For this first article on the management course, I decided to start with the business calculations. Indeed, this is a chapter that you absolutely must know.
The students in BTS MCO, management teachers, and even professionals such as managers or salespeople must absolutely master these calculations because they are the fundamentals of any salesperson worthy of the name.
Here's what you'll learn in this article:
- List of 36 formulas
- List of business calculations to know
- The multiplier coefficient
- VAT
- Discounts
- The increases
- Margin
- The margin rate
- The mark rate
- The evolutions
List of 36 commercial calculation formulas:
[Multiplier coefficient (2)]
- Formula n°1: PA excluding tax x CM = PV including tax
- Formula no. 2: CM = PV including tax / PA excluding tax
[VAT (8)]
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- Formula No. 3: VAT amount = Price including tax – Price excluding tax
- Formula No. 4: VAT collected on sales = PV excluding VAT x VAT rate
- Formula No. 5: Deductible VAT on purchases = Amount of expenditure x VAT rate
- Formula no. 6: PV including tax = PV excluding tax x (1 + VAT rate)
- Formula no. 7: PV including tax = PV excluding VAT + Amount of VAT
- Formula no. 8: PV excluding VAT = PV including VAT / (1 + VAT rate)
- Formula no. 9: VAT to be paid (for month M) = VAT collected for month M – Deductible VAT for month M – VAT credit (M-1)
- Formula No. 10: VAT to be paid = VAT to be paid for the month (M-1)
[Discounts (3)]
- Formula #11: Discount Amount = Base Price x Discount Rate
- Formula #12: Discounted price = Base price x (1- Discount rate)
- Formula #13: Base price = Discounted price ÷ (1- Discount rate)
[Increases (4)]
- Formula No. 14: Amount of the increase = Base price excluding tax x Increase rate
- Formula No. 15: Increased price (after increase) = base price excluding tax x (1 + Increase rate)
- Formula No. 16: Increased price (after increase) = Base price excluding tax + increase (the increase)
- Formula No. 17: Base price excluding VAT = Increased price (after increase) ÷ (1 + Increase rate)
[Margin (8)]
- Formula No. 18: Turnover (TO HT) = Sum of the company's sales excluding tax (goods, products, services)
- Formula #19: Fixed cost = cost that does not depend on the company's activity (e.g.: rent, salaries)
- Formula #20: Variable cost = cost that depends on the level of activity of the company (e.g.: purchases of raw materials, purchases of goods, purchases of supplies)
- Formula #21: Margin (overall) = Turnover – Costs
- Formula No. 22: Margin (unit) = PV HT – PA HT
- Formula #23: Gross margin = Turnover – Variable costs
- Formula #24: Net margin = Turnover – Variable costs – Fixed costs
- Formula #25: Net margin = Profit for the financial year
[Margin rate (4)]
- Formula #26: Margin rate = [(PV HT – PA HT) ÷ PA HT)] x 100
- Formula No. 27: Margin rate = (commercial margin ÷ PA HT) x 100
- Formula #28: PV HT = PA HT x (1 + Margin rate)
- Formula #29: PA HT = PV HT ÷ (1 + Margin rate)
[Mark Rate (4)]
- Formula #30: Mark rate = [(PV HT – PA HT) ÷ PV HT)] x 100
- Formula #31: Markup rate = (Commercial margin ÷ PV excluding tax) x 100
- Formula No. 32: Sales price excluding tax (SVP excluding tax) = HT PA ÷ (1 – Markup rate)
- Formula No. 33: Purchase price excluding tax (PA HT) = PV HT x (1 – Markup rate)
[Evolutions (3)]
- Formula #34: [(End Value – Start Value) ÷ Start Value] x 100
- Formula n°35: [(V2 – V1) ÷ V1] x 100
- Formula #36: (VA/VD)^{1/n} – 1 (“n” corresponds to the number of intervals between each period)
List of business calculations to know
- VAT calculation
- Margin calculation
- Calculation of turnover
- Calculation of pvht selling price excluding tax
- Calculation of the sales price including tax
- Margin rate calculation
- Calculation of the mark rate
- Gross margin calculation
- Calculation of net margin
- Calculation of the commercial margin
- Calculation of the mscv margin on variable cost
- Discount calculation
- Calculation of increase
- Calculation of the rate of change
The Multiplier Coefficient (MC)
The CM or the multiplier coefficient is a figure which allows you to go directly from the purchase price excluding tax (PA HT) to the sale price including tax (PV TTC).
