6. (14 points) Mac-in-the-Box sells computer equipment by mail and telephone ord
ID: 342522 • Letter: 6
Question
6. (14 points)
Mac-in-the-Box sells computer equipment by mail and telephone order. Mac sells 1,200 flat-bed scanners per year. Ordering cost is $300 and annual holding cost is 16 percent of the item's price. The scanner manufacturer offers the following price structure to Mac-in-the Box
Order Quantity Price per Unit
1 to 100 $520.00
101 to 140 $500.00
141 or more $400.00
a) Given the above information and basing your decision on a cost analysis, what order quantity do you recommend that Mac order from the scanner manufacturer? Why?
b) Provide the total inventory cost of the next best option including the acquisition cost of the scanners (calculate total cost)
Explanation / Answer
Economic Order Quantity ( EOQ) is calculated as
= Square root ( 2 x Co x D / Ch)
Where,
D = annual demand = 1200 flat bed scanners
Co = Ordering cost = $300
Ch = Annual unit holding cost = 16% of unit price
Annual unit holding cost is normally calculated as certain percentage of Unit price of item.
Therefore when unit price decreases ( as it happens with quantity discount) , Value of Ch also decreases.
With Ch being in denominator in the EOQ formula, reduction in Ch increases value of EOQ.Therefore, we can comment that all other things remaining same, reduction in unit price while applying quantity discount, increases value of EOQ
Because of applicable quantity discount, same item will have different prices for different quantity slabs and corresponding calculated value of EOQ corresponding to that quantity slab. However we have to examine whether such calculated EOQ will correspond to the quantity slab. To illustrate as per following example :
Item quantity
Price ( $/ Unit)
Annual unit holding cost , Ch ( 16% of Price $/unit)
Calculated value of EOQ ( rounded to nearest whole number0
1 – 100
520
83.2
93
101 – 140
500
80
95
141 +
400
64
106
It is evident from the above table that calculated values of EOQ do not match with their corresponding quantities in row 2 and row3. Therefore, both above are rejected as EOQ and Correct EOQ will be 93
It is to be the noted that at EOQ, total annual ordering cost plus total annual inventory holding cost is minimum .
Therefore , for the above item , total annual cost of ordering plus total annual inventory holding cost is minimum.
However quantity discount applicable on higher quantity slabs will result in reduced procurement cost vis a vis EOQ slab of 1 – 100 .Such reduction in annual procurement can probably will offset its increased annual cost of ordering and inventory holding cost . What will matter therefore is the cumulative cost for each slab which is Annual cost of procurement plus Annual cost of ordering and inventory holding cost. Refer below table:
Item quantity
Annual ordering cost (Co x D/Order quantity), $
Annual inventory holding cost ( Ch x Order quantity / 2)
Annual procurement cost ( Price/ unit x Total annual demand), S
Total cost , $
EOQ of 93
3870.96
3868.8
624,000
631739.76
101
3564.35
4040
600,000
607604.35
141
2553.19
4512
480,000
487071.19
Item quantity
Price ( $/ Unit)
Annual unit holding cost , Ch ( 16% of Price $/unit)
Calculated value of EOQ ( rounded to nearest whole number0
1 – 100
520
83.2
93
101 – 140
500
80
95
141 +
400
64
106
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