Welcome to this article with the aim of helping you with 11 Inventory Management Exercises with Detailed Answers 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.
The 11 Inventory Management Exercises with Detailed Answers cover storage cost, transfer cost, possession cost, alert stock calculation, minimum stock.
In this section:
- Application: Light Tech
- Application: TechNow
- Application: Luxury-Cars
- Application: The Elegance Boutique
- Application: Sumptuous Shoes
- Application: High Tech House
- Application: TechnoWorld
- Application: The Delights of the Mound
- Application: BioPleinNature
- Application: The Beautiful Grocery Store
- Application: Green Light
Application: Light Tech
States :
Lumière Tech, a company specializing in the sale of high-tech lighting fixtures, must manage its stock of LED street lamps. At the beginning of the year, it had an initial stock of 400 street lamps. During the year, it purchased an additional 3000 street lamps. At the end of the year, the final stock was 500 street lamps.
The purchase price of a street lamp is €50. The stock holding rate is 2%.
Work to do :
1. Calculate the company's inventory consumption for the year.
2. Determine the Average Monthly Cost (AMC) of consumption.
3. Calculate the inventory turnover coefficient (RC).
4. Determine the Average Flow Period (AF) of the stocks.
5. Calculate the inventory carrying cost.
Proposed correction:
1. The stock consumption for the year is: Initial stock + Purchases – Final stock = 400 + 3000 – 500 = 2900 street lamps
2. The CMM of consumption is: Consumption ÷ Period, or 2900 ÷ 12 = 241,67 street lamps per month.
3. The CR is obtained by QM ÷ CMM, where QM is the average quantity in stock [(Initial stock + Final stock ÷ 2) or (400 + 500) ÷ 2 = 450]. CR is therefore 450 ÷ 241,67 = 1,86.
4. The PA is obtained by Total duration of the period ÷ CR, i.e. 12 ÷ 1,86 = 6,45 months.
5. The cost of carrying the stock is Cost of purchasing the stock * carrying rate, i.e. (2900 street lamps * €50) * 2/100 = €2900.
Summary of Formulas Used:
| Formulas | Meaning |
|---|---|
| Initial stock + Purchases – Final stock = Consumption | Calculation of stock consumption |
| CMM = Consumption ÷ Period | Calculation of Average Monthly Cost (AMC) |
| CR = QM ÷ CMM | Calculation of the inventory turnover coefficient (CR), where QM is the average quantity in stock |
| PA = Total period duration ÷ CR | Calculate the average flow period (AP) of stocks |
| Cost of ownership = Cost of purchasing inventory * holding rate | Calculating the cost of carrying inventory |
Application: TechNow
States :
TechNow, a company that sells electronic devices, is facing an inventory management problem. They are having trouble determining the reorder level and safety stock. The following information was collected:
1. The unit purchase cost of a device is €100.
2. Daily consumption is on average 20 devices per day.
3. The replenishment time is 7 days.
4. Delivery time is 3 days.
5. The unit storage cost per month is €2.
6. The unit stock-out cost is €45.
Work to do :
1. Calculate the total purchase cost for 30 days.
2. Calculate the carrying cost for 30 days.
3. Determine the total cost for 30 days.
4. Determine the replenishment level.
5. Determine the safety stock.
Proposed correction:
1. The total purchase cost for 30 days is calculated as follows: Total purchase cost = Quantity x Unit price = 20 devices x 30 days x €100 = €60.
2. The carrying cost for 30 days is calculated as follows: Carrying cost = (Storage cost + Out-of-stock cost) x Quantity = (€2 + €45) x (20 devices x 30 days) = €1.
3. The total cost for 30 days would be: Total cost = Purchase cost + carrying cost = €60 + €000 = €1.
4. The replenishment level is calculated as follows: Replenishment level = Daily consumption x Replenishment time = 20 devices x 7 days = 140 devices.
