Business Calculations: Corrected Exercises | 9 Exercises

Application: The Corner Bakery

States :

La Boulangerie du Coin wants to analyze its costs and margins to better understand the profitability of its new pastries. Here is the data concerning a new range of fruit tarts:

• Unit purchase price excluding VAT (PA excluding VAT): €2
• Unit selling price excluding VAT (PV excluding VAT): €4,5
• Quantity sold: 100 units

Work to do :

1. Calculate the unit margin obtained on each pie sold.
2. Determine the overall margin made on the sale of the 100 pies.
3. Calculate the margin rate obtained on the pies.
4. Calculate the markup rate of the pies.
5. Analyze the impact of a 10% increase in unit selling price on the margin rate.

Proposed correction:

1. Unit margin = PV HT – PA HT = €4,5 – €2 = €2,5. The unit margin per pie is €2,5.

2. Overall margin = Unit margin x Quantity sold = €2,5 x 100 = €250. The overall margin achieved is €250.

3. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((€4,5 – €2) ÷ €2) x 100 = 125%. The margin rate is 125%.

4. Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((€4,5 – €2) ÷ €4,5) x 100 = 55,56%. The markup rate is 55,56%.

5. New PV HT = PV HT x 1,1 = €4,5 x 1,1 = €4,95.
   New margin rate = ((€4,95 – €2) ÷ €2) x 100 = 147,5%.
   A 10% increase in the unit selling price would increase the margin rate to 147,5%.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Overall margin	Unit margin x Quantity sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New PV HT	PV HT x (1 + Increase %)
New margin rate	((New PV HT – PA HT) ÷ PA HT) x 100

Application: Futuristic Electronics

States :

Futuristic Electronics, a company specializing in electronic gadgets, is offering a new product: a connected personal assistant. The financial data for this product is as follows:

• Unit production cost excluding tax: €75
• Current unit sale price excluding VAT: €150
• Estimated annual sales: 1 units

Work to do :

1. Calculate the unit profit made on each personal assistant sold.
2. What is the expected annual gross margin?
3. Calculate the margin rate on each personal assistant sold.
4. If the cost of production increases by 10%, what would be the new margin rate?
5. Analyze the effect of a 5% decrease in sales price on unit profit.

Proposed correction:

1. Unit profit = PV excluding VAT – Production cost excluding VAT = €150 – €75 = €75. Each assistant brings in a unit profit of €75.

2. Annual gross margin = Unit profit x Annual sales = €75 x 1 = €000. The expected annual gross margin is €75.

3. Margin rate = ((PV HT – Production cost HT) ÷ Production cost HT) x 100 = ((150 € – 75 €) ÷ 75 €) x 100 = 100%. The margin rate is 100%.

4. New production cost excluding tax = €75 x 1,1 = €82,5.
   New margin rate = ((€150 – €82,5) ÷ €82,5) x 100 = 81,82%.
   With a 10% increase in production costs, the margin rate would fall to 81,82%.

5. New PV excluding VAT = €150 x 0,95 = €142,5.
   New unit profit = €142,5 – €75 = €67,5.
   A 5% drop in the selling price reduces the unit profit to €67,5.

Formulas Used:

Title	Formulas
Unit profit	PV HT – Production cost HT
Annual gross margin	Unit Profit x Annual Sales
Margin rate	((PV HT – Production cost HT) ÷ Production cost HT) x 100
New production cost excluding tax	Production cost excluding tax x (1 + Increase %)
New margin rate	((PV HT – New production cost HT) ÷ New production cost HT) x 100
New PV HT	PV HT x (1 – Decrease %)
New unit profit	New PV HT – Production cost HT

Application: Eco-friendly Mode

States :

Eco-Friendly Fashion offers a new collection of clothing made from recycled materials. The manufacturing cost and the sale price are particularly well studied to maximize the profitability of each item:

• Unit manufacturing cost excluding tax: €20
• Unit sale price excluding VAT: €45
• Estimated quantity to be sold: 500 units

Work to do :

1. What is the margin achieved per unit?
2. Calculate the total overall margin for the collection.
3. Determine the margin rate on these eco-friendly clothes.
4. Calculate the markup rate of this collection.
5. What could be the new markup rate if the selling price is reduced by 15%?

Proposed correction:

1. Unit margin = PV excluding VAT – Manufacturing cost excluding VAT = €45 – €20 = €25. The margin per item is €25.

2. Overall margin = Unit margin x Estimated quantity = €25 x 500 = €12. The total overall margin is €500.

3. Margin rate = ((PV HT – Manufacturing cost HT) ÷ Manufacturing cost HT) x 100 = ((€45 – €20) ÷ €20) x 100 = 125%. The margin rate is 125%.

