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Chapter 8
Question 3
EOQ and discounts
A company has annual demand for its product of 50,000 units. Each unit costs
$1.50. Ordering costs are $55 per order and the annual holding cost per unit is
$1.
Calculate the EOQ.
Determine if the optimum ordering quantity would change if the supplier offered
a discount of 1% as long as at least 4,000 units were ordered each time.
EOQ = √(2 × $55 × 50,000/$1) = 2,345 units per order.
Total costs at 2,345 units (purchasing + ordering + holding costs):
50,000 × $1.50 + 50,000/2,345 × $55 + 2,345/2 × $1
$75,000 + $1,172.71 + $1,172.50 = $77,345
Total costs at 4,000 units:
50,000 × $1.50 × 99% + 50,000/4,000 × $55 + 4,000/2 × $1
$74,250 + $687.50 + $2,000 = $76,938
With the discount, the optimum ordering quantity rises to 4,000 to save $407
per year.
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