Inventory management and supply 11 corrected exercises

Welcome to this article aimed at helping you with 11 corrected stock and supply management exercises from the Operational Management subject of the BTS MCO.

If you would like to first review the course on the same theme, Inventory Management, I invite you to read my article Inventory Management: The 7 Key Points to Master and also the article Supply Management: The 3 essential principles.

Application: Fashion Fabrics Company

States :

The company "Fashion Fabrics" is a company specializing in the sale of quality textiles. The company would like to obtain assistance with its inventory management and supply.

Here is the data you have:
– The initial stock of Guipure fabrics is 500 meters.
– The cost of a unit of Guipure fabric is €15.
– 3000 meters of Guipure fabric were purchased during the year for a total cost of €45000.
– The sale price is €25 per meter.
– During the year, the company sold 2500 meters of Guipure fabric.

Work to do :

1. Calculate the average unit purchase cost.
2. Calculate the ending stock in quantity.
3. Calculate the value of the ending inventory.
4. Calculate the turnover generated by the sale of Guipure fabrics.
5. Calculate the margin rate.

Proposed correction:

1. The average unit purchase cost is calculated by dividing the total purchase cost by the total quantity purchased. Here, we have €45000 ÷ 3000 m = €15/m.

2. The final stock quantity is determined by taking the initial stock, adding purchases and then subtracting sales. Therefore, 500 m + 3000 m – 2500 m = 1000 m of remaining Guipure fabrics.

3. The value of the final stock is calculated by multiplying the final stock in quantity (1000 m) by the average unit purchase cost (15 €/m). This gives us a final stock of 15000 €.

4. The turnover is calculated by multiplying the quantity sold by the selling price. Here, 2500 m * 25 €/m = 62500 €.

5. The margin rate is calculated using the formula ((PV HT – PA HT) ÷ PA HT) x 100. By replacing, we obtain ((25 € – 15 €) ÷ 15 €) x 100 = 66,67%.

Summary of Formulas Used:

Concept	Formulas
Average unit purchase cost	Total purchase cost ÷ Total quantity purchased
Final stock in quantity	Initial stock + Purchases – Sales
Final stock value	Final stock in quantity x Average unit purchase cost
Turnover	Quantity sold x Sale price
Margin rate	((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100

Application: Les Gourmandises Bakery

States :

Boulangerie Les Gourmandises has hired you as a financial management consultant to help with management control. The data available for the month of March are as follows: Initial stock of flour 500 kg, Flour purchases during the month: 1000 kg, Final stock of flour at the end of March: 600 kg. The cost of flour is €0,75 per kg.

Work to do :

1. Calculate the flour consumption for the month of March.
2. Calculate the total cost of consumption.
3. Calculate the average flour stock for the month of March.
4. Calculate the flour stock turnover for the month of March.
5. Interpret the inventory turnover ratio.

Proposed correction:

1. Flour consumption for the month of March = Initial Stock + Purchases – Final Stock = 500 kg + 1000 kg – 600 kg = 900 kg

2. Total cost of consumption = Consumption x Unit cost = 900 kg x €0,75 = €675

3. Average flour stock for the month of March = (Initial Stock + Final Stock) ÷ 2 = (500 kg + 600 kg) ÷ 2 = 550 kg

4. Flour stock turnover for the month of March = Cost of goods sold ÷ Average stock = €675 ÷ ((550 kg) x (€0,75/kg)) = €675 ÷ €412,5 = 1,64 times

5. The inventory turnover ratio of 1,64 means that the flour inventory was sold and replaced approximately 1,64 times during the month of March. This can help the company understand its efficiency in inventory management and procurement.

Summary of Formulas Used:

Formulas	Explanation
Initial Stock + Purchases – Final Stock = Consumption	Formula for calculating consumption
Consumption x Unit Cost = Total Cost of Consumption	Formula for calculating the total cost of consumption
(Initial Stock + Final Stock) ÷ 2 = Average Stock	Formula for calculating average stock
Cost of Goods Sold ÷ Average Inventory = Inventory Turnover	Formula for calculating inventory turnover

Application: Patisserie LeBoulanger

States :

Patisserie LeBoulanger is located in the heart of Paris, specializing in the creation of breads, pastries, and cakes. To ensure its daily production, the pastry shop must maintain an inventory of flour, eggs, and butter, key ingredients for the majority of its products.

