# The Economic Batch Quantity Example 4 and 5

1. says

hey pls help me out wit dis ques…..A company produces 50000 units per annum has decided to use nails which cost \$10 each to purchase,the odering cost is 1.25% of purchase price per month the company has decided that the manufacture of the nails will be in house,The necessary machines has been purchased which has a capacity of 250,000 nails per annum,,,,calculate the EBQ

• says

In future please ask this sort of question in the Ask the Tutor Forum – not as a comment on a lecture.

You need to use the EBQ formula on the formula sheet.
D = 50,000; Ch = 1.25% x 10 = \$0.125; R = 250,000.
You have not typed the whole question but Co is the set-up cost each time a batch is produced.

• says

50,000/50,000 gives you 1. 50,000/500,000 gives you 0.1.
(1 – 0.1= 0.9)
(1 – 1 = 0)
1,361 x 0.9 = 1,224.9
1,224.9 x \$3 = \$3,675.
Hence, we should be worried about the zeros because we can result in the wrong answer.

• says

Of course they give different answers!!! I am not stupid!
However I got the correct answer even if I missed writing one zero in my workings. In the exam nobody looks at you workings – only the answer (because a computer marks it!)

2. says

I have trouble with a seemingly basic theory question. It goes like this:

What is the economic batch quantity used to establish?

Optimal:

1. Reorder quantity
2. Recorder level
3. Order quantity
4. Inventory level for production

The answer is no. 3 and I don’t understand what’s the difference between reorder quantity and order quantity?

• says

I don’t know where you found the question, but it is rather unfair – reorder quantity and order quantity really do mean the same thing.

• says

It was from the BPP revision kit and got me really worried. Thought they meant the same thing too!

3. says

I just watched the lecture on Economic Batch Quantity example 4 and i don’t understand how you calculated the holding cost as i get a different answer i keep getting \$1361. Please explain in detail how you got that answer.

• says

I assume that you are happy arriving at the EBQ as 2,722.

This means that the average inventory (using the formula immediately above the example in the course notes) is 2722/2 x 3(1 – 50000/500000)
Which is 1361 x 3 x 0.9 = 3675.

Did you check the answer at the back of the Course Notes?

4. says

I don’t have this section in the notes I downloaded, they jump from EOQ with discounts to the JIT system?

• says

It is on page 27 of the Paper F2 course notes.

(If you are taking F9, the the economic batch quantity is not examinable in F9)

5. says

Hi ACCA Tutors
I would like to thank you and open tuition for all your help in my studies of ACCA. Your notes, videos & help makes it easy to study.

I watched the video of example 4 where workings under square root of 2x50000x200 over 3×0.9 = 2722 units (order quantity) however when I checked it my calculator gives the following answer 2449 units.
Could you please tell me how you got 2722 units?
Thanks.

• says

I was calculating it incorrectly too. the correct calculation is..

2x50000x200= 20,000,000 and 3×0.9= 2.7

so 20,000,000 over 2.7=7,407,407,407 then find square root which equals to 2721.6

rounded off to the nearest whole number gives you 2722

Hope this helps

• says

Tamara hit the nail on the head with how to calculate that particular example.

6. says

QUESTION
A company is able to manufacture its own components for inventory at the rate of 4,000 units a week. Demand for the company is at the rate of 2,000 units a week. Set up costs for each production run is \$ 50. The cost of holding one unit of inventory is \$ 0.001 a week.
Required
Calculate the economic production run .

Q = ?((2 ???? 50 ???? 2,000)/0.001(1?2,000/4,000) ) = 20,000 units (giving an inventory cycle of 10 weeks)
MY QUESTION

What makes the production run “economic”? How is it ‘economical’ at 10 weeks and not 9 weeks for example? Please use a TABULAR form to explain.
For example
WEEK 1 WEEK 2 WEEK 3 WEEK 4 WEEK 5 WEEK 6 WEEK 7 WEEK 8 WEEK 9 WEEK 10
OPEN INV 0 2000 4000 6000 8000 10000 12000 14000 16000 18000
ORDER ?
DEMAND -2000 -2000 -2000 -2000 -2000 -2000 -2000 -2000 -2000 -2000
PRODN RATE 4000 4000 4000 4000 4000 4000 4000 4000 4000 4000
CLOS INV 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
HOLD COST ?
ORDERING COST?
I do not understand how (My Question 1) Holding cost and Ordering cost fit in this table and why ( My Question 2) the Q = 20 000 units and is a 10 week cycle and not a 5 week cycle for example. Why is 10 weeks used? Please explain

• says

Your table is wrong in that they will not be producing 4,000 units a week – that would be ridiculous since they are only selling 2,000 a week.
The question says that they are able to manufacture 4,000 a week – not that they do manufacture 4,000 a week. That is simply telling you how fast they are capable of producing (and therefore how long it will take for them to make the 2,000 that are ordered each time).

