commercial calculations final year bac pro commerce | 9 Exercises

Application: Sophie's Treats

States :

Les Gourmandises de Sophie is a small artisanal company specializing in the manufacture of pastries. In order to better understand the margins of its products, Sophie would like to calculate the margins and rates associated with its star cakes. A cake has a purchase price excluding tax of €15, and a sale price excluding tax of €25. The VAT rate applicable to this product is 5,5%.

Work to do :

1. Calculate the unit margin of this cake.
2. What is the margin rate for this product?
3. Determine the markup rate of this cake.
4. If Sophie wants to increase her margin rate to 50%, what would be the new selling price excluding tax?
5. Analyze the implications for the business if Sophie chooses not to increase the price despite the increase in manufacturing costs.

Proposed correction:

1. The unit margin is calculated as follows: Unit margin = PV HT – PA HT.

   So, Unit Margin = €25 – €15 = €10.

   The unit margin of the cake is €10.

2. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

   So, Margin rate = ((€25 – €15) ÷ €15) x 100 = 66,67%.

   The product margin rate is 66,67%.

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

So, Markup Rate = ((€25 – €15) ÷ €25) x 100 = 40%.

The cake's markup rate is 40%.

4. To obtain a margin rate of 50%, we use the formula: PV HT = PA HT x (1 + Margin rate).

   By replacing, PV excluding tax = €15 x (1 + 0,50) = €22,50.

   For a margin rate of 50%, the selling price excluding tax must be €22,50.

5. If Sophie chooses not to increase the price despite an increase in manufacturing costs, her margins will decrease, potentially affecting the profitability of her business in the long run. Not adjusting the price could maintain customer satisfaction but at a financial cost to the business.

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 HT	PA HT x (1 + Margin rate)

Application: TechZone Informatique

States :

TechZone Informatique is a company specializing in the sale of computer equipment. Currently, a graphics card is sold for €300 excluding VAT with a purchase price of €240 excluding VAT. To boost sales, the company is considering offering a 10% discount. The VAT rate is 20%.

Work to do :

1. Calculate the current unit margin on the graphics card.
2. What is the current price including VAT of this graphics card?
3. Determine the selling price excluding VAT after the 10% discount.
4. What would the markup rate be after applying the discount?
5. Discuss whether the discount option is a good strategy considering the margin.

Proposed correction:

1. The unit margin is calculated as follows: Unit margin = PV HT – PA HT.

   So, Unit Margin = €300 – €240 = €60.

   The current unit margin is €60.

2. The price including tax is calculated: PV including tax = PV excluding tax x (1 + VAT rate).

   So, PV including tax = €300 x (1 + 0,20) = €360.

   The current price including VAT is €360.

3. The selling price excluding VAT after a 10% discount is: New PV excluding VAT = PV excluding VAT x (1 – Discount).

New PV excluding tax = €300 x (1 – 0,10) = €270.

The new selling price excluding VAT is €270.

4. After discount, the markup rate is calculated: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.

   New markup rate = ((€270 – €240) ÷ €270) x 100 = 11,11%.

   The markup rate after discount is 11,11%.

5. If the discount increases sales enough to offset the decrease in the margin rate, it can be a good strategy. However, the company must monitor its margins to ensure that profitability is maintained.

Formulas Used:

Title	Formulas
Unit margin	PV HT – PA HT
PV including tax	PV excluding VAT x (1 + VAT rate)
New PV HT	PV HT x (1 – Discount)
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: Urban Style Clothing

States :

Urban Style, a trendy clothing store, wants to evaluate its pricing policies around its new jeans models. A popular model has a purchase cost of €40 excluding VAT and a sales price of €80 excluding VAT. The company decides to apply cost optimization by modifying its prices.

Work to do :

1. Determine the gross margin per pair of jeans sold.
2. Calculate the current margin rate for this product.
3. If the objective is a gross margin of €50, what should the new selling price excluding VAT be?
4. What would be the new markup rate with this target gross margin?
5. Analyze the effect of this price adjustment on the store's brand image.

