11 Corrected exercises on inventory management

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.

The 11 corrected inventory management exercises cover storage costs, transfer costs, possession costs, calculation of alert stock, minimum stock.

Application: BeautyFlowers Cosmetics

States :

The BeautéFleurs Cosmetics company specializes in the sale of 100% natural beauty products. For the month of March 2022, the BeautéFleurs accounting department recorded the following management information for the flagship product: argan oil.
The initial stock of argan oil was 1200 bottles, the company received an order of 800 bottles and sold 1400 bottles during this month.

Work to do :

1. Calculate the ending stock of argan oil for the month of March 2022.
2. Determine the inventory turnover ratio if the average monthly consumption is 1000 bottles.
3. Calculate the average storage duration.
4. Calculate the storage cost, knowing that each bottle costs €8 and that the annual storage cost is 0,1 (10%) of the average stock cost.
5. Estimate the safety stock if it is necessary to ensure coverage of 3 days of sales, knowing that the company opens 6 days a week.

Proposed correction:

1. The final stock of argan oil for the month of March 2022 is calculated as follows:
Initial stock + Purchases – Sales = Final stock
1200 vials + 800 vials – 1400 vials = 600 vials

2. The inventory turnover ratio is calculated by the formula: Average consumption ÷ Average inventory
Average stock = (Initial stock + Final stock) ÷ 2
Average stock = (1200 vials + 600 vials) ÷ 2 = 900 vials
Inventory turnover ratio = 1000 vials ÷ 900 vials = 1,11 times

3. The average storage duration is obtained by dividing the number of days in the year (365 days) by the inventory turnover ratio:
Average storage time = 365 days ÷ 1,11 = 328,83 days, or approximately 329 days.

4. The average stock cost is 900 bottles x €8 = €7.
The storage cost is therefore €7 x 200 = €0,1.

5. Daily consumption is 1000 vials ÷ 24 days (6 days x 4 weeks) = 41,67 vials per day.
The safety stock for 3 days of sales is therefore 41,67 bottles x 3 days = 125 bottles.

Summary of Formulas Used:

Formulas	Description
Initial stock + Purchases – Sales = Final stock	Calculation of final stock
Average consumption ÷ Average stock	Inventory turnover ratio
365 days ÷ Inventory turnover ratio	Average storage duration
Average inventory cost x Annual storage cost	Storage cost
Daily consumption x Number of days	Security stock

Application: VerTech

States :

VerTech is a company specializing in the sale of electronic devices. In order to optimize its inventory management, it has carried out an inventory of its products. Here is some information on a particular item:

– Initial stock quantity (IQ): 1500 units
– Unit purchase price (PA excluding VAT): €50
– Final stock (FS): 500 units
– Supplier returns (SR): 200 units
– Goods in transit: 300 units
– Unit sale price (excluding VAT): €80

The shipping costs are borne by the VerTech company and amount to €1000 for each order placed. In addition, the company practices a margin rate of 30%.

Work to do :

1. What is the quantity of items purchased by VerTech company?
2. What is the amount of purchases excluding tax?
3. How much profit did the company make?
4. Estimate the cost of storage taking into account shipping costs.
5. Should stock be increased or decreased to optimize inventory rotation?

Proposed correction:

1. The quantity of items purchased by VerTech is obtained by the formula: (SF + RF – QI)
Here, this gives: (500 + 200 – 1500) = -800 units. Knowing that the goods in transit (300 units) have not yet been received, the quantity purchased is then -500 units.

2. The amount of purchases excluding tax is calculated using the formula: (Quantity of items purchased x PA excluding tax)
Here, this gives: -500 units x €50 = -€25000

3. The profit made by the company is obtained by the formula: ((PV HT – PA HT) x Quantity sold – Shipping costs)
Here, this gives: ((€80 – €50) x 1000 units – €1000) = €29

4. The storage cost taking into account shipping costs can be estimated by the formula: (Purchase cost + Shipping costs)
Here it gives: (-25000 € + 1000 €) = -24000 €

5. To answer this question, we need to analyze inventory turnover. The goal is to maintain optimum inventory. In this company, since the quantity of items purchased is negative, it means that the company has sold more products than it has purchased. Therefore, it would be wise to increase inventory to avoid a stockout.

