Welcome to this article whose sole purpose is to help you progress with break-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: Maestro Company
- Application: Le Pain Quotidien Bakery
- Application: TechnoSpeed Company
- Application: SweetLife Confectionery Company
- Application: Local Bakeries
- Application: GigaOrdinary Supermarket
- Application: Sonia's Delights
- Application: The Little Gourmet
- Application: Sweet Bakery
- Application: Julie's Sweets
- Application: Le Beau Bistro Restaurant Chain
Application: Maestro Company
States :
Maestro Company is a company that manufactures violins. It is wondering how many sales or turnover it needs to achieve to cover all its costs. To do this, it provides you with the following information:
– Unit sale price of the violin: €1
– Unit variable cost: €800
– Fixed company costs for the year: €200
– Annual sales forecast: 1 violins.
Work to do :
1) How to calculate the Break-Even Point in turnover (CA) for the Maestro Company?
2) How can we determine the break-even point in time for this company?
3) What is the formula for establishing a differential income statement for Maestro Company?
4) How to determine the volume break-even point for Maestro Company?
5) What is the profit or loss of Maestro Company if it sells its 1 violins planned for the year?
Proposed correction:
1) The Break-Even Point in turnover is calculated as follows: Fixed Costs ÷ (1 – (Variable Costs ÷ Turnover)). In this case, the fixed costs are €200 and the variable costs are €000 (€800 x 000 violins). The turnover is therefore €800 (€1 x 000 violins). The Break-Even Point in turnover is therefore €1 ÷ (500 – (000 ÷ 1) = €500.
2) To determine the break-even point in time, we use the formula: (Fixed Costs ÷ Turnover) x 365. In this case, the fixed costs are €200 and the turnover is €000, so we obtain: (1 ÷ 500) x 000 = 200 days.
3) The differential income statement is established by subtracting variable and fixed expenses from turnover. In this case, this gives: €1 – (€500 + €000) = €800.
4) The break-even point in volume is determined by dividing fixed costs by the margin on variable cost (Unit selling price – Unit variable cost). In this case, this gives: 200 ÷ (€000 – €1) = 500 violins.
5) Maestro Company makes a profit of €500 if it sells its 000 violins planned for the year (Turnover – Variable Costs – Fixed Costs).
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Break-even point in turnover (TO) | Fixed Charges ÷ (1 – (Variable Charges ÷ CA)) |
| Dead Point (DP) in time | (Fixed Charges ÷ CA) x 365 |
| Differential Income Statement | CA – (Variable Charges + Fixed Charges) |
| Break-even point in volume | Fixed Costs ÷ (Unit Selling Price – Unit Variable Cost) |
Application: Le Pain Quotidien Bakery
States :
The bakery "Le Pain Quotidien" wants to improve its financial management. In order to understand its costs, it is launching a break-even analysis and looking for the break-even point of its activity.
Among its products, it sells traditional baguettes at a unit price of €1 excluding VAT. The production cost of a baguette is €0,50 excluding VAT.
The bakery's fixed costs (rent, electricity bills, etc.) amount to €4 per month. The VAT rate applies at 500%.
Work to do :
1. What is the bakery's unit margin on each traditional baguette sold?
2. What is the bakery's margin rate on a traditional baguette?
3. How is the volume break-even point calculated?
4. What is the break-even point of the bakery?
5. When does the company reach its break-even point in the month?
Proposed correction:
1. The unit margin is calculated by taking the difference between the sales price excluding tax and the purchase price excluding tax. In our case, the unit margin would therefore be 1 – 0,5 = €0,50.
2. The margin rate is calculated by doing ((PV HT – PA HT) ÷ PA HT) x 100. Here, this gives ((1 – 0,5) ÷ 0,5) x 100 = 100%.
3. The break-even point in volume is calculated by dividing fixed costs by the unit margin. This is the number of units that must be sold from which the turnover covers all costs (fixed and variable).
