Welcome to this article on exercises on business calculations and more specifically on how to remove VAT from a price. Here you will find no less than 11 detailed corrected management exercises on business calculations for Operational Management.
At the end of this article, you will know how to remove VAT from a price in business calculations without any worries.
In this section:
Techno Products Application
States :
You are the financial manager of the company Techno Products, which specializes in the sale of technological products. Following an internal audit, you must recalculate certain revenues in HT (Excluding tax) from TTC (All taxes included) amounts. The VAT rate used by the company is 20%.
1. The price including tax of a smartphone is €600.
2. The price including tax of a tablet is €360.
3. The price including tax of a laptop is €1.
4. The price including tax of a Bluetooth headset is €180.
5. The price including tax of a connected watch is €240.
Work to do :
1. How to calculate the price excluding tax of the smartphone from the price including tax?
2. How to calculate the tax-free price of the tablet from the tax-inclusive price?
3. How to calculate the price excluding tax of the laptop from the price including tax?
4. How to calculate the tax-free price of the Bluetooth headset from the tax-inclusive price?
5. How to calculate the price excluding tax of the smartwatch from the price including tax?
Proposed correction:
1. To calculate the price excluding tax (HT) from the price including all taxes (TTC), we use the following formula:
Price excluding VAT = Price including VAT ÷ (1 + VAT rate/100).
So, the price excluding tax of the smartphone is: €600 ÷ (1 + 20/100) = €500.
2. Using the same formula, the price excluding VAT of the tablet is: €360 ÷ (1 + 20/100) = €300.
3. The price excluding VAT of the laptop is therefore: €1200 ÷ (1 + 20/100) = €1000.
4. The price excluding VAT of the Bluetooth headset is: €180 ÷ (1 + 20/100) = €150.
5. The price excluding tax of the connected watch is: €240 ÷ (1 + 20/100) = €200.
Summary of Formulas Used:
– Price excluding VAT = Price including VAT ÷ (1 + VAT rate/100)
Coffee House App
States :
You work as a management assistant for the company Maison du Café. The company buys coffee beans from different suppliers and then sells them on its website to its customers.
When you look at your sales data, you notice that some sales prices include VAT, which is currently set at 20% in France where your business is located.
Work to do :
1. If the selling price including tax of a packet of coffee is €6, what is the price excluding tax?
2. If another packet of coffee costs €15 including tax, how much does it cost excluding tax?
3. What is the amount of VAT for a packet of coffee sold at €20 including VAT?
4. How to calculate the price excluding VAT from the price including VAT?
5. Why is it important to know how to deduct VAT from a price?
Proposed correction:
1. To find the price excluding VAT from the price including VAT, we use the formula: Price excluding VAT = Price including VAT ÷ (1 + (VAT rate / 100)). Here, the price excluding VAT = €6 ÷ (1 + 20 ÷ 100) = €5.
2. Similarly, for a packet of coffee at €15 including tax, the price excluding tax will be: Price excluding tax = €15 ÷ (1 + 20 ÷ 100) = €12,5.
3. To find the VAT amount, subtract the price excluding VAT from the price including VAT. In this case, VAT = €20 – (€20 ÷ (1 + 20 ÷ 100)). Therefore, VAT = €20 – €16,67 = €3,33.
4. To deduce the price excluding VAT from the price including VAT, divide the price including VAT by 1 plus the VAT rate divided by 100: Price excluding VAT = Price including VAT ÷ (1 + VAT rate ÷ 100).
5. It is important to know how to remove VAT from a price in order to distinguish the part of the sale price that goes to the company from that which goes to the State. This also allows for fairer price comparisons between different countries and to better anticipate the financial consequences of a change in the VAT rate.
Summary of Formulas Used:
Formula for calculating the price excluding VAT from the price including VAT: Price excluding VAT = Price including VAT ÷ (1 + (VAT rate / 100)).
Formula for calculating the amount of VAT: VAT = Price including VAT – Price excluding VAT.
Chronicles Application
States :
Chronicles Publishing House specializes in publishing science fiction books. The company plans to publish its latest book Spaceship Detective. The sales price including VAT is €24,90. In France, the VAT rate on books is 5,5%. However, the company must calculate the sales price excluding VAT, to determine its margin and profits. In addition, the management of 'Chronicles' is considering changing its pricing policy in the near future.
