11 commercial calculation exercises bac pro sales

Application: Delight Electronics Store

States :

Delight Electronics is a company specializing in the sale of high-tech electronic products. She recently purchased 200 units of a brand new smartphone with a purchase price excluding taxes (HT) of €450 per unit. She wishes to apply a commercial margin of 25% on the sales price excluding tax (PV excluding tax).

For a promotional event, Delight Electronics decides to apply a 15% discount on the sales price all taxes included (PV incl. VAT). Please note that the VAT rate applied to electronic products is 20%.

Work to do :

1. Calculate the sales price excluding tax (PV excluding tax) of each smartphone.
2. Define the sales price including tax (PV including tax) of each smartphone.
3. Calculate the VAT amount for each smartphone unit sold.
4. Establish the new sales price including tax after applying the 15% discount.
5. What is the overall margin made by Delight Electronics after the sale of the 200 smartphones.

Proposed correction:

1. The PV excluding tax of the smartphone is given by the formula: PV excluding tax = PA excluding tax + (PA excluding tax x margin rate). So: €450 + (€450 x 0,25) = €562,50

2. The PV including VAT of the smartphone is calculated by the formula: PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate). So: €562,50 + (€562,50 x 0,20) = €675

3. The amount of VAT per smartphone is calculated by the formula: VAT = PV including tax – PV excluding tax. So: €675 – €562,50 = €112,50

4. The new PV including tax after the discount is calculated by the formula: new PV including tax = PV including tax – (PV including tax x discount rate). So: €675 – (€675 x 0,15) = €573,75

5. The overall margin is calculated by the formula: Overall margin = Unit margin x quantity sold. So: (€562,50 – €450) x 200 = €22

Summary of Formulas Used:

Formulas	Description
PV excluding tax = PA excluding tax + (PA excluding tax x margin rate)	Calculation of the sales price excluding taxes
PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate)	Calculation of the sales price all taxes included
VAT = PV including VAT – PV excluding VAT	Calculation of the VAT amount
new PV incl. tax = PV incl. tax – (PV incl. tax x discount)	Calculation of the new sales price including tax after discount
Overall margin = Unit margin x quantity sold	Calculation of the overall margin

Application: The House of the Lamp

Summary of Formulas Used:

Formulas	Description
PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate)	This formula allows you to calculate the Sales Price All Taxes Included from the Sales Price Excluding Taxes and the VAT rate in%.
Unit margin = PV excluding tax – PA excluding tax	This formula gives the unit margin achieved on each good sold.
Overall margin = Unit margin x Quantity sold	This formula gives the total margin made on all goods sold.
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	It allows you to calculate the margin rate in %, it gives the ratio between the margin made on each item and its purchase cost.
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100	It allows you to calculate the brand rate in%, it gives the ratio between the margin made on each good and its sales price excluding VAT.
PV excluding VAT after discount = PV excluding VAT – (PV excluding VAT x discount rate)	It allows you to calculate the Sales Price excluding taxes after a discount based on its rate.

States :

La Maison de la Lampe is a store specializing in the sale of home lamps. For a particular lamp, the purchase price excluding tax is €120 and the selling price excluding tax is €200. The applicable VAT rate is 20%. La Maison de la Lampe occasionally offers discounts on its products. During a promotional period, it offered a 10% discount on the sale price of this specific lamp.

Work to do :

1. What is the sales price including tax of the lamp?
2. What is the unit margin achieved on this lamp?
3. If La Maison de la Lampe sells 50 lamps, what is the overall margin achieved?
4. What is the margin rate made by La Maison de la Lampe on the sale of this lamp?
5. After the discount, what is the new sales price excluding tax of the lamp?

Proposed correction:

1. The sales price including VAT of the lamp is calculated by adding VAT to the sales price excluding VAT. So, PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate) = €200 + (€200 x 20/100) = €240.

