Welcome to this article aimed at helping you with exercises on inventory management with detailed corrections 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 exercises on inventory management cover storage cost, transfer cost, possession cost, alert stock calculation, minimum stock.
In this section:
TechnoPark Application
States :
TechnoPark, a company specializing in the sale of technological equipment, has recently experienced a boom in its activities. You are the financial manager of the company, and you are asked to evaluate the inventory management of a particular product, a new model of laptop.
Here is the data at your disposal:
1. Unit purchase cost excluding tax (PA excluding tax): €400
2. Unit sale price excluding VAT (PV excluding VAT): €600
3. VAT: 20%
4. Initial quantity in stock: 500 units
5. Quantity sold during the financial year: 400 units
6. Quantity remaining in stock at the end of the financial year: 100 units
7. Cost of placing an order: €100
8. Storage cost per unit per year: €10
Work to do :
1. Calculate the overall margin made during the financial year on these laptops.
2. Calculate margin rate and brand rate.
3. Estimate the average inventory level for the year and the annual storage cost.
4. What would be the total annual inventory management cost if the company decides to order the computers in two batches instead of one large order?
5. How could the company optimize its inventory management?
Proposed correction:
1. Overall margin = Unit margin x Quantity sold = (PV HT – PA HT) x Quantity sold = (€600 – €400) x 400 = €80
2. Margin rate = ((PV HT – PA HT) / PA HT) x 100 = ((600 – 400) / 400) x 100 = 50%
Mark rate = ((PV HT – PA HT) / PV HT) x 100 = ((600 – 400) / 600) x 100 = 33.33%
3. Average stock level = (Initial quantity + Final quantity) / 2 = (500 + 100) / 2 = 300 units
Annual storage cost = Storage cost x Average stock level = €10 x 300 = €3
4. The ordering cost would be doubled by ordering 2 times.
Total annualized cost = (Number of orders x Cost of placing) + Annual storage cost = (2 x 100) + 3 = €000.
5. To optimize stock management, the company can:
mechanize your inventory management system
use the Just-in-time technique which consists of ordering the goods only when they are necessary for the sale
or it could lower the cost of storage by renegotiating rates with suppliers or looking for a more economical alternative for storage.
Summary of Formulas Used:
1. Overall Margin = Unit Margin x Quantity Sold
2. Margin rate = ((PV HT – PA HT) / PA HT) x 100
3. Mark rate = ((PV HT – PA HT) / PV HT) x 100
4. Average stock level = (Initial quantity + Final quantity) ÷ 2
5. Annual storage cost = Storage cost x Average stock level
6. Total annualized cost = (Number of orders x Cost of placing) + Annual storage cost
Tech World Application
States :
The electronics company Tech World imports and sells tablet computers. In recent months, inventory management has become increasingly difficult. Here is some information on how the company currently operates:
– The best-selling tablet costs €150 (excluding VAT) and is sold at €300 (excluding VAT).
– The company sells an average of 1200 tablets per month.
– The restocking cost per order is €500.
– The storage cost per tablet per month is €2.
– Tech World would like to maintain a safety stock of 100 tablets.
Work to do :
1. Calculate the overall margin that Tech World makes each month.
2. Determine the number of orders Tech World should place each month.
3. Calculate monthly storage costs for Tech World.
4. Calculate the total monthly storage and replenishment costs for “Tech World”.
5. Calculate the margin rate and brand rate of the best-selling tablet.
Proposed correction:
1. The overall margin that “Tech World” makes each month is calculated using the formula: Overall margin = Unit margin x quantity sold. The unit margin is therefore €300 – €150 = €150. Therefore, the overall margin is €150 x 1200 = €180.
2. The number of orders Tech World should place each month is determined by the total quantity of tablets sold divided by the safety stock. Therefore, Tech World should place 1200 ÷ 100 = 12 orders each month.
3. Tech World’s monthly storage costs are calculated by taking the storage cost per tablet and multiplying it by the total number of tablets stored each month (including safety stock). Therefore, the storage costs are €2 x (1200 + 100) = €2.