Work to do :
1 – Calculate the sales price excluding tax (HT) of the book Spaceship Detective.
2 – Suppose Chronicles decides to increase the price of the book to €27,90, including VAT. Calculate the new selling price excluding VAT.
3 – What is the difference between the two calculated prices excluding VAT?
4 – What is the amount of VAT for each book, in both price scenarios?
5 – If the company decides not to pass on the increase in the VAT price to its customers and absorbs the additional cost. What would be the impact on the new VAT price and how does this affect the amount of VAT?
Proposed correction:
1 – To calculate the price excluding VAT from the price including VAT, we use the following formula:
Price excluding VAT = Price including VAT / (1 + VAT rate / 100)
That is: Price excluding tax = €24,90 ÷ (1 + 5,5 / 100) = €23,64
2 – Applying the same formula, we obtain:
Price excluding VAT = €27,90 ÷ (1 + 5,5 / 100) = €26,45
3 – The difference between the two prices excluding tax is:
€26,45 – €23,64 = €2,81
4 – The amount of VAT for each book in both price scenarios is calculated by subtracting the price excluding VAT from the price including VAT:
* For the first prize: €24,90 – €23,64 = €1,26
* For the second prize: €27,90 – €26,45 = €1,45
5 – If Chronicles decides not to pass on the increase in VAT to its customers, it must absorb the additional cost. This means that the price excluding VAT remains the same: €23,64. The increase in VAT will therefore be greater than expected, i.e.:
€1,45 – €1,26 = €0,19 extra per book.
Summary of Formulas Used:
– Price excluding VAT = Price including VAT ÷ (1 + VAT rate / 100)
– VAT amount = Price including tax – Price excluding tax
– Difference = New price excluding VAT – Old price excluding VAT
Gisele's Delights Application
States :
The company Les Délices de Gisèle is a bakery and pastry shop renowned for its delicious breads and freshly prepared pastries. "Les Délices de Gisèle" sells a range of diverse and varied products, each with a different price including all taxes (i.e. including VAT (Value Added Tax)).
Here is a list of some products with their prices including VAT and the corresponding VAT rates:
1) A traditional baguette: €1,10 (VAT: 5,5%)
2) A chocolate éclair: €2,50 (VAT: 5,5%)
3) A chicken and raw vegetable sandwich: €4,50 (VAT: 10%)
4) A mini fruit cake: €3,20 (VAT: 5,5%)
5) A cappuccino: €2,60 (VAT: 20%)
Work to do :
1) Calculate the price excluding tax (excluding VAT) of the traditional baguette.
2) Calculate the price excluding tax of the chocolate éclair.
3) Calculate the price excluding tax of the chicken and raw vegetables sandwich.
4) Calculate the price excluding tax of the mini fruit cake.
5) Calculate the price excluding tax of the cappuccino.
Proposed correction:
1) To calculate the price excluding VAT of a product from its price including VAT, we use the formula: Price excluding VAT = Price including VAT ÷ (1 + (VAT rate/100)) = €1,10 ÷ (1 + 5,5/100) = €1,04
2) Price excluding tax of the chocolate éclair = €2,50 ÷ (1 + 5,5/100) = €2,37
3) Price excluding tax for the chicken and raw vegetable sandwich = €4,50 ÷ (1 + 10/100) = €4,09
4) Price excluding VAT of the mini fruit cake = €3,20 ÷ (1 + 5,5/100) = €3,03
5) Price excluding tax of cappuccino = €2,60 ÷ (1 + 20/100) = €2,17
Summary of Formulas Used:
Formula used to deduce the price excluding VAT from the price including VAT: Price excluding VAT = Price including VAT ÷ (1 + (VAT rate/100))
Williams Auto App
States :
Williams Auto is a garage that sells both new and used cars. The company works with several suppliers to obtain vehicles from different brands.
Rigorous financial management of the company involves determining precisely the amount of VAT applied to each sale, and therefore, understanding how to remove VAT from a price.
Recent sales by the company include:
1. A new Tesla Model S sold for €75 including tax
2. A used Renault Clio sold for €15 including tax
The VAT rate applicable to the sale of new vehicles is 20%. For used vehicles, the rate is 5,5%.