5. Safety stock is calculated as follows: Safety stock = Daily consumption x Delivery time = 20 devices x 3 days = 60 devices.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Purchase cost = Quantity x Unit price | Used to calculate the total cost of purchasing products. |
| Cost of ownership = Cost of storage + Cost of stockout | Used to calculate the total cost associated with storing products. |
| Total cost = Purchase cost + ownership cost | Used to calculate the total cost of products including purchasing and storage. |
| Replenishment Level = Daily Consumption x Replenishment Time | Used to determine the stock level at which an order should be placed to avoid running out of stock. |
| Safety stock = Daily consumption x Delivery time | Used to determine the minimum stock to maintain to deal with unforeseen events. |
Application: Luxury-Cars
States :
The company Luxe-Voitures specializes in the sale of luxury cars. The Manager, Mrs. Claire, carries out precise management of car stocks to avoid unnecessary costs. Currently, she has 500 cars in stock. The unit cost of a vehicle is €60.
Sales for the year are estimated at 2 cars. The cost of placing an order with a supplier is €500 and the cost of holding a car in stock is 200% of the unit cost per year.
Ms. Claire would like to have a detailed overview of the cost of managing car inventory to optimize her business.
Work to do :
1. Calculate the order cost (Co) taking into account the cost of placing an order.
2. Determine the unit ownership cost per car (Cp) based on the cost of owning a car in inventory per year.
3. Calculate the optimum number of cars to order to minimize costs (Q).
4. Estimate the total number of orders to be placed in the year (N).
5. Calculate the total annual inventory management cost (CT).
Proposed correction:
1. The order cost (Co) is the cost of placing an order, so Co = €200.
2. The unit cost of ownership per car (Cp) is equal to 10% of the unit cost per year, so Cp = 10% x €60 = €000 per year.
3. The optimum number of cars to order to minimize costs (Q) is given by the formula Q = ?(2xCoxD)/Cp.
Here D is the number of cars sold in the year, that is, 2 cars.
So, Q = ?(2×€200x2 cars)÷€500 = 6 cars.
4. The total number of orders to be placed in the year (N) is given by the formula N = D/Q. Therefore, N = 2 cars ÷ 500 cars = 25 orders.
5. The total annual inventory management cost (CT) is given by the formula CT = (D/Q) x Co + (Q(Cp)/2), so CT = (2 cars ÷ 500 cars) x €25 + (200 cars x €25) ÷ 6 = €000 + €2 = €20.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Order Cost (Co) = Cost of placing an order | The order cost is equal to the cost of placing an order with the supplier. |
| Unit cost of ownership (Cp) = 10% of the unit cost of a car | Unit cost of ownership is calculated as a percentage of a car's unit cost. |
| Optimum quantity (Q) = ?(2xCoxD)/Cp | The formula for the optimum number of cars to order in order to minimize costs. |
| Number of orders (N) = D/Q | This is the formula to calculate the total number of orders to be placed in the year. |
| Total annual inventory management cost (CT) = (D/Q) x Co + (Q x Cp)/2 | The formula for calculating the total annual cost of inventory management. |
Application: The Elegance Boutique
States :
Boutique Élégance is a company specializing in the sale of high-end clothing. The company has only one product in stock: a coat with a unit purchase value of €100. On January 1, the company has 200 coats in stock. During the month, the company receives a delivery of 50 additional coats and sells 150 coats. The cost of these sales is €15.
Work to do :
1. Calculate the value of the opening stock, entries and closing stock.
2. Determine inventory turnover.
3. Calculate the inventory turnover time.
4. Evaluate the effectiveness of the company's inventory management.
5. Suggest some improvements for optimal inventory management.
Proposed correction:
1. Value of initial stock = (Unit purchase price x Initial quantity) = (€100 x 200) = €20.
Value of inputs = (Unit purchase price x Quantity input) = (€100 x 50) = €5.
Final quantity = Initial quantity + Quantity entered – Quantity sold = 200 + 50 – 150 = 100.
Final stock value = (Unit purchase price x Final quantity) = (€100 x 100) = €10.
