Welcome to this article on exercises on business calculations and more specifically on how to calculate VAT from the inclusive of VAT. You will find here 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 calculate VAT from the inclusive of tax in business calculations without any worries.
In this section:
TechGuru App
States :
TechGuru company specializes in the sale of electronic equipment. The company's products are subject to a VAT rate of 20%.
1. The company recorded total sales including VAT of €12 during the last month.
2. For a specific item, whose sales price including VAT is €300, the company sold 50 units last month.
3. Next, the product manager is concerned about the profitability of two specific products. One sells for €1200 including VAT and the other for €750 including VAT. He wants to determine the corresponding VAT for each of these products.
4. The marketing manager offers a promotion offering a 15% discount on all products for the next month. He wonders how this will affect the amount of VAT to be collected.
Work to do :
1. How much VAT did TechGuru collect for the last month?
2. Calculate the amount of VAT that would be collected for the 50 units sold of the specific product at €300 including VAT.
3. What would be the VAT for products at €1200 including tax and €750 including tax respectively?
4. What impact would the 15% promotion have on the amount of VAT collected on sales?
Proposed correction:
1. To calculate the amount of VAT from the turnover including tax, we use the formula for tax included: VAT = (Turnover including tax ÷ (1 + VAT rate)) x VAT rate.
So, VAT = (€12000 ÷ (1 + 0,20)) x 0,20 = €2000
2. For the product sold at €300 including tax, we apply the same formula by multiplying by the number of units sold:
VAT = ((€300 ÷ (1 + 0,20)) x 0,20) x 50 = €2500
3. For products sold at €1200 including tax and €750 including tax:
For the product at €1200, VAT = (€1200 ÷ (1 + 0,20)) x 0,20 = €200
For the product at €750, VAT = (€750 ÷ (1 + 0,20)) x 0,20 = €125
4. The 15% price reduction will reduce the amount of VAT collected.
For example, for a product that originally cost €300 including tax, the new price would be €255 including tax (after a 15% reduction).
The new VAT would be ((€255 ÷ (1 + 0,20)) x 0,20) = €42,5. The impact of this price reduction would be a decrease in the amount of VAT collected.
Summary of Formulas Used:
1. VAT = (Turnover incl. VAT ÷ (1 + VAT rate)) x VAT rate; to calculate the VAT amount from sales incl. VAT.
2. New VAT PV = Old VAT PV x (1 – Reduction rate); to determine the new VAT sales price after a price reduction.
Flamenco Arts Application
States :
Flamenco Arts, a company specializing in the sale of paintings and works of art, traditionally used management software that automatically calculated VAT for each sale. However, following a software malfunction, they have to calculate VAT manually. In addition, they realize that they have not applied the correct VAT rate for some works of art.
The cost including tax for five works of art sold is given below:
1. Work A: €2
2. Work B: €4
3. Work C: €5
4. Work D: €3
5. Work E: €5
The VAT rate initially applied to all works is 20%. However, they realize that the rate for work A and B should be 5,5%.
Work to do :
1. Calculate the VAT for each work of art using the VAT rate initially applied (20%).
2. Correct the VAT rate for work A and B and recalculate the VAT.
3. What is the difference between the initially calculated and corrected VAT for work A and B?
4. Compare the original total VAT amount for all artworks with the corrected amount.
5. Analyze the results obtained in the previous questions.
Proposed correction:
1. Calculation of VAT at 20%:
VAT = VAT included – (TTC ÷ (1 + VAT rate))
For work A: VAT = €2 – (€400 ÷ (2 + 400/1)) = €20
Work B: VAT = €4 – (€600 ÷ (4 + 600/1)) = €20
Work C: VAT = €5 – (€400 ÷ (5 + 400/1)) = €20
Work D: VAT = €3 – (€000 ÷ (3 + 000/1)) = €20
Work E: VAT = €5 – (€200 ÷ (5 + 200/1)) = €20
2. VAT correction for work A and B at 5,5%:
For work A: VAT = €2 – (€400 ÷ (2 + 400/1)) = €5,5
Work B: VAT = €4 – (€600 ÷ (4 + 600/1)) = €5,5
3. VAT difference:
For work A: Difference = €400 – €126 = €274
Work B: Difference = €767 – €241 = €526
4. Comparison of the initial total VAT amount with the corrected amount:
Total amount of initial VAT = €400 + €767 + €900 + €500 + €867 = €3
Total amount of corrected VAT = €126 + €241 + €900 + €500 + €867 = €2
5. Analyses:
We can see a noticeable readjustment of the VAT values when the correct rate is applied. This results in a substantial decrease in the total VAT amount of €800. This shows how important it is to ensure that the correct VAT rate is applied.