Summary of Formulas Used:

Formulas	Description
(SF + RF – QI)	Quantity of items purchased
(Quantity of items purchased x PA excluding tax)	Amount of purchases excluding tax
((PV HT – PA HT) x Quantity sold – Shipping costs)	Profit made by the company
(Purchase cost + Shipping costs)	Storage cost including shipping costs

Application: The Corner Grocery Store

States :

At “L’épicerie du Coin”, a small grocery business based in Paris, inventory management is a crucial aspect of their business. The company stocks a wide variety of products, ranging from fruits and vegetables to canned goods. Each item has a different shelf life and demand, therefore, effective inventory management is essential to maximize profits and minimize losses. Recently, they have observed an increase in their storage costs as well as high levels of wastage.

The director, Mrs. Vasseur, has hired you to assess their current situation and suggest improvements. She has provided you with the following data:

The average annual stock is €15, the cost of sales is €000, the cost of purchasing goods sold is €120.

The company applies a margin rate of 30% to all products. The company has no liabilities and has a capital of €20. The VAT rate applied is 000%.

Work to do :

1. Calculate the inventory turnover rate.
2. Calculate the margin rate.
3. Calculate the mark rate.
4. Calculate the turnover excluding tax.
5. Make recommendations to improve inventory management.

Proposed correction:

1. The inventory turnover rate is calculated by dividing the cost of sales by the average inventory, i.e. (€120 ÷ €000) = 15.

2. The margin rate is calculated using the formula ((PV HT – PA HT) ÷ PA HT) x 100. Since the selling price excluding tax is already multiplied by the margin rate, we obtain (€30 ÷ €000) x 80 = 000%.

3. The mark-up rate is calculated using the formula ((PV HT – PA HT) ÷ PV HT) x 100. By replacing the values, we obtain (€30 ÷ €000) x 110 = 000%.

4. The turnover excluding tax is the cost of goods sold plus the margin, i.e. (€80 + €000) = €30.

5. To improve inventory management, the Corner Grocery Store could consider implementing an automated inventory management system to track product demand in real time and adjust inventory levels accordingly. In addition, techniques like JIT (Just-In-Time) could be useful to minimize storage costs by keeping inventory levels as low as possible while satisfying customer demand.

Summary of Formulas Used:

Spas	Formulas
Inventory turnover rate	Cost of sales ÷ Average inventory
Margin rate	((PV HT – PA HT) ÷ PA HT) x 100
Brand taxes	((PV HT – PA HT) ÷ PV HT) x 100
Turnover excluding tax	Cost of goods sold + Margin

Application: Glamour Jewelry

States :

The store "Bijoux Glamour" specializes in the sale of luxury jewelry. As part of its inventory management, here are some data for the month of September. The initial inventory of jewelry was €200. Sales made during this month are €000. The purchase cost of the goods sold is €150. Purchases made during this same month amount to €000.

Work to do :

1. Calculate the ending stock for the month of September.
2. Estimate the Cost of Goods Sold (COGS).
3. Calculate the inventory turnover rate.
4. Estimate the average storage duration.
5. Comment on the results obtained.

Proposed correction:

1. The ending stock for the month of September is calculated using the formula: Opening Stock + Purchases – Sales. Which gives: €200 + €000 – €60 = €000. The ending stock for the month of September is €150.

2. The Cost of Goods Sold (CAMV) for the month of September is given in the statement. It is €100.

3. The inventory turnover ratio is calculated using the formula: Cost of goods sold ÷ ((Opening inventory + Ending inventory) / 2). Which gives: €100 ÷ ((€000 + €200) / 000) = 110. The inventory turnover ratio for the month of September is 000.

4. The average storage duration is calculated using the formula: 365 ÷ Inventory turnover rate. Which gives: 365 ÷ 0,67 = 544,78 days. The average storage duration for the month of September is approximately 544,78 days.

