Business and Financial Calculations cap | 9 Exercises

Application: Sophie's Delights

States :

Les Délices de Sophie is a Rennes-based pastry shop specializing in the sale of cakes to order. At the moment, it sells a chocolate cake with a Purchase Price excluding VAT of €10. It sells it at a Sale Price of €18 excluding VAT. The pastry shop sells an average of 200 cakes per month. It wants to carry out an analysis of its margins and associated costs to optimize its profitability.

Work to do :

  1. Calculate the cake margin rate and explain what this rate means.
  2. Determine the markup rate and explain the difference with the margin rate.
  3. Calculate the overall margin achieved each month by Les Délices de Sophie.
  4. If Les Délices de Sophie wishes to apply a markup rate of 40%, what would be the new Selling Price excluding VAT?
  5. Analyze the strategic implications of changing the selling price in the context of a highly competitive market.

Proposed correction:

  1. The margin rate is calculated using the following formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, Margin rate = ((18 – 10) ÷ 10) x 100 = 80%.
    This means that for every cake sold, 80% of the purchase price goes back to the company as profit.

  2. The markup rate is calculated using the formula: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, Markup Rate = ((18 – 10) ÷ 18) x 100 = 44,44%.
    Unlike the margin rate, the markup rate indicates the proportion of profit in the selling price.

  3. The overall margin is calculated with: Overall margin = Unit margin x Quantity sold.

Unit margin = PV excluding tax – PA excluding tax = €18 – €10 = €8.
So, Total Margin = €8 x 200 = €1 per month.

  1. To obtain a markup rate of 40%, we use the formula: PV HT = PA HT ÷ (1 – Markup rate).
    By replacing, PV excluding tax = 10 ÷ (1 – 0,4) = €16,67.
    The new selling price excluding VAT should be €16,67 to achieve a mark-up rate of 40%.

  2. By changing the selling price to a 40% markup rate, it could attract more price-sensitive consumers. However, it could reduce the unit margin, and Les Délices de Sophie must ensure that the increase in volumes is sufficient to compensate for the decrease in unit margin.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
Overall margin Unit margin x Quantity sold
New PV HT for brand rate PV HT = PA HT ÷ (1 – Mark rate)

Application: Tech Innovators

States :

Tech Innovateurs is a growing French startup that sells smartphone accessories. Their latest product, a wireless charging station, has a purchase price excluding VAT of €15 and sells excluding VAT for €25. They want to calculate financial indicators to optimize their sales strategy. Currently, they plan to sell 500 units per month.

Work to do :

  1. Calculate unit profit and explain its importance to Tech Innovators.
  2. Estimate the total gross margin for the full month.
  3. Determine the net contribution of each station in covering fixed costs if these amount to €2 per month.
  4. If the company wants to achieve a unit margin of €12, what should the new selling price excluding tax be?
  5. Analyze how increased competition could impact Tech Innovators' pricing strategy.

Proposed correction:

  1. The unit profit is the difference between the selling price excluding VAT and the purchase price excluding VAT.
    Unit profit = PV excluding tax – PA excluding tax = €25 – €15 = €10.
    This result is crucial to help Tech Innovators understand the profitability of each unit sold.

  2. Total gross margin is calculated as: Total gross margin = Unit profit x Quantity sold.
    Total gross margin = €10 x €500 = €5.
    This is the total profit before deducting fixed costs.

  3. The net contribution of each station is: Net contribution = Unit profit – Fixed costs ÷ Quantity sold.

Net contribution = €10 – (€2 ÷ €000) = €500.
Each unit contributes €6 towards covering monthly fixed costs.

  1. For a unit margin of €12, new unit margin = PV excluding VAT – PA excluding VAT = €12.
    PV HT must therefore be = PA HT + 12 € = 15 € + 12 € = 27 €.
    The new selling price excluding tax must be €27 to achieve a unit margin of €12.

  2. Increased competition may require Tech Innovators to revise its pricing strategy to remain competitive. This could lead to lower prices, forcing the company to optimize its costs to maintain profitability.

Formulas Used:

Title Formulas
Unit profit PV HT – PA HT
Total gross margin Unit Profit x Quantity Sold
Net contribution Unit Profit – Fixed Costs ÷ Quantity Sold
New PV HT for unit margin PA HT + New unit margin

Application: Health and You

States :

Santé et Vous is a company that offers natural health care products. One of the flagship products, a skin cream, has a purchase price of €20 excluding VAT and is sold at €35 excluding VAT. The company has an ambitious sales target of 1 units per quarter. They want to evaluate the financial impact of their activity.