4. Markup rate = ((PV HT – Manufacturing cost HT) ÷ PV HT) x 100 = ((€45 – €20) ÷ €45) x 100 = 55,56%. The markup rate for this collection is 55,56%.

5. New PV excluding VAT = €45 x 0,85 = €38,25.
   New markup rate = ((€38,25 – €20) ÷ €38,25) x 100 = 47,71%.
   If the sale price is reduced by 15%, the new markup rate would be 47,71%.

Formulas Used:

Title	Formulas
Unit margin	PV HT – Manufacturing cost HT
Overall margin	Unit Margin x Estimated Quantity
Margin rate	((PV HT – Manufacturing cost HT) ÷ Manufacturing cost HT) x 100
Brand taxes	((PV HT – Manufacturing cost HT) ÷ PV HT) x 100
New PV HT	PV HT x (1 – Decrease %)
New mark rate	((New PV HT – Manufacturing cost HT) ÷ New PV HT) x 100

Application: Delicatessen Restoration

States :

Restauration Délicatesse is a high-end caterer that offers gourmet dishes delivered to your home. To optimize its costs, the company wants to understand the impact of price variations on its margins. As an example, here is the data for one of their flagship dishes:

• Cost of ingredients per dish excluding VAT: €8
• Unit sale price excluding VAT: €25
• Number of dishes expected to be sold: 300 units

Work to do :

1. Calculate the profit margin per dish.
2. What total margin does the company expect with the expected sales?
3. Calculate the margin rate of the proposed dish.
4. If the cost of ingredients increases by 20%, what will be the impact on the unit margin?
5. How would the margin rate be affected if, at the same time, the selling price is adjusted to €30?

Proposed correction:

1. Profit margin per dish = PV excluding VAT – Cost of ingredients = €25 – €8 = €17. Each dish generates a margin of €17.

2. Total margin = Margin per dish x Number of dishes sold = €17 x 300 = €5. The total margin expected is €100.

3. Margin rate = ((PV HT – Cost of ingredients) ÷ Cost of ingredients) x 100 = ((25 € – 8 €) ÷ 8 €) x 100 = 212,5%. The margin rate is 212,5%.

4. New cost of ingredients = €8 x 1,2 = €9,6.
   New unit margin = €25 – €9,6 = €15,4.
   With a 20% increase in the cost of ingredients, the unit margin would drop to €15,4.

5. New PV excluding VAT = €30.
   New margin rate = ((€30 – €9,6) ÷ €9,6) x 100 = 212,5%.
   With the increased cost of ingredients and a new selling price of €30, the margin rate would remain at 212,5%.

Formulas Used:

Title	Formulas
Margin per dish	PV HT – Cost of ingredients
Total margin	Margin per dish x Number of dishes sold
Margin rate	((PV HT – Cost of ingredients) ÷ Cost of ingredients) x 100
New cost of ingredients	Ingredient Cost x (1 + % Increase)
New unit margin	PV HT – New cost of ingredients
New margin rate	((New PV HT – New ingredient cost) ÷ New ingredient cost) x 100

Application: ViteFait Transport

States :

Transport ViteFait, a taxi company, wants to introduce a new premium service option billed at a higher price. Here is the data for this first year of launch:

• Annual operating cost per vehicle excluding tax: €10
• Expected annual revenue per vehicle excluding tax: €22
• Number of vehicles affected: 50

Work to do :

1. Determine the annual profit per vehicle.
2. What is the total margin expected for all vehicles?
3. Calculate the margin rate for this premium service.
4. Analyze the impact of a 5% increase in operating cost on profit per vehicle.
5. Discuss the strategic implications if annual revenue is increased by 10% but the number of vehicles decreases to 45.

Proposed correction:

1. Annual profit per vehicle = Annual revenue – Operating cost = €22 – €000 = €10. The annual profit per vehicle is €000.

2. Total Margin = Profit per vehicle x Number of vehicles = €12 x 000 = €50. The expected total margin is €600.

3. Margin rate = ((Annual revenue – Operating cost) ÷ Operating cost) x 100 = ((€22 – €000) ÷ €10) x 000 = 10%. The margin rate is 000%.

4. New operating cost = €10 x 000 = €1,05.
   New profit per vehicle = €22 – €000 = €10.
   A 5% increase in operating costs would reduce the profit per vehicle to €11.

