Question

1.

ABC Home Improvement Supplies, Inc. sells Ironton 72 inch digging bars. The annual demand for the digging bars is estimated to be 5000 bars. The ordering cost is $60 per order and the carrying cost is 20% of the unit price paid. Its supplier offers quantity discounts as shown in the following table

Order Quantity	Unit Price
Up to 499	$25
500 up to 999	$24
1000 and more	$23

  
If ABC is willing to pay a unit price of $25.00, determine the actual order quantity to take advantage of the quantity discounts

2.

ABC Home Improvement Supplies, Inc. sells Ironton 72 inch digging bars. The annual demand for the digging bars is estimated to be 5000 bars. The ordering cost is $60 per order and the carrying cost is 20% of the unit price paid. Its supplier offers quantity discounts as shown in the following table

Order Quantity	Unit Price
Up to 499	$25
500 up to 999	$24
1000 and more	$23

If ABC is willing to pay a unit price of $23.00, determine the total, including the purchase, carrying and ordering, cost

3.

ABC Home Improvement Supplies, Inc. sells Ironton 72 inch digging bars. The annual demand for the digging bars is estimated to be 5000 bars. The ordering cost is $60 per order and the carrying cost is 20% of the unit price paid. Its supplier offers quantity discounts as shown in the following table

Order Quantity	Unit Price
Up to 499	$25
500 up to 999	$24
1000 and more	$23

Which order quantity do you recommend to ABC so as to minimize total inventory cost?

Answer 1

1. Calculation of Order quantity to take advantage of quantity discount

Economic order quantity = Sq rt 2AB/C

A = Annual usage of inventory (units) = 5000

B = Ordering cost = $ 60 per order

C = Carrying cost per unit 20% of $25 = $5

EOQ = Sqrt (2 x 5000 x $60) / $5 = Sqrt 600000/5 = Sqrt 120000 = 346 units

2. Calculation of Total, Purchase, ordering and carrying cost

Total cost = Purchase cost + Ordering cost + carrying cost

Purchase cost = $23 x 5000 = $ 115000

Ordering Cost = $60 x (5000/1000) = $300

Carrying Cost = 20% x $23 X (1000/2) = $2300

Total Cost = $115000 + $300 + $23000 = $117600

3. Calculation of optimum order quantity to minimize Total Inventory cost

Unit req	Order Qty	Avg Stock	No of Order	Unit	Purchase Price	Carrying cost pu	Carrying Cost	Ordering cost	Total cost
A	B	C =(B/2)	D=(A/B)	Price E	(A * E) = F	(20% * F)= G	C X G) = H	(D X 60) = I	(F+H+I)
5000	346	173	15	25	125000	5	865	900	126765
5000	500	250	10	24	120000	4.8	1200	600	121800
5000	1000	500	5	23	115000	4.6	2300	300	117600

Since the Total cost for order quantity 1000 is lower and should be considered to minimize total inventory cost