Summary
Application: Green Grocery
States :
An organic grocery store, Épicerie Verte, wants to analyze the profitability of its various products. The manager, Mr. Martin, has the following information about a recent product: the purchase cost excluding tax (HT) is €18 per unit and the selling price (SPP) excluding tax is set at €30 per unit. The annual demand for this product is estimated at 500 units, the ordering cost is €60, and the annual storage cost is €2 per unit.
Work to do :
- Calculate the margin rate for this product.
- Determine the markup rate for this product.
- Calculate the overall margin for the entire annual demand.
- Calculate the total annual storage cost for the entire demand.
- Evaluate the QEC (Economic Order Quantity).
Proposed correction:
-
To calculate the margin rate, use the following formula:
[ \text{Margin rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PA HT}}\right) \times 100 ]
Replacing with the provided values:
[ \left(\frac{30 – 18}{18}\right) \times 100 = 66,67% ]
So the margin rate is 66,67%.
-
To determine the markup rate, use the formula:
[ \text{Brand rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PV HT}}\right) \times 100 ]
By replacing the values:
[ \left(\frac{30 – 18}{30}\right) \times 100 = 40% ]
The markup rate of this product is 40%.
-
For the overall margin, use the formula:
[ \text{Overall margin} = \text{Unit margin} \times \text{Quantity sold} ]
[ \text{Unit margin} = 30 – 18 = 12 ]
So, the overall margin:
[12 \times 500 = 6\,000, €]
The overall margin for the year is €6.
-
The total storage cost is calculated by:
[ \text{Annual storage cost} = \text{Quantity requested} \times \text{Storage cost per unit} ]
[500 \times 2 = 1\,000, €]
The total annual storage cost is therefore €1.
-
Finally, the QEC is calculated with:
[ \text{QEC} = \sqrt{\left(\frac{2 \times \text{Annual demand} \times \text{Ordering cost}}{\text{Storage cost}}\right)} ]
[ \sqrt{\left(\frac{2 \times 500 \times 60}{2}\right)} = \sqrt{30\ 000} = 173,21 ]
The economic order quantity is approximately 173 units.
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 |
| Annual storage cost | Quantity demanded x Storage cost per unit |
| Economic Order Quantity (EOQ) | ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) |
Application: TechnoGadget
States :
TechnoGadget sells computer accessories. One of their flagship products, the ergonomic mouse, has a purchase price excluding VAT of €9 and a sales price excluding VAT of €15. Their projections indicate that they sell 1 units per year. TechnoGadget estimates its ordering cost at €200 per order, and the annual storage cost per unit is €80.
Work to do :
- Calculate the profit made on each mouse sold.
- What is the markup rate for this product?
- Determine the total margin obtained on the entire annual production.
- Calculate the total annual storage cost.
- Evaluate the economic order quantity to be placed to optimize costs.
Proposed correction:
-
Unit profit is calculated as follows:
[ \text{Unit profit} = \text{PV HT} – \text{PA HT} ]
[ 15 – 9 = 6 , € ]
So the profit for each mouse sold is €6.
-
Use the markup rate formula for the following calculation:
[ \text{Brand rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PV HT}}\right) \times 100 ]
By applying the values:
[ \left(\frac{15 – 9}{15}\right) \times 100 = 40% ]
The markup rate for this mouse is 40%.
-
The total margin is calculated by:
[ \text{Total margin} = \text{Unit profit} \times \text{Quantity sold} ]
[6\times 1\200 = 7\200,€]
TechnoGadget achieves a total margin of €7 over the year.
-
Calculate the total annual storage cost:
[ \text{Storage cost} = \text{Total quantity} \times \text{Unit storage cost} ]
[1\200\times 3 = 3\600, €]
The total storage cost is €3.
-
The QEC is determined by:
[ \text{QEC} = \sqrt{\left(\frac{2 \times \text{Annual demand} \times \text{Ordering cost}}{\text{Storage cost}}\right)} ]
[ \sqrt{\left(\frac{2 \times 1\ 200 \times 80}{3}\right)} = \sqrt{64\ 000} = 253,98 ]
The economic order quantity is approximately 254 units.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit profit | PV HT – PA HT |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Total margin | Unit Profit x Quantity Sold |
| Annual storage cost | Total quantity x Unit storage cost |
| Economic Order Quantity (EOQ) | ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) |
Application: Fashion & Chic
States :
At Mode&Chic, a ready-to-wear boutique, Ms. Dubois wants to analyze the profitability of the range of watches she sells. Their purchase price excluding tax is €25 and their sale price excluding tax is €45. The annual demand is 800 watches, with an ordering cost of €50 and a storage cost of €1,5 per watch.
Work to do :
- Calculate the unit margin for each watch sold.
