Welcome to this article whose sole purpose is to help you progress with examples ofbreak-even exercises of the Operational Management subject of the BTS MCO.
Each example ofbreak-even exercise is unique and targets different objectives.
If you would like to first see or review the course on the same theme, I invite you to read my article Calculation of the break-even point.
Lesson 11 Corrected exercises on the break-even point of this page mainly concern the break-even point, the dead point, differential income statement.
In this section:
- Application: ChicModa Clothing Store
- Application: Prestigio Restaurant Company
- Application: The Flaming Scents
- Application: FashionCorp
- App: Sweet Treats Bakery
- Application: Conservifruits Company
- Application: Paul's Treats
- Application: TechGuru Enterprise
- Application: Extrema Energy
- Application: The Parisian Gourmet
- Application: Chocolate Delights Company
Application: ChicModa Clothing Store
States :
ChicModa Clothing Store decides to launch a new clothing collection for the spring-summer season. They have determined that the fixed costs will total €25, while the unit variable costs are €000 for each garment. The unit selling price has been set at €15.
Work to do :
1/ What is the amount of fixed costs?
2/ What is the unit selling price?
3/ What is the unit variable cost?
4/ How many units does ChicModa need to sell to reach the break-even point?
5/ What is the total income at break-even point?
Proposed correction:
1/ Fixed costs are €25.
2/ The unit sale price is €40.
3/ The unit variable cost is €15.
4/ The Break-Even Point (BEP) is calculated as follows: Fixed Cost ÷ (Unit Selling Price – Unit Variable Cost). So, in the case of ChicModa, the BEP is 25 ÷ (000 – 40) = 15 pieces. The store must therefore sell 1 pieces to reach the break-even point.
5/ Total revenue at break-even point is Unit Sales Price x Break-even Sales Volume. So in this case, total revenue at break-even point is 40 x 1 = €000.
Summary of Formulas Used:
| Packages |
|---|
| Break-even Point (BTP) = Fixed Cost ÷ (Unit Selling Price – Unit Variable Cost) |
| Total Revenue at Break-Even Point = Unit Selling Price x Break-Even Sales Volume |
Application: Prestigio Restaurant Company
States :
The Prestigio Restaurant Company is a high-end restaurant located in the heart of Paris. The manager of the establishment is questioning the financial viability of his company. He has prepared a new menu for the next season and wants to estimate his break-even point in order to determine the minimum number of meals to sell to cover all costs.
Here is the information collected:
– Menu sale price excluding tax: €50
– Cost of purchasing the menu excluding tax: €20
– Number of meals sold per year: 20
– Annual fixed charges (rent, fixed salaries, etc.): €360
– VAT = 20%
After the first year of operation, the manager notices that fixed costs have increased by 10% and the pre-tax purchase price of the menu has also increased by €2. What happens to the break-even point? What can he do?
Work to do :
1. Calculate the break-even point of Prestigio Restaurant Company for the first year.
2. Calculate the new break-even point for Prestigio Restaurant Company for the second year.
3. How does the increase in fixed costs and the purchase price excluding VAT affect the break-even point?
4. What options are available to the manager to maintain profitability?
5. What would be the new break-even point if the manager decided to increase the menu's selling price excluding tax by 5%?
Proposed correction:
1. The break-even point is the quantity of product that must be sold to cover all costs. Its formula is: Break-even point = Fixed costs ÷ (Selling price excluding VAT – Purchase cost excluding VAT)
Break-even point = €360 ÷ (€000 – €50) = 20 menus to sell
2. For the second year, fixed charges increased by 10% and the purchase cost excluding tax increased by €2.
New fixed charges = €360 x 000 = €1,10
New purchase cost excluding tax = €20 + €2 = €22
New Break-Even Point = €396 ÷ (€000 – €50) = 22 menus to sell
3. The increase in fixed costs and the cost of purchasing excluding VAT has increased the break-even point. This means that the restaurant must sell more menus to cover all its costs.
4. The manager can either increase the selling price excluding tax, or reduce costs (fixed charges or purchase cost excluding tax), or both, to maintain profitability.
