Welcome to this article aimed at helping you with 11 corrected inventory 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.
The 11 corrected inventory management exercises cover storage cost, transfer cost, possession cost, alert stock calculation, minimum stock.
In this section:
- Application: The Company “Innovative Technologies”
- Application: Dream Furniture
- Application: Paper & Company
- Application: Fashion Feet Luxury Shoe Store
- Application: E-Luxury Company
- Application: LectioRégal Bookstore
- Application: DécoCasa Company
- Application: Superstore Ltd
- Application: High-Techy Company
- Application: Klein Developments Company
Application: The Company “Innovative Technologies”
States :
The company "Innovative Technologies" is a distributor specializing in computer hardware. The main products sold are desktop computers and laptops. In recent years, the company has invested heavily in diversifying its products to include accessories such as keyboards, mice, laptop stands, etc.
The financial data for the previous year are as follows:
– Initial stock of laptops: 200 units at a price of €500 per unit
– Purchases of the year: 800 units at a price of €520 per unit
– Final stock of laptops: 150 units
– Unit sale price: €700
Work to do :
1. Calculate the consumption for the year in number of units and in euros.
2. Calculate the unit margin and the overall margin on laptops.
3. Calculate margin rate and brand rate.
4. Evaluate the impact on unit margin and overall margin if the number of laptops sold increases by 10%.
5. Evaluate the impact on unit margin and overall margin if the unit purchase price increases by 3%.
Proposed correction:
1. Consumption of the year = Initial stock + Purchases – Final stock = 200 units + 800 units – 150 units = 850 units. Consumption in euros = Consumption of the year in units x Unit purchase price = 850 units x €520 = €442
2. Unit margin = Unit selling price – Unit purchasing price = €700 – €520 = €180. Overall margin = Unit margin x Quantity sold = €180 x 850 units = €153
3. Margin rate = ((Unit selling price – Unit purchase price) ÷ Unit purchase price) x 100 = ((€700 – €520) ÷ €520) x 100 = 34,62%. Markup rate = ((Unit selling price – Unit purchase price) ÷ Unit selling price) x 100 = ((€700 – €520) ÷ €700) x 100 = 25,71%
4. If the number of laptops sold increases by 10%, the unit margin remains the same because it does not depend on the quantity sold, but the overall margin will increase to: €180 x 850 units x 1,1 = €168
5. If the unit purchase price increases by 3%, the new unit purchase price will be €520 x 1,03 = €535,6. In this case, the new unit margin will be €700 – €535,6 = €164,4 and the overall margin will be €164,4 x 850 units = €139
Summary of Formulas Used:
| Consumption of the year in units | Initial stock + Purchases – Final stock |
| Consumption in euros | Consumption of the year in units x Unit purchase price |
| Unit margin | Unit selling price – Unit purchase price |
| Overall margin | Unit margin x Quantity sold |
| Margin rate | ((Unit Selling Price – Unit Purchase Price) ÷ Unit Purchase Price) x 100 |
| Brand taxes | ((Unit Selling Price – Unit Purchase Price) ÷ Unit Selling Price) x 100 |
Application: Dream Furniture
States :
You are the manager of a furniture store called Dream Furniture. At the beginning of January, you had an initial inventory of 500 pieces of furniture. During the month of January, you received two shipments of furniture from your supplier, one of 200 pieces of furniture and another of 150 pieces of furniture. At the end of January, you counted the remaining inventory and found that there were 350 pieces of furniture remaining.
Work to do :
1. What is the total number of purchases you made in January?
2. What is the cost of goods sold (COGS) in January?
3. How many pieces of furniture did you sell in January?
4. If each piece of furniture is purchased for €120, what is the total cost of purchases in January?
5. If each piece of furniture is sold for €200, what is the turnover in January?
Proposed correction:
1. Total purchases in January are 200 + 150 = 350 pieces of furniture.
2. The cost of goods sold (COGS) in January is calculated as follows: COGS = SI+AV = 500 + 350 – 350 = 500 pieces of furniture.