5. Analyzing the results, we can say that “Glamour Jewelry” has a low inventory turnover rate, which means that the average storage period is relatively long (around 1,5 years). This could indicate that the company is having trouble selling its inventory, which can be a concern, especially for luxury products that can become obsolete or go out of fashion quickly.

Summary of Formulas Used:

Concept	Formulas
Initial Stock	Final Stock of the previous period
Final Stock	Initial Stock + Purchases – Sales
Cost of goods sold (CAMV)	(Initial Stock + Purchases) – Final Stock
Inventory turnover rate	Cost of goods sold ÷ ((Initial inventory + Final inventory) / 2)
Average storage duration	365 ÷ Inventory turnover rate

Application: Universal Prestige

States :

Prestige Universel is a company specializing in the sale of luxury products. The company manager has provided you with the following information regarding one of their popular items, the Anaconda handbag:

– The initial stock of Anaconda bags at the beginning of the year was 90 pieces.
– The company purchased 400 additional pieces during the year.
– There were 30 pieces left in stock at the end of the year.
– The cost of purchasing a piece is €200.
– The cost of each order is €50.
– The possession rate is 10%.
– The stock-out cost per unit per year is €20.

Work to do :

1. Calculate the number of items sold during the year.
2. Calculate the total cost of items sold during the year.
3. Calculate the economic order quantity.
4. Calculate the annual purchase cost.
5. Calculate the total cost of inventory management.

Proposed correction:

1. The number of items sold during the year is equal to the beginning inventory plus purchases made during the year minus the inventory remaining at the end of the year. So, Items sold = Beginning inventory + Purchases – Ending inventory = 90 + 400 – 30 = 460 items sold.

2. Total cost of items sold is the number of items sold multiplied by the unit purchase cost. So Total cost of items sold = Number of items sold x Unit purchase cost = 460 x €200 = €92.

3. The economic order quantity is calculated using the following formula: ECQ = ?( (2 x D x S) ÷ H), where D is the annual demand, S is the ordering cost and H is the carrying cost. Therefore ECQ = ?( (2 x 460 x €50) ÷ 0,10) = 96,3, approximated to 97 bags.

4. The annual purchase cost is calculated by multiplying the number of items sold by the unit purchase cost. Therefore, Annual purchase cost = Number of items sold x Unit purchase cost = 460 x 200 € = 92 €.

5. The total cost of inventory management is the sum of the annual purchase cost, the inventory carrying cost and the stockout cost. Therefore, Total inventory management cost = Annual purchase cost + Inventory carrying cost + stockout cost = €92 + (000 x €0,10) + (€92 x 000) = €20.

Summary of Formulas Used:

Items sold	= Initial stock + Purchases – Final stock
Total cost of items sold	= Number of items sold x Unit purchase cost
Economic Order Quantity (EOQ)	= ?( (2 x Annual Demand x Ordering Cost) ÷ Cost of Ownership )
Annual purchase cost	= Number of items sold x Unit purchase cost
Total cost of inventory management	= Annual purchase cost + Inventory holding cost + Stockout cost

Application: ModaChic

States :

ModaChic Fashion Boutique, located in the heart of Paris, sells designer clothing and high-end accessories. At the moment, the boutique is facing many challenges related to inventory management. We provide you with the following information:
– Initial stock of the year: 650 pieces
– Entrances (purchases): 1200 coins
– Releases (sales): 1500 pieces
– Safety stock: 100 pieces
– Average weekly consumption: 35 pieces
– Cost of placing an order: €40
– Storage cost per room per year: €5
– Number of orders placed during the year: 15

Work to do :

1. Calculate the ending stock at the end of the year.
2. Calculate the delivery time in days.
3. Calculate the average stock over a year.
4. Calculate the value of your average inventory.
5. Calculate the total cost of carrying the inventory.

Proposed correction:

1. The final stock at the end of the year is calculated as follows: Initial Stock + Entries – Exits. Therefore: 650 pieces + 1200 pieces – 1500 pieces = 350 pieces.