2. Average stock value = (Initial stock value + Ending stock value) ÷ 2 = (€20 + €000) ÷ 10 = €000.
Inventory turnover = Cost of sales ÷ Average inventory value = €15 ÷ €000 = 15.
3. Inventory turnover duration = (360 ÷ Inventory turnover) = (360 ÷ 1) = 360 days.
4. Inventory management appears inefficient, as a turnover rate of 1 and a turnover period of 360 days indicate that the company sells its inventory only once a year.
5. To improve inventory management, the company might consider increasing its sales volume or reducing its inventory levels. For example, it might launch marketing campaigns to boost sales or adjust its orders to better match demand.
Summary of Formulas Used:
| Packages | Meanings |
|---|---|
| Initial stock value = (Unit purchase price x Initial quantity) | The value of the opening inventory corresponds to the total cost of the products that the company initially owns. |
| Input value = (Unit purchase price x Input quantity) | The value of inputs is the total cost of the products the company receives. |
| Final Inventory Value = (Unit Purchase Price x Final Quantity) | The value of the ending inventory corresponds to the total cost of the products that the company has after a given period. |
| Inventory turnover = (Cost of sales ÷ Average inventory value) | Inventory turnover gives an indication of how often the company sells its inventory. |
| Inventory turnover time = (360 ÷ Inventory turnover) | The inventory turnover period gives an indication of the average time a company has to sell its inventory. |
Application: Sumptuous Shoes
States :
We are in the company "Somptueux Souliers", a business specializing in the sale of high-end shoes. The company wants to improve its inventory management and to do this it needs to carry out an in-depth analysis of its inventory over the past year.
Here is some relevant information:
– Stocks as of January 1, 2020: 500 pairs, total value €25
– Purchases during the year 2020: 2500 pairs, total value €125
– Stocks as of December 31, 2020: 400 pairs, total value €20
– Sales during 2020: 2600 pairs, total value €185 excluding VAT
Work to do :
1. Calculate the value of the initial stock.
2. Calculate the cost of goods sold (COGS).
3. Calculate the inventory turnover rate and explain its importance.
4. Analyze the company's inventory management situation and suggest possible improvements.
5. Why is it important for the company to have good inventory management?
Proposed correction:
1. The value of the opening inventory is €25. This is the total value of inventory that the company holds at the beginning of the year.
2. Cost of goods sold (COGS) is calculated using the formula COGS = Opening inventory + Purchases – Closing inventory. Which gives COGS = €25 + €000 – €125 = €000.
3. The inventory turnover ratio is the number of times the company sold and replaced inventory during a given period. It is calculated by the ratio Cost of Goods Sold / Average Inventory. Average inventory = (Beginning inventory + Ending inventory) / 2, or ($25 + $000) / 20 = $000. So the turnover ratio = $2 / $22 = 500. This means that the company sold and replaced its inventory approximately 130 times during the year. The higher this ratio, the more it means that the company is managing its inventory efficiently.
4. The company appears to have good inventory management. However, it could further improve this by reducing its opening and closing inventory levels. This would free up capital that could be used elsewhere in the business.
5. Good inventory management allows the company to maximize its efficiency and profits. By maintaining an optimal inventory level, the company can reduce its storage costs, minimize the possibility of obsolete goods, ensure timely delivery to customers and optimize the use of its capital.
Summary of Formulas Used:
- Value of opening stock = Total value of stocks at the beginning of the year
- Cost of Goods Sold (COGS) = Beginning Inventory + Purchases – Ending Inventory
- Average stock = (Initial stock + Final stock) / 2
- Inventory Turnover Ratio = Cost of Goods Sold / Average Inventory
Application: High Tech House
States :
High Tech House is a store that sells electronic devices and computer equipment. Here is the information available for the year 2022:
– Initial stock of goods: €200
– Purchases of goods: €500
– Final stock of goods: €150
Work to do :
1. Calculate the consumption of goods for the year 2022.
2. Calculate the average stock for the year 2022.
3. Calculate the inventory turnover rate for the year 2022.
4. Calculate the average storage duration for the year 2022.
Proposed correction:
1. To calculate the consumption of goods, we use the formula: Initial stock + Purchases – Final stock = €200 + €000 – €500 = €000. Therefore, the consumption of goods for the year 150 is €000.