3. The number of pieces of furniture sold in January is SI+A-SF = 500 + 350 – 350 = 500 pieces of furniture.
4. The total cost of purchases in January is 350 x €120 = €42.
5. The turnover in January is 500 x 200 € = 100 €.
Summary of Formulas Used:
| Packages | Description |
|---|---|
| Initial stock (IS) | This is the stock you have at the beginning of the period. |
| Purchases (A) | All acquisitions of goods during the period. |
| Final stock (FS) | This is the stock you have at the end of the period. |
| Sales (V) | This is the number of items sold during the period. |
| Cost of Goods Sold (COGS) | CMV=SI+AV |
Application: Paper & Company
States :
The company Papier & Compagnie sells various office supplies. For one of its references, a set of ballpoint pens, here is some information on its inventory management:
– Initial stock: 5000 units
– Deliveries received during one year: 25000 units
– Sales made during the same year: 23000 units
– Purchase cost per pen unit: €0,10
– Selling price per pen unit: €0,30
Work to do :
1. Calculate the ending stock at the end of the year.
2. Calculate the value of the initial stock in euros.
3. Calculate the value of the ending stock in euros.
4. What is the amount of sales made during the year?
5. What is the inventory turnover rate?
Proposed correction:
1. The ending inventory at the end of the year is obtained by subtracting the number of units sold from the number of units in the beginning inventory and then adding the shipments received. This gives: 5000 units (beginning inventory) – 23000 units (units sold) + 25000 units (shipments received) = 7000 units
2. The value of the initial stock is calculated by multiplying the number of units in initial stock by the purchase cost per unit. This gives: 5000 units x €0,10 = €500
3. The value of the ending inventory is calculated by multiplying the number of units in ending inventory by the purchase cost per unit. This gives: 7000 units x €0,10 = €700
4. The amount of sales made during the year is calculated by multiplying the number of units sold by the sales price per unit. This gives: 23000 units x €0,30 = €6900
5. The inventory turnover ratio is the ratio of the number of units sold to the average of the beginning inventory and the ending inventory. This gives: 23000 units ÷ ( (5000 units (beginning inventory) + 7000 units (ending inventory) ) ÷ 2) = approximately 3,83. This means that the company renews its inventory approximately 3,83 times per year.
Summary of Formulas Used:
- Final stock = Initial stock – Units sold + Deliveries received
- Inventory Value = Number of Units in Stock x Purchase Cost per Unit
- Sales Amount = Units Sold x Selling Price per Unit
- Inventory turnover rate = Units sold ÷ ( (Opening inventory + Ending inventory) ÷ 2 )
Application: Fashion Feet Luxury Shoe Store
States :
Fashion Feet Boutique is a luxury shoe boutique, located in the center of Paris. The boutique wants to analyze and evaluate its inventory management processes to possibly improve its performance and productivity.
The financial data for the current year are as follows:
– New pairs of shoes purchased: 2000 pairs
– Shoes sold: 1500 pairs
– Cost of each pair of shoes: €200
– Selling price of each pair of shoes: €500
– Initial stock of shoes: 500 pairs
Work to do :
1. Calculate the inventory turnover rate for the current year.
2. Calculate the store's margin rate.
3. Calculate the store's markup rate.
4. Calculate the overall margin of the store.
5. Based on the previous results, evaluate the performance of inventory management.
Proposed correction:
1. The inventory turnover rate is an indicator that measures the number of times a stock is replaced by new merchandise. It is calculated with the formula: (Number of shoes sold ÷ ((Initial stock + Number of shoes purchased) ÷ 2)). So for Fashion Feet, the calculation is as follows (1500 ÷ ((500 + 2000) ÷ 2)) or approximately 1.5.
2. The margin rate is calculated by doing ((Sales price excluding VAT – Purchase cost excluding VAT) ÷ Purchase cost excluding VAT) x 100 = ((500 – 200) ÷ 200) x 100 = 150%.
3. The markup rate is calculated by doing ((Selling price excluding VAT – Purchase cost excluding VAT) ÷ Selling price excluding VAT) x 100 = ((500 – 200) ÷ 500) x 100 = 60%.
4. The overall margin is calculated by multiplying the unit margin by the number of pairs of shoes sold. That is (Selling price – Purchase cost) x Number of shoes sold = (500 – 200) x 1500 = €450,000.
5. The analysis of these indicators shows that the store's inventory management is relatively efficient. Indeed, an inventory turnover rate of 1.5 shows that the store managed to renew its stock 1.5 times during the year. In addition, thanks to its high margin rate (150%), the store generated an overall margin of €450,000. However, the markup rate of 60% indicates that the store could work more on its pricing strategy to further optimize its margin.
