Welcome to this article on exercises on business calculations and more specifically on how to calculate the price excluding 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 the price excluding VAT in business calculations without any worries.
List of formulas used in this article:
| Formulas | Description |
|---|---|
| Margin = Margin Rate x Purchase Price excluding VAT | Calculation of unit margin |
| Selling price excluding VAT = Purchase price excluding VAT + Margin | Calculation of the sales price excluding taxes |
| Price including tax = Price excluding tax (1 + VAT rate) | Calculation of the price including all taxes |
| Margin rate = ((Sale Price excluding VAT – Purchase Price excluding VAT) / Purchase Price excluding VAT) x 100 | Calculation of the margin rate |
| Price excluding VAT from VAT inclusive: Price including VAT ÷ (1 + VAT rate) | Calculation of the price excluding VAT from the price including VAT |
| Calculation of the price including tax from the price excluding tax: Price excluding tax x (1 + VAT rate) | Calculation of the price including tax from the price excluding tax |
| VAT amount = Price including VAT – (Price including VAT ÷ (1 + VAT rate)) | Calculation of the VAT amount |
| Price excluding VAT = Price including VAT – VAT amount | Calculation of the price excluding VAT by subtracting the VAT |
| New Price including VAT = Price excluding VAT x (1 + New VAT Rate) | Calculation of the new price including VAT with a different VAT rate |
| Difference = First Prize including tax – Second Prize including tax | Calculating the difference between two prices including tax with different VAT rates |
| Total purchase cost excluding VAT = Quantity purchased x Unit purchase price excluding VAT | Calculation of the total purchase cost excluding taxes |
| Total profit excluding tax = Unit margin x quantity sold | Calculation of total profit excluding taxes |
| Cost excluding VAT after discount = Catalog price x (1 – discount rate) | Calculation of the cost excluding tax after application of a discount |
| Gross margin = Cost excluding tax after discount x gross margin rate | Gross margin calculation |
| Selling price including tax = Selling price excluding tax + VAT | Calculation of the sales price including tax |
In this section:
Electro-World Application
States :
The electronics company "Electro-World" is considering importing and marketing a new model of smartphone. It has received an offer from its supplier that offers the phone at €200 per unit (purchase price excluding tax). In addition, the company has decided that it wants to earn a 40% margin (in cost margin rate) on each unit sold.
Work to do :
1. What is the amount of unit margin desired by the company Electro-World per smartphone sold?
2. What would be the pre-tax (ET) selling price of the smartphone that the company should set to achieve its desired margin?
3. If the company wants to include the 20% VAT rate in its sales price, what would be the VAT-inclusive price of the smartphone?
4. What would be the margin rate achieved if the company decided to reduce its price excluding tax to €280?
5. What would happen if the company decided to increase its price excluding VAT to €320?
Proposed correction:
1. The desired unit margin amount is calculated using the formula
Margin = Margin Rate x Purchase Price excluding VAT.
This is 40% x €200 = €80.
2. The sales price excluding tax (HT) required to achieve the desired margin is the Purchase Price excluding tax + Margin
or €200 + €80 = €280.
3. The price including tax is calculated by adding VAT to the price excluding tax:
So we have: €280 + (20% x €280) = €336.
4. The margin rate if the price excluding tax was €280 is calculated by the formula ((Sale Price excluding tax – Purchase Price excluding tax) / Purchase Price excluding tax) x 100, i.e. ((€280 – €200) / €200) x 100 = 40%.
5. If the price excluding tax was increased to €320, the calculated margin rate would be ((€320 – €200) / €200) x 100 = 60%.
Summary of Formulas Used:
Margin = Margin Rate x Purchase Price excluding VAT
Selling price excluding VAT = Purchase price excluding VAT + Margin
Price including tax = Price excluding tax (1 + VAT rate)
Margin rate = ((Sale Price excluding VAT – Purchase Price excluding VAT) / Purchase Price excluding VAT) x 100
HighTechShop Application
States :
HighTechShop, a company specializing in the sale of consumer electronics, offers high-quality smartphones. As a financial management expert, you are responsible for helping to calculate the tax-free price (HT) of these products from different values provided. Today, we will take into account the VAT rate of 20%.