Inventory management is therefore a crucial point of its activity in order to avoid stock-outs and waste as much as possible. Dough that is not used the same day is considered waste, so it is essential to order appropriate quantities of ingredients.

At the beginning of the month, the bakery has an initial stock of 50 kg of flour, 200 eggs and 30 kg of butter.

In the middle of the month, the bakery counts the product sales and finds that it has used 40 kg of flour, 150 eggs and 25 kg of butter.

Supply orders are placed at the end of the month.

Work to do :

1. What is the final stock level of flour, eggs and butter at the end of the month?
2. How much flour, eggs and butter should the bakery order for the next month assuming it wants to maintain the same initial stock level?
3. What happens if demand for pastry products increases and requires 10% more of each ingredient in each order?
4. What is the cost of purchasing each ingredient if flour costs €1,5/kg, eggs cost €0,2/each and butter costs €7/kg?
5. What will be the total cost of orders if demand increases by 10%?

Proposed correction:

1. Stock level:

Ending stock = Initial stock – Usage
Final flour stock = 50kg – 40kg = 10kg
Final stock eggs = 200 eggs – 150 eggs = 50 eggs
Final butter stock = 30kg – 25kg = 5kg

2. Quantity to order:

Quantity to order = Initial stock – Final stock
Quantity to order for flour = 50kg – 10kg = 40kg
Quantity to order for eggs = 200 eggs – 50 eggs = 150 eggs
Quantity to order for butter = 30kg – 5kg = 25kg

3. New quantities to be ordered if demand increases by 10%:

New quantity = Old quantity + (Old quantity x 10 / 100)
New quantity of flour = 40kg + (40kg x 10 / 100) = 44kg
New quantity of eggs = 150 eggs + (150 eggs x 10 / 100) = 165 eggs
New quantity of butter = 25kg + (25kg x 10 / 100) = 27,5kg

4. Purchase cost:

Purchase cost = Quantity ordered x Price per unit
Purchase cost for flour = 40kg x €1,5/kg = €60
Purchase cost for eggs = 150 eggs x €0,2/egg = €30
Purchase cost for butter = 25kg x €7/kg = €175

5. New purchasing costs if demand increases by 10%:

Purchase Cost = New Order Quantity x Price per Unit
Purchase cost for flour = 44kg x €1,5/kg = €66
Purchase cost for eggs = 165 eggs x €0,2/egg = €33
Purchase cost for butter = 27,5kg x €7/kg = €192,5

Summary of Formulas Used:

The goal	Formulas
Calculation of final stock	Ending stock = Initial stock – Usage
Calculating the quantity to order	Quantity to order = Initial stock – Final stock
Calculation of the new quantity to order	New quantity = Old quantity + (Old quantity x 10 / 100)
Calculation of purchase cost	Purchase cost = Quantity ordered x Price per unit

Application: TechnoGear Company

States :

TechnoGear is a company specializing in the sale of computer equipment. Its main activity is the sale of 500 GB SSD hard drives for laptops. You are a management assistant in this company and your supervisor asks you to help him in the management of stocks and supplies.

Here is the information you have:

– The initial stock of SSDs as of January 1 is 250 units.
– During the first half of the year, the company placed three supplier orders for 200, 250 and 300 units.
– SSD sales during the first half of the year were 800 units.

Work to do :

1. What is the final SSD stock at the end of the first half?
2. What was the average SSD stock during the first half of the year?
3. What was the total number of SSD units purchased during the first half of the year?
4. What is the average SSD inventory relative to the total number of units purchased?
5. What is the SSD inventory turnover during the first half of the year?

Proposed correction:

1. Closing stock = Opening stock + Purchases – Sales = 250 units + 200 units + 250 units + 300 units – 800 units = 200 units.

