Commercial Calculations: 17 Corrected Exercises – Operational Management

Welcome to this article dedicated to exercises on business calculations. Here you will find no less than 17 management exercises on business calculations for Operational Management.

The corrected management exercises mainly focus on:

• the margin rate
• markup rate

1/ Simple margin rate

States

The following elements are given:

Purchase price excluding VAT: €140

Selling price excluding VAT: €220

 

Work to do

1. Calculate the margin rate
2. Interpret your result

 

Proposed correction

In this exercise, we simply apply the basic margin rate formula:

[(PV HT – PA HT) ÷ PA HT × 100]

[(220 – 140) ÷ 140 × 100]

 

Interpretation of the result

The margin made on a sale is 57,14%.

 

2/ Margin rate (a little) difficult

States

The following elements are given:

Purchase price excluding VAT: €140

Selling price excluding VAT: €220

Installation fee: €30

Frais de port : €40

 

Work to do

1. Calculate the margin rate

 

Proposed correction

First, you need to calculate the purchase cost. This is the purchase price plus fees.

Purchase cost = 140 + 30 + 40 or a total of €210

Then we apply the basic formula of the margin rate taking into account the purchase cost:

[(PV HT – Purchase cost HT) ÷ Purchase cost HT × 100]

[(220 – 210) ÷ 210 × 100] = 4,76%

 

Interpretation of the result

The margin made on a sale represents 4,76%

 

3/ Calculation of a margin rate (TTC => HT)

Change from an amount including tax to an amount excluding tax.

States

The following elements are given:

Purchase price excluding VAT: €140

Selling price including VAT: €264 (VAT rate: 20%)

 

Work to do

1. Calculate the margin rate.

 

Proposed correction

To calculate a margin rate, the elements must be exclusive of tax.

It is therefore necessary to first calculate the selling price excluding tax.

We will apply the following formula:

[PV HT = PV TTC ÷ (1 + VAT rate)]

PV HT = 264 ÷ (1 + 20%)

PV HT = 264 ÷ 1,2

PV excluding VAT = €220

Now we will apply the margin rate formula:

[(PV HT – PA HT) ÷ PA HT] × 100

[(220 – 140) ÷ 140 × 100] = 57,14%

 

4/ Calculation of a simple markup rate

States

The following elements are given:

Purchase price excluding VAT: €140

Selling price excluding VAT: €220

 

Work to do

1. Calculate the markup rate.
2. Interpret your result.

 

Proposed correction

In this exercise, we simply apply the basic formula for the markup rate:

[(PV HT – PA HT) ÷ PV HT × 100]

[(220 – 140) ÷ 220 × 100] = 36,36%

 

Interpretation of the result

The margin made on a sale represents 36,36% of the sale price.

 

5/ Calculation of a (slightly) difficult mark rate

States

The following elements are given:

Multiplier coefficient: 1,3

Cost price: €190

VAT rate: 20%

 

Work to do

1. Calculate the markup rate.

 

Proposed correction

In this corrected management exercise, you must first calculate various elements before being able to apply the markup rate formula.

Let me remind you of the formula for the multiplier coefficient:

PV incl. VAT ÷ Cost price × CM

So we have :

PV incl. VAT = 190 × 1,3

PV incl. VAT = €247

 

Then you must transform the PV including tax using the following management formula:

[PV HT = PV TTC ÷ (1 + VAT rate)]

So we have :

PV HT = 247 ÷ (1 + 20%)

PV HT = 247 ÷ 1,2

PV excluding VAT = €205,83

 

Now we can calculate the markup rate by applying the following formula:

[(PV HT – PA HT) ÷ PV HT × 100]

[(205,83 – 190) ÷ 205,83 × 100] = 7,69%

The markup rate is therefore 7,69%.

 

6/ Calculation of a markup rate (TTC => HT)

Change from an amount including tax to an amount excluding tax.

States

The following elements are given:

Purchase price excluding VAT: €140

Selling price including VAT: €264 (VAT: 20%)

 

Work to do

1. Calculate the markup rate

 

Proposed correction

To calculate a markup rate, the elements must be exclusive of tax.

It is therefore necessary to first calculate the selling price excluding tax.