1. The price including all taxes (TTC) of a smartphone is €600.
2. For another smartphone model, the price excluding VAT is known to be €500, and the company wants to make a margin of 30%.
3. HighTechShop wants to sell a high-end model for €1200 including tax with a margin of 25%.
4. A new range of smartphones is coming onto the market with a price of €700 including tax and the company is aiming for a margin of 35%.
5. A latest smartphone model is put on sale with a sale price of €750 including tax and the company wants to make a margin of 40%.
Work to do :
1. What is the price excluding VAT of the first smartphone from the price including VAT?
2. What would be the price including tax of the second smartphone?
3. What is the price excluding VAT of the third smartphone based on the price including VAT and the expected margin?
4. What would be the price including tax of the fourth smartphone based on the price excluding tax and the expected margin?
5. What is the price excluding VAT of the fifth smartphone based on the price including VAT and the expected margin?
Proposed correction:
1. The price excluding VAT of the first smartphone is calculated by dividing the price including VAT by 1,20 (VAT rate of 20%) as follows: €600 ÷ 1,20 = €500.
2. The price including tax of the second smartphone is calculated by adding 20% to the price excluding tax. This gives: €500 x 1,20 = €600.
3. For the third smartphone, we first need to calculate the price excluding VAT using the formula:
Price including tax = Price excluding tax + (Price excluding tax x VAT rate).
We therefore obtain: €1200 = Price excluding VAT + Price excluding VAT x 0,20.
By solving this equation, we obtain a price excluding tax of €1000.
4. For the fourth smartphone, we follow the same method as for the second: €700 x 1,20 = €840
5. For the fifth smartphone, we use the same method as for the third, but this time with a margin of 40%. We therefore obtain a price excluding VAT of €625.
Summary of Formulas Used:
1. Price excluding VAT from VAT inclusive: Price including VAT ÷ (1 + VAT rate).
2. Calculation of the Price including tax from the price excluding tax: Price excluding tax x (1 + VAT rate).
3. Calculation of the price excluding VAT: Price including VAT = Price excluding VAT + (Price excluding VAT x VAT rate).
FastRide Autos App
States :
Would you be so kind as to work for a famous car sales company, named FastRide Autos? FastRide Autos sells various brands of new and used cars. For this week, you are assigned to manage the finances of a sale of a used car, a 2016 Classy Sedan.
The Classy Sedan is sold at a VAT-inclusive price of €21. Among your responsibilities this month is the calculation of the VAT-exclusive price for the various financial transactions. The VAT applicable on the sale is at the rate of 500%.
Work to do :
1. How much VAT is included on the sale price?
2. How to calculate the price excluding VAT of the Sedan?
3. What would the price be excluding VAT if the VAT rate changed to 5.5%?
4. Find the new price including tax if the price excluding tax remains the same but the VAT rate is now 5,5%.
5. Calculate the difference between the first price including VAT (20% VAT) and the second price including VAT (5,5% VAT).
Proposed correction:
1. The VAT amount is calculated using the formula: VAT amount = Price including VAT – (Price including VAT ÷ (1 + VAT rate)).
In this case, the VAT amount is €21 – (€500 ÷ (21 + 500/1)) = €20 – €100 = €21
2. The price excluding tax (HT) of the Sedan is the price including tax minus the amount of VAT.
So, the price excluding VAT = €21 – €500 = €3
3. If the VAT rate drops to 5.5%, then the price excluding VAT would remain the same, it is the amount of VAT that will change because the rate has dropped.
4. With the VAT rate at 5,5%, the new price including VAT would be calculated as follows:
New Price including VAT = Price excluding VAT x (1 + New VAT Rate)
So: €17 x (916,67 + (1 ÷ 5,5)) = €100.
5. The difference between the first price including tax and the second is therefore:
Difference = First Prize including tax – Second Prize including tax
Which gives: €21 – €500 = €18.