4. The break-even point for daily bread is therefore 4 ÷ 500 = 0,50 baguettes.
5. Assuming that the bakery is open 30 days a month, the business would reach its break-even point after 9 ÷ 000 = 30 baguettes sold per day.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Unit margin | Unit margin = PV excluding tax – PA excluding tax |
| Margin rate | Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 |
| Break-even point in volume | Break-even point in volume = Fixed costs ÷ Unit margin |
| Neutral | Break-even point = Break-even point in volume ÷ Number of working days per month |
Application: TechnoSpeed Company
States :
TechnoSpeed is a small company specializing in the sale of spare parts for electronic devices. In April, the company purchased parts at a unit cost of €70 excluding VAT. These parts are resold at €120 excluding VAT per unit. Fixed costs amount to €6000 per month and the VAT rate is 20%. The company aims to sell 200 parts per month.
Work to do :
1. Determine the margin rate.
2. Calculate the mark rate.
3. Calculate the break-even point in value.
4. What is the break-even point in days (30 days per month)?
5. Estimate the differential income statement if 200 pieces are sold.
Proposed correction:
1. The margin rate is calculated using the formula: ((PV HT – PA HT) ÷ PA HT) x 100). Here, it is ((120€ – 70€) ÷ 70€) x 100, or 71,43%.
2. The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100. Here, it is ((120€ – 70€) ÷ 120€) x 100, or 41,67%.
3. The break-even point in value is calculated by dividing fixed costs by the cost margin rate. Which gives: €6000 ÷ 0,7143 = €8395,35 excluding VAT.
4. The break-even point is the moment when the company covers its costs without making a profit. It is calculated in days by the ratio between the break-even point in value / daily turnover excluding tax. Here, this gives: €8395,35 / ((200 x €120) ÷ 30) = 10,49 days. That is, approximately 11 days.
5. The differential income statement allows us to analyze the impact of the volume variation of sales on the company's results. Here, for a sale of 200 pieces, the net sales would be 200×120€=24000€. By deducting the variable costs, i.e. 200×70€=14000€ and the fixed costs, 6000€, the result would be 24000€ – 14000€ – 6000€ = 4000€.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Value break-even point | Fixed costs ÷ Margin rate on variable costs |
| Breakeven point in days | Break-even point in value ÷ daily turnover excluding tax |
| Differential income statement | CA HT – Variable costs – Fixed charges |
Application: SweetLife Confectionery Company
States :
SweetLife is a candy company that manufactures and sells candy. During a fiscal year, the company produced one type of candy called "Sweet Drops". SweetLife has the following information about "Sweet Drops":
– Unit sales price excluding tax (PV HT): €2
– Unit purchase price excluding tax (PA HT): €1
– Quantity sold: 8 units
– Fixed charges: €12
– VAT rate: 20%
Work to do :
1. Calculate the unit margin excluding VAT of “Sweet Drops” and explain what this means.
2. Calculate the overall net margin of “Sweet Drops” and explain what this means.
3. Calculate the break-even point in value and volume of “Sweet Drops”, and explain what this means.
4. Calculate the break-even point, and explain what this measurement represents.
5. Prepare the differential income statement for “Sweet Drops”.
Proposed correction:
1. The unit margin excluding tax is the difference between the sales price excluding tax and the purchase price excluding tax. Unit margin excluding tax = PV excluding tax – PA excluding tax = €2 – €1 = €1. This means that SweetLife makes a gross profit of €1 for each “Sweet Drops” candy sold, before taking into account fixed costs.
2. The overall margin excluding tax is the unit margin multiplied by the quantity sold. Overall margin excluding tax = Unit margin x Quantity sold = €1 x 8 = €000. This means that SweetLife makes a total gross profit of €8 for all the “Sweet Drops” candies sold, before taking into account fixed costs.
3. The break-even point in value is the amount of sales needed to cover all the company's expenses, both fixed and variable. It is calculated as follows: Break-even point in value = Fixed expenses ÷ (1- (PA HT ÷ PV HT)) = €12 ÷ (000- (€1 ÷ €1)) = €2.
The break-even point in volume, on the other hand, corresponds to the number of units that must be sold to cover all the company's expenses. It is calculated as follows: Break-even point in volume = Break-even point in value / PV excluding tax = €24 / €000 = 2 units.
4. The break-even point is when the company is neither making a profit nor making a loss. It is calculated as follows: Break-even point = Profitability in volume / quantity sold per day. To calculate it, we need additional information on the number of candies sold per day.
5. The differential income statement is a document that presents the company's result by highlighting the variable cost margin and the operating result. To establish it, we need additional information on the company's variable expenses.