- What is the margin rate for this product?
- Study the overall margin for all watches annually.
- Calculate the cost of storing all watches sold per year.
- Calculate QEC to optimize orders.
Proposed correction:
-
The unit margin is calculated by:
[ \text{Unit margin} = \text{PV HT} – \text{PA HT} ]
[ 45 – 25 = 20 , € ]
The unit margin for each watch sold is €20.
-
For the margin rate:
[ \text{Margin rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PA HT}}\right) \times 100 ]
By substituting:
[ \left(\frac{45 – 25}{25}\right) \times 100 = 80% ]
The margin rate on this product is 80%.
-
The overall margin is determined as follows:
[ \text{Overall margin} = \text{Unit margin} \times \text{Quantity sold} ]
[20 \times 800 = 16\,000, €]
The overall margin for watches is therefore €16 annually.
-
For the annual storage cost:
[ \text{Annual storage cost} = \text{Total quantity} \times \text{Unit storage cost} ]
[800 \times 1,5 = 1\,200, €]
The total storage cost for the year is therefore €1.
-
Calculate the QEC:
[ \text{QEC} = \sqrt{\left(\frac{2 \times \text{Annual demand} \times \text{Ordering cost}}{\text{Storage cost}}\right)} ]
[ \sqrt{\left(\frac{2 \times 800 \times 50}{1,5}\right)} = \sqrt{53\ 333,33} = 230,9 ]
The economic order quantity for watches is approximately 231 units.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Overall margin | Unit margin x Quantity sold |
| Annual storage cost | Total quantity x Unit storage cost |
| Economic Order Quantity (EOQ) | ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) |
Application: Sports Vital
States :
Sports Vital, a sports equipment store, is looking to evaluate the commercial effectiveness of its tennis rackets. The purchase price excluding VAT per racket is €50, while the sale price excluding VAT is set at €90. The annual demand is 600 rackets, with an ordering cost of €70 and an annual storage cost of €4 per racket.
Work to do :
- Determine the net profit on each racket sold.
- Calculate the mark rate of the rackets.
- Estimate the total margin expected for the year.
- Determine the total storage cost for the year.
- Calculate the optimal order quantity (OQ).
Proposed correction:
-
Net profit per racket is calculated by:
[ \text{Unit profit} = \text{PV HT} – \text{PA HT} ]
[ 90 – 50 = 40 , € ]
The net profit on each racket sold is €40.
-
The markup rate is calculated as follows:
[ \text{Brand rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PV HT}}\right) \times 100 ]
Using numbers:
[ \left(\frac{90 – 50}{90}\right) \times 100 = 44,44% ]
The mark rate of the rackets is 44,44%.
-
For the total annual margin:
[ \text{Total margin} = \text{Unit profit} \times \text{Quantity sold} ]
[40 \times 600 = 24\,000, €]
The total margin for the year is €24.
-
The total storage cost is obtained with:
[ \text{Annual storage cost} = \text{Total quantity} \times \text{Storage cost per unit} ]
[600 \times 4 = 2\,400, €]
So the total annual storage cost is €2.
-
For the calculation of the QEC:
[ \text{QEC} = \sqrt{\left(\frac{2 \times \text{Annual demand} \times \text{Ordering cost}}{\text{Storage cost}}\right)} ]
[ \sqrt{\left(\frac{2 \times 600 \times 70}{4}\right)} = \sqrt{21\ 000} = 144,91 ]
So the economic order quantity is approximately 145 rackets.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit profit | PV HT – PA HT |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Total margin | Unit Profit x Quantity Sold |
| Annual storage cost | Total quantity x Storage cost per unit |
| Economic Order Quantity (EOQ) | ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) |
Application: Sweet Delights
States :
The Délices Sucrés brand, specializing in artisanal confectionery, wants to evaluate the commercial performance of its boxes of chocolate. Each box has a purchase price excluding tax of €10 and a sale price excluding tax of €25. The annual sales forecast is 1 boxes. The ordering cost is €000, and the storage cost per unit is €40.
Work to do :
- Calculate the unit margin made on each box of chocolate.
- Determine the margin rate for these boxes.
- Calculate the annual gross margin based on the sales forecast.
- Determine the total storage cost per year.
- Evaluate the economic order quantity (EOQ) to optimize operations.
Proposed correction:
-
The unit margin is calculated as follows:
[ \text{Unit margin} = \text{PV HT} – \text{PA HT} ]
[ 25 – 10 = 15 , € ]
Each box of chocolate brings in a unit margin of €15.
-
The margin rate is obtained by the formula:
[ \text{Margin rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PA HT}}\right) \times 100 ]
By applying the values:
[ \left(\frac{25 – 10}{10}\right) \times 100 = 150% ]
The margin rate for these boxes is 150%.
