How to Calculate a Percentage in BTS MCO

What is a percentage?

A percentage is a way of representing a proportion or fraction of a whole. It is often used to compare quantities, indicate reductions, increases, or proportions. For example, if you have 20 apples and you eat 5 of them, you have consumed 25% of your apples.

Why is it important to know how to calculate a percentage?

Knowing how to calculate a percentage is an essential skill in many areas of daily and professional life. Whether it is to calculate a discount during sales, to understand a statistic in a report, or to evaluate the evolution of your savings, the percentage is everywhere. It is therefore crucial to know how to calculate it and interpret it correctly.

The Basics of Percentage Calculation

What is the base in percentage calculation?

The base in percentage calculation is the total number or total quantity from which we calculate the percentage. For example, if you want to know what percentage 20 is of 100, 100 is the base.

How to determine the basis in different situations?

Determining the base in different situations depends on what you are trying to find. If you want to know what percentage of a class passed a test, the total number of students in the class would be the base. If you want to know what percentage of your salary goes to taxes, your total salary would be the base.

How to Calculate Percentage: Simple Steps

What is the basic formula for calculating a percentage?

The basic formula for calculating a percentage is: (part / whole) * 100. For example, if you want to know what percentage of 20 is of 100, you divide 20 by 100 to get 0.2, then multiply by 100 to get 20%.

How to apply this formula in real situations?

Applying this formula in real-world situations is simple once you understand the logic. For example, if you want to calculate what percentage of your salary goes to taxes, divide the tax amount by your total salary, then multiply by 100.

Calculate a Percentage of a Quantity

How to calculate a percentage of a specific quantity?

To calculate a percentage of a specific quantity, you divide the part you are looking at by the whole, then multiply by 100. For example, if you want to know what percentage of 30 is of 150, you divide 30 by 150 to get 0.2, then multiply by 100 to get 20%.

Practical examples to understand the calculation of percentage of a quantity

Let's take the example of a class of 30 students where 15 students passed an exam. To find the percentage of students who passed, we divide the number of students who passed (15) by the total number of students (30), then multiply by 100. This gives (15/30)*100 = 50%. So, 50% of the students passed the exam.

Calculate a Discount Percentage

How to calculate a discount percentage?

To calculate a discount percentage, you first need to determine the difference between the original price and the discounted price. Then, divide this difference by the original price and multiply by 100. For example, if an item cost $50 and is now selling for $40, the discount is (50-40)/50*100 = 20%.

How to use the discount percentage to save money?

The discount percentage can help you determine if a deal is worth it. For example, if an item is on sale for 20% off, that means you're saving 20% ​​of the original cost. This can help you decide if the purchase is worth it.

Calculate a Percentage Increase

How to calculate a percentage increase?

To calculate a percentage increase, you first need to determine the difference between the new number and the old number. Then, divide this difference by the old number and multiply by 100. For example, if your salary goes from $2000 to $2200, the increase is (2200-2000)/2000*100 = 10%.

When is it necessary to calculate a percentage increase?

Calculating a percentage increase is necessary when you want to know how much a quantity has increased in percentage terms. This can be useful in many contexts, such as evaluating your salary increase, price increases, or population growth.

Calculate a Percentage of Percentage

How to calculate a percentage of another percentage?

To calculate a percentage of another percentage, you must first convert the original percentage to a decimal, then multiply by the percentage you want to find. For example, if you want to find 50% of 20%, convert 20% to 0.20, then multiply by 50 to get 10.

Examples to clarify the concept

Let's take the example of a population where 60% are women and we want to know what percentage of these women are students. If 30% of the women are students, then the percentage of female students among the total population would be (60/100)*30 = 18%.

Calculate a Percentage on Excel

How to use Excel to calculate a percentage?

Excel can be a very handy tool for calculating percentages. To do this, you need to divide the part you are looking at by the total, and then format the cell as a percentage. For example, if you want to calculate the percentage of 20 out of 100, you would type "=20/100" into a cell, and then format that cell as a percentage.

