Looking to see if you all agree with my thinking here.
Let’s take inventory turnover as an example. From the CFA curriculum:
“Because cost of goods sold measures the cost of inventory that has been sold, [the inventory turnover] ratio measures how many times per year the entire inventory was theoretically turned over, or sold. (We say that the entire inventory was “theoretically” sold because in practice companies do not generally sell out their entire inventory.)” My contention : inventory turnover doesn’t even tell you “theoretically” how many times the entire inventory was turned over. A simple example will make this clear: Suppose you purchase $5 of inventory and then sell it in even installments over the course of 3 months. You then do the same thing for the subsequent 3 months (ie, add $5 to inventory and then gradually sell it down to zero). You do this a total of 4 times in the year. That is, you turn over your inventory (going from $5 to zero) four times in the year. Contrast that with what you’d calculate using the inventory turnover formula. For COGS, you’d have $20 and it’s pretty obvious that $5 --> $0 in even installments implies average inventory of $2.50. But that suggests that you turned over your inventory 8 ($20/$2.50) times, not 4. So even in a highly stylized example where we do in fact run inventory down to zero before restocking, the inventory turnover calculation doesn’t actually show how many times we turned inventory. Now, if we were to change the definition so that as our denominator we used beginning period inventory ($5 in my example) the calculation’s output would match reality. And this seems to make more intuitive sense; in effect, you’re saying “I started the year with $5 in inventory and then generated $20 of sales over the year, so I cycled my inventory 4 times.” Maybe we use average inventory in the denominator to smooth out the impact of any outliers (say, for example, we randomly began the year with much higher than usual inventory for some reason)? In other words, we’re taking average inventory to be a “normalized” beginning inventory. What do you guys/gals think?
The easiest way to calculate the average inventory is to do the average of (beginning inventory + ending inventory). I guess that’s also the best estimate you can get using financial statements.
In your example, imagine you calculate the average inventory based on daily data > you should get something close to 2.5, not 5.
If your average inventory is 2.5, and you sell 20 a year, that’s the equivalent of selling your average inventory 8 times. That’s just what the inventory ratio’s telling you. Nothing more. Don’t overthink it.
Calculated turnover ratios are always theoretical ratios. In your example you have an exact turnover of 4 using 4 endpoints.
An outside analyst without access to the enterprise resource system (ERP) however has only 2 endpoints. The assumption he takes in calculating turnover ratios from the balance sheet is that the inventory is turned over on a linear basis between the two endpoints. Try to sketch it: In your “real world” example you’ll have a graph with 4 spikes with a value of 5 at the beginning of each quarter and a 0 at the end of each quarter. The best estimate an outsider however can make is that between the beginning and the end of the year the inventory flow is linear from 5-0 over the 12 month. That’s basically the reason for the difference.
Note that the calculated ratios by an outside analyst will never match the real turnover of the company. That’s just because an analyst does not have any insides in the real daily flow of the inventory. In the end if you compare different companies that does not matter, because you always assume linear inventory consumption across all analyzed companies. Best,
Let’s change your condition slightly: suppose, you buy your $5 goods at the end of each quarter and then sell it over the nex three months. The starting point inventory is $5, the ending point inventory is the same $5, so the average throughout the year is $5. Thus you come to the inventory turnover ratio to be $20 / $5 = 4, and it fully complies with your reality.
I believe it’s impossible to always get a true figure from a statement, so averaging gives us just an approximation to reality. In your case the approximation is not so perfect, while in my case it is. On average, we’re both close.
@Kotausi_77: there is indeed a range of alternatives for calculating the average, which results from the fact that you can assume purchases occur at different points relative to your start/end points. So, you could just as easily assume that purchases occur in the exact middle of any given 3-month period, so that you’d begin/end each 3-month period with $2.50 worth of inventory. You could also envision a scenario where you use ending inventory to derive the average and, because in my example ending inventory is assumed to be $0, you’d have an average inventory of $0!
The “point” here (as it were) is that any such approach of using the average inventory–aside from when average inventory = beginning inventory of $5–will lead to an overstatement of the number of inventory turns as compared to the actual number of turns, per my stylized example.
Based on this, I think that if the curriculum’s author insists on saying that inventory turnover “theoretically” generates the number of inventory turns in a period, he should also say that we use average inventory as an approximation for beginning inventory–what we might call “normalized” beginning inventory. That’s really all I wanted to get across.
Totally agree with this, that because you apply this metric consistently across various companies my pedantic point doesn’t really matter. But my argument/issue here isn’t about the application of the metric. It’s about how it’s described by the author.
I think that you’re fixating on beginning inventory, according it more significance than ending inventory, or average inventory, or mid-year inventory, and certainly according it more significance than it is due.
The income statement covers a period of time, usually one year. The balance sheet covers an instant in time. One instant in time is no more important inherently than another. Using the average of beginning and ending inventory tries to approximate the actual average level of inventory throughout the period of time covered by the income statement, and it is that actual average level of inventory that is turned over (some number of times). If you wanted to be perfectly accurate, you’d have to integrate the inventory level throughout the period and compute the average inventory level from that; inasmuch as the average accountant or CFA candidate isn’t quite that adept at integral calculus, we choose a simple average of the beginning and ending levels. It’s an imperfect approximation, but the theoretical turnover is sound.
Did you follow my example? You know, where you “theoretically” sell down your entire inventory before restocking? In that example the “actual” average inventory was $2.50, but that led to a gross overstatement of turnover.
I could live with it being an imperfect approximation (whether the text sufficiently emphasizes that this is approximate is up for debate), but my point is that the theoretical basis here is NOT sound.
