Welcome to this article dedicated to exercises on business calculations and more precisely on calculations on how to find a percentage. You will find here no less than 11 detailed corrected management exercises on business calculations for Operational Management.
By the end of this article, you will know how to find percentage in business calculations without any worries.
Here is a table that summarizes the formulas used in the article:
In this section:
- How to Find a Percentage – Formulas Used
- Application 1: ElectroShop Company
- Application 2: Maison du Monde Company
- Application 3: Budding Bakery
- Application 4: Golden Almonds
- Application 5: DiamondTech Company
- Application 6: SuperBijoux Company
- Application 7: TechStorm Company
- Application 8: Spice-Everything Grocery Store
- Application 9: Chic & Fashion Business
- Application 10: Divine Beauty
- Application 11: Process Productions
How to Find a Percentage – Formulas Used
| Concept | Packages |
|---|---|
| Sales price excluding tax (PV excluding tax) |  |
| Margin |  |
| Margin rate |  |
| Brand taxes |  |
| VAT |  |
| Profit |  |
| Percent reduction |  |
| Discount amount |  |
| Average selling price |  |
Application 1: ElectroShop Company
States :
ElectroShop, an electronics retailer, sold a television for €1 including VAT. The purchase price excluding tax (PA HT) of the television was €200. The VAT rate applied is 800%.
Work to do :
1. What is the sales price excluding tax (PV HT) of the television?
2. What is the margin made on the sale of this television?
3. Calculate the margin rate on this TV.
4. Calculate the markup rate of this TV.
5. Determine the amount of VAT on the sale of this television.
Proposed correction:
1. We know that the sales price including VAT is €1. If the VAT rate is 200%, then the sales price excluding VAT (PV excluding VAT) of the television will therefore be €20 / (1 + 200/1) = €20.
2. The margin is the difference between the selling price excluding tax (PV HT) and the purchasing price excluding tax (PA HT). Therefore, the margin made on this sale is:
€1 (PV excluding tax) – €000 (PA excluding tax) = €800.
The margin achieved is therefore €200.
3. The margin rate is calculated as follows:
[(PV excluding tax – PA excluding tax) / PA excluding tax] * 100.
So the markup on this TV is [(€1 – €000) / €800] * 800 = 100%.
The margin rate is therefore 25%.
4. The markup rate is calculated using the following formula:
((PV HT – PA HT) / PV HT) * 100.
In this case, the markup rate would be ((€1 – €000) / €800) * 1 = 000%.
5. VAT is calculated by subtracting the price excluding VAT from the price including VAT. Therefore, the VAT on the sale of this television is €1 (Price including VAT) – €200 (Price excluding VAT) = €1.
Application 2: Maison du Monde Company
States :
You work as a financial manager in the company "Maison du Monde". Your role is to evaluate and measure the financial performance of the company. To do this, you regularly use percentages and ratios in order to better understand the figures.
The figures for the last month have just been released:
– The turnover for the month is €50 excluding VAT.
– The cost of sales for the month is €30 excluding VAT.
– Overhead costs amount to €7 for the month.
Work to do :
1. What is the company's profit for this month?
2. What is the company's margin rate for this month?
3. What is the percentage of overhead expenses compared to sales this month?
4. If the goal is to reduce overheads to 5% of turnover, by how much should they be reduced?
5. If the company wants to increase its margin to 45%, what should the new turnover be?
Proposed correction:
1. The company's profit for this month is equal to sales revenue – (cost of sales + overheads) = €50 – (€000 + €30) = €000.
2. The margin rate for this month is calculated as follows: ((Profit / turnover) x 100) = (€13 / €000) x 50 = 000%.
3. The percentage of overheads to sales this month is ((Overheads / Sales) x 100) = (€7 / €000) x 50 = 000%.
4. If the goal is to reduce overheads to 5% of turnover, then they should be (5/100) x €50 = €000 per month. This means that we need to reduce them by €2 – €500 = €7.
5. If the company wants to increase its margin to 45%, this means that the profit must be 45% of the turnover. So the turnover should be: profit / (45/100) = €13 / 000 = €0,45 (rounded to two decimal places).
So to reach a margin of 45%, the company must increase its turnover to €28.
Application 3: Budding Bakery
States :
The Boulangerie en Herbe company recently carried out an inventory in order to evaluate its activity. It provides you with several pieces of information:
– She sold 1 baguettes of bread at a unit price excluding tax (ET) of €000.
