Welcome to this article aimed at helping you with 11 corrected exercises on inventory management 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.
In this section:
- Application: ABC Company
- Application: TechnoLog Company
- Application: Gourmet Delight Company
- Application: Modestyle shoes sale
- Application: Enterprise TechnoGears
- Application: Electronix Company
- Application: The Golden Bakery
- Application: ElectroExpress
- Application: Natural
- Application: ModernTech
- Application: OmegaTech
Application: ABC Company
States :
ABC Company is an electronics distribution company. According to the information provided by the purchasing and inventory department, it is known that the cost of placing an order is €200, the unit holding cost is €25 per year, and the annual demand is 2000 units. In addition, the stockout cost is estimated at €500.
Work to do :
1. Calculate the total cost of inventory transfers and holdings for the year if the company decides to purchase the equipment at one time.
2. Calculate the economic order quantity that minimizes total cost.
3. Calculate safety stock.
4. Compare the total cost if there is a stockout with the total cost if the company follows the economic order quantity.
5. Recommend an inventory management strategy for ABC Company.
Proposed correction:
1. Total cost of placing and holding inventory = Cost of placing x number of orders + Cost of holding x average quantity of inventory = €200 x 1 + €25/unit x 2000 units = €200 + €50 = €000
2. Economic order quantity = square root of ((2 x D x S) ÷ H) = square root of ((2 x 2000 units x €200) ÷ €25/unit) ? 360 units.
3. Safety stock = (Stock-out cost x annual demand) ÷ unit holding cost = (€500 x 2000 units) ÷ €25/unit ? 40 units.
4. Total cost in case of stockout = unit holding cost x safety stock + stockout cost x annual demand = €25/unit x 40 units + €000 x 500 units = €2000 + €1 = €000
5. ABC Company is recommended to place orders following the economic order quantity which is 360 units. This will help it minimize the total inventory cost. However, the company should also keep a safety stock to avoid stock-outs which could prove costly.
Summary of Formulas Used:
| Packages | Description |
|---|---|
| Total cost of inventory transfer and ownership (TC) | CT = Cost of placing x number of orders + Cost of holding x average quantity of stock |
| Cost of passing | Cost incurred to obtain the goods |
| Cost of ownership | Cost incurred to store the goods (including storage costs and opportunity costs) |
| Economic order quantity (Q) | Q = square root of ((2 x D x S) ÷ H) where D = annual demand, S = cost of acquisition, H = unit carrying cost |
| Safety Stock (SS) | SS = (Stock-out cost x annual demand) ÷ unit carrying cost |
Application: TechnoLog Company
States :
TechnoLog, a company specializing in the sale of computer equipment, is looking to improve its inventory management. TechnoLog's inventory manager provides the following information for each of the previous three months:
– In January: The company had 150 units of a specific product in stock at a cost of €25 per unit. Their sale generated €7.
– In February: TechnoLog purchased 100 more units of the same product at €28 each. They sold 180 units that month, generating €9.
– In March: They bought 50 additional units at €30 each and sold 70 units, generating €3.
The end of March signals the close of the financial year.
Work to do :