We will apply the following formula:

[PV HT = PV TTC ÷ (1 + VAT rate)]

PV HT = 264 ÷ (1 + 20%)

PV HT = 264 ÷ 1,2

PV excluding VAT = €220

 

Now we will apply the markup rate formula:

[(PV HT – PA HT) ÷ PV HT × 100]

[(220 – 140) ÷ 220 × 100] = 36,36%

 

7/ Margin calculation with margin rate (simple)

States

The following elements are given:

Purchase price excluding VAT: €320

Margin rate: 15%

 

Work to do

1. Calculate the trade margin.

 

Proposed correction

To calculate the trade margin, we will use the following formula:

Margin = PA HT × Margin rate

So we have:

Margin = 320 × 15%

Margin = 320 × 0,15 (this is what you should type into your calculator)

Margin = €48

 

Interpretation of the result

On each sale, the business unit makes a margin of €48.

 

8/ Margin calculation with margin rate (difficult)

States

The following elements are given:

Purchase price excluding VAT: €320

Shipping costs: €80

Selling price excluding VAT: €480

It should be noted that in this corrected management exercise, the aim is to use a margin rate.

 

Work to do

1. Calculate the trade margin using a margin rate.

 

Proposed correction

First, you need to calculate the purchase cost because you have to take into account the shipping costs.

For this, we will use the following formula:

Purchase cost = Purchase price + Transport costs

So we have:

Purchase cost = 320 + 80

Purchase cost = €400

Then you need to calculate the margin rate using the following formula:

Margin rate = [(PV HT – PA HT) ÷ PA HT × 100]

So we have:

Margin rate = [(480 – 400) ÷ 400 × 100] = 20%

The margin can be calculated using the following formula:

Margin = PA HT × Margin rate

So we have:

Margin = 400 × 20%

Margin = 400 × 0,2

Margin = €80

 

If you would like to practice with other corrected management exercises on commercial calculations, do not hesitate to visit my article entitled Commercial Calculations: 13 Corrected Exercises – Operational Management.

 

9/ Margin calculation with markup rate (simple)

States

The following elements are given:

Selling price excluding VAT: €480

Markup rate: 30%

 

Work to do

1. Calculate the margin amount.

 

Proposed correction

For the requested work, we will use the following formula:

Margin = PV HT × Markup rate

So we have:

Margin = 480 × 30%

Margin = 480 × 0,3

Margin = €144

The margin is therefore €144.

 

10/ Calculation of a cost price with a multiplying coefficient

States

The following elements are given:

Selling price excluding VAT: €480

Multiplier coefficient: 1,4

VAT rate: 20%

 

Work to do

1. Calculate the cost price.

 

Proposed correction

To carry out the requested work, you must first determine the sales price including tax.

The formula that relates the elements provided is as follows:

Cost price × CM = PVTTC

Calculation of the PV including tax:

PV including tax = PV excluding tax × (1 + VAT rate)

So we have:

PV incl. VAT = 480 × 1,2

PV incl. VAT = €576

We can now calculate the cost price:

Cost price = PV including tax ÷ CM

Which give :

Cost price = 576 ÷ 1,4

Cost price = €411,43

The cost price is therefore €411,43.

 

11/ Calculation of a cost price using a margin rate

States

The following elements are given:

Margin rate: 25%

Selling price including tax: €250

VAT rate: 20%

 

Work to do

1. Calculate the cost price.

 

Proposed correction

First, you need to remove the VAT from the sales price using the following formula:

PV HT = PV TTC ÷ (1 + VAT rate)

Which give :

PV HT = 250 ÷ 1,2

PV excluding VAT = €208,33

 

To find the cost price, we will modify the following basic formula:

PV HT = Cost price × (1 + Margin rate)

So we have:

Cost price = PV excluding tax ÷ (1 + Margin rate)

Which give :

Cost price = 208,33 ÷ (1 + 25%)

Cost price = 208,33 ÷ 1,25

Cost price = €166,66

The cost price is therefore €166,66.

 

12/ Calculation of a cost price with a percentage increase

States

The following elements are given:

Cost price as of 15/01/N: €350

Increase on 04/02/N: 15%

 

Work to do

1. Calculate the cost price as of 04/02/N.

 

Proposed correction

To perform this calculation you must use the following formula:

Initial cost price × (1 + Percentage increase)

So:

Cost price = 350 × (1 + 15%)

Cost price = 350 × 1,15

Cost price = €402,50

The cost price as of 04/02/N is therefore €402,50.