2. To calculate the average stock, we use the formula: (Initial stock + Final stock) ÷ 2 = (€200 + €000) ÷ 150 = €000. Therefore, the average stock for the year 2 is €175.
3. To calculate the inventory turnover rate, we use the formula: Consumption ÷ Average inventory = €550 ÷ €000 = 175 times. Therefore, the inventory turnover rate for the year 000 is 3,14.
4. To calculate the average storage duration, we use the formula: 365 days ÷ Inventory turnover rate = 365 days ÷ 3,14 = 116,24 days. Therefore, the average storage duration for the year 2022 is approximately 116 days.
Summary of Formulas Used:
| Formulas | Explanation |
| Initial stock + Purchases – Final stock | This is the formula for commodity consumption. |
| (Initial stock + Final stock) ÷ 2 | This is the average stock formula |
| Consumption ÷ Average stock | This is the formula for inventory turnover rate. |
| 365 days ÷ Inventory turnover rate | This is the formula for average storage duration. |
Application: TechnoWorld
States :
TechnoWorld is a company specializing in the sale of consumer electronics. During the last financial year, the company experienced the following inventory movements for a particular type of tablet computer:
– Initial stock of the year: 100 units
– Purchases during the year: 500 units
– Final stock of the year: 150 units
– The total cost of the purchases was €180
Work to do :
1. Calculate the annual consumption of these tablets.
2. Determine the average purchase cost per tablet.
3. Determine the average stock of these tablets.
4. Calculate the inventory turnover rate.
5. Finally, calculate the average storage duration.
Proposed correction:
1. To determine annual consumption, we subtract the ending stock from the total of the beginning stock and purchases: (100 + 500) – 150 = 450 tablets
Annual consumption = 450 tablets
2. To find the average purchase cost per tablet, we divide the total cost of purchases by the number of units purchased: 180 ÷ 000 = €500
Unit purchase cost = €360
3. The calculation of the average stock is the average of the initial stock and the final stock: (100 + 150) ÷ 2 = 125 tablets
Average stock = 125 tablets
4. To calculate inventory turnover, we divide consumption by average inventory: 450 ÷ 125 ~ 3.6
Inventory turnover = 3.6
5. To find the average storage duration, we divide the number of days in the year by the inventory turnover: 365 ÷ 3.6 ~ 101 days
Average storage time = 101 days
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Initial stock + Purchases – Final stock = Consumption | This formula is used to determine the consumption of an item over a given period. |
| Unit purchase cost = Total purchase cost ÷ Quantity purchased | This allows us to know the average cost of acquiring an item. |
| Average stock = (Initial stock + Final stock) ÷ 2 | This calculation gives the average stock level over a period. |
| Inventory turnover = Consumption ÷ Average inventory | This formula allows you to know the number of times the stock is renewed over a given period. |
| Average storage time = 365 ÷ Stock turnover | This gives the average number of days an item remains in stock. |
Application: The Delights of the Mound
States :
The supermarket “Les Délices du Tertre” has contacted its dairy product supplier to replenish its stocks. The replenishment works on the principle of Maximum Stock and Safety Stock.
Based on the following data:
– Quantity ordered: 2000 L
– Delivery time: 4 days
– Average daily consumption: 450 L / day
– Current stock: 810 L
Work to do :
1. What is the safety stock of “Les Délices du Tertre”?
2. What is the maximum stock that “Les Délices du Tertre” can have for dairy products?
3. How many days can “Les Délices du Tertre” continue to operate without restocking, using its current stock?
4. Once “Les Délices du Tertre” has placed the order, how long can the supermarket operate without a new delivery?
5. If “Les Délices du Tertre” placed an additional order for a delivery time of 3 days and an average daily consumption of 490 L, what will its new safety stock be?
