commercial calculation multiplier coefficient | 9 Exercises

Application: Bakery Breads and Delights

States :

The bakery Pains et Délices wants to increase its sales prices while keeping the same profit level. Currently, bread sells for €1,20. The purchase cost is €0,80. They want to evaluate the ideal sales price to increase their markup rate by 20% to 25%.

Work to do :

1. Determine the initial sales price excluding tax (SVP HT) with the current markup rate of 20%.
2. Calculate the new tax-free sales price needed to achieve a 25% markup rate.
3. What would be the effect on the unit margin if the VAT rate is 5,5% and the selling price increases to €1,50?
4. Calculate the initial multiplier between the purchase cost and the current selling price.
5. Discuss the strategic implications for the bakery when changing the branding rate from 20% to 25%.

Proposed correction:

1. The initial markup rate is 20%. The formula is: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.
   Replacing: 20 = ((PV HT – 0,80) ÷ PV HT) x 100, i.e. PV HT = €1,00.
   The initial sale price, excluding taxes, is €1,00.

2. For a markup rate of 25%, the formula is: PV HT = PA HT ÷ (1 – Markup rate).
   By replacing: PV excluding tax = 0,80 ÷ (1 – 0,25) = €1,067.
   The selling price excluding VAT must be €1,067.

3. With a VAT rate of 5,5%, the final sales price is €1,50. The unit margin becomes: (1,50 ÷ 1,055) – 0,80 = €0,64.

The margin change represents an increase in the bakery's share.

4. The multiplier coefficient is calculated by: PV ÷ PA.
   With the initial data: 1,00 ÷ 0,80 = 1,25.
   The initial multiplier coefficient was 1,25.

5. Moving from a 20% to 25% markup rate means an increase in the tax-free selling price, which could affect demand if customers are price sensitive. However, it does increase the margin per unit sold.

Formulas Used:

Title	Formulas
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
PV HT for a given mark rate	PA HT ÷ (1 – Mark rate)
Multiplier coefficient	PV ÷ PA

Application: TechZone Equipment

States :

TechZone Équipements, a company specializing in the sale of computer equipment, has a product whose purchase price is €320 excluding VAT. Currently, they sell this product at €400 excluding VAT. They are considering a redesign of their pricing strategy and want to know how this will impact their results.

Work to do :

1. Describe the current margin rate.
2. If TechZone wants to achieve a 30% margin, what should the new sales price excluding tax be?
3. Determine the multiplier coefficient that would correspond to this new sale price.
4. Analyze the current unit profit and that with the new price for a VAT rate of 20%.
5. What strategic elements should TechZone consider to implement this new pricing?

Proposed correction:

1. Calculation of the current margin rate with the following formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   Replacing: ((400 – 320) ÷ 320) x 100 = 25%.
   The current margin rate is 25%.

2. To achieve a margin rate of 30%, use the formula: PV HT = PA HT x (1 + Margin rate).
   Which gives: 320 x (1 + 0,30) = €416.
   The new sales price excluding tax should be set at €416.

3. The multiplier coefficient with the new price is: 416 ÷ 320 = 1,3.

With this multiplier, the company would achieve the desired margin rate.

4. Let's consider the unit profit for a VAT rate of 20%.
   Current unit profit: (400 x 1,20 – 320 x 1,20) = €96.
   Profit with the new price: (416 x 1,20 – 320 x 1,20) = €115,20.
   The increase in unit profit is positive.

5. The company must analyze whether the market will accept this new price. This includes studying the price sensitivity of customers and the behavior of competitors in order not to be depositioned.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
PV HT with desired margin rate	PA HT x (1 + Margin rate)
Multiplier coefficient	PV ÷ PA

Application: Marine Delights Restaurant

States :

The restaurant Délices Marine has decided to review its menu to optimize its profitability. Currently, they buy fish at €15 per kilo and resell it after preparation for €30 per dish. They want to evaluate different potential margins.

Work to do :

1. What is the restaurant's current margin rate?
2. If the restaurant wants to obtain a markup rate of 40%, what should the selling price excluding tax be?
3. What would be the multiplier coefficient for this new sale price?
4. Estimate the unit margin if the selling price is adjusted to €35 with a VAT rate of 5,5%.
5. Consider the implications of setting a high price on customer influx, taking into account current economic data.

Proposed correction:

1. The margin rate is calculated by: ((PV HT – PA HT) ÷ PA HT) x 100.
   ((30 – 15) ÷ 15) x 100 = 100%.
   The current margin rate is 100%.

2. For a markup rate of 40%, we have: PV HT = PA HT ÷ (1 – Markup rate).
   Replacing: 15 ÷ (1 – 0,40) = €25.
   The new selling price excluding VAT must be €25 to ensure a 40% mark.

3. The multiplier coefficient for this new price is: 25 ÷ 15 = 1,67.

This coefficient shows the relevant adjustment for the restaurant.