4. Total monthly storage and replenishment costs for Tech World are calculated by adding storage costs and replenishment costs.
The restocking costs are €500 x 12 = €6. Therefore, the total costs are €000 + €2 = €600.
5. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) / PA HT) x 100), which gives us ((300 – 150) ÷ 150) x 100 = 100%.
The markup rate is calculated using the formula: Markup rate = ((PV HT – PA HT) / PV HT) x 100), which gives us ((300 – 150) ÷ 300) x 100 = 50%.
Summary of Formulas Used:
Overall margin = Unit margin x quantity sold
Margin rate = ((PV HT – PA HT) / PA HT) x 100
Mark rate = ((PV HT – PA HT) / PV HT) x 100
Number of orders = total quantity of tablets sold ÷ safety stock
Monthly storage costs = storage cost per tablet x total number of tablets stored each month
Total storage and replenishment costs = storage costs + replenishment costs
TechnoStore Application
States :
TechnoStore sells a variety of electronic products. The company's management is trying to improve its inventory management and is looking to you for help. Here is some financial information:
– Article: Luxor model smartphone
– Purchase price excluding tax (PA HT): €400
– Sales price excluding tax (PV HT): €800
– Initial stock at the start of the year: 500 units
– Purchases made during the year: 1500 units
– Sales made during the year: 1800 units
Work to do :
1. Calculate the overall margin made by selling Luxor smartphones.
2. Calculate the margin rate achieved through the sale of Luxor smartphones.
3. Calculate the markup rate for the sale of Luxor smartphones.
4. What is the company's inventory level at the end of the year?
5. What is the cost of goods sold (COGS)?
Proposed correction:
1. The overall margin made by selling Luxor smartphones is calculated according to the formula:
Unit margin * quantity sold.
The unit margin is the Selling Price excluding VAT (PV excluding VAT) minus the Purchase Price (PA excluding VAT).
Therefore, Unit Margin = PV HT – PA HT = €800 – €400 = €400.
Overall margin = Unit margin * quantity sold = €400 * 1800 = €720
2. The margin rate is calculated using the formula: Margin rate = ((PV HT – PA HT) / PA HT) * 100.
So, the margin rate = ((€800 – €400) / €400) * 100 = 100%.
3. The markup rate is calculated using the formula: ((PV HT – PA HT) / PV HT) * 100.
So, the markup rate = ((€800 – €400) / €800) * 100 = 50%.
4. The company's inventory level at the end of the year is calculated by subtracting the year's sales from the opening inventory plus the year's purchases.
So, Ending Stock = Beginning Stock + Purchases – Sales = 500 units + 1500 units – 1800 units = 200 units.
5. The Cost of Goods Sold (CAMV) is calculated by multiplying the number of goods sold by the unit purchase price.
So, CAMV = quantity sold * unit PA = 1800 units * €400 = €720.
Summary of Formulas Used:
– Overall margin = Unit margin * quantity sold
– Margin rate = ((PV HT – PA HT) / PA HT) * 100
– Mark rate = ((PV HT – PA HT) / PV HT) * 100
– End of year stock = Initial stock + Purchases – Sales
– Cost of Goods Sold (CAMV) = quantity sold * unit PA
ChezMarcel Application
States :
ChezMarcel, a luxury shoe retailer, is keen to optimize its inventory management, particularly for the Club Loafer shoe model which is in high demand. The following information was noted during the month-end inventory:
– Safety stock: 40 pairs
– Initial stock: 500 pairs
– Deliveries of the month: 300 pairs
– Sales of the month: 700 pairs
Work to do :
1. Determine the ending stock at the end of the month.
2. Determine the company's average inventory during the month.
3. If the company replenishes, what quantity will be required to order?
4. How many days of sales does the safety stock represent, knowing that the safety stock represents 8 days of sales.
5. Is the safety stock sufficient?
Proposed correction:
1. The formula to calculate the ending stock is: Beginning stock + Shipments – Sales. So the ending stock is 500 pairs + 300 pairs – 700 pairs = 100 pairs.