5. If the manager increases the menu's selling price excluding VAT by 5%, the new selling price excluding VAT would be €50 x 1,05 = €52,50.
New Break-Even Point = €396 ÷ (€000 – €52,50) = 22 menus to sell
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Break-even point = Fixed costs ÷ (Selling price excluding VAT – Purchase cost excluding VAT) | Calculation of the break-even point in number of products to sell |
| New fixed charges = Old charges x 1,10 | Calculation of the 10% increase in fixed charges |
| New purchase cost excluding tax = Old cost + €2 | Calculation of the increase in the purchase cost of €2 |
| New Selling Price excluding VAT = Old Price x 1,05 | Calculation of the 5% increase in the selling price excluding tax |
Application: The Flaming Scents
States :
The boutique "Les Senteurs Enflammées", specializing in the manufacture and sale of scented candles, would like to take stock of its profitability. Here is their annual report:
– Quantity sold: 10 candles
– Unit sale price (including tax): €20
– Unit sale price (excluding VAT): €16,67
– Unit variable cost (excluding VAT): €7
– Fixed cost (excluding VAT): €30
Work to do :
1. Calculate the company's break-even point in number of units.
2. Determine the turnover (excluding tax) of Les Senteurs Enflammées.
3. Assuming the company reaches exactly its break-even point, how many sales (in number of units) do they have left to reach their annual sales volume?
4. If Les Senteurs Enflammées decides to increase its unit variable cost to €8, how does this impact the break-even point?
5. What would be the impact on the break-even point if the company decides to reduce its fixed costs to €25?
Proposed correction:
1. To calculate the break-even point (BTP), we use the formula: BTP = Fixed Ct ÷ ((Unit Pv – Unit Cv) ÷ Unit Pv). With the information given by the statement, the BTP = €30 ÷ ((€000 – €16,67) ÷ €7) which gives us a BTP of approximately 16,67 units.
2. To calculate the company's turnover (TO), we use the formula: TO = unit sales x quantity sold. Therefore, TO = €16,67 x 10 units = €000.
3. The company's annual sales volume is 10 units while the break-even point is 000 units. Our subtractions give 4 – 773 = 10 units. So there are 000 units left to sell to reach the annual sales volume.
4. If the unit variable cost increases to €8, the SR = €30 ÷ ((€000 – €16,67) ÷ €8) = approximately 16,67 units. The break-even point increases as the unit variable cost increases.
5. If the company decides to reduce its fixed costs to €25, the SR = €000 ÷ ((€25 – €000) ÷ €16,67) = approximately 7 units. The break-even point decreases as fixed costs decrease.
Summary of Formulas Used:
| Spas | Formulas |
|---|---|
| Break-Even Point (BEP) | SR = Fixed Ct ÷ ((Unit PV – Unit Cv) ÷ Unit PV) |
| Turnover (CA) | CA = Unit PV x quantity sold |
| Unit variable cost (Unit CV) | Unit CV = Total variable cost ÷ quantity produced |
| Selling price (unit PV) | From the data in the statement |
Application: FashionCorp
States :
FashionCorp, a fashion company, wants to increase its sales of ready-to-wear clothing. To do this, it analyzes its break-even point to ensure that it reaches at least that level of sales to cover its costs.
For the current year, here is some relevant information:
– Unit selling price (USP): €50
– Unit purchase price (PAU): €23
– Fixed costs: €6
Work to do :