-
The annual gross margin is obtained with:
[ \text{Annual gross margin} = \text{Unit margin} \times \text{Quantity sold} ]
[15\times 1\000 = 15\000,€]
The proven annual gross margin is €15.
-
The total annual storage cost is calculated by:
[ \text{Annual storage cost} = \text{Total quantity} \times \text{Unit storage cost} ]
[1\000\times 2,5 = 2\500, €]
So the total storage cost is €2.
-
Calculation of the economic order quantity (EOQ):
[ \text{QEC} = \sqrt{\left(\frac{2 \times \text{Annual demand} \times \text{Ordering cost}}{\text{Storage cost}}\right)} ]
[ \sqrt{\left(\frac{2 \times 1\ 000 \times 40}{2,5}\right)} = \sqrt{32\ 000} = 178,89 ]
The economic order quantity is about 179 boxes.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Annual gross margin | Unit margin x Quantity sold |
| Annual storage cost | Total quantity x Unit storage cost |
| Economic Order Quantity (EOQ) | ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) |
Application: EcoTechnic
States :
EcoTechnic, a company that manufactures solar chargers, is analyzing the potential profits from its sales. The purchase price of a charger excluding VAT is €40, and its selling price excluding VAT is €80. They plan to sell 500 units per year. Each order costs €60 to place, while the storage cost is €3 per unit per year.
Work to do :
- Calculate the unit profit earned on each charger sale.
- What is the markup rate of these chargers?
- Calculate the total anticipated annual margin.
- Determine the annual storage cost.
- Evaluate QEC to optimize ordering costs.
Proposed correction:
-
Unit profit is calculated by:
[ \text{Unit profit} = \text{PV HT} – \text{PA HT} ]
[ 80 – 40 = 40 , € ]
Each charger sold brings in a profit of €40.
-
The markup rate is calculated as follows:
[ \text{Brand rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PV HT}}\right) \times 100 ]
Replacing with the values:
[ \left(\frac{80 – 40}{80}\right) \times 100 = 50% ]
The markup rate for chargers is 50%.
-
For the total annual margin:
[ \text{Total annual margin} = \text{Unit profit} \times \text{Quantity sold} ]
[40 \times 500 = 20\,000, €]
The total annual forecast margin is €20.
-
The annual storage cost is determined by:
[ \text{Annual storage cost} = \text{Total quantity} \times \text{Unit storage cost} ]
[500 \times 3 = 1\,500, €]
The storage cost for the year is €1.
-
For the QEC, the assessment is done by:
[ \text{QEC} = \sqrt{\left(\frac{2 \times \text{Annual demand} \times \text{Ordering cost}}{\text{Storage cost}}\right)} ]
[ \sqrt{\left(\frac{2 \times 500 \times 60}{3}\right)} = \sqrt{20\ 000} = 141,42 ]
The economic order quantity is around 141 chargers.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit profit | PV HT – PA HT |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Total annual margin | Unit Profit x Quantity Sold |
| Annual storage cost | Total quantity x Unit storage cost |
| Economic Order Quantity (EOQ) | ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) |
Application: Art&Design
States :
The Art&Design gallery sells paintings. Each painting has an acquisition cost excluding tax of €150 and is resold at a price excluding tax of €250. The gallery expects to sell 300 paintings this year. The cost for each order is €75, and the storage cost is calculated at €5 per painting per year.
Work to do :
- Calculate the unit profit made on each painting sold.
- What is the margin rate of the tables?
- Calculate the total annual margin for this product category.
- Estimate the annual storage cost for all tables.
- Calculate the economic order quantity (EOQ).
Proposed correction:
-
The unit gain is determined by:
[ \text{Unit gain} = \text{PV HT} – \text{PA HT} ]
[ 250 – 150 = 100 , € ]
Each painting sold brings in a unit profit of €100.
-
For the margin rate:
[ \text{Margin rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PA HT}}\right) \times 100 ]
By replacing:
[ \left(\frac{250 – 150}{150}\right) \times 100 = 66,67% ]
The margin rate of the tables is 66,67%.
-
For the total annual margin:
[ \text{Total annual margin} = \text{Unit profit} \times \text{Quantity sold} ]
[100 \times 300 = 30\,000, €]
The total margin expected for the year is €30.
-
Regarding the storage cost for the year:
[ \text{Annual storage cost} = \text{Total quantity} \times \text{Unit storage cost} ]
[300 \times 5 = 1\,500, €]
The annual storage cost is €1.