 

13/ Calculation of a cost price using a mark-up rate

States

The following elements are given:

Markup rate: 15%

Selling price including tax: €500

VAT rate: 20%

 

Work to do

1. Calculate the cost price.

 

Proposed correction

To do this, you must first remove the VAT from the sale price using the following formula:

PV HT = PV TTC ÷ (1 + VAT rate)

So we have :

PV HT = 500 ÷ (1 + 20%)

PV HT = 500 ÷ 1,2

PV excluding VAT = €416,66

 

Then you need to calculate the margin using the following formula:

Margin = PV HT × Markup rate

So:

Margin = 416,66 × 15%

Margin = 416,66 × 0,15

Margin = €62,50

 

You can calculate the margin using the following management formula:

Cost price = PV excluding VAT – Margin

So we have:

Cost price = 416,66 – 62,50

Cost price = €354,16

The cost price is therefore €354,16.

 

14 / Checol case

The Caschecol business unit produces and markets high-end scarves. We give you some elements to perform some calculations.

Element  :

Purchase price excluding VAT: €47,89

Selling price including tax: €114

VAT at the standard rate

 

Work to do :

1. Calculate the purchase cost knowing that the incidental costs on purchases amount to 75% of the purchase price excluding tax?
2. Calculate the commercial margin?
3. What is the margin rate applied?
4. What is the markup rate applied?
5. Determine the multiplier coefficient?

 

Proposed correction :

 

1. Calculate the purchase cost knowing that the incidental costs on purchases amount to 75% of the purchase price excluding tax?

The purchase cost is equal to the purchase price plus incidental costs on purchases.

Calculation of the amount of incidental costs on purchases:

Purchase price × 0,75 or 47,89 × 0,75 = 35,91 €

The purchase cost therefore amounts to:

47,89 + 35,91 or 83,80 € HT

 

2. Calculate the trade margin

The commercial margin is equal to the difference between the sale price and the purchase price, all excluding taxes.

However, you have to be careful and adapt the formula according to the situations.

In fact, very often other elements come into play in the calculation and increase the purchase price.

To calculate the sales price excluding tax, the following formula must be applied:

PV HT = PV TTC ÷ (1 + VAT rate)

So:

PV HT = 114 ÷ 1,2

PV excluding VAT = €95,00

We can therefore write:

Margin = 95,00 – 83,80 hence margin = 11,20 €

The margin amount is therefore €11,20.

 

3. What is the margin rate applied?

Margin rate = [(PV HT – PA HT) ÷ PA HT] x 100

Margin rate = [(95,00 – 83,80) ÷ 83,80] x 100

Margin rate = (11,20 ÷ 83,80) x 100

Margin rate = 13,36%

The margin rate applied is therefore 13,36%.

 

4. What is the markup rate applied?

Mark rate = [(PV HT – PA HT) ÷ PV HT] x 100

Markup rate = [(95,00 – 83,80) ÷ 95,00] x 100

Markup rate = (11,20 ÷ 95,00) x 100

Brand rate = 11,79%

The margin on sales is 11,79%

 

5. Determine the multiplier coefficient?

The multiplier coefficient is the ratio between the PV including tax and the PA excluding tax (to be adapted of course).

Multiplier coefficient = 114 ÷ 83,80 or 1,36

This coefficient allows you to go directly from the purchase price excluding tax to the sale price including all taxes.

Here is the first part of this corrected management exercise on commercial calculations in video:

 

15 / Shirt case

The Caschemisère business unit has just created a new product range.

This is a new range of very elegant sweaters. However, the sale price has not yet been set and the manager is consulting you on this.

Mr Lebeau, the manager, tells you that the business unit usually charges a markup of 15% and that the cost of purchasing a sweater is €18,50, with additional purchasing costs estimated at 40% of the purchase cost.

All transactions are subject to the standard rate.

 

Work to do

1. What rate should the business unit charge to actually have a 15% margin on its sales?
2. What is the margin of Caschemisère compared to the purchase cost of the sweater?
3. If the sweater is sold for €53,82 including tax, does the business unit generate a margin? If so, how much?