Work to do :
1. What is the price excluding tax of the Tesla Model S and the Renault Clio?
2. How much VAT is charged for each sale?
3. What is the company's margin rate on the sale of each car?
4. How does the VAT rate influence the margin rate?
5. If the company offers a 10% discount on the next purchase, how will this affect the net price and the margin rate?
Proposed correction:
1. To calculate the price excluding VAT, we use the formula: Price including VAT / (1 + (VAT rate / 100)). Therefore, the price of the Tesla Model S is €75 ÷ (000 + 1/20) = €100 excluding VAT. The price of the Renault Clio is €62 ÷ (500 + 15/000) = €1 excluding VAT.
2. VAT is the difference between the price including VAT and the price excluding VAT. So for the Tesla Model S, the VAT is €75 – €000 = €62. For the Renault Clio, it is €500 – €12 = €500.
3. We do not have the necessary information on the purchase price to calculate the margin rate for each vehicle.
4. The VAT rate does not change the margin rate since the latter is calculated on the basis of the purchase price and the sales price excluding tax.
5. A 10% reduction applied to the price excluding VAT will also reduce the sales price excluding VAT, and consequently the margin rate, unless the company manages to negotiate more favorable purchasing conditions with its suppliers.
Summary of Formulas Used:
– Price excluding VAT = Price including VAT / (1 + (VAT rate / 100))
– VAT = Price including tax – Price excluding tax
– Margin rate = ((Sale Price excluding VAT – Purchase Price excluding VAT) / Purchase Price excluding VAT) * 100
– Post-reduction margin rate = ((Sale Price excluding VAT * (1-10%) – Purchase Price excluding VAT) / Purchase Price excluding VAT) * 100
Chic and Elegance Application
States :
Chic et Élégance is a company specializing in the sale of luxury brand clothing. It wants to review its pricing strategy for its items. You are the company's financial expert and you are responsible for analyzing and reviewing the sales prices of certain items after removing the Value Added Tax (VAT). The VAT applied to clothing items is 20%.
The products concerned are:
– A designer coat, sold for €3 including tax.
– A designer handbag, sold for €2 including tax.
– A branded set (jacket and pants), sold for €4 including tax.
– A branded perfume, sold for €150 including tax.
– A branded wallet, sold for €350 including tax.
Work to do :
1. Calculate the price excluding tax (HT) for each item.
2. How will you implement these tax-free prices into the company's pricing strategy?
3. How can the company Chic et Élégance maintain its profitability while removing VAT from its sales prices?
4. What could be the impact of this strategy on the image of the Chic et Élégance company?
5. What advice would you give the company to manage the potential consequences of this price change?
Proposed correction:
1. The calculation of the price excluding VAT is obtained by dividing the price including VAT by 1 + the VAT rate. In this case, it is 1,20 (1 + 0,20). Thus, the price excluding VAT of each item is:
– Coat: 3000 ÷ 1,20 = €2
– Handbag: 2500 ÷ 1,20 = €2
– Together: 4000 ÷ 1,20 = €3
– Perfume: 150 ÷ 1,20 = €125
– Wallet: 350 ÷ 1,20 = €291,67
2. The implementation of these prices first requires communication both internally (to employees) and externally (to customers). It must be explained that the company is adopting a pricing strategy excluding VAT and that there will be no increase in costs for consumers. The company can also consider renegotiating its contracts with its suppliers to reduce purchasing costs and thus compensate for the loss of VAT.
3. To maintain profitability while removing VAT from sales prices, the company can consider several options. It can optimize its operating costs, look for ways to increase sales volumes or consider selling complementary value-added products.
4. The perception of the company by its customers could be improved because the prices will be clearer and more transparent. However, it is crucial that the company communicates this change properly to avoid misunderstandings and confusion.
5. One of the main tips would be to adopt a good communication strategy to clearly explain the price change. In addition, the company should closely monitor the impact of this change on sales and profitability and be ready to make adjustments if necessary.
Summary of Formulas Used:
– Calculation of the price excluding VAT from the price including VAT: Price including VAT ÷ (1 + VAT rate)
– Maintain profitability: Optimize operating costs + Increase sales volumes + Sell value-added products.
Luxury Deco Application
States :
In our scenario, we will position ourselves from the point of view of the company Luxe Déco, which is a company specializing in the sale of high-end interior decorations. The administrative director of Luxe Déco is currently reviewing the pricing positioning of the company's products and needed you, an expert in financial management, to better understand how VAT works.
