[I'm, Ron Burgundy?]

I am stumped on how they are coming up with this one. Please someone help to explain this. Thank you in advance:

Question:

A company sells 1,500 units of a particular item each year and orders the items in equal quantities of 500 units at a price of $5 per unit. No safety stocks are held. If the company had a cost of capital of 12%, its annual cost of carrying inventory is:

Answer: $150

Calculated as follows: Average inventory level x Unit Cost x Cost of Capital

(500/2) x 5 x .12

How is it that they are coming up with the Average inventory level of 250?

"If you're going through hell, keep going"
- Winston Churchill

"I've missed over 9,000 shots in my career. I've lost over 300 games. 26 times I've been trusted to take the game winning shot, and missed. I've failed, over and over and over again in my life. And that is why, I succeed."
- Michael Jordan

BEC: (54), (72), 80 (losing credit on 02/02/15 - nervous)
AUD: 78
REG: (74), 91
FAR: (71)

[Anonymous]

Hmm, the only way I can come up with an explantion is the fact that they order every 500 units so…

January 1st, 20XX –> 500 Units

4 months later…

April 30th, 20XX –> 0 Units

500 + 0 / 2 = 250 average.

Let me know if that helps!

[pnielsen1982]

This is an Operations Management concept.

Carrying cost per year = iCQ/2

Where i = carrying rate, percentage of dollar value per year

C = unit cost, dollars per unit

Q = lot size, units

Q/2 = average inventory

So, in the example you're looking at, you'd have:

(.12)*(5)*(500/2) = 150

CA licensed CPA

AUD - 08/31/13 - 84
BEC - 11/26/13 - 84
FAR - 08/10/14 - 85
REG - 11/30/14 - 72, 02/20/15 - 87

What have I gotten myself into?

[I'm, Ron Burgundy?]

I appreciate both responses. However, this still makes no sense to me. All I really need to understand is how they are coming up with the 500/2? How is the average inventory amount 250? If they are ordering every 500 units and the amount of sales is 1500 units per year, why would they not make 3 orders per year?

I'm still missing something here.

"If you're going through hell, keep going"
- Winston Churchill

"I've missed over 9,000 shots in my career. I've lost over 300 games. 26 times I've been trusted to take the game winning shot, and missed. I've failed, over and over and over again in my life. And that is why, I succeed."
- Michael Jordan

BEC: (54), (72), 80 (losing credit on 02/02/15 - nervous)
AUD: 78
REG: (74), 91
FAR: (71)

[Anonymous]

Hmm, let me try to re-phrase my explanation.

The period here is 4 months. Based on the fact patter, the company orders 500 units every four months which is three order for the year in total like you said.

(1500 Units Per Year / 500 Unit Orders = 3 Orders Per Year, 12 months/ 3 orders = an order every 4 months.)

Average Inventory = (Beginning Inventory for the Period + Ending Inventory for the Period) / 2

(500 + 0) / 2 = 250

Every period will start with 500 units and every period will end with 0 units. Think of it like a guy has selling cans of soup. He has 500 cans slowly getting to zero at the end of the fourth month then he gets more from Shop-rite on the last day of the period. On average he has 250 on hand.

[Author]

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