1. Calculate the unit variable cost margin (MCV).
2. Calculate the margin rate on unit variable cost.
3. Calculate the break-even point in quantity.
4. Calculate the break-even point in terms of turnover.
5. What is the impact if fixed costs increase by 10%?
Proposed correction:
1. Unit MCV = PVU – PAU = €50 – €23 = €27
2. Unit MCV rate = (MCV ÷ PVU) x 100 = (27 ÷ 50) x 100 = 54%
3. Break-even point in quantity = Fixed Costs ÷ Unit MCV = 6000 ÷ 27 ? 222 units (rounded up)
4. Break-even point in turnover = Break-even point in quantity x PVU = 222 x 50 = €11100
5. If fixed costs increase by 10%:
New fixed costs = Fixed costs x 1,10 = €6000 x 1,10 = €6600
New break-even point in quantity = New fixed costs ÷ unit MCV = 6600 ÷ 27 ? 244 units (rounded up)
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| MCV unit = PVU – PAU | Calculates the margin on unit variable cost |
| Unit MCV rate = (MCV ÷ PVU) x 100 | Calculates the margin rate on unit variable cost |
| Break-even point in quantity = Fixed Costs ÷ Unit MCV | Calculate the break-even point in quantity |
| Break-even point in sales = Break-even point in quantity x PVU | Calculates the break-even point in terms of sales figures |
| New fixed costs = Fixed costs x 1,10 | Calculates new fixed costs after 10% increase |
| New break-even point in quantity = New fixed costs ÷ unit MCV | Calculates the new break-even point in quantity after a 10% increase in fixed costs |
App: Sweet Treats Bakery
States :
Sweet Treats Bakery is a cottage industry that bakes and sells cakes, biscuits and other sweet baked goods. The company's annual fixed costs are €45 and its variable costs per unit are €000.
The unit selling price of their products is €5,00. The VAT applied is 20%.
The company wants to increase its unit selling price to €5,50 to increase its margins, but is concerned about the impact on its break-even point.
Work to do :
1. Calculate the company's current break-even point.
2. Calculate the company's break-even point after the price increase.
3. Based on these calculations, will the company need to sell more or fewer units to break even after the price increase?
4. Should the company increase its price?
5. What would be the impact on the margin rate and the brand rate after the increase in the selling price?
Proposed correction:
1. The break-even point is calculated by dividing annual fixed costs by the marginal contribution per unit, which is the difference between the unit selling price and the unit variable costs. Therefore, the current break-even point is €45 ÷ (€000 – €5,00) = 3,20 units.
2. If the price increases to €5,50, the break-even point will be €45 ÷ (€000 – €5,50) = 3,20 units rounded to 19 units.
3. Based on these calculations, the company will need to sell fewer units to break even after the price increase.
4. Raising prices would reduce the number of units the firm must sell to cover its costs, which could allow it to generate more profits. However, the possible consequences on demand would also have to be taken into account.
5. The impact on the margin rate would be ((€5,50 – €3,20) ÷ €3,20) x 100 = 72,5%. For the brand rate, it would be ((€5,50 – €3,20) ÷ €5,50) x 100 = 41,81%.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Break-even point = Fixed costs ÷ (Unit selling price – Unit variable costs) | This formula is used to determine the quantity of units the company must sell to cover all of its expenses. |
| Margin rate = ((Unit selling price – Unit purchase cost) ÷ Unit purchase cost) x 100 | This formula is used to calculate the margin as a percentage of the unit purchase cost. |
| Markup Rate = ((Unit Selling Price – Unit Purchase Cost) ÷ Unit Selling Price) x 100 | This formula is used to calculate the margin as a percentage on the unit selling price. |
Application: Conservifruits Company
States :
The company Conservifruits specializes in the production and sale of fruit preserves. It wants to calculate its break-even point for the next fiscal year. Here are some financial data about the company:
– Turnover: €2
– Variable expenses: €1
– Fixed charges: €500
Work to do :
1. Calculate the margin rate on variable cost.
2. Calculate the break-even point in terms of turnover.
3. Calculate the result of the exercise.
4. Determine the number of cans to sell to reach the break-even point if the unit selling price is €50.
5. What does the break-even point mean?
Proposed correction:
1. The variable cost margin rate is calculated by subtracting the amount of variable costs from the turnover, the whole divided by the turnover. It is expressed as a percentage.
So TMCV = ((CA – CV) ÷ CA) x 100
TMCV = ((€2 – €000) ÷ €000) x 1
TMCV = 40%
2. The break-even point in terms of turnover is obtained by dividing fixed costs by the variable cost margin rate.
So SR = CF ÷ TMCV
SR = €500 ÷ 000
SR = €1
3. The result for the financial year is obtained by subtracting expenses (fixed and variable) from turnover.
So R = CA – (CF + CV)
R = €2 – (€000 + €000)
R = €300
4. The break-even point in number of units is calculated by dividing the break-even point in turnover by the unit sales price.