-
Calculate the QEC to optimize order management:
[ \text{QEC} = \sqrt{\left(\frac{2 \times \text{Annual demand} \times \text{Ordering cost}}{\text{Storage cost}}\right)} ]
[ \sqrt{\left(\frac{2 \times 300 \times 75}{5}\right)} = \sqrt{9\ 000} = 94,87 ]
The economic order quantity is approximately 95 paintings.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit gain | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Total annual margin | Unit gain x Quantity sold |
| Annual storage cost | Total quantity x Unit storage cost |
| Economic Order Quantity (EOQ) | ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) |
Application: TechnoByte
States :
TechnoByte, an electronics dealer, wants to improve the profitability of its mobile phones. The purchase price excluding VAT for each unit is €300, while the selling price excluding VAT is €550. The company plans to sell 400 units over the year. The ordering cost is estimated at €100, and each phone costs €10 per year to store.
Work to do :
- Calculate the profit made on each phone sold.
- Determine the brand rate of the phones.
- Calculate the total margin expected over the year.
- Establish the annual cost of storing phones.
- Evaluate the QEC to streamline the ordering process.
Proposed correction:
-
Profit per phone is calculated as follows:
[ \text{Unit profit} = \text{PV HT} – \text{PA HT} ]
[ 550 – 300 = 250 , € ]
Each phone sold generates a profit of €250.
-
The markup rate is determined by:
[ \text{Brand rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PV HT}}\right) \times 100 ]
By replacing:
[ \left(\frac{550 – 300}{550}\right) \times 100 = 45,45% ]
The brand rate of phones is 45,45%.
-
For the total margin:
[ \text{Total margin} = \text{Unit profit} \times \text{Quantity sold} ]
[250 \times 400 = 100\,000, €]
The total margin expected for the year is €100.
-
The annual storage cost is expressed as:
[ \text{Annual storage cost} = \text{Total quantity} \times \text{Unit storage cost} ]
[400 \times 10 = 4\,000, €]
So the annual storage cost is €4.
-
Calculate QEC to optimize orders:
[ \text{QEC} = \sqrt{\left(\frac{2 \times \text{Annual demand} \times \text{Ordering cost}}{\text{Storage cost}}\right)} ]
[ \sqrt{\left(\frac{2 \times 400 \times 100}{10}\right)} = \sqrt{8\ 000} = 89,44 ]
The economic order quantity is about 89 phones.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit profit | PV HT – PA HT |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Total margin | Unit Profit x Quantity Sold |
| Annual storage cost | Total quantity x Unit storage cost |
| Economic Order Quantity (EOQ) | ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) |
Application: Wines & Spirits
States :
Vins & Spiritueux, a high-end wine distributor, wants to decipher the profitability of its Bordeaux bottles. The purchase cost excluding tax per bottle is €12, and they are resold at a price excluding tax of €30. The company expects to sell 2 bottles during the year. Each order generates a cost of €000, and the annual storage cost is €50 per bottle.
Work to do :
- Calculate the net margin made on each bottle sold.
- What is the margin rate on these Bordeaux bottles?
- Calculate the overall margin expected over the year.
- Estimate the total cost of storage over the year.
- Calculate QEC to optimize inventory.
Proposed correction:
-
The unit net margin is calculated by:
[ \text{Unit margin} = \text{PV HT} – \text{PA HT} ]
[ 30 – 12 = 18 , € ]
Thus, each bottle sold generates a net margin of €18.
-
The margin rate is calculated as follows:
[ \text{Margin rate} = \left(\frac{\text{PV HT} – \text{PA HT}}{\text{PA HT}}\right) \times 100 ]
Let's apply the values:
[ \left(\frac{30 – 12}{12}\right) \times 100 = 150% ]
The margin rate for Bordeaux bottles is 150%.
-
For the overall margin:
[ \text{Overall margin} = \text{Unit margin} \times \text{Quantity sold} ]
[18\times 2\000 = 36\000,€]
The overall margin expected for the year is €36.
-
The total annual storage cost is:
[ \text{Total storage cost} = \text{Total quantity} \times \text{Unit storage cost} ]
[2\000\times 1 = 2\000, €]
The total storage cost is therefore €2.
-
Calculate QEC to improve inventory management:
[ \text{QEC} = \sqrt{\left(\frac{2 \times \text{Annual demand} \times \text{Ordering cost}}{\text{Storage cost}}\right)} ]
[ \sqrt{\left(\frac{2 \times 2\ 000 \times 50}{1}\right)} = \sqrt{200\ 000} = 447,21 ]
The economic order quantity is approximately 447 bottles.
Formulas Used:
| Title | Formulas |
|---|---|
| Unit margin | PV HT – PA HT |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Overall margin | Unit margin x Quantity sold |
| Total storage cost | Total quantity x Unit storage cost |
| Economic Order Quantity (EOQ) | ?((2 x Annual Demand x Ordering Cost) ÷ Storage Cost) |