Proposed correction:
1. Safety stock is the minimum stock that the company must have to ensure its operation during the delivery time of the next order. Its formula is: Safety stock = Average daily consumption x Delivery time
Safety stock = 450 L x 4 days = 1800 L
2. Maximum stock is the total quantity that the company can store. Using the formula: Maximum stock = Safety stock + Ordered quantity
Maximum stock = 1800 L + 2000 L = 3800 L
3. The number of days that “Les Délices du Tertre” can continue to operate without restocking is obtained by dividing the total stock by the average daily consumption:
Number of days = Current stock ÷ Average daily consumption
Number of days = 810 L ÷ 450 L/day = 1,8 days or approximately 2 days.
4. Once the order is placed, the supermarket can operate without new delivery depending on the delivery time and the quantity ordered. Using the formula: Number of days = (Current stock + Quantity ordered) ÷ Average daily consumption
Number of days = (810 L + 2000 L) ÷ 450 L/day = 6,24 days or approximately 6 days.
5. With the new delivery time and average daily consumption, the new safety stock is:
Safety stock = Average daily consumption x Delivery time
Safety stock = 490 L x 3 days = 1470 L
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Safety stock = Average daily consumption x Delivery time | Formula for calculating safety stock |
| Maximum stock = Safety stock + Ordered quantity | Formula to calculate maximum stock |
| Number of days = Current stock ÷ Average daily consumption | Formula to determine how many days the business can continue to operate without restocking |
| Number of days = (Current stock + Quantity ordered) ÷ Average daily consumption | Formula to determine how many days the business can continue to operate after placing an order |
Application: BioPleinNature
States :
The company BioPleinNature is a supermarket specializing in organic products. The company carries out inventory management of its products every year. This process is essential to maintain a good balance between inventory and sales.
For this year, BioPleinNature is focusing on one of its best-selling products, organic rice. The company has an initial stock of 16 kg of organic rice. BioPleinNature purchases the organic rice at a unit purchase price of €000 per kilo excluding VAT. The company chooses to sell this rice at a unit sales price of €2 excluding VAT.
During the year, the company sold 12 kg of organic rice.
Work to do :
1. Calculate the overall margin generated by the company on organic rice for this year.
2. Calculate the company's margin rate for organic rice.
3. Calculate the markup rate for organic rice.
4. Estimate the final stock of organic rice at the end of the year.
5. BioPleinNature plans to increase the unit selling price of organic rice to €3,5 excluding VAT next year. How will this affect the indicators calculated in 1, 2 and 3?
Proposed correction:
1. The overall margin is calculated by multiplying the unit margin by the quantity sold. The unit margin is the difference between the selling price excluding VAT and the purchasing price excluding VAT ((€3 – €2) = €1). The overall margin is therefore €12 x €000 = €1.
2. The margin rate is calculated by doing ((PV HT – PA HT ÷ PA HT) x 100) or ((3 € – 2 €) ÷ 2 €) x 100 = 50%.
3. Similarly, the markup rate is calculated as follows: ((PV HT – PA HT) ÷ PV HT) x 100 or ((€3 – €2) ÷ €3) x 100 = 33,33%.
4. The ending stock of organic rice at the end of the year is the opening stock minus the quantity sold (16 kg – 000 kg = 12 kg).
5. With the new unit sales price of €3,5 excluding VAT, the unit margin becomes (€3,5 – €2 = €1,5). If the company sells the same quantity of organic rice, the overall margin will therefore be €12 x €000 = €1,5, the margin rate will be ((€18 – €000) ÷ €3,5) x 2 = 2% and the markup rate will be ((€100 – €75) ÷ €3,5) x 2 ? 3,5%.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Overall margin = Unit margin x quantity sold | This formula is used to calculate the overall margin. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100) | This formula is used to calculate the margin rate. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100) | This formula is used to calculate the markup rate. |
Application: The Beautiful Grocery Store
States :
The company "La Belle Epicerie" is a small local business that specializes in the sale of quality grocery products. Inventory management is a major issue for the company in order to ensure good product rotation and limit waste.