Advantages of Using Excel for Percentage Calculation

Excel offers several advantages for calculating percentages. It allows you to perform calculations quickly and accurately, work with large amounts of data, and visualize the results in graphs and tables.

Calculate a Percentage on a Calculator

How to use a calculator to calculate a percentage?

To calculate a percentage on a calculator, you divide the part you are looking at by the whole, then multiply by 100. For example, to calculate what percentage 20 is of 100, you would type “20 ÷ 100 × 100” into your calculator.

What are some common mistakes to avoid when calculating a percentage on a calculator?

A common mistake when calculating a percentage on a calculator is forgetting to multiply by 100 at the end. This can lead to incorrect results. Another common mistake is not using the correct operation. For example, to calculate a percentage, you must divide, not multiply.

Common Mistakes in Calculating Percentage

What are common mistakes in calculating percentage?

Besides the mistakes mentioned above, other common errors in calculating percentage include reversing the part and total, forgetting to convert percentages to decimals before using them in calculations, and using incorrect percentages for increases and decreases.

How to avoid these mistakes?

To avoid these mistakes, make sure you understand the formula for calculating a percentage, double-check your calculations, and practice regularly. Additionally, using tools like Excel or a calculator can help avoid mistakes.

Tips for Calculating a Percentage Quickly

What are some tips for calculating a percentage quickly?

Some tips for calculating a percentage quickly include learning common percentages (for example, knowing that 50% is half), using the rule of three, and learning how to use a calculator or Excel effectively.

How can these tips help in everyday life?

These tips can help you perform percentage calculations quickly and accurately, whether you're determining a discount during a sale, understanding a statistic in a report, or evaluating how your savings are growing.

Conclusion

Summary of key points covered in the article

In this article, we covered how to calculate a percentage, including the basic formula, how to determine the base, how to calculate a percentage of a quantity, a reduction, an increase, and another percentage. We also discussed how to use Excel and a calculator to calculate percentages, common mistakes to avoid, and tips for calculating a percentage quickly.

Importance of knowing how to calculate a percentage in daily life

Knowing how to calculate percentages is an essential life skill. Whether it’s understanding statistics, making smart purchases, or managing your finances, percentages are a powerful tool for understanding and comparing quantities. By mastering percentage calculations, you can make more informed decisions and achieve success in various areas of your life.

10 Exercises on Calculating percentages of increase, decrease…

Statement 1: Nice Shoe

The company "Belle Chaussure" specializes in the sale of luxury shoes. At a board meeting, the store manager provided the following data:

– Cost of purchasing a pair of shoes excluding tax (PA excluding tax) = €150
– Sales price excluding tax (PV HT) set by the company = €200
– Quantity of shoes sold in the year = 500 pairs
– The company is considering a 10% reduction in the net selling price for next year to stimulate sales.

Work to do :

1. Calculate the unit margin excluding tax for each pair of shoes.
2. Calculate the overall margin for the year.
3. Calculate the margin rate.
4. What will be the new selling price excluding VAT if the company reduces prices by 10%?
5. What will be the new unit margin and margin rate if the company reduces prices by 10%?

Proposed correction:

1. The unit margin excluding tax = PV excluding tax – PA excluding tax = €200 – €150 = €50.

2. The overall margin = Unit margin excluding tax * Quantity sold = €50 * 500 = €25000.

3. Margin rate = ((PV HT – PA HT) / PA HT) * 100 = ((200€ – 150€) / 150€) * 100 = 33,33%.

4. The new selling price excluding tax = PV excluding tax – (PV excluding tax * 10%) = €200 – (€200 * 10/100) = €180.

5. The new unit margin excluding tax = New PV excluding tax – PA excluding tax = €180 – €150 = €30.
The new margin rate = ((New PV HT – PA HT) / PA HT) * 100 = ((180€ – 150€) / 150€) * 100 = 20%.