1. Calculate the cost of goods sold (COGS) for each month.
2. Calculate the value of the stock at the end of each month.
3. Calculate the gross profit for each month.
4. Calculate the inventory turnover rate for a year using information from each month (January to March).
5. What advice would you give to TechnoLog to improve its inventory management?
Proposed correction:
1. CMV can be calculated as follows: CMV = (Opening inventory + Purchases) – Closing inventory
For January: CMV = [150 x €25] – €7 = €500
For February: CMV = [(150 x €25 + 100 x €28) – €7] – €500 = €9
For March: COGS = [(150 x €25 + 100 x €28 + 50 x €30) – €7 – €500] – €9 = €000
2. The value of inventory at the end of each month can be calculated as follows: Inventory Value = Opening Inventory + Purchases – COGS
For January: Stock value = [150 x €25] + €7 – €500 = €750
For February: Stock value = [150 x €25 + 100 x €28] + €7 – €500 = €1
For Mars: Stock value = [150 x €25 + 100 x €28 + 50 x €30] + €9 – €000 = €650
3. Gross profit can be calculated as follows: Gross profit = Sales – COGS
For January: Gross profit = €7 – €500 = €750
For February: Gross profit = €9 – €000 = €1
For Mars: Gross profit = €3 – €500 = €650
4. The inventory turnover ratio can be calculated as follows: Inventory turnover ratio = COGS / Average inventory value. Average inventory value = (Opening inventory + Ending inventory) / 2. Assuming that the opening inventory for the year is January and the ending inventory is March:
Turnover rate = (€750 + €1 + €400) ÷ [(€650 + €3) ÷ 000] = 13 times per year
5. For inventory management, TechnoLog should first seek to maintain optimal inventory rotation. This will minimize storage costs without compromising sales. In addition, optimal inventory rotation promotes inventory liquidity, which is beneficial financially. TechnoLog should also consider negotiating better purchase prices with its suppliers to increase its margins.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Cost of Goods Sold (COGS) | COGS = (Initial stock + Purchases) – Ending stock |
| Stock value | Inventory Value = Initial Inventory + Purchases – COGS |
| Gross profit | Gross Profit = Sales – COGS |
| Inventory turnover rate | Turnover rate = CMV / average inventory value |
Application: Gourmet Delight Company
States :
Gourmet Delight is a small business importing and distributing fine food products. They need help to manage their inventory properly to minimize their storage costs while avoiding stockouts. This month, they sold 500 bottles of Italian wine at €15 excluding VAT each. The purchasing costs per bottle are €10 excluding VAT. The storage costs per bottle are €0,50.
Work to do :
1. Calculate the unit margin for Italian wine.
2. Calculate the overall margin on wine sales.
3. Calculate the total storage cost for this month.
4. Calculate the margin rate.
5. Calculate the mark rate.
Proposed correction:
1. The unit margin is equal to the Selling Price (SPP) excluding VAT minus the Purchasing Price (PP) excluding VAT, i.e. €15 – €10 = €5.
2. The overall margin is equal to the unit margin multiplied by the quantity sold, i.e. €5 x 500 = €2.
3. The total storage cost is equal to the storage costs per bottle multiplied by the quantity sold, i.e. €0,50 x 500 = €250.
4. The margin rate is equal to ((Sale Price excluding VAT – Purchase Price excluding VAT) ÷ Purchase Price excluding VAT) x 100 or ((€15 – €10) ÷ €10) x 100 = 50%.
5. The markup rate is equal to ((Sale Price excluding VAT – Purchase Price excluding VAT) ÷ Sale Price excluding VAT) x 100 or ((€15 – €10) ÷ €15) x 100 = 33,33%.
Summary of Formulas Used:
| Formula | Description |
|---|---|
| Unit margin = Selling price excluding tax – Purchase price excluding tax | Calculates the profit made on each unit sold |
| Overall margin = Unit margin x Quantity sold | Calculates the total profit made from selling a certain quantity of products |
| Storage cost = Storage cost per bottle x Quantity sold | Calculates the total costs of storing the sold products |
| Margin rate = ((Sale Price excluding VAT – Purchase Price excluding VAT) ÷ Purchase Price excluding VAT) x 100 | Calculates the margin rate which shows the profitability of a product |
| Markup rate = ((Sale Price excluding VAT – Purchase Price excluding VAT) ÷ Sale Price excluding VAT) x 100 | Calculates the markup rate which is the percentage difference between the cost of a good or service and its selling price |
Application: Modestyle shoes sale
States :
The shoe retailer Modestyle has centralized inventory management. On January 1, the initial stock of shoes is €20.
The company carried out the following operations during the year:
– Purchases of goods: €70
– Returns of goods: €5
– Discounts obtained: €2
As of December 31, the closing stock is €15.
Work to do :
1. Calculate the company's net purchases
2. Calculate the cost of goods sold (COGS)
3. Calculate inventory turnover
4. Calculate the average inventory turnover time
5. Analyze the average stock turnover period
Proposed correction:
1. The company's net purchases are calculated by subtracting returns and discounts from gross purchases, i.e. 70 – 000 – 5 = €000.
2. The cost of goods sold is calculated by subtracting the ending inventory from the sum of the opening inventory and net purchases, i.e. 20 + 000 – 63 = €000.
