# Days of Capital Returns

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*or, what would Method Man think of Return on Equity?*

If a company’s cash conversion cycle halved, what would that do to its ROE? This question may seem peculiarly unanswerable. Surely, we need more information, assuming this information alone is relevant in the first place? In fact, we do not. There is more than enough information across the financial statements to make immediate sense of the question and apply it to every returns ratio we ultimately might care about.

I aim to solve the problem posed above with an invented metric I call *days of capital returns*. While I reserve the exclusive right to use this expression as the title of an eventual memoir, I define it as something fairly mundane that for some reason is not a part of traditional financial analysis literature.

I suspect part of the reason is an obsession with the income statement and all the effectively meaningless valuation metrics derived from it that people like to quote. Painful as this is for me to have to say, nothing written here constitutes investment advice. 99% is criticism of one method of financial analysis and advocation of another, and in the 1% I mention actual companies, the information is publicly available and no commentary is provided.

My central thesis is that while the cash flow statement is true, the balance sheet is a little made-up and the income statement is a lot made-up. In the words of Clifford ‘Method Man’ Smith of the esteemed rap group *The Wu-Tang Clan*:

“Cash rules everything around me. C.R.E.A.M. Get the money. Dollar, dollar bill, y’all.”

**The problem we are trying to solve**

I begin with a basic observation: ROE is, fundamentally, a growth rate. Given the equity invested in a business, over the course of one year, what proportion of that equity is generated as earnings that can be reinvested the following year? Hence, by what proportion can equity grow and, all else equal, how much can the whole company grow if the same process is repeated with this stated growth rate in its equity financing.

Fair enough, this is textbook stuff. But how about this: when did those earnings happen? If ROE is 10%, does that mean that after investing $100 on day 0, we got back $10 on day 365? Notice that this is important because we couldn’t possibly have gotten it on day 1, unless we also happened to not reinvest *at all*, such that equity and earnings remained unchanged for 364 days. If we got back $10 any time before day 365 *and *we reinvested it, then ROE would have been above 10%.

Here’s a more teasing way of approaching the same problem: say company 1 has an ROE of *x*% and each unit of earnings took on average *y *months to arrive after being initially provided as equity investment. Now say company 2 takes *z *months to achieve this. Say this company 2 somehow took *z *arbitrarily close to zero, over a time period *t*. What ROE defined over *t* rather than over one year would give the same ROE, x%, as company 1 over one year? In other words, if equity invested *immediately *produced earnings that could be reinvested, what would happen to ROE? Can equity *continuously compound*, and does this involve the natural logarithm, the greatest Scottish invention of all time? Yes, and yes. This is getting more interesting, but can we calculate any of it? Yes …

**Funding, Working Capital, and Operating Assets**

We often split the balance sheet into short-term and long-term assets and liabilities. The distinction between being ‘short term’ and ‘long term’ is a fairly arbitrary one, which is actually based on different criteria for assets than it is for liabilities. The starting point of this approach is to observe that a better distinction is between working capital and everything else.

This doesn’t require much fiddling with the balance sheet. It is intended to reflect a theoretical difference, not an accounting one. When a business gets funding (non-working capital liabilities) it will spend it on assets and then operate the assets. It is through this process that a working capital position develops, but the causal direction is key and cannot be reversed. An easy way to conceive of this is to imagine taking out a loan (liabilities up, cash up) and deciding whether to spend the cash on a widget-making machine or on accounts receivable.

Having made this distinction, it becomes easy to think of the ‘everything else’ — as distinguished from working capital — as ‘operational’ in the case of assets, and ‘funding’ in the case of liabilities. The idea behind the entire theory can be handily summed up at this point before we dive into the details: ‘Working capital’ is a measure of efficiency, not of output. In the simplest returns equation of all, money / stuff, an efficient working capital position should subtract from stuff, not add to money.

