Use the following scenario to answer the next two questions: Brady Jones is a manager at a local store that sells computers. He needs to decide how many computers to order based on the quantity discount schedule below. Annual demand is 3,000 computers, annual inventory carrying cost as a percent of unit cost is 20% (due to problems with obsolescence), and ordering costs are $10 per order.

Quantity Price per Unit ($)

1-25 475.00
26-50 445.00
51+ 420.00

Required:
What is the optimal total annual inventory cost?

The optimal total annual inventory cost is:

= $1,512,588

by ordering 51 units with each order.

Explanation:

a) Data and Calculations:

Annual demand of computers = 3,000

Annual inventory carrying cost = 20% of unit cost

Ordering costs per order = $10

Options  

Quantity  Price per Unit ($)

1-25              $475.00

26-50          $445.00

51+               $420.00

Total annual inventory cost:

With 1 = 25 units at $475,

EOQ = square root of (2 * D * Ordering cost)/Holding cost

=(2 * 3,000 * $10)/$95

= 25 units

Total inventory costs when each order is 25 units:

Unit costs = $1,425,000 (3,000 * $475)

Ordering cost = $1,200 ($10 * 3,000/25)

Holding cost = $285,000 ($1,425,000 * 20%)

Total annual inventory costs = $1,711,200

With 26 - 50 units at $445,

EOQ = square root of (2 * D * Ordering cost)/Holding cost

= (2 * 3,000 * 10)/$89

= 26 units

Total inventory costs when each order is 26 units:

Unit costs = $1,335,000 (3,000 * $445)

Ordering cost = $1,154 ($10 * 3,000/26)

Holding cost = $267,000 ($1,335,000 * 20%)

Total annual inventory costs = $1,603,154

With 51+ units at $420,

EOQ = square root of (2 * D * Ordering cost)/Holding cost

= (2 * 3,000 * 10)/$84

= 27 units

Total inventory costs when each order is 27 units:

Unit costs = $1,335,000 (3,000 * $445)

Ordering cost = $1,111 ($10 * 3,000/27)

Holding cost = $267,000 ($1,335,000 * 20%)

Total annual inventory costs = $1,603,111

Total inventory costs when each order is 51 units:

Unit costs = $1,260,000 (3,000 * $420)

Ordering cost = $588 ($10 * 3,000/51)

Holding cost = $252,000 ($1,260,000 * 20%)

Total annual inventory costs = $1,512,588

However, to take advantage of the reduced cost per unit due to discount, ordering 51 units per order minimizes the total inventory cost.

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