3. Inventory turnover is calculated by dividing CAMV by the average of the opening and closing inventory, i.e. 68 ÷ ((000 + 20) / 000) = 15 times.
4. The average inventory turnover period is 365 ÷ 3,89 = 94 days.
5. The average inventory turnover of 94 days means that the company sells and renews its inventory on average every 94 days. This is positive since the company does not have inventory sitting idle for too long.
Summary of Formulas Used:
| Concept | Formulas |
|---|---|
| Net purchases | Gross Purchases – Returns – Discounts |
| Cost of goods sold | SI + AN – SF |
| Stock rotation | CAMV ÷ ((SI + SF) / 2) |
| Average inventory turnover time | 365 ÷ R |
Application: Enterprise TechnoGears
Summary of Formulas Used:
States :
TechnoGears is a company that buys and sells technology parts. The following data is available regarding the company's inventory for the past year:
– Initial stock: 1 units at €000 per unit
– Purchases: 5 units at €000 per unit
– Final stock: 1 units at €500 per unit
– Annual demand is 12 units
– The company works 240 days a year
– The restocking time is 10 days
Work to do :
1. Calculate the cost of the company's purchases.
2. Determine the company's consumption.
3. Calculate safety stock.
4. Calculate the average inventory.
5. Calculate inventory turnover.
Proposed correction:
1. The cost of purchases is calculated as follows:
Purchase cost = Quantity x Unit cost
That is: 5 x 000 = €32
2. The company's consumption is determined by the formula:
Initial Stock + Purchases – Final Stock = Consumption
That is: 1 + 000 – 5 = 000 units
3. Safety stock is calculated as follows:
Safety Stock = (Annual Demand / Working Days per Year) x Replenishment Lead Time
That is: (12 / 000) x 240 = 10 units
4. The average stock is calculated by:
Average Stock = (Initial Stock + Final Stock) / 2
That is: (1 + 000) / 1 = 500 units
5. Inventory turnover is calculated as follows:
Inventory turnover = Cost of sales / average inventory
Here, the cost of sales is the cost of purchase because the company sells the parts directly after purchase. So:
That is: €160 / €000 = 1 times
Summary of Formulas Used:
| Packages | Description |
|---|---|
| Purchase cost = Quantity x Unit cost | Calculates the total cost of purchases |
| Initial Stock + Purchases – Final Stock = Consumption | This formula is used to calculate the consumption of a product. |
| Safety Stock = (Annual Demand / Working Days per Year) x Replenishment Lead Time | This formula is used to calculate the safety stock required based on annual demand and replenishment lead time. |
| Average Stock = (Initial Stock + Final Stock) / 2 | Calculates the average stock over a given period |
| Inventory turnover = Cost of sales / average inventory | Indicates how many times inventory was sold and replaced during a defined period. |
Application: Electronix Company
States :
Electronix, a company specializing in the sale of electronic equipment, is concerned with good inventory management. It tries to find the right balance between maintaining a sufficient level of stock to meet customer demand and minimizing storage costs. Here are some relevant details:
– Initial stock of mobile phones: 200 units
– Purchases during the year: 800 units
– Sales during the year: 700 units
– Final stock: ?
– Cost of ownership per unit in stock: €15
– Cost of placing an order: €200
Work to do :
1. What is the ending inventory of Electronix company for mobile phones?
2. What is the total inventory carrying cost for this product?
3. What is the total cost of delivery for this product over the year?
4. What is the total cost of inventory management for this product for the year?
5. Does Electronix have effective inventory management? Justify your answer.
Proposed correction:
1. Ending Stock = Opening Stock + Purchases – Sales. Here we have ending stock = 200 + 800 – 700 = 300 units.
2. The total cost of inventory holding is calculated by multiplying the ending inventory by the carrying cost per unit. In this case, the total cost of inventory holding = 300 units * €15/unit = €4500.
3. The total cost of placing does not depend on the quantity of units, but on the number of orders placed. In the lack of information on the number of orders placed, we cannot determine this cost.
4. The total cost of inventory management is the sum of the carrying cost and the handling cost. Since we do not have the handling cost, we cannot calculate this cost.
