Question

Bagley Bags is trying to determine its optimal inventory policy.

Answer the questions – show all work.

The following relationships and conditions exist for the firm:

1. Annual sales are 120,000 units - assume a 360-day year
2. Purchase price is $500 per unit
3. Carrying costs are 20% of inventory value
4. Order costs, per order, are $600
5. Optimal safety stock of 500 units is currently in the company’s inventory

1. What is the Economic Order Quantity?

2. What is the company’s annual Total Inventory Costs?
3. How often will the company reorder?
4. What is the purpose of safety stock?

Answer 1

Annual Sales = 120,000 units | Purchase Price = $500 | Carrying Cost = 20% of inventory value |

Order costs per order = $600 | Safety Stock = 500 units

Economic Order Quatity Formula = ((2 * Annual Demand * Cost per order) / Holding Cost)^1/2

Holding Cost per unit = Carrying cost as Percentage of Inventory Value * Purchase Price = 20% * 500 = $100

Annual Demand = Annual Sales = 120,000 | Cost per order = $600

Putting all the values in the formula

Economic Order Quatity = ((2 * 120,000 * 600) / 100)^1/2 = (240,000 * 6)^1/2 = (1,440,000)^1/2

Economic Order Quatity = 1,200 Units

Now using the Economic Order Quantity which becomes our Lot size, we can calculateTotal Annual Inventory cost

Total Annual Inventory cost = Annual Ordering costs + Annual Holding costs

Annual Order costs = (Annual Demand / Order Quatity)*Order costs per order

We will use EOQ as Order Quatity to find the optimal Inventory cost

Annual Order costs = (120,000 / 1,200) * 600 = 100 * 600 = $60,000

Annual Holding costs = (Order Quatity / 2) * Holding cost per unit

Annual Holding costs = (1,200 / 2) * 100 = $60,000

Putting Annual order costs and holding costs in Total Annual Inventory cost formula

Total Annual Inventory cost = 60,000 + 60,000

Total Annual Inventory cost = $120,000

Reorder Point Formula = Daily Demand * Lead Time + Safety Stock

As Lead time is not given, Assuming it to be 1.

Reorder Point is now sum of Daily Demand and Safety Stock

Reorder point = Annual Demand / 360 + Safety stock = 120000 / 360 + 500 = 333.33 + 500 = 833.33 or 833

As soon as Inventory level reaches 833, the company will reorder.

Safety Stocks are the extra inventory maintained to avoid stockouts and loss of sales. Safety stocks are an attempt to mitigate risks of an uncertainity in supply chain and demand.