5. New annual revenue = €22 x 000 = €1,1.
   New profit per vehicle = €24 – €200 = €10.
   Total margin for 45 vehicles = €14 x 200 = €45.
   Despite a reduction in the number of vehicles, the increase in revenue increases the total margin to €639, which could compensate for the drop in the number of vehicles.

Formulas Used:

Title	Formulas
Profit per vehicle	Annual revenue – Operating cost
Total margin	Profit per vehicle x Number of vehicles
Margin rate	((Annual Revenue – Operating Cost) ÷ Operating Cost) x 100
New operating cost	Operating cost x (1 + Increase %)
New profit per vehicle	Annual revenue – New operating cost
New annual recipe	Annual revenue x (1 + % increase)
Reduced total margin	New profit per vehicle x New number of vehicles

Application: Couture Elegance

States :

Couture Elegance, a high-end fashion brand, is launching a new line of women's suits. They need to know the potential profitability of this collection. Here are the financial details:

• Unit manufacturing cost excluding tax: €120
• Unit sale price excluding VAT: €300
• Sales forecast: 600 tailors

Work to do :

1. Calculate the unit profit per tailor.
2. What is the overall margin expected for this collection?
3. Determine the margin rate on each tailor.
4. Estimate the impact of a 10% reduction in selling price on unit profit.
5. What does a 15% increase in sales represent for the overall margin?

Proposed correction:

1. Unit profit = Selling price excluding VAT – Manufacturing cost excluding VAT = €300 – €120 = €180. The unit profit is €180.

2. Overall margin = Unit profit x Sales forecast = €180 x 600 = €108. The expected overall margin is €000.

3. Margin rate = ((Sales price excluding VAT – Manufacturing cost excluding VAT) ÷ Manufacturing cost excluding VAT) x 100 = ((€300 – €120) ÷ €120) x 100 = 150%. The margin rate is 150%.

4. New selling price excluding VAT = €300 x 0,9 = €270.
   New unit profit = €270 – €120 = €150.
   A 10% reduction in the selling price reduces the unit profit to €150.

5. New sales forecast = 600 x 1,15 = 690.
   New overall margin = €180 x 690 = €124.
   A 15% increase in sales would increase the overall margin to €124.

Formulas Used:

Title	Formulas
Unit profit	Selling price excluding VAT – Manufacturing cost excluding VAT
Overall margin	Unit Profit x Sales Forecast
Margin rate	((Selling price excluding VAT – Manufacturing cost excluding VAT) ÷ Manufacturing cost excluding VAT) x 100
New sale price	Selling price excluding VAT x (1 – Reduction %)
New unit profit	New selling price – Manufacturing cost excluding VAT
New sales forecast	Sales forecast x (1 + Increase %)
New overall margin	Unit Profit x New Sales Forecast

Application: Invisible Technologies

States :

Invisible Technologies, an innovative startup, is developing augmented reality glasses. Their goal is to maximize profit while launching their product on the market. Here is the available financial information:

• Unit development cost excluding tax: €200
• Unit sale price excluding VAT: €450
• Sales target: 1 pairs

Work to do :

1. Determine the profit margin per pair of glasses.
2. Calculate the total expected margin.
3. Calculate the markup for these glasses.
4. What is the impact of a 25% increase in development cost on profit margin?
5. Discuss the strategic importance of achieving a sales volume 20% higher than the initial target.

Proposed correction:

1. Profit margin per pair = Selling price excluding VAT – Development cost excluding VAT = €450 – €200 = €250. The profit margin per pair is €250.

2. Total Margin = Margin per Pair x Sales Target = €250 x €1 = €200. The expected total margin is €300.

3. Margin rate = ((Sales price excluding VAT – Development cost excluding VAT) ÷ Development cost excluding VAT) x 100 = ((€450 – €200) ÷ €200) x 100 = 125%. The margin rate is 125%.

4. New development cost = €200 x 1,25 = €250.
   New profit margin = €450 – €250 = €200.
   A 25% increase in development cost would lower the profit margin to €200.

5. New sales target = 1 x 200 = 1,2.
   New total margin = €250 x €1 = €440.
   Achieving a 20% higher sales volume would increase the total margin to €360, which is crucial to increase their competitiveness in the market.