2. Average stock is calculated by: (Opening stock + Ending stock) ÷ 2. Therefore, the average stock for the month is (500 pairs + 100 pairs) ÷ 2 = 300 pairs.
3. The company wants to replenish to maintain safety stock. Therefore, the company should order: Safety stock – Ending stock, i.e. 40 pairs – 100 pairs = -60 pairs. This means that the inventory is higher than the safety stock. In this case, the company does not need to place an order.
4. If the safety stock covers 8 days' sales, then one day's sales is equivalent to: Safety stock ÷ 8, or 40 pairs ÷ 8 = 5 pairs per day.
5. The current ending stock of 100 pairs is well above our safety stock of 40 pairs. Thus, the safety stock is more than sufficient.
Summary of Formulas Used:
– Final stock = Initial stock + Deliveries – Sales
– Average stock = (Initial stock + Final stock) ÷ 2
– Quantity of items to order = Safety stock – Final stock
– Safety stock in days of sale = Safety stock ÷ Number of days
Sport-Fit application
States :
Sport-Fit is a sports equipment store. The store manager wants to keep a close eye on its inventory management. Here is some information about one of the products in stock at Sport-Fit:
– Purchase price excluding tax (PA excluding tax): €50
– Sales price excluding tax (PV HT): €80
– Initial stock quantity: 400 units
– Quantity purchased during the month: 200 units
– Quantity sold during the month: 380 units
Work to do :
1. Calculate the amount of the initial stock.
2. Calculate the amount of purchases for the month.
3. Calculate the amount of sales for the month.
4. Calculate the ending stock amount.
5. Did the stock increase or decrease during the month?
Proposed correction:
1. The initial stock amount is 400 units x €50 = €20.
2. The amount of purchases for the month is 200 units x €50 = €10.
3. The amount of sales for the month is 380 units x €80 = €30.
4. Ending inventory is calculated by adding the opening inventory and purchases, then subtracting sales. So we have 400 units + 200 units – 380 units = 220 units. The ending inventory amount is therefore 220 units x €50 = €11.
5. The stock has decreased because the amount of the ending stock (€11) is less than the amount of the beginning stock (€000).
Summary of Formulas Used:
– Initial stock amount = Initial stock quantity x PA excluding tax
– Amount of purchases for the month = Quantity purchased during the month x PA excluding tax
– Amount of sales for the month = Quantity sold during the month x PV excluding tax
– Final stock amount = (Initial stock quantity + Quantity purchased during the month – Quantity sold during the month) x PA excluding tax.
Lustre Company Application
States :
The company Lustre, specialized in the production and marketing of luxury chandeliers, wishes to optimize the management of its stocks. It calls on your expertise to analyze its current situation and propose concrete recommendations. Here is some additional information:
– She sells each chandelier for €1 excluding VAT.
– The production cost of each chandelier is €750.
– The holding costs per unit of stock, per year, are €20.
– The ordering costs are €200.
– Currently, she sells 1200 chandeliers per year.
– It uses the economic batch replenishment method which corresponds to the stock level for which the logistics costs of storage and ordering are minimized.
Work to do :
1. Calculate the company's margin rate and markup rate.
2. Calculate the economic order lot.
3. Estimate the number of orders the company needs to place each year.
4. Calculate the company's average inventory.
5. Propose recommendations to optimize the company's inventory management.
Proposed correction:
1. The margin rate is calculated using the following formula: Margin rate = ((PV HT – PA HT) / PA HT) * 100).
So, for our case: Margin rate = ((€1500 – €750) / €750) * 100) = 100%.
The markup rate is calculated using the formula: Markup rate = ((PV HT – PA HT) / PV HT) * 100). Hence: Markup rate = ((€1500 – €750) / €1500) * 100 = 50%.