Summary of Formulas Used:
| Formulas | Description |
| Inventory turnover rate = Number of shoes sold ÷ ((Opening inventory + Number of shoes purchased) ÷ 2) | The formula for calculating inventory turnover rate. |
| Margin rate = ((Selling price excluding VAT – Purchase cost excluding VAT) ÷ Purchase cost excluding VAT) x 100 | The formula for calculating the margin rate. |
| Markup rate = ((Selling price excluding VAT – Purchase cost excluding VAT) ÷ Selling price excluding VAT) x 100 | The formula for calculating the markup rate. |
| Overall margin = (Selling price – Purchase cost) x Number of shoes sold | The formula for calculating the overall margin. |
Application: E-Luxury Company
States :
E-Luxe, an online store for second-hand luxury goods, must manage a large number of references. Inventory management is therefore an essential task for the company. At the beginning of the year, the stock was €2. During the year, the company made purchases for €500,00. The total value of stock withdrawals (sales) was €7. At the end of the year, the stock is €500,00.
Work to do :
1. Check that inventory management is consistent.
2. Calculate the average stock in value.
3. Determine stock coverage.
4. Calculate inventory turnover.
5. Evaluate the inventory turnover time.
Proposed correction:
1. We first check the correct sequence of stock movements: Initial stock + Purchases – Issues = Final stock. Here, €2 + €500,00 – €7 = €500,00. The final stock corresponds well, stock management seems coherent.
2. The average stock value is calculated as follows: (Stock value at the start of the period + Stock value at the end of the period) ÷ 2. Therefore, (€2 + €500,00) ÷ 2 = €750,00.
3. Inventory coverage is obtained by: Average inventory ÷ (Cost of sales ÷ number of days). If we take the entire year, i.e. 365 days, we obtain: €2 ÷ (€625,00 ÷ 7) ? 250,00 days. The store therefore has inventory covering approximately 365 days of sales.
4. Inventory turnover is calculated as: Cost of sales ÷ Average inventory. Which gives: €7 ÷ €250,00 ? 2. The store therefore rotates its inventory approximately 625,00 times per year.
5. The inventory turnover period is calculated as: 365 days ÷ Inventory turnover, or: 365 ÷ 2,76 ? 132 days. Therefore, approximately 132 days elapse between two complete inventory turnovers.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Initial stock + Purchases – Issues = Final stock | Calculating stocks |
| (Stock value at start of period + Stock value at end of period) ÷ 2 | Average stock value |
| Inventory Coverage = Average Inventory ÷ (Cost of Sales ÷ Days) | Calculating stock coverage |
| Inventory turnover = Cost of sales ÷ Average inventory | Calculating Inventory Turnover |
| Inventory turnover time = 365 days ÷ Inventory turnover | Calculating inventory turnover time |
Application: LectioRégal Bookstore
States :
At LectioRegal, a dynamic bookstore located in the city center, you are in charge of inventory management. The management team would like to make an assessment of the stock for the last quarter. During the period, the company purchased 1500 copies of a certain book at a unit price (excluding VAT) of €15 and sold them at a unit price (excluding VAT) of €20. The VAT rate is 20%.
Work to do :
1. What was the total purchase price excluding VAT of these books?
2. What was the total selling price excluding VAT of these books?
3. What was the overall margin achieved over this period?
4. Calculate the margin rate of these books.
5. Calculate the markup rate of these books.
Proposed correction:
1. The total purchase price excluding VAT is calculated by multiplying the unit purchase price by the total quantity purchased. Thus, the total purchase price excluding VAT = 1500 pounds x €15 = €22.
2. The total selling price excluding VAT is obtained by multiplying the unit selling price by the quantity sold. Thus, the total selling price excluding VAT = 1500 pounds x €20 = €30.
3. The overall margin is calculated by subtracting the total purchase price from the total sale price. Thus, the overall margin is €30 – €000 = €22.
4. The margin rate is calculated by dividing the margin by the total purchase price and multiplying the result by 100. Thus, the margin rate = ((€20 – €15) ÷ €15) x 100 = 33,33%.
5. The markup rate is calculated by dividing the margin by the total selling price and multiplying the result by 100. Thus, the markup rate = ((€20 – €15) ÷ €20) x 100 = 25%.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| Total purchase price excluding VAT = PA excluding VAT x Quantity purchased | To calculate the total purchase price excluding taxes |
| Total selling price excluding VAT = PV excluding VAT x Quantity sold | To calculate the total sales price excluding taxes |
| Overall margin = total PV excluding tax – total PA excluding tax | To calculate the overall margin |
| Margin rate = ((PV HT – PA HT) ÷ PA HT) x 100 | To calculate the margin rate |
| Mark Rate = ((PV HT – PA HT) ÷ PV HT) x 100 | To calculate the markup rate |
Application: DécoCasa Company
States :
The company DécoCasa is a store specializing in the sale of interior decoration products. The manager, Mr. Dupont, asks you to help him manage his stocks properly.