Work to do :

  1. Calculate the gross margin rate for each cream sold.
  2. What is the expected total democratic margin for the quarter?
  3. Determine the expected quarterly revenue if all units are sold.
  4. If the goal is to achieve a 50% markup rate, what should be the maximum purchase price for the cream?
  5. Discuss the potential economic impacts of increased production costs on prices and consumption.

Proposed correction:

  1. The margin rate is calculated as follows: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Margin rate = ((€35 – €20) ÷ €20) x 100 = 75%.
    Each unit generates a beneficial return of 75% on its purchase cost.

  2. The expected total margin is: Total margin = Unit margin x Quantity sold.
    Unit margin = €35 – €20 = €15.
    So, Total Margin = €15 x €1 = €000.

  3. The quarterly turnover is given by: Turnover = PV HT x Quantity sold.

Turnover = €35 x €1 = €000.

  1. A markup rate of 50% implies: PA HT = PV HT x (1 – Markup rate).
    PA excluding VAT = €35 x (1 – 0,5) = €17,5.
    The maximum purchase price to reach this markup rate is €17,5.

  2. The increase in production costs could force Santé et Vous to reassess its sales prices, which could affect demand if consumers are sensitive to price variations.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Total margin Unit margin x Quantity sold
Turnover PV HT x Quantity sold
Max purchase price for markup rate PV HT x (1 – Mark rate)

Application: Arty Mode

States :

Mode Arty is a French clothing brand specializing in streetwear. The most popular hoodie in their collection has a purchase price excluding VAT of €25 and is sold at €50 excluding VAT. Mode Arty is looking to increase its margins and wants to analyze different strategies based on the sale of 300 units per quarter.

Work to do :

  1. Calculate the gross margin rate per hoodie sold.
  2. What is the total quarterly margin achieved?
  3. If Mode Arty wants to get a 120% margin, at what price could he buy a hoodie?
  4. Determine the profit obtained if 10% of the hoodies are sold on sale with a 15% discount on the net selling price.
  5. Consider possible strategies to improve margins without reducing perceived quality.

Proposed correction:

  1. The margin rate is calculated using this formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, Margin rate = ((€50 – €25) ÷ €25) x 100 = 100%.
    The margin rate here shows that the product earns 100% of its purchase price.

  2. The total quarterly margin is calculated as follows: Total margin = Unit margin x Quantity sold.
    Unit margin = €50 – €25 = €25.
    Total margin = €25 x €300 = €7.

  3. For a margin rate of 120%: PA max = PV HT ÷ (1 + Margin rate).

Max AP = €50 ÷ (1 + 1,2) = €50 ÷ 2,2 = €22,73.
The maximum purchase price to guarantee a 120% margin rate would be €22,73.

  1. Profit with discount: Discount = PV HT x Discount %.
    Price after discount = €50 – (€50 x 0,15) = €42,5.
    Margin with discount = €42,5 – €25 = €17,5.
    Quantity sold on sale = 300 x 0,1 = 30.
    Profit = (270 x €25) + (30 x €17,5) = €6 + €750 = €525.

  2. Mode Arty could improve its margins through better supply chain management, strategic partnerships with suppliers or by showcasing its products to justify a higher price.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Total margin Unit margin x Quantity sold
Max purchase price for margin rate PV HT ÷ (1 + Margin rate)
Hand off PV HT x Discount %

Application: Cooking and Health

States :

Cuisine et Santé is a company that focuses on the distribution of eco-friendly kitchen accessories. The main product, a set of bamboo utensils, has a purchase price of €8 excluding VAT and sells for €15 excluding VAT. They plan to sell 1 units during this semester.

Work to do :

  1. Calculate the markup rate per utensil set sold.
  2. What is the expected half-yearly turnover?
  3. If storage costs increase by 10%, forecast the potential impact on the break-even point, taking into account the €5 overhead.
  4. What would be the minimum selling price to maintain a 40% markup rate?
  5. Consider the implications of a dynamic pricing policy on brand perception.

Proposed correction:

  1. The markup rate is calculated as follows: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, Markup rate = ((€15 – €8) ÷ €15) x 100 = 46,67%.
    This means that 46,67% of the sales price is gross profit.