Summary of Formulas Used:
– Calculation of VAT: VAT = VAT inc. – (TTC ÷ (1 + VAT rate))
– Comparison of VAT amounts: Difference = Initial VAT – Corrected VAT
– Total VAT amount: Sum of VAT calculated for each product
Gourmet Delight App
States :
We are in the company Gourmet Delight, specialized in the sale of high quality food products. You are responsible for financial management and lately you have carried out various transactions.
1) You sold 50 bottles of extra virgin olive oil at a tax-inclusive price of €30 each.
2) You have purchased a new coffee machine at a cost of €1200 including tax.
3) You bought 100 kg of fine cheeses at €25 including tax per kg.
4) You sold 200 bottles of wine at €15 including tax each.
5) You have purchased furniture for your store at a cost of €800 including tax.
In all these cases, the applicable VAT rate is 20%.
Work to do :
1) How much VAT did you pay on the purchase of the coffee machine?
2) What is the VAT you collected on the sale of olive oil?
3) How much VAT is charged on the purchase of cheese?
4) What is the VAT you collected on the sale of wine?
5) How much VAT did you pay on the purchase of the furniture?
Proposed correction:
1) For the calculation of VAT from the inclusive of VAT, we use the formula [VAT = inclusive of VAT – (inclusive of VAT ÷ (1 + VAT rate/100))]. So, for the coffee machine, the VAT is €1200 – (€1200 ÷ (1 + 20/100)) = €200.
2) For olive oil, we sold 50 bottles at a VAT-inclusive price of €30 each. Thus, the VAT collected will be [50 x (€30 – (€30 ÷ (1 + 20/100)))] or €250.
3) For the purchase of cheese, we know that the price including tax is €25 per kg and that we bought 100 kg. The VAT will therefore be [100 x (€25 – (€25 ÷ (1 + 20/100)))] or €416,67.
4) For wine, 200 bottles were sold at €15 including VAT each. The VAT collected will therefore be [200 x (€15 – (€15 ÷ (1 + 20/100)))] or €500.
5) For the purchase of the furniture, the company paid €800 including VAT. The VAT is therefore equal to €800 – (€800 ÷ (1 + 20/100)) = €133,33.
Summary of Formulas Used:
– Calculation of VAT from the inclusive of tax: VAT = inclusive of tax – (inclusive of tax ÷ (1 + VAT rate/100))
– Calculation of VAT for a quantity: VAT = quantity x (TTC – (TTC ÷ (1 + VAT rate/100)))
Guillaume's Words Application
States :
Guillaume owns a bookstore called "Les Mots de Guillaume" and frequently works with different French publishing houses. Guillaume is faced with a situation where he must deduct the VAT amount from the VAT-inclusive price of several books he has recently sold. You are his financial assistant and he asks you to help him solve this problem by giving you the following information:
1. The first book, a flagship novel from a popular publishing house, was sold for €24,90 including tax.
2. The second book, a children's comic strip, was sold for €14,95 including tax.
3. The third book, a travel guide to France, was sold for €26,00 including tax.
4. The fourth book, an autobiography of a famous person, was sold for €30,00 including tax.
5. The fifth book, a school textbook, was sold for €34,90 including tax.
He specifies that the VAT rate applied is 5,5%.
Work to do :
1. How much is the VAT for the first book?
2. How much is the VAT for the second book?
3. How much is the VAT for the third book?
4. How much VAT is there on the fourth book?
5. How much VAT is charged on the fifth book?
Proposed correction:
1. The VAT amount for the first book is €24,90 ÷ (1 + (5,5 ÷ 100)) = €1,30
2. The VAT amount for the second book is €14,95 ÷ (1 + (5,5 ÷ 100)) = €0,78
3. The VAT amount for the third book is €26,00 ÷ (1 + (5,5 ÷ 100)) = €1,36
4. The VAT amount for the fourth book is €30,00 ÷ (1 + (5,5 ÷ 100)) = €1,57
5. The VAT amount for the fifth book is €34,90 ÷ (1 + (5,5 ÷ 100)) = €1,83
Summary of Formulas Used:
To calculate the amount of VAT from the price including VAT, we used the following formula:
VAT = Price including VAT ÷ (1 + (VAT rate ÷ 100))
Where “Price including VAT” is the Price including all taxes and “VAT rate” is the Value Added Tax rate (expressed as a percentage).