4. Taking into account the price of €35 with a VAT rate of 5,5%, the unit margin is:
   ((35 ÷ 1,055) – 15) = €18,14.
   This shows an increased positive margin.

5. Setting higher prices could deter customers, especially in times of economic instability. The restaurant should then focus on communicating the quality and special experience offered.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
PV HT for a given mark rate	PA HT ÷ (1 – Mark rate)
Multiplier coefficient	PV ÷ PA

Application: Esprit Mode Boutique

States :

The Boutique Esprit Mode, specializing in the sale of fashion accessories, is looking to adjust its prices. Currently, a bag is purchased for €50 excluding VAT and sold for €100 excluding VAT. With a competitive market, the boutique is considering changing its prices while remaining profitable.

Work to do :

1. What is the current markup rate applied by the store?
2. How much should the selling price be adjusted to achieve a 60% margin rate?
3. Calculate the multiplier coefficient from the new sale price.
4. With a VAT rate of 20% and a sale at €90, estimate the net margin obtained by Esprit Mode.
5. What changes in marketing strategy could support price adjustments in this market section?

Proposed correction:

1. Use the formula: Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.
   ((100 – 50) ÷ 100) x 100 = 50%.
   The current markup rate is 50%.

2. To achieve a margin rate of 60%, we have: PV HT = PA HT x (1 + Margin rate).
   Replacing: 50 x (1 + 0,60) = €80.
   A price of €80 will ensure the desired margin rate.

3. With this price, the multiplier coefficient is: 80 ÷ 50 = 1,6.

This coefficient confirms the change.

4. With a VAT rate of 20% on €90, the net margin is:
   ((90 ÷ 1,20) – 50) = €25.
   Esprit Mode would continue to benefit from favorable margins.

5. The store should review its loyalty campaigns and exclusive promotions to justify the price change. Building awareness around quality and exclusivity is fundamental to the perception of value.

Formulas Used:

Title	Formulas
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
PV HT for a desired margin rate	PA HT x (1 + Margin rate)
Multiplier coefficient	PV ÷ PA

Application: HealthBack Pharmacy

States :

Pharmacie SantéDos wants to review its pricing policies to optimize the flow of pharmaceutical products while ensuring good profitability. A certain medicine is purchased at €25 excluding VAT and sold at €50 excluding VAT.

Work to do :

1. Calculate the current margin rate applied to the sale of this drug.
2. If the pharmacy wants to get a 30% markup rate, what should the new selling price be?
3. Determine the multiplier coefficient with this new sale price.
4. Evaluate how the unit margin is affected if nothing is changed but the price increases to €55 with 5,5% VAT.
5. Discuss potential strategies to maintain high sales while adjusting pricing.

Proposed correction:

1. Formula for the margin rate: ((PV HT – PA HT) ÷ PA HT) x 100.
   ((50 – 25) ÷ 25) x 100 = 100%.
   The margin applied is 100%.

2. For a markup rate of 30%, the formula is: PV HT = PA HT ÷ (1 – Markup rate).
   25 ÷ (1 – 0,30) = €35,71.
   The new sale price should then be €35,71.

3. Multiplier coefficient: 35,71 ÷ 25 = 1,428.

We can see how it changes.

4. With a VAT rate of 5,5% and a price of €55, the unit margin is:
   ((55 ÷ 1,055) – 25) = €26,11.
   Slightly better margins are noted.

5. The pharmacy could introduce value-added services, such as consultations or discounts for complementary products, to attract and retain customers while raising its prices.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
PV HT for a given mark rate	PA HT ÷ (1 – Mark rate)
Multiplier coefficient	PV ÷ PA

Application: Culture & Knowledge Bookstore

States :

The Culture & Savoir bookstore is questioning the profitability of one of its flagship works. It currently buys this book for €18 excluding VAT and resells it for €30 excluding VAT. In order to stimulate sales, it wants to adjust its prices.

Work to do :

1. Calculate the current margin rate for this book.
2. If the bookstore wants to adjust its margin rate to 40%, what should be the sales price excluding tax of the book?
3. What is the multiplier for the current price?
4. With a sales price adjusted to €28 instead of €30, what will the net margin be for a VAT rate of 5,5%?
5. What measures can the bookstore take to compensate for the price reduction without losing profitability?

Proposed correction:

1. The margin rate is determined by: ((PV HT – PA HT) ÷ PA HT) x 100.
   ((30 – 18) ÷ 18) x 100 = 66,67%.
   The current margin rate is 66,67%.

2. To achieve a margin rate of 40%, use: PV HT = PA HT x (1 + Margin rate).
   18 x (1 + 0,40) = €25,20.
   The price should be adjusted to €25,20.

3. The current multiplier coefficient is: 30 ÷ 18 = 1,67.

This coefficient indicates the multiplier for the current price.

4. With 5,5% VAT and a price adjusted to €28, the net margin becomes:
   ((28 ÷ 1,055) – 18) = €8,53.
   The margin is maintained appropriate with the new price adjustment.