The multiplier coefficient is used to determine the selling price from the purchase cost of their goods.
We can therefore write the following formula:
PA HT x CM = PV TTC
If we want to obtain the formula for the multiplier coefficient, we can transform the previous formula as follows:
CM = PV including tax / PA excluding tax
To illustrate the above formulas, I will take an example.
PA HT = 15 € and CM = 1,9
PV incl. VAT = 15 x 1,9 = €28,5
Example No. 1: How to find the PV including tax?
Let's take the example of a company that applies a multiplier coefficient of 4,5 on kitchen items from international brands.
The unit price of a product excluding VAT is €96,60 excluding tax. Let's calculate the selling price including VAT.
It is therefore necessary to multiply the purchase price excluding tax by the multiplier coefficient, which amounts to writing the following operation:
€96,64 x 4,5 = €434,88 including tax
To interpret this result, it is enough to say that for a product purchased for €96,60, it is sold at the price including all taxes of €434,88.
Example No. 2: How to calculate the multiplier coefficient?
I will now take a second example in which we are looking for the multiplier coefficient.
In this second example we will assume that the sales price including tax is €28,50 and that the purchase price is €15.
If we apply the formula CM = PV including tax / PA excluding tax then we will have with the encrypted elements the following calculation:
28,50 € / 15 € = 1,9
Note 1
I would like to point out that you should not indicate a unit because it is a coefficient. This is why you should not put a currency and even less specify that it is a percentage.
Note 2
You have probably noticed that we are moving from one number without taxes single digit VAT Incl..
In fact, we must conclude that there is VAT in the multiplier coefficient since we are moving from a PA excluding VAT to a PV including VAT.
Multiplier coefficient – 2 Formulas to remember
- PA HT x CM = PV TTC
- CM = PV including tax / PA excluding tax
VAT
VAT corresponds to the value added tax which applies to products and services and which is collected by the State.
VAT Rates
Since 01/01/2014 the various VAT rate are the following :
- le normal rate, which applies to the majority of goods and services, increases from 19,6% to 20%;
- le intermediate rate, which particularly concerns catering, the sale of prepared food products, transport, renovation work in old housing, is increased from 7% to 10%;
- the rate applicable in Corsica increases from 8% to 10%.
- Le reduced rate, applicable to products considered essential (food products, non-alcoholic drinks, school canteens and energy) and live entertainment (theater, concerts, circus), remains fixed at 5,5%.
We distinguish the Deductible VAT which corresponds to the amount of VAT during an expense (a purchase for example) and the VAT collected which corresponds to the amount of VAT during a sale.
The difference between the VAT collected and the deductible VAT is called the VAT payable.
The VAT payable for one month becomes the VAT to be paid the following month. The VAT amount is not changed, it is actually paid to the state.
If you want to know much more about VAT, I invite you to visit the government website at this address.
Important Note :
When the amount of VAT collected is less than the amount of deductible VAT, the difference gives a VAT credit. Which generates an amount owed by the State to the company. Generally, this VAT credit is used to reduce the next declaration owed by the company.
Example 1 : How to calculate the VAT collected?
Let's take a first example with the following elements in order to find the amount of the VAT collected :
PV incl. tax = €150 and PV excl. tax = €125
Let's calculate the amount of VAT collected with the formula:
VAT collected = 150 – 125 = €25
Example 2 : How to calculate deductible VAT?