So SRN = SR ÷ unit PV
SRN = €1 ÷ €250
SRN = 25 units
5. The break-even point obtained means that the company Conservifruits must sell at least 25 cans of fruit to cover its costs (fixed and variable) and make neither profit nor loss.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Variable cost margin rate (VCM) = ((CA – CV) ÷ CA) x 100 | It measures the portion of turnover that contributes to covering fixed costs and generating profit. |
| Break-even point in turnover (SR) = CF ÷ TMCV | It indicates the turnover necessary for the company to make neither a profit nor a loss. |
| Result of the exercise (R) = CA – (CF + CV) | It allows you to know whether the company made a profit or a loss during the financial year. |
| Break-even point in number of units (BTU) = BTU ÷ Unit PV | It shows how many units the company needs to sell to break even. |
Application: Paul's Treats
States :
Paul runs a small bakery called "Les Gourmandises de Paul". Every day, he produces different types of bread and pastries, but his flagship product is the baguette.
He recently purchased a new machine for producing baguettes, which increased his production costs. The unit variable cost is €0,50 per baguette, and the annual fixed cost is €70. Paul sells each baguette for €000.
Work to do :
1. Calculate the unit variable cost margin for each baguette.
2. Calculate the break-even point in number of baguettes.
3. If Paul sells 150 baguettes this year, will he be able to cover his expenses?
4. What would be the new break-even point if fixed costs increased by €10?
5. If Paul wants to reduce his break-even point by 15%, what should the new unit contribution margin be?
Proposed correction:
1. The margin on the unit variable cost of each baguette is calculated by taking €1,10 – €0,50 = €0,60.
2. The break-even point is calculated by dividing fixed costs by the margin on unit variable cost, i.e. €70 ÷ €000 = 0,60 baguettes.
3. If Paul sells 150 baguettes, he exceeds his break-even point, which means he covers his expenses and makes a profit.
4. If fixed costs increased by €10, the new break-even point would be €000 ÷ €80 = 000 baguettes.
5. To reduce the break-even point by 15%, the new margin on unit variable cost should be €70 ÷ (000 baguettes x 116%) = €667.
Summary of Formulas Used:
| Packages | Detailed explanation |
|---|---|
| Fixed charges | These are expenses that do not vary according to the volume of the company's activity. |
| Margin on unit variable cost | It is calculated by deducting the unit variable cost from the unit selling price. |
| Break even | It is calculated by dividing fixed costs by the margin on unit variable cost. |
Application: TechGuru Enterprise
States :
TechGuru is a company specializing in the sale of computer equipment. It aims to expand its offering by launching a new product: a virtual reality headset.
The acquisition cost of the product is €500 excluding VAT per unit. The annual distribution cost is estimated at €150. The company plans to sell each unit of product at €000 excluding VAT. The applicable VAT rate is 950%.
Work to do :
1. Calculate the break-even point in number of units sold.
2. What will be the break-even turnover?
3. At a margin rate of 60%, how much would it cost to sell the VR headset excluding tax to reach the same profitability threshold?
4. If the distribution cost increases by 10%, what is the impact on the break-even point?
5. Evaluate the viability of the project based on these calculations.
Proposed correction:
1. Break-even point formula in number of units sold: Fixed costs / (Unit selling price excluding VAT – Unit purchase price excluding VAT).
That is: €150 / (€000 – €950) = 500 ? 333,33 units. The company must therefore sell at least 334 units to reach the break-even point.
2. The turnover at the break-even point is the break-even point in number of units multiplied by the sales price (Unit sales price excluding VAT x quantity). That is: €950 x 334 = €317.
3. For a margin rate of 60%, the selling price excluding VAT should be: Purchase cost excluding VAT / (1 – Margin rate) = €500 / (1 – 0,6) = €1. Therefore, the break-even point in number of units would be: €250 / (€150 – €000) = 1 units.
