Q. Compute the economic order quantity?
TNG has a current order size of 50000 units
Average number of orders per year = demand/order size = 255380/50000 = 5·11 orders
Annual ordering cost = 5·11 * 25 = $127·75
Buffer stock held = 255380 × 28/365 = 19591 units
Average inventory held = 19591 + (50000/2) = 44591 units
Annual holding cost = 44591 × 0·1 = $4459·10
Annual cost of current ordering policy = 4459·10 + 127·75 = $4587
We need to compute the economic order quantity:
EOQ = ((2 × 255380 × 25)/0·1)0·5 = 11300 units
Average number of orders per year = 255380/11300 = 22·6 orders
Annual ordering cost = 22·6 × 25 = $565·00
Average inventory held = 19591 + (11,300/2) = 25241 units
Annual holding cost = 25241 × 0·1 = $2524·10
Annual cost of EOQ ordering policy = 2524·10 + 565·00 = $3089
Saving compared to current policy = 4587 - 3089 = $1498
(c)
Annual credit purchases = 255380 × 11 = $2809180
Current payables = 2809180 × 60/365 = $461783
Payables if discount is taken = 2809180 × 20/365 = $153928
Reduction in payables = 461,783 - 153,928 = $307,855
Finance cost increase = 307855 × 0·08 = $24628
Discount gained = 2809180 × 0·01 = $28091
Net benefit of taking discount = 28091 - 24628 = $3463
The discount is monetarily acceptable.
An alternative approach is to compute the annual percentage benefit of the discount.
This is able to be done on a simple interest basis
(1/(100 - 1)) × (365/40) = 9·2%
On the other hand the equivalent annual rate can be calculated
(100/(100 - 1))365/40 - 1 = 9·6%
Both methods point out that the annual percentage benefit is greater than the current cost of short-term debt (8%) of TNG and therefore can be recommended on financial grounds.