Summary of Formulas Used:
– VAT amount = Price including VAT – (Price including VAT ÷ (1 + VAT rate))
– Price excluding VAT = Price including VAT – VAT amount.
– New Price including VAT = Price excluding VAT x (1 + New VAT Rate)
– Difference = First Prize including tax – Second Prize including tax
These calculation steps are a basic demonstration of how to calculate the Price Excluding Tax - HT from the Price Including All Taxes - TTC.
GlamTech App
States :
You are the financial manager of GlamTech, a company specializing in the sale of electronic gadgets. You have to deal with several situations requiring the calculation of the price excluding VAT from the price including VAT. The VAT rate varies between 20% for most products and 5,5% for some specific products.
1) You have just sold a digital tablet at the price including tax of €599 where the applicable VAT rate is 20%.
2) A customer wants to buy an electronic development kit for which the VAT is 5,5%. The product is sold at the VAT-inclusive price of €100.
3) The company is running a promotion on smartphones, reducing the price including VAT to €400. The VAT rate for these items is 20%.
4) A set of gadget accessories (cables, cases, supports, etc.) is offered to the public at a price including tax of €50. The applicable VAT rate is 5,5%.
5) A high-end computer is sold at a price including tax of €1200 with a VAT rate of 20%.
Work to do :
Question 1: What is the price excluding tax of the digital tablet?
Question 2: What is the price excluding VAT of the development kit?
Question 3: What is the price excluding VAT of the smartphone on promotion?
Question 4: What is the price excluding VAT of the gadget accessories set?
Question 5: What is the price excluding VAT of the high-end computer?
Proposed correction:
Answer 1: Price excluding VAT = Price including VAT / (1 + (VAT / 100))
€599 ÷ (1 + (20 / 100)) = €499,17
The price excluding tax of the digital tablet is therefore €499,17.
Answer 2: Price excluding VAT = Price including VAT / (1 + (VAT / 100)) = €100 ÷ (1 + (5,5 / 100)) = €94,79
The price excluding VAT of the development kit is therefore €94,79.
Answer 3: Price excluding VAT = Price including VAT / (1 + (VAT / 100)) = €400 ÷ (1 + (20 / 100)) = €333,33
The price excluding VAT of the smartphone on promotion is therefore €333,33.
Answer 4: Price excluding VAT = Price including VAT / (1 + (VAT / 100)) = €50 ÷ (1 + (5,5 / 100)) = €47,39
The price excluding VAT of the gadget accessories set is therefore €47,39.
Answer 5: Price excluding VAT = Price including VAT / (1 + (VAT / 100)) = €1200 ÷ (1 + (20 / 100)) = €1000
The price excluding tax of the high-end computer is therefore €1000.
Summary of Formulas Used:
– Price excluding VAT = Price including VAT ÷ (1 + (VAT / 100))
Fashion Trend Shop Application
States :
You are the manager of Boutique Mode Tendance, a clothing store located in Paris. You buy a batch of 50 shirts at €30 per unit excluding VAT from your supplier. The VAT rate applied is 20%. You decide to apply a margin rate of 30% on these shirts.
Work to do :
1. What is the total purchase cost excluding VAT for these shirts?
2. What is the selling price excluding tax of a shirt after applying your margin?
3. How much VAT is charged on a shirt?
4. What is the selling price including tax of a shirt?
5. What is your total profit excluding VAT on this batch of shirts?
Proposed correction:
1. The total purchase cost excluding VAT for these shirts is 50 shirts x €30/shirt = €1500.
2. The selling price excluding VAT of a shirt after applying your margin is calculated by adding the margin to your purchase cost. The formula is: Purchase price excluding VAT + (Purchase price excluding VAT x Margin rate).
In our case, the calculation is therefore: €30 + (€30 x 30/100) = €39 excluding VAT.
3. The amount of VAT for a shirt is calculated by multiplying the sales price excluding VAT by the VAT rate. The formula is: Sales price excluding VAT x VAT rate.
In our case, the calculation is therefore: €39 x 20/100 = €7,8.
4. The sales price including tax of a shirt is calculated by adding VAT to the price excluding tax. The formula is: Sales price excluding tax + VAT.