4. If the distribution cost increases by 10%, i.e. €150 x 000 = €1,1, the break-even point becomes: €165 / (€000 – €165) = 000 ? 950 units.
5. According to the results, the project seems viable if the company is able to sell more than 367 units of VR headsets, taking into account the possible increase in distribution costs. However, other factors such as market demand or competitor actions should also be studied before making a final decision.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Break-even point in number of units | Fixed costs / (Unit selling price excluding VAT – Unit purchase price excluding VAT) |
| Break-even turnover | Unit selling price excluding VAT x Quantity at break-even point |
| Selling price with margin | Purchase cost excluding tax / (1 – Margin rate) |
Application: Extrema Energy
States :
Extréma Énergie is a small company specializing in the production and sale of solar energy. The company offers a range of solar panels to its customers. Recent financial information includes:
– The unit sale price excluding VAT is €600.
– The unit variable cost is €300.
– Annual fixed costs are €120.
– The company sold 1 solar panels last year.
Work to do :
1. What is the break-even point in quantity?
2. What is the break-even point in terms of turnover?
3. How much must Extréma Énergie sell to make a profit?
4. What is the margin on variable cost?
5. What is the margin rate on variable cost?
Proposed correction:
1. The break-even formula in quantity is: Fixed costs ÷ (Unit selling price – Unit variable cost). Therefore, the break-even point in quantity for Extréma Énergie is €120 ÷ (€000 – €600) = 300 solar panels.
2. The formula for the break-even point in terms of turnover is: Break-even point in terms of quantity x Unit sales price. Therefore, the break-even point in terms of turnover for Extréma Énergie is 400 x €600 = €240.
3. To make a profit, Extréma Énergie must sell more than its break-even point in quantity, i.e. more than 400 solar panels.
4. The variable cost margin is calculated by subtracting the unit variable cost from the unit selling price. Therefore, Extréma Énergie’s variable cost margin is €600 – €300 = €300.
5. The variable cost margin rate is calculated by dividing the variable cost margin by the unit sales price and multiplying by 100. Therefore, the variable cost margin rate of Extréma Énergie is (€300 ÷ €600) x 100 = 50%.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Fixed costs ÷ (PV excluding VAT – CVU) | Break-even formula in quantity |
| Break-even point in Qty x PV HT | Break-even formula in turnover |
| PV HT – CVU | Formula for margin on variable cost |
| ((PV excluding tax – CVU) ÷ PV excluding tax) x 100 | Formula for the variable cost margin rate / (CVU) |
Application: The Parisian Gourmet
States :
Le Gourmet Parisien is a Michelin-starred restaurant located in the heart of the French capital. They have a capacity of 50 people per day. The restaurant offers homemade menus at €40 excluding VAT per person. The variable costs per meal are €15 excluding VAT and the monthly fixed costs of the restaurant amount to €10000.
Work to do :
1. Calculate the annual turnover excluding tax.
2. Calculate the annual variable cost.
3. Calculate the annual variable cost margin.
4. Calculate the break-even point in units and euros.
5. What is the applicable VAT rate and calculate the annual turnover including VAT.
Proposed correction:
1. The annual turnover excluding tax is calculated by multiplying the number of meals served in a day by the price of a meal, all multiplied by the number of working days in the year. Thus, (50 meals/day x €40/meal x 365 days/year) = €730000/year.
2. The annual variable cost is obtained by multiplying the unit variable cost by the total number of meals served during a year. Thus, (50 meals/day x €15/meal x 365 days/year) = €273750/year.
3. The annual variable cost margin is calculated by subtracting the annual variable cost from the annual turnover. Thus, (€730000 – €273750) = €456250.
4. The break-even point in units is obtained by dividing fixed costs by the unit variable cost margin. For the calculation in euros, the break-even point in units must be multiplied by the unit sales price. Thus, Break-even Point in units = €10000 ÷ ((€40 – €15)
= 370,37 units. Rounded to 371 meals. Break-even point in euros = 371 meals x €40 = €14840.