– The unit purchase cost excluding tax for each baguette is €0,40.
– The company also sold 500 croissants at a unit price excluding VAT of €1.
– The unit purchase cost excluding tax for each croissant is €0,50.
Work to do :
1. Calculate the overall margin in euros for baguettes. How is the unit margin obtained?
2. What is the margin rate on baguettes?
3. Find the markup rate for baguettes.
4. Calculate the overall margin for the croissants.
5. What is the markup rate on croissants?
Proposed correction:
1. For baguettes, the unit margin is the difference between the selling price excluding VAT and the purchase price excluding VAT, i.e. €0,80 – €0,40 = €0,40.
Then, to get the overall margin, we multiply the unit margin by the number of products sold, i.e. €0,40 * 1 = €000.
2. The margin rate is the ratio between the unit margin and the purchase price excluding tax, i.e. ((€0,80 – €0,40) / €0,40) * 100 = 100%.
3. The mark-up rate for baguettes is the ratio between the unit margin and the selling price excluding tax, i.e. ((€0,80 – €0,40) / €0,80) * 100 = 50%.
4. For croissants, the unit margin is €1 – €0,50 = €0,50.
By multiplying this unit margin by the quantity sold, we obtain the overall margin: €0,50 * 500 = €250.
5. The markup rate for croissants is ((€1 – €0,50) / €1) * 100 = 50%.
Finding a percentage may seem complicated, but with a structured method, it is easy to navigate through the numbers and rates. The calculation of the percentage is based on the proportionality between the initial value and the final value.
For example, let's say that during a sales period, a retailer offers a discount on an item. To calculate the value of the discount as a percentage, we start by deducting the final price from the starting price, and this result is then multiplied by 100 and divided by the starting price.
This method uses the rule of three, a simplified form of multiplication and division, to determine the percentage corresponding to a price change.
Application 4: Golden Almonds
States :
The company "Les Amandes Dorées" sells bags of almonds. 100 bags of almonds were produced by the company. Of these 100 bags, 45 bags of almonds were sold at a unit price of €10 excluding VAT. The rest of the bags have not yet found a buyer.
Work to do :
1- What percentage of the bags of almonds were sold?
2- What is the net turnover generated by the sale of bags of almonds?
3- If the company spent the sum of €200 excluding VAT for the production of 100 bags, what is the unit production cost excluding VAT of a bag of almonds?
4- If the unit production cost is €2 excluding VAT, what is the margin rate?
5- If the selling price excluding tax is €10, what is the markup rate?
Proposed correction:
1- The percentage of bags sold is calculated as follows: (number of bags sold / total number of bags produced) * 100. Thus, (45 / 100) * 100 = 45%. 45% of the bags of almonds produced were sold.
2- The turnover is obtained by multiplying the number of bags sold by the unit price. That is 45 bags * €10/bag = €450. The turnover excluding tax generated by the sale of bags of almonds is €450.
3- The unit production cost excluding VAT of a bag is obtained by dividing the total production cost by the total number of almonds produced. That is €200 / 100 bags = €2. The unit production cost excluding VAT of a bag of almonds is €2.
4- The margin rate is obtained using the formula:
((Sales price excluding VAT – Unit production cost excluding VAT) / Unit production cost excluding VAT) * 100.
With the figures we obtain: ((10 € – 2 €) / 2 €) * 100 = 400%.
The margin rate is 400%.
5- The markup rate is calculated using the formula: ((Sales price excluding VAT – Production cost excluding VAT) / Sales price excluding VAT) * 100.
So we have ((10 € – 2 €) / 10 €) * 100 = 80%.
The mark rate is 80%.
Application 5: DiamondTech Company
States :
DiamondTech is a wholesaler of technology products. It purchases products at a purchase price excluding tax (PA HT) and resells them at a sale price excluding tax (PV HT). The VAT rate is 20%.
For example, DiamondTech buys a certain type of smartphone at a gross sales price of €300 and resells it at a gross sales price of €400.
Work to do :
1. What is the unit margin in euros?
2. Calculate the margin rate.
3. Calculate the mark rate.
4. What is the overall margin if the company sells 500 of these smartphones?
5. What is the amount of VAT for a smartphone sale?
Proposed correction:
1. The unit margin is calculated by the formula: Unit margin = PV HT – PA HT.
In our example, Unit margin = €400 – €300 therefore, the unit margin is €100.