BioHealth Application
States :
You work for BioHealth, a company specializing in the sale of organic food products. You have recently been promoted to the position of financial manager and have been asked to perform some VAT calculations. You have a list of products with their prices including VAT and you need to calculate the VAT applied to these products. The VAT rates that you know are 20% for some products and 5,5% for others.
1. Organic apples: €7,50 (VAT at 20%)
2. Organic orange juice: €3,95 (VAT at 5,5%)
3. Organic almond milk: €2,98 (VAT at 5,5%)
4. Organic wholemeal bread: €2,70 (VAT at 5,5%)
5. Organic olive oil: €8,60 (VAT at 20%)
Work to do :
1. Calculate the VAT for the product “Organic apples”
2. Calculate the VAT for the product “Organic orange juice”
3. Calculate the VAT for the product “Organic almond milk”
4. Calculate the VAT for the product “Organic wholemeal bread”
5. Calculate VAT for the product “Organic olive oil”
Proposed correction:
1. To calculate VAT from the inclusive of tax, we use the formula: VAT = inclusive of tax – (inclusive of tax / (1 + VAT rate)). For organic apples, this gives: VAT = €7,50 – (€7,50 / 1,20) = €1,25
2. For organic orange juice, we use the same formula with a VAT rate of 5,5%: VAT = €3,95 – (€3,95 / €1,055) = €0,20
3. For organic almond milk, we do the same: VAT = €2,98 – (€2,98 / €1,055) = €0,14
4. The calculation is the same for organic wholemeal bread: VAT = €2,70 – (€2,70 / 1,055) = €0,13
5. Finally, for organic olive oil, we use the initial formula with a VAT rate of 20%: VAT = €8,60 – (€8,60 / €1,20) = €1,43
Summary of Formulas Used:
– To calculate VAT from the price including VAT, we use the formula: VAT = including VAT – (including VAT ÷ (1 + VAT rate))
Sweet Treat Application
States :
You are the financial director of the company Régale-Sucré. As usual, you must check the monthly sales report for gourmet desserts. Here are the costs including tax for the five best-selling products:
1. Tarte Tatin: €23,80 incl. tax
2. Raspberry tiramisu: €21,10 incl. VAT
3. Vanilla millefeuille: €27,60 incl. tax
4. Lemon cheesecake: €25,90 incl. VAT
5. Chocolate profiteroles: €21,50 incl. tax
The VAT applied in your company is 20%.
Work to do :
1. Calculate the VAT amount for the Tarte Tatin.
2. Calculate the VAT amount for the Raspberry Tiramisu.
3. Calculate the VAT amount for the Vanilla Millefeuille.
4. Calculate the VAT amount for the Lemon Cheesecake.
5. Calculate the VAT amount for the Chocolate Profiteroles.
Correction suggestion:
1. To calculate VAT from the amount including VAT, we use the formula: VAT = amount including VAT ÷ (1 + (VAT rate ÷ 100)) x (VAT rate ÷ 100)
So, the VAT for the Tarte Tatin is: €23,80 ÷ (1 + (20 ÷ 100)) x (20 ÷ 100) = €3,96
2. The VAT for Raspberry Tiramisu is: €21,10 ÷ (1 + (20 ÷ 100)) x (20 ÷ 100) = €3,52
3. The VAT for the Vanilla Millefeuille is: €27,60 ÷ (1 + (20 ÷ 100)) x (20 ÷ 100) = €4,60
4. The VAT for the Lemon Cheesecake is: €25,90 ÷ (1 + (20 ÷ 100)) x (20 ÷ 100) = €4,32
5. The VAT for Chocolate Profiteroles is: €21,50 ÷ (1 + (20 ÷ 100)) x (20 ÷ 100) = €3,58
Summary of Formulas Used:
– VAT = amount including VAT ÷ (1 + (VAT rate ÷ 100)) x (VAT rate ÷ 100): this formula is used to calculate the VAT amount from the amount including VAT
TechInnov Application
States :
TechInnov Company is a well-established supplier of innovative electronic gadgets. It specializes in selling smartphones, tablets, and laptops. You are the CFO of this company and have been entrusted with the responsibility of handling various financial tasks.