2. The delivery time in days is calculated as follows: (Safety stock ÷ Weekly consumption) x 7. Therefore: (100 pieces ÷ 35 pieces) x 7 = approximately 20 days.

3. The average stock during a year is calculated by adding the initial stock and the final stock then dividing by 2. Therefore: (650 pieces + 350 pieces) ÷ 2 = 500 pieces.

4. The value of your average inventory is calculated by multiplying the average inventory by the unit cost of the inventory (here, the storage cost per piece and per year). So: 500 pieces x €5 = €2500.

5. The total cost of inventory holding is calculated as follows: (Placement cost x Number of orders) + (Storage cost x Average inventory).
So: (€40 x 15 orders) + (€5 x 500 pieces) = €600 + €2500 = €3100.

Summary of Formulas Used:

Formulas	Description
Initial Stock + Inputs – Outputs = Final Stock	This formula was used to determine ModaChic's ending inventory at year-end.
(Safety stock ÷ Weekly consumption) x 7	This formula was used to calculate the delivery time in days for ModaChic.
(Sum of stocks ÷ Number of days) x 360	This formula was used to calculate the average stock during the year for ModaChic.
Average inventory x Unit inventory cost	The average inventory was multiplied by the unit cost of inventory to obtain the average inventory value.
(Placement cost x Number of orders) + (Storage cost x Average stock)	This formula was used to calculate the total cost of inventory ownership for ModaChic.

Application: Duracell Enterprise

States :

Duracell Enterprise is a battery manufacturing company. The company purchases raw materials at €8,00 per unit. Each year, the company is able to sell 250 units of its finished products at a sales price excluding tax of €000 each. Inventory costs cost the company approximately 16,00% of the unit cost per year while ordering costs are estimated at €2 per order.

Work to do :

1. What is the total annual cost of raw materials for Duracell Enterprise?
2. Calculate the annual cost of inventory management given the above information.
3. How many orders should Duracell Enterprise place each year if the optimal size of each order is 5 units?
4. What is the total cost of placing orders for Duracell Enterprise each year?
5. Calculate the total inventory management cost for Duracell Enterprise (i.e. total ordering cost + total warehousing cost).

Proposed correction:

1. The total annual cost of raw materials for Duracell Enterprise is calculated by multiplying the annual quantity sold by the cost per unit.
So the cost is 250 units x €000 = €8,00.

2. The annual inventory management cost is calculated by multiplying the total cost of raw materials by the holding cost percentage.
So the cost is €2 x 000 = €000,00.

3. The number of orders Duracell Enterprise should place each year is calculated by dividing the total quantity sold by the optimal order size.
So the number of orders is 250 units ÷ 000 units = 5 orders.

4. The total cost of orders is calculated by multiplying the number of orders by the cost per order.
So the cost is 50 orders x €500,00 = €25.

5. Total inventory management cost is the sum of total ordering cost and inventory holding cost.
Therefore, the total cost of inventory management is €25 + €000,00 = €40.

Summary of Formulas Used:

Packages	Description
CT = Q x P	Total cost of raw materials (CT) is the total quantity sold (Q) multiplied by the unit cost (P).
CC = CT x T	Inventory holding cost (ICC) is the total cost of raw materials (TC) multiplied by the inventory holding cost rate (T).
N = Q ÷ S	Number of orders (N) is the total quantity sold (Q) divided by the optimal order size (S).
PC = N x P	Total ordering cost (PC) is the number of orders (N) multiplied by the cost per order.
GSC = PC + CC	Total inventory management cost (TMC) is the sum of total ordering cost (OC) and inventory holding cost (IC).

Application: Bakery Chez Paul

States :

Chez Paul is a well-known bakery in its area. The owners would like to have access to a more robust inventory management tool in order to minimize losses and maximize their profits.

Paul recently took an inventory and found the following numbers:

– Initial stock of flour: 500 kg
– Purchases during the month: 1000 kg
– Final stock of flour: 300 kg

The cost of purchasing the flour is €2/kg.

