commercial calculations course cap | 9 Exercises

Sweet Flavor Pastry

States :

Pâtisserie Douce Saveur, which specializes in custom cakes, wants to optimize its sales prices to increase its profitability on a fruit tart that is in high demand. The purchase price of the ingredients is €5 per unit and the current sales price is €12 excluding VAT. The pastry shop sells about 200 tarts per month. It wants to analyze its pricing strategy using margin indicators.

Work to do :

1. Calculate the unit margin made on each pie sold.
2. Determine the current margin rate of the pie.
3. Calculate the markup rate.
4. The bakery wants to increase its markup rate to 40%. What would be the new selling price excluding tax to achieve this objective?
5. Analyze the impact of this price change on monthly revenue, assuming that the quantity sold remains unchanged.

Proposed correction:

1. The unit margin is calculated as follows: Unit margin = PV HT – PA HT.
   So, unit margin = €12 – €5 = €7.
   The unit margin made on each tart is €7.

2. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   So, margin rate = ((€12 – €5) ÷ €5) x 100 = 140%.
   The current margin rate of the pie is 140%.

3. The mark rate is obtained by: Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.

So, markup rate = ((€12 – €5) ÷ €12) x 100 = 58,33%.
The current markup rate is 58,33%.

4. To obtain a markup rate of 40%, we use the formula: PV HT = PA HT ÷ (1 – Markup rate).
   Therefore, PV HT = €5 ÷ (1 – 0,40) = €8,33.
   The new selling price excluding VAT should be €8,33 to achieve a mark-up rate of 40%.

5. The current monthly turnover is 200 x 12 € = 2 €.
   With the new selling price of €8,33, the turnover would be 200 x €8,33 = €1.
   Monthly turnover would decrease, which shows the importance of a balanced pricing strategy.

Formulas Used:

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

BioHarmony Shop

States :

BioHarmony, a boutique specializing in organic products, is studying its stocks to improve its finances through its supply management. They observe a constant sales rate for a certain type of honey sold at a price of €15 excluding VAT per 500g jar. The purchase cost is €8 per jar. BioHarmony sells and renews its stock of honey at a rate of 600 jars per year.

Work to do :

1. Calculate the overall annual margin generated by the sale of honey.
2. Determine the margin rate for this product.
3. What is the current markup rate on honey?
4. Calculate the QEC (Economic Order Quantity) if the cost of each order is €10 and the storage cost per pot is €1,50.
5. Analyze the impact of a €1 reduction in the selling price on the unit margin and determine whether this reduction is desirable if demand increases by 10%.

Proposed correction:

1. The overall margin is obtained by multiplying the unit margin by the quantity sold: Overall margin = Unit margin x Quantity.
   Unit margin = €15 – €8 = €7.
   Overall margin = €7 x 600 = €4.
   The annual overall margin is €4.

2. The margin rate is calculated by: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€15 – €8) ÷ €8) x 100 = 87,5%.
   The margin rate on honey is 87,5%.

3. The markup rate is: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Markup rate = ((€15 – €8) ÷ €15) x 100 = 46,67%.
The current markup rate on honey is 46,67%.

4. Let's use the formula for QEC: QEC = ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost).
   QEC = ?((2 x 600 x 10) ÷ 1,50) = ?(8) ? 000.
   Mathematically approximated, BioHarmony would have to order about 89 pots to minimize its costs.

5. If the selling price is reduced by €1, the new unit margin becomes €15 – €1 – €8 = €6.
   New request = 600 + 10% = 660 pots.
   New overall margin = €6 x 660 = €3.
   Although demand increases, the overall margin decreases (€4 to €200), making the reduction undesirable.

Formulas Used:

Title	Formulas
Overall margin	Unit Margin x Quantity
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
QEC (Economic Order Quantity)	?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)
New unit margin	New PV – PA HT

EscapadeSérénité Travel Agency

States :

The EscapadeSérénité Travel Agency offers trips to Italy. The package includes flight, accommodation and activities for a sales price excluding tax of €1 per trip. The cost price of the trip for the agency is €200. The agency must analyze its economic feasibility. Currently, the agency sells 850 trips per year.

Work to do :

1. Calculate the unit margin generated by each stay sale.
2. What is the margin rate associated with this offer?
3. Determine the current markup rate for this stay.
4. If the agency wants to increase its unit margin by 10%, what should the new selling price excluding tax be?
5. Analyze the effect of reducing the cost price to €800 on the margin rate, assuming that the selling price is unchanged.

Proposed correction:

1. The unit margin is: Unit margin = PV HT – PA HT.
   Unit margin = €1 – €200 = €850.
   The unit margin is €350 per stay.