2. The unit margin is the difference between the sales price excluding tax and the purchase price excluding tax. So, the unit margin = PV excluding tax – PA excluding tax = €200 – €120 = €80.

3. The overall margin is the unit margin multiplied by the number of lamps sold. So, the overall margin = Unit margin x Quantity sold = €80 x 50 = €4000.

4. The margin rate is the ratio of the margin to the purchase price excluding tax. So, the margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€200 – €120) ÷ €120) x 100 = 66.67%.

5. The sales price excluding tax after the discount is calculated by deducting the discount from the sales price excluding tax. So, PV excluding tax after discount = PV excluding tax – (PV excluding tax x discount rate) = €200 – (€200 x 10/100) = €180.

Summary of Formulas Used:

Formulas	Description
PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate)	Sales price including tax
Unit margin = PV excluding tax – PA excluding tax	Unit margin
Overall margin = Unit margin x Quantity sold	Overall margin
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Margin rate
PV excluding VAT after discount = PV excluding VAT – (PV excluding VAT x discount rate)	Sales price excluding tax after discount

Application: The Pêche Perfecte company

States :

The Pêche Parfaite company is a company selling high quality fishing equipment. As one of the leaders in its sector, it is faced with delicate business decisions. It must set the sales price excluding tax (PVHT) and the sales price all taxes included (PV including tax) of its new product, a high-end fishing reel.

To this end, it has established that the purchase price excluding taxes (PA excluding VAT) of the reel is €120 and it wishes to achieve a unit margin of 50%. In addition, the company offers a 5% discount to its customers for the purchase of 5 reels and more.

Work to do :

1. Calculate the sales price excluding tax (PVHT) of the high-end fishing reel.
2. Determine the sales price including VAT of the reel, considering a VAT rate of 20%.
3. What is the overall margin if the company sells 200 reels?
4. If a customer buys 5 reels, what would be the amount of discount given?
5. How does the margin rate fluctuate if the purchase price excluding tax increases by €10 without the sales price excluding tax changing?

Proposed correction:

1. The PVHT is calculated as follows: PA excluding VAT + Unit margin = €120 + 50% of €120 = €120 + €60 = €180. So, the sales price excluding taxes is €180.

2. The PV including tax is obtained by adding VAT (20%) to the PVHT: PVHT + VAT = €180 + 20% of €180 = €180 + €36 = €216. Thus, the sales price including tax of the reel is €216.

3. The overall margin is calculated by multiplying the unit margin by the quantity sold: Unit margin x Quantity = €60 x 200 = €12. The overall margin on the sale of 000 reels is therefore €200.

4. The discount is 5% of the PV excluding VAT of 5 reels: 5% of (5 x 180 €) = 5% of 900 € = 45 €. Thus, the amount of the discount granted for the purchase of 5 reels is €45.

5. If the PA excluding tax increases by €10, the unit margin decreases: (PV excluding tax – (PA excluding tax + €10)) ÷ (PA excluding tax + €10) x 100 = (€180 – (€120 + €10) ) ÷ (€120 + €10) x 100 = 31,6%. So the margin rate drops to 31,6%.

Summary of Formulas Used:

Concept	Formulas
Sale price excl. VAT	Purchase Price excluding VAT + Unit Margin
Sales price including tax	PV excluding tax + (VAT x PV excluding tax)
Overall Margin	Unit Margin x quantity sold
Discount amount	Discount in % x Total price excluding tax
Margin rate	(PV HT – PA HT)/(AP HT + Increase) x 100

Application: Easy Stationery

States :

Papeterie Facile is a small company specializing in the sale of stationery items. She bought a set of 100 ballpoint pens for €150 excluding tax. She got a 2% invoice discount. The applicable VAT rate is 20%.

La Papeterie Facile wishes to have a unit margin of €1,50 excluding VAT on each pen.