Work to do :

1. Calculate Chez Paul’s flour consumption for the month.
2. Determine the purchase cost of the flour consumed.
3. Estimate the flour inventory turnover ratio.
4. Suppose the lead time is 10 days. What should be the safety stock?
5. If Paul wants to maintain a minimum stock level of 200 kg, should he place an order today, if so, how much?

Proposed correction:

1. Monthly consumption: Initial stock + Purchases – Final stock = 500kg + 1000kg – 300kg = 1200kg

2. Cost of flour consumed: Consumption x Unit price = 1200 kg x 2 €/kg = 2400 €

3. The inventory turnover ratio is the ratio between consumption and average inventory: Consumption / ((Initial inventory + Final inventory) ÷ 2) = 1200 kg / ((500 kg + 300 kg) ÷ 2) = approximately 3 times per month

4. Safety stock can be determined by multiplying daily consumption by lead time. Daily consumption = monthly consumption/30. Therefore, Safety stock = Daily consumption x Lead time = (1200 kg ÷ 30) x 10 days = 400 kg

5. The current stock is at 300 kg, which is higher than the minimum desired stock. So, Paul does not need to place an order today.

Summary of Formulas Used:

Packages	Explanations
Consumption = Initial stock + Purchases – Final stock	To calculate the amount of flour consumed
Cost of consumption = Consumption x Unit price	To calculate the cost of purchasing the flour consumed
Inventory turnover ratio = Consumption ÷ ((Opening inventory + Ending inventory) ÷ 2)	To estimate the number of times stock is replaced in a period
Safety stock = Daily consumption x Lead time	To calculate the stock level needed to cover the supply lead time
Order required = if (Current stock < Minimum stock) then Order = Minimum stock – Current stock	Determining the opportunity and quantity of an order

Application: Multitech

States :

Multitech is a computer hardware distributor. As the inventory manager, you are responsible for ensuring that the inventory runs smoothly. You have the following data regarding one of their flagship products, the Ultrabook laptop:

– Initial stock on January 1: 500 units
– Purchases made during the year: 3000 units
– Sales made during the year: 2800 units
– Final stock as of December 31: 700 units

Work to do :

1. How many units of the Ultrabook does the company have in stock at the beginning of the year?
2. How many units of the Ultrabook did she buy during the year?
3. How many units of the Ultrabook did it sell during the year?
4. How many units of the Ultrabook are left in stock at the end of the year?
5. What is the company's average stock level over the year?

Proposed correction:

1. The company has 500 units of the Ultrabook in stock at the beginning of the year.

2. The company purchased 3000 units of the Ultrabook during the year.

3. The company sold 2800 units of the Ultrabook during the year.

4. There are 700 units of the Ultrabook left in stock at the end of the year.

5. The average stock level is calculated on the basis of the initial stock and the final stock. Thus,
Average stock = (Initial stock + Final stock) ÷ 2
That is, Average stock = (500 units + 700 units) ÷ 2 = 600 units.

Summary of Formulas Used:

Average stock

=(Initial stock + Final stock) ÷ 2

Application: Fashion Retailers

States :

Fashion Retailers is a ready-to-wear company that needs to properly manage its inventory to maximize profitability. At the end of January, the company conducted an inventory count to obtain the following data:
– Initial stock: 600 pieces
– Final stock: 150 pieces
– Purchases of the month: 300 pieces at €50 per unit excluding tax
– Sales of the month: 750 pieces at €100 each excluding VAT

You are asked to calculate:

Work to do :

1. Cost of goods sold (CAMV)
2. The cost of the final inventory
3. The overall margin
4. The margin rate
5. The markup rate

Proposed correction:

1. The cost of goods sold (CAMV) is calculated as follows: CAMV = (opening inventory + monthly purchase) – closing inventory. Here, this gives: CAMV = (600 + 300) – 150 = 750 pieces. Multiplying by the purchase cost gives the CAMV in €: CAMV = 750 x €50 = €37.

2. The cost of the ending inventory is equal to the number of parts remaining in the inventory multiplied by the unit purchase cost: Cost of the ending inventory = ending inventory x unit purchase cost. Here, this gives: Cost of the ending inventory = 150 x €50 = €7.