With this distinction in mind, the first new metric we come across is *Funds From Operations*, or FFO. To get this, you go down the lines of Operating Cash Flow (OCF) and reverse what is usually the final alteration, *changes in working capital*. This metric isn’t quoted often, but it is in almost every credit rating agency report you will ever see.

Rating agencies don’t like the income statement because, as I mentioned, it is all made up, but the reason they seem to prefer FFO to OCF is that it captures the causal distinction between ‘working capital’ and ‘operating assets’. Working capital swings may or may not be connected to the core business and can even be manipulated. Credit agencies prefer to monitor the long-term stability of the debt position, and so will typically talk about ‘FFO/Net Debt’.

Of course, Free Cash Flow (FCF) is often thought of as a kind of sturdier representation of cash generation than either OCF, which assumes no maintenance costs, or EBITDA or EBIT. Maintenance costs are important — crucially so if we are theorising about the *sustainability *of cash generation — but we have just done away with OCF.

A new metric, which I call Cash Profit,** **is FFO minus either maintenance capex if known, or depreciation and amortization if not. I think that this is a good representation of: *how much cash was generated in an essentially sustainable way? *Another potentially helpful way to think about this is that FFO is a kind of cash proxy for EBDA, since the ‘I’ and ‘T’ have already been stripped by that point in the OCF calculation. Given that I want to then subtract ‘DA’ as well, and explicitly avoid working capital movements, which also don’t affect net income, ‘Cash Profit’ is a kind of cash proxy for Net Income.

But what about growth? Well, we are actually only a few steps away from approximating the DuPont analysis for ROE. I also think the steps have clear correspondents, but we have to first return to the theoretical differences between working capital and operating assets to tease them out.

The first is easy: you can’t invest in accounts receivable. Nor can you invest in cash. If by ‘invest’ we mean, spend funding for the business on stuff for the business, you can only *really *invest in fixed assets, intangibles, goodwill, and investment assets. But of course, if a business is already up and running, it will have a Net Working Capital (NWC) position. We should add this too. I will define ‘Net Operating Assets’ as the sum of net fixed assets, intangibles, goodwill, investment assets, *and *NWC. I realize there are other definitions of ‘Net Operating Assets’ but I can’t think of anything clearer for what I mean here. Suggestions welcome.

This deserves a tad more attention since NWC could be negative (which would be a good thing? A bad thing? Can we say for sure?). Returning to the idea of ‘spending funding for the business on stuff for the business’, imagine we want to buy some stuff — some fixed assets, intangibles, goodwill, investment assets — worth $10m. But imagine also that our NWC is negative $1m. What this means is that our business model is *giving us a $1m interest-free loan in cash* through the efficiency of the ongoing working capital position. So, assuming we can pay it back without issue, we only need $9m in funding now, not $10m. We need the other $1m at the end of the cash conversion cycle, but maybe we have actually earned the cash with this investment by then anyway.

If we interpret this as potential equity holders who thought they needed to finance a capital raise with $10m, but actually it turns out only need to give $9m for the same thing, it should be clear why this is a good thing after all. Of course, this is provided the working capital position is sustainable and is not a temporary blip that may reverse.

So now we can work out Sales/Net Operating Assets. This is very much like asset turnover, clearly, except that we have a more nuanced view of what assets matter and why.

We can also work out Cash Profit/Sales, which is very much like Net Profit Margin, but with a greater emphasis on solid cash earnings rather than accruals-based earnings.

Finally, we can work out Net Operating Assets/Equity, which is very much like the leverage multiplier, but in the sense of *financial leverage *only: the portion of leverage provided by working capital I would argue is worth splitting out.

These are interesting on their own, but when multiplied together we get ‘Cash Profit/Equity’, which is very much like ROE:

Not meaning to pile on the math, but there is one final adjustment to be made to get a really helpful number. We need to account for the fact that equity may be diluted. The same stuff goes in and the same money comes out, but in the background, we are getting a smaller return than this ratio suggests. So we need to finally take this ‘CP/E’ figure and multiply it by (1-equity issued/total equity). It may be reassuring that most of the time, this will mean multiplying by a number very close to 1. They will only differ markedly in situations that really ought to get our attention anyway.