Work to do :

1. What is the Net Purchase Price excluding tax (PAHT) of the lot of pens?
2. What is the Unit Sales Price (PVHTu) of the pen?
3. What is the unit sales price including tax (PVTTu) of the pen?
4. Calculate Papeterie Facile's overall margin on the sale of the lot.
5. What are the margin and brand rates of Papeterie Facile on this sale?

Proposed correction:

1. The PAHT is calculated by deducting the discount from the PACH excluding HT. So, PAHT = PA HT × (1 – discount rate / 100) = €150 × (1 – 2%) = €147.

2. The PVHTu is calculated by adding the unit margin to the unit Net Purchase Price excluding tax (PANuHT). Therefore, PVHTu = PANuHT + unit margin = (147 ÷ 100) € excluding tax + €1,50 excluding tax = €2,97 excluding tax.

3. The PVTTu is calculated by adding VAT to the PVTTu. So, PVTTu = PVHTu × (1 + VAT rate / 100) = €2,97 × 1,2 = €3,56 including tax.

4. The overall margin is the product of the unit margin and the quantity sold. So, overall margin = unit margin × quantity sold = €1,50 × 100 = €150.

5. The margin rate is the difference between PVHT and PAHT compared to PAHT. So, margin rate = ((PVHT – PAHT) ÷ PAHT) x 100 = ((2,97 – 1,47) ÷ 1,47) x 100 = 102%. And the mark rate is the difference between PVHT and PAHT compared to the PVHT. So, brand rate = ((PVHT – PAHT) ÷ PVHT) x 100 = ((2,97 – 1,47) ÷ 2,97) x 100 = 50%.

Summary of Formulas Used:

Formulas	Explanation
PAHT = PA HT × (1 – discount rate / 100)	Calculation of the Net Purchase Price excluding tax after deduction of the discount
PVHTu = PANuHT + unit margin = (PAHT ÷ quantity) + unit margin	Calculation of the Unit Sales Price excluding VAT
PVTTu = PVHTu × (1 + VAT rate / 100)	Calculation of the Unit Sales Price including VAT
Overall margin = unit margin x quantity sold	Calculation of the overall margin
Margin rate = ((PVHT – PAHT) ÷ PAHT) x 100	Calculation of the margin rate
Brand rate = ((PVHT – PAHT) ÷ PVHT) x 100	Calculation of the mark rate

App: SuperAuto Center

States :

SuperAuto Center is a company specializing in the trade of automobile parts. The company buys a batch of Michelin tires at €70 excluding tax per unit. She plans to sell these tires at €100 excluding tax. In addition to the cost of purchasing the tires, SuperAuto Center also spent €500 for the transportation and storage of the tires.

We inform you that the applicable VAT rate is 20%. However, the company plans to offer a 5% discount on the sales price excluding tax to attract more customers.

Work to do :

1. Calculate the unit sales margin of tires.
2. Calculate the overall margin if the company sells 100 tires.
3. Determine the sales price including tax after the discount.
4. What is the VAT amount for a tire sold?
5. Calculate the margin rate.

Proposed correction:

1. The unit margin is calculated by subtracting the purchase price excluding tax from the selling price excluding tax. Here, the unit margin is calculated as follows: Unit margin = PV excluding VAT – PA excluding VAT = €100 – €70 = €30. SuperAuto Center therefore makes a margin of €30 per tire sold.

2. The overall margin is calculated by multiplying the unit margin by the number of tires sold. In this case, the overall margin is: Overall margin = Unit margin x quantity sold = €30 x 100 = €3.

3. The sales price including tax after the discount is obtained by subtracting the amount of the discount from the sales price excluding tax, then adding VAT. The sales price including tax is therefore: PV including tax = (PV excluding tax – Discount) x (1 + VAT rate). With a 5% discount, this gives: (€100 x (1 – 0,05)) x (1 + 20/100) = €95 x 1,2 = €114.