Here is some data to help you:
– Initial stock as of January 01, 2021: 500 units
– Final stock as of December 31, 2021: 600 units
– Current purchases 2021: 2000 units
– Unit purchase price: €10
– Unit sale price: €15
Work to do :
1. Calculate the amount of the initial stock.
2. Calculate the amount of purchases.
3. Calculate the ending stock amount.
4. Determine the margin rate.
5. Determine the markup rate.
Proposed correction:
1. The amount of the initial stock is obtained by multiplying the quantity of the initial stock by the unit purchase price. Therefore: Initial stock = Quantity of initial stock x Unit purchase price = 500 units x €10 = €5000.
2. The amount of purchases is determined in the same way. Therefore: Amount of purchases = Quantity purchased x Unit purchase price = 2000 units x €10 = €20000.
3. The amount of the final stock is also obtained by multiplying the final quantity by the unit purchase price. Therefore: Final stock = Final quantity x Unit purchase price = 600 units x €10 = €6000.
4. The margin rate is calculated using the formula: Margin rate = ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100. Therefore: Margin rate = ((€15 – €10) ÷ €10) x 100 = 50%.
5. The markup rate is obtained using the formula: Markup rate = ((Selling price excluding VAT – Purchase price excluding VAT) ÷ Selling price excluding VAT) x 100. Therefore: Markup rate = ((€15 – €10) ÷ €15) x 100 = 33,33%.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Initial stock amount | Initial stock quantity x Unit purchase price |
| Amount of purchases | Quantity purchased x Unit purchase price |
| Final stock amount | Final quantity x Unit purchase price |
| Margin rate | ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 |
| Brand taxes | ((Sales price excluding tax – Purchase price excluding tax) ÷ Sales price excluding tax) x 100 |
Application: Superstore Ltd
States :
SUPERSTORE Ltd is a large retailer specialising in the sale of household goods and consumables. It is currently reviewing its stock management policy, particularly that of its flagship product: the intelligent kitchen robot.
The operations manager provided you with the following information on the inventory management costs of the smart kitchen robot:
– Cost of placing an order: €150
– Cost of holding a unit stock per year: €200
– The annual need for smart kitchen robots is 10 units
– The safety stock is 100 units.
Work to do :
1. Calculate the optimal number of orders to place each year.
2. Calculate the optimal quantity to order each time.
3. What is the minimum annual cost of inventory management?
4. What are the inventory management tools that SUPERSTORE Ltd could implement to improve its inventory management?
5. Analyze the impact of increased ordering costs on inventory management.
Proposed correction:
1. The optimal number of orders to place each year is: Annual requirement ÷ Optimal quantity ordered per time. For this question, we first need to calculate the optimal quantity which is given by the formula: square root ((2 x Annual requirement x Cost of placing an order) / Cost of holding a unit inventory per year). In this case, this gives square root ((2 x 10 x 000) / 150) = 200 ? 547,72 robots.
2. The optimal quantity to order each time is, as previously stated, 548 robots.
3. The minimum annual inventory management cost is obtained by adding the inventory holding cost (Optimal quantity / 2 x annual unit inventory holding cost) and the ordering cost (Number of orders x cost per order). This gives here ((548 / 2 x 200) + ((10 / 000) x 548)) = €150.
4. SUPERSTORE Ltd could implement different tools such as ABC classification tool (to prioritize products based on their cost), performance indicators (such as inventory turnover rate), demand forecasting software, or inventory management software to automate inventory tracking.
5. An increase in ordering costs would result in an increase in the quantity ordered in each order (to make the cost of each order profitable) and therefore decrease the number of orders placed in the year. This could lead to a higher risk of stockouts if the demand forecast is not accurate.
Summary of Formulas Used:
| Formulas | Explanation |
|---|---|
| Optimal order quantity = ?((2 x Annual unit requirement x Cost of placing an order) ÷ Cost of holding a unit inventory per year) | Determines the optimal quantity to order each time to minimize inventory management costs. |
| Optimal number of orders per year = Annual requirement in units ÷ Optimal order quantity | Indicates the optimal number of orders to place per year to minimize inventory management costs. |
| Minimum annual inventory management cost = (Optimal order quantity / 2 x Cost of holding a unit of inventory per year) + (Optimal number of orders per year x Cost per order) | Calculates the minimum annual inventory management cost which is the sum of the inventory carrying cost and the ordering cost. |
Application: High-Techy Company
States :
High-Techy is a distributor specializing in high-tech products. The company uses the cumulative weighted average cost (WACC) method to value its inventory. Here is the information on the movements of one of their flagship products, a digital camera, for the month of January 2022:
– January 01: Initial stock of 100 units at €200 per unit
– January 05: Purchase of 200 units at €210 per unit
– January 10: Sale of 150 units
– January 20: Purchase of 150 units at €220 per unit
– January 30: Sale of 200 units
Work to do :