For the last quarter, you achieved a turnover (including tax) of:
– €50 for smartphones
– €37 for tablets
– €45 for laptops
The VAT applied is 20% for smartphones and laptops, while for tablets the VAT is 5,5%.
Work to do :
1. How much VAT is charged on smartphones sold?
2. How much VAT is charged on the tablets sold?
3. How much VAT is charged on laptops sold?
4. What is the total amount of VAT collected by TechInnov?
5. How would you check if the VAT has been calculated correctly?
Proposed correction:
1. The VAT amount for smartphones is calculated as follows: (Price including VAT / (1 + VAT rate)) x VAT rate. Therefore, (€50 / (000+1/20)) x 100/20 = €100.
2. The VAT amount for tablets is calculated as follows: (Price including VAT / (1 + VAT rate)) x VAT rate. Therefore, (€37 / (500+1/5.5)) x 100/5.5 = €100.
3. The VAT amount for laptops is calculated as follows: (Price including VAT / (1 + VAT rate)) x VAT rate. Therefore, (€45 / (000+1/20)) x 100/20 = €100.
4. The total amount of VAT collected by the company TechInnov is therefore the sum of the VAT on smartphones, tablets and laptops, i.e.: €8 + €333,33 + €1 = €883,98.
5. To check if the VAT has been calculated correctly, you can perform a reverse check by subtracting the calculated VAT amount from the inclusive of VAT price. This should give you the amount excluding tax (ET). If the amounts match, this means that the VAT has been calculated correctly.
Summary of Formulas Used:
– To calculate VAT from the VAT inclusive: (Price inclusive of VAT / (1 + VAT rate)) x VAT rate.
– To check whether the VAT has been calculated correctly, you can carry out a reverse check by subtracting the calculated VAT amount from the price including VAT, to obtain the amount excluding VAT.
Flowery Application
States :
Fleurie is a plant and flower sales company. Recently, the tax authorities asked them to provide detailed reports on the VAT amounts they paid on their sales. Unfortunately, they had problems with their accounting system and were only able to recover the VAT-inclusive amounts of their sales. They turn to you, their financial management consultant, to help them solve this problem.
Work to do :
1. If Fleurie sold a tree for €120 including VAT, what is the amount of VAT included according to a VAT rate of 20%?
2. What is the amount of VAT included in a sale of €250 including VAT if the VAT rate applied is 5,5%?
3. In a sale of €670 including VAT where the VAT rate is 20%, how much is VAT?
4. A seed sale generates a tax-inclusive income of €75 with a VAT rate of 5,5%. How much of this amount is dedicated to VAT?
5. If a total sale of plants for the day is €1500 including VAT with a VAT rate of 20%, how much is the VAT for this sale?
Proposed correction:
1. VAT = VAT included – (TTC ÷ (1 + VAT rate)) = €120 – (€120 ÷ 1,20) = €20
2. VAT = €250 – (€250 ÷ 1,055) = approximately €13,22
3. VAT = €670 – (€670 ÷ 1,20) = €112
4. VAT = €75 – (€75 ÷ 1,055) = approximately €3,95
5. VAT = €1500 – (€1500 ÷ 1,20) = €250
Summary of Formulas Used:
– Formula for calculating VAT from the inclusive tax: VAT = inclusive tax – (inclusive tax ÷ (1 + VAT rate))
The Beautiful Car App
States :
The company La Belle Voiture is a car dealership that sells different types of cars. In January, it sold a car for €36 including VAT. The final sale price includes a VAT of 000,00%. In the same month, it also sold a vintage collector's car for €20 including VAT, the VAT applicable for this category is 15%.
Work to do :
1. How much is the VAT on the first car sold?
2. How much is the VAT on the sold classic car?
3. What is the price excluding tax of the first car sold?
4. What is the price excluding tax of the collector car sold?
5. What is the total VAT amount for the two cars sold?
Proposed correction:
1. For the first car, the VAT amount is calculated as follows:
VAT = Price including VAT ÷ (1 + VAT rate) x VAT rate
VAT = €36 ÷ (000 + 1) x 0,20 = €0,20.
2. For the collector's car, the amount of VAT is calculated as follows:
VAT = Price including VAT ÷ (1 + VAT rate) x VAT rate
VAT = €15 ÷ (000,00 + 1) x 0,055 = €0,055.