5. Based on the available data, it appears that Electronix has a reasonable inventory management, as it maintains a level of stock that allows it to meet its sales. However, without additional information on for example the number of orders placed and other associated costs (such as selling, purchasing, storage costs, etc.), it is difficult to give a complete assessment.
Summary of Formulas Used:
| Formula used | Formula name |
|---|---|
| Final stock = Initial stock + Purchases – Sales | Calculation of final stock |
| Total Cost of Ownership = Ending Inventory x Ownership Cost per Unit | Calculating the total cost of ownership |
| Total Cost of Inventory Management = Carrying Cost + Handover Cost | Calculating the total cost of inventory management |
Application: The Golden Bakery
States :
Boulangerie Dorée, a local business, does a lot of business around pastries. The manager, Mrs. Dupont, has to deal with complex stock management. For her croissants, she has the following information: the average stock is 600 croissants, the minimum stock is 400 croissants, and the maximum stock is 800 croissants. The croissants are sold for €1,00 per unit including tax (VAT at 5,5%). The purchase cost from the supplier is €0,50 excluding tax per croissant.
Work to do :
1. Calculate the unit margin, margin rate and markup rate.
2. Calculate Safety Stock.
3. Calculate the Alert Stock.
4. Calculate inventory turnover and average inventory turnover time.
5. Evaluate the impact of a 10% increase in safety stock and stock rotation on the management of Boulangerie Dorée.
Proposed correction:
1. Unit margin = PV inc. VAT – PA excl. VAT = €1,00 – €0,50 = €0,50. Sales excl. VAT = PV inc. VAT ÷ (1 + VAT) = €1,00 ÷ (1 + 5,5 / 100) = €0,95. Margin rate = ((PV excl. VAT – PA excl. VAT) ÷ PA excl. VAT) x 100 = ((€0,95 – €0,50)÷ €0,50) x 100 = 90%. Markup rate = ((PV excl. VAT – PA excl. VAT) ÷ PV excl. VAT) x 100 = (€0,45 ÷ €0,95) x 100 = ~ 47.37%
2. Safety stock = Minimum stock = 400 croissants.
3. Alert Stock = Minimum Stock + 0.5 * (Average Stock – Minimum Stock) = 400 + 0.5 * (600 – 400) = 500 croissants.
4. Inventory Turnover = (Average Inventory / Maximum Inventory) x 365 days = (600 / 800) x 365 = ~ 274 days.
5. A 10% increase in safety stock would increase the alert stock level to 550 croissants. This would mean that Mrs. Smith would have to order earlier to avoid stockouts, which could generate additional costs for more frequent orders. In addition, a 10% increase in inventory turnover to 301 days would mean that inventory would be in the company longer, which could result in higher carrying costs and depreciation risk.
Summary of Formulas Used:
| Calculs | Packages |
|---|---|
| Unit margin | PV including tax – PA excluding tax |
| Margin rate | ((PV HT – PA HT) ÷ PA HT) x 100 |
| Brand taxes | ((PV HT – PA HT) ÷ PV HT) x 100 |
| Security stock | Minimum Stock |
| Alert stock | Minimum Stock + 0.5 * (Average Stock – Minimum Stock) |
| Stock rotation | (Average Stock / Maximum Stock) x 365 days |
Application: ElectroExpress
States :
ElectroExpress company specializes in the production and distribution of electronic equipment. One of their flagship products is the GamersEYE HD screen, whose specifications are highly appreciated by customers.
Each GamersEYE screen costs the company €700 to produce (Purchase Price excluding VAT). ElectroExpress sells each unit to its distributors for €1 excluding VAT (Sales Price excluding VAT).
The current VAT rate is 20%.
The company is keen to maintain a satisfactory level of stock to meet demand while trying to minimize storage costs. ElectroExpress estimates monthly storage costs at 2% of the acquisition cost of the GamersEYE monitor. The company sells approximately 1 monitors per month.
Work to do :
1. Calculate the overall margin over a month of sales?
2. Calculate the margin rate?
3. Calculate the markup rate?
4. What is the storage cost per screen each month?
5. What is the total storage cost for one month?
Proposed correction:
1. The overall margin is calculated by multiplying the unit margin by the quantity sold. In this case, the unit margin is €1 (Sale Price excluding VAT) – €000 (Purchase Price excluding VAT) = €700. The overall margin is therefore €300 x 300 units sold = €1.
