Question 1 (6 points): The regular price of a DVD component is S20. On order of
ID: 368257 • Letter: Q
Question
Question 1 (6 points): The regular price of a DVD component is S20. On order of 75 units or more, the price is discounted to $18.50. On orders of 100 units or more, the discount price is $15.75. At present, Sound Business, Inc., a manufacturer of high-fidelity components, has an inventory carrying cost of 5% of unit price per nit per year, and its ordering cost is $10. Annual demand is 45 components. A. How much should Sound Business, Inc., order under different prices? B. What are the annual holding cost, annual setup cost, annual product cost and the total cost under each price?Explanation / Answer
Since annual holding cost is percentage of Unit product price, it would be different for different quantity slabs .
Given are:
Annual demand = D = 45 components
Ordering cost = Co = $10
Ch = Inventory carrying cost = 5% of price of DVD
Thus economic order quantity ( EOQ) which minimizes total annual inventory carrying cost and total annual inventory holding cost will be as per following:
EOQ = Square root ( 2 x Co x D / Ch )
Following table illustrates different values of inventory holding cost and EOQ for different quantity slabs
Quantity slab
Price of component ( $ / unit )
Ch ( 5% of unit price)
Derived EOQ ( rounded to nearest whole number )
1 – 74
20
1
30
75 – 99
18.50
0.925
31
100 and more
15.75
0.7875
34
Out of above , Derived EOQ value in row #1 only corresponds to relevant quantity slab.
Therefore , Economic Order Quantity ( EOQ ) = 30
There are following options of order size :
Total cost at EOQ = 30 :
Annual purchase cost = Unit price x Annual demand = $20 x 45 = $900
Annual ordering cost
= Ordering cost x Number of orders
= Co x Annual demand / EOQ
= 10 x 45/ 30
= $15
Annual inventory carrying cost
= Annual unit inventory holding cost x Average Inventory
= Ch x EOQ / 2
= 1 X 30/2
= $15
Hence,
Total cost = Annual purchase cost + Annual Ordering cost + Annual inventory carrying cost
= $900 + $ 15 + $ 15
= $930
Total cost at order quantity = 75:
Annual purchase cost = Unit price x Annual demand = $18.50 x 45 = $832.50
Annual ordering cost
= Ordering cost x Number of orders
= Co x Annual demand / Order quantity
= 10 x 45/ 75
= $6
Annual inventory carrying cost
= Annual unit inventory holding cost x Average Inventory
= Ch x Order quantity / 2
= 0.925 x 75/2
= $34.69
Hence,
Total cost = Annual purchase cost + Annual Ordering cost + Annual inventory carrying cost
= $832.50 + $6 + $34.69
= $ 873.19
Total cost at order quantity = 100:
Annual purchase cost = Unit price x Annual demand = $15.75 x 45 = $ 708.75
Annual ordering cost
= Ordering cost x Number of orders
= Co x Annual demand / Order quantity
= 10 x 45/ 100
= $4.5
Annual inventory carrying cost
= Annual unit inventory holding cost x Average Inventory
= Ch x Order quantity / 2
= 0.7875 x 100/2
= $39.375
Hence,
Total cost = Annual purchase cost + Annual Ordering cost + Annual inventory carrying cost
= $708.75 + $4.5 + $39.375
= $ 752.62
Quantity slab
Price of component ( $ / unit )
Ch ( 5% of unit price)
Derived EOQ ( rounded to nearest whole number )
1 – 74
20
1
30
75 – 99
18.50
0.925
31
100 and more
15.75
0.7875
34
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