2. The margin rate is calculated as follows: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€1 – €200) ÷ €850) x 850 = 100%.
   The margin rate on the stay is 41,18%.

3. The markup rate: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Markup rate = ((€1 – €200) ÷ €850) x 1 = 200%.
The current markup rate is 29,17%.

4. To increase the unit margin by 10%, new margin = €350 x 1,10 = €385.
   New PV HT = PA HT + New Margin = €850 + €385 = €1.
   The new selling price excluding VAT should be €1.

5. New PA excluding tax = €800, margin rate = ((€1 – €200) ÷ €800) x 800 = 100%.
   Reducing the cost price improves the margin rate to 50%, indicating better profitability.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New PV for increased margin	PA HT + New Margin
New margin rate	((PV HT – New PA HT) ÷ New PA HT) x 100

The Curious Bookstore

States :

Le Bouquin Curieux, an independent bookstore, offers a popular book at €18 excluding VAT. The cost of purchasing from the publisher is €11 per book. The bookstore sells about 400 books per month. In order to optimize their sales, they are considering revising their pricing and inventory strategy.

Work to do :

1. Calculate the unit margin for each book sold.
2. Determine the margin rate charged on this book.
3. Calculate the current markup rate for this book.
4. If the bookstore wants to reduce the sale price by €2 to stimulate demand estimated at 10% more, what will the new monthly turnover be?
5. Analyze the implications of this reduction on the overall margin.

Proposed correction:

1. The unit margin is given by: Unit margin = PV HT – PA HT.
   Unit margin = €18 – €11 = €7.
   The unit margin is €7.

2. The margin rate is calculated as follows: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€18 – €11) ÷ €11) x 100 = 63,64%.
   The margin rate is 63,64%.

3. The markup rate: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Markup rate = ((€18 – €11) ÷ €18) x 100 = 38,89%.
The current markup rate is 38,89%.

4. New PV excluding VAT = €18 – €2 = €16, new quantity = 400 x 110% = 440 pounds.
   New turnover = 440 x 16 € = 7 €.
   The new monthly turnover would be €7.

5. New unit margin = €16 – €11 = €5, new overall margin = €440 x €5 = €2.
   The overall margin decreases from €2 to €800, making the reduction disadvantageous.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New turnover	New Quantity x New PV HT
New overall margin	New Unit Margin x New Quantity

TechInnov Electronics Company

States :

TechInnov, an electronics company, sells a security device for €350 excluding VAT, with a production cost of €250. The company currently sells 2 units per year. In this period of increased competition, it is evaluating the impact of a possible basic reduction in its production cost.

Work to do :

1. Determine the current unit margin on each device sold.
2. What is the current margin rate applied?
3. Calculate the markup rate for this safety device.
4. If the cost of production is reduced by 20%, what would be the new unit margin?
5. Discuss the potential benefits of investing in reducing production costs for TechInnov.

Proposed correction:

1. Unit margin = PV HT – PA HT.
   Unit margin = €350 – €250 = €100.
   The unit margin is €100 per device.

2. Margin rate: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€350 – €250) ÷ €250) x 100 = 40%.
   The current margin rate is 40%.

3. Markup rate: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Markup rate = ((€350 – €250) ÷ €350) x 100 = 28,57%.
The current markup rate is 28,57%.

4. New production cost = €250 x 0,80 = €200.
   New unit margin = €350 – €200 = €150.
   With a 20% reduction, the new unit margin would be €150.

5. Investing in reducing production costs could increase the unit margin by €50, thus increasing profits despite the same sales prices excluding VAT. This change would improve their competitiveness and net profit.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New unit margin	PV HT – New production cost
Benefits of discounts	New unit margin – Old unit margin

GymnastPolis – Fitness Center

States :

GymnastPolis, a fitness center, wants to analyze the effectiveness of its annual memberships available at €650 each, with an estimated cost of €400 per membership. The gym has 200 memberships sold per year and is considering a promotional offer to boost sales.

Work to do :

1. Calculate the unit margin per subscription sold.
2. Determine the current margin rate for subscriptions.
3. What is the markup rate associated with subscriptions?
4. If the subscription is reduced by €50 in the promotional offer, what is the new unit margin?
5. Explain the strategic impact of this promotion on revenue and profitability.

Proposed correction:

1. The unit margin is: Unit margin = PV HT – PA HT.
   Unit margin = €650 – €400 = €250.
   The unit margin is €250.

2. Margin rate: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€650 – €400) ÷ €400) x 100 = 62,5%.
   The current margin rate is 62,5%.

3. Markup rate: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Markup rate = ((€650 – €400) ÷ €650) x 100 = 38,46%.
The markup rate is 38,46%.