Formulas Used:

Title	Formulas
Profit margin	Selling price excluding VAT – Development cost excluding VAT
Total margin	Margin per pair x Sales target
Margin rate	((Sales price excluding VAT – Development cost excluding VAT) ÷ Development cost excluding VAT) x 100
New development cost	Development cost excluding tax x (1 + Increase %)
New profit margin	Selling price excluding VAT – New development cost
New sales target	Sales Target x (1 + % Increase)
New total margin	Margin per pair x New sales target

Application: Health Plus

States :

Santé Plus, a company manufacturing food supplements, wants to evaluate the profitability of a new product intended for well-being. The following elements are given to you:

• Unit production cost excluding tax: €10
• Unit sale price excluding VAT: €30
• Estimated sales volume: 10 units

Work to do :

1. Calculate the unit profit made on each supplement sold.
2. Estimate the overall profit for the 10 units.
3. Determine the margin rate for this product.
4. Calculate the effect on the margin rate if the cost of production decreased by 20%.
5. Analyze the strategic implications if sales volume increased by 30%.

Proposed correction:

1. Unit profit = Selling price excluding tax – Production cost excluding tax = €30 – €10 = €20. The unit profit is €20.

2. Overall Profit = Unit Profit x Sales Volume = €20 x 10 = €000. The overall profit is €200.

3. Margin rate = ((Sales price excluding VAT – Production cost excluding VAT) ÷ Production cost excluding VAT) x 100 = ((€30 – €10) ÷ €10) x 100 = 200%. The margin rate is 200%.

4. New production cost = €10 x 0,8 = €8.
   New margin rate = ((€30 – €8) ÷ €8) x 100 = 275%.
   A 20% decrease in production cost would increase the margin rate to 275%.

5. New sales volume = 10 x 000 = 1,3.
   New overall profit = €20 x €13 = €000.
   The 30% increase in sales volume would bring the overall profit to €260, which is significant for strengthening one's position in the market.

Formulas Used:

Title	Formulas
Unit profit	Selling price excluding VAT – Production cost excluding VAT
Overall profit	Unit Profit x Sales Volume
Margin rate	((Sales price excluding VAT – Production cost excluding VAT) ÷ Production cost excluding VAT) x 100
New production cost	Production cost excluding tax x (1 – Reduction %)
New margin rate	((Sales price excluding VAT – New production cost) ÷ New production cost) x 100
New sales volume	Sales volume x (1 + % increase)
New overall profit	Unit Profit x New Sales Volume

Application: Fitness Evolution

States :

Fitness Evolution, a sports equipment company, has just developed a new fitness device. They want to analyze its profitability before finalizing agreements with retailers. Here is the information available:

• Unit manufacturing cost excluding tax: €50
• Unit sale price excluding VAT: €125
• Sales forecast: 3 units

Work to do :

1. Calculate the unit margin.
2. How much profit does the company expect to make from all the expected sales?
3. What is the margin rate for this fitness equipment?
4. Evaluate the impact of a 10% discount offered to retailers on unit profit.
5. What would be the strategic effects if sales volume were reduced by 25%?

Proposed correction:

1. Unit margin = Unit selling price excluding VAT – Unit manufacturing cost excluding VAT = €125 – €50 = €75. The unit margin is €75.

2. Total expected profit = Unit margin x Sales forecast = €75 x 3 = €000. The expected profit is €225.

3. Margin rate = ((Unit selling price excluding VAT – Unit manufacturing cost excluding VAT) ÷ Unit manufacturing cost excluding VAT) x 100 = ((€125 – €50) ÷ €50) x 100 = 150%. The margin rate is 150%.

4. New selling price excluding VAT after discount = €125 x 0,9 = €112,5.
   New unit margin = €112,5 – €50 = €62,5.
   A 10% discount offered would reduce the unit margin to €62,5.

5. New sales volume = 3 x 000 = 0,75.
   New total profit = €75 x 2 = €250.
   Reducing sales volume by 25% would lower total profit to €168, which could endanger the company's financial projections.

Formulas Used:

Title	Formulas
Unit margin	Unit selling price excluding VAT – Unit manufacturing cost excluding VAT
Estimated total profit	Unit Margin x Sales Forecast
Margin rate	((Unit selling price excluding VAT – Unit manufacturing cost excluding VAT) ÷ Unit manufacturing cost excluding VAT) x 100
New sale price after discount	Unit selling price excluding VAT x (1 – Discount %)
New unit margin	New sale price after discount – Unit manufacturing cost excluding VAT
New sales volume	Sales forecast x (1 – Reduction %)
New total profit	Unit Margin x New Sales Volume