business calculations operational management | 9 Exercises

Application: Sweet Pastries

States :

Les Pâtisseries Douceur, a company specializing in the making of high-end cakes, wants to optimize its margins for a new product: the "Délice aux Noix" cake. The purchase cost excluding tax (PA HT) of this cake is €5 per piece and it is sold at a price of €12 excluding tax (PV HT). The company plans to sell 800 pieces per month and wants to evaluate the financial performance of the product.

Work to do :

  1. Calculate the unit margin made on each “Walnut Delight” cake.
  2. Determine the overall margin achieved on the expected monthly sales.
  3. Calculate the margin rate, and explain its importance to the business.
  4. Identify the markup rate, and discuss its relevance to the pricing strategy.
  5. Think about a potential strategy to improve the profitability of this product.

Proposed correction:

  1. The unit margin is the difference between the selling price excluding tax (PV HT) and the purchasing cost excluding tax (PA HT).

    Unit margin = PV excluding tax – PA excluding tax = €12 – €5 = €7.

    Each “Délice aux Noix” cake generates a unit margin of €7.

  2. The overall margin is the unit margin multiplied by the quantity sold.

    Overall margin = Unit margin x quantity sold = €7 x 800 = €5.

    The overall margin on expected monthly sales is €5.

  3. The margin rate is calculated as follows:

Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((12 € – 5 €) ÷ 5 €) x 100 = 140%.

A margin rate of 140% indicates high profitability compared to the purchase cost.

  1. The markup rate is determined by the following formula:

    Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((12 € – 5 €) ÷ 12 €) x 100 = 58,33%.

    A markup rate of 58,33% is high, illustrating that the selling price includes a significant margin to cover indirect costs and generate profit.

  2. To improve the profitability of the “Délice aux Noix” cake, Les Pâtisseries Douceur could consider increasing sales volume by increasing the visibility of the product, or reducing purchasing costs by negotiating with suppliers to reduce the PA excluding tax.

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

Application: TechnoVision

States :

TechnoVision is a company specializing in innovative technologies. It recently launched a new device, the "SmartLens", a revolutionary device for digital photography. The unit production cost is €200 and it is sold for €450 excluding taxes. TechnoVision wants to understand the impacts of its forecast sales on its cash flow. The forecast announces the sale of 1 units during the first quarter.

Work to do :

  1. Determine the result of the exercise for a sale of a single unit of “SmartLens”.
  2. Calculate the forecast revenue for the first quarter.
  3. What would be the amount of the overall quarterly margin?
  4. Calculate the margin rate, and comment on the competitiveness of this product on the market.
  5. Provide a recommendation to improve sales taking into account margin analysis.

Proposed correction:

  1. Profit per unit is calculated by subtracting the unit cost from the selling price.

    Unit result (gross margin) = PV excluding tax – unit cost = €450 – €200 = €250.

    The sale of one unit of “SmartLens” generates a profit of €250.

  2. The forecast turnover is obtained by multiplying the unit sales price by the number of units expected to be sold.

    Turnover = PV HT x quantity sold = €450 x €1 = €200.

    The forecast turnover for the first quarter is €540.

  3. The overall margin is calculated by multiplying the unit margin by the number of units sold.

Total margin = €250 x €1 = €200.

The overall quarterly margin expected is €300.

  1. The margin rate is calculated as follows:

    Margin rate = ((PV HT – unit cost) ÷ unit cost) x 100 = ((€450 – €200) ÷ €200) x 100 = 125%.

    A margin rate of 125% is excellent, revealing strong competitiveness of the “SmartLens” on the market.

  2. To improve sales, TechnoVision could organize time-limited promotions, strengthen its digital marketing strategy to reach a wider audience, or diversify its distribution channels.

Formulas Used:

Title Formulas
Unit result PV HT – unit cost
Turnover PV HT x quantity sold
Overall margin unit margin x quantity sold
Margin rate ((PV HT – unit cost) ÷ unit cost) x 100

Application: Chic Clothing

States :

Vêtements Chic is a start-up that offers eco-friendly clothing. For its flagship product, an organic t-shirt, the company wants to analyze profitability. Currently, the sales price excluding tax of the t-shirt is €25 and the total cost price is €15. The company plans to sell 500 t-shirts per month. It questions the relevance of its business model.

