Commercial calculations in CAP

Business Calculations in CAP | 9 Exercises

by

Application: Sophie's Delights

States :

Les Délices de Sophie is a small artisanal pastry shop located in Paris. She wants to calculate various commercial indicators to optimize her operation. The following data is available to her: the cost of purchasing her raw materials for a lemon tart is €4 excluding tax, and she sells this tart for €10 excluding tax. She sells an average of 500 tarts per month.

Work to do :

  1. Calculate the margin rate for a lemon tart.
  2. Determine the markup rate for a lemon tart.
  3. Calculate the overall margin over a month for the pies sold.
  4. Sophie wants to achieve a markup rate of 30% for her new red fruit tarts. Calculate the necessary selling price excluding tax if the purchase cost excluding tax is €5.
  5. Analyze the impact of a 10% increase in monthly lemon tart sales on overall margin.

Proposed correction:

  1. The margin rate is calculated using the following formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((10 – 4) ÷ 4) x 100 = 150%. The margin rate for a pie is therefore 150%.

  2. The markup rate is calculated using the formula: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((10 – 4) ÷ 10) x 100 = 60%. The markup rate for a pie is therefore 60%.

  3. The overall margin is calculated by multiplying the unit margin by the quantity sold.

Calculation: (10 – 4) x 500 = €3. The overall margin over one month for the pies sold is €000.

  1. To achieve a markup rate of 30%, the formula to use is: PV HT = PA HT ÷ (1 – Markup rate).
    Substituting, 5 ÷ (1 – 0,30) = €7,14. The required selling price excluding VAT is therefore €7,14.

  2. A 10% increase in sales means 500 x 1,10 = 550 pies sold.
    The new overall margin is: (10 – 4) x 550 = €3. The impact on the overall margin is an increase of €300.

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
Selling price excluding VAT required PA HT ÷ (1 – Mark rate)

Application: ElectroFacile

States :

ElectroFacile, a local electronics store, wants to evaluate its sales performance. The purchase price excluding tax of a vacuum cleaner is €80, and it is resold at the price of €120 excluding tax. The store usually sells 100 vacuum cleaners per month.

Work to do :

  1. Calculate the margin rate for a vacuum cleaner.
  2. Determine the mark rate for a vacuum cleaner.
  3. Estimate the overall monthly margin made on the sale of vacuum cleaners.
  4. If ElectroFacile decides to apply a 5% discount on each vacuum cleaner sold, what would be the new selling price excluding tax?
  5. Estimate the effect of this discount on the overall margin, assuming that sales would increase by 15% as a result of the discount.

Proposed correction:

  1. The margin rate is obtained by the formula: ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((120 – 80) ÷ 80) x 100 = 50%. The margin rate for a vacuum cleaner is 50%.

  2. For the markup rate, the formula used is: ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((120 – 80) ÷ 120) x 100 = 33,33%. The markup rate for a vacuum cleaner is 33,33%.

  3. The monthly overall margin is obtained by the calculation: (120 – 80) x 100 = €4. The monthly overall margin is therefore €000.

  1. The new formula for the selling price excluding tax with discount is: PV excluding tax x (1 – Discount).
    By replacing, 120 x (1 – 0,05) = €114. The new selling price excluding VAT is €114.

  2. A 15% increase in sales gives: 100 x 1,15 = 115 vacuum cleaners.
    The new overall margin is: (114 – 80) x 115 = €3. The discount causes the overall margin to decrease by €910 despite the increase in sales.

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 selling price excluding VAT PV HT x (1 – Discount)

Application: Elegant Shoes

States :

Chaussures Élégantes, a fashion boutique, bought shoes for €40 excluding VAT per pair and is selling them for €85 excluding VAT. The boutique plans to sell around 200 pairs per month.

Work to do :

  1. Determine the markup on a pair of shoes.
  2. Calculate the markup rate for a pair of shoes.
  3. Estimate the overall expected margin for a month of sales.
  4. If the store decides to promote a temporary €10 discount on each pair, what will the new markdown rate be?
  5. Consider a scenario where such a promotion increases sales by 20%. Calculate the impact on overall margin.

Proposed correction:

  1. The margin rate is obtained by the formula: ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((85 – 40) ÷ 40) x 100 = 112,5%. The margin rate for a pair is 112,5%.

  2. For the mark rate: ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((85 – 40) ÷ 85) x 100 = 52,94%. The markup rate for a pair is therefore 52,94%.

