11 BTS MCO Commercial Calculation Exercises

Welcome to this article on exercises on business calculations and more specifically on 11 commercial calculation exercises for BTS MCO. Here you will find no less than 11 detailed corrected management exercises on commercial calculations for Operational Management.

At the end of this article, you will know how to calculate brand rates, margin rates, sales prices excluding tax or tax without any worries.

Application: Chic and Charming Clothing Store

States :

The clothing store Chic et Charme specializes in selling high-end clothing. It buys dresses for €50 excluding VAT from its supplier. To attract more customers, the store offers a 10% discount on the excluding VAT sale price. Despite this discount, the store wants to maintain a margin rate of 70%. The applicable VAT rate is 20%.

Work to do :

1. Calculate the selling price excluding tax before any reduction.
2. Calculate the discount amount.
3. Calculate the selling price excluding tax after reduction.
4. Calculate the sales price including tax.
5. Calculate the mark rate.

Proposed correction:

1. To calculate the selling price excluding VAT before any reduction, we use the formula: Purchase Price excluding VAT x (1 + Margin rate). That is: €50 x (1 + 70%) = €85.

2. To calculate the amount of the reduction, we use the formula: Initial sales price excluding tax x Reduction rate. That is: €85 x 10% = €8,5.

3. To obtain the net selling price after reduction, we subtract the discount from the initial net price. That is: €85 – €8,5 = €76,5.

4. To calculate the sales price including tax, we use the formula: Sales price excluding tax x (1 + VAT rate). That is: €76,5 x (1 + 20%) = €91,8.

5. To calculate the markup rate, we use the formula: (Sale price excluding tax – Purchase price excluding tax) ÷ Sale price excluding tax x 100. That is: (€76,5 – €50) ÷ €76,5 x 100 = 34,64%.

Summary of Formulas Used:

FormulasDescription
Selling price excluding tax before reduction = Purchase price excluding tax x (1 + Margin rate)Calculation of the selling price excluding tax before any reduction
Amount of the reduction = Initial selling price excluding tax x Reduction rateCalculation of the reduction amount
Selling price excluding VAT after reduction = Initial selling price excluding VAT – Amount of the reductionCalculation of the selling price excluding tax after reduction
Sales price including tax = Sales price excluding tax x (1 + VAT rate)Calculation of the sales price including tax
Markup rate = (Selling price excluding VAT – Purchase price excluding VAT) ÷ Selling price excluding VAT x 100Calculation of the mark rate

Application: The Exploded Shoe

States :

La Chaussure Eclatée is a company that sells different types of shoes. Each of its shoes has a purchase price excluding tax of €30. The company sells 5000 pairs of shoes per year, with a margin rate of 60%. In addition, La Chaussure Eclatée wants to set up a 20% promotion on its shoes to increase its sales. In addition, the management is considering a 10% increase in the purchase price excluding tax for future purchases.

Work to do :

1. What is the selling price excluding VAT of the shoes?
2. What is the amount of VAT for each pair of shoes with a rate of 20%?
3. What is the selling price including tax of the shoes?
4. What is the overall margin for the year?
5. What will be the new purchase price excluding VAT after the planned increase?

Proposed correction:

1. The margin rate is 60%, so the selling price excluding tax of the shoes is €30 x (1+60/100) = €48.

2. The VAT amount for each pair of shoes is 20% x €48 = €9,60.

3. The sales price including tax of the shoes is €48 + €9,60 = €57,60.

4. The overall margin for the year is (€48 – €30) x 5000 pairs = €90.

5. The new purchase price excluding VAT after the 10% increase will be €30 x (1+10/100) = €33.

Summary of Formulas Used:

ConceptFormulas
VATAmount excluding VAT x VAT rate
Overall MarginUnit margin x quantity sold
Margin rate((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100
Brand taxes((Sales price excluding tax – Purchase price excluding tax) ÷ Sales price excluding tax) x 100
Sales price including taxSelling price excluding VAT + VAT
DiscountInitial price x Discount percentage ÷ 100
IncreaseInitial price x Percentage increase ÷ 100

Application: Perfect Style Clothing Company

States :

StyleParfait is a company specializing in the production and sale of high-end clothing. Having acquired a certain notoriety on the market, the company wishes to evaluate its financial performance in order to plan its next strategic actions. The company has sold 5000 units of a particular product with a Purchase Price excluding Tax (PA HT) of €30 and a Sale Price excluding Tax (PV HT) of €60. A 10% increase is planned for the sale price and a 5% reduction for the purchase price.

