the new PV after the 10% increase will be €150+ (€150 x 10%) = €165.
5. To determine the new PV after a 15% decrease, we use the formula: new PV = previous PV – (previous PV x rate of decrease). So, the new PV after the 15% decrease will be €165 – (€165 x 15%) = €140,25.
Summary of Formulas Used:
| Formula Name | Formulas |
|---|---|
| New purchase price | PA – (PA x discount percentage) |
| Gross margin | PV – PA |
| Margin rate | (MB ÷ PA) x 100 |
| New sale price after increase | HP + (HP x increase rate) |
| New sale price after reduction | previous PV – (previous PV x rate of decrease) |
Application: Megastore
States :
Megastore is a company selling various electronic devices. It mainly specializes in laptops, smartphones and televisions.
Over the past month, it has sold a total of 1200 units divided as follows: 600 units of laptops, 400 units of smartphones and 200 units of televisions.
The sales prices excluding VAT of these devices are respectively €800, €600 and €1000. Management decided to increase the sales price excluding tax of each device by 10%, then changed its mind and decided to reduce it by 5%.
Work to do :
1. What is the proportion of sales of each type of device compared to the total?
2. Calculate the percentage of sales for each product compared to the total.
3. What will the price of each product be after the first 10% increase?
4. What will be the price of each product after the 5% reduction?
5. What will be the overall rate of change from the initial price to the final price after the increase and decrease?
Proposed correction:
1.
– For laptops, the proportion is 600 units / 1200 units = 0,5.
– For smartphones, the proportion is 400 units / 1200 units = 0,333.
– For televisions, the proportion is 200 units / 1200 units = 0,166.
2.
– For laptops, the percentage is (600 units / 1200 units) x 100 = 50%.
– For smartphones, the percentage is (400 units / 1200 units) x 100 = 33,33%.
– For televisions, the percentage is (200 units / 1200 units) x 100 = 16,66%.
3.
– The price of the laptop after a 10% increase is €800 x (1 + 10% / 100) = €880.
– The price of the smartphone after a 10% increase is €600 x (1 + 10% / 100) = €660.
– The price of the TV after a 10% increase is €1000 x (1 + 10% / 100) = €1100.
4.
– The price of the laptop after a 5% decrease is €880 x (1 – 5% / 100) = €836.
– The price of the smartphone after a 5% reduction is €660 x (1 – 5% / 100) = €627.
– The price of the television after a 5% reduction is €1100 x (1 – 5% / 100) = €1045.
5.
– The overall laptop change rate is ((€836 – €800) / €800) x 100 = 4,5%.
– The overall smartphone change rate is ((€627 – €600) / €600) x 100 = 4,5%.
– The overall TV change rate is ((€1045 – €1000) / €1000) x 100 = 4,5%.
Summary of Formulas Used:
| Proportion | Percentage | Increase | Decrease |
| x = Part / Total | P = (Share / Total) x 100 | Price after increase = Initial price x (1 + % increase / 100) | Price after reduction = Initial price x (1 – % reduction / 100) |
Application: “FashionTrends” clothing store
States :
The clothing store “FashionTrends” has experienced several fluctuations in its sales in recent months. Here are some key data:
– In January, the store sold 1000 items of clothing.
– In February, sales increased by 20% compared to January.
– In March, sales decreased by 15% compared to February.
– In April, sales increased by 30% compared to March.
– The average selling price of a piece of clothing is €50.
Work to do :
1. How many clothes were sold in February?
2. How many clothes were sold in March?
3. How many clothes were sold in April?
4. What is the turnover achieved in March?
5. What percentage of March's turnover represents that of April's?
Proposed correction:
1. In February, sales increased by 20% compared to January. So, the number of clothes sold in February: 1000 clothes + (1000 clothes x 20/100) = 1200 clothes.
2. In March, sales decreased by 15% compared to February. So, the number of clothes sold in March: 1200 clothes – (1200 clothes x 15/100) = 1020 clothes.
3. In April, sales increased by 30% compared to March. So, the number of clothes sold in April: 1020 clothes + (1020 clothes x 30/100) = 1326 clothes.