Summary of Formulas Used:
Unit margin excluding tax = PV excluding tax – PA excluding tax
Total margin excluding tax = Unit margin x Quantity sold
Break-even point in value = Fixed costs ÷ (1- (PA HT ÷ PV HT))
Break-even point in volume = Break-even point in value / PV excluding tax
Break-even point (in days) = Break-even point in volume / quantity sold per day
Application: Local Bakeries
States :
Luc, the owner of "Les Boulangeries du Coin", sells various products, but we will focus on pains au chocolat. According to the information provided, the selling price excluding tax of a pain au chocolat is €0,80 and the purchasing price excluding tax is €0,35. The company sells an average of 500 pains au chocolat per day.
The company's fixed costs are €4000 per month and the VAT rate is 5,5%. Based on this, Luc would like to understand better his breakeven point and differential results account.
Work to do :
1. What is the unit margin on each pain au chocolat sold?
2. What is the margin rate?
3. What is the break-even point in terms of volume of pain au chocolat?
4. What is break-even point in days?
5. How is the differential income statement structured?
Proposed correction:
1. The unit margin is the difference between the selling price excluding VAT and the purchasing price excluding VAT. Therefore, the unit margin is €0,80 – €0,35 = €0,45.
2. The margin rate is calculated by doing ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100. Therefore, the margin rate is ((€0,80 – €0,35) ÷ €0,35) x 100 = 128,57%.
3. The break-even point in volume is calculated by dividing fixed costs by the unit margin. Therefore, the break-even point in volume is €4000 ÷ €0,45 = 8889 pains au chocolat.
4. The break-even point in days is calculated by dividing the break-even point in volume by the average sales volume per day. Therefore, the break-even point is 8889 pains au chocolat ÷ 500 pains au chocolat/day = 17,78 days.
5. The differential income statement is structured as follows:
* Sales = Quantity sold x Selling price excluding VAT
* Margin on variable cost = Sales – (Quantity sold x Purchase price excluding VAT)
* Result = Margin on variable cost – Fixed costs
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Unit margin | Sales price excluding tax – Purchase price excluding tax |
| Margin rate | ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 |
| Break-even point in volume | Fixed charges ÷ Unit margin |
| Breakeven point in days | Break-even point in volume ÷ Average daily sales volume |
| Differential income statement | Sales = Quantity sold x Selling price excluding VAT Margin on variable cost = Sales – (Quantity sold x Purchase price excluding VAT) Result = Margin on variable cost – Fixed costs |
Application: GigaOrdinary Supermarket
States :
The GigaOrdinaire supermarket has a wide range of products, including a range of organic tomato sauces under the own brand "Tom'Bio". Each jar of sauce is sold at a price of €3,50 excluding VAT and costs €1,50 excluding VAT to produce. This production cost is entirely variable. The supermarket also has annual fixed costs of €250 excluding VAT related to this range of products. In 000, GigaOrdinaire sold 2021 jars of Tom'Bio sauce.
Work to do :
1. Calculate the break-even point in volume of the Tom'Bio range of sauces.
2. What is the volume profitability threshold for this range produced by GigaOrdinaire?
3. Determine the break-even point in value for this range of sauces.
4. Estimate GigaOrdinaire's result for the sale of Tom'Bio sauces in 2021 using the differential income statement.
5. Based on the results obtained in the previous questions, assess GigaOrdinaire's operational risk for the sale of Tom'Bio sauces.
Proposed correction:
1. Break-even point = Fixed costs ÷ Margin on Unit Variable Cost = €250 ÷ (€000 – €3,5) = 1,5 units.
2. The break-even point is also the volume break-even point because the company makes neither profit nor loss at this level of sales volume. Therefore, the volume break-even point is 125 units.
3. Break-even point in value = Break-even point in volume x Selling price = 125 units x €000 = €3,5.
4. Differential Income Statement = Revenue – Total variable cost – Fixed cost = (130 units x €000) – (3,5 units x €130) – €000 = €1,5 – €250 – €000 = €455. Sales generated a profit of €000.
