commercial-calculations-exercises-pdf

exercises on business calculations pdf | 9 Exercises

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Application: Sophie's Delights

States :

Les Délices de Sophie, an artisanal pastry shop, wants to analyze the performance of its apple pie sales in order to optimize its commercial strategy. Each pie has a purchase cost set at €3,50 excluding VAT. On average, the pastry shop sells 200 pies per month at a price of €6 excluding VAT per unit.

Work to do :

  1. Calculate the margin rate on apple pies.
  2. What is the overall margin generated by pie sales over a month?
  3. If Sophie wants to have a markup rate of 30%, what selling price excluding tax should she apply for her tarts?
  4. Analyze the financial impact if the purchase cost increases by 10% and the selling price remains the same.
  5. Assuming monthly demand increases by 25%, while maintaining the same price and cost, what would be the new overall margin?

Proposed correction:

  1. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((6 – 3,50) ÷ 3,50) x 100 = 71,43%.
    The margin rate on apple pies is 71,43%.

  2. The overall margin is given by the formula: Overall margin = Unit margin x quantity sold.
    Unit margin = PV HT – PA HT = 6 – 3,50 = €2,50.
    Overall margin = 2,50 x 200 = €500.
    The overall margin generated each month is €500.

  3. To obtain a markup rate of 30%, we use the formula: PV HT = PA HT ÷ (1 – Markup rate).

PV excluding tax = 3,50 ÷ (1 – 0,30) = €5.
For a markup rate of 30%, the selling price excluding tax should be €5.

  1. If the purchase cost increases by 10%, the new PA excluding tax = 3,50 x 1,10 = €3,85.
    The new unit margin = 6 – 3,85 = €2,15.
    The overall margin = 2,15 x 200 = €430.
    With the 10% increase in costs, the company would see its overall margin decrease to €430.

  2. If monthly demand increases by 25%, new quantity sold = 200 x 1,25 = 250.
    New overall margin = 2,50 x 250 = €625.
    With a 25% increase in monthly demand, the overall margin would increase to €625.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Overall margin Unit margin x quantity sold
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
PV HT for mark rate PA HT ÷ (1 – Mark rate)

Application: TechnoGadgets

States :

TechnoGadgets, an electronics accessories distribution company, evaluates its sales performance on a smartphone docking station. The purchase price excluding VAT of a unit is €25. TechnoGadgets sells each unit at €50 excluding VAT and sells 500 units per quarter.

Work to do :

  1. Determine the markup rate of the docking stations.
  2. Calculate the quarterly turnover achieved.
  3. If the market imposes a 10% reduction in the selling price, what would be the new unit margin?
  4. Consider the overall margin difference if demand increases by 150 units.
  5. Evaluate the impact of a promotion offering a discount of €5 excluding VAT per unit on the overall margin.

Proposed correction:

  1. The markup rate is given by the formula: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((50 – 25) ÷ 50) x 100 = 50%.
    The markup rate of docking stations is 50%.

  2. The turnover is calculated as follows: CA = PV HT x quantity sold.
    CA = 50 x 500 = €25.
    The quarterly turnover is €25.

  3. In the event of a 10% reduction, the new selling price excluding VAT = 50 – (50 x 0,10) = €45.

New unit margin = 45 – 25 = €20.
The new unit margin would be €20 after a 10% reduction.

  1. With an increase in demand of 150 units, the new quantity = 500 + 150 = 650.
    New overall margin = (50 – 25) x 650 = €16.
    The overall margin difference with the increase would be €16 – (250 x 25) = €500.

  2. During a promotion offering a €5 discount, the new PV excluding tax = €50 – €5 = €45.
    New unit margin = 45 – 25 = €20.
    New overall margin = 20 x 500 = €10.
    The impact of this promotion would be a reduction in the overall margin to €10.

Formulas Used:

Title Formulas
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
Turnover PV HT x quantity sold
Unit margin PV HT – PA HT
New overall margin (PV HT – PA HT) x new quantity

Application: Fashion Forever

States :

Fashion Forever, a ready-to-wear brand, sells leather jackets at a price of €160 excluding VAT per unit, with a purchase cost of €100 excluding VAT. Each month, 300 jackets are sold on average.

Work to do :

  1. Calculate the markup on these leather jackets.
  2. Determine the overall monthly margin generated by sales.
  3. If the company wants to lower the selling price to €145 excluding VAT, what would the new margin rate be?
  4. If sales increase by 20%, what would be the impact on turnover?
  5. Consider the effect of reducing the purchase cost to €90 while maintaining the original price.

Proposed correction:

  1. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((160 – 100) ÷ 100) x 100 = 60%.
    The markup on leather jackets is 60%.

  2. The overall margin is calculated by: Overall margin = Unit margin x quantity sold.
    Unit margin = 160 – 100 = €60.
    Overall margin = 60 x 300 = €18.
    The overall monthly margin is €18.