Assuming 52 weeks in a year:

The total order cost per year will always be the number of orders x set-up cost each time.
This is: (Demand per year)/(order quantity) x (cost each time)
At an order quantity of 20,000, this comes to ((52 x 2,000) / 20,000 ) x \$50 = \$260 per year

The total holding cost per year will always be average inventory x cost of holding 1 unit for 1 year
This is: ((order quantity) / 2) x (1 – Demand/Production rate) x holding cost per unit per year
At an order quantity of 20,000, this comes to (20,000 / 2) x (1 – 2,000/4,000) x (52 x 0.001) = \$260 per year

So the total cost per year is \$260 + \$260 = \$520 per annum

Try any other order quantity you like and the total cost will be great than \$520 – that is why 20,000 is the economic batch quantity (i.e. the cheapest total cost per year).

Since best is to order 20,000 each time and they are selling 2,000 each week, it means that they will be placing an order every 10 weeks. (If they placed an order every 5 weeks then they would be ordering far more than they were selling which would be stupid – in total they are only selling 2,000 every week (i.e. 104,000 a year) and so they will only be ordering 104,000 a year in total.

I have no intention of producing a table – I told you before that it cannot be asked for and is wasting time.

If you want to then fine. On Day 1, an order will be placed for 20,000 units. It will take 5 weeks for all 20,000 to arrive (because the rate of production is 4,000 a week). During those 5 weeks, they will have sold 10,000 units (because they sell 2,000 a week and they are continuing to sell while the order is being delivered). So the maximum inventory level is 20,000 – 10,000 = 10,000. After a further 5 weeks the inventory will have fallen to zero (again because they are selling 2,000 a week). Then a new order is placed and the cycle repeats itself.
So…..the level of inventory is fluctuating between 10000 (maximum) and 0 (minimum) and is therefore on average 5,000 units throughout the year. At \$0.001 per unit per week, this means that the holding cost over the year is 5,000 x 52 x \$0.001 = \$260 per year (as above).

Since the total demand is 52 x 2,000 = 104,000 per year, and since they are ordering 20,000 each time, they will place 104,000 / 20,000 = 5.2 orders a year and so the total set-up cost is 5.2 x \$50 per year = \$260 per year (as above).

( Before you ask (although this is also dealt with in my lecture), they will actually place 6 order in the first year, but have inventory remaining and so only need 5 orders the second year, and so on. We always assume it to be a long-term policy and therefore on average there will be 5.2 orders a year.)

• says

Thank you so much. The 4000 being able to manufacture, but doesn’t manufacture, answers my questions. Only thing though, the reason I’ve asked for a table is because I’m trying to understand the logic of the EQB formula. If you didn’t have the formula, how would you calculate (get to) 20 000 being the economic order qty? Sorry if this is a stupid question, but I’m obviously missing something somewhere.

• says

In the exam, you will have the formula

However, the only other way you could do it (apart from deriving the formula – but that involves differentiating which is not in the syllabus for any ACCA exams), would be to calculate the total cost per year for several different order quantities. (In exactly the same way as in my previous answer – doing it (for example) for order quantities of 5,000, 10,000, 15,000, 20,000, 25000, etc.). Then you could plot them on a graph – total cost on the vertical axis and order quantity on the horizontal axis. You would find that you got a curve and you could then read off from the graph the order quantity that gave minimum total cost.

But…..you cannot be asked to do this in the exam. You will be given the formula.

• says

I was hoping you would say that lol Thank you so much. It was in one of the EOQ tables where I couldn’t understand where the different Order quantities had suddenly come from / have been calculated that confused me which you have now cleared up. I also understand the EQB better now. Thank you so much.

• says

A last question on EBQ please – if the rate of production is 50 units a day and the order quantity is a 100. Is the production run 50 or 100? I’m assuming the ‘inventory cycle’ would be the qty ordered?

• says

The production run is 100 units. Every time an order is placed for 100 units, a production run takes place and that many will be produced (and at the rate of 50 a day, it will take 2 days to produce them).

The inventory cycle depends on how many they are selling per day. For example, if they order 100 each time and they are selling 10 units a day, then the inventory cycle is 100/10 = 10 days. (They will place an order every 10 days)

7. says

I do not see the ebq formula or the example 4 and 5 in the course notes. Where can I find this?

• says

The examples are on pages 27 and 28 of our course notes.