Work to do :
1. What is the formula for calculating the amount of VAT from a price including VAT?
2. The price of a lamp is displayed at €120,00 including VAT. What is the amount of VAT if the VAT rate is 20%?
3. A vase is sold for €60,00 including VAT with a VAT rate of 5,5%. What is the amount of VAT?
4. What is the formula for calculating the price excluding VAT from the price including VAT and VAT?
5. From the answers to questions 2 and 4, calculate the price excluding VAT of the lamp.
Proposed correction:
1. The formula for calculating the VAT amount from a price including VAT is: VAT amount = Price including VAT – (Price including VAT / (1 + VAT rate/100))
2. To calculate the VAT amount of the lamp, we use the formula given above and we obtain: VAT amount = €120,00 – (€120,00 / (1 + 20/100)) = €120,00 – €100,00 = €20,00
3. Similarly, for the vase, we obtain: VAT amount = €60,00 – (€60,00 / (1 + 5,5/100)) = €60,00 – €56,88 = €3,12
4. The formula for calculating the price excluding VAT from the price including VAT and the VAT amount is: Price excluding VAT = Price including VAT – VAT amount
5. Using the formula from question 4, we obtain: Price excluding VAT of the lamp = €120,00 – €20,00 = €100,00
Summary of Formulas Used:
VAT amount = Price including VAT – (Price including VAT / (1 + VAT rate/100))
Price excluding VAT = Price including VAT – VAT amount
Garden Delights Application
States :
The company Les Délices du Jardin specializes in the sale of gardening products. It applies a VAT rate of 20% on all its products. One day, you buy a lawnmower with a price including tax (All Taxes Included) of €360. You want to know the price of this lawnmower excluding tax (HT).
Work to do :
1. What is the formula for removing VAT from a price?
2. How can you calculate the price excluding VAT of the lawnmower?
3. How much VAT is included on this price?
4. Does the company have the right not to tell you the price excluding tax?
5. How can you check your calculation?
Proposed correction:
1. The formula for removing VAT from a price including VAT is: Price excluding VAT = Price including VAT ÷ (1 + (VAT rate/100)).
2. To calculate the price excluding VAT of the lawnmower, we apply the formula: Price excluding VAT = €360 ÷ (1 + (20/100)) = €300.
3. The amount of VAT on this price is therefore €360 – €300 = €60.
4. The company has a legal obligation to communicate the price excluding VAT and the VAT rate applied in addition to the price including VAT of its products. This allows customers to know the exact breakdown of the cost, and it is also a requirement of accounting and financial management.
5. You can check your calculation by adding the VAT amount to the price excluding VAT. Thus, €300 (price excluding VAT) + €60 (VAT) = €360 (price including VAT), which corresponds to the price you paid.
Summary of Formulas Used:
– Formula to remove VAT from a price including VAT: Price excluding VAT = Price including VAT ÷ (1 + (VAT rate/100))
– Formula for calculating the amount of VAT: Amount of VAT = Price including VAT – Price excluding VAT.
Sunshine App
States :
The company Sunshine, which specializes in the sale of computer equipment, decides to take a closer look at the issue of VAT on its products.
In this week's exercise, the Sunshine manager found that the price including VAT of a computer monitor is €240. The VAT applied is 20%.
Use the information to answer the following questions.
Work to do :
1. What is the formula to use to remove VAT from a price?
2. Calculate the amount of VAT in the case of the computer screen?
3. What is the price excluding VAT of the computer screen?
4. What would the price of the computer screen be excluding VAT if the VAT rate was 5,5%?
5. If the price excluding VAT is increased by €15, what will the new price including VAT be with 20% VAT?
Proposed correction:
1. To remove VAT from a price, the formula is: Price including VAT ÷ (1 + VAT rate/100).
2. The amount of VAT is: Price including VAT * (VAT rate/100) ÷ (1 + VAT rate/100), i.e. €240 * (20/100) ÷ (1 + 20/100) = €40.
3. The price excluding tax of the computer screen is therefore €240 – €40 = €200.
4. If the VAT rate was 5,5%, the price excluding VAT would be: Price including VAT ÷ (1 + VAT rate/100) or €240 ÷ (1 + 5.5/100) = €227,50.
5. If the price excluding VAT increases by €15 to €215, the new price including VAT would be: Price excluding VAT x (1 + VAT rate/100) or €215 x (1 + 20/100) = €258.