  3. With a selling price of €145, the new margin rate = ((145 – 100) ÷ 100) x 100 = 45%.

The new margin rate would be 45% after the price cut.

  1. If sales increase by 20%, new quantity = 300 x 1,20 = 360.
    New turnover = 160 x 360 = €57.
    The increase in sales would generate a turnover of €57.

  2. If the purchase cost is reduced to €90, unit margin = €160 – €90 = €70.
    New overall margin = 70 x 300 = €21.
    A reduction in the purchase cost would increase the overall margin to €21.

Formulas Used:

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

Application: EcoBike Rentals

States :

EcoBike Rentals rents electric bikes for €15 excluding VAT per day. The daily maintenance cost for each bike is €5. On average, 50 bikes are rented each day.

Work to do :

  1. What is the markup rate for a daily rental?
  2. What is the daily overall margin achieved?
  3. If the maintenance cost increases to €7, how is the unit margin affected?
  4. If the rental price is increased to €18 excluding VAT, what would be the new markup rate?
  5. Analyze the impact of a 10% increase in the number of daily rentals.

Proposed correction:

  1. The markup rate is calculated using the formula: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((15 – 5) ÷ 15) x 100 = 66,67%.
    The markup rate for a daily rental is 66,67%.

  2. The overall margin is obtained by: Overall margin = Unit margin x quantity.
    Unit margin = 15 – 5 = €10.
    Overall margin = 10 x 50 = €500.
    The daily overall margin is €500.

  3. With a maintenance cost of €7, new unit margin = 15 – 7 = €8.

The unit margin decreases to €8.

  1. If the rental price is increased to €18, the new markup rate = ((18 – 5) ÷ 18) x 100 = 72,22%.
    The new markup rate would be 72,22%.

  2. With a 10% increase in the number of rentals, new quantity = 50 x 1,10 = 55.
    New overall margin = 10 x 55 = €550.
    The increase in daily rentals would bring the overall margin to €550.

Formulas Used:

Title Formulas
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
Unit margin PV HT – PA HT
Overall margin Unit margin x quantity

Application: Natural Medics

States :

Natural Medics, a pharmacy specializing in natural products, sells food supplements at a unit price of €40 excluding VAT with a purchase cost of €25 excluding VAT. On average, 150 units are sold per month.

Work to do :

  1. Determine the margin rate of these food supplements.
  2. Calculate the overall monthly margin obtained by the pharmacy.
  3. If the sale price drops to €35 excluding VAT, how is the markup rate affected?
  4. If, as a result of a marketing campaign, sales increase by 30%, how many supplements will be sold?
  5. Analyze the effect of a reduced purchase cost of €20 per unit on the margin rate.

Proposed correction:

  1. The margin rate is calculated as follows: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((40 – 25) ÷ 25) x 100 = 60%.
    The margin rate is 60%.

  2. The overall margin is calculated by: Overall margin = Unit margin x quantity sold.
    Unit margin = 40 – 25 = €15.
    Overall margin = 15 x 150 = €2.
    The overall monthly margin is €2.

  3. With a sale price of €35, the new markup rate = ((35 – 25) ÷ 35) x 100 = 28,57%.

The mark rate would decrease to 28,57%.

  1. With a 30% increase in sales, new quantity = 150 x 1,30 = 195.
    He expects to sell 195 units per month after the marketing campaign.

  2. With a purchase cost of €20, new unit margin = 40 – 20 = €20.
    New margin rate = ((40 – 20) ÷ 20) x 100 = 100%.
    A reduced purchase cost would increase the margin rate to 100%.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Overall margin Unit margin x quantity sold
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100

Application: DIY Express

States :

Bricolage Express sells drills at a price of €120 excluding VAT with a purchase cost of €80 excluding VAT. The average monthly sale is 100 units.

Work to do :

  1. Calculate the markup rate of drills.
  2. Determine the overall monthly margin.
  3. If the selling price is reduced to €110 excluding VAT, calculate the new unit margin.
  4. What is the impact on turnover if sales increase by 15%?
  5. If the purchase cost is negotiated at €75, what is the revised margin rate?

Proposed correction:

  1. The markup rate is: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((120 – 80) ÷ 120) x 100 = 33,33%.
    The markup rate of drills is 33,33%.

  2. Overall margin: Overall margin = Unit margin x quantity sold.
    Unit margin = 120 – 80 = €40.
    Overall margin = 40 x 100 = €4.
    The overall monthly margin is €4.

  3. With a selling price of €110, new unit margin = €110 – €80 = €30.

The new unit margin is €30.

  1. 15% increase in sales, new quantity = 100 x 1,15 = 115.
    New turnover = 120 x 115 = €13.
    The turnover would increase to €13.