2. The margin rate is calculated as follows: ((Sale price excluding VAT – Purchase price excluding VAT) / Purchase price excluding VAT) x 100. Therefore ((€1 – €000) / €700) x 700 = 100%.
3. The markup rate is calculated as follows: ((Sale price excluding VAT – Purchase price excluding VAT) / Sale price excluding VAT) x 100. Therefore ((€1 – €000) / €700) x 1 = 000%.
4. The storage cost per screen each month is €700 x 2% = €14.
5. To obtain the total storage cost for a month, multiply the storage cost per screen by the number of screens sold in the month: €14 x 1 = €200.
Summary of Formulas Used:
| BUILD YOUR VIRTUAL TOUR | Description |
|---|---|
| Overall margin = Unit margin x quantity sold | Allows you to calculate the overall margin made on a product. |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Allows you to calculate the margin rate on each unit sold. |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | Allows you to calculate the markup rate, i.e. the portion of each euro of sale that is due to the margin. |
| Storage cost per screen = PA excluding tax x storage cost percentage | Allows you to calculate the unit storage cost of each screen. |
| Total storage cost = Storage cost per screen x quantity sold | Allows you to calculate the total storage cost for a given period. |
Application: Natural
States :
Naturelle, is a company that produces and distributes natural cosmetic products. Over the past year, the company has kept statistics on its stock of a certain essential oil: Moisturizing. You can access the following data:
– Initial stock on January 1: 150 units
– Final stock as of December 31: 100 units
– Unit purchase price excluding tax of the oil: €20
– Quantity sold during the year: 5000 units
– A standard deviation in daily sales of: 10 units was observed
Work to do :
1. Calculate the average stock value of the Moisturizing essential oil.
2. Establish the rotation of stocks of the Moisturizing essential oil.
3. Determine the average storage life of the Moisturizing essential oil.
4. Calculate the coefficient of variation of sales of the Moisturizing essential oil.
5. Define the safety stock for the Hydrating essential oil.
Proposed correction:
1. The average stock value is calculated using the formula: VMS = ((Initial Stock + Final Stock) ÷ 2) x Unit purchase price excluding VAT. In our case, this gives VMS = ((150 + 100) ÷ 2) x 20 = €2500
2. Inventory turnover is calculated using the formula: RS = Cost of goods sold ÷ VMS. Here it gives: RS = (5000 x 20) ÷ 2500 = 40 times
3. The average storage duration is deduced by: DSM = 360 ÷ RS. For our company this gives: DSM = 360 ÷ 40 = 9 days
4. The coefficient of variation is determined by: CV = Standard deviation ÷ Mean. Here we have: CV = 10 ÷ ((5000 ÷ 360) = 0,72
5. The safety stock is calculated as follows: SS = Standard deviation x CV x ?DSM. For the Moisturizing essential oil, this gives: SS = 10 x 0,72 x ?9 = 20,52 units rounded to 21 units.
Summary of Formulas Used:
| Packages | Formula details |
|---|---|
| Average Stock Value (ASV) | VMS = ((Initial Stock + Final Stock) ÷ 2) x Unit purchase price excluding VAT |
| Stock Rotation (SR) | RS = Cost of Goods Sold ÷ VMS |
| Average Storage Duration (MSD) | DSM = 360 ÷ RS |
| Coefficient of Variation (CV) | CV = Standard Deviation ÷ Mean |
| Safety Stock (SS) | SS = Standard Deviation x CV x ?DSM |
Application: ModernTech
States :
ModerneTech is a computer hardware sales company. It offers laptops of a certain brand.
Here is some financial information regarding this line of computers:
– The unit purchase cost excluding tax of these computers from the supplier is €850.
– The company applies a margin of €200 on each computer.
– The VAT rate is 20%.
– The initial stock of computers at the beginning of January is 150 units.
– During the month of January, the company sold 100 units and received a delivery of 70 units.