Readers may have noticed that I have ticked off every balance sheet entry other than ‘cash and cash equivalents’. Surely a highly productive asset base that neither pays down debt nor distributes or reinvests earnings, but just lets the cash accumulate, ought to muck up the concept of ‘growth’ we are trying to capture?

As frustrating as this may be, the reader will have to trust me that the necessary calculation to adjust the individual metrics in light of the potential for hoarding cash is so obscenely complex as to not be worth wasting time even understanding, never mind implementing. It also almost never changes the above metrics in any meaningful way and so I will skip over it.

As a kind of handwavy justification of this, consider that we would only care about such a circumstance if the disproportionate cash hoarding was meaning that this ‘fundamental growth’ number we are after was a poor reflection of the growth of the business. This could only really happen if *both *a large proportion of the generated cash was going into cash and not operating assets, *and *the dormant cash pile was much, much bigger than the operating assets.

For example, operating assets of $10m produce Cash Profit of $5m, of which all is put back into a cash pile that starts at $90m. The cash return on operating assets is 50%, but the cash return to the business is 5%. If the same thing happens next year, the business will ‘grow’ by 4.8%, not 50%, and this will asymptotically approach zero over time. However, it would surely be obvious that a business that is 90% cash and only generates 5% of its cash pile each year ought not to be valued on the basis of *any *conception of ‘growth’ in the first place. For ‘normal’ businesses, I argue that this adjustment is not relevant.

I’d also point out that no matter how bad it is, it can’t change the *final* figure we are aiming for at all, which is Cash Profit / Equity, arrived at by multiplying out lots of other individually helpful metrics. Whether we multiply out (Sales / Assets) * (Assets / Equity) or (Sales / Net Op Assets) * (Net Op Assets / Equity) we get the same numerical answer. All I’m arguing is that the latter presentation is just *more helpful* as it gives a better idea of *what is actually going on*; it treats working capital as a measure of efficiency, not of output.

We can easily imagine two scenarios in which this analysis is superior. Firstly, imagine a company that makes little or no profit because what in spirit are investments have to be accounted for as expenses, and yet mysteriously grows its equity base every year, forever (the way you ought to treat this, by the way, is to move these expenses off the income statement, from CFO to CFI, add them to an intangible asset on the balance sheet, amortize that asset, and put amortization *back on *the income statement). CPRE will be much higher than ROE and will almost certainly capture the growth in book value nearly perfectly.

Secondly, imagine a company that is an absolute wizard at inventory management. By the ROE DuPont analysis it may well look very levered on Assets / Equity and not very productive on Sales / Assets. Yet this would be extremely misleading given this “leverage” is in the form of an interest-free loan generated my managing working capital efficiently. Under CPRE, Net Op Assets / Equity will be much lower (i.e. not levered) and Sales / Net Op Assets will be much higher (i.e. super productive).

CPRE will be very similar, if not identical, to ROE, but the DuPont breakdown will be a far more accurate analysis of the business. For readers curious to play around with this more, I suggest running the numbers on Salesforce and Inditex.

Having made the dilution adjustment to ‘Cash Profit/Equity’, we arrive at a metric I call *Cash Profit Return to Equity *(CPRE). We won’t use this again, as it is just FFO we want to continue working with, but the adjustments we make to the DuPont to get clearer on the difference between working capital, operating assets, and funding were worth the tangent. Also, I will refer to ROE throughout, in order to strictly solve the problem I originally posed, but I contend that CPRE makes a lot more sense, and the two can be swapped in and out at any point in the following discussion.

Cash Profit is cash that has come only from essentially sustainable sources and hence is available for paying down debt, distributing, or reinvesting in operating assets. It may be useful in determining the attractiveness of a valuation in a variety of circumstances for which other metrics make a perfectly healthy company look hideously expensive or misleadingly risky. With all these distinctions at front of mind, we can return to our original problem.