2. The economic order lot is obtained using the following formula: ? ((2 x Order placement cost x Annual demand) / Holding costs). Therefore, for the company Lustre: ? ((2 x €200 x 1200 chandeliers) / €20) = 200 chandeliers.
3. The number of annual orders is obtained by dividing the annual demand by the economic order lot: 1200 chandeliers / 200 chandeliers = 6 orders.
4. The company's average stock is equal to half of the economic order lot: 200 chandeliers / 2 = 100 chandeliers.
5. To optimize its inventory management, Lustre could seek to reduce its holding costs and its ordering costs.
It could negotiate with its suppliers to obtain better prices or look for solutions to reduce its logistics costs.
Furthermore, it could consider improving its sales forecasts in order to better anticipate its inventory needs.
Summary of Formulas Used:
1. Margin rate = ((PV HT – PA HT) / PA HT) * 100.
2. Mark rate = ((PV HT – PA HT) / PV HT) * 100.
3. Economic order lot = ? ((2 x Ordering cost x Annual demand) / Holding costs).
4. Number of annual orders = Annual demand / Economic order lot.
5. Average stock = Economic order lot / 2.
Zenith Application
States :
Zenith is a distributor of electronic equipment based in Lyon. The company is experiencing several problems related to its inventory management, including frequent unavailability of key products and excessive accumulation of certain less sold items. The company is looking for new strategies to improve its inventory management.
This year, the company sold 10 units of one of its flagship products, the D000 drone. The unit purchase price of this drone is €10 excluding VAT and it is resold at €200 excluding VAT. The annual storage cost per unit is €300.
Work to do :
1. Calculate the total annual cost of storing the D10 drone.
2. Calculate the unit margin obtained on each sale of the D10 drone.
3. Calculate the overall margin made on the D10 drone in 1 year.
4. Propose and describe an inventory management optimization strategy that could be implemented by the Zenith company.
5. What is the impact of a 30% reduction in storage cost on the total annual storage cost?
Proposed correction:
1. The total annual cost of storing the D10 drone is calculated by multiplying the annual storage cost per unit by the total quantity sold. This gives us: €20 x 10 = €000.
2. The unit margin is calculated by subtracting the purchase price excluding VAT from the sale price excluding VAT. This gives us: €300 – €200 = €100.
3. The overall margin is calculated by multiplying the unit margin by the total quantity sold. This gives us: €100 x 10 = €000.
4. Zenith could opt for a just-in-time (JIT) inventory management strategy. This strategy, which emphasizes efficiency and waste reduction, seeks to acquire products at the exact moment they are needed in the production process.
By implementing such a strategy, the company can reduce its storage costs, minimize the risk of inventory obsolescence and improve its cash flow.
However, this strategy requires excellent coordination with suppliers and careful supply chain management to avoid stockouts.
5. A 30% reduction in storage costs would reduce the total annual storage cost: €200 – (€000 x 200/000) = €30.
Summary of Formulas Used:
– Total annual storage cost = Annual storage cost per unit x Total quantity sold
– Unit margin = Selling price excluding VAT – Purchase price excluding VAT
– Overall margin = Unit margin x Total quantity sold
– Total annual storage cost after reduction = Total annual storage cost – (Total annual storage cost x Reduction percentage / 100)
The Gourmet Pand Application
States :
Let's say you work for a company called Le Pand du Gourmet that sells gourmet baked goods.
The following information is available:
– The cost of a baguette is €0,70.
– Le Pand du Gourmet sells an average of 500 baguettes per day.
– The cost of placing an order for baguettes from the supplier is €50.
– The stock possession rate is estimated at 20% per year.
– The storage cost per baguette is €0,01 per day.
Work to do :
1. What is the annual purchase cost for baguettes?
2. What is the inventory carrying cost per year?
3. What is the cost of placing orders per year if the company places one order every day?
4. How much does it cost to store baguettes per year?
5. What is the total cost of maintaining baguette inventory per year?
Proposed correction:
1. The annual purchase cost for baguettes is calculated by multiplying the cost of each baguette by the number of baguettes sold per day, and then multiplying this by the number of days per year: (€0,70 x 500 baguettes/day) x 365 days/year = €127.