The manager, Mrs. Claudine, provides you with the following information for inventory management for the month of April:
– Initial stock: 200 kg of apples
– Purchases of the month: 500 kg of apples
– Sales of the month: 550 kg of apples
– Desired final stock: 150 kg of apples
Work to do :
1. What is the actual ending stock of apples at the end of April?
2. What is the average stock of apples for the month of April?
3. What is the inventory turnover ratio for the month of April?
4. What is the average storage time for apples in days for the month of April?
5. How many apples should be purchased in May to maintain the desired final stock?
Proposed correction:
1. The actual ending inventory at the end of April is calculated by subtracting April sales from the beginning inventory plus April purchases. Thus, the ending inventory is 200 kg + 500 kg – 550 kg = 150 kg of apples.
2. The average stock for the month of April is calculated by adding the opening stock and the closing stock and then dividing by 2. Thus, the average stock is (200 kg + 150 kg) ÷ 2 = 175 kg of apples.
3. The inventory turnover ratio is calculated by dividing the sales for the month by the average inventory. Thus, the inventory turnover ratio is 550 kg ÷ 175 kg = 3,14 times.
4. The average storage duration is calculated by dividing the number of days in the month by the inventory turnover ratio. Thus, the average storage duration is 30 days ÷ 3,14 = 9,55 days.
5. The quantity of apples to be purchased in May to maintain the desired ending stock is calculated by adding the quantity of apples sold in April to the desired ending stock and then subtracting the initial stock. Thus, the quantity of apples to be purchased is 550 kg + 150 kg – 200 kg = 500 kg of apples.
Summary of Formulas Used:
| The goal | Formulas |
|---|---|
| Calculation of final stock | Initial stock + Purchases – Sales |
| Calculation of average stock | (Initial stock + Final stock) ÷ 2 |
| Calculating Inventory Turnover Ratio | Sales ÷ Average inventory |
| Calculation of average storage duration | Number of days in month ÷ Inventory turnover ratio |
| Calculating the quantity to purchase for a desired final stock | Sales + Desired final stock – Initial stock |
Application: Green Light
States :
The company Lumière Verte, which specializes in the sale of ecological products, has several types of inventory in its warehouse. The company uses the unified cost method to manage its inventory. At the end of the financial year, the following information was collected:
– The opening stock is €10
– Tax-free purchases are €65
– The incidental purchase costs are €2
– Returns on purchases are €1
– The final stock amounts to €11
Work to do :
1. Calculate the cost of goods on hand (CAMD) for Lumière Verte.
2. Determine the company's consumption during the financial year.
3. Estimate the inventory turnover rate.
4. On average, how many days do stocks remain in the company?
5. What suggestions can you make to improve the management of Lumière Verte stocks?
Proposed correction:
1. Cost of Goods Available (CAMD) = Opening inventory + Purchases + Incidental purchase costs – Returns on purchases
= €10 + €100 + €65 – €200
£76
2. Company consumption = CAMD – Final stock
= €76 – €700
£65
3. Inventory turnover rate = Consumption / ((Opening inventory + Ending inventory) ÷ 2)
= €65 / ((€300 + €10) ÷ 100)
= €65 / (€300)
? 6,07 times
4. Average number of days of storage = 365 days / Inventory turnover rate
= 365 days / 6,07
? 60 days
5. To improve inventory management, the company may consider using more advanced inventory management systems, implementing inventory optimization techniques such as the ABC method, or implementing a policy to reduce downtime and delivery times.
Summary of Formulas Used:
| Formulas | Meaning |
|---|---|
| CAMD = Opening stock + Purchases + Incidental purchase costs – Returns on purchases | Cost of Purchase of Available Goods |
| Consumption = CAMD – Final stock | Consumption during exercise |
| Inventory turnover rate = Consumption / ((Opening inventory + Ending inventory) ÷ 2) | Inventory turnover rate |
| Average number of days of storage = 365 days / Inventory turnover rate | Average number of storage days |