 

Proposed correction

1. What rate should the business unit charge to actually have a 15% margin on its sales?

As is very often the case when you have a financial year with a mark rate, the following formula is frequently applied:

PV = PA ÷ (1 – Mark Rate)

Let's apply this formula to determine the selling price:

PV = (18,50 + (18,50 × 0,4)) ÷ (1 – 0,15)

PV = 25,90 ÷ 0,85 or PV = 30,47 € HT

The sale price must be €30,47 excluding VAT, or €36,56 including VAT, if the company wishes to generate a margin on its sales of 15%.

 

2. What is the margin of Caschemisère compared to the purchase cost of the sweater?

This question comes down to calculating the margin rate. We will therefore apply the following formula:

Margin rate = [(PV HT – PA HT) ÷ PA HT] x 100

Please note that this formula needs to be adapted as is very often the case; you need to take into consideration the purchase cost (by default this is given excluding VAT) and not the purchase price.

Let's calculate the purchase cost:

It is equal to the purchase price plus the purchase fee.

We therefore have: 18,50 + (40% of 18,50) or therefore 25,90 € HT

The formula therefore becomes: [(30,47 – 25,90) ​​÷ 25,90] × 100 = 17,64%

The margin rate is therefore 17,64%.

 

3. If the sweater is sold for €53,82 including tax, does the business unit generate a margin? If so, how much?

First of all, you must indicate the sales price excluding tax because a margin is always calculated this way.

PV HT = PV TTC ÷ (1 + VAT rate)

We therefore have: PV HT = 53,82 ÷ 1,2 or therefore 44,85 € HT

Then the margin calculation is carried out as follows:

Margin = Selling price excluding VAT – Purchase price excluding VAT

Here again, the formula must be adapted and therefore the purchase cost and not the purchase price must be taken into consideration.

Margin = 44,85 – 25,90

Margin = 18,95 € HT

When the business unit sells a sweater, it makes a margin of €18,95 excluding VAT.

 

 

16/ Chet Case

The Caschet business unit produces and markets medicines.

Its manager, Mrs. Lafarmacie, informs you of various elements of the cost price of the drug referenced “mdr-lol-28”:

Granule: €0,90

Margin rate: 25%

Box: €1,00

Equipment rental: €0,35

Staff costs: €1,25

VAT rate: 20%

 

Work to do

1. Calculate the sales price including tax of the drug “mdr-lol-28”.

 

Proposed correction

1. Calculate the sales price including tax of the drug “mdr-lol-28”.

Using the elements provided, we can first calculate the cost price:

0,90 € + 1,00 € + 0,35 € + 1,25 € or 3,50 €

Le cost price of the medicine is 3,50 €.

Adding the margin using the margin rate gives the selling price excluding tax :

3,50 + (3,50 × 0,25) = 4,375 €

Or 3,50 × 1,25 = €4,375

We just need to take into account the VAT and we get the PVTTC :

4,375 × (1 + VAT rate) or 4,375 × 1,2 = 5,25 €

Le selling price including VAT of the drug "mdr-lol-28" is 5,25 €.

 

17 / Chottier case

The Caschottier business unit produces and markets high-tech elements.

You must complete the table below to demonstrate your mastery of business calculations.

 

Work to do :

1. Complete the table

(1): 350 ÷ 0,12

(2): (1) × (1 + VAT rate) or 2 × 916,66

(3): (2) – (1)

(4): (1) + Commercial margin

(5): (4) × (1 + VAT rate) or 3 × 266,66

(6): (5) – (4)

(7) : (5) ÷ (1)

(8): [Trade margin ÷ (4)] × 100

(9): PV HT × (1 + VAT rate) or 850 × 1,2

(10): (9) – PV HT

(11): Purchase cost excluding VAT × (1 + VAT rate) or 450 × 1,2

(12): (11) – Purchase cost excluding tax

(13): PV HT – Purchase cost HT i.e. 850 – 450

(14): (Trade margin ÷ Purchase cost excluding tax) × 100 or (400 ÷ 450) x 100

(15): (Commercial margin ÷ PV HT) × 100 or (400 ÷ 850) x 100

(16): PV including tax ÷ Purchase cost excluding tax i.e. (9) ÷ 450

 

If you would like to practice with other corrected management exercises on commercial calculations, do not hesitate to visit my article entitled Commercial Calculations: 13 Corrected Exercises – Operational Management.