2. The inventory carrying cost is calculated by multiplying the annual purchase cost by the carrying rate: €127 x 750/20 = €100.
3. The cost of placing orders is calculated by multiplying the cost of placing an order by the number of days per year: €50 x 365 days/year = €18.
4. The cost of storing baguettes is calculated by multiplying the storage cost per baguette by the number of baguettes sold per day, and then multiplying this value by the number of days per year: (€0,01 x 500 baguettes/day) x 365 days/year = €1.
5. The total cost of maintaining baguette inventory is the sum of the purchase cost, the inventory holding cost, the ordering cost, and the storage cost: €127 + €750 + €25 + €550 = €18.
Summary of Formulas Used:
– Annual purchase cost = (Unit cost x Daily quantity) x Number of days per year
– Inventory carrying cost = Annual purchasing cost x Carrying rate
– Cost of placing orders = Cost of an order x Number of days per year
– Storage cost = (Storage cost per unit x Daily quantity) x Number of days per year
– Total inventory management cost = Annual purchasing cost + Inventory carrying cost + Ordering cost + Storage cost
ABC Company Application
States :
You are the CFO of ABC Company, which sells electronics. The company recently launched a new product: the ABC-X laptop. You are wondering whether the current inventory management of this product is efficient. Here is some data you have collected:
– Initial stock of ABC-X computers on January 1: 200 units
– Purchases of ABC-X computers during the year: 800 units
– Sales of ABC-X computers during the year: 750 units
– Stock of ABC-X computers as of December 31: 250 units
– Unit purchase price excluding tax of the ABC-X computer: €500
– Unit selling price excluding VAT of the ABC-X computer: €700
– VAT rate: 20%
Work to do :
1. Calculate the purchase cost of ABC-X computers sold during the year.
2. Calculate the margin made on each ABC-X computer sold.
3. Calculate the overall margin made on sales of ABC-X computers.
4. Calculate the margin rate of computer ABC-X.
5. Calculate the markup rate of the ABC-X computer.
Proposed correction:
1. The purchase cost of ABC-X computers sold during the year is equal to the quantity sold x the unit purchase price excluding VAT. This formula gives: 750 x €500 = €375.
2. The margin on each ABC-X computer sold is equal to the unit selling price excluding VAT – the unit purchase price excluding VAT. This formula gives: €700 – €500 = €200.
3. The overall margin on sales of ABC-X computers is equal to the unit margin x the quantity sold. This formula gives: €200 x 750 = €150.
4. The margin rate of the ABC-X computer is equal to ((PV HT – PA HT) / PA HT) x 100. This formula gives: ((700 € – 500 €) / 500 €) x 100 = 40%.
5. The markup rate of the ABC-X computer is equal to ((PV HT – PA HT) / PV HT) x 100. This formula gives: ((700 € – 500 €) / 700 €) x 100 = 28,57%.
Summary of Formulas Used:
– Purchase cost = Quantity sold x Unit purchase price excluding tax
– Unit margin = Unit selling price excluding VAT – Unit purchase price excluding VAT
– Overall margin = Unit margin x Quantity sold
– Margin rate = ((Unit selling price excluding VAT – Unit purchase price excluding VAT) / Unit purchase price excluding VAT) x 100
– Markup rate = ((Unit selling price excluding VAT – Unit purchase price excluding VAT) / Unit selling price excluding VAT) x 100
Beautiful Flowers Application
States :
Welcome to Belles Fleurs, a floral business located in the heart of Paris. You are the inventory manager of the company and need to perform an inventory management analysis. Currently, you have 500 bouquets of red roses in stock, each costing €5 to purchase. You sell them at a price of €15 per unit. The ordering cost (C) is €20 per order and the inventory carrying cost (P) is €0,25 per unit in stock per year.