2. The margin rate is calculated by the formula: Margin rate = ((PV HT – PA HT) / PA HT) * 100).
In this exercise, we therefore obtain:
Margin rate = ((€400 – €300) / €300) * 100 = 33,33%.
So the margin rate is 33,33%.
3. The markup rate is calculated by the formula: Markup rate = ((PV HT – PA HT) / PV HT) * 100).
In our example, Markup rate = ((€400 – €300) / €400) * 100 = 25%. So, the markup rate is 25%.
4. The overall margin is calculated by the formula: Overall margin = Unit margin * quantity sold.
The overall margin is therefore = €100 * €500, or €50.
So the overall margin is €50.
5. The amount of VAT is calculated using the formula: VAT = PV excluding VAT * VAT rate.
In our example, VAT = €400 * 20% = €80. So the VAT amount is €80.
Application 6: SuperBijoux Company
States :
The company SuperBijoux is a manufacturer of luxury jewelry. The company buys a diamond necklace for €1 excluding VAT from its suppliers and sells it to its customers for €000 excluding VAT. The applicable VAT is 1%.
Work to do :
1. Calculate the amount of VAT on the sale of this necklace.
2. Calculate the overall margin made on the sale of this necklace.
3. Calculate margin rate and brand rate.
4. If SuperBijoux wants to increase its margin rate to 50%, at what price should the necklace be sold excluding tax?
5. If VAT increased to 25%, what would be the new markup rate?
Proposed correction:
1. The amount of VAT on the sale of this necklace is calculated as follows:
VAT = Selling price excluding VAT * VAT rate.
So, VAT = €1 * 400% = €20.
2. The overall margin is calculated by the difference between the Selling Price excluding VAT and the Purchase Price excluding VAT.
We therefore have margin = Selling price excluding tax – Purchase price excluding tax = €1 – €400 = €1.
3. The margin rate is calculated as follows: Margin rate = ((Selling price excluding VAT – Purchase price excluding VAT) / Purchase price excluding VAT) * 100.
So, Margin rate = ((€1 – €400) / €1) * 000 = 1%.
The markup rate is calculated with the following formula:
Markup rate = ((Selling price excluding VAT – Purchase price excluding VAT) / Selling price excluding VAT) * 100.
Hence Markup rate = ((€1 – €400) / €1) * 000 = 1%.
4. If the company SuperBijoux wants to have a margin rate of 50%, it must increase its selling price.
To calculate the new selling price excluding VAT, we must first calculate the new purchasing price excluding VAT: Purchasing price excluding VAT = Selling price excluding VAT / (1 + Margin rate / 100).
So, Purchase price excluding VAT = €1 / (000 + 1/50) = €100.
Then, the new Selling price excluding VAT = Purchase price excluding VAT + Margin = €666,67 + €500 = €1.
5. If VAT increases to 25%, this means that the sales price including VAT increases, but be careful because the sales price excluding VAT remains the same.
In this case, the new mark rate is calculated as follows:
Markup rate = ((Selling price excluding VAT – Purchase price excluding VAT) / Selling price excluding VAT) * 100.
Markup rate = ((€1 – €166,67) / €1) x 000 = 1%.
The use of technological tools greatly facilitates these calculations. For example, Excel, a widely used spreadsheet program, offers pre-installed formulas that make it easy to calculate percentages, the total value, or even the partial value of a sum.
For sales, if a merchant wants to apply a percentage discount on a product, he only has to multiply the initial price by the multiplier coefficient corresponding to this percentage. Then, to obtain the amount of the discount, simply subtract this result from the initial price.
Additionally, online calculators and converters can also be used to determine the percentage or rate of change based on the initial and final value.
Application 7: TechStorm Company
States :
The company "TechStorm" manufactures and sells laptops. For a certain computer model, the company has the following financial data:
– Purchase price excluding tax (PA excluding tax): €500
– Sales price excluding tax (PV HT): €800
– Quantity sold: 1000 units
Work to do :
1. What is the unit margin achieved by the company on the computer model?
2. What is the margin rate made by TechStorm on each computer sold?
3. What is the markup rate achieved by TechStorm on the computer model?
4. What is the overall margin made by the company on the computer model?
5. If TechStorm wants to increase its unit margin by 10%, what would the new selling price be?
Proposed correction:
1. The unit margin is the difference between the selling price excluding tax (PV HT) and the purchasing price excluding tax (PA HT).
