Question

Cesar Rego Computers, a Mississippi chain of computer hardware and software retail outlets, supplies both educational and commercial customers with memory and storage devices. It currently faces the following ordering decision relating to purchases of very high-density disks:

D = 36,000 disks

S = $25

H = $0.45

Purchase price = $0.85

Discount price = $0.82

Quantity needed to qualify for the discount = 6,000 disks

Should the discount be taken?

Answer 1

Given, D (Annual demand) = 36,000 disks;

S (Ordering or setup cost per order) = $25;

H (Holding cost per unit per year) = $0.45;

Purchase price = $0.85;

Discount price = $0.82 ;

Quantity needed to qualify for the discount = 6,000 disks.

Hence, the economic order quantity (EOQ) (Q) = Square root of [(2*D*S) / H]

= Square root of [(2 *(36,000) * (25)) / 0.45]

= Square root of [(1,800,000)/0.45] = 2,000 units

Now , Total cost (Holding Cost + Ordering Cost + Purchase Cost) for this quantity will be

= [Q/2 *H] + [D/Q * S] + [D *Purchase price]

= [(2,000/2) * 0.45] + [(36,000/2,000) * 25] + [36,000 * 0.85]

= ($450) + ($450) + ($30,600)

= $ 31,500

In case to buy 6,000 disks, the total cost will come to

= [Q/2 *H] + [D/Q * S] + [D *Discount price]

= [(6,000/2) * 0.45] + [(36,000/6,000) * 25] + [36,000 * 0.82]

= [$1,350] + [$150] + [$29,520]

= $31,020

As the total cost with discounted volume is less than ($31,020) the total cost at the EOQ volume ($ 31,500), Cesar Rego should take the discount. Answer is YES.