  3. The overall margin for one month is calculated: (85 – 40) x 200 = €9. The overall margin is €000.

  1. Calculating the new price after reduction gives: 85 – 10 = €75.
    The new markup rate is: ((75 – 40) ÷ 75) x 100 = 46,67%. The markup rate with discount is 46,67%.

  2. A 20% increase in sales means 200 x 1,20 = 240 pairs sold.
    The new overall margin would be: (75 – 40) x 240 = €8. The increase in sales would result in a €400 reduction in the overall margin, even with more pairs sold.

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 sale price PV HT – Reduction

Application: Jardin'Co

States :

Jardin'Co, a gardening equipment company, sells lawnmowers. The purchase price excluding VAT of a lawnmower is €150 and is sold at €300 excluding VAT. Currently, Jardin'Co sells about 50 lawnmowers per month.

Work to do :

  1. Calculate the margin rate of a mower.
  2. Determine the mark rate of a mower.
  3. Evaluate the overall monthly margin for mowers.
  4. If Jardin'Co wants to offer a 20% discount on the sale price, what will the new sale price be after the discount?
  5. Forecast the implications if sales increase by 30% due to this discount. What is the new overall margin?

Proposed correction:

  1. The margin rate is given by: ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((300 – 150) ÷ 150) x 100 = 100%. The margin rate of a mower is 100%.

  2. For the markup rate, the formula is: ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((300 – 150) ÷ 300) x 100 = 50%. The markup rate of a mower is 50%.

  3. The overall margin is found by: (300 – 150) x 50 = €7. The monthly overall margin is €500.

  1. With a 20% discount, the new price is calculated as follows: 300 x (1 – 0,20) = €240.
    The new sale price after discount is €240.

  2. A 30% increase in sales gives: 50 x 1,30 = 65 mowers sold.
    The new overall margin becomes: (240 – 150) x 65 = €5. The new overall margin reduces significantly despite the increase in sales.

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 sale price PV HT x (1 – Discount)

Application: Precious Jewelry

States :

Bijoux Précieux is a specialty retailer that offers elegant necklaces. The purchase cost excluding VAT of each necklace is €150, and it is sold for €290 excluding VAT. The store sells about 30 necklaces each month.

Work to do :

  1. Calculate the margin rate for a necklace.
  2. Determine the markup rate for a necklace.
  3. Estimate the overall monthly margin on necklace sales.
  4. If a temporary promotion offers €20 off per necklace, what will the new selling price excluding VAT be?
  5. What would be the effect on overall margin if this promotion increased sales by 10%?

Proposed correction:

  1. The margin rate is obtained using: ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((290 – 150) ÷ 150) x 100 = 93,33%. The margin rate for a collar is 93,33%.

  2. The markup rate is calculated by: ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((290 – 150) ÷ 290) x 100 = 48,28%. The markup rate for a necklace is therefore 48,28%.

  3. The monthly overall margin is calculated as follows: (290 – 150) x 30 = €4. The monthly overall margin for collars is €200.

  1. The new selling price excluding VAT after discount will be: 290 – 20 = 270 €.
    The selling price excluding tax after delivery of a necklace is €270.

  2. A 10% increase in sales gives: 30 x 1,10 = 33 necklaces sold.
    The new overall margin becomes: (270 – 150) x 33 = €3. Although the number of sales has increased, the overall margin is slightly reduced.

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 sale price PV HT – Reduction

Application: Bookstore of the Future

States :

Librairie de L'Avenir is a modern bookstore. It buys a particular book at the price of €10 excluding VAT and sells it at €25 excluding VAT. It sells an average of 400 of these books per month.

Work to do :

  1. Calculate the margin rate for this book.
  2. Determine the markup rate for this book.
  3. Calculate the overall monthly margin generated by the sale of these books.
  4. Librairie de L'Avenir wants to reduce the price by €3 to attract more customers. What will be the new selling price excluding VAT?
  5. If this reduction results in a 50% increase in sales, what would be the new overall margin?

Proposed correction:

  1. The margin rate is calculated as follows: ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((25 – 10) ÷ 10) x 100 = 150%. The margin rate for this book is 150%.

  2. For the markup rate, we use the formula: ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((25 – 10) ÷ 25) x 100 = 60%. The markup rate for this book is 60%.