Work to do :

1. Calculate the unit margin in € and the overall margin in €.
2. Determine the margin rate and the markup rate.
3. Calculate the new sales price including tax after the planned increase.
4. Estimate the new purchase price after the planned reduction.
5. Calculate the new margin rate and markup rate.

Proposed correction:

1. The unit margin is calculated by subtracting the Purchase Price excluding Tax (PA HT) from the Sale Price excluding Tax (PV HT). Thus, the unit margin is €60 – €30 = €30. The overall margin is calculated by multiplying the unit margin by the quantity sold, i.e. €30 x 5000 = €150.

2. The margin rate is obtained by dividing the unit margin by the HT PA multiplied by 100, which gives ((€60 – €30) ÷ €30) x 100 = 100%. The markup rate is obtained by dividing the unit margin by the HT PV multiplied by 100, which gives ((€60 – €30) ÷ €60) x 100 = 50%.

3. The new sales price including tax after the planned increase is calculated by adding the planned increase of 10% to the old sales price excluding tax, i.e. €60 x (1 + 10%) = €66 excluding tax. Then add VAT at 20%, which gives €66 x 1,20 = €79,2 including tax.

4. The new purchase price is estimated by subtracting the expected 5% reduction from the purchase price excluding VAT, i.e. €30 x (1 – 5%) = €28,5.

5. The new margin rate is calculated by dividing the new unit margin by the new HT PA multiplied by 100, i.e. ((€66 – €28,5) ÷ €28,5) x 100 = 131,58%. The new markup rate is obtained by dividing the new unit margin by the new HT PV multiplied by 100, i.e. ((€66 – €28,5) ÷ €66) x 100 = 56,82%.

Summary of Formulas Used:

ConceptFormulas
Unit marginPV HT – PA HT
Overall marginUnit margin x Quantity sold
Margin rate((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes((PV HT – PA HT) ÷ PV HT) x 100
New sales price including VATPV HT x (1 + increase rate) x (1 + VAT rate)
New purchase price excluding VATPA HT x (1 – reduction rate)

Application: Saturn Boutique

States :

Saturne Boutique is a cute little boutique based in France. It sells homewares such as furniture, cushions, lamps, etc. Here are some of the financial details provided:
1. Unit purchase cost excluding tax of an armchair: €100
2. Quantity sold of the chair is 500
3. The company proposes a 30% increase on the purchase price to calculate the unit selling price excluding tax.
4. The VAT rate is 20%
5. A 10% discount is offered on the unit sales price including tax.

Work to do :

1. What is the unit selling price excluding tax of the chair?
2. How to calculate unit VAT?
3. How to determine the unit sales price including tax?
4. What is the unit discount?
5. What is the margin rate and unit markup rate?

Proposed correction:

For question 1:
1. The unit selling price excluding VAT is calculated using the formula PV excluding VAT = PA excluding VAT + (PA excluding VAT * increase rate). Therefore, PV excluding VAT = 100 + (100 * 0,30) = €130

The calculation of the unit VAT is given by the formula:
2. VAT = (PV HT * VAT rate). Therefore, VAT = 130 * 0,20 = €26

The unit sales price including tax is calculated using the formula:
3. PV including VAT = PV excluding VAT + VAT. So, PV including tax = 130 + 26 = €156

The unit reduction is calculated with the following formula:
4. Reduction = PV incl. VAT x reduction rate. Therefore, Reduction = 156 x 0,10 = €15,60

To calculate the unit margin and markup rate, the following formulas are used:
5. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100. Therefore, Margin rate = ((130 – 100) / 100) x 100 = 30%
Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100. Therefore, Markup rate = ((130 – 100) ÷ 130) x 100 = 23,08%

Summary of Formulas Used:

PackagesDescription
PV HT = PA HT + (PA HT * % increase)To calculate the unit selling price excluding tax
VAT = PV excluding VAT x VAT rateTo calculate the unit VAT
PV including VAT = PV excluding VAT + VATTo calculate the unit sales price including tax
Reduction = PV incl. VAT x % reductionTo calculate the reduction
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100To calculate the unit margin rate
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100To calculate the unit markup rate

Application: Albert Pharmacy in Marseille

States :

The Albert Pharmacy in Marseille is responsible for the purchase and resale of medicines. During the month of June, the pharmacy purchased a batch of medicines worth €8000 excluding VAT from a wholesaler. The pharmacy then resold these medicines for a value of €10 excluding VAT. In addition, the pharmacist, as part of a promotion, made a 000% reduction on the price including VAT of certain medicines.