4. The amount of VAT for a tire sold is obtained by subtracting the sales price excluding VAT from the selling price including VAT, i.e. VAT = PV including VAT – PV excluding VAT = €114 – €95 = €19.

5. The margin rate is calculated by dividing the margin on purchase cost by the purchase cost then multiplied by 100. Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((100 € – €70) ÷ €70) x 100 = 42,85%.

Summary of Formulas Used:

Formulas	Explanation
Unit margin = PV excluding tax – PA excluding tax	Unit sales margin
Overall margin = Unit margin x quantity sold	Overall sales margin
PV including VAT = (PV excluding VAT – Discount) x (1 + VAT rate)	Sales price including tax after discount
VAT = PV including VAT – PV excluding VAT	Amount of VAT on a product sold
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Margin rate on purchase cost

Application: Fruitz Company

Summary of Formulas Used:

Packages	Explanations
Sales price including tax = Sales price excluding tax x (1 + VAT rate)	To calculate the sales price including tax, the value of VAT must be added to the price excluding tax, which is the product of the sales price excluding tax and the VAT rate.
VAT = PV including VAT – PV excluding VAT	VAT is the difference between the sales price including tax and the sales price excluding tax.
Unit margin = PV excluding tax – Purchase price excluding tax	The unit margin is the difference between the Sales Price excluding VAT and the Purchase Price excluding VAT. This is the profit directly made on the sale of an item excluding taxes.
Overall margin = Unit margin x Quantity sold	The overall margin is the product of the unit margin and the quantity sold. This is the total profit made from the sale of all items.
Margin rate = ((PV excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100)	The margin rate is the ratio between the unit margin and the purchase price. It gives the percentage of profit compared to the purchase cost excluding taxes.
Selling price after discount = Selling price before discount – (Selling price before discount x Discount rate)	The selling price after discount is obtained by subtracting the value of the discount from the selling price before discount. The discount is the product of the sales price before discount and the discount rate.

States :

The Fruitz Company sells high quality fruits to customers. She recently purchased a large quantity of apples at a purchase price excluding tax (excl. VAT) of €0,5 per apple. The apples were sold at a sales price excluding tax of €1,2 per apple. A VAT rate of 5,5% was applied. During one sales period, 2000 apples were sold. Due to a reduction in demand, a 20% discount has been granted on the sales price excluding tax.

Work to do :

1. Calculate the all-tax sales price (TTC) of the apples.
2. Calculate VAT for an apple.
3. Calculate the unit margin and overall margin.
4. Calculate the margin rate.
5. Calculate the sales price excluding tax after the discount.

Proposed correction:

1. The sales price including VAT of apples is calculated by the formula: PV including VAT = PV excluding VAT x (1 + VAT rate) = €1,2 x (1 + 5,5 ÷ 100) = €1,266.

2. The VAT for an apple is calculated by subtracting the price excluding tax from the price including tax. VAT = PV including VAT – PV excluding VAT = €1,266 – €1,2 = €0,066.

3. The unit margin is calculated by subtracting the purchase price excluding tax from the sales price excluding tax. Unit margin = PV excluding tax – Purchase price excluding tax = €1,2 – €0,5 = €0,7. The overall margin is calculated by multiplying the unit margin by the quantity sold. Overall margin = Unit margin x Quantity sold = €0,7 x 2000 = €1400.

4. The margin rate is calculated by dividing the unit margin by the purchase price excluding tax and multiplying the result by 100. Margin rate = ((PV excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 = ((€1,2 – €0,5) ÷ €0,5) x 100 = 140%.

5. The sales price excluding tax after the discount is calculated by subtracting the product from the sale price of the discount. Sales price after discount = PV excluding tax – (PV excluding tax x Discount rate) = €1,2 – (€1,2 x 20 ÷ 100) = €0,96.