5. GigaOrdinaire's current sales level is very close to the break-even point (125 units compared to 000 units sold in 130). This indicates that the company is running a relatively high operational risk. A small drop in sales volume could quickly turn the profit made into a loss.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Break-even point = Fixed costs ÷ Margin on Unit Variable Cost | Used to calculate the break-even point in the first question. |
| Break-even point in volume = Fixed costs ÷ (Selling price – Unit variable cost) | Used to calculate the volume break-even point in the second question. |
| Break-even point in value = Break-even point in volume x Selling price | Used to calculate the break-even point in value in the third question. |
| Differential Income Statement = Turnover – Total variable cost – Fixed cost | Used to calculate the differential income statement in the fourth question. |
Application: Sonia's Delights
The company "Les Délices de Sonia" is a small business that manufactures and sells traditional cakes. The company was created two years ago by Sonia, a baking enthusiast. She noticed that her cakes are a great success with her customers. However, she is having difficulty managing her finances and wants to understand some financial management concepts to improve the profitability of her business.
States :
Sonia sold 5000 cakes last year at a unit sales price excluding tax of €4. Unit variable costs amount to €2 and annual fixed costs are €4000.
Work to do :
1. What is Sonia's unit variable cost margin?
2. What is Sonia's unit variable cost margin rate?
3. What is the company's break-even point in terms of turnover?
4. What is the company's break-even date if Sonia works 300 days a year?
5. If Sonia wants to increase her turnover by 10%, what will be her new break-even point in volume?
Proposed correction:
1. The unit variable cost margin is the difference between the selling price excluding tax and the unit variable cost. In Sonia's case, it is therefore €4 – €2 = €2.
2. The unit variable cost margin rate is the unit variable cost margin divided by the sales price excluding tax, all multiplied by 100. For Sonia, it is therefore (€2 ÷ €4) x 100 = 50%.
3. The break-even point in terms of turnover is the ratio between fixed costs and the margin rate on variable costs. For Sonia, it is therefore €4000 ÷ 50% = €8000.
4. The break-even date is the day of the year when the company reaches its profitability threshold. In Sonia's case, considering that she works 300 days a year, this will be (€8000 ÷ (€5000 x €4)) x 300 = 120th day of the year.
5. If Sonia wants to increase her turnover by 10%, the new break-even point in volume will be €8000 ÷ (€4 x 1,10) = 1818 cakes.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Margin on unit variable cost | Unit selling price excluding VAT – Unit variable cost |
| Margin rate on unit variable cost | ((Unit selling price excluding VAT – Unit variable cost) ÷ Unit selling price excluding VAT) x 100 |
| Break-even point in turnover | Fixed costs ÷ Margin rate on unit variable cost |
| Break-even date | (Break-even point in turnover ÷ Annual turnover) x Number of days in the year |
| Break-even point in volume following an increase in turnover | Break-even point in turnover ÷ (Unit selling price excluding VAT x (1 + Rate of increase in turnover)) |
Application: The Little Gourmet
States :
The restaurant Le Petit Gourmet is appreciated by the inhabitants of its locality. The manager, Mr. Dupuis, seeks to better understand the finances of his establishment. He plans to revise the budgets for the next financial year and improve the profitability of the restaurant. The current data is as follows:
Turnover: 520 000 €
Variable charges: 260 000 €
Fixed charges: 200 000 €
Work to do :
1. Calculate the break-even point of the restaurant Le Petit Gourmet.
2. Estimate at what time of year the restaurant will reach its break-even point?
3. Create a differential income statement based on the data provided.
4. What is the break-even point in volume?
5. Based on the financial information, what would be the recommendations to increase profitability?
Proposed correction:
1. The break-even point is the turnover that exactly covers all costs. It is calculated as follows: Fixed Costs ÷ [(Turnover – Variable Costs) ÷ Turnover] = €200 ÷ [(€000 – €520) ÷ €000] = €260. Le Petit Gourmet must therefore achieve a turnover of €000 to reach its break-even point.
2. To estimate the break-even point, we must first calculate the percentage of turnover that represents the break-even point: (Break-Even Point ÷ Turnover) x 100 = (€400 ÷ €000) x 520 = 000%. Thus, the break-even point for Le Petit Gourmet would be around the end of the 100th month (76,92% of 9 months = 76,92 months).