Summary of Formulas Used:
– VAT amount = Price including VAT * (VAT rate/100) ÷ (1 + VAT rate/100)
– Price excluding VAT = Price including VAT ÷ (1 + VAT rate/100)
– New Price including VAT = Price excluding VAT x (1 + VAT rate/100)
Royal Jewelery App
States :
La Bijouterie Royale, a company specializing in high-end jewelry, offers different types of products to its customers. In order to improve its financial management, the company wants to know the tax-free price of its products. The products are sold with a 20% VAT.
One of its flagship products, a solid gold ring, is currently selling for €1200 including tax.
Work to do :
1. How to calculate the amount of VAT included in the sale price of the ring?
2. What is the price excluding VAT of the ring?
3. If Bijouterie Royale wishes to set its price excluding VAT and then add VAT to obtain the price including VAT, what would the amounts be?
4. How can we find the applicable VAT rate from the price including VAT and the price excluding VAT?
5. What is the difference between the VAT rate and the VAT amount?
Proposed correction:
1. VAT can be calculated by taking the price including VAT and dividing it by the index 1.2 (100% + 20% of the VAT rate). The formula is therefore: VAT = Price including VAT ÷ 1,2.
In this case, the VAT for the ring is €1200 ÷ 1,2 = €1000. The VAT is therefore €1200 – €1000 = €200.
2. To find the price excluding VAT of a product from its price including VAT and the VAT rate, the formula is: Price excluding VAT = Price including VAT ÷ (1 + VAT rate).
Here, the price excluding tax of the ring is €1200 ÷ 1,2 = €1000.
3. If the company sets its price excluding VAT at €1000 and then adds VAT at 20%, it can calculate the price including VAT using the formula: Price including VAT = Price excluding VAT + (Price excluding VAT x VAT rate).
So, the price including tax of the ring would be €1000 + (€1000 x 0,2) = €1200.
4. The VAT rate can be calculated by using the difference between the price including VAT and the price excluding VAT, then dividing this difference by the price excluding VAT. The formula is therefore: VAT rate = (Price including VAT – Price excluding VAT) ÷ Price excluding VAT x 100.
In this example, the VAT rate would be (€1200 – €1000) ÷ €1000 x 100 = 20%.
5. The VAT rate is the tax percentage set by the State, it is applied to the price excluding VAT to obtain the VAT amount. The difference between the VAT rate and the VAT amount is that the rate is a proportion (a percentage) while the VAT amount is a figure in euros which represents this proportion of the product's price excluding VAT.
Summary of Formulas Used:
1. VAT = Price including VAT ÷ 1,2.
2. Price excluding VAT = Price including VAT ÷ (1 + VAT rate).
3. Price including tax = Price excluding tax x (1 + VAT rate).
4. VAT rate = (Price including tax – Price excluding tax) ÷ Price excluding tax x 100.
Chic Time App
States :
Chic Time is a high-end watch retailer. In order to provide its customers with quality products, the company sources from many suppliers around the world. When they received their supplier's quote, they noticed that the price displayed was inclusive of all taxes. However, the company "Chic Time" needs to know the price excluding taxes in order to determine its subsequent sale price.
According to the quote, the price of a watch from a Swiss supplier is €1 including VAT with a VAT rate of 200%.
Work to do :
1. How to get the price excluding VAT from the price including VAT?
2. Calculate the VAT amount.
3. Calculate the price excluding VAT of the watch.
4. What happens if the VAT rate changes to 10%?
5. Calculate the new price excluding VAT of the watch if the VAT becomes 10%.
Proposed correction:
1. To obtain the price excluding VAT from the price including VAT, we use the formula: Price excluding VAT = Price including VAT ÷ (1 + (VAT rate)).
2. The VAT amount is calculated using the formula: VAT = Price including VAT – Price excluding VAT. Let’s apply this formula once we have calculated the price excluding VAT.
3. Using the formula provided, the price excluding VAT = €1 ÷ (200 + 1) = €0,20.
4. If the VAT rate changes to 10%, this would affect the VAT amount and therefore the price excluding VAT.
5. With a VAT rate of 10%, the new price excluding VAT would be = €1 ÷ (200 + 1) = €0,10.
Summary of Formulas Used:
– Price excluding VAT = Price including VAT ÷ (1 + (VAT rate))
– VAT amount = Price including tax – Price excluding tax