Work to do :

1. Calculate the increase between the PA HT and the PV HT.
2. Calculate the margin rate and the markup rate made by the pharmacy.
3. Calculate the amount of VAT as well as the VAT-inclusive sales tax.
4. If a product sold including tax at €100 benefits from the promotional reduction, what will its new price be?
5. How much did the pharmacy make on the batch of medication?

Proposed correction:

1. Increase = PV excluding tax – PA excluding tax = €10 – €000 = €8
The pharmacy has increased its prices by €2.

2. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100) = ((10 € – 000 €) ÷ 8 €) x 000 = 8%
The margin rate is 25%.
Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100) = ((10 € – 000 €) ÷ 8 €) x 000 = 10%
The mark rate is 20%.

3. VAT = PV HT x VAT rate = €10 x 000% = €20
The VAT amount is €2.
PV including VAT = PV excluding VAT + VAT = €10 + €000 = €2
The selling price including tax is €12.

4. 5% discount on €100 = €100 – (€100 x 5%) = €100 – €5 = €95
The new price of the product after the discount is €95.

5. Overall margin on the lot = PV excluding tax – PA excluding tax = €10 – €000 = €8
The pharmacy made €2 on the batch of medicines.

Summary of Formulas Used:

TerminologiesPackages
VATVAT = PV excluding VAT x VAT rate
Margin rateMargin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100)
Brand taxesBrand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100)
PV including taxPV including VAT = PV excluding VAT + VAT
MarginOverall margin = Unit margin x quantity sold
DiscountDiscount = Initial price – Final price
IncreaseIncrease = Final price – Initial price

Application: Finance Tour

States :

Tour de la finance is a small shop selling cycling and running items. Here are the figures for the Suprem mountain bike model:

– Purchase price excluding tax (PA excluding tax): €250
– VAT rate: 20%
– Their goal is a 30% margin on the purchase price.
– Due to financing a new project, they need to make a 10% increase on the sales price including tax.
– But for the first month, they want to make a 15% discount to attract customers.

Work to do :

1. Calculate the sales price excluding tax (PV HT).
2. Indicate the amount of VAT.
3. Calculate the sales price including all taxes (PV TTC).
4. After the 10% increase, what will the new price be?
5. What will be the price for the first month with the 15% discount?

Proposed correction:

1. To calculate the PV HT, we use the formula: PV HT = PA HT + (PA HT x Margin rate). Which gives us: PV HT = €250 + (€250 x 0,30) = €325

2. The amount of VAT is calculated by: PV HT x VAT rate. Which gives: €325 x 0,20 = €65

3. The PV including tax is obtained by: PV excluding tax + VAT amount. That is: €325 + €65 = €390

4. After a 10% increase, the new price is: PV incl. tax + (PV incl. tax x Rate of increase i.e. €390 + (€390 x 0,10) = €429

5. The price for the first month with the 15% discount will be calculated by: Price after increase – (Price after increase x Discount rate). This gives: €429 – (€429 x 0,15) = €364,65

Summary of Formulas Used:

PackagesExplanations
PV excluding tax = PA excluding tax + (PA excluding tax x Margin rate)Form for calculating the Sales Price excluding Tax
VAT amount = PV excluding VAT x VAT rateForm for calculating the amount of VAT
PV incl. tax = PV excl. tax + VAT amountForm for calculating the Sales Price Including All Taxes
Price after increase = PV incl. tax + (PV incl. tax x Rate of increase)Calculate the new price after increase
Price after reduction = Price after increase – (Price after increase x Reduction rate)Calculate the new price after reduction

Application: Graphic Studio

States :

Le Studio Graphique, a company that sells graphic design services, has established the following information for one of their services:
– Purchase Price Excluding Tax (PA HT) for the purchase of a necessary software license: €45
– Sale Price excluding Tax (PV HT): €104
– Quantity sold: 50
– There is an increase in the price of purchasing the license by 3%
– They offer a 10% discount during a promotional operation.

VAT rate = 20%

Work to do :

1. Calculate the margin rate on the service.
2. Calculate the markup rate on the service.
3. Calculate the overall margin on the service.
4. Calculate the new PA HT after increase.
5. Calculate the new PV including tax after discount on the initial PV excluding tax.

