Example of Quantity Discounts
Consider illustration one and suppose that a quantity discount of 5 percent is given whether a minimum 200 units is ordered.
Required
Find out whether the discount should be in used and the quantity to be ordered.
Suggested Solution
We require considering the saving in purchase costs; savings in ordering costs and rise in holding costs.
Savings in purchase price:
New purchase price = 50 x 95% = Sh.47.50 per unit
Savings in purchase price per unit = 50 - 47.50
= Sh.2.50
Total units per year = 2,000
Total savings = 2,000 x 2.50
= Sh.5,000
Savings in Ordering Cost
Assuming an order quantity of 200 units per order, the total ordering cost will be:
= (2,000/100) * 50
= Sh.500
Ordering cost if 100 units is ordered
(2,000/100) * 100
= Sh.1, 000
Consequently savings in ordering costs = 1,000 - 500 = Sh.500
Increase in holding costs
Holding cost if 200 units are ordered
½(200)19.75 = Sh.1, 975
Holding costs if 100 units are ordered
½(100(20) = Sh.1, 000
Increase in holding costs = 1,975 - 1,000 = Sh.975
The Net Effect therefore:
Shs.
Savings in purchases costs 5,000
Savings in ordering costs 500
Total savings 5,500
Less increase in holding costs 975
Net savings 4,525
C_{n} = 15 + 10% x 4.75 = Shs.19.75
The discount should be taken because the net savings is positive. To determine the number of units to order we recomputed Q with discount Q_{d}.
= 100.6 units
Decision rule:
Order the minimum discount quantity if Q_{d} < minimum discount quantity.
Order Q_{d }if Q_{d} < minimum discount quantity.