A company uses an item of inventory as follows.
Purchase price
$25 per unit
Annual demand
1,800 units
Ordering cost
$32
Annual holding cost
$4.5 per unit
EOQ
160 units
What is the minimum total cost assuming a discount of 2% given on orders of 300 and over?
The correct answer is: $44,953.50
Please note that the holding cost is fluctuated by the purchase price.
The company could order the EOQ amount of 160 or it could order 300 units and take a discount of 2%. We need to work out which is the cheapest option.
Purchases (no discount)
1,800 x $25
Holding costs (W1)
Ordering costs (W2)
Total annual costs
Workings
(1)
Holding costs
= average inventory x holding cost for one unit of inventory for one year
Average inventory
= order quantity/2
= 160/2
= 80 units
Holding cost for one unit of inventory for one year
= $4.50
holding costs
= 80 units x $4.50
= $360
(2)
Ordering costs
= number of orders x ordering costs per order ($32)
Number of orders
= Annual demand/order quantity
= 1,800/160
= 11.25 orders
ordering cost
= 11.25 orders x $32
With a discount of 2% and an order quantity of 300 units, unit costs are as follows.
Purchases
$45,000 x 98%
= 300/2
= 150 units
= $4.50 x 98%
= $4.41
= 150 units x $4.41
= $661.50
= 1,800/300
= 6 orders
= 6 orders x $32
= $192
The cheapest option is to order 300 at a time and accept the discount.
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