Work to do :

  1. What is the gross profit per t-shirt sold?
  2. Calculate expected monthly income based on estimated sales.
  3. Evaluate the overall monthly margin that Vêtements Chic can expect.
  4. Calculate the markup rate and explain its strategic importance.
  5. Discuss opportunities for cost and profitability improvement.

Proposed correction:

  1. Gross profit per t-shirt is the difference between the selling price and the cost price.

    Gross profit = PV – cost price = €25 – €15 = €10.

    The gross profit per t-shirt sold is €10.

  2. Monthly revenue is calculated by multiplying the sales price by the number of t-shirts sold.

    Monthly income = PV x quantity sold = €25 x 500 = €12.

    The expected monthly income is €12.

  3. The overall margin is the sum of gross profits made on monthly sales.

Overall margin = €10 x 500 = €5.

The expected monthly overall margin is €5.

  1. The markup rate consists of evaluating the share of the margin in the selling price.

    Markup rate = ((PV – cost price) ÷ PV) x 100 = ((€25 – €15) ÷ €25) x 100 = 40%.

    A 40% markup rate demonstrates that Vêtements Chic has a pricing strategy aligned with its desired margin.

  2. To improve profitability, Vêtements Chic could strive to reduce its production costs by negotiating with suppliers, optimize logistics to reduce indirect costs, or consider a gradual increase in the selling price based on the perception of added value of the product.

Formulas Used:

Title Formulas
Gross profit PV – cost price
Monthly income PV x quantity sold
Overall margin M x quantity sold
Brand taxes ((PV – cost price) ÷ PV) x 100

Application: Nature Well-being

States :

Bien-être Nature produces and markets organic beauty creams. Among its products, the “Pure Éclat” cream, sold at €50 excluding tax, has a production cost of €20. For this quarter, the objective is to sell 3 units. Bien-être Nature wants to analyze the financial impact on its overall strategy.

Work to do :

  1. Calculate the unit profit margin of the “Pure Éclat” cream.
  2. Determine the total revenue expected for the quarter.
  3. What is the expected quarterly total margin?
  4. Calculate and evaluate the margin rate of “Pure Éclat”.
  5. Propose a strategy to maximize profits while achieving sales goals.

Proposed correction:

  1. Unit profit margin is measured by subtracting cost from the selling price:

    Unit margin = PV excluding tax – production cost = €50 – €20 = €30.

    Each sale of “Pure Éclat” brings in a unit margin of €30.

  2. Revenue for the quarter is determined by multiplying the selling price by the number of units expected.

    Turnover = PV HT x quantity sold = €50 x €3 = €000.

    The quarterly turnover is €150.

  3. The total margin is obtained by multiplying the unit margin by the expected sales.

Total quarterly margin = €30 x €3 = €000.

Bien-être Nature expects a total quarterly margin of €90.

  1. The margin rate is calculated as follows:

    Margin rate = ((PV HT – production cost) ÷ production cost) x 100 = ((€50 – €20) ÷ €20) x 100 = 150%.

    The 150% margin rate shows that “Pure Éclat” is a highly profitable product for the company.

  2. To maximize profits while meeting sales targets, Bien-être Nature could offer volume discounts to encourage larger purchases, explore partnerships with specialty distributors to expand its market, or invest in targeted promotional campaigns.

Formulas Used:

Title Formulas
Unit margin PV HT – production cost
Turnover PV HT x quantity sold
Total margin Unit margin x quantity sold
Margin rate ((PV HT – production cost) ÷ production cost) x 100

Application: Gourmet Flavors

States :

Les Saveurs Gourmets is a catering company that offers gourmet takeaway meals. It wants to promote one of its flagship dishes, the “Ravioli Truffles”, sold at €30 per unit (excluding VAT) with a material cost of €12. The monthly objective is to sell 1 units.

Work to do :

  1. Identify the profit made per unit of “Ravioli Truffles” sold.
  2. Calculate the potential monthly revenue.
  3. What is the cumulative margin expected this month for this dish?
  4. Calculate the markup rate, and assess its significance for product positioning.
  5. Think of a technique to increase profitability while increasing sales.

Proposed correction:

  1. Profit per unit is the selling price minus the material cost:

    Unit profit = PV – material cost = €30 – €12 = €18.