In this second example I will calculate the amount of the Deductible VAT from the following elements: PA including tax = €18 and PA excluding tax = €15
Let’s calculate the amount of deductible VAT:
VAT collected = 18 – 15 = €3
Example 3 : How to calculate an amount excluding tax from an amount including tax?
In this third example I will calculate the amount of selling price including VAT from the following elements: PV HT = €18 and VAT rate = 20%
Let's calculate the PV including tax:
PV incl. VAT = 18 x (1 + 20%)
PV incl. VAT = 18 x 1,2
PV incl. VAT = €21,60
Example 4 : How to calculate a PV including tax?
In this fourth example I will calculate the amount of selling price including VAT from the following elements: PV excluding tax = €78 and VAT collected = €15,60
Let's calculate the PV including tax:
PV including tax = 78 + 15,60 = €93,60
Example 5 : How to find the PV HT?
In this fifth example I will calculate the amount of selling price excluding tax from the following elements: PV including tax = €253,20 and VAT rate = 5,5%
Let’s calculate the PV HT:
PV HT = 253,20 ÷ (1 + 5,5%)
PV HT = 253,20 ÷ (1 + 0,055)
PV HT = 253,20 ÷ 1,055
PV excluding VAT = €240
Example 6 : How to calculate the VAT to be paid?
In this sixth example I will calculate the amount of the VAT payable to the State based on the following elements: VAT collected = €45 and deductible VAT = €000
Let's calculate the amount of VAT to be paid to the State:
VAT payable = 45 – 000 = €32
Example 7 : How to calculate the VAT to be paid?
In this seventh example I will calculate the amount of the VAT to be paid from the following elements: VAT payable for the month of August = €45 – VAT payable for the month of September = €000 – VAT payable for the month of October = €28
Let’s calculate the amount of VAT to be paid:
VAT to be paid in September = €45
VAT to be paid in October = €28
VAT to be paid in November = €33
VAT – 8 Formulas to remember
- VAT amount = Price including tax – Price excluding tax
- VAT collected on sales = PV excluding VAT x VAT rate
- Deductible VAT on purchases = Amount of expenditure x VAT rate
- PV including VAT = PV excluding VAT x (1 + VAT rate)
- PV including VAT = PV excluding VAT + Amount of VAT
- PV excluding VAT = PV including VAT / (1 + VAT rate)
- VAT payable (for month M) = VAT collected for month M – Deductible VAT for month M – VAT credit (M-1)
- VAT to be paid = VAT to be paid for the month (M-1)
Discounts
Principle :
This is usually a rate that is applied to a price. It is possible to have several consecutive reductions. It is then necessary to do the cascade calculations, that is to say gradually, one after the other. In addition, reductions cannot be combined with increases.
I will take three examples to illustrate reduction calculations.
Example 1 :
In this first example I will calculate the amount of the reduction from the following elements: Discount rate = 3% and Base price excluding VAT = €155
Let's calculate the amount of the discount:
Discount amount = 155 x 3%
Amount of reduction = 155 x 0,03
Discount amount = €4,65
Example 2 :
In this second example I will calculate the amount of discounted price from the following elements: Discount rate = 5% and Base price excluding VAT = €190
Let's calculate the discounted price (or net amount), that is, the amount after the reduction:
Discounted price = 190 x (1- 5%)
Discounted price = 190 x (1 – 0,05)
Discounted price = 190 x 0,95
Discounted price = €180,50
Example 3 :
In this third example I will calculate the amount of base price excluding VAT from the following elements: Discount rate = 5% and Discounted price = €210
Let's calculate the base price:
Base price = 210 ÷ (1 – 5%)
Base price = 210 ÷ (1 – 0,05)
Base price = 210 ÷ 0,95
Base price = €221,05
Discounts – 3 formulas to remember
- Discount Amount = Base Price x Discount Rate
- Discounted price = Base price x (1- Discount rate)
- Base price = Discounted price ÷ (1- Discount rate)
The Increases (Increases)
Principle :
This is usually a rate that is applied to a price. It is possible to have several consecutive increases. It is then necessary to do the calculations in cascade, that is to say gradually, one after the other. In addition, it is not possible to combine reductions with increases.