3. The overall margin is obtained by subtracting the CAMV from the net turnover (excluding taxes): Overall margin = net turnover – CAMV. Here, this gives: Overall margin = (750 x €100) – €37 = €500.

4. The margin rate is calculated as follows: Margin rate = ((Sale price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100. Here, this gives: Margin rate = ((€100 – €50) ÷ €50) x 100 = 100%.

5. The markup rate is calculated as follows: Markup rate = ((Sale price excluding VAT – Purchase price excluding VAT) ÷ Sale price excluding VAT) x 100. Here, this gives: Markup rate = ((€100 – €50) ÷ €100) x 100 = 50%.

Summary of Formulas Used:

Formulas	Meaning
CAMV = (initial stock + monthly purchases) – final stock	Cost of goods sold
Cost of ending inventory = ending inventory x unit cost	Cost of ending inventory
Overall margin = net turnover – CAMV	Overall margin
Margin rate = ((Selling price excluding tax – Purchase price excluding tax) ÷ Purchase price excluding tax) x 100	Margin rate
Brand rate = ((Sales price excluding tax – Purchase price excluding tax) ÷ Sales price excluding tax) x 100	Brand taxes

Application: MegaPrices Supermarket

States :

MegaPrices is a supermarket that offers a wide variety of food and non-food products. Due to its expansion, MegaPrices is experiencing inventory management problems. Management wants to solve these problems to maximize profits and improve customer service.

A particularly problematic product is rice, for which MegaPrices has difficulty determining the quantities to order in order to optimize inventory management costs and avoid stockouts.

Unit purchase price excluding tax of rice = €1

Unit sale price excluding VAT = €1,5

The VAT rate applicable to this product is the standard rate of 20%.

The company estimates that it sells 10 bags of rice per year.

The cost of order launch is €50

The storage cost per bag of rice per year is estimated at €0,10

Work to do :

1. Calculate the margin made on each bag of rice sold.
2. Calculate the total annual cost of rice orders.
3. Determine the optimal number of bags to order using the Economic Ordering Lot (EOL) formula.
4. Calculate the annual profit generated by the sale of rice.
5. Propose an inventory management strategy to improve the profitability of the company.

Proposed correction:

1. To calculate the margin on each bag of rice sold, we use the formula: Unit margin = Selling price excluding tax – Purchase price excluding tax. That is: Unit margin = €1,5 – €1 = €0,5

2. The total annual cost of rice orders is calculated by multiplying the number of annual orders by the launch cost of each order. Consider the estimated annual sales (10 bags of rice) and the launch cost per order (€000). We obtain: Total annual cost = (50 bags ÷ LEC) x €10

3. The LEC (Economic Order Lot) corresponds to the quantity of goods that the company must order to minimize the costs related to ordering and storing the products. To obtain it, we use the Wilson formula: LEC = square root of ((2 x D x S) ÷ H) where D is the annual demand (10 bags), S is the cost of launching an order (€000), and H is the cost of storing one unit per year (€50). Therefore, the LEC is the square root of ((0,10 x 2 x €10) ÷ €000) = approximately 50 bags.

4. The annual profit generated by the sale of rice is calculated by multiplying the margin per bag by the total number of bags sold per year: Annual profit = Unit margin × Quantity sold = €0,5 × 10 = €000

5. To improve the profitability of the company, the company could consider establishing an inventory management system based on the continuous replenishment model (CRM). Using this system, the company would order a fixed number of bags of rice each time it reaches the reorder point. This could help minimize storage and ordering costs and avoid stockouts.

Summary of Formulas Used:

Packages	Explanation
Unit margin = Sales price excluding tax – Purchase price excluding tax	Calculate the margin made on each bag of rice sold.
Total annual cost = (Annual quantity of bags ÷ LEC) x Start-up cost per order	Calculates the total annual cost of rice orders.
LEC = square root of ((2 x D x S) ÷ H)	Determine the optimal number of bags to order.
Annual Profit = Unit Margin × Quantity Sold	Calculate the annual profit generated by selling rice.