2. Average stock = (Starting stock + Ending stock) ÷ 2 = (250 units + 200 units) ÷ 2 = 225 units.

3. Total purchases during the first half of the year = Sum of orders = 200 units + 250 units + 300 units = 750 units.

4. The average stock during the first half represents 225 units out of the 750 units purchased, i.e. (225÷750) x 100 = 30% of the total units purchased.

5. Inventory turnover = Sales ÷ Average inventory = 800 units ÷ 225 units = 3,56 times over the half-year.

Summary of Formulas Used:

Concept	Formulas
Ending stock	Initial stock + Purchases – Sales
Average stock	(Initial stock + Final stock) ÷ 2
Total purchases during the period	Sum of orders
Proportion of average stock to purchases	(Average inventory ÷ Total purchases) x 100
Stock rotation	Sales ÷ Average inventory

Application: Caramel Company

States :

Caramel is a company that specializes in selling candies. Currently, due to a substantial increase in sales, the company is evaluating its ability to manage its inventory effectively. Inventory management is crucial for this company because any delay or overstocking could lead to financial losses and customer dissatisfaction.

Here is some relevant information about one of the company's best-selling candies, the Harlequin candy:

– The unit purchase cost of the candy (PA excluding VAT) is €0,05.
– The harlequin candy is sold individually at a price of €0,20 excluding VAT (PV excluding VAT)
– The company sells an average of 5000 candies per day.
– The storage cost per candy per day is €0,01.
– The order cost is estimated at €400 per order.
– The VAT rate is 20%.

The company's CFO wants to identify the best way to minimize costs while maintaining inventory management efficiency.

Work to do :

1. Calculate the company's unit margin excluding tax and overall margin excluding tax.
2. Calculate margin rate and brand rate.
3. Determine the optimal number of candies to order each time (Economy Order Lot).
4. Calculate the total annual cost of purchasing, storing and ordering candy.
5. Deduce whether Caramel Company should increase or decrease the quantity ordered each time to minimize costs.

Proposed correction:

1. The unit margin excluding tax = PV excluding tax – PA excluding tax = €0,20 – €0,05 = €0,15/candy
The overall margin excluding tax = unit margin x quantity sold = €0,15 x 5000 = €750/day

2. Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 = ((€0,20 – €0,05) ÷ €0,05) x 100 = 300%
Markup rate = ((PV HT – PA HT) ÷ PV HT) x 100 = ((0,20 € – 0,05 €) ÷ 0,20 €) x 100 = 75%

3. Economic Order Lot (LEC) = Square root ((2 x Order Cost x Annual Quantity) ÷ Storage Cost per unit) = Square root ((2 x €400 x (5000 x 365)) ÷ €0,01) = 30000 candies

4. Total annual purchase cost = PA HT x Annual quantity = €0,05 x (5000 x 365) = €91250
Total annual storage cost = 0,5 x LEC x Storage cost = 0,5 x 30000 x 0,01 € = 150 €
Total annual order cost = (Annual quantity ÷ LEC) x Order cost = ((5000 x 365) ÷ 30000) x 400 = €7300
So the total annual cost of purchasing, storing and ordering candy = €91250 + €150 + €7300 = €98700

5. Caramel Company has to order 30000 candies each time to minimize costs.

Summary of Formulas Used:

Concept	Formulas
Unit margin excluding tax	PV HT – PA HT
Total margin excluding tax	Unit margin excluding tax x Quantity sold
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
Economical order lot	Square root ((2 x Ordering cost x Annual quantity) ÷ Storage cost per unit)
Total annual cost	Total annual purchasing cost + Total annual storage cost + Total annual ordering cost

Application: The Wines of the Valley

We will use the data of the company "Les Vins de la Vallée" which is a store specializing in the sale of varieties of wines.

However, the manager has difficulty managing his stock quantity and very often finds himself out of stock, causing a loss of sales and therefore income for his company. He therefore wants to set up effective management of his stocks and supplies.