**How Quickly Do Investments Produce Cash?**

What we now want is a kind of invested-capital-only proxy of the cash conversion cycle. As a reminder, the cash conversion cycle tells you for how many days the business must cover its need for liquidity brought about by the differing demands of suppliers and customers. It is of course possible for the cash conversion cycle to be negative, which is a very good thing provided it can be sustained, in that it effectively means that the business is being paid for the end good produced *before *it pays for the components that go into making it.

We can in turn think of this as the extent to which the business has a float it can earn interest on. With apologies for the confusing negatives flipping around, a negative cash conversion cycle gives a positive float on which interest can be earned, while a positive cash conversion cycle is a financing need on which interest must be paid. But this is all assuming that operational assets are up and running (in fact, it makes no sense if this is not the case).

What we want is a figure that is similar in principle but tells us something like: *how many days do we have to wait while cash we invest turns back into cash we can invest again?* Rather than how long it takes cash to cycle through working capital and become cash again, how long does it take to cycle through invested capital?* *And, as a mathematically interesting side note, can this be negative too?* *What would that mean?

Our starting point is to look at the components of the cash conversion cycle. To get the ‘average days of’ figure, you divide 365 by the relevant ‘turnover’ figure. Now ‘turnover’ means something quite different to a return or other growth rate. It means ‘in one year, how much of this stock is replenished?’ or ‘how much of this stock is cycled through?’ or some other variation as appropriate.

To be specific in this case, we want ‘in one year, how much of the stock of capital invested is returned as cash earnings?’ For the ‘capital invested’ there is a pleasant symmetry with working capital and the cash conversion cycle in that what we are really looking for is all assets *except *working capital.

As per the previous section, I argue that FFO is the most appropriate cash earnings return, as it explicitly excludes working capital movements. Working capital arises as a result of running the operating assets, but is causally completely different and the two should not be conflated. So we want long-term assets plus cash, plus any marketable securities or short-term financial assets.

The intuition here is just any productive assets the business owns, rather than being an obligation from or to customers or suppliers. i.e. things the business has spent money on itself. With the intuition out the way, however, it is a lot easier to calculate by simply subtracting all working capital assets from total assets. FFO over the average of this figure (call it ‘assets-minus-WC’) is our ‘invested capital turnover’, and 365 divided by invested capital turnover is the figure we want, which I call, *days of invested capital*:

The distinction being driven at throughout (and in CPRE also) is between ‘working capital’ and ‘invested capital’, which is hopefully now clear and complete. When you think about it, the ‘cash conversion cycle’ should really be called ‘days of working capital’ instead of the current very silly meaning of the latter expression. When the CFA Institute changes this in its syllabus, I will know I have finally won.

The reader may have a few niggling concerns about how we arrived here, and so we will do some housekeeping before getting back to solving the core problem. In the previous section, I made a big deal about Cash Profit, which I defined as FFO minus maintenance capex if known, or DA if not. Where is DA here? Are we dramatically overstating everything?

No, because ‘DA’ is an accruals measure, not a cash one. We include it there *precisely *because we want a growth metric, not a turnover metric. In fact, we have accounted for ‘DA’ here without ever making it explicit: every year we have a new assets-less-WC in the calculation, within which depreciation has been subtracted from gross PPE.

Next, I claimed the intuition was that we wanted all the assets the business ‘owns’ as opposed to obligations to or from others. Surely it owns inventory? It does, but I said *productive *assets it owns. Inventory is not ‘productive’: it is the result of productivity that hasn’t been sold yet.

As per the commentary above on the cash conversion cycle, it’s not really a good thing, either. You want to sell it, not have it sitting around. Because we are only interested in (potentially) productive assets, by excluding ‘inventory’ we have also avoided any double-counting with this figure as compared to ‘working capital’, which is what it really is.