Summary of Formulas Used:

Packages	Explanations
Sales price including tax = Sales price excluding tax x (1 + VAT rate)	The sales price including tax is the sum of the sales price excluding tax and the amount of VAT.
VAT = PV including VAT – PV excluding VAT	VAT is the difference between the sales price including tax and the sales price excluding tax.
Unit margin = PV excluding tax – Purchase price excluding tax	The unit margin is the difference between the Sales Price excluding VAT and the Purchase Price excluding VAT.
Overall margin = Unit margin x Quantity sold	Overall margin is the total profit from all sales.
Margin rate = ((PV excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100)	The margin rate is the ratio between the unit margin and the purchase price. It gives the percentage of profit compared to the purchase cost excluding taxes.
Selling price after discount = Selling price before discount – (Selling price before discount x Discount rate)	The sales price after discount is the sales price excluding tax less the discount.

Application: The AthléRun shoe store

States :

The AthléRun shoe store sells a pair of sneakers at the sales price excluding tax (PV excl. VAT) of €60. She buys this same pair from the supplier for a purchase price excluding tax (PA excluding tax) of €40. VAT is 20%.

It also grants a 5% discount to its loyal customers on the sales price all taxes included (PV including tax).

Work to do :

1. Calculate the sales price including tax (PV including tax) of the pair of sneakers.
2. Calculate the unit margin made by the store on the sale of this pair of sneakers.
3. Calculate the overall margin if the store sells 50 pairs of sneakers.
4. Calculate the sales price including tax of the pair of sneakers after discount for a loyal customer.
5. Determine the margin rate made by the store on the sale of this pair of sneakers.

Proposed correction:

1. The PVC including VAT is calculated by adding the VAT (20% of the PV excluding VAT) to the PV excluding VAT:

PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate)
= €60 + (€60 x 20/100)
= €60 + €12
= 72 €

2. The unit margin is the difference between the PV HT and the PA HT:

Unit margin = PV excluding tax – PA excluding tax
= €60 – €40
= 20 €

3. The overall margin is calculated by multiplying the unit margin by the quantity sold:

Overall margin = Unit margin x quantity sold
= €20 x 50
= 1000 €

4. The sales price including tax after discount is calculated by subtracting the discount (5% of the PV including tax) from the PV including tax:

PV including tax after discount = PV including tax – (PV including tax x Discount rate)
= €72 – (€72 x 5/100)
= €72 – €3,60
= 68,40 €

5. The margin rate is the ratio between the unit margin and the PA excluding tax, all multiplied by 100 to convert it into a percentage:

Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100
= ((€60 – €40) ÷ €40) x 100
= (€20 ÷ €40) x 100
= 0,5x100
= 50%

Summary of Formulas Used:

Calculs	Packages
Sales price including tax (PV including tax)	PV excluding VAT + (PV excluding VAT x VAT rate)
Unit margin	PV HT – PA HT
Overall margin	Unit margin x Quantity sold
Sales price including tax after discount	PV including tax – (PV including tax x Discount rate)
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100

Application: Leclerc Supermarket

States :

Supermarché Leclerc is a department store that operates in the retail sector. It specializes in the sale of various merchandise, including a variety of food products. One of their best-selling items is a specific bottle of wine. Leclerc bought each bottle for €5,00 excluding VAT. Currently, they are running a 10% discount on this product to boost sales.

In order to optimize its profits, the manager of Supermarché Leclerc wishes to review the pricing strategy. He set the sales price excluding tax (PV excl. VAT) of bottles of wine at €8,00.

Work to do :

1. Calculate the VAT on the sale price, knowing that the applicable VAT rate for this type of product is 20%.
2. Determine the sales price including tax of the bottle of wine.
3. Calculate the unit margin and the overall margin if Leclerc sells 500 bottles.
4. What will the new discount be if Leclerc decides to increase it to 15%?
5. Determine the margin rate.