Work to do :
1. Calculate the selling price excluding tax of each computer.
2. Calculate the sales price including tax of each computer.
3. Calculate margin rate and brand rate.
4. What is the stock level at the end of January?
5. What is the cost of purchasing the goods sold?
Proposed correction:
1. The selling price excluding tax is calculated by adding the margin to the purchase cost excluding tax, therefore: €850 + €200 = €1050.
2. The sales price including tax is obtained by adding VAT to the sales price excluding tax, therefore: €1050 + (€1050 x 20%) = €1050 + €210 = €1260.
3. The margin rate is calculated using the formula: ((PV HT – PA HT) ÷ PA HT) x 100 = ((1050 € – 850 €) ÷ 850 €) x 100 = 23,53%.
The markup rate is calculated using the formula: ((PV HT – PA HT) ÷ PV HT) x 100 = ((1050 € – 850 €) ÷ 1050 €) x 100 = 19%.
4. The inventory level is determined by subtracting the units sold from the initial inventory and adding the units received.
So the stock level at the end of January is: 150 units + 70 units – 100 units = 120 units.
5. The cost of purchasing goods sold is calculated by multiplying the unit purchase cost by the number of units sold, i.e.: €850 x 100 = €85.
Summary of Formulas Used:
| Formulas | Description |
|---|---|
| PV excluding tax = PA excluding tax + Margin | Sale price excluding tax |
| PV including VAT = PV excluding VAT + (PV excluding VAT x VAT rate) | Selling price including all taxes |
| Margin rate = ((PV excluding tax – PA excluding tax) ÷ PA excluding tax) x 100 | Margin rate |
| Brand rate = ((PV excluding tax – PA excluding tax) ÷ PV excluding tax) x 100 | Brand taxes |
| Final stock = Initial stock + Deliveries – Sales | Inventory management |
| Cost of purchasing goods sold = PA excluding VAT x Quantity sold | The cost of purchasing goods sold |
Application: OmegaTech
States :
OmegaTech is a company specializing in the sale of electronic and computer equipment. During 2020, the company kept the following statistics for one of its flagship products, an external hard drive:
– Initial stock as of January 1, 2020: 1500 units
– Purchases made during the year: 7000 units
– Final stock as of December 31, 2020: 800 units
– Unit purchase cost excluding tax: €50
– Selling price excluding tax: €100
The applicable VAT rate is 20%.
Work to do :
1. Calculate the consumption for the year 2020.
2. Calculate the cost of goods consumed (CAMC).
3. Determine the net turnover achieved on this item.
4. Calculate the amount of VAT collected.
5. Calculate the overall margin obtained on this item during the year 2020.
Proposed correction:
1. Consumption is calculated by taking into account the initial stock, purchases made and the stock remaining at the end of the period. It is expressed by the formula:
Consumption = Initial stock + Purchases – Final stock
Consumption = 1500 + 7000 – 800 = 7700 units
2. The cost of goods consumed (CAMC) is the total cost of purchasing the goods that the company has actually sold. It is calculated by the formula:
CAMC = Consumption x Unit purchase cost excluding tax
CAMC = 7700 x €50 = €385
3. To calculate the turnover excluding tax (CA HT), we multiply the consumption by the selling price excluding tax. This is the total income obtained by selling the company's goods or services, excluding value added tax.
CA HT = Consumption x Selling price HT
CA excluding tax = 7700 x 100 € = 770 €
4. The amount of VAT collected is calculated by applying the VAT rate to the turnover excluding VAT. This is the amount of value added tax that the company must pay to the State.
VAT collected = Net turnover x VAT rate
VAT = €770 x 000% = €20
5. The overall margin is the net turnover minus the cost of purchasing the goods consumed. It is the company's gross operating surplus (EBE), i.e. what remains once the costs of purchasing the goods sold have been deducted.
Overall margin = HT turnover – CAMC
Total margin = €770 – €000 = €385
Summary of Formulas Used:
| Indicator | Formulas |
|---|---|
| Consumption | Consumption = Initial stock + Purchases – Final stock |
| Cost of goods consumed (CAMC) | CAMC = Consumption x Unit purchase cost excluding tax |
| Net turnover (net turnover) | CA HT = Consumption x Selling price HT |
| VAT collected | VAT collected = Net turnover x VAT rate |
| Overall margin | Overall margin = HT turnover – CAMC |