Statement 2: Beewear

You work as a financial manager for Beewear, a company that sells clothing online. The company wants to understand the impact of a series of changes it is planning on its sales prices and margins. The initial data is as follows:

Purchase Price Excluding Tax (PA HT) of a sweater: €30
Sale Price excluding Tax (PV excluding tax): €60
VAT: 5% or 20% (depending on the product).

Work to do :

1. If Beewear decides to increase the selling price of its sweaters by 15%, what will be the new selling price excluding tax (PV HT)?
2. If Beewear then decides to reduce its purchase prices by 10%, how will this affect the company's profit margin?
3. What is the markup rate on a sweater before the changes?
4. If, as a result of the market fluctuation, Beewear suffers a 20% drop in sales following the increase in the selling price, how is this reflected in terms of turnover?
5. If Beewear decides to reduce the selling price of its sweaters by 20% compared to the increased price, what will be the new selling price excluding tax (PV HT)?

Proposed correction:

1. If the company decides to increase the sales price by 15%, the new sales price excluding tax will be: initial sales price excluding tax * (1 + increase rate) or €60 * (1 + 15%) = €69.

2. If the purchase prices are reduced by 10%, the new purchase price will be €30 * (1 – 10%) = €27. The margin rate will therefore become: ((PV HT – new PA HT) / new PA HT) * 100 or ((€69 – €27) / €27) * 100 = 155,56%.

3. The markup rate on a sweater before the changes is: ((PV HT – PA HT) / PV HT) * 100 or ((€60 – €30) / €60) * 100 = 50%.

4. If the company suffers a 20% drop in sales following the increase in the selling price, this is reflected in terms of turnover by: Initial turnover * (1 – drop in sales) or €60 * (1 – 20%) = €48 per sweater sold.

5. If Beewear decides to reduce the sale price by 20% compared to the increased price, the new sale price excluding tax will therefore be: PV excluding tax after increase * (1 – reduction percentage) or €69 * (1 – 20%) = €55,20.

Statement 3: BricoBlanc

The company "BricoBlanc" is a DIY store that has been around for over 10 years. It has a wide range of products including tools, building materials, paint, etc.

The manager of BricoBlanc, in order to improve its profitability, decided to review its prices by increasing or decreasing them depending on several factors such as demand, competition, production costs, etc.

Here is some information:

1. The purchase price excluding tax (PA HT) of a 5L pot of paint is €25.
2. The initial sales price excluding tax (PV HT) of this pot of paint is €45.
3. Faced with the increase in the cost of raw materials, the manager decided to increase his net profit by 15%.
4. To remain competitive on the market, the manager decided to reduce its PV HT by 10%.
5. After one year, the PV HT is readjusted upwards by 5%.

Work to do :

1. Calculate the new purchase price excluding tax (PA HT) after a 15% increase.
2. Calculate the new sales price excluding tax (PV HT) after a 10% reduction.
3. Calculate the margin rate before the increase in the HT PA and the reduction in the HT PV.
4. Calculate the mark rate before the increase in the HT PA and the reduction in the HT PV.
5. Calculate the new sales price excluding tax after the 5% upward adjustment.

Proposed correction:

1. The new PA HT = initial PA HT + (initial PA HT * 15/100) = 25€ + (25€ * 15/100) = 25€ + 3,75€ = 28,75€

2. The new PV HT = Initial PV HT – (Initial PV HT * 10/100) = €45 – (€45 * 10/100) = €45 – €4,5 = €40,5

3. Margin rate = ((PV HT – PA HT) / PA HT) * 100 = ((45€ – 25€)/25€) * 100 = (20/25) * 100 = 80%

4. Markup rate = ((PV HT – PA HT) / PV HT) * 100 = ((45€ – 25€)/45€) * 100 = (20/45) * 100 = 44,44%

5. The PV HT after adjustment = PV HT after reduction + (PV HT after reduction * 5/100) = €40,5 + (€40,5 * 5/100) = €40,5 + €2,025 = €42,525. The final PV HT will be rounded to €42,53.