Proposed correction:

1. The gross margin is: Gross margin = PV HT – PA HT.

   So, Gross Margin = €80 – €40 = €40.

   The gross margin per pair of jeans is currently €40.

2. The current margin rate is: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

   Margin rate = ((€80 – €40) ÷ €40) x 100 = 100%.

   The current margin rate is 100%.

3. For a gross margin of €50, the new gross profit would be: Gross profit = Gross profit + New margin.

New PV excluding tax = €40 + €50 = €90.

The new selling price excluding VAT should be €90.

4. The new markup rate would be: Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100.

   Markup rate = ((€90 – €40) ÷ €90) x 100 = 55,56%.

   The new mark rate is 55,56%.

5. The price increase could reinforce Urban Style's perception of premium product, but may also impact the perception of good value for money if the target market is price sensitive.

Formulas Used:

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

Application: FitLife equipment

States :

FitLife is a distributor of fitness equipment. The company wants to calculate the economic cost of inventory for a new treadmill whose purchase price is €500 excluding VAT. The estimated annual demand is 200 units, the ordering cost is €100, and the storage cost is estimated at €30 per unit.

Work to do :

1. Calculate the economic order quantity (EOQ) for the conveyor belt.
2. What is the total storage cost for an order quantity of 20 units?
3. Determine the total annual order cost with an economic order quantity.
4. If FitLife maintains an average inventory equivalent to half the QEC, what would be the corresponding storage cost?
5. Discuss the benefits of optimizing QEC for FitLife.

Proposed correction:

1. The QEC is calculated by: QEC = ?((2 x Annual demand x Ordering cost) ÷ Storage cost).

   QEC = ?((2 x 200 x 100) ÷ 30) = ?(40000 ÷ 30) = ?1333,33 ? 36,5.

   The economic order quantity is about 37 units.

2. For 20 units, the total storage cost is: Total storage cost = Storage cost x Quantity.

   Total storage cost = €30 x 20 = €600.

   The total cost to store 20 units is €600.

3. With a QEC of 37 units, the total ordering cost is: Number of orders = Annual demand ÷ QEC.

Number of orders = 200 ÷ 37 ? 5,41.

Total order cost = Number of orders x Order cost.

Total order cost = 5,41 x €100 = €541.

The total cost of the annual order is €541.

4. If average inventory = 18,5 (i.e. half of 37), Storage Cost = average inventory x Storage Cost.

   Average inventory cost = 18,5 x €30 = €555.

   The storage cost for this average stock is €555.

5. Optimizing QEC reduces total inventory and ordering costs, improving FitLife's profitability and cash flow.

Formulas Used:

Title	Formulas
Economic Quantity	?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost)
Total storage cost	Storage cost x Quantity
Number of orders	Annual request ÷ QEC
Total order cost	Number of orders x Order cost

Application: Wild Food

States :

Wild Food is a company specializing in the production of energy bars based on natural ingredients. It wants to analyze its cash flow for the new range of bars. The average monthly turnover is €50, the monthly expenses are on average €000, and the cash reserve at the beginning of the month is €30.

Work to do :

1. Determine the company's monthly gross margin.
2. Calculate the cash flow at the end of the month after operations.
3. If the company increases its expenses to €35, what would the new cash flow be?
4. Suppose revenue increases to €55, how would this affect cash flow at €000 monthly expenses?
5. Provide a cash management recommendation based on this data.

Proposed correction:

1. The monthly gross margin is: Gross margin = Revenue – Expenses.

   Gross margin = €50 – €000 = €30.

   The gross monthly margin is €20.

2. The cash flow at the end of the month is: Ending cash = Beginning reserve + Gross margin.

   Final cash flow = €10 + €000 = €20.

   The cash flow at the end of the month is €30.