    Each “Ravioli Truffles” sold generates a profit of €18.

  2. The potential monthly revenue is found by multiplying the sales price by the expected quantity.

    Monthly turnover = PV x quantity sold = €30 x 1 = €500.

    The potential monthly turnover is €45.

  3. Cumulative margin is calculated by multiplying unit profit by the number of expected sales.

Cumulative margin = €18 x €1 = €500.

The cumulative margin expected this month for this dish is €27.

  1. The markup rate is calculated as follows:

    Markup rate = ((PV – material cost) ÷ PV) x 100 = ((€30 – €12) ÷ €30) x 100 = 60%.

    A 60% markup rate indicates that “Ravioli Truffes” have a significant margin, essential to maintain their premium positioning.

  2. To increase profitability while increasing sales, Les Saveurs Gourmets could explore attractive packaging that justifies a slight price increase or introduce a loyalty program to encourage repeat purchases while offering benefits for regular customers.

Formulas Used:

Title Formulas
Unit profit PV – material cost
Turnover PV x quantity sold
Cumulative margin Unit profit x quantity sold
Brand taxes ((PV – material cost) ÷ PV) x 100

Application: GreenTech Solutions

States :

GreenTech Solutions offers innovative renewable energy solutions. For its new range of solar panels, the company wants to analyze its costs and margins. The sales price excluding tax of the panels is €1, with a production cost of €200. The monthly sales plan provides for 750 units.

Work to do :

  1. Calculate the unit margin for each solar panel.
  2. What is the expected monthly turnover?
  3. Estimate the total margin expected for the month.
  4. Calculate the margin rate and explain its relevance to GreenTech's competitiveness.
  5. Suggest a plan to increase market share while preserving margins.

Proposed correction:

  1. The unit margin is obtained by subtracting the production cost from the selling price.

    Unit margin = PV excluding tax – production cost = €1 – €200 = €750.

    Each solar panel brings in a unit margin of €450.

  2. The expected monthly revenue is the product of the sales price and the number of units sold.

    Turnover = PV excluding VAT x quantity sold = €1 x 200 = €200.

    The expected monthly turnover is €240.

  3. Total margin is calculated by multiplying the unit margin by the number of units sold.

Total margin = €450 x €200 = €90.

The total margin expected for the month is €90.

  1. The margin rate is calculated as follows:

    Margin rate = ((PV HT – production cost) ÷ production cost) x 100 = ((€1 – €200) ÷ €750) x 750 = 100%.

    A margin rate of 60% confirms that GreenTech solar panels are absolutely competitive and allow good profitability.

  2. To increase market share while preserving margins, GreenTech could invest in research and development to improve the efficiency of its panels, offer financing solutions to make purchasing more accessible, or explore partnerships with construction companies to integrate its panels into new construction projects.

Formulas Used:

Title Formulas
Unit margin PV HT – production cost
Turnover PV HT x quantity sold
Total margin Unit margin x quantity sold
Margin rate ((PV HT – production cost) ÷ production cost) x 100

Application: The Artisan Chocolatier

States :

L'Artisan Chocolatier is renowned for its handmade chocolate boxes, which are priced at €35 each (excluding VAT). The manufacturing cost per box is €14. With a sales forecast of 600 boxes this month, the company wants to optimise its financial management.

Work to do :

  1. Calculate the unit margin for each box of chocolate.
  2. What is the forecast monthly turnover?
  3. Determine the total margin expected this month.
  4. Calculate the markup rate and discuss its implications for L'Artisan Chocolatier's marketing strategy.
  5. Recommend an approach to retain customers taking into account calculated margins.

Proposed correction:

  1. The unit margin is the difference between the selling price and the manufacturing cost.

    Unit margin = PV excluding tax – manufacturing cost = €35 – €14 = €21.

    Each box generates a unit margin of €21.

  2. The forecast monthly turnover is obtained by the sale price multiplied by the number of boxes planned for sale.

    Turnover = PV HT x quantity sold = €35 x 600 = €21.

    The forecast monthly turnover is €21.

  3. The total margin is calculated by multiplying the unit margin and the units sold.

Total margin = €21 x €600 = €12.

The total margin expected for this month is €12.

  1. The markup rate is calculated by:

    Markup rate = ((PV excluding VAT – manufacturing cost) ÷ PV excluding VAT) x 100 = ((€35 – €14) ÷ €35) x 100 = 60%.