States :

In January, Les Vins de la Vallée sold 500 bottles of a particular wine. The company applies a 20% margin on this product. The wine is purchased from a producer for €10 per bottle (excluding VAT).

The company wants to maintain a safety stock of 10% of monthly sales. The company uses a sales-based replenishment method.

Work to do :

1. What is the selling price excluding tax of the wine?
2. What is the margin in € per bottle of wine?
3. What is the overall margin in January for this wine?
4. What is the safety stock for this wine?
5. How much wine should the company order for the next month if it plans to maintain its safety stock and assuming that sales remain constant?

Proposed correction:

1. The selling price excluding tax of the wine is calculated by adding the margin to its purchase price. Here, the margin is 20% on a purchase price of €10. The calculation is therefore: PV excluding tax = PA excluding tax + (PA excluding tax x margin rate). That is: PV excluding tax = €10 + (€10 x 20/100) = €12.

2. The margin per bottle of wine is the sale price minus the purchase price. That is: Margin = PV HT – PA HT = €12 – €10 = €2.

3. The overall margin for January is the margin per bottle multiplied by the number of bottles sold. That is: Overall margin = Unit margin x quantity sold = €2 x 500 = €1000.

4. Safety stock is calculated by taking 10% of monthly sales. That is: Safety stock = monthly sales x safety stock rate = 500 x 10/100 = 50 bottles.

5. For the next month, the company wants to maintain its safety stock and expects constant sales. The number of bottles to order is therefore: Quantity to order = Quantity sold + Safety stock = 500 + 50 = 550 bottles.

Summary of Formulas Used:

Formulas	Explanation
PV excluding tax = PA excluding tax + (PA excluding tax x margin rate)	Calculation of the sales price excluding tax
Margin = PV excluding tax – PA excluding tax	Calculation of the margin in euros per unit
Overall margin = Unit margin x quantity sold	Calculation of the overall margin for a given period
Safety stock = monthly sales x safety stock rate	Calculation of safety stock
Quantity to order = Quantity sold + Safety stock	Calculating the number of bottles to order

Application: Enterprise TechnoGadgets

States :

The company TechnoGadgets specializes in selling high-end technological gadgets. It buys a product called "Gadget X" for €100,00 excluding VAT and resells it for €150,00 excluding VAT. The supply costs are €5,00 per product. The company sells an average of 500 units per month.

Work to do :

1. Calculate the company's gross margin on the product "Gadget X".
2. Determine the company's margin rate.
3. Determine the company's markup rate.
4. Calculate the average inventory outstanding if the company has an average of 150 units in stock.
5. What would be the company's overall margin if it could increase its sales to 550 units per month?

Proposed correction:

1. Gross margin is defined as the selling price minus the purchase cost. In our case, this gives:
Gross margin = PV HT – PA HT – Supply costs
Gross margin = €150,00 – €100,00 – €5,00 = €45,00.

2. The margin rate can be calculated using the formula:
Margin rate = ((PV HT – PA HT – Supply costs) ÷ PA HT) x 100
Margin rate = ((€150,00 – €100,00 – €5,00) ÷ €100,00) x 100 = 45%.

3. The markup rate can be calculated using the formula:
Markup rate = ((PV HT – PA HT – Supply costs) ÷ PV HT) x 100
Markup rate = ((€150,00 – €100,00 – €5,00) ÷ €150,00) x 100 = 30%.

4. The average stock outstanding can be calculated using the formula:
Average inventory outstanding = Average unit cost x Average number of units in stock
Average stock outstanding = €100,00 x 150 = €15.

5. If the company manages to increase its sales to 550 units per month, its overall margin would be:
Overall margin = Unit margin x quantity sold
Overall margin = €45,00 x 550 = €24.

Summary of Formulas Used:

Formulas	Meaning
Gross margin = PV HT – PA HT – Supply costs	Gross margin
Margin rate = ((PV HT – PA HT – Supply costs) ÷ PA HT) x 100	Margin rate
Markup rate = ((PV HT – PA HT – Supply costs) ÷ PV HT) x 100	Brand taxes
Average inventory outstanding = Average unit cost x Average number of units in stock	Average stock outstanding
Overall margin = Unit margin x quantity sold	Overall margin

Application: Paul's Bakery

States :

The bakery Chez Paul is a booming business in the heart of the city of Lyon. Recently, the manager decided to improve the management of his stock to minimize supply costs and reduce unsold items. To do this, new calculations must be made.