Proposed correction:

1. VAT is calculated as follows: VAT = PV excluding VAT x VAT rate = €8,00 x 20% = €1,60

2. The sales price including tax is calculated by adding VAT to the sales price excluding tax. Sales price including VAT = PV excluding VAT + VAT = €8,00 + €1,60 = €9,60

3. The unit margin is the difference between the sales price excluding tax and the purchase price excluding tax. Unit margin = PV excluding tax – PA excluding tax = €8,00 – €5,00 = €3,00. The overall margin is the unit margin multiplied by the quantity sold. So, Overall margin = Unit margin x Quantity sold = €3,00 x 500 = €1.

4. The new discount is calculated by multiplying the Sales Price including tax by the new discount rate. New discount = Sales price including tax x New discount rate = €9,60 x 15% = €1,44.

5. The margin rate is calculated using the following formula: Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€8,00 – €5,00) ÷ €5,00 ) x 100 = 60%

Summary of Formulas Used:

Formulas	Description
PV excluding VAT x VAT rate	VAT calculation
PV excluding VAT + VAT	Calculation of the Sales Price including tax
PV HT – PA HT	Calculation of unit margin
Unit margin x Quantity sold	Calculation of the overall margin
Sales price including tax x New discount rate	Calculation of the new discount
((PV HT – PA HT) ÷ PA HT) x 100	Calculation of the margin rate

Application: The ElectroTech Company

States :

The ElectroTech Company is a distributor specializing in the sale of electronic equipment. She plans to launch a new product: a high-tech laptop. The following data is available: the unit purchase cost excluding tax (PA excluding tax) of this computer is €650, the commercial discount granted by the supplier is 4% on the PA excluding tax, the margin rate desired by ElectroTech is 25% on the sales price excluding tax (PV excluding tax), the VAT rate is 20%.

Work to do :

1. Calculate the net purchase price excluding tax (PA net excluding tax).
2. Calculate the sales price excluding tax (PV excluding tax).
3. Calculate the sales price including tax (PV including tax).
4. Calculate the unit margin.
5. Calculate the margin rate.

Proposed correction:

1. Net purchase price excluding tax = PA excluding tax – (PA excluding tax x Discount rate) = €650 – (€650 x 4%) = €624.

2. Sales price excluding VAT = net PA excluding VAT ÷ (1 – Margin rate) = €624 ÷ (1 – 25%) = €832.

3. Sales price including VAT = PV excluding VAT x (1 + VAT rate) = €832 x (1 + 20%) = €998,40.

4. Unit margin = PV excluding tax – net PA excluding tax = €832 – €624 = €208.

5. Margin rate = (Unit margin ÷ PV excluding tax) x 100 = (€208 ÷ €832) x 100 = 25%.

Summary of Formulas Used:

Net purchase price excluding tax	PA excluding tax – (PA excluding tax x Discount rate)
Selling price excluding tax	Net PA excluding VAT ÷ (1 – Margin rate)
Sales price including tax	PV excluding VAT x (1 + VAT rate)
Unit margin	PV HT – PA net HT
Margin rate	(Unit margin ÷ PV excluding VAT) x 100

Application: Chicasa Shop

States :

The Chicasa boutique is a clothing store located in Paris. Here is important information regarding one of its flagship products, a summer dress:
– Purchase price excluding tax (PA excluding tax): €18
– Desired margin rate: 70%
– Commercial discount granted: 10%
– Cost of VAT: 20%

Work to do :

1. Calculate the Sales Price excluding tax (PV excluding tax).
2. Calculate the Sales Price All Taxes Included (PV including VAT).
3. Determine the unit margin.
4. Calculate the overall margin if 85 dresses are sold.
5. What is the margin rate achieved?

Proposed correction:

1. The sales price excluding tax (PV excluding tax) is calculated as follows: PV excluding tax = PA excluding tax x (1 + Margin rate).

PV excluding tax = €18 x (1 + 70/100) = €30,6.