Statement 4: LumenTech

In the current context, the CFO of LumenTech, a company specializing in LED lighting technology, needs to perform several percentage calculations to assess the financial performance of the company as well as the potential for certain future investments.

Here are some financial situations he must analyze:

1. One of their LED bulb suppliers increased their prices by 15% last year. The unit price of these bulbs was initially €10 excluding VAT.

2. LumenTech successfully negotiated a 10% commercial discount with another supplier for an order of electrical cables whose initial price was €5000 excluding VAT.

3. LumenTech plans to increase the selling price of some of its products by 5%. The current selling price of these products is €20 excluding VAT.

4. The company managed to reduce its production costs by 7% this year. The initial production costs were €10.

5. LumenTech is considering investing in a new production machine that costs €50. They expect this investment to increase their productivity (and therefore their revenue) by 000%.

Work to do :

1. What is the new unit cost of LED bulbs after the supplier's 15% increase?
2. What is the new price of electric cable order after 10% discount?
3. What will be the new selling price of the products after the 5% increase?
4. What are the new production costs after the 7% reduction?
5. How much additional revenue can LumenTech generate in percentage terms with the investment in the new machine?

Proposed correction:

1. The new unit cost of LED bulbs is €10 + 15% of €10 = €10 + €1,5 = €11,5.

2. The new price of the electric cable order is €5000 – 10% of €5000 = €5000 – €500 = €4500.

3. The new selling price of the products is €20 + 5% of €20 = €20 + €1 = €21.

4. The new production costs are €10000 – 7% of €10000 = €10000 – €700 = €9300.

5. Investing in a new machine can potentially increase LumenTech's revenue by 8%, meaning the company can potentially generate an additional 8% of €50 = €000 in additional revenue.

Statement 5: Giraffe Tech

The company Giraffe Tech specializes in the sale of technological equipment. In 2020, the company achieved a turnover of €210. In 000, the company recorded a turnover of €2021.

Work to do :

1. Calculate the percentage decrease in turnover between 2020 and 2021.
2. In 2022, the company wants to increase its turnover by 25%. What will be the target turnover in 2022?
3. In 2020, the price of a flagship product was €500 excluding taxes. In 2021, the price increased by 5%. What is the new price?
4. In 2022, the company plans to lower the price of the flagship product by 10%. What will the new price be?
5. If the flagship product is sold at a 25% margin on the purchase cost excluding VAT, what is the purchase price?

Proposed correction:

1. Percentage decrease = (2020 turnover – 2021 turnover) / 2020 turnover * 100 = (€210 – €000) / €180 * 000 = 210%. The turnover therefore decreased by 000% between 100 and 14,29.

2. Target turnover 2022 = Turnover 2021 + (Turnover 2021 * 25/100) = €180 + (€000 * 180/000) = €25. The company therefore wants to achieve a turnover of €100 in 225.

3. New price = 2020 price + (2020 price * 5/100) = €500 + (€500 * 5/100) = €525. The new price of the flagship product is therefore €525.

4. New price = 2021 price – (2021 price * 10/100) = €525 – (€525 * 10/100) = €472,5. The price of the flagship product would therefore drop to €472,5 in 2022.

5. Purchase price = Selling price excluding tax / (1 + margin rate) = €500 / (1 + 25/100) = €400. The purchase price of the flagship product is therefore €400.

Statement 6: AutoGarage

AutoGarage, a company that sells car tires, has made price adjustments on some of its products. You are a financial manager working for AutoGarage and you need to analyze the impacts of these price adjustments.

1. The price of a Bridgestone tire has increased by 20%, from €120 to €144.
2. The price of a Michelin tire has been reduced by 15%, from €150 to €127.50.
3. The price of a Pirelli tire has been reduced by 25%, bringing the price down from €200 to €150.
4. Goodyear tires increased by 10%, taking the price from €100 to €110.
5. The price of a Hankook tire has been reduced by 50%, from €80 to €40.