Currently, the average stock of flour bags is 75, and the unit of flour costs €20. This stock is consumed in 30 days. The cost of placing an order is €10, and the cost of holding the stock is 15% of the purchase cost.

Work to do :

1. What is the total cost of ownership of flour inventory?
2. What is the total cost of ordering flour?
3. What is the inventory turnover rate?
4. How many orders should Chez Paul place each year to replenish its flour supply?
5. If the manager decides to reduce the average inventory to 60, how will this affect the total cost of ownership and the number of orders placed each year?

Proposed correction:

1. The total cost of ownership of flour inventory is the cost of purchasing the inventory multiplied by the inventory holding rate. Therefore, Total Cost of Ownership = Cost of Purchase x Holding Rate = 75 x €20 x 15% = €225

2. The total cost of ordering flour is the cost of placing an order divided by the number of bags used per day, multiplied by the number of days of use. So, Ordering Cost = Cost of placing an order ÷ (Average inventory / Number of days) = €10 ÷ (75 / 30) = €4

3. Inventory turnover rate is the ratio of average inventory to the number of days it takes to deplete it. So, Inventory turnover rate = Average inventory ÷ Number of days = 75 ÷ 30 = 2,5

4. The number of orders placed each year is the number of days per year divided by the number of days to consume the average inventory. So, Number of orders = 365 ÷ Number of days = 365 ÷ 30 = 12,17, or approximately 13 orders per year.

5. If the manager reduced the average inventory to 60, this would reduce the total cost of ownership to 60 x €20 x 15% = €180. To determine how many orders would be needed, we use the same formula as for question 4, but with the new average inventory: 365 ÷ (60 / 30) = 91,67, or approximately 92 orders per year.

Summary of Formulas Used:

Packages	Use
Total Cost of Ownership = Purchase Cost x Ownership Rate	Calculate the total cost of inventory ownership
Ordering cost = Placement cost ÷ (Average inventory ÷ Number of days)	Calculate the total cost of placing orders
Turnover rate = Average stock ÷ Number of days	Calculate inventory turnover rate
Number of orders = 365 ÷ Number of days	Calculate the number of orders placed each year

Application: “Trends” Shop

States :

The clothing store "Trends" is a fashion company that sells clothing items such as dresses, shirts, and pants. Currently, the store manager is analyzing the stock of shirts. He noted the following information:

– Initial quantity in stock: 200 shirts
– Final quantity in stock: 100 shirts
– Quantity purchased during the period: 0 shirts
– Quantity sold during the period: ?

Work to do :

1. Calculate the number of shirts sold during the period.
2. What formula did you use to obtain this result?
3. What does this result mean for store inventory management?
4. How many shirts should the store order if it wants to maintain its stock at the initial level?
5. What is the name of the inventory management method that involves maintaining a certain level of stock?

Proposed correction:

1. The number of shirts sold during the period is 100 units. (Initial Quantity – Final Quantity)

2. I used the formula: Quantity sold = Initial quantity in stock – Final quantity in stock.

3. This result means that the “Trends” store sold 100 shirts during the period studied. This can help the manager assess the appeal of this item to customers and adjust his stock accordingly.

4. The store should order 100 shirts if it wants to maintain its stock at the initial level.

5. The inventory management method of maintaining a certain level of stock is called the reorder point method.

Summary of Formulas Used:

Packages	Explanation
Quantity sold = Initial quantity in stock – Final quantity in stock	This formula is used to calculate the number of units of an item that were sold during a given period.

Application: Small Market

States :

Petit Marché is a neighborhood grocery store that sells several lines of food products. Inventory management is essential for this company because of the perishable nature of the majority of its products.