I will take 4 examples to illustrate the commercial calculations of increases (=markups).
Example 1 :
In this first example I will calculate the amount of the increase from the following elements: Increase rate = 3% and Base price excluding tax = €155
Let’s calculate the amount of the increase:
Amount of the increase = 155 x 3%
Amount of the increase = 155 x 0,03
Amount of the increase = €4,65
Example 2 :
In this second example I will calculate the increased price from the following elements: Increase rate = 5% and Base price excluding tax = €190
Let’s calculate the increased price (net amount):
Increased price = 190 x (1+ 5%)
Increased price = 190 x (1 + 0,05)
Increased price = 190 x 1,05
Increased price = €199,50
Example 3 :
In this third example I will calculate the increased price from the following elements: Amount of the increase = €38 and Basic amount excluding tax = €149
Let's calculate the increased price:
Increased price = €149 + €38
Increased price = €187
Example 4 :
In this fourth and final example I will calculate the base price excluding VAT from the following elements: Increased price = €238 and Increase rate = 2%.
Let's calculate the base price:
Base price excluding VAT = €238 ÷ (1 + 2%)
Base price excluding VAT = 238 ÷ (1 + 0,02)
Base price excluding VAT = 238 ÷ 1,02
Base price excluding VAT = €233,33
The Increases – 4 Formulas to Remember
- Amount of the increase = Base price excluding tax x Increase rate
- Increased price (after increase) = base price excluding VAT x (1 + Increase rate)
- Increased price (after increase) = Base price excluding VAT + increase (the increase)
- Base price excluding VAT = Increased price (after increase) ÷ (1 + Increase rate)
Margins
Turnover :
Before talking about margins, it is important and necessary to recall the definition of net turnover.
The net turnover corresponds to all sales of goods and/or services of the company for an accounting year. Generally, it is indicated excluding taxes (HT).
La Marge :
Margin is the difference between turnover and a cost. It is always calculated excluding taxes (HT). We can distinguish between gross margin (also called "margin on variable costs") and net margin. For this distinction, it is necessary to know two types of costs: the fixed costs and variable costs.
A fixed cost does not depend on the activity of the company. This includes, for example, rent or salaries.
A variable cost depends on the level of activity of the companyExamples include purchases of raw materials or purchases of goods.
To illustrate the commercial calculations on the margin, I will take 7 examples so that you can master them well.
Example 1 : How to calculate turnover?
In this first example I will calculate the amount of turnover excluding tax from the following elements: Sales of goods = €150, Sales of finished products = €000 and Provision of services = €25.
Let’s calculate the amount of turnover (CA):
Turnover = 150 + 000 + 25 = €000
Example 2 : How to calculate unit margin?
In this second example I will calculate the amount of the unit margin from the following elements: Sales price excluding tax (PV HT) = €15 and Purchase price excluding tax (PA HT) = €4,50.
Let's calculate the margin amount:
Margin = 15 – 4,50 = €10,50
Example 3 : How to calculate variable costs and net costs?
In this third example I will calculate the amount of variable charges and net charges from the following elements: Rent = €5, Purchases of goods = €000, Salaries = €85, Bonuses = €000.
Let’s calculate the amount of fixed charges, then variable charges:
Fixed charges = 5 + 000 = €105
Variable charges = 85 + 000 = €38
Example 4 : How to calculate the overall margin?
In this fourth example I will calculate the amount of the overall margin from the following elements: Turnover excluding tax = €20 and total expenses = €000.