  2. Turnover = PV HT x Quantity sold.
    Turnover = €15 x €1 = €500.
    This is the total revenue expected for the semester.

  3. A 10% increase in storage cost can impact the break-even point.

Break-even point in units = Fixed costs ÷ Unit margin.
Unit margin = PV excluding tax – PA excluding tax = €15 – €8 = €7.
New overheads = €5 (500% increase).
Threshold = €5 ÷ €500 = 7 units.
About 786 units must be sold to cover the new fixed costs.

  1. To maintain a markup rate of 40%, the minimum selling price: PV min = PA HT ÷ (1 – Markup rate).
    Min PV = €8 ÷ (1 – 0,4) = €8 ÷ 0,6 = €13,33.
    The minimum sale price to maintain this markup rate is €13,33.

  2. A dynamic pricing policy, which varies based on demand and supply, can potentially harm the brand's perception of consistent quality if price differences are not well justified to the consumer.

Formulas Used:

Title Formulas
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
Turnover PV HT x Quantity sold
Break-even point (units) Fixed costs ÷ Unit margin
Minimum selling price for markup rate PA HT ÷ (1 – Mark rate)

Application: Studio Verdur

States :

Studio Verdur, an interior design agency, offers a unique consultation and design creation package for commercial premises. Each package is offered at a purchase price of €150 excluding VAT and sells for €320 excluding VAT. Studio Verdur generally sells around 100 per year.

Work to do :

  1. Calculate profitability per package sold.
  2. What would be the annual turnover for 100 packages sold?
  3. Determine the overall annual profitability if operating costs are €10 per year.
  4. If Studio Verdur decided to lower its prices by 10%, what impact would this have on unit profitability?
  5. Consider the strategic challenges of expanding the service offering to conquer new market segments.

Proposed correction:

  1. Profitability per package = PV excluding tax – PA excluding tax.
    By replacing, Profitability per package = €320 – €150 = €170.
    Each package sold brings a gross profitability of €170.

  2. Annual turnover = PV excluding VAT x Number of packages sold.
    Annual turnover = €320 x 100 = €32.
    The expected annualized income is €32.

  3. Overall annual profitability = (Unit profitability x Quantity sold) – Operating costs.

Overall annual profitability = (€170 x 100) – €10 = €000.
Studio Verdur would anticipate an annual net profitability of €7 after covering costs.

  1. A 10% price drop reduces the selling price to:
    New PV = €320 x 0,9 = €288.
    New unit profitability = €288 – €150 = €138.
    The price drop would have the effect of reducing unit profitability by €32.

  2. By expanding the service offering, Studio Verdur could penetrate new market segments, but this would probably require additional investments in training, marketing and development, which must be carefully evaluated within the framework of a cost-benefit analysis.

Formulas Used:

Title Formulas
Profitability by package PV HT – PA HT
Annual sales PV HT x Number of packages sold
Overall annual profitability (Unit profitability x Quantity sold) – Operating costs
New sale price after reduction PV x (1 – Reduction %)

Application: Natural

States :

Au Natural specializes in the production and sale of natural beauty products. They sell an organic facial mask with a purchase price of €12 excluding VAT and a sale price of €25 excluding VAT. With an annual production of 700 units, they are looking to analyze their profits and explore expansion options.

Work to do :

  1. Determine the unit margin made on each mask sold.
  2. What is the total annual profit for mask sales?
  3. Calculate the annual break-even point if fixed costs amount to €6 per year.
  4. What will the selling price have to be to cover a 5% increase in purchasing costs while maintaining the same margin rate?
  5. Elaborate on strategic considerations for entering foreign markets for Au Natural.

Proposed correction:

  1. Unit margin = PV HT – PA HT.
    By replacing, Unit margin = €25 – €12 = €13.
    Each mask sold brings a gross margin of €13.

  2. Total annual profit = Unit margin x Quantity sold.
    Total annual gain = €13 x 700 = €9.
    Au Natural makes an annualized profit of €9 from masks alone.

  3. Break-even point (units) = Fixed costs ÷ Unit margin.

Threshold = €6 ÷ €000 = €13.
It takes about 462 masks to break even.

  1. New HT PA after 5% = HT PA x 1,05.
    New PA HT = €12 x 1,05 = €12,6.
    To keep the same margin rate: Margin rate = (PV HT – PA HT) ÷ PA HT.
    1,08333 (unit margin rate) = (New PV – €12,6) ÷ €12,6.
    New PV = (1,08333 x €12,6) + €12,6 = €26,66.
    To maintain the same margin rate with higher costs, the price will have to be €26,66.