5. The bookstore can improve its marketing, offer bundle discounts or introduce loyalty programs to drive purchasing at other levels of the category.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
PV HT for a desired margin rate	PA HT x (1 + Margin rate)
Multiplier coefficient	PV ÷ PA

Application: VéloMax Workshop

States :

Atelier VéloMax is a company that sells bicycle parts. It would like to establish an optimal price for its rims, which cost €20 to purchase. At present, they are sold for €40 each. The company is planning strategic adjustments.

Work to do :

1. What is the markup rate currently practiced by VéloMax?
2. What should the sales price excluding tax be for an expected margin rate of 50%?
3. Determine the multiplier coefficient with this expected price.
4. Analyze the new unit margin if the price is set at €38 with a VAT rate of 20%.
5. What communication policy could VéloMax adopt to justify price adjustments to customers?

Proposed correction:

1. Mark rate calculated by: ((PV HT – PA HT) ÷ PV HT) x 100.
   ((40 – 20) ÷ 40) x 100 = 50%.
   The current markup rate is 50%.

2. For a margin rate of 50%, we have: PV HT = PA HT x (1 + Margin rate).
   20 x (1 + 0,50) = €30.
   The selling price to aim for 50% margin must be €30.

3. Multiplier coefficient for 30 € is: 30 ÷ 20 = 1,5.

This represents the adjusted price relationship.

4. With 20% VAT for a price of €38, the unit margin becomes:
   ((38 ÷ 1,20) – 20) = €11,67.
   The analysis shows the strength maintained in the margin.

5. VéloMax can focus on product quality and performance benefits, emphasizing why a different price point is justified.

Formulas Used:

Title	Formulas
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
PV HT for a given margin rate	PA HT x (1 + Margin rate)
Multiplier coefficient	PV ÷ PA

Application: Nature & Plant Nursery

States :

Pépinière Nature & Végétal, which specializes in selling potted plants, wants to reconsider its pricing strategies to maximize its profits. Currently, it buys a variety of plant for €8 and resells it for €20.

Work to do :

1. What is the current margin rate on this plant?
2. To define a more aggressive strategy with a markup rate of 35%, what would be the right selling price?
3. What would be the multiplier coefficient with this new pricing?
4. If the price is adjusted to €18, what will be the effective margin with a VAT of 20%?
5. Discuss the changes needed in retail to maintain the company's financial performance following this price reduction.

Proposed correction:

1. Calculation of the margin rate with: ((PV HT – PA HT) ÷ PA HT) x 100.
   ((20 – 8) ÷ 8) x 100 = 150%.
   The current margin rate is 150%.

2. For a markup rate of 35%, we have: PV HT = PA HT ÷ (1 – Markup rate).
   Substituting, 8 ÷ (1 – 0,35) = €12,31.
   An adjusted price of €12,31 would also optimize the brand.

3. Multiplier coefficient at this price: 12,31 ÷ 8 = 1,54.

This shows the relevant adjustment.

4. The margin with 20% VAT and a price of €18 is:
   ((18 ÷ 1,20) – 8) = €7.
   Profit remains healthy despite adjustment.

5. The Nursery could introduce new services, such as workshops or maintenance advice, to engage customers differently and penalize less the price reduction.

Formulas Used:

Title	Formulas
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
PV HT for a given mark rate	PA HT ÷ (1 – Mark rate)
Multiplier coefficient	PV ÷ PA

Application: Music Melody Course

States :

Cours de Musique Mélodie offers private lessons to beginners and advanced students. They want to exploit more competitive rates for the courses given. To date, they have set the price of each course at €60, while they pay €30 to their teacher, excluding taxes.

Work to do :

1. Estimate the operable markup rate for current music lessons.
2. For a different margin orientation at 50%, what is the optimal rate that should be announced?
3. What is the multiplier coefficient up to this target threshold?
4. What would be the net profitability for the teacher with a VAT rate set at 5,5%?
5. Suggest loyalty ideas to offset the impact of the price increase on members.

Proposed correction:

1. Use the formula for calculation: ((PV HT – PA HT) ÷ PV HT) x 100.
   ((60 – 30) ÷ 60) x 100 = 50%.
   So the current markup rate is 50%.

2. For a change with a margin rate of 50%: PV HT = PA HT x (1 + Margin rate).
   By reproducing, 30 x (1 + 0,50) = €45.
   The announced price would then be €45.

3. For this price, the multiplier coefficient is: 45 ÷ 30 = 1,5.

Expressing there the calculated proportion.

4. With 5,5% VAT, net profitability would be:
   ((60 ÷ 1,055) – 30) = €26,99.
   This figure represents a preserved profitability.

5. Courses could offer monthly subscriptions, referral discounts or monthly open sessions to boost interest through price increases.

Formulas Used:

Title	Formulas
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
PV HT for a given margin rate	PA HT x (1 + Margin rate)
Multiplier coefficient	PV ÷ PA