Work to do :
1) What is the unit margin made on each bouquet of roses sold?
2) What is the margin rate on each bouquet of roses sold?
3) What is the total inventory cost for a year?
4) What is the economical quantity of orders to place to minimize storage and ordering costs?
5) What is the minimum number of orders required to be placed each year?
Proposed correction:
1) Unit margin is calculated by subtracting the purchase price (PP) from the sale price (SP) of a product. Therefore, Unit margin = SP – PPM = €15 – €5 = €10 per bouquet sold.
2) The margin rate is the ratio of this margin to the purchase price. Margin Rate = ((PV – PA) / PA) x 100 = ((€15 – €5) / €5) x 100 = 200%.
3) The total inventory cost for a year is calculated by multiplying the number of bouquets by the cost of possession: Total inventory cost = number of bouquets x cost of possession = 500 x €0,25 = €125.
4) The economic order quantity (Q) is calculated using the formula: Q = ?((2 x C x D) / P), where D is the annual demand. Here, it is assumed that demand is equivalent to stock, so D = 500.
So, Q = ?((2 x €20 x 500) / €0,25) ? 160 units.
5) The minimum number of orders needed to be placed each year is obtained by dividing the annual demand by the economic quantity of orders: Number of orders = D / Q = 500 / 160 ? 3,13, so approximately 4 orders per year (because we cannot place a fraction of an order).
Summary of Formulas Used:
– Unit margin = PV – PA
– Margin Rate = ((PV – PA) / PA) x 100
– Total inventory cost = number of bouquets x cost of possession
– Economic order quantity = ?((2 x C x D) / P)
– Number of orders = D / Q
TendanceStock Application
States :
TendanceStock, a company specializing in the sale of fashion items, has ordered a quantity of sweaters for the winter season. The unit cost of purchasing the sweaters is €20 excluding VAT. It sells them at a price of €50 excluding VAT per unit.
In order to carry out a profitability analysis and optimal management of its stocks, it uses your expertise.
We offer you the following information for this analysis:
– Quantity ordered: 500 sweaters
– VAT rate: 20%
– Storage costs for the season: €1000
– Cost of stock shortages (loss of earnings, loss of customers, etc.) estimated at €1500 per season.
Work to do :
1. Calculate the total purchase price excluding VAT of the order.
2. Calculate the total selling price excluding VAT of the goods.
3. Calculate the overall margin achieved.
4. What is the total storage cost for this season?
5. If the company sells only 80% of its inventory this season, what is the stockout cost?
Proposed correction:
1. The total purchase price excluding VAT of the order is calculated by multiplying the unit cost of a sweater by the quantity ordered. That is to say:
Total PA excluding VAT = Unit cost excluding VAT x Quantity ordered
Total PA excluding tax = €20 x 500 = €10
2. The total selling price excluding VAT (total turnover) of the goods is calculated by multiplying the unit selling price excluding VAT by the quantity ordered. That is to say:
Total PV excluding VAT (total turnover) = Unit sales price excluding VAT x Quantity ordered
Total PV excluding tax (total turnover) = €50 x 500 = €25
3. The overall margin is the difference between the total sales price excluding tax (total turnover) and the total purchase price excluding tax. That is to say:
Overall margin = total PV excluding tax (total turnover) – total PA excluding tax
Total margin = €25 – €000 = €10
4. The total storage cost for this season is €1000 (according to the statement).
5. If the company sells only 80% of its stock, it means that it has not sold 20% of its stock. The cost of the stockout is estimated at €1500 per season. This amount remains the same, regardless of the quantity sold.
So the amount of the stock-out cost is €1500.
Summary of Formulas Used:
– Total PA excluding VAT = Unit cost excluding VAT x Quantity ordered
– Total PV excluding VAT (total turnover) = Unit sales price excluding VAT x Quantity ordered
– Overall margin = total PV excluding tax – total PA excluding tax
Thank you for these details and all these calculations on inventory management which remains the most important
You're welcome.