Work to do :

1. Calculate the increase in euros of the Bridgestone tire.
2. Calculate the reduction in euros of the Michelin tire.
3. Calculate the reduction in euros of the Pirelli tire.
4. Calculate the increase in euros of the Goodyear tire.
5. Calculate the discount in euros for the Hankook tire.

Proposed correction:

1. The increase in euros for the Bridgestone tire is 144€ – 120€ = 24€.

2. The reduction in euros for the Michelin tire is 150€ – 127.50€ = 22.50€.

3. The reduction in euros for the Pirelli tire is 200€ – 150€ = 50€.

4. The increase in euros for the Goodyear tire is 110€ – 100€ = 10€.

5. The discount in euros for the Hankook tire is 80€ – 40€ = 40€.

Statement 7: Sun Cereals

Les Céréales du Soleil is a company that manufactures and sells various types of cereals. When analyzing the financial report for the second quarter of 2021, the CFO noted the following:

– The total profit in the first quarter was €150. In the second quarter, this figure reached €000.
– The total cost of cereals produced in the first quarter was €75, while it reached €000 in the second quarter.
– The selling price of a box of cereal in the first quarter was €3, but was reduced to €2,70 in the second quarter.
– The number of boxes sold in the first quarter was 50, while in the second quarter it was 000.

Work to do :

1. Calculate the percentage increase in profit between the first and second quarters.
2. Calculate the percentage increase in total grain cost between the first quarter and the second quarter.
3. Calculate the percentage decrease in the price of cereal boxes between the first quarter and the second quarter.
4. Calculate the percentage increase in the number of boxes sold between the first quarter and the second quarter.
5. If the selling price of a box of cereal had been maintained at €3 in the second quarter, what would the total profit have been? What is the percentage increase compared to the current profit?

Proposed correction:

1. Percentage increase in profit = ((Profit Q2 – Profit Q1) / Profit Q1) x 100 = ((180000€ – 150000€) / 150000€) x 100 = 20%

2. Percentage increase in total costs = ((Cost Q2 – Cost Q1) / Cost Q1) x 100 = ((€80000 – €75000) / €75000) x 100 = 6.67%

3. Percentage decrease in box prices = ((Price Q1 – Price Q2) / Price Q1) x 100 = ((3€ – 2,70€) / 3€) x 100 = 10%

4. Percentage increase in sales volumes = ((Q2 Sales – Q1 Sales) / Q1 Sales) x 100 = ((67000 – 50000) / 50000) x 100 = 34%

5. If the price had been kept at €3, the total profit would have been €3 x €67 = €000. This represents an increase of, ((€201 – €000) / €201000) x 180 = 000%.

Statement 8: Fruits Delight

The company "Fruits Delight", specialized in the sale of fresh fruits, has decided to adjust its prices due to seasonal changes and new operational expenses.

• For the first half of the year, the company saw a 15% increase in the cost of oranges.
• At the same time, due to the abundant supply of apples, it was able to reduce its purchase price by 8%.
• As for bananas, they have seen a significant increase of 25% due to transportation problems.
• The company also managed to reduce its operational expenses by 5% through cost-cutting measures.
• Due to competition, the selling price of the fruit had to be reduced by 10%.

Work to do :

1. Calculate the new cost of oranges considering the initial price as being 2€ / kg.
2. What is the new cost of purchasing apples if the initial price was 1.5€/kg?
3. Considering the initial price of bananas at 1.8€/kg, what is their new cost?
4. If the initial operating expenses were €10000/month, what will the new expenses be after reduction?
5. What will the new selling price be if the initial price was €3/kg?