Next, I also started by talking about ‘equity financing’ and then switched to ‘productive assets’ halfway through. Does this obscure an important difference that is captured, for example, by comparing ROE to ROCE? This is a good question, and the answer is quite complicated. In short, no, because we aren’t finding out what ROE *should be*, but rather how it will change from whatever it already is if we improve something that causes it. We could do the exact same thing with ROCE or ROA if we wanted to, by using our preferred metric as the input.

There is a slightly more complicated reason as to why it is okay to use ROE in the first place rather than adjusting for leverage. We *could *take assets-less-WC and divide that by equity to get a kind of ratio for WC-less leverage. While this figure might be of interest, there are two issues with taking it any further. Firstly, it might not mean anything at all if the net working capital position is highly negative: it might look like the business is substantially lacking leverage when actually a form of leverage is provided by the working capital liabilities. Or vice versa, of course.

So, in isolation, it could potentially be misleading. Secondly, as we will see shortly, the problem we are aiming to solve involves a calculation that has nothing to do with leverage in the first place. Choosing to begin with ROE, ROA, ROCE, as covered above, is the only place the consideration of leverage exists within the realm of our calculations, so introducing it here adds complexity without having any obvious utility.

Finally, just because I teased it, no, *days of invested capital *cannot be negative. One of assets-less-WC or FFO would need to be negative to achieve this. Assets-less-WC clearly can’t be, and while FFO *could*, I think the best approach is to treat this as clearly just being an error: it doesn’t mean that when you invest the equity you get the earnings back in the past — it means you don’t get them back at all.

If you want to spend 10 minutes on the philosophy of mathematics that you will never get back, you could ponder this scenario as entailing that the loss of money is a gain that happens *more than* infinitely far in the future and hence wraps around into the past. Then again, ‘error’ is probably the more fruitful approach at this juncture.

I suggested in the introduction that equity can *continuously compound*, however. What does this mean? That days of capital returns is zero? Not quite. We have one step left. As has been belabored to this point, businesses have two relevant but unrelated cash cycles. Days of invested capital and the cash conversion cycle. We need to combine the two.

**Combining the Conversion Cycles**

The way we combine the two is by adding them. What the sum *means *is something like: across the entire business, how many days do we have in which cash is tied up not yet having returned 100%. As ‘working capital’ and ‘invested capital’ partition the balance sheet, and hence add up to ‘capital’, I call this figure, *days of capital returns*.

To justify this by example, imagine that our cash conversion cycle is minus 10 days. This means we get paid by our customers 10 days before we pay our suppliers, and have free money to play with for that period, but which of course we must pay back. Suppose also our days of invested capital is 10 days. That means we invest capital and get 100% of our money back after 10 days.

What we do is take $10 from customers, invest it in a widget machine, wait 10 days for it to have produced the $a of widgets of which $10 is the profit, fulfil our obligations to widget-buying customers, and then pay our widget-machine-making suppliers. Clearly, we need other financing in order to do this as we still have operating costs, as it isn’t as if the other circumstances relieve us of this responsibility. But what ‘zero’ days of capital returns tells us is that there are zero days in which *earnings *specifically are tied up, relative to the capital and sales that produced them.

So for example, if the cash conversion cycle were negative 20 days, with days of invested capital still 10: we get $10 from customers, buy the machine for $10, wait 10 days to get $a of widgets, fulfil our obligations to customers, and then wait 10 more days before we have to pay our widget raw material suppliers. Hence our profits have 10 days of ‘freedom’, during which they could potentially earn interest or be reinvested in another widget machine.

If the days of invested capital were 20, but the cash conversion cycle negative 10: we get $10 from widget-buying customers, buy the machine for $10, but then after 10 days must pay the widget raw materials suppliers. We can do this because we have financing, but we still need to wait 10 more days to finish making the widgets and fulfil our obligations to customers. Our capital can’t ‘reboot’ to start a new period of productivity for 10 more days. We might think of this as implying our profits are ‘tied up’ for 10 further days.