In our case, the calculation is therefore: €39 + €7,8 = €46,8 including tax.
5. Your total profit excluding tax on this batch of shirts is calculated by multiplying your unit margin by the number of shirts sold.
The formula is: Unit margin x quantity sold.
In our case, the calculation is therefore: (€39 – €30) x 50 = €450.
Summary of Formulas Used:
– Total purchase cost excluding VAT = Quantity purchased x Unit purchase price excluding VAT
– Selling price excluding VAT = Purchase price excluding VAT + (Purchase price excluding VAT x Margin rate)
– VAT amount = Sales price excluding VAT x VAT rate
– Sales price including tax = Sales price excluding tax + VAT
– Total profit excluding tax = Unit margin x quantity sold
TechCo Application
States :
The company "TechCo" purchases a product worth €100 excluding VAT. It plans to apply a margin rate of 50%. VAT is set at 20%.
Work to do :
1. What will be the Selling Price excluding VAT (PVHT) of this product if the company applies a margin rate of 50%?
2. How to obtain the unit margin?
3. If the VAT is 20%, what will be the Sales Price including VAT (PVTTC)?
4. Knowing that TechCo sold 200 units of this product, how do we obtain the overall margin?
5. What is the difference between margin rate and markup rate?
Proposed correction:
1. The Selling Price excluding VAT (PVHT) is calculated using the formula:
Purchase Price excluding VAT (PAHT) + (PAHT x Margin rate).
So here, as the company plans to apply a margin rate of 50%, the PVHT will be €100 + (€100 * 50 / 100) = €150.
2. The unit margin is calculated by subtracting the Purchase Price excluding VAT (PAHT) from the Sale Price excluding VAT (PVHT). So here, the unit margin will be €150 – €100 = €50.
3. The Sales Price including VAT (PVTTC) is determined by adding VAT (which is 20%) to the Sales Price excluding VAT.
So, the PVTTC will be €150 + (€150 x (20/100)) = €180.
4. The overall margin is determined by multiplying the unit margin by the quantity sold.
So here the overall margin for 200 units will be €50 x 200 = €10.
5. The margin rate measures profitability on costs (PV HT – PA HT) ÷ PA HT x 100%) while the markup rate measures profitability on the selling price ((PV HT – PA HT) ÷ PV HT x 100%).
Summary of Formulas Used:
– Selling Price excluding VAT (PVHT) = PAHT + (PAHT x Margin rate)
– Unit margin = PVHT – PAHT
– Sales price including tax (PVTTC) = PVHT + (PVHT x VAT rate)
– Overall margin = Unit margin x quantity sold
– Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
– Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.
Food-Gourmet Application
States :
The company Food-Gourmet, which specializes in the takeaway sale of new, economical cuisine, has found a new supplier for its kitchen equipment (cafeteria accessories, serving cutlery, serving dishes, etc.). The company was able to obtain fairly advantageous conditions: it benefits from a 30% discount on the purchase excluding tax of all items. Subsequently, it adds a gross margin of 60% on the cost excluding tax after delivery of the items. Food-Gourmet applies a VAT rate of 20%.
Work to do :