  3. The overall margin is obtained by multiplying: (25 – 10) x 400 = €6. The monthly overall margin is €000.

  1. With the reduction of €3, the new sale price becomes: €25 – €3 = €22.
    The new selling price excluding VAT is €22.

  2. A 50% increase in sales means 400 x 1,50 = 600 pounds.
    The new overall margin is: (22 – 10) x 600 = €7. Therefore, the overall margin increases despite the price drop due to the increase in sales.

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 sale price PV HT – Reduction

Application: Sylvie Fashion

States :

Sylvie Fashion is a trendy clothing store. It offers jackets whose purchase cost is €50 excluding VAT, sold at €130 excluding VAT per unit. On average, 150 jackets are sold each month.

Work to do :

  1. Calculate the margin rate for a jacket.
  2. Determine the markup rate for a jacket.
  3. What is the overall monthly margin on jacket sales?
  4. Sylvie Fashion is planning a 15% discount promotion. What will the sale price be after the discount?
  5. Suppose this discount results in a 25% increase in sales, what would be the impact on the overall margin?

Proposed correction:

  1. The margin rate for a jacket is: ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((130 – 50) ÷ 50) x 100 = 160%. The margin rate for a jacket is 160%.

  2. For the mark rate: ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((130 – 50) ÷ 130) x 100 = 61,54%. The markup rate is therefore 61,54%.

  3. The monthly overall margin is: (130 – 50) x 150 = €12. The monthly overall margin is €000.

  1. The sale price after 15% discount is: 130 x (1 – 0,15) = €110,50.
    The new sale price after discount is €110,50.

  2. With a 25% increase, the number of jackets sold becomes: 150 x 1,25 = 187,5 (rounded to 188 jackets).
    The new overall margin is: (110,50 – 50) x 188 = €11. The overall margin decreases slightly but remains significant thanks to the increase in sales.

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 sale price PV HT x (1 – Discount)

Application: Modern Kitchen

States :

Cuisine Moderne is a kitchen equipment store selling food processors that the company buys for €200 excluding VAT and resells for €450 excluding VAT. It sells about 20 of them each month.

Work to do :

  1. Calculate the margin rate of each food processor.
  2. Determine the markup rate for these food processors.
  3. Estimate the overall monthly margin for the sale of these devices.
  4. If an instant discount of €50 is offered, what will the corrected selling price excluding VAT be?
  5. If this discount increases sales by 40%, estimate the new overall margin.

Proposed correction:

  1. The margin rate is calculated by: ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((450 – 200) ÷ 200) x 100 = 125%. The margin rate for a food processor is 125%.

  2. To calculate the markup rate: ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((450 – 200) ÷ 450) x 100 = 55,56%. The markup rate is 55,56%.

  3. The overall monthly margin is: (450 – 200) x 20 = €5. The monthly margin is €000.

  1. With a discount of €50, the selling price excluding tax becomes: €450 – €50 = €400.
    The corrected sale price is €400.

  2. Sales increased by 40% means: 20 x 1,40 = 28 robots sold.
    The new margin will be: (400 – 200) x 28 = €5. So, despite the discount, the overall margin increases due to increased sales.

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 sale price PV HT – Reduction

Application: Technology Plus

States :

Technologie Plus, an electronics store, sells laptops at a purchase price of €600 excluding VAT and resells them at €900 excluding VAT. About 50 units are sold each month.

Work to do :

  1. Calculate the margin rate for each laptop.
  2. Determine the markup rate of these computers.
  3. Calculate the overall monthly margin on sales of these laptops.
  4. If a special offer reduces the sale price by 10%, what is the new sale price excluding VAT?
  5. Discuss the impact on overall margin if sales increase by 20% as a result of this offer.

Proposed correction:

  1. The margin rate is given by: ((PV HT – PA HT) ÷ PA HT) x 100.
    Substituting, ((900 – 600) ÷ 600) x 100 = 50%. The margin rate is 50%.

  2. Mark rate calculated by: ((PV HT – PA HT) ÷ PV HT) x 100.
    Substituting, ((900 – 600) ÷ 900) x 100 = 33,33%. The markup rate is 33,33%.

  3. The monthly overall margin is: (900 – 600) x 50 = €15. The monthly overall margin reaches €000.

  1. A 10% reduction in price gives: 900 x (1 – 0,10) = €810.
    The new selling price excluding VAT, after discount, is €810.

  2. A 20% increase in sales means: 50 x 1,20 = 60 laptops sold.
    The new overall margin is: (810 – 600) x 60 = €12. The special offer results in a slight decrease in margin, although sales volume has increased.

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 sale price PV HT x (1 – Reduction)

Leave comments