What the intricacies in each example point to is that zero or negative days of capital returns in no way implies the financial equivalent of perpetual motion. We still have a base of invested capital and a margin structure in the business that dictates what kind of profits can be made. It is simply a measure of time, and what this time is telling us is how quickly we must operate to maintain that structure of earnings and returns. What altering this time would tell us is what would improve if we did things quicker.

It is *possible* to juice everything to infinity, but it is clearly not realistic. It is like suggesting that if we lever up to arbitrary highs, then ROE can go arbitrarily high too. In fact, it is more strictly impossible since a foolish CFO *could actually *lever up to some arbitrary level, but taking the cash conversion cycle to arbitrarily high (negative) values depends on conditions in the real world that are only within the company’s control within reasonable bounds. Nobody in the world gets paid 10 years before they deliver.

While it’s theoretically possible, I would find it hard to believe that any company had negative days of capital returns, or anything close to even two or three years. I gave the extreme cases here as a conceptual aid to understand the mechanics. However, below I ran the numbers on some large, well-known companies over the past several years to give an idea of a range of what is realistic:

As a brief aside, I am still waiting for an apology from Benedict Evans, whom I decided several years ago was my nemesis, on the topic of Amazon’s returns. He has obviously been in America too long and can no longer recognise good old British sarcasm.

Oh by the way, **THIS IS NOT INVESTMENT ADVICE. THESE ARE NOT OPINIONS: THEY ARE PUBLICLY AVAILABLE FACTS.**

Got it? Excellent. Let’s move on.

**Solving the Problem**

The problem was: If a company’s cash conversion cycle halved, what would that do to its ROE? We may as well ask, if days of capital returns shortened or lengthened by *x *days, etc., since we can now cover every possibility. If we are only interested in the cash conversion cycle, we assume the days of invested capital stays constant in our inputs.

Step one is to calculate what I call a ‘capital turnover ROE’, the answer to the question I teased earlier: given, a) a company’s annual ROE, and, b) the known days of capital returns, what is the ROE defined over this period, *t*? (where *t *is unlikely to be an exact year) To get this we take the turnover figure for days of capital returns (so 365 / DCR, call this ‘capital turnover’ or ‘CT’), and along with the actual ROE, apply this formula:

From this we can calculate the potential ROE given a potential CT. We can assume a change in cash conversion cycle or days of invested capital, use these inputs to get a potential DCR value, hence a potential CT value, and input that into the formula below:

For anybody who wants to dive into this formula, the next section explains the derivation. If not, putting it in Excel and playing around with the inputs ought to convince you it works, and you can skip straight to the conclusion.

**Derivation of Capital Turnover Period Indexed ROE and its Linked Potential ROE**

(*apologies in advance for this section that Medium doesn’t seem to allow subscripts or superscripts — hopefully, the notation isn’t too muddled)*

The continuous compounding counterpart of a given growth rate, x%, is a simple calculation: ln(1+x%). The challenge is that capital does not compound continuously. Think about what this would mean in real life: you invest capital and instantaneously receive the earnings you hoped it would ultimately provide, which you then reinvest and instantaneously receive more, etc. However, the purpose of the rest of this post to this point is to derive over precisely what time period this happens in real life: days of capital returns.

By analogy to the derivation of *e*, the base of the natural logarithm, as:

We instead want not the limit, but the discrete answer for a given *n*. Again, by analogy to this cool method of deriving *e*, what is happening here is we are assuming the year is chopped up into smaller and smaller increments and nonetheless compounded back to a full year. We want to take the precise increment corresponding to ‘days of capital returns’, which of course is ‘capital turnover’, or 365/DCR. So now we want to know this:

Call this number ‘c’ for clarity. We then want to use this as our logarithmic base to correspond to *not quite continuous *compounding:

Referring to the question above, *what continuous compounding rate corresponds to the ROE of x%? *This number tells us the answer to the more realistically useful question, *what compounding rate over the non-continuous period at which capital compounds corresponds to the ROE of x%?*

Most of us don’t have a fancy enough calculator to work this out, however, but we can use some sneaky tricks of logarithmic algebra to turn it into the following, using only the natural logarithm, which we can work with, and which I quoted in the main text above:

Remember that this still isn’t what we are after, and actually isn’t even very useful in and of itself. This is an ROE over a fairly arbitrary period — very likely not at all like one 365-day year. What we want is how ROE changes if DCR changes. We can begin to see why this is important, though, because changing DCR will change the CT period, and hence will clearly affect the ROE over this period too.

The reason we need this number is that it provides a way of indexing the annual ROE to the capital turnover period, rather than one year, so that we have a starting point to see what happens to it if we then change the capital turnover period (I’m using ‘indexing’ slightly metaphorically here). The way we do this is rather philosophical, as the derivation involves understanding the* *meaning of *e*, the base of the natural logarithm.

One *meaning *of e^x is the multiplicative growth factor corresponding to some continuous growth rate x. Or, perhaps more easily understood, e^x — 1 will give a percentage growth rate over one unit of time. An easy way of realising this is to invert the claim made above, that, ln(1+x%) gives us a continuously compounding rate.

By the same logic, we can reintroduce the number we called ‘c’ above, or (1+(1/CTp))^CTp and be more precise about what this means also. Firstly, by the ‘p’ we mean ‘potential’ capital turnover period rather than actual. ‘cp’ is a number increasing arbitrarily to e, as the capital turnover period gets higher and higher (recall ‘capital turnover period’ is 365/DCR, or, how many times in a year do we cycle through our capital).

The primary utility of this number is that ln(cp) will give us a number increasingly close to 1 from below the closer cp is to e. What ln(cp) *means *is* *the number we need to multiply a growth rate, g, by to turn it into the continuously compounding rate that would give the same growth over one unit of time as g does over ‘CTp’ increments of that time. In this case our growth rate is the ROE indexed to the *actual* capital turnover period.

Hence ln(c)*ROE(CT) is the continuous growth rate corresponding to this indexed ROE. Or, in other words, this is how we reconcile indexing the actual ROE to the actual capital turnover period with our desired *potential *capital turnover period. We can now calculate the continuous growth rate that doing this would correspond to, and so we need to turn that back into a normal growth rate.

This is the final interpretive step. We can now derive the desired growth rate over one unit of time — potential ROE over one year, as usual, in our case — given the corresponding continuously compounding rate — the rate described in the paragraph above. (n.b. several steps involve standard algebra I do not explain):

*g is growth rate we want, x is corresponding continuously compounding growth rate:*

**Conclusion**

Funding, operating assets, and working capital are different things. Not only are they qualitatively different, but they are causally different. A business (ideally) turns cash into more cash via investment in productive capital. In the lingo adopted here, it turns funding into operating assets and runs the operating assets to generate a return.

The fact of doing this *causes *a working capital position to develop, which can be thought of as either a drain on or a source of short-term cash. But beyond this effect on cash, working capital does not itself *cause *anything. It is a reflection of efficiency, not a contributor to output. The distinction between ‘current’ and ‘noncurrent’ assets and liabilities obfuscates all of this, as do the components of the DuPont formulation of ROE.

But as my good friend Method Man knows well, cash rules everything around us. We may have good reason to believe that changes in an industry or in the strategy or operations of a business will materially affect a company’s cash conversion cycle or days of invested capital. In such a scenario, we shouldn’t reach this point and simply say: that seems like a good thing. We should say precisely what will happen to returns.

Preferably Cash Profit Returns to Equity, but if you want to stick with ROE then that wouldn’t be so bad.

*follow me on Twitter @allenf32*

*thanks to Sacha Meyers, Robert Natzler, and Gemma Barkhuizen for edits and contributions*