I find respectable discussions on the content of key issues of our life especially rewarding. Here is an issue my friend Alejandro Fernandez had during his presentation at the 2022 TOCICO Conference.

The topic was *The Measurement Nightmare Solved with Throughput Economics Approach*. The idea is to judge the added value of a new move or idea, opening the door to evaluate the contribution of the new move to the Goal of the organization.

One of the financial measurements that can be used is the return-on-investment of the new move. Here is the formula stated by Alejandro:

Sanjeev Gupta and Filippo Pescara, two well-known TOC experts, claimed that the above formula is incorrect. The situation of presenting live could be too pressing to fully understand the criticism and its validity. Moreover, one of the most common, but also trickiest problems is **when a specific expression can be interpreted in two very different ways. ** I believe this is the situation here.

Let us use an example:

Imagine a restaurant chain with four restaurants spread over the city. The owner is contemplating adding a fifth branch. He believes that such a restaurant, at a location far away from the others, would add mainly new customers, who are aware of the reputation of the chain, but highly prefer the new location.

- The new restaurant requires a net investment of $500K.
- The additional operating expenses of the chain would go up by $1.2M a year.
- The evaluation of overall Throughput (revenues minus the truly-variable-costs, like the purchased food) comes to 1.5M a year.
- This means the chain of restaurants will gain, due to the additional branch, net-profit, before tax, of (1.5M – $1.2M) = $300K a year.
- The ROI of the investment in the new restaurant is $300 / $500 = 60%.

But here is the clarity issue: **The ROI of 60% is only for the new restaurant** – it is NOT the ROI of the chain and it is obvious that the total ROI is NOT going up by 60%! To calculate the new ROI for the whole chain we need to consider the new total throughput of all five restaurants minus the operating expenses of all the restaurants, then dividing it by the total of the current investment plus the new one.

The point here is: **what do you understand from the expression: Delta-ROI? **

Is it the change in ROI for the whole organization? Or is it the ROI of just the new move?

**The above formula refers to the later interpretation**!

Comment: The full Throughput Economics method involves TWO series of calculations, one is based on conservative assessments of the additional Throughput and additional Operating Expenses, and one is based on optimistic assessments. To understand the reason for going through the calculations twice, see Alejandro’s whole presentation, or read the book:** Throughput Economics**, by Henry Camp, Rocco Surace, and me.

Please, come up with your reservations to continue the open discussion.

Well, the formula looks like totally incorrect…

Delta ROI = ROI(1) – ROI(0)

Which means NP(1)/I(1) – NP(0)/I(0)

where I(1) = I(0) – delta I

So Delta ROI = (NP(0)+delta NP)/(I(0)+delta I) – NP(0)/I(0)

It is definitely not the same as Delta NP/ Delta I in presented formula

That’s why I think it’s wrong

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Is it ‘wrong’ or just calculating a different thing?

Such as the change in the ROI of the total business, v the individual investment decision.

Why can’t you have a project ROI of 60%, and which changes the overall business ROI from (say) 12% to 12.37%.

If I am driving from A to C via a waypoint B, I can say I drove at an average of 55mph between points A and B, but between A and C I averaged 40mph. Neither 40 or 55 is ‘wrong’, just measuring something different.

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You assume that the only possible meaning of Delta(ROI) is ROI(2) – ROI(0). This is the regular meaning.

In this case the “delta” refers to a specific new investment. Alejandro should have written ROI (new move), but when he didn’t need it when he wrote delta(throughput), which conforms to both interpretations.

OK, calling it Delta(ROI) was a mistake. But when you look at the righthand expression isn’t it obvious the delta(ROI) is actually the ROI of just the new move?

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I’ve started from term “delta I”. Normally “delta” means “the change of…”

So, hidden assumption is: we are evaluating change of ROI for an organization. From this perspective the formula is totally wrong.

Evaluating separate action is definitely different case. In such case formula is quite obvious and may be used for isolated evaluation of alternatives.

