Welcome to this article dedicated to exercises on business calculations. Here you will find no less than 13 management exercises on business calculations for Operational Management.
This article on Management, commercial calculations corrected exercises, mainly concerns:
- the margin rate
- markup rate
- margin
- the PV including tax
- VAT collected
- deductible VAT
- the PA HT
- the multiplier coefficient
1/ How to calculate the margin
States
The following elements are given:
Selling price excluding VAT: €150
Purchase price excluding VAT: €90
Work to do
- Calculate the margin amount.
Proposed correction
In this exercise, we simply apply the basic margin formula:
PV HT – PA HT = Margin
150 – 90 = 60 €
Interpretation of the result
The margin made on a sale amounts to €60.
2/ How to calculate the PV including tax
States
The following elements are given:
Selling price excluding VAT: €150
VAT rate: 20%
Work to do
- Calculate the amount of the PV including tax.
Proposed correction
In this exercise, you just need to apply the formula for the PV including tax:
PV HT × (1 + VAT rate) = PV TTC
150 × (1 + 20%)
150 × 1,2 = €180
Interpretation of the result
The sales price including all taxes, PV TTC, is €180
3/ How to calculate the markup rate
States
The following elements are given:
Selling price excluding VAT: €150
Purchase price excluding VAT: €90
Work to do
- Calculate the markup rate.
Proposed correction
In this exercise, simply apply the markup rate formula:
[(PV HT – PA HT) ÷ PV HT] × 100 = Mark rate
[(150 – 90) ÷ 150] × 100 = 40%
Interpretation of the result
The value margin represents 40% of the amount of the sale price excluding taxes.
4/ How to calculate deductible VAT
States
The following elements are given:
Purchase price excluding VAT: €90
VAT rate: 20%
Work to do
- Calculate the amount of deductible VAT.
Proposed correction
In this exercise, it is sufficient to apply the deductible VAT formula:
PA HT × VAT rate = Deductible VAT
90 × 20% = €18
Interpretation of the result
The amount of deductible VAT is €18.
5/ How to calculate the margin rate
States
The following elements are given:
Purchase price excluding VAT: €90
Selling price: €150
Work to do
- Calculate the amount of deductible VAT.
Proposed correction
In this exercise, simply apply the margin rate formula:
[(PV HT – PA HT) ÷ PA HT] × 100 = Margin rate
[(150 – 90) ÷ 90] × 100 = 66,66%
Interpretation of the result
The value margin represents 66,66% of the amount of the purchase price excluding taxes.
6/ How to calculate the VAT collected
States
The following elements are given:
VAT rate: 20%
Sale price excluding tax: €150
Work to do
- Calculate the amount of VAT collected.
Proposed correction
In this exercise, simply apply the formula for the VAT collected:
PV HT × VAT rate = VAT collected
150 × 20% = €30
Interpretation of the result
The amount of VAT collected is €30.
7/ How to calculate the multiplier coefficient
States
The following elements are given:
Purchase price excluding tax: €90
Selling price including all taxes: €180
Work to do
- Calculate the multiplier coefficient.
Proposed correction
In this exercise, simply apply the multiplier coefficient formula:
PV TTC ÷ PA HT = Multiplier coefficient
180 ÷ 90 = 2
Interpretation of the result
The merchant applies a multiplier coefficient of 2 on his purchases.
If you would like to practice with other corrected management exercises on commercial calculations, do not hesitate to visit my article entitled Commercial Calculations: 17 Corrected Exercises – Operational Management.
8/ How to calculate the sales price excluding tax
States
The following elements are given:
Purchase price excluding tax: €1
Markup rate: 18%
Work to do
- Calculate the amount of the PV excluding tax.
Proposed correction
In this exercise, it is sufficient to apply the formula for the selling price excluding tax from a mark-up rate:
PA HT ÷ (1 – Mark rate) = PV HT
1 ÷ (000 – 1%)
1 ÷ (000 – 1)
1 ÷ 000 = €0,82
Interpretation of the result
The sales price excluding tax is therefore €1.
9/ How to calculate the VAT collected
States
The following elements are given:
Selling price excluding VAT: €1
Selling price including tax: €1
Work to do
- Calculate the amount of VAT collected.
Proposed correction
In this exercise, simply apply the formula for the VAT collected:
PV including VAT – PV excluding VAT = VAT collected
1 – 463,41 = €1
Interpretation of the result
The VAT collected on sales is therefore €243,90.
10/ How to calculate the selling price excluding tax
States
The following elements are given:
Margin amount: €1
Amount of the purchase price excluding taxes: €3
Work to do
- Calculate the PV HT.
Proposed correction
In this exercise, simply apply the formula for the sales price excluding tax:
PA HT + Margin = PV HT
3 + 500 = €1
Interpretation of the result
The sales price excluding tax is therefore €4.
11/ How to calculate the sales price excluding tax
States
The following elements are given:
Selling price including all taxes: €2
Markup rate: 11%
VAT rate: 20%
Work to do
- Calculate the amount of the PV excluding tax.
Proposed correction
In this exercise, it is sufficient to apply the formula for the selling price excluding tax from a mark-up rate:
PV incl. VAT ÷ (1 + VAT rate) = PV excl. VAT
2 ÷ (500 + 1%)
2 ÷ (500 + 1)
2 ÷ 500 = €1,2
Interpretation of the result
The sales price excluding tax is therefore €2.
12/ How to calculate the sales price excluding tax
States
The following elements are given:
Amount of VAT collected: €500
Multiplier coefficient: 1,8
VAT rate: 20%
Work to do
- Calculate the amount of the PV excluding tax.