3. With expenses of €35, the new margin is: New margin = Revenue – Increased expenses.

New margin = €50 – €000 = €35.

Final cash flow = €10 + €000 = €15.

The new cash flow would be €25.

4. With a new turnover of €55, the new margin is: New margin = New turnover – Expenses.

   New margin = €55 – €000 = €30.

   Final cash flow = €10 + €000 = €25.

   The cash flow would be €35.

5. It is recommended to monitor expense balances to maximize cash flow. Increasing revenue while keeping expenses under control will help maintain a healthy cash flow.

Formulas Used:

Title	Formulas
Gross margin	Revenue – Expenses
Final treasury	Beginning reserve + Gross margin
New margin	Revenue or New Revenue – Expenses

Application: Green Light

States :

Luminosité Verte, an innovative company in ecological lighting solutions, markets an LED bulb with a purchase price of €8 excluding VAT and a sale price of €15 excluding VAT. The company wants to boost its sales by offering a promotion to its loyal customers.

Work to do :

1. Calculate the gross margin per unit of this LED bulb.
2. What margin rate does the company currently achieve?
3. If Luminosité Verte offers a discount of €2, what will the new selling price excluding tax be?
4. What will the new markup rate be with this discount applied?
5. Discuss the potential effects of this discount on customer relationships and margins.

Proposed correction:

1. The unit gross margin is calculated as: Gross margin = PV HT – PA HT.

   Gross margin = €15 – €8 = €7.

   The gross margin per unit of the LED bulb is €7.

2. The current margin rate is calculated as follows: Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100.

   Margin rate = ((€15 – €8) ÷ €8) x 100 = 87,5%.

   The current margin rate is 87,5%.

3. With a discount of €2, the new selling price excluding VAT is: New PV excluding VAT = PV excluding VAT – Discount.

New PV excluding tax = €15 – €2 = €13.

The new selling price excluding VAT is €13.

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

   New markup rate = ((€13 – €8) ÷ €13) x 100 = 38,46%.

   The new markup rate after discount is 38,46%.

5. Discounting can increase customer loyalty and boost sales in the short term, but it risks reducing margins. It is crucial to monitor the effect on sales volume to offset the decline in margins.

Formulas Used:

Title	Formulas
Gross margin	PV HT – PA HT
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
New PV HT	PV HT – Discount
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100

Application: Art Deco Housing

States :

Art Déco Habitation is an interior design company that wants to evaluate its profitability with a new consulting service offered at €120 excluding VAT per hour. The variable cost for this service is €80 excluding VAT per hour. The market requires a VAT of 20%.

Work to do :

1. Calculate the contribution margin per consulting hour.
2. What is the margin rate for this service?
3. Determine the hourly price including tax for this service.
4. If the company wants a margin rate of 50%, what should the new selling price excluding tax be?
5. Analyze the strategic implications of changing the price of this service for Art Déco Habitation.

Proposed correction:

1. The contribution margin is: Contribution = PV excluding tax – Variable cost.

   Contribution = €120 – €80 = €40.

   The contribution margin per hour is €40.

2. The margin rate is calculated: Margin rate = ((PV HT – Variable cost) ÷ Variable cost) x 100.

   Margin rate = ((€120 – €80) ÷ €80) x 100 = 50%.

   The margin rate is 50%.

3. The hourly price including tax is: PV including tax = PV excluding tax x (1 + VAT rate).

PV including tax = €120 x (1 + 0,20) = €144.

The hourly price including tax is €144.

4. For a margin rate of 50%: PV HT = Variable cost x (1 + Margin rate).

   PV excluding tax = €80 x (1 + 0,50) = €120.

   The new selling price excluding tax should remain at €120 for a margin rate of 50%.

5. Changing the price could reposition Art Déco Habitation in the market. An increase could signal added value, but could risk reducing the customer base if the perception of value does not follow.