  2. Purchase cost at €75, new unit margin = €120 – €75 = €45.
    New margin rate = ((120 – 75) ÷ 75) x 100 = 60%.
    The revised margin rate is 60%.

Formulas Used:

Title Formulas
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
Overall margin Unit margin x quantity sold
Unit margin PV HT – PA HT

Application: GreenTech Solutions

States :

GreenTech Solutions sells solar panels at €500 excluding VAT per unit, while the purchase cost is €300 excluding VAT. The company sells an average of 200 panels each quarter.

Work to do :

  1. Calculate the margin rate of solar panels.
  2. What is the company's overall quarterly margin?
  3. If the market pushes to reduce the price to €450 excluding VAT, what are the implications for the unit margin?
  4. Discuss the impact on overall margin if demand increases by 40 units.
  5. Analyze the consequences of a lower purchase cost, revised to €280, on the margin rate.

Proposed correction:

  1. The margin rate is: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((500 – 300) ÷ 300) x 100 = 66,67%.
    The margin rate is 66,67%.

  2. Overall margin: Overall margin = Unit margin x quantity sold.
    Unit margin = 500 – 300 = €200.
    Overall margin = 200 x 200 = €40.
    The overall quarterly margin is €40.

  3. For a sale price of €450, new unit margin = €450 – €300 = €150.

The unit margin would drop to €150.

  1. Increase demand by 40 units, new quantity = 200 + 40 = 240.
    New overall margin = 200 x 240 = €48.
    The overall margin would increase to €48.

  2. Purchase cost at €280, new unit margin = €500 – €280 = €220.
    New margin rate = ((500 – 280) ÷ 280) x 100 = 78,57%.
    A reduction in the purchase cost would increase the margin rate to 78,57%.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Overall margin Unit margin x quantity sold
Unit margin PV HT – PA HT

Application: PureWater Systems

States :

PureWater Systems sells water purifiers for €350 excluding VAT, with a purchase cost of €200 excluding VAT. The company typically sells 80 units per month.

Work to do :

  1. Calculate the brand rate of purifiers.
  2. What is PureWater Systems' overall monthly margin?
  3. If the sale price is reduced to €330, how is the markup rate changed?
  4. Evaluate the impact of a 25 unit sales increase on revenue.
  5. Consider the impact on the margin if the purchase cost drops to €180.

Proposed correction:

  1. The markup rate: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((350 – 200) ÷ 350) x 100 = 42,86%.
    The brand rate of purifiers is 42,86%.

  2. The overall margin is: Overall margin = Unit margin x quantity sold.
    Unit margin = 350 – 200 = €150.
    Overall margin = 150 x 80 = €12.
    The overall monthly margin is €12.

  3. With a sale price of €330, the new markup rate = ((330 – 200) ÷ 330) x 100 = 39,39%.

The markup rate would be changed to 39,39%.

  1. Increase by 25 units, new quantity = 80 + 25 = 105.
    New turnover = 350 x 105 = €36.
    The turnover would increase to €36.

  2. Purchase cost at €180, new unit margin = €350 – €180 = €170.
    New overall margin = 170 x 80 = €13.
    A reduced purchase cost would improve the overall margin to €13.

Formulas Used:

Title Formulas
Brand taxes ((PV HT – PA HT) ÷ PV HT) x 100
Overall margin Unit margin x quantity sold
Unit margin PV HT – PA HT

App: SnackBox Delivery

States :

SnackBox Delivery offers snack boxes at €20 excluding VAT each, with the direct cost of preparation being €8 excluding VAT per box. On average, 400 boxes are prepared and sold each week.

Work to do :

  1. Determine the margin rate for snack boxes.
  2. Calculate the overall weekly margin.
  3. If the preparation cost is reduced to €7, what is the new unit margin?
  4. What is the effect of increasing sales to 450 boxes per week on the overall margin?
  5. Discuss the implications of a 10% off sales promotion.

Proposed correction:

  1. Margin rate: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((20 – 8) ÷ 8) x 100 = 150%.
    The margin rate is 150%.

  2. Overall margin: Overall margin = Unit margin x quantity sold.
    Unit margin = 20 – 8 = €12.
    Overall margin = 12 x 400 = €4.
    The overall weekly margin is €4.

  3. With a cost of €7, new unit margin = €20 – €7 = €13.

The new unit margin is €13.

  1. Sales increase to 450, new overall margin = 12 x 450 = €5.
    The overall margin would amount to €5.

  2. 10% promotion, new sale price = 20 – (20 x 0,10) = €18.
    New unit margin = 18 – 8 = €10.
    New overall margin = 10 x 400 = €4.
    The promotion would reduce the overall margin to €4.

Formulas Used:

Title Formulas
Margin rate ((PV HT – PA HT) ÷ PA HT) x 100
Overall margin Unit margin x quantity sold
Unit margin PV HT – PA HT

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