1. What is the value of the initial stock?
2. What is the cost of purchases in January?
3. What is the value of the ending stock?
4. Based on the information provided, what is the weighted average purchase cost per unit at the end of January?
5. What is the cost of sales for the month of January?
Proposed correction:
1. The value of the initial inventory is calculated by multiplying the quantity of inventory by the unit cost. So, 100 units at €200 per unit gives €20.
2. The cost of purchases for the month of January is calculated by adding the total cost of each purchase. Here, (200 units x €210) + (150 units x €220) = €42 + €000 = €33.
3. The value of the ending inventory, using the WACC method, is determined by subtracting the cost of sales from the total cost of inventory on hand (opening inventory + purchases). However, we need to determine the cost of sales first.
4. To calculate the weighted average cost per unit, divide the total cost of inventory on hand by the total quantity of inventory on hand. Therefore (initial inventory + cost of purchases) ÷ (initial quantity + quantity purchased) = (€20 + €000) ÷ (75 units + 000 units + 100 units) = €200/unit.
5. Cost of sales for the month of January is calculated by multiplying the weighted average cost per unit by the number of units sold. So, €210/unit x (150 units + 200 units) = €73.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Stock value | Quantity x Unit Cost |
| Cost of purchases | ? (Quantity purchased x Unit cost) |
| Weighted average cost | (Total cost of available inventory) ÷ (total quantity of available inventory) |
| Cost of sales | Quantity sold x Weighted average cost |
Application: Klein Developments Company
States :
Klein Developments is a company that specializes in selling high-tech electronics. They have a physical store and an online store. Proper inventory management is vital to their business. Ms. Sanchez, who is responsible for inventory management, receives a detailed report of the company's inventory every month. This month's report shows the following information for one of their best-selling products, the "Smartcamera X250":
– Opening stock (on the 1st of the month): 500 units
– Purchases of the month: 1000 units
– Safety stock: 100 units
– Sales of the month: 1300 units
– Expected closing stock (as of the 30th of the month): (?) units
– Unit purchase cost excluding tax: €150
– Unit sale price excluding VAT: €299
Work to do :
1. What is the expected closing stock for the current month?
2. Calculate the overall margin on the product for this month.
3. What is the margin rate and markup rate on the product for the current month?
4. If 60% of sales were made online, what is the minimum stock of “Smartcamera X250” that the company should have in its warehouse for its online sales based on the current month’s sales?
5. What would be the impact of a 5% increase in purchasing cost on the unit margin and the overall margin?
Proposed correction:
1. The expected closing stock can be calculated using the following formula: Opening stock + Purchases – Sales.
We therefore obtain: 500 units + 1000 units – 1300 units = 200 units.
2. The overall margin is obtained using the formula: Unit margin x quantity sold.
Unit margin = Selling price excluding tax – Cost price = €299 – €150 = €149.
So, Overall Margin = €149 x 1300 = €193.
3. The margin rate and the markup rate are calculated as follows:
– Margin rate = ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Purchase price excluding VAT) x 100.
That is, ((€299 – €150) ÷ €150) x 100 = 99,33%.
– Markup rate = ((Selling price excluding VAT – Purchase price excluding VAT) ÷ Selling price excluding VAT) x 100.
That is, ((€299 – €150) ÷ €299) x100 = 49,83%.
4. For online sales, the company should stock at least: 60% x (Opening stock + purchases – safety stock).
That is: 60% x (500 + 1000 -100) = 840 units.
5. A 5% increase in the purchase cost means that the unit purchase cost excluding VAT would increase to €157,50.
– The new unit margin would be: €299 – €157,50 = €141,50.
– So the new overall margin would be: €141,50 x 1300 = €184.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Expected closing stock | Opening stock + Purchases – Sales |
| Unit margin | Sales price excluding tax – Purchase price excluding tax |
| Overall margin | Unit margin x Quantity sold |
| Margin rate | ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100 |
| Brand taxes | ((Sales price excluding tax – Purchase price excluding tax) ÷ Sales price excluding tax) x 100 |