Is a Quantity Discount Worthwhile? by Brian Willcox

IS A QUANTITY DISCOUNT WORTHWHILE?

by
Brian Willcox CFPIM
of
Action MRPII

It is not unusual for a buyer when asking for the price of an item, to be given a reply that the price depends on the quantity you buy. The sales representative will have a price break table, which shows for an order quantity, a unit price and the more you buy at one time, the less the unit price is. The buyer has to decide whether it is better to place an order for the larger quantity because then he is buying at a much lower unit cost. Unfortunately, if he does, he will carry that stock for some time to come and as the current inventory holding cost is as much as 35% per annum in some countries, it must be thought over with care.

There is a further factor, every time we place and process a purchase order, it costs us a considerable amount of money. This includes the cost of placing the order, goods receiving when the item arrives, incoming inspection to check the batch and of course, accounts payable. To establish what that cost is, you must add the total budget for those four departments and divide by the number of receipts for the year. In South Africa this is between R250.00 and R450.00 per receipt, depending on the organisation of the company and the procedures used.

Under normal circumstances where there is only one price for the item, the economic order quantity (EOQ) is a good guide to the correct quantity to buy at one time. This is a formula which takes the ordering cost and holding cost into account.

Which Price is Best?
The major question is, how do we calculate which price is best for the company, taking into account these two opposing costs. Although it would appear that the EOQ is the logical solution, it is not strictly so, due to the fact that it does not take into account the varying unit cost per order quantity. Remember, the more we buy, the longer we need to hold the part, or the more orders we place, the more we spend in processing the orders. The only solution is to establish the total annual cost using each price break. The first point to establish is which order quantity do we use for each price break? First we must calculate the EOQ for each unit price in the price break table. Where the maximum order quantity for a unit price is less than the EOQ, that price break should be ignored as it is going to cost more than by using the EOQ quantity. Where the EOQ falls within the order quantity range for a unit price, then we calculate the total cost using the EOQ. Where the price break order quantity range minimum is greater than the EOQ, then that minimum order quantity is used to calculate the total cost.

The Cost Elements
To establish the annual total cost, there are three elements to resolve.
The first one is the annual item cost, which is the unit cost x the annual quantity.
The second one is the annual order cost, which is the cost of one order x the number of orders placed during a year. The number of orders placed is calculated by dividing the annual quantity by the order quantity.
The third element to establish is the annual holding cost. The holding cost is the unit cost x the inventory holding cost % x the average stock holding. The average stock holding is the order quantity divided by 2.
Once these three elements are calculated, the sum of the three costs will give the total cost per annum for that item. When each of the price break total costs are compared, whichever has the lowest total cost, that is the best order quantity to use. To demonstrate this, I think it best to use an example.

Calculation Example

Given that:-

U = Annual Quantity = 9 000
I = Inventory Holding Cost = 35%
C = Item Unit Cost = see price break table
S = Ordering Cost = R150
Q = Order Quantity = * see Figure 2

Price Break Table		EOQ
1 - 275	R12,00	801
276 - 500	R10,00	878
501 -1 000	R 9,50	900
1 001 -5 000	R 9,30	910
5 001 - over	R 9,00	925

The above information shows the detail of a particular product. The price break table is supplied and along side that I have shown the EOQ for each of the unit prices for the annual quantity of 9 000.

As the EOQ is greater than the first two quantity ranges in the price break table, they are ignored. The third one, 501 to 1 000 at R9,50 each, the EOQ is 900 so is falls within that, so in that case, the EOQ will be used as the batch size.

For the following two price breaks, the EOQ is less than the price break quantity, therefore we need to use the minimum for each of those price ranges.

FIGURE 2

Total Cost Calculations
1	2	3	4	5	6	4+5+6
Min Lot Size	EOQ	Item Unit Cost	Annual Item Cost	Annual Order Cost	Annual Holding Cost	Total Cost
	Q	C	Cu	SU/Q	C IQ/2
501	900*	9,50	85 500	1 500	1 496	88 496
1 001*	910	9,30	83 700	1 349	1 629	86 678
5 001*	925	9,00	81 000	270	7 877	89 147

In Figure 2 I have shown the detailed calculation and it will be seen that for the 501 minimum batch size the EOQ is used for the order quantity and then the following two batches, the minimum lot size is used. This is indicated by the asterisk. Columns 4, 5 and 6 are the detailed calculations that need to be made and the addition of these give the total cost. It will be seen that the price break 1 001 to 5 000 is the most economical way to buy that item per year as it has the lowest annual total cost.

Practical Applications

One also has to be practical. If there was a space problem and it was a bulky item, it may not be practical to buy 1001 at a time, then we get into a trade-off position where the cost is only one of the main inputs, but other restrictions will also have to be allowed for.

Companies that have moved into the MRPII arena will have planners to determine the quantity and the required date of material. The buyer and planner need to discuss these price breaks and establish which is the better one for the company from a financial point of view. When it is agreed, the MRPII system batching rules need to be set. The system will then generate order requirements in line with the price break table to give the company the greater benefit.

Where companies set up an annual contract with a vendor, the price break table is not normally applicable. A special price has usually been organised dependent upon the annual quantity of this and other items with the planner controlling the call-off.

Now the logic of this little exercise is explained, next time the salesman comes in offering wonderful discounts, and he leaves it with you, it is a five minute job to calculate and it may save you thousands, so be careful.

March 1997

Articles coming soon in this series......

April 1997: Why doe MRP fail?
May 1997: Who needs CRP?
June 1997: Customer Service
July 1997: How often MRP?