5. The VAT rate applicable to restaurants is 10%. The annual turnover including VAT is therefore €730000 x 1,10 = €803000.
Summary of Formulas Used:
| Packages | Comments |
|---|---|
| Annual turnover excluding tax = Price x Quantity x Number of days/year | Price excluding VAT per meal, Quantity of meals per day and 365 days per year |
| Annual variable cost = Variable cost per meal x Quantity x Number of days/year | Variable costs per meal, Quantity of meals per day and 365 days per year |
| Margin on variable cost = Annual turnover excluding tax – Annual variable cost | Calculation of margin for one year |
| Break-Even Point in Units = Fixed Costs ÷ (Unit Selling Price – Unit Variable Cost) | Calculation of the threshold from when the company begins to be profitable in number of meals |
| Break-even point in euros = Break-even point in units x Unit selling price | Calculation of the threshold from when the company begins to be profitable in value |
| Annual turnover including tax = Annual turnover excluding tax x (1 + VAT rate) | Calculation of turnover with the VAT rate of 10% for the catering sector |
Application: Chocolate Delights Company
States :
The small business “Chocolat Délices” makes artisanal chocolates. It would like to assess its financial situation and has decided to apply the break-even method. In order to understand the situation, some financial data has been identified.
The unit selling price of its chocolates is €2,50 excluding VAT and the unit production cost is €1,30 excluding VAT. Over a year, the company's fixed costs are estimated at €10000. The company works 200 days a year and does not have any storage. It would like to know from how many chocolates sold it could cover its costs.
Work to do :
1. What is the margin on unit cost?
2. What is the margin rate on unit cost?
3. What quantity would need to be sold to cover fixed costs?
4. What turnover would be necessary to reach the break-even point?
5. What would be the overall margin at this break-even point?
Proposed correction:
1. The margin on unit cost is obtained by subtracting the unit cost from the unit selling price. Here, this gives: €2,50 – €1,30 = €1,20.
2. The margin rate on unit cost is calculated by dividing the unit margin by the unit cost and then multiplying the result by 100 to obtain a percentage. Here, this gives: (€1,20 ÷ €1,30) x 100 = 92,31%.
3. To calculate the quantity to be sold to cover fixed costs, divide the latter by the unit margin. This gives: €10000 ÷ €1,20 = approximately 8333 chocolates.
4. The turnover required to reach the break-even point is obtained by multiplying the quantity to be sold by the unit selling price. Here, this gives: 8333 x €2,5 = €20832,50.
5. The overall margin at this break-even point is equal to the unit margin multiplied by the quantity sold. So, this gives: €1,20 x 8333 = €10000.
Summary of Formulas Used:
| Indicators | Packages |
|---|---|
| Unit margin | Unit PV excluding VAT – Unit cost excluding VAT |
| Margin rate | ((Unit PV excluding VAT – Unit cost excluding VAT) ÷ Unit cost excluding VAT) x 100 |
| Qty to sell (breakeven point) | Fixed charges ÷ Unit margin |
| CA required (break-even point) | Unit selling price excluding VAT x Qty for sale |
| Overall margin (break-even point) | Unit margin x Qty to sell |
Hello, please note that for the Société Restaurant Prestigio application, it seems to me that there is an error in the answer to question 5: profitability threshold = 396/000-52,5 = 22 and not 12.
Hello Jonquille,
Thank you very much for this comment. Indeed I confirm my error, it is indeed 12 menus for sale.
thanks again
Hello,
Exo: Sweet Treats Bakery
Question 1: I find €25000 by calculating €45 ÷ (€000 – €5,00) and not 3,20 units. How do you find this result?
1. The break-even point is calculated by dividing annual fixed costs by the marginal contribution per unit, which is the difference between the unit selling price and the unit variable costs. Therefore, the current break-even point is €45 ÷ (€000 – €5,00) = 3,20 units.
Question 2 I find: 19565,22 and not: "€45 ÷ (€000 – €5,50) = 3,20 units." How do you find this result?
Hello,
You're totally right !
I rectify.
Thank you and good luck if you take the exam next week 🙂