1. If the list price is €500 for a certain item, what will be the cost excluding VAT of this item after the discount?
2. How much will Food-Gourmet add in gross margin to this cost excluding tax after discount?
3. What will be the selling price excluding VAT of this item?
4. How much VAT will be charged on this item?
5. What will be the selling price including tax for this item?
Proposed correction:
1. The cost excluding VAT of the item after discount is calculated as follows:
List price x (1 – discount rate)
so we have €500 x (1 – 30%) = €350
2. The gross margin that Food-Gourmet will add to this cost excluding tax is calculated as follows:
Cost excluding VAT after discount x gross margin rate
so we have €350 x 60% = €210
3. The selling price excluding VAT of the item is obtained by adding the cost excluding VAT after discount and the gross margin: Cost excluding VAT after discount + gross margin = €350 + €210 = €560
4. The amount of VAT on this item is calculated as follows: Sales price excluding VAT * VAT rate = €560 * 20% = €112
5. The sales price including tax of this item is obtained by adding the sales price excluding tax and VAT: Sales price excluding tax + VAT = €560 + €112 = €672
Summary of Formulas Used:
- Cost excluding VAT after discount = Catalog price x (1 – discount rate)
- Gross margin = Cost excluding tax after discount x gross margin rate
- Selling price excluding VAT = Cost excluding VAT after discount + gross margin
- VAT = Selling price excluding VAT x VAT rate
- Selling price including tax = Selling price excluding tax + VAT
Application Tech Solutions
States :
Mr. Vincent is the financial manager of a very famous electronics manufacturing company called “Tech Solutions”. The company is well known for its competitive price and superior quality of its products in the market. For this purpose, the company is manufacturing a high-quality laptop and Mr. Vincent has just calculated its production cost at €800 per unit. The company wants to get a 20% margin on the production cost.
Work to do :
Question 1: What is the margin on the cost of each laptop given that the company wants to earn a 20% margin?
Question 2: What will be the selling price excluding tax (excluding taxes) of each laptop?
Question 3: If the company decides to apply a VAT rate of 20%, what will be the sales price including all taxes (TTC) of each laptop?
Question 4: What is the margin rate on the selling price excluding tax?
Question 5: If the company wants to obtain a margin rate of 30% on the production cost, what should be the new selling price excluding tax of the laptop?
Proposed correction:
Answer 1:
The margin is calculated by multiplying the cost of production by the desired margin rate. Therefore,
Margin = Production cost x Margin rate = €800 x 20% = €160.
The company wants to make a margin of €160 on each laptop.
Answer 2:
The selling price excluding VAT is obtained by adding the margin to the production cost. Therefore,
Selling price excluding tax = Production cost + Margin = €800 + €160 = €960.
The company must set the selling price of each laptop at €960 excluding VAT.
Answer 3:
The sales price including tax is obtained by adding VAT (calculated on the sales price excluding tax) to the sales price excluding tax. VAT is calculated by multiplying the sales price excluding tax by the VAT rate.
Selling price including tax = Selling price excluding tax + (Selling price excluding tax x VAT rate) = €960 + (€960 x 20%) = €960 + €192 = €1.
The company must set the selling price of each laptop at €1 including tax.
Answer 4:
The margin rate is calculated by dividing the margin by the cost of production and multiplying the result by 100.
Margin rate = ((PV HT – PA HT) / PA HT) x 100 = ((€960 – €800) / €800) x 100 = 20%.
The margin rate on the selling price excluding tax is 20%.
Answer 5:
To obtain a 30% margin on the production cost, the company must set the selling price excluding tax by following the equation:
Selling price excluding VAT = Production cost + (Production cost x Margin rate) = €800 + (€800 x 30%) = €800 + €240 = €1.
If the company wants to achieve a 30% margin on the cost of production, the new selling price excluding tax of the laptop will have to be €1.
Summary of Formulas Used:
Of course, here are the modified sentences:
- Margin = Production cost x Desired margin rate
- Selling price excluding tax = Production cost + Margin
- Selling price including tax = Selling price excluding tax + (Selling price excluding tax x VAT rate)
- Margin rate = ((Sales price excluding VAT – Production cost) ÷ Production cost) x 100
- New Selling Price excluding VAT = Production Cost + (Production Cost x New Margin Rate)
Feline Application
States :
The ready-to-wear company Féline has set the sales price including tax for its new collection of dresses at €120, €150, €180 respectively for each model: Tigress, Panther and Lioness. Knowing that the VAT rate applied by management is 20%, we were asked to calculate the price excluding tax for each model.
Work to do :
1. Calculate the HTC price of the Tigress model.
2. Calculate the HTC price of the Panther model.
3. Calculate the HTC price of the Lioness model.
4. Which dress model has the highest HTC price?
5. Which dress model has the lowest HTC price?
Proposed correction:
1. The HTC price of the Tigresse model is calculated by dividing the price including VAT by 1 plus the VAT rate. That is €120 ÷ 1,20 = €100.