Just example from our practice (all numbers are real):

There are two alternatives of orders to supplier for the same SKU:

1. Order for $7000

2. Order for $12 000

First variant is evaluated as T – $7350, related OE (delta OE) – $3500, time to sell 180 days. So, we have NP $3850 (or $7700 for an year) and ROI 111,5% per year (3850/7000*2)

Second: T – $12600, OE – 4800, time to sell 309 days. So: NP $7800 (or $9100 for an year) and ROI 76% per year.

Here we can look at alternatives and make our choice. HERE we can talk about “delta I” between these alternatives. (In the case from example the choice is not obvious). And it is quite obvious and common practice in our supply chain management projects. We use it widely when we need to substantiate benefits of frequent and relatively small supplies.

But i’s very local use of “the formula” and it doesn’t evaluating impact of specific action on performance of organization as a whole.

So using “delta I” confused me very much.

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Hi I would like to understand ypur example but could not follow the logic. Is the order a sales order or a purchasing order. Please assist me by inboxing me -unless clarity can add value to more people not understanding.

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Hi, in my example we consider two alternatives of purchasing order from organization to supplier. Original question was: should we wait until the need will increase to $12000 in order to save OE or make an order when the need for supply is $7000. Difference between ROI was an argument for the smaller one due to organization was limited in cash for that moment

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This discussion reminds me of a very basic scenario.

a guy invents a new kind of knife aimed at cutting shoes.

a 2nd guy says, “your knife is bad/wrong.”

1st guy: “what do you mean it’s wrong?”

2nd guy: “I mean that your knife doesn’t have the features needed to cut steaks.”

1st guy: “but it’s not for cutting steaks.”

The point illustrated here is that “wrongness” of an idea/tool depends on what the goal is.

Bringing it back to the blog post, when someone says an idea is wrong, they should be able to explain the goal of the idea, and why the idea fails to achieve the goal, and in some cases, why some rival idea does not fail to achieve that goal.

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It´s my interpretation that placing the delta before the I is what causes the Wright / Wrong perception.

As ready stated in some other comments, formula is to evaluate the ROI of a particular new initiative. This is of special help when having to compare different options, but have to choose just one, most often due to the lack of Investment resources (I) so the formula stands valid (without the delta ROI).

Of course, most often too this ROI will not be possible without the rest of the investment already made for the company already, think about new products that use the same machines, but require additional inventory by definition.

Yes the ROI is a relative measure to the whole system, where I is the total investment of the shareholders, meaning actual plus new initiative amounts.

Hope this helps in the discussion.

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It seems to me that controversy is not in either mathematics or underlying concept of the the formula but regarding notation used in formula. I don’t think that any of the expert mentioned here doubts or misunderstands the mathematics or underlying ideas involved but language used to express them is under question. Personally I think delta ahead of “ROI” needs to be replaced with something else because keeping formula as it is will cause communication issues especially when talking with people who does not have TOC or financial/accounting background. In the example you used it is possible that someone may misunderstand that additional restaurant causes ROI to change by 60% because thats what literal interpretation of delta ROI means, i.e. “change in ROI”. Solution of the issue is basically to use two separate notation for both cases. Formula which implies change in organization wide ROI must have different notation than formula which signify ROI of specific decision (in this case restaurant). Using same notation for both cases may lead to misunderstanding.

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Even for new initiative, I think there’s something fishy with the formula. Let’s say that the initiative is increasing shipment frequency to stores. In both scenarios (pessimistic and optimistic) net profit will increase because the additional throughput covers additional expenses. Regarding investment, actually, there’s no investment to be made because with more frequent deliveries, inventories will reduce between 20% and 50%. So is the investment negative, and therefore the ROI for the initiative is negative as well?

The easy explanation would be that since there’s no investment, then I should be zero, but if we are comparing initiatives, I would like to see which ones are not only increasing NP but also freeing up working capital.

Maybe the solution is to look at the whole picture and compare ROI before and after the iniative.

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Alejandro, I don’t understand your claim. When you take an example that doesn’t need any investment then there is no problem. I agree with you that when there is a significant change to the working capital, no matter whether it goes up or down, it should be considered together with the