Let's calculate the amount of the overall margin:
Margin = 20 – 000 = €7
Example 5 : How to calculate gross margin?
In this fifth example I will calculate the amount of the Gross margin from the following elements: Turnover = €40 and variable costs = €000.
Let’s calculate the gross margin amount:
Gross margin = 40 – 000 = €7
Example 6 : How to calculate net margin?
In this sixth example I will calculate the amount of the net margin from the following elements: Turnover excluding tax = €250, gross expenses = €000 and fixed expenses = €7.
Let’s calculate the net margin amount:
Net margin = 250 – 000 – 7 = €500
If you want to know more about net margin and gross margin, I suggest you watch this video:
Example 7 : How to find the net margin amount?
In this seventh and final example I will calculate the amount of the net margin from the following element: Debit balance: Profit = €150.
Let’s calculate the net margin amount:
The profit corresponds to the result of the financial year, so the net margin is €150.
Margin – 8 Formulas to Remember
- Turnover (TO HT) = Sum of the company's sales excluding tax (goods, products, services)
- Fixed cost = cost that does not depend on the activity of the company (e.g.: rent, salaries)
- Variable cost = cost that depends on the level of activity of the company (eg: purchases of raw materials, purchases of goods, purchases of supplies)
- Margin (overall) = Turnover – Costs
- Margin (unit) = PV HT – PA HT
- Gross margin = turnover – variable costs
- Net margin = Turnover – Variable costs – Fixed costs
- Net margin = Profit for the financial year
The Margin Rate
The Margin Rate represents the commercial margin expressed as a percentage of the purchase price excluding tax (PA excluding tax). It is also called "Gross margin rate" or "Commercial margin rate". The notion of purchase price (PA HT) is to be taken in the broad sense. Indeed, it is, in truth, according to the statement of the problem, to take into account the highest cost.
To illustrate the commercial calculations on the margin rate, I will take 4 examples.
Example 1 : How to calculate the margin rate with the PV HT?
In this first example I will calculate the margin rate from the following elements: Sales price excluding tax (PV HT) = €25 and Purchase price excluding tax (PA HT) = €20
Let's calculate the margin rate:
Margin rate = ((25 – 20) ÷ 20) x 100 = 25%
Example 2 : How to calculate the margin rate with the commercial margin?
In this second example I will calculate the margin rate from the following elements: Commercial margin = €58 and purchase price excluding tax (PA HT) = €208
Commercial margin = €58 and purchase price excluding tax (PA HT) = €208
Let's calculate the margin rate:
Margin rate = (58 ÷ 208) x 100 = 27,88%
Example 3 : How to calculate the PV HT with the PA HT?
In this third example I will calculate the selling price excluding VAT from the following elements: Purchase price (PA excluding VAT) = €150 and margin rate = 20%
Purchase price (PA HT) = €150 and margin rate = 20%
Let’s calculate the selling price (PV excluding VAT):
PV HT = 150 x (1 + 20%)
PV HT = 150 x (1 + 0,2)
PV HT = 150 x 1,2
PV excluding VAT = €180
Example 4 : How to calculate the PA HT with the PV HT?
In this fourth example I will calculate the purchase price excluding VAT from the following elements: Selling price (excluding VAT) = €195 and margin rate = 10%
Let’s calculate the purchase price (PA excluding VAT):
PA HT = 195 ÷ (1 + 10%)
PA HT = 195 ÷ (1 + 0,1)
PA HT = 195 ÷ 1,1
PA HT = €177,27
The Margin Rate – 4 Formulas to Remember
- Margin rate = [(PV HT – PA HT) ÷ PA HT)] x 100
- Margin rate = (commercial margin ÷ PA HT) x 100
- PV excluding tax = PA excluding tax x (1 + Margin rate)
- PA HT = PV HT ÷ (1 + Margin rate)
The Mark Rate
The markup rate represents the commercial margin expressed as a percentage of the selling price excluding tax (PV excluding tax). In applications, the notion of purchase price (PA HT) is to be taken in the broad sense. Indeed, it is, in truth, according to the statement of the problem, to take into account the highest cost.