  2. Penetrating foreign markets involves challenges such as cultural differences, export logistics, and legal requirements, which is why it is important to conduct a thorough market analysis and ensure that the brand has the adequate support resources.

Formulas Used:

Title Formulas
Unit margin PV HT – PA HT
Total annual gain Unit margin x Quantity sold
Break-even point (units) Fixed charges ÷ Unit margin
Selling price with increased cost ((Margin Rate x New PA) + New PA)

Application: Frozen Pleasures

States :

Plaisirs Glacés is a company that sells artisanal ice cream. The ice cream ball costs €0,50 excluding VAT in raw materials and is sold at €2 excluding VAT. This summer season, they plan to sell 20 balls. They want to optimize their profitability and explore new distribution possibilities.

Work to do :

  1. Calculate the unit margin made on each scoop of ice cream.
  2. What is the total profit expected for the summer season?
  3. Determine the quantity needed to arrive at a net profit of €30, after deducting €000 in fixed costs.
  4. What impact would a 20% reduction in the selling price have on the unit margin?
  5. Analyze the implications of partnering with cafes and restaurants for the brand.

Proposed correction:

  1. The unit margin is PV HT – PA HT.
    Unit margin = €2 – €0,50 = €1,50.
    Each scoop of ice cream sold generates a gross margin of €1,50.

  2. Total Profit = Unit Margin x Quantity Sold.
    Total profit = €1,50 x €20 = €000.
    Glacés Pleasures expects to make a profit of €30 this summer.

  3. Total desired net profit = Profit + Fixed costs.

€30 + €000 = €10.
Quantity required = Total profit ÷ Unit margin = €40 ÷ €000 = €1,50.
Approximately 26 balls must be sold to obtain a net profit of €667.

  1. New unit margin if 20% reduction = New PV – PA excluding tax.
    New PV = €2 x 0,8 = €1,60.
    New margin = €1,60 – €0,50 = €1,10.
    The price reduction would bring the unit margin to €1,10.

  2. Partnering with cafes and restaurants would allow Plaisirs Glacés to expand its distribution and reach new customers, while potentially increasing demand. However, this would require thinking about delivery logistics and preferential pricing conditions tailored to these partners.

Formulas Used:

Title Formulas
Unit margin PV HT – PA HT
Total profit Unit margin x Quantity sold
Quantity needed for net profit (Desired net profit + Fixed costs) ÷ Unit margin
New margin after reduction New PV – PA HT

Application: Prestige Jewelry

States :

Joaillerie Prestige is a high-end company that manufactures gold jewelry. A handcrafted pendant has a manufacturing cost of €300 excluding VAT and is sold for €750 excluding VAT. With sales estimated at 80 units for the year, Joaillerie Prestige wishes to analyze the profitability of this activity.

Work to do :

  1. Calculate the unit profit for each pendant sold.
  2. What is the expected turnover for the year?
  3. Determine the break-even point in quantity if the annual fixed costs amount to €25.
  4. If Joaillerie Prestige wants to increase the selling price by 10%, what would be the new unit profit?
  5. Consider the impact of fluctuating gold prices on the company's profit margins.

Proposed correction:

  1. Unit profit = PV HT – PA HT.
    By replacing, Unit profit = €750 – €300 = €450.
    Each pendant sold brings in a gross profit of €450.

  2. Expected turnover = PV HT x Estimated sales.
    Turnover = €750 x 80 = €60.
    We therefore expect a turnover of €60 for the year.

  3. Break-even point (units) = Fixed costs ÷ Unit profit.

Threshold = €25 ÷ €000 = 450 units.
So, you would need to sell about 56 pendants to break even.

  1. New PV after 10% increase = PV x 1,1.
    New PV = €750 x 1,1 = €825.
    New unit profit = €825 – €300 = €525.
    With this increase, the unit profit would rise to €525.

  2. Fluctuations in gold prices can significantly affect profit margins. An increase in the price of gold could reduce profitability if manufacturing costs increase proportionally without being able to adjust the selling price in an equivalent manner.

Formulas Used:

Title Formulas
Unit profit PV HT – PA HT
Turnover PV HT x Estimated sales
Break-even point (units) Fixed costs ÷ Unit profit
New PV after increase PV x 1,1

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