So the unit margin = PV HT – PA HT = €800 – €500 = €300.
2. The margin rate corresponds to the unit margin divided by the purchase price excluding tax (PA HT), multiplied by 100.
Margin rate = ((PV HT – PA HT) / PA HT) x 100
Margin rate = ((€800 – €500) / €500) x 100 = 60%.
3. The markup rate is the unit margin divided by the selling price excluding tax (SVP HT), multiplied by 100.
So, Markup rate = ((PV HT – PA HT) / PV HT) x 100 = ((800 € – 500 €) / 800 €) x 100 = 37,5%.
4. The overall margin is the unit margin multiplied by the quantity sold. Therefore, Overall margin = Unit margin * quantity sold = €300 x 1000 = €300.
5. To increase the unit margin by 10%, the selling price must be increased by 10% of the current margin.
The calculation is therefore as follows:
Increase = unit margin x 10% hence €300 x 10/100 = €30.
The new sale price would then be PV excluding tax + increase = €800 + €30 = €830.
Application 8: Spice-Everything Grocery Store
States :
Mr. Dupont is the owner of a grocery store called "Epice-Tout". As manager, he is responsible for the financial management of his business. He recently held a flash sale and would like to determine the effectiveness of this sale. The following information is available:
– Initial sale price of cans of tuna: €2,5
– Flash sale price: €2
– Quantity sold during flash sale: 1500 pieces
– Purchase price from supplier: €1,5 per piece
Work to do :
1. What is the discount rate applied during the flash sale?
2. What is the unit margin made on each can of tuna sold during the flash sale?
3. What is the margin rate following this flash sale?
4. What is the overall margin made during this flash sale?
5. What is the markup rate following this flash sale?
Proposed correction:
1. The discount rate is calculated by subtracting the original sale price from the flash sale price, then dividing by the original sale price and multiplying by 100.
In this case, we therefore have: ((€2,5 – €2) / €2,5) x 100 = 20%.
2. The unit margin is calculated by subtracting the purchase price from the sale price. In this case: €2 – €1,5 = €0,5.
3. The margin rate is calculated by subtracting the purchase price from the sale price, dividing by the purchase price, and multiplying by 100. So: ((€2 – €1,5) / €1,5) x 100 = 33,33%.
4. The overall margin is calculated by multiplying the unit margin by the quantity sold. Therefore: €0,5 x 1500 = €750.
5. The markup rate is calculated by subtracting the purchase price from the sale price, dividing by the sale price, and multiplying by 100. So: ((€2 – €1,5) / €2) x 100 = 25%.
Application 9: Chic & Fashion Business
States :
You are the financial manager of the company "Chic & Mode", a luxury clothing store. The company has carried out several financial transactions during the last quarter. You must analyze the results and calculate various percentages to report to management.
1) During the month of March, the company purchased a designer suit for €200 excluding VAT and sold it for €350 excluding VAT.
2) The company also sold five evening dresses purchased at €150 excluding VAT each and sold at €300 excluding VAT each.
3) Management would like to understand the percentage that VAT represents (20%) on the selling price excluding VAT of these items.
4) Additionally, management wants to understand what percentage designer suit represents in total sales for the month.
5) Finally, management would like to know whether the target margin on the total cost of clothing of 40% has been achieved or not.
Work to do :
1) Calculate the margin rate for the designer suit.
2) Calculate the overall margin for evening dresses.
3) Calculate the amount of VAT for each type of item (suit and dresses), then find its percentage in relation to the selling price excluding VAT.
4) Calculate the percentage that designer suits represent in the total sales for the month.
5) Assess whether the 40% margin target has been achieved.
Proposed correction:
1) For the designer suit, the margin rate is ((PV HT – PA HT) / PA HT) x 100), or ((€350 – €200) / €200) x 100) = 75%.
The margin rate is therefore 75%.
2) For evening dresses, the overall margin is the unit margin times the quantity sold, so (€300 – €150) x 5 = €750.
3) The VAT amount for the suit is €350 * 20% = €70, or a percentage of (€70 / €350) * 100 = 20%. For dresses, the VAT is €300 * 20% * 5 = €300, or a percentage of (€300 / (€300 * 5)) * 100 = 20%.
4) Total sales for the month are sales of the suit plus sales of the dresses, i.e. €350 + (€300 * 5) = €1850.
The costume therefore represents a percentage of (€350 / €1850) * 100 = 18,92%.