Proposed correction
In this exercise, it is sufficient to apply the formula for the selling price excluding tax from the amount of value added tax:
VAT rate × PV excluding VAT = VAT collected
from where : PV HT = VAT collected ÷ VAT rate
500 ÷ 0,2 = €2
Interpretation of the result
The sales price excluding tax is therefore €2.
13/ Commercial calculations: PV HT – Margin – Margin rate
States
You work as an intern at the Carrège company to help them set the selling price of a product.
She tells you that the charges on purchases are estimated at 45% of purchases.
The company typically achieves a margin of around 20% on its sales.
The purchase price of the product is €220 excluding VAT.
It also specifies that the applicable VAT rate is 20%.
Work to do
- Calculate the product's sales price including tax, taking into account that the company wishes to maintain its usual margin.
- Calculate the margin rate.
- The Carrège company decides to sell the product at the price including tax of €490. What would be the margin thus achieved on the product?
- With this same selling price, what should be the proportion of its charges on purchases while preserving its usual markup rate?
Proposed correction
1/ Calculate the product's sales price including tax, taking into account that the company wishes to preserve its usual margin.
Calculation of fees on purchases
First, you can calculate the amount of fees on purchases with the following calculation:
Fees on purchases = 45% of the purchase price excluding VAT
Fees on purchases = €220 × 45%
Fees on purchases = 220 × 0,45
Fees on purchases = €99
The amount of the purchase fees therefore amounts to €99.
Calculation of purchase cost
We can now calculate the purchase cost using the purchase price and the purchase fees calculated above.
Purchase cost = Purchase price + Purchase fees
Purchase cost = €220 + €99, or a total of €319.
The purchase cost amount is therefore €319.
Calculation of the selling price excluding VAT
We can now calculate the selling price excluding VAT using the following formula:
PV HT = Purchase cost ÷ (1 – Markup rate)
In fact, the rate given in the statement is indeed a markup rate because it represents a percentage in relation to sales.
We can apply the formula as follows:
PV HT = 319 ÷ (1 – 20%)
PV HT = 319 ÷ 0,8
PV excluding VAT = €398,75
The sales price excluding tax of the product is therefore €398,75.
Calculation of the sales price including tax
We can finally answer the question posed, namely, the determination of the sales price including tax.
For this we will apply the following formula:
PV including tax = PV excluding tax × (1 + VAT rate)
So we have :
PV incl. VAT = 398,75 × (1 + 20%)
PV incl. VAT = 398,75 × 1,2
PV incl. VAT = €478,50
The product's sales price including tax is therefore €478,50.
2/ Calculate the margin rate.
To calculate the margin rate, simply apply the following formula:
Margin rate = [(PV HT – Purchase cost) ÷ Purchase cost] × 100
We obtain the following calculation:
[(398,75 – 319) ÷ 319] × 100 = 25%
3/ The Carrège company decides to sell the product at the tax-inclusive price of €490. What would be the margin thus achieved on the product?
To calculate the margin, you must have an HT base at the sales price level. We will therefore apply the following formula to transform the PV TTC into PV HT:
PV HT = PV TTC ÷ (1 + VAT rate)
With the numbers this gives us the following calculation:
PV HT = 490 ÷ (1 + 20%)
PV HT = 490 ÷ 1,20
PV excluding VAT = €408,33
We can now calculate the margin using the following formula:
Margin = PV HT – Purchase cost
With the numbers this gives us the following calculation:
Margin = 408,33 – 319
Margin = €89,33
If the Carrège company sells its product at €490 including tax, it will achieve a unit margin of €89,33.
4/ With this same sale price, what should be the proportion of its charges on purchases while preserving its usual markup rate?
To answer this question, you have to think "backwards."
You must calculate the margin then perform the calculations to find the new purchase cost then the requested proportion.
Margin Calculation
To calculate the margin, we will apply the following formula:
Margin = PV HT × Markup rate
With the encrypted elements, this gives us the following calculation:
Margin = 408,33 × 20%
Margin = €81,66
The margin, taking into account the usual markup rate, therefore amounts to €81,66.
Calculation of the new purchase cost
We will apply the following formula for this calculation:
Purchase cost = PV excluding tax – Margin (since Purchase cost + Margin = PV excluding tax)
With the numbers this gives:
Purchase cost = 408,33 – 81,66
Purchase cost = €326,67
The new purchase cost is therefore €326,67.
Calculation of the new amount of fees on purchases
Now we know that the purchase cost is made up of two elements: the purchase price and the purchase costs.
The purchase price excluding VAT remains unchanged, so it is €220. To find the amount of the purchase fees, simply subtract the purchase cost from the purchase price.
The new amount of fees on purchases therefore amounts to:
Fees on purchases = 326,67 – 220
Fees on purchases = €106,67
The purchase fees are now €106,67.
Calculation of the desired proportion
To find the required proportion, we will do the following calculation:
Proportion = (Purchase costs ÷ Purchase cost) × 100
Proportion = (106,67 ÷ 326,67) × 100
Proportion = 32,65%
The Carrège company must therefore reduce the proportion of its purchasing costs to 32,65% if it wishes to maintain its usual mark-up rate while selling its product at €408,33 excluding VAT (€490 including VAT).
If you would like to practice with other corrected management exercises on commercial calculations, do not hesitate to visit my article entitled Commercial Calculations: 17 Corrected Exercises – Operational Management.
Very well