3. A differential income statement is based on the concept of variable cost. By focusing on variable costs rather than total costs, we obtain the marginal contribution, i.e. the contribution of each euro of turnover to covering fixed costs. It would look like this:
Marginal Contribution: Turnover – Variable costs = €520 – €000 = €260
Result: Marginal Contribution – Fixed Charges = €260 – €000 = €200
4. The break-even point in volume corresponds to the volume of activity necessary for the company to cover all its costs. We do not have enough information to calculate it in this exercise.
5. Based on the information provided, Mr. Dupuis could consider reducing variable or fixed costs to increase the profitability of his restaurant. He could also consider ways to increase his turnover, for example by increasing prices or finding ways to attract more customers.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Break-even point = Fixed costs ÷ [(Sales – Variable costs) ÷ Sales] | Allows you to know the turnover needed to cover all costs. |
| Break-even point = (Break-even point ÷ Turnover) x 100 | Establishes the point at which revenue exactly covers costs, expressed as a percentage of the year. |
| Marginal Contribution: Turnover – Variable costs | Represents the contribution of each euro of turnover to covering fixed costs. |
| Result: Marginal Contribution – Fixed Charges | Indicates the profit or loss made after covering all costs. |
Application: Sweet Bakery
Sweet Bakery, a bakery and pastry shop, wants to refine its financial management to improve its economic situation. The data provided are as follows:
1. Turnover = €500
2. Unit variable cost of a cake = €3
3. Unit selling price of a cake = €8
4. Quantity sold annually = 50 units
5. Fixed costs = €150
States :
Sweet Bakery needs to assess its financial situation to better manage its financial activities. To do this, it needs to calculate its break-even point in value and volume, determine its break-even point and establish a differential income statement.
Work to do :
1. Calculate the break-even point in value.
2. Calculate the break-even point in volume.
3. Determine the break-even point.
4. Prepare a differential income statement.
5. Determine and interpret the margin rate and markup rate that Sweet Bakery makes on the sale of each cake.
Proposed correction:
1. The break-even point in value is calculated as follows: Break-even point in value = Fixed costs ÷ ((Unit selling price – Unit variable cost) ÷ Unit selling price).
That is: Break-even point in value = €150 ÷ ((€000 – €8) ÷ €3) = €8.
2. The volume break-even point is calculated as follows: Volume break-even point = Fixed costs ÷ (Unit selling price – Unit variable cost).
That is: Break-even point in volume = €150 ÷ (€000 – €8) = 3 units.
3. The break-even point is the moment when the company reaches its profitability threshold. It is therefore equal to the profitability threshold in volume divided by the quantity sold annually multiplied by 365 (if we want it in days).
That is: Break-even point = (Break-even point in volume ÷ quantity sold annually) x 365
That is: Break-even point = (30 units ÷ 000 units) x 50 = 000 days.
4. The differential income statement is as follows:
| Designation | Amount |
|---|---|
| Turnover excluding tax | 500 000 € |
| (-) Variable costs | 150 000 € |
| (=) Margin on variable cost | 350 000 € |
| (-) Fixed costs | 150 000 € |
| (=) Result | 200 000 € |
5. The margin rate is calculated as follows: Margin rate = ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100
That is: Margin rate = ((€8 – €3) ÷ €3) x 100 = 166,67%.
The markup rate is calculated as follows: Markup rate = ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Sale price excluding VAT) x 100
That is: Markup rate = ((€8 – €3) ÷ €8) x 100 = 62,5%.
Summary of Formulas Used:
| Value break-even point | Fixed costs ÷ ((Unit selling price – Unit variable cost) ÷ Unit selling price) |
|---|---|
| Break-even point in volume | Fixed costs ÷ (Unit selling price – Unit variable cost) |
| Neutral | (Break-even point in volume ÷ quantity sold annually) x 365 |
| 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 |
Application: Julie's Sweets
States :
Julie runs a small business that makes and sells artisanal cakes. For the current year, here is some information from her financial data:
– Turnover excluding tax: €250
– Variable costs: €150
– Fixed costs: €80
– Quantity of cakes sold: 50
Work to do :
1. Calculate the break-even point (in turnover)
2. Calculate the break-even point (in days)
3. Construct the differential income statement
4. Determine the break-even point in volume
5. What does the break-even point mean for a business?
Proposed correction:
1. The break-even point in terms of turnover is calculated by doing Fixed costs ÷ (1 – (Variable costs ÷ Turnover)). In our case, this gives 80 ÷ (000 – (1 ÷ 150)) = €000. This figure indicates the level of turnover that the company must reach in order to cover all its costs.