5) The margin target on the total cost of clothing is 40%. The total cost of clothing is €200 for the suit and €150 x 5 for the dresses, or €950.
The total margin achieved is (€350 – €200) for the suit and (€300 – €150) x 5 for the dresses, i.e. €750.
The margin rate is therefore (€750 / €950) x 100 = 78,95%, which exceeds the target of 40%.
Application 10: Divine Beauty
Statement:
Let’s imagine a fictitious company called “Divine Beauty”. Divine Beauty is a distributor of beauty and home care products.
Beauté Divine decides to introduce a new anti-aging product to its range. The unit purchase cost excluding VAT of this product from their supplier is €30. To gain the loyalty of its customers, Beauté Divine wants to offer them a safe percentage discount on this product. In addition, Beauté Divine also wants to determine the relevant margin and brand rate.
Work to do :
1. If Beauté Divine wants to make a 50% margin on the purchase price, what would be the tax-free selling price of the product?
2. What would the margin rate be if the selling price excluding tax is set at €45?
3. If a 20% discount rate is offered to customers, what will be the new selling price excluding VAT?
4. What would be the 20% VAT on this new selling price excluding VAT?
5. What would be the final selling price (including VAT) for this product after discount and addition of VAT?
Proposed correction:
1. To find the PV HT with a margin of 50% on the PA HT, we use the following formula: PV HT = PA HT + (50/100) * PA HT
So we have: €30 + (50/100) x €30 = €30 + €15 = €45.
2. The margin rate is calculated as follows: margin rate = ((sale price excluding VAT – purchase price excluding VAT)/purchase price excluding VAT) x 100. Therefore margin rate = ((€45 – €30) / €30) x 100 = 50%.
3. If a 20% reduction is applied, the new selling price excluding VAT would be: new PV excluding VAT = PV excluding VAT – (20/100) x PV excluding VAT
With the figures we therefore have: €45 – (20/100) x €45 = €45 – €9 = €36.
4. The 20% VAT on this new excluding VAT sale price would be: VAT = (20/100) x new excluding VAT sales price, therefore (20/100) x €36, i.e. €7,20.
5. The final sale price after reduction and addition of VAT would be:
PV incl. VAT = new PV excl. VAT + VAT = €36 + €7,20 = €43,20.
Application 11: Process Productions
States :
The company "Process Productions", specialized in the production of electronic equipment, wishes to evaluate the performance of its sales. It sold 3000 products during the previous year for a turnover excluding tax of €450.
For this year, the company sold 3500 products with a turnover excluding tax of €525. In addition, it granted discounts on certain product lines which represented 000% of the turnover.
Work to do :
1. What is the evolution of the number of products sold as a percentage?
2. How has the net turnover changed as a percentage?
3. Calculate the amount of the reduction granted in €.
4. What is the average selling price per product this year?
5. Calculate the margin rate knowing that the purchase price excluding tax of the products is €100 per unit.
Proposed correction:
1. The evolution of the number of products sold is calculated as follows:
[(Current Value – Previous Value) / Previous Value] x 100.
So here the evolution is [(3500 – 3000) / 3000] x 100 = 16,67%. The number of products sold has therefore increased by 16,67% this year.
2. The change in net turnover is calculated in the same way: [(Current value – Previous value) / Previous value] x 100.
So in our case it's [(€525 – €000) / €450] x 000 = 450%.
There was therefore an increase of 16,67% in net turnover.
3. The amount of the reduction granted is calculated by taking 3% of the turnover.
So: €525 x 000/3 = €100. The reductions granted in total therefore represent €15.
4. The average selling price per product is calculated by dividing the turnover by the total number of products sold: €525 / 000 = €3500.
The average selling price per product is therefore €150 this year.
5. The margin rate is calculated by subtracting the pre-tax purchase price from the pre-tax sale price, divided by the pre-tax purchase price, the whole multiplied by 100: [(€150 – €100) / €100] x 100 = 50%.
The margin rate is therefore 50%.
In a foreign business context or when establishing trade margins, determining the percentage involves multiplying the starting value by a multiplier or coefficient to obtain the new value.
For example, to calculate a percentage increase or decrease in sales, we take the difference between the first value and the final value, then divide it by the starting value, and finally, multiply the result by 100.
Whether it's for discounts, salary increases, or even to see how prices change during winter sales, understanding how to calculate the percentage is essential in daily and professional life.