3. The price excluding tax of the first car sold is calculated by subtracting the amount of VAT from the price including tax. That is:
Price excluding VAT = Price including VAT – VAT
Price excluding VAT = €36 – €000,00 = €6.
4. The price excluding tax of the collector car sold is calculated by subtracting the amount of VAT from the price including tax. That is:
Price excluding VAT = Price including VAT – VAT
Price excluding VAT = €15 – €000,00 = €773,01.
5. The total VAT amounts for the two cars sold are the sum of the VATs calculated previously:
Total VAT = VAT car 1 + VAT car 2
Total VAT = €6 + €000,00 = €773,01.
Summary of Formulas Used:
1. VAT = Price including VAT ÷ (1 + VAT rate) x VAT rate
2. Price excluding VAT = Price including VAT – VAT
3. Total VAT = Sum of VAT for each car sold
TechnoWorld Application
States :
TechnoWorld sells various technological equipment. A customer recently purchased a batch of laptops for a total of €6 including VAT and would like to understand how VAT is calculated from this inclusive price.
Work to do :
1) What is the amount of VAT if the applicable rate is 20%?
2) What would be the amount of VAT if the applicable rate was 5,5%?
3) Calculate the price excluding VAT for the VAT rate of 20%.
4) Calculate the price excluding VAT for the VAT rate of 5,5%.
5) Did the customer pay more VAT with a 20% rate than with a 5,5% rate?
Proposed correction:
1) The calculation of VAT from an amount inclusive of VAT is carried out according to the following formula: VAT = Price inclusive of VAT ÷ (1 + (VAT rate ÷ 100)) x VAT rate ÷ 100. Thus, with a VAT rate of 20%, the amount of VAT is €6 ÷ 000 x 1,20 = €0,20.
2) Applying the same formula with a VAT rate of 5,5%, the VAT amount would be €6 ÷ 000 x 1,055 = €0,055.
3) To calculate the price excluding tax (HT) with a VAT of 20%, the formula is: Price excluding tax = Price including tax / (1 + (VAT rate ÷ 100)). We therefore obtain: Price excluding tax = €6 / 000 = €1,20.
4) Similarly, with a VAT rate of 5,5%, the price excluding VAT would be: €6 / 000 = €1,055.
5) Yes, the customer paid more VAT with a rate of 20% than with a rate of 5,5%. Indeed, the amounts calculated previously show that the VAT is higher with a rate of 20% than with a rate of 5,5% (€1000 versus €287,30).
Summary of Formulas Used:
– Calculation of VAT from an amount including VAT: VAT = Price including VAT ÷ (1 + (VAT rate ÷ 100)) x VAT rate ÷ 100
– Calculation of the price excluding VAT: Price excluding VAT = Price including VAT / (1 + (VAT rate ÷ 100))
Local Flavors Application
States :
We are at Les Saveurs du Terroir, a company that distributes local products in France. The manager of the company needs your help to analyze his invoices and determine the VAT on different transactions.
Here is some useful information for the exercise:
– Product A: Price including tax = €48,00 (VAT at 20%)
– Product B: Price including tax = €55,00 (VAT at 5,5%)
– Product C: Price including tax = €45,00 (VAT at 20%)
Work to do :
1. Calculate the amount of VAT for product A.
2. Calculate the amount of VAT for product B.
3. Calculate the amount of VAT for product C.
4. What is the difference between the Price including VAT and the Price excluding VAT?
5. Analyze and evaluate the impact of VAT on the price of products for the consumer.
Proposed correction:
The formula for calculating VAT from the inclusive tax is:
VAT = Price including VAT – (Price including VAT ÷ (1+VAT rate%))
1. For product A: VAT = €48,00 – (€48,00 ÷ (1+20%)) = €48,00 – €40,00 = €8,00.
2. For product B: VAT = €55,00 – (€55,00 ÷ (1+5,5%)) = €55,00 – €52,13 = €2,87.
3. For product C: VAT = €45,00 – (€45,00 ÷ (1+20%)) = €45,00- €37,50 = €7,50.
4. The difference between the Price including VAT and the Price excluding VAT represents the amount of VAT.
5. VAT increases the cost of products for the consumer. In fact, it is added to the price excluding tax and must be paid by the consumer. In this example, for product A, the consumer pays €8,00 in VAT, for product B he pays €2,87 in VAT and for product C he pays €7,50 in VAT.
Summary of the formulas used:
– VAT = Price including VAT – (Price including VAT ÷ (1+VAT rate%))