To illustrate the commercial calculations on the Markup Rate, I will take 4 examples.
Example 1 : How to calculate the mark rate with the PV excluding tax?
In this first example I will calculate The Mark Rate from the following elements: Sales price excluding tax (PV HT) = €25 and Purchase price excluding tax (PA HT) = €15
Let's calculate the markup rate:
Markup rate = ((25 – 15) ÷ 25) x 100 = 40%
Example 2 : How to calculate the markup rate with the commercial margin?
In this second example I will calculate The Mark Rate from the following elements: Commercial margin = €60 and sales price excluding tax (PV HT) = €100
Let’s calculate the Markup Rate:
Markup rate = (60 ÷ 100) x 100 = 60%
Example 3 : How to find the PVHT with the mark rate?
In this third example I will calculate the selling price excluding VAT from the following elements: Purchase price excluding tax (PA HT) = €25 and Brand rate = 20%
Let’s calculate the selling price (PV excluding VAT):
PV HT = 25 ÷ (1 – 20 %)
PV HT = 25 ÷ (1 – 0,2)
PV HT = 25 ÷ 0,8 = €31,25
Example 4 :
In this fourth and final example I will calculate the purchase price excluding VAT from the following elements: Sales price excluding tax (SRP excluding tax) = €45 and Markup rate = 20%
Let’s calculate the purchase price (PA excluding VAT):
PA HT = 45 x (1 – 20%)
PA HT = 45 x (1 – 0,2)
PA HT = 45 x 0,8 = €36
The Markup Rate – 4 Formulas to Remember
- Mark rate = [(PV HT – PA HT) ÷ PV HT)] x 100
- Markup rate = (Commercial margin ÷ PV excluding tax) x 100
- Selling price excluding tax (PV HT) = PA HT ÷ (1 – Markup rate)
- Purchase price excluding tax (PA HT) = PV HT x (1 – Markup rate)
The evolutions
In this last part of the business calculations, we will see two possibilities to show an evolution. These are the classic evolution rate and the average annual evolution rate.
The Classic Rate of Evolution :
This is a percentage that allows us to know how an element has evolved over time between two periods.
The Average Annual Growth Rate (AAGER) :
This is a percentage that allows us to know how an element has evolved over time over more than two periods..
I will show you two examples to illustrate the above definitions.
Example 1 :
In this first example I will determine the classic rate of evolution from the following elements: Turnover N-1 = €150 and turnover N = €000
Let's calculate the classical rate of change:
Rate of change = ((275 – 000) ÷ 150) x 000
Rate of change = 83,33%
Example 2 :
In this second example I will determine the average annual rate of change from the following elements: Turnover N-2 = €150, turnover N-000 = €1 and turnover N = €275
Let's calculate the average annual rate of change (AARC):
Average annual growth rate (AAR) = (200000/150000) ^ {1/2} – 1
Average annual growth rate (AAR) = 0,1547 or 15,47%
The developments – 3 formulas to remember
- [(Arrival Value – Start Value) ÷ Start Value] x 100
- [(V2 – V1) ÷ V1] x 100
- (VA/VD)^{1/n} – 1 (“n” corresponds to the number of intervals between each period)
Conclusion
Commercial calculations must be known by all those who want to pass the BTS MCO or any other BTS Tertiary. Essential, they will help you understand and solve Management exercises in different chapters of the BTS operational commercial management program.
If you want to apply everything you have just learned, I strongly encourage you to read the article on corrected management exercises entitled Commercial Calculations: 17 Corrected Exercises – Operational Management.
There you have it, now you have at your disposal a list of business calculation formulas. You no longer have any excuses for not reaching your goal: Get an excellent grade in the Operational Management test!