Proposed correction:

1. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((104 € – 45 €) ÷ 45 €) x 100 = 131,11%

2. Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((104 € – 45 €) ÷ 104 €) x 100 = 56,73%

3. Overall margin = Unit margin x quantity sold = (PV HT – PA HT) x quantity = (104 € – 45 €) x 50 = 2 €

4. New PA HT after 3% increase on the initial price: PA HT x (1 + percentage increase/100) = €45 x (1 + 3/100) = €46,35

5. New PV including tax after 10% discount on the initial PV excluding tax: (PV excluding tax x (1 – discount percentage/100)) x (1 + VAT rate/100) = (€104 x (1 – 10/100)) x (1 + 20/100) = €89,28

Summary of Formulas Used:

ConceptFormulas
Margin rate((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes((PV HT – PA HT) ÷ PV HT) x 100
Overall marginUnit margin x quantity sold
PA HT after increasePA HT x (1 + percentage increase/100)
PV including tax after discount(PV HT x (1 – discount percentage/100)) x (1 + VAT rate/100)

Application: Market Grocery Store

States :

The Marché grocery store sells various products. It buys high-quality coffee packets at the tax-free purchase price (TPP) of €7 per packet. It applies a 50% margin on the purchase cost. The store manager grants a 10% discount on the tax-inclusive sale price during special sales days.

Work to do :

1. What is the sales price excluding tax (SRP HT) of the packet of coffee?

2. What is the sales price including all taxes (PV TTC) if the VAT rate applied is 20%?

3. What is the selling price after the 10% discount?

4. What is the margin rate and brand rate of the coffee package?

5. If the purchase price is increased by 5%, what will be the new sales price including tax?

Proposed correction:

1. The selling price excluding VAT is calculated by adding the margin to the purchase price. Margin = HT PA x Margin rate = €7 x 0,5 = €3,5. Therefore, the PV excluding VAT = HT PA + Margin = €7 + €3,5 = €10,5.

2. The VAT-inclusive PV is calculated by adding the VAT to the VAT-exclusive PV. VAT = VAT-exclusive PV x VAT rate = €10,5 x 0,2 = €2,1. Therefore, the VAT-inclusive PV = VAT-exclusive PV + VAT = €10,5 + €2,1 = €12,6.

3. The sale price after the discount is calculated by subtracting the discount from the VAT-inclusive price. Discount = VAT-inclusive price x Discount rate = €12,6 x 0,1 = €1,26. Therefore, the Price after discount = VAT-inclusive price – Discount = €12,6 – €1,26 = €11,34.

4. The margin rate is calculated as the margin divided by the purchase price excluding VAT multiplied by 100 to obtain a percentage. Margin rate = ((PV excluding VAT – PA excluding VAT) ÷ PA excluding VAT) x 100 = ((€10,5 – €7) ÷ €7) x 100 = 50%. The markup rate is calculated as the margin divided by the sale price excluding VAT. Markup rate = ((PV excluding VAT – PA excluding VAT) ÷ PV excluding VAT) x 100 = ((€10,5 – €7) ÷ 10,5) x 100 = 33,33%.

5. The increase in the purchase price translates into an increase in the sale price. If the HT PA increases to €7 x (1 + 0,05) = €7,35, the new HT PV is calculated in the same way as before: €7,35 x (1 + 0,5) = €11,025. By adding VAT, the new TTC PV is €11,025 x (1 + 0,2) = €13,23.

Summary of Formulas Used:

FormulasDescription
PV excluding tax = PA excluding tax + MarginSale price excluding tax
PV including tax = PV excluding tax x (1 + VAT rate)Selling price including all taxes
Price after reduction = PV including VAT – DiscountSale price after discount
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100Margin rate on purchase cost
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100Markup rate on sale price
New HT PA = HT PA x (1 + increase rate)Purchase price after an increase

Application: At Chic Boutique

States :

The boutique "Chez Chic" offers women's clothing and accessories. It offers a sweater under the reference CHIC/001 sold at €120 including tax. The VAT rate applicable in the new clothing sector is 20%. The purchase price (pa) excluding tax of this sweater is €50.

The company is offering a €10 discount on the original retail price for this sweater. In addition, it has decided to increase the purchase price from its supplier by 10%.

Work to do :

Question 1: What is the sales price excluding tax (SRP) of this sweater?
Question 2: Calculate the VAT.
Question 3: What is the margin rate achieved on this sweater?
Question 4: What is the markup rate for this sweater?
Question 5: What is the new margin after reduction and increase of the HT pa?