We give you the following information regarding inventory management for the month of March:

– Initial stock of rice: 200 kg
– Deliveries received during the month: 500 kg
– Final stock at the end of the month: 150 kg

The company's management is particularly interested in managing rice stocks, which are a product in high demand by its customers.

Work to do :

1. Calculate the rice consumption for the month of March.
2. Calculate the rice stock turnover rate for the month of March.
3. Determine the average rice storage period for the month of March.
4. Estimate the average rice stock for the month of March.
5. Propose a simple method to optimize rice stock management.

Proposed correction:

1. Rice consumption for the month of March is calculated using the formula: Initial stock + Deliveries – Final stock. Which gives: 200 kg + 500 kg – 150 kg = 550 kg.

2. The inventory turnover rate is calculated using the formula: Consumption ÷ Average inventory. The average inventory is calculated using the formula: (Opening inventory + Closing inventory) ÷ 2. Thus, the average inventory for the month of March is: (200 kg + 150 kg) ÷ 2 = 175 kg. The turnover rate is therefore: 550 kg ÷ 175 kg = 3,14.

3. The average storage period is calculated using the formula: 365 days ÷ Turnover rate. Which gives: 365 days ÷ 3,14 = 116 days.

4. As mentioned above, the average rice stock for the month of March is 175 kg.

5. To optimize rice inventory management, the company can increase the frequency of orders but reduce their size, which would allow it to reduce its average inventory and thus the value of its inventory. However, this requires better coordination with suppliers.

Summary of Formulas Used:

Formulas	Use
Initial stock + Deliveries – Final stock	To calculate consumption
(Initial stock + Final stock) ÷ 2	To calculate the average stock
Consumption ÷ Average stock	To calculate the inventory turnover rate
365 ÷ Turnover rate	To calculate the average storage period

Application: Cuisin'Art Company

States :

Cuisin'Art, a company specializing in the sale of high-end kitchen utensils, is experiencing inventory management and supply issues. It recently purchased a large quantity of non-stick frying pans, at a unit purchase price excluding tax (UPT) of €30. The initial quantity purchased was 550 pieces. The applicable VAT rate is 20%. Despite promotional campaigns, the company has sold only 230 pieces at a unit sale price excluding tax (USP) of €50. The company would like to optimize its operations.

Work to do :

1. Calculate the total value of the initial inventory before the sale.
2. Calculate the overall margin achieved by the company.
3. Determine the margin rate.
4. Calculate the value of the inventory remaining after sales.
5. Propose a strategy to manage remaining inventory.

Proposed correction:

1. The value of the initial stock is calculated by multiplying the unit purchase price by the number of units purchased. Therefore, the value of the initial stock = PA HT x Initial quantity; i.e. €30 x €550 = €16.

2. The overall margin is the difference between the total selling price and the total purchase price of the units sold. It is therefore (PV HT – PA HT) x Quantity sold; or (€50 – €30) x 230 = €4.

3. The margin rate is the ratio between the unit margin and the HT PA. It is therefore ((HT_PV – HT PA) ÷ HT PA) x 100 or ((€50 – €30) ÷ €30) x 100 = 66,67%.

4. The value of the remaining stock is the value of the initial stock reduced by the value of the stock sold, i.e. (Initial quantity – Quantity sold) x PA_HT or (550 – 230) x €30 = €9.

5. In order to manage the remaining inventory, the company could consider several strategies, including lowering the selling price to encourage purchases, organizing flash sales or group sales, offering promotions on the purchase of multiple units, or even using unsold inventory as promotional gifts with the purchase of other products.

Summary of Formulas Used:

Packages	Description
Initial stock value = PA HT x Initial quantity	Calculates the total value of an inventory by multiplying the unit purchase price by the total number of units
Overall margin = (PV HT – PA HT) x Quantity sold	Provides the total profit made on units sold
Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100	The margin rate is the ratio between the unit margin and the purchase price excluding taxes.
Remaining stock = (Initial quantity – Quantity sold) x PA_HT	The value of the remaining stock is the value of the initial stock less the value of the stock sold.