Proposed correction:

1. Increasing the cost of oranges by 15% on an initial price of €2/kg gives: €2 + (2 * 15/100) = €2 + €0.30 = €2.30/kg

2. Reducing the cost of purchasing apples by 8% on an initial price of €1.5/kg gives: €1.5 – (1.5 * 8/100) = €1.5 – €0.12 = €1.38/kg

3. Increasing the cost of bananas by 25% on an initial price of €1.8 gives: €1.8 + (1.8 * 25 / 100) = €1.8 + €0.45 = €2.25 / kg

4. Reducing operational expenses by 5% on an initial amount of €10000 gives: €10000 – (10000 * 5 / 100) = €10000 – €500 = €9500 / month

5. Reducing the sale price by 10% on an initial price of €3/kg gives: €3 – (3 * 10/100) = €3 – €0.30 = €2.70/kg

Statement 9: Alpha Store

Alpha Store is a retail store that sells a variety of products. Alice, the owner, wants to perform some analysis on how her sales and margins are performing. The information for 2020 is as follows:

– Purchase price excluding VAT of the “SuperSoft” jacket: €40
– Selling price excluding tax of the “SuperSoft” jacket: €80
– Quantity sold of “SuperSoft” jackets during the year: 1000 pieces.
– The VAT rate is 20% for this product.

Work to do :

1. Calculate the percentage of margin achieved on the “SuperSoft” jacket excluding VAT.
2. Calculate the sales price including tax of the “SuperSoft” jacket.
3. If the quantity sold of these jackets decreases by 20% in 2021, how many jackets will be sold in 2021?
4. What is the percentage decrease in “SuperSoft” jackets sold from 2020 to 2021?
5. Calculate the overall margin made on the sale of “SuperSoft” jackets in 2020.

Proposed correction:

1. Margin rate = ((PV HT – PA HT) / PA HT) * 100 = ((80€ – 40€) / 40€) * 100 = 100%, so Alpha Store makes a margin of 100% on the “SuperSoft” jacket.

2. The sales price including VAT is calculated by adding VAT to the sales price excluding VAT. Sales price including VAT = PV excluding VAT + (PV excluding VAT * VAT rate) = €80 + (€80 * 20%) = €96. Therefore the sales price including VAT of the “SuperSoft” jacket is €96.

3. If the quantity sold decreases by 20%, the new quantity will be 1000 – (1000 * 20%) = 800 jackets. So in 2021, 800 “SuperSoft” jackets will be sold.

4. The percentage decrease is calculated as follows: (Decrease / Original Quantity) * 100 = ((1000-800) / 1000) * 100 = 20%. So, there is a 20% decrease in sales of “SuperSoft” jackets from 2020 to 2021.

5. Overall margin = Unit margin * quantity sold = (PV HT – PA HT) * quantity sold = (80€ – 40€) * 1000 = 40,000€. Therefore, the overall margin made on the sale of “SuperSoft” jackets in 2020 is 40,000€.

Statement 10: Fashion Trends

Fashion Trends, a company specializing in the sale of high-end clothing, is taking into account various changes in its business and financial environment. The main changes concern costs, sales, margins and taxes.

1. Increase in the cost of raw materials: The cost of fabrics, which is the highest production cost, has increased by 15%.

2. Change in sales volumes: Sales of dresses, their best-selling product, increased by 25%.

3. Margin policy: The company decides to increase its gross margin on its pants by 10%.

4. Tax change: The government has decided to reduce the VAT rate applicable to clothing from 20% to 5%.

5. New Sales Price Strategy: The company has decided to reduce the sales prices excluding tax of its shirts by 7%.

Work to do :

1. How much does the fabric cost now if its original price was €50 per meter?
2. If the company initially sold 200 dresses per month, how many does it sell now?
3. If the company's gross margin on pants was initially €20 per unit, how much is it now?
4. What is the new impact of VAT on a product whose price excluding VAT was initially €120?
5. What is the new selling price excluding tax of a shirt if its initial price was €100?

Proposed correction:

1. The cost of the fabric after a 15% increase is 50€ *(1+15/100) = 57.5€.

2. The company now sells 200 dresses * (1+25/100) = 250 dresses.

3. The gross margin on pants after a 10% increase is €20 * (1+10/100) = €22.

4. The new VAT impact is: (120€ * 5%) = 6€. Before the tax change, the VAT impact was (120€ * 20%) = 24€.

5. The new selling price excluding tax is €100 * (1-7/100) = 9