2. The sales price including tax is determined by adding VAT to the PV excluding tax: PV including tax = PV excluding tax x (1 + VAT rate).

PV including tax = €30,6 x (1 + 20/100) = €36,72.

3. The unit margin is calculated by subtracting the PA excluding tax from the PV excluding tax: Unit margin = PV excluding tax – PA excluding tax.

Unit margin = €30,6 – €18 = €12,6.

4. The overall margin is the product of the unit margin and the quantity sold: Overall margin = Unit margin x Quantity sold.

Overall margin = €12,6 x 85 = €1071.

5. The margin rate is the ratio between the unit margin and the PA excluding tax: Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100.

Margin rate = ((€30,6 – €18) ÷ €18) x 100 = 70%.

Summary of Formulas Used:

Formulas	Description
PV excluding tax = PA excluding tax x (1 + Margin rate)	Formula to calculate the Sales Price excluding tax (PV excluding tax)
PV including VAT = PV excluding VAT x (1 + VAT rate)	Formula to calculate the Sales Price All Taxes Included (PV including VAT)
Unit margin = PV excluding tax – PA excluding tax	Formula for determining Unit Margin
Overall margin = Unit margin x Quantity sold	Formula to calculate the overall margin
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Formula to determine the Margin Rate

Application: The Economic Store

States :

Le Magasin Économique is a small retail business that sells various household items. All products are purchased excluding VAT and are subject to VAT at the rate of 20%. The company also applies a 10% discount on certain items at the end of the season.

Here is the information about a particular product:
– Purchase price excluding tax (PA excluding tax): €60
– Quantity sold: 15
– Discount: yes

Work to do :

1. Calculate the Sales Price excluding tax (PV excluding tax) if the margin achieved is 20% on the PA excluding tax.
2. Then calculate the Sales Price including tax (PV including tax) of this product and specify the amount of VAT.
3. What is the unit margin in € of this product?
4. Calculate the overall margin obtained after selling all products.
5. Finally, what would be the new PV excluding tax after applying the discount and the corresponding margin rate?

Proposed correction:

1. The PV HT can be calculated using the formula: PV HT = PA HT + (Margin rate x PA HT). If the margin rate is 20%, then the PV excluding tax = €60 + (20% x €60) = €60 + €12 = €72.

2. The PV including VAT is calculated by adding VAT to the PV excluding VAT. So, the PV including tax = PV excluding tax + (VAT rate x PV excluding tax). If the VAT rate is 20%, then the PV including tax = €72 + (20% x €72) = €72 + €14,40 = €86,40. The amount of VAT is therefore €14,40.

3. The unit margin is the difference between the PV excluding tax and the PA excluding tax, i.e.: Unit margin = PV excluding tax – PA excluding tax = €72 – €60 = €12.

4. The overall margin is the unit margin multiplied by the quantity sold, i.e. 15 in this case: Overall margin = unit margin x quantity sold = €12 x 15 = €180.

5. When applying a 10% discount, the new PV excluding tax after discount = PV excluding tax – (Discount rate x PV excluding tax) = €72 – (10% x €72) = €72 – 7,20, €64,80 = €XNUMX.
The corresponding margin rate is: Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 = ((€64,80 – €60) ÷ €60) x 100 = 8%.

Summary of Formulas Used:

Formulas	Explanation
PV excluding tax = PA excluding tax + (Margin rate x PA excluding tax)	Calculation of the sales price excluding taxes
PV including VAT = PV excluding VAT + (VAT rate x PV excluding VAT)	Calculation of the sales price all taxes included
Unit margin = PV excluding tax – PA excluding tax	Calculation of margin per unit of product
Overall margin = Unit margin x quantity sold	Calculation of the total margin after the sale of all products
PV excluding tax after discount = PV excluding tax – (Discount rate x PV excluding tax)	Calculation of the new sales price excluding taxes after applying a discount
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	Calculation of the margin rate as a percentage on the purchase price excluding taxes