Formulas Used:

Title	Formulas
Contribution margin	PV HT – Variable cost
Margin rate	((PV HT – Variable cost) ÷ Variable cost) x 100
All taxes included price	PV excluding VAT x (1 + VAT rate)
New PV HT	Variable cost x (1 + Margin rate)

Application: Maple Solar Solutions

States :

Solutions Solaires en Érable offers eco-friendly solar panels at a price of €1 excluding VAT. Their cost price excluding VAT is €200. The company plans to reduce their price to compete more effectively.

Work to do :

1. Calculate the current unit margin of solar panels.
2. What is the current margin rate for a panel?
3. If the company applies a discount of €100, what will the new unit margin be?
4. Determine the new margin rate after this reduction.
5. Discuss the long-term financial implications of reducing the price of solar panels.

Proposed correction:

1. Unit margin = PV excluding VAT – Cost.

   Unit margin = €1 – €200 = €900.

   The current unit margin is €300.

2. The margin rate is calculated by: Margin rate = ((PV HT – Cost) ÷ Cost) x 100.

   Margin rate = ((€1 – €200) ÷ €900) x 900 = 100%.

   The current margin rate is 33,33%.

3. New unit margin after reduction: New margin = (PV HT – Reduction) – Cost.

New margin = (€1 – €200) – €100 = €900.

The new unit margin is €200.

4. New margin rate = ((New PV HT – Cost) ÷ Cost) x 100.

   New PV excluding tax = €1 – €200 = €100.

   New margin rate = ((€1 – €100) ÷ €900) x 900 = 100%.

   The new margin rate is 22,22%.

5. In the long term, reducing panel prices to compete can boost sales in the short to medium term, but it is crucial to ensure that increased sales volume offsets reduced margins to protect profitability.

Formulas Used:

Title	Formulas
Unit margin	PV HT – Cost
Margin rate	((PV HT – Cost) ÷ Cost) x 100
New unit margin	(New PV HT – Cost)
New margin rate	((New PV HT – Cost) ÷ Cost) x 100

Application: Gourmet Cafés of the World

States :

Gourmet Cafés du Monde specializes in the distribution of high-quality coffees. One of their blends is sold at €20 excluding VAT per pack, with a supply cost of €12 excluding VAT. The company plans to expand its offering by adding an option of packaging in individual sachets.

Work to do :

1. Calculate the current unit margin per pack of coffee sold.
2. What is the current margin rate for this product?
3. Estimate the required selling price excluding VAT for sachets if the supply cost is €1 per sachet to maintain the same margin rate.
4. Determine the markup rate for the current package of coffee.
5. Analyze the potential impact of product diversification on the company's market position.

Proposed correction:

1. The current unit margin is: Unit margin = PV excluding VAT – Cost.

Unit margin = €20 – €12 = €8.

The current unit margin is €8 per pack.

2. The margin rate is: Margin rate = ((PV HT – Cost) ÷ Cost) x 100.

Margin rate = ((€20 – €12) ÷ €12) x 100 = 66,67%.

The current margin rate is 66,67%.

3. Required selling price for the bags: PV excluding tax = Cost of bag x (1 + Margin rate).

   PV sachet = €1 x (1 + 0,6667) = €1,67.

   The required selling price excluding VAT for the bags is €1,67.

4. Markup rate for the pack: Markup rate = ((PV HT – Cost) ÷ PV HT) x 100.

   Markup rate = ((€20 – €12) ÷ €20) x 100 = 40%.

   The current markup rate of the coffee packet is 40%.

5. Diversifying products with single-serve pouches can open new market segments, providing the flexibility and convenience some consumers seek, while maximizing company recognition in the marketplace.

Formulas Used:

Title	Formulas
Unit margin	PV HT – Cost
Margin rate	((PV HT – Cost) ÷ Cost) x 100
PV HT required for bags	Cost per bag x (1 + Margin rate)
Brand taxes	((PV HT – Cost) ÷ PV HT) x 100