4. New PV excluding tax = €650 – €50 = €600, New unit margin = €600 – €400 = €200.
   The new unit margin is €200.

5. This promotion could potentially increase the number of new subscriptions. Although the unit margin decreases from €250 to €200, the volume of increased sales could compensate for this decrease and increase total revenue.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New unit margin	New PV HT – PA HT
Strategic impact	New unit margin – Old unit margin

Ecological decorations éLilou

States :

Eco-friendly home decor manufacturer éLilou sells a popular line of cushions for €25 excluding VAT, while the manufacturing cost is €14. By selling 1 units per year, éLilou is looking to increase its yield without compromising its eco-friendly philosophy.

Work to do :

1. Calculate the unit margin on each cushion sold.
2. Determine the margin rate for the cushions.
3. What is the current markup rate for this product?
4. If éLilou increases the sale price to €28, what happens to the markup rate?
5. What strategy could éLilou consider to further improve its margin without increasing the initial selling price?

Proposed correction:

1. The unit margin is: Unit margin = PV HT – PA HT.
   Unit margin = €25 – €14 = €11.
   The unit margin on each cushion sold is €11.

2. Margin rate: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€25 – €14) ÷ €14) x 100 = 78,57%.
   The margin rate for cushions is 78,57%.

3. Markup rate: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Markup rate = ((€25 – €14) ÷ €25) x 100 = 44%.
The current markup rate for this product is 44%.

4. With PV excluding tax at €28, the new markup rate = ((€28 – €14) ÷ €28) x 100 = 50%.
   The mark rate would increase to 50%.

5. éLilou could explore initiatives to reduce manufacturing costs, such as more economical production methods or purchasing materials in larger quantities to obtain discounts, without affecting the initial selling price.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New mark rate	((New PV HT – PA HT) ÷ New PV HT) x 100
Strategies for improvement	Cost reduction or other strategic initiative

Silk and Confidences Textile Company

States :

Soie et Confidences designs refined scarves sold at €45 excluding VAT with a raw material cost of €20. Women are so fond of these accessories that the company makes 3 sales per year. It wants to evaluate the effectiveness of its business model.

Work to do :

1. Calculate the unit margin made on each scarf.
2. Determine the markup on scarves.
3. What is the current markup rate for this item?
4. If the cost of raw materials decreases by €5, what will the new margin rate be?
5. Suggest strategic actions that Soie et Confidences could undertake to increase its visibility and maximize its sales.

Proposed correction:

1. Unit margin = PV HT – PA HT.
   Unit margin = €45 – €20 = €25.
   The unit margin made on each scarf is €25.

2. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€45 – €20) ÷ €20) x 100 = 125%.
   The margin rate is 125%.

3. Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Markup rate = ((€45 – €20) ÷ €45) x 100 = 55,56%.
The current markup rate is 55,56%.

4. New PA HT = €20 – €5 = €15.
   New margin rate = ((€45 – €15) ÷ €15) x 100 = 200%.
   After cost reduction, the margin rate would be 200%.

5. Soie et Confidences could launch a marketing campaign on social networks, organize pop-ups in strategic locations, or collaborate with influencers to amplify their reach and boost sales.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New margin rate	((PV HT – New PA HT) ÷ New PA HT) x 100
Strategic actions	Marketing initiatives and collaboration

Cooking class Cuisine Violaine

States :

Cuisine Violaine offers regional cooking classes at €90 excluding tax per session. Each session has a cost of €50 in ingredients and materials. With 500 sessions annually, they want to assess whether their offer is correctly positioned on the market.

Work to do :

1. Determine the unit margin for each course session sold.
2. What is the margin rate for these sessions?
3. Calculate the mark rate for sessions.
4. If the number of sessions increases by 15% following an advertising campaign, what will the new revenue be?
5. Discuss strategies for diversifying or expanding services for Cuisine Violaine to maintain interest over the long term.

Proposed correction:

1. Unit margin = PV HT – PA HT.
   Unit margin = €90 – €50 = €40.
   The unit margin for each session is €40.

2. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.
   Margin rate = ((€90 – €50) ÷ €50) x 100 = 80%.
   The margin rate for sessions is 80%.

3. Mark rate = ((PV HT – PA HT) ÷ PV HT) x 100.

Markup rate = ((€90 – €50) ÷ €90) x 100 = 44,44%.
The mark rate for sessions is 44,44%.

4. New quantity = 500 x 115% = 575 sessions.
   New turnover = 575 x 90 € = 51 €.
   With a 15% increase in sessions, the turnover would become €51.

5. Cuisine Violaine can diversify its offering by adding thematic workshops, extend its services with private or online courses, or even form partnerships with companies for exclusive culinary events.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
New turnover	New Quantity x PV HT
Diversification strategies	Extension of services and thematic offers