    A 60% brand rate suggests that L'Artisan Chocolatier enjoys a strong margin, allowing it to adopt marketing strategies focused on quality and a premium image.

  2. To build customer loyalty, L'Artisan Chocolatier could launch a loyalty program allowing points to be accumulated that can be converted into discounts, offer chocolate-making workshops for an enhanced customer experience, or develop a range of personalized products to order.

Formulas Used:

Title Formulas
Unit margin PV HT – manufacturing cost
Turnover PV HT x quantity sold
Total margin Unit margin x quantity sold
Brand taxes ((PV HT – manufacturing cost) ÷ PV HT) x 100

Application: SolarEnergia

States :

SolarEnergia sells and installs photovoltaic systems for individuals. Each kit is sold at €3 and the purchase cost is €500. The company hopes to sell 2 kits each month. SolarEnergia wants to analyze its financial performance by product.

Work to do :

  1. Calculate the profit per photovoltaic kit sold.
  2. What is the projected monthly turnover?
  3. Estimate the total expected monthly margin.
  4. Calculate the margin rate and discuss the competitiveness of the product.
  5. Propose an initiative to increase sales while keeping margins high.

Proposed correction:

  1. Profit per kit is the difference between the selling price and the purchase cost:

    Unit profit = PV – purchase cost = €3 – €500 = €2.

    Each photovoltaic kit sold brings a profit of €1.

  2. Projected monthly sales are the sales price multiplied by the number of monthly sales.

    Turnover = PV x quantity sold = €3 x 500 = €100.

    The projected monthly turnover is €350.

  3. The total monthly margin is unit profit multiplied by units sold.

Total margin = €1 x 000 = €100.

The total expected monthly margin is €100.

  1. The margin rate is determined as follows:

    Margin rate = ((PV – purchase cost) ÷ purchase cost) x 100 = ((€3 – €500) ÷ €2) x 500 = 2%.

    A margin rate of 40% ensures good product competitiveness, allowing an adequate profit margin while remaining attractive on the market.

  2. To increase sales and maintain high margins, SolarEnergia could develop bundled offers with installation services, increase visibility via social networks targeting ecology and energy saving, or offer subsidies and financing assistance to improve financial accessibility for its customers.

Formulas Used:

Title Formulas
Unit profit PV – purchase cost
Turnover PV x quantity sold
Total margin Unit profit x quantity sold
Margin rate ((PV – purchase cost) ÷ purchase cost) x 100

Application: BioCook

States :

BioCook, a company specializing in ecological kitchen utensils, sells a complete pack for €120 with a total production cost of €70. The company will market 550 packs next month. BioCook wants to evaluate its revenues and margins to adjust its production strategy.

Work to do :

  1. Determine the profit margin per pack sold.
  2. What will be the projected turnover for the following month?
  3. Calculate the total expected margin for next month.
  4. Evaluate the brand rate and its relevance in BioCook’s communication plan.
  5. Suggest a method to improve profitability while increasing product visibility.

Proposed correction:

  1. The margin per pack is the selling price minus the production cost:

    Margin per pack = PV – production cost = €120 – €70 = €50.

    Each pack sold generates a profit margin of €50.

  2. Projected revenue is the selling price multiplied by the number of units sold.

    Turnover = PV x quantity sold = €120 x 550 = €66.

    The projected turnover for the following month is €66.

  3. The total expected margin is the margin per pack multiplied by monthly sales.

Total margin = €50 x €550 = €27.

The total margin expected for next month is €27.

  1. The markup rate is calculated by:

    Markup rate = ((PV – production cost) ÷ PV) x 100 = ((€120 – €70) ÷ €120) x 100 = 41,67%.

    A brand rate of 41,67% is strategically favorable for promoting the product within the framework of communication focused on value for money.

  2. To improve profitability and increase visibility, BioCook could launch an active online advertising campaign highlighting the eco-friendly nature of the utensils, organize in-store demonstrations, or propose collaborations with influential chefs to increase consumption and product appeal.

Formulas Used:

Title Formulas
Margin per pack PV – production cost
Turnover PV x quantity sold
Total margin Margin per pack x quantity sold
Brand taxes ((PV – production cost) ÷ PV) x 100

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