Other Topics in Working Capital Management

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• Chapter 23 - III
• Other Topics in Working Capital Management

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ECONOMIC ORDERING QUANTITY (EOQ) MODEL

• The EOQ model assumes that sales are steady and
  predictable
• Lead time on inventory shipments are steady and
  predictable
• Same as the Baumol cash model, just applied to
  holding inventory instead of holding cash.

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If Q is the size of each order (in units), then
the average inventory is Q/2
Order Size (Q)
Q/2
0 1 2 3 4 5 6 7 8
9 10 11 12 weeks
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• Terms
• F fixed cost per order
• S annual sales in units
• C cost (as a of sales price) to
• carry a unit in inventory for a year
• P purchase cost of a unit of inv
• Q inventory order size
• EOQ optimal inventory order size

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• TIC Carrying Costs Ordering Costs

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• Consider this firm
• - annual sales are 30,000 phones
• - cost to carry a phone in inventory for a year
  is 25 of its cost
• - purchase cost per phone is 10
• - fixed cost to place an order is 200
• If our order size (Q) is 1,000 phones, what are
  our total inventory costs?

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Determining EOQ

Total Inventory Costs (TIC)
Total Carrying Costs (TCC)
Total Ordering Cost (TOC)
0 EOQ Order Size (units)
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• Ideally, we want to operate on the lowest point
  (minimum cost)
• What is the formula for that minimum point?

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• Based on the EOQ model, what is the optimal order
  size?
• EOQ 2(F)(S)/(C)(P)0.5
• What are the total inventory costs if we use the
  optimal order size?

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In-Class Exercise

• - annual sales are 10,000 PCs
• - cost to carry a PC in inventory for a year is
  50 of its cost
• - purchase cost per PC is 400
• - fixed cost to place an order is 150
• If our order size (Q) is 1,000 PCs, what are our
  total inventory costs?

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• Based on the EOQ model, what is the optimal order
  size?
• What are the total inventory costs if we use the
  optimal order size?

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• If the company makes infrequent and larger
  orders, carrying costs will be excessive. These
  include
• storage
• handling
• property taxes
• insurance
• depreciation obsolescence
• interest expense

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• If the company makes frequent and small orders,
  ordering costs will be excessive. These include
• cost to place an order
• set-up costs for production runs
• fixed portion of shipping, handling
• lost sales lost customer goodwill
• disruption of production

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EOQ MODEL EXTENSIONSQuantity Discounts

• Assume that a 3 discount is offered on orders of
  at least 3,000 phones.
• - What is the purchase cost per phone?
• - What is the total inventory cost?
• - What is the discount savings?

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In-Class Exercise

• If a 1 discount is offered on orders of at least
  5,000 phones
• - What is the purchase cost per phone?
• - What is the total inventory cost?
• - What is the discount savings?
• - Should the firm change to an order size of
  5000 phones?

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Order Point

• Assume shipment takes 2.6 weeks.
• How many phones are sold each week?

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• How many phones are used during the shipment
  period?
• If we want a zero safety stock, what is our order
  point?

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• What is our order point if we want a safety stock
  of 500 phones?
• What is our total inventory cost with the EOQ
  order size and a 500-phone safety stock?

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In-Class Exercise

• Assume shipment takes 1 week.
• - What is the inventory level when there is 1
  week of inventory in stock?
• - With a zero safety stock, what is the order
  point?
• - What is the order point if we want a safety
  stock of 200 phones?

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• - What is our total inventory cost with the EOQ
  order size and a 200-phone safety stock?

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Safety Stocks

• A higher safety stock of inventory
• gives room for a faster sales rate than predicted
  (in the event that sales unexpectedly pick up)
• allows for some unexpected delay in shipping (due
  to weather, supplier production problems, etc.)
• but, safety stocks increase carrying costs
  (higher average inventory)

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• So far, we assumed a safety stock of zero or a
  given safety stock.
• Now, we need to determine the optimal level of
  the safety stock.
• Safety stocks should be increased as long as the
  additional expected profit covers the additional
  carrying costs.

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• Assume sales during the 2.6-week shipment time
  are now uncertain, as follows
• Probability Unit Sales
• .2 1000 phones
• .6 1500 phones
• .2 2000 phones

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• What is the average time between orders (i.e.,
  the inventory cycle)?

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• What is the cost to carry one phone in inventory
  for an inventory cycle?

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• If the selling price of each phone is 15, how
  much profit is lost when you lose a sale?
  (Recall that the cost to produce a phone is 10.)

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Recall order size 1500 phones

• Safety Lost
• Stock Prob. Sales Shortage Profit
• 200 .2 1000 ? ?
• .6 1500 ? ?
• .2 2000 ? ?
• 400 .2 1000 ? ?
• .6 1500 ? ?
• .2 2000 ? ?

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• Safety Expected Carry
  Total
• Stock Lost Profit Cost
  Cost
• 200 ? ? ?
• 400 ? ? ?
• Which safety stock level is expected to produce
  the lower total cost?

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In-Class Exercise

• Re-work the analysis assuming a 4 week shipping
  time, a 300 phone safety stock, and the following
  sales possibilities during the 4-week shipment
  time
• Probability Unit Sales
• .2 1500 phones
• .6 2250 phones
• .2 3000 phones

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Inflation

• Would an increase in inflation cause carrying
  costs to be greater or smaller?
• Because inflation increases the value of
  inventory held over time, it reduces the carrying
  costs of inventory.

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• If inflation in inventory values were expected to
  be 5 in our example, then C would be changed
  from 15 to 10.
• This causes the EOQ to be higher.

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Final Notes

• Are total inventory costs sensitive to changes in
  the order size?
• Not much. The TIC changes very little over a
  fairly wide range of order sizes (i.e., it is
  shaped more like a saucer than a V)
• Consequently, the EOQ should be better thought of
  as a range than a single point.