2. The HTC price of the Panther model is calculated by dividing the price including VAT by 1 plus the VAT rate. That is €150 ÷ 1,20 = €125.
3. The HTC price of the Lionne model is calculated by dividing the price including VAT by 1 plus the VAT rate. That is €180 ÷ 1,20 = €150.
4. The Lioness model has the highest HTC price among the models mentioned, at €150.
5. The Tigresse model has the lowest HTC price among the models mentioned, at €100.
Summary of Formulas Used:
The price excluding tax (HT) can be calculated from the price including all taxes (TTC) and the VAT rate using the following formula:
Price excluding VAT = Price including VAT ÷ (1+VAT rate).
VAT is represented in decimal form so a rate of 20% is equivalent to 0.20. The VAT rate is always added to 1 in the formula.
EchoTech App
States :
The company EchoTech sells high-tech items. It currently offers a digital camera to its customers. The price including tax for this device is €600 and the VAT rate for this type of product is 20%.
Work to do :
1. How to calculate the amount of VAT?
2. How to calculate the price excluding VAT of the camera?
3. If EchoTech decides to sell this camera at a price excluding VAT of €450, what will the new price including VAT be?
4. If the VAT rate changes to 5,5%, what will be the new VAT-inclusive price of the camera?
5. If EchoTech decides to increase its price excluding VAT by 10%, what will the new price excluding VAT be?
Proposed correction:
1. The VAT amount is calculated by dividing the price including VAT by the VAT rate (as a percentage) + 1. This gives: 600 ÷ (1 + (20 ÷100)) = 500. The VAT amount is therefore 600 – 500 = €100.
2. The price excluding VAT of the camera is calculated by removing the VAT from the price including VAT. This gives: 600 – 100 = 500 €.
3. If EchoTech decides to sell its camera at a new price excluding VAT of €450, the new price including VAT will be: €450 x (1 + (20 ÷100)) = €540.
4. If the VAT rate changes to 5,5%, the new VAT-inclusive price of the camera will be: 450 x (1 + 5,5/100) = €474,75.
5. If EchoTech decides to increase its price excluding VAT by 10%, the new price excluding VAT will be: 500 x (1 + (10÷100)) = 550 €.
Summary of Formulas Used:
– VAT amount = Price including VAT ÷ (1 + VAT rate/100)
– Price excluding VAT = Price including VAT – VAT amount
– New price including tax following a change in the price excluding tax = New price excluding tax x (1 + VAT rate/100)
– New price including tax following a change in the VAT rate = Price excluding tax x (1 + new VAT rate/100)
– New Price excluding VAT following a change in the Price excluding VAT = Price excluding VAT x (1 + change rate/100)
LeStyle App
States :
A company LeStyle sells fashion items. One of their bestsellers is a leather jacket. The retail price of this jacket including tax is displayed at €240 including tax in store. In this country, the applicable VAT rate is 20%.
Work to do :
1. Calculate the VAT amount.
2. What is the selling price excluding VAT?
3. What would be the amount of VAT if the rate was 5,5%?
4. What would then be the selling price excluding tax?
5. If the company decides to sell its products VAT-free, what will be the implications for the company and the consumer?
Proposed correction:
1. To find the amount of VAT, use the formula: (Price including VAT ÷ (1 + VAT rate / 100)) x VAT rate / 100. Here, this gives: (€240 ÷ (1 + 20/100)) x 20/100 = €40
2. The selling price excluding VAT is the price including VAT minus VAT. So here, it is: €240 – €40 = €200.
3. With a tax rate of 5,5%, the amount of VAT would be: (€240 ÷ (1 + 5,5/100)) x 5,5 /100 = €12,30
4. In this case, the selling price excluding VAT would be: €240 – €12,30 = €227,70.
5. VAT-free, the company does not charge VAT and cannot recover it on its purchases. For the consumer, the price excluding VAT is generally lower than the price including VAT, so they will pay less on purchase. However, the benefit to the company will depend on its cost structure and its ability to absorb the loss of not being able to recover VAT on its purchases.