Proposed correction:

Answer 1: The PV excluding tax = PV including tax / (1 + VAT rate) or PV excluding tax = €120 / 1,20 = €100

Answer 2: VAT = PV excluding VAT * VAT rate i.e. VAT = €100 * 20% = €20

Answer 3: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100) therefore Margin rate = ((100€ – 50€) ÷ 50€) x 100 = 100%

Answer 4: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100) therefore Markup rate = ((100€ – 50€) ÷ 100€) x 100 = 50%

Answer 5:
– New sale price = €120 – €10 = €110 including tax, therefore €110 / 1,20 = €91,67 excluding tax
– New purchase price = €50 + €50*10% = €55 excluding VAT
– New margin = PV HT – PA HT = €91,67 – €55 = €36,67

Summary of Formulas Used:

FormulasDetails
PV HT = PV TTC / (1 + VAT rate)Formula for calculating the sales price excluding tax
VAT = PV excluding VAT * VAT rateFormula for calculating VAT
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100)Formula for calculating margin rate
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100)Formula to calculate the markup rate
Margin = PV excluding tax – PA excluding taxFormula for calculating margin

Application: Leclerc Supermarket

States :

Supermarché Leclerc is a local grocery store in a small town. The owner, Mr. Leclerc, has recently started selling homemade orange juice. He buys it from a local producer at a Purchase Price Excluding Tax (PP) of €2 per bottle. He decides to sell it at a Sales Price Excluding Tax (SP) of €2,80 per bottle, and to make a special offer of a 10% discount on the Sales Price Including Tax to promote the product. The VAT rate applied is 20%.

Work to do :

1. What is the unit margin on each bottle of orange juice?
2. What is the margin rate?
3. What is the markup rate?
4. What will be the sales price including tax?
5. What will be the price after the 10% off promotion?

Proposed correction:

1. The Unit Margin is calculated by subtracting the purchase price excluding tax from the sale price excluding tax. In this case, the formula will be: Unit Margin = PV excluding tax – PA excluding tax = €2,80 – €2 = €0,80.

2. The margin rate is the ratio of the unit margin to the purchase price excluding taxes, expressed as a percentage. The formula is: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((€2,80 – €2) ÷ €2) x 100 = 40%.

3. The markup rate is the ratio of the unit margin to the selling price excluding tax, expressed as a percentage. The formula is: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((€2,80 – €2) ÷ €2,80) x 100 = 28.57%.

4. The Sales Price including VAT is calculated by adding VAT to the PV excluding VAT. In this case, VAT is 20% of the PV excluding VAT. Therefore, PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate) = €2,80 + (€2,80 x 20%) = €3,36.

5. The price after the 10% discount will be calculated by subtracting 10% from the Sales Price including VAT. Therefore, the price after discount = PV including VAT – (PV including VAT x discount rate) = €3,36 – (€3,36 x 10%) = €3,02.

Summary of Formulas Used:

FormulasDescription
Unit margin = PV excluding tax – PA excluding taxThis formula is used to calculate the unit margin.
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100This formula is used to calculate the margin rate.
Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100This formula is used to calculate the markup rate.
PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate)This formula is used to calculate the Sales Price including VAT.
Price after reduction = PV including tax – (PV including tax x reduction rate)This formula is used to calculate the price after discount.

Application: Boutique Chic

States :

Boutique Chic is a high-end ready-to-wear boutique. Recently, it imported a batch of designer bags. The bag was purchased for €80 excluding VAT abroad. Boutique Chic decided to resell it for €120 excluding VAT to obtain a decent margin.

Chic Boutique plans to sell 50 bags in the next month. It is also known that Chic Boutique offers an additional 5% discount on the excluding VAT price for its preferred customers.

In addition, the government increased the VAT rate from 20% to 22%.

Work to do :

1. Calculate the unit margin and the expected overall margin.
2. Calculate the margin rate.
3. Calculate the mark rate.
4. What would be the sales price including VAT for a non-privileged customer after the increase in VAT?
5. How much discount would a preferred customer get before the VAT increase?

Proposed correction:

1. The unit margin is €120 – €80 = €40. The overall margin is therefore €40 x 50 = €2000.

2. The margin rate is calculated using the formula: ((PV HT – PA HT) ÷ PA HT) x 100), which gives ((120 € – 80 €) ÷ 80 €) x 100) = 50%.

3. The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100), which gives ((120 € – 80 €) ÷ 120 €) x 100) = 33,33%.

4. The sales price including tax for a non-privileged customer after the increase in VAT is PV HT x (1 + VAT rate/100), i.e. €120 x (1 + 22/100) = €146,40.

5. The amount of the discount granted to a preferred customer before the VAT increase is 5% x €120 = €6.

Summary of Formulas Used:

ConceptFormulas
Overall marginUnit margin x quantity sold
VAT rate(VAT amount ÷ Price excluding VAT) x 100
Margin rate((PV HT – PA HT) ÷ PA HT) x 100)
Brand taxes((PV HT – PA HT) ÷ PV HT) x 100)
PV including taxPV HT x (1 + VAT rate/100)
DiscountInitial sale price – Final sale price
IncreaseFinal Sale Price – Initial Sale Price

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