2. To calculate the break-even point in days, multiply the break-even point by 365 and then divide by the annual turnover. So, (200 x 000) ÷ 365 gives approximately 250 days. This figure indicates the number of days of sales required to reach the break-even point.
3. The differential income statement is as follows:
| Turnover | 250 000 € |
| -Variable Costs | -€150 |
| = Margin on variable cost | 100 000 € |
| - Fixed costs | -€80 |
| = Result | 20 000 € |
4. The break-even point in volume is calculated using the formula Fixed costs ÷ Unit selling price – Unit variable cost. For example, let’s say each cake is sold for €5 excluding VAT and the variable cost per cake is €3. The break-even point in volume is therefore 80 ÷ (000 – 5) = 3 cakes.
5. The break-even point of a company represents the level of production and sales (in volume or value) that allows the company to cover all its costs. Above this threshold, the company makes a profit; below this threshold, it makes a loss.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Break-even point in turnover = Fixed costs ÷ (1 – (Variable costs ÷ Turnover)) | This formula seeks to determine the level of turnover from which a company is profitable. |
| Break-even point = Profitability point x 365 ÷ Turnover | This formula establishes the number of days of sales needed to cover all costs, in other words to reach the break-even point. |
| Break-even point in volume = Fixed costs ÷ (Unit selling price – Unit variable cost) | This formula seeks to determine the quantity of products to sell for the business to be profitable. |
Application: Le Beau Bistro Restaurant Chain
States :
The restaurant chain Le Beau Bistro is planning to open a new restaurant in the city center. Here is the information collected:
– Fixed cost of the operation: €250 (including rent and kitchen equipment).
– Unit variable cost: €6 (including ingredient costs, salaries and other direct costs)
– The bistro intends to sell each meal at a unit price of €14 (excluding VAT).
VAT is 20%.
Work to do :
1. Calculate the break-even point in value and volume.
2. Determine when Le Beau Bistro will reach break-even point.
3. Prepare a differential income statement.
4. What is the impact on the break-even point if the fixed cost increases by 10%?
5. What impact would a 5% increase in the selling price have on the break-even point and the break-even point?
Proposed correction:
1. Break-even point in value and volume.
The break-even point in volume is calculated as follows: Fixed costs ÷ unit margin = €250 ÷ (€000 – €14) = approximately 6 meals.
The break-even point in value is obtained by multiplying the break-even point in volume by the selling price excluding tax: 35 meals x €714 = €14.
2. The dead center.
To calculate the break-even point, we divide the fixed costs by the contribution margin. The break-even point = €250 ÷ (€000 – €14) = 6 meals. Le Beau Bistro will therefore reach the break-even point after selling approximately 35 meals.
3. Differential income statement.
Turnover – Variable costs = Contribution to covering fixed costs.
Contribution to covering fixed costs – Fixed costs = Result.
(€14 x Quantity sold) – (€6 x Quantity sold) – €250 = Result.
4. Impact on the break-even point if the fixed cost increases by 10%.
New fixed cost = €250 x 000 = €1,10.
New break-even point in volume = New fixed cost ÷ unit margin = €275 ÷ €000 = approximately 8 meals.
New break-even point in value = Break-even point in volume x Selling price excluding tax = 34 meals x €375 = €14.
5. Impact of a 5% increase in the selling price on the break-even point and the break-even point.
New sale price = €14 x 1,05 = €14,70.
New break-even point in volume = fixed cost ÷ new unit margin = €250 ÷ (€000 – €14,70) = approximately 6 meals.
New break-even point in value = Break-even point in volume x new selling price excluding tax = 29 x €630 = €14,70.
The break-even point is therefore reached more quickly: approximately after 29 meals sold.
Summary of the formulas used:
– Break-even point in volume = Fixed costs ÷ unit margin.
– Break-even point in value = Break-even point in volume x selling price excluding tax.
– Break-even point = Fixed costs ÷ margin on variable cost.
– Differential income statement = (Sales price excluding tax x Quantity sold) – (Unit variable cost x Quantity sold) – Fixed costs.
– New fixed cost = Old fixed cost x (1 + % increase).
– New selling price = Old selling price x (1 + % increase).