4. The turnover achieved in March is: 1020 items of clothing x €50 = €51.
5. Percentage of March turnover compared to April is: (€51 / (000 items of clothing x €1326)) x 50 = 100%.
Summary of Formulas Used:
| Turnover | Quantity sold x Sale price |
| Increase | Initial value + (Initial value x Increase rate/100) |
| Decrease | Initial value – (Initial value x Decrease rate/100) |
| Percentage | (Part / Total) x 100 |
Application: Fashion 365 ready-to-wear house
States :
La Maison Fashion 365 is a company specializing in the sale of ready-to-wear clothing for men and women. The company plans to evaluate the performance of its products in order to implement new pricing. Financial information for the new collection jackets is as follows:
– The unit purchase cost of jackets excluding taxes (CA excluding tax) is €40
– The annual operating costs of the company are estimated at €50000
– The company sold 2000 jackets in the past year.
– The company plans to increase the unit selling price of jackets by 5% for the next year.
Work to do :
1. What is the total cost of the jacket collection for the past year?
2. Considering a 5% increase in the selling price, what would be the new unit selling price for the jackets?
3. What would be the new unit margin if the increase in the unit sales price is implemented?
4. What would be the new margin rate for jackets if the price increase is implemented?
5. What would be the new mark rate for jackets if the price increase is implemented?
Proposed correction:
1. Total costs of the jacket collection = CA excluding VAT x quantity of jacket sold + operating costs = €40 x 2000 + €50000 = €130000.
2. New unit sales price = Old price + (Old price × Percentage increase) = €40 + (€40 × 5 ÷ 100) = €42.
3. To calculate unit margin, we need the current sales price excluding tax. Without this information, we would not be able to calculate the exact increase in euros in the unit margin with the new pricing.
4. Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100). We need the current sales price excluding tax to calculate the margin rate.
5. Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100). We also need the current sales price excluding tax to calculate the mark rate.
Summary of the formulas used:
| Packages | Explanation |
|---|---|
| Total costs of the jacket collection = turnover excluding tax x quantity of jacket sold + operating costs | Total expenses incurred for the jacket collection in a year |
| New unit sales price = Old price + (Old price × Percentage increase) | Calculation of the new selling price after a determined increase |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Allows you to know the proportion of the purchase price excluding taxes in the selling price excluding taxes |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | Allows you to know the proportion of the profit in the sales price excluding taxes |
Application: Chauss'Fast Boutique
States :
The Chauss'Fast Boutique is a small business that sells sports shoes. During the previous year, the store achieved a turnover of €100. However this year, the store decided to increase the price of its shoes by 000%, reduce its costs by 15% and managed to increase its sales by 10%.
Work to do :
1. What is the new selling price after the 15% increase if the initial price was €70?
2. What is the new cost after the 10% reduction if the original cost was €500?
3. What is the new turnover obtained after an increase of 5%?
4. What is the percentage increase in turnover compared to the previous year?
5. If the store reduces the new sales price by 20%, what would the price of the shoes be after the reduction?
Proposed correction:
1. The 15% increase on an initial selling price of €70 is calculated as follows: €70 x 15% = €10,5. So the new selling price after the increase is €70 + €10,5 = €80,5
2. The 10% reduction on an initial cost of €500 is calculated as follows: €500 x 10% = €50. So the new cost after the reduction is €500 – €50 = €450.
3. The 5% increase in sales on an initial turnover of €100 is obtained like this: €000 x 100% = €000. Therefore, the new turnover after increase is €5 + €5 = €000.
4. The percentage increase in turnover compared to that of the previous year is calculated as follows: (€105 – €000) ÷ €100 x 000 = 100%.
5. The 20% reduction on the new selling price of €80,5 is obtained as follows: €80,5 x 20% = €16,1. So, the price of the shoes after reduction would be €80,5 – €16,1 = €64,4.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Price after increase = Initial price + (Initial price x percentage increase) | Used to calculate the new selling price after an increase. |
| Price after reduction = Initial price – (Initial price x reduction percentage) | Used to calculate the new price after a reduction. |
| Turnover after increase = Initial turnover + (Initial turnover x percentage of increase) | Used to calculate the new turnover after increase. |
| Percentage increase = ((New turnover – Initial turnover) ÷ Initial turnover) x 100 | Used to calculate the percentage increase in turnover. |