Why the fuss about beginning inventory you ask? Because that’s where we start, within my stylized example, and from there proceed to sell down to zero. So the beginning inventory captures the amount we turn as we deplete.
Assume an anlayst would take quarterly reports as per your example. Then he would come to the same conclusion as you. If quarterly reports are not available and the only source available is the end year B/S the only assumption he could make is that inventory is sold on a linear basis per month. Basically, the shorter the time periods used the closer the calculated value will be to the real value.
I began to reply to your last comment, S2000, but found myself merely re-wording what I’ve already written; essentially what you did.
By the way, thank you for your engagement here. It’s hard to read tone online, but hopefully it shines through that I harbor no hostility.
I think the issues here are actually rather subtle. If you take a step back and think about how we go about calculating “average inventory” from the balance sheet, you realize we’re averaging begining balances (technically also ending balances, but the difference doesn’t really matter). And so it seems appropriate to regard this average inventory as a sort of “normalized” beginning balance. You smooth out any outliers and you end up with a number that, if we assume it were sold down to zero before being replenished, would generate the number of turns if divided into total COGS.
Even if we were able to calculate the “true” average inventory over a period (like we were in my example), that number divided into the COGS for the period would not necessarily equal the number of turns.
So, let me recap:
CFA curriculum says that the inventory turnover ratio “measures how many times per year the entire inventory was theoretically turned over,” highlighting that it’s only “theoretical” because “in practice companies do not generally sell out their entire inventory.”
Therefore, it’s implied that an embedded assumption in the ratio is that a company DOES in fact sell out its entire inventory
By examining an example of a company that sells its inventory down to zero before restocking–consistent with the underying assumption highlighted in point #2–it’s clear that dividing COGS by the actual average inventory does not result in a turnover ratio that matches reality (within the example)
My thought was to re-label “average inventory” to be something along the lines of “normalized” or “smoothed” beginning inventory balance. Assuming sales are made at a constant (linear) pace over the period like in the example, this “normalized” beginning balance represents the amount of inventory you’d need on hand at the onset of each period, such that if sold down in a linear fashion to zero, when divided into total COGS would generate the correct turnover ratio.
I simply disagree with the premise of your example. You believe that turnover should be determined with respect to beginning inventory. I believe (as do the folks who defined the ratio) that turnover should be determined with respect to average inventory.
I think we should clarify what we mean by “average inventory” to the extent we want the turnover ratio to imply it’s the number of times inventory actually gets turned.
What my example showed was that using the *actual* average inventory leads to the incorrect result.
I have no problem with the way the calculation is currently formulated and am not saying it should be changed. I’m merely pointing out that the way the curriculum defines the ratio is inconsistent with how it describes the ratio.
Renaming the “average inventory” to something like “normalized beginning period inventory” or something like that would rectify the inconsistency and would not in any way change the way we go about calculating the ratio.
As I said in my first post, computing average inventory accurately is essentially a calculus problem, and nobody’s going to bother with that.
If you alter your original example slightly – you start with $5 in inventory, immediately (or the next day, to avoid quibbles) purchase $5 more, then follow your sell-it-evenly-every-quarter-then-restock scheme – the situation isn’t materially different, but the true average inventory is now $7.50.
Is there anything to be gained by trying to distinguish the two?
Actually, it’s worse than that. We wouldn’t ever have the data necessary to calculate the *true* average inventory using only the financial statements. So, we’re essentially in agreement on this point.
The key point was that you run your inventory down to zero each period, as in my example. This version of inventory flows fails to meet that criterion.
Look: I never said this wasn’t extremely pedantic. I’m just pointing out an inconsistency in the text that frustrated me.
IS accounts and BS accounts cannot be comparable directly because the difference of the nature. IS uses a period of time (a flow of value) and BS is the value as of a determined date (a stock of value, accumulation). So when you differentiate a BS account with its past you are creating a “flow” of value, hence they are now comparable. Doing this you can use COGS / avg inventory with no problem.
A good example is ROE, ROA. They use average equity and average assets respectively, not only ending or beginning equity/assets values.
I would argue that the average inventory that would be calculated from your example would be 0. If you start with 0, make $5 in purchases, sell $5, and end with $0, the beginning and ending values of inventory are $0. A much more realistic (yet simple, again) assumption is starting with $5, buying $5, selling $5 and therefore end with $5 for an average of $5. Although beginning and ending balances are the same, you are purchasing and then selling (converting to cogs) a certain amount of inventory each period, which is what the turnover ratio calculates. Do this for four quarters and you get a TO ratio of 4. Inventory going to 0 is just not a realistic assumption for a going concern, although I can see how your example would make you question the turnover ratio.
"Now, if we were to change the definition so that as our denominator we used beginning period inventory ($5 in my example) the calculation’s output would match reality. And this seems to make more intuitive sense; in effect, you’re saying “I started the year with $5 in inventory and then generated $20 of sales over the year, so I cycled my inventory 4 times.”
Your calculation of using beginning inventory is only correct if the company bought the same level of inventory as the beginning inventory every 3 months. What happens when the company bought $100 in the 2nd quarter but also sold it in even installments over the 3 months in 2nd quarter? Calculating the ratio based on beginning inventory would not be accurate, it may be even more inaccurate than using the average inventory.
You are right that inventory turnover doesn’t tell you “theoretically” how many times the entire inventory was turned over EVEN IF companies sell out their entire inventory.
“Maybe we use average inventory in the denominator to smooth out the impact of any outliers (say, for example, we randomly began the year with much higher than usual inventory for some reason)? In other words, we’re taking average inventory to be a “normalized” beginning inventory.”
I just think that when we have 2 data points, taking the average to represent the period makes intuitive sense.