The formulae are given on the formula sheet that is given in the exam – the formula sheet is printed on one of the first few pages of our course notes.

8. says

Chapter 5, Test question 2, the answer is D. Could you please explain why? As per my understanding, the impact on EOQ should be “lower”, but on Annual holding cost should be “Higher”.

• says

If the order quantity is lower, then the average inventory will be lower as well (average inventory = order quantity / 2).

If the average inventory is lower, then the cost of holding it per annum will be lower also.

9. says

Hi.

To day I was doing the EBQ formula and visualizing how it can get to our real day to day activities, so in my finding I realized(if i am not wrong that this formula is just a modification of the EOQ) and that it is intended only when resupply is gradual instead of quickly so later while I was reviewing the “revision notes for this paper in F2″ I found out that i can be used even when the average order quantity is half of the quantity ordered as shown in the working, but in my previous comprehension to this, was that the EBQ’s average quantity is (Q-QD/R), but referring to the revision kit under Page 9 of the revision notes ,Example of stock control- the working is just like EOQ, so could you please undoubt me the two so that the usage of both of them can be straight forward??????????

• says

The EOQ formula and the EBQ formula are exactly the same, except that (as you say) EOQ assumes that we get delivery of all units at once, whereas EBQ assumes that the units ordered arrive gradually because we are making them ourselves (as you state).

With EOQ, because all the units arrive at once, the average inventory will be the order quantity divided by 2.

With EBQ, because we are selling units during the time that the units are arriving, the maximum inventory will not be the order quantity and so the average inventory will be a little lower – it will be (order quantity x (1 – D/R)) divided by 2.

Have you watched the main lecture on this, because I explain this in slightly more detail?

10. says

A company uses 5000 units of a component per anum. ordering cost is \$36. holding cost of one unit of component is \$4 What is the e.o.q for that component, assuming 52 weeks year, what is the average frequency at which purchase orders should be placed? plz help me on this question

• says

I am not sure why you have a problem with the EOQ – you simply stick the figures in the formula.
D = 5,000; Co = 36; and Ch = 4. So the EOQ is 300 units.

As far as the frequency of orders is concerned, since they use 5000 units a year and order 300 each time, it means that they place 5000/300 = 16.67 orders a year. With 52 weeks in a year, this means that they place an order every 52/16.67 = 3.12 weeks on average.

• says

I’m also struggling with this! How can a company or anyone make .67 of an order? Do they make the other .33 next year? Would it be right to say “either 16 or 17″ or even “50 in a three year period”?

• says

In some years they will place 17 orders and in some years 16 orders. On average it will be 16.66 orders are year.

This question was actual asking for the average frequency of orders which is every 3.12 weeks – this itself implies that some years will have 17 orders and some years 16.

• says

EOQ calculations are in the syllabus for Paper F9 and do get asked. However, examples 4 and 5 are not asked in F9.

• says

what does R stands for ?

• says

tengku: Have you watched the lecture? R in the formula on the formula sheet is the rate of production (the number of units that they are capable of producing per year).

11. says

I watched this video after clicking on a link under the “F9 lectures” list. However, I can’t see the EBQ formula or anything relating to it in my BPP text book, nor can I find the relevant examples in the Open Tuition F9 notes. Therefore, is this video relavant to F9? Thanks!

• says

In theory EBQ could be asked in F9 (as assumed knowledge from F2) but it never has been (and probably never will – the formula is not given for EBQ in F9, only the EOQ formula).

However, everything else in inventory control from F2 has been asked in F9 (EOQ and discounts), and certainly will be asked again

12. says

i am writing the june 2013 exams and i have not studied at all. pls can anyone advise on the best way to study and pass this f2 and f3 with such short notice. i have a very tight schedule and i dont have any accounting background and i have tried viewing the lectures but it does not open . pls help….
thanks

13. says

Thank you Opentuition, special thanks to johnmoffat. You are a Great lecturer May God Bless you.

14. says

Dear Sir
I have been through the luctures on inventory and you explained evrything so simple.However I am a bit confused with ordering cost.Is it always fixed(for every batch we used the same ordering cost).If so how it applies in real life circumstances?

• says

In F2 it is always a fixed amount per order.

It is not realistic in real life because since the most likely order cost relates to delivery then the delivery charge is likely to change depending on the quantity ordered.

(In practice, if the delivery cost was something like “\$0.10 per unit + a standing charge of \$10 per order” then in fact we could deal with it. In total over the year the variable cost would be fixed (number of units ordered over the year x \$0.10) and could therefore be ignored in the formula. All we would put in the formula would be the \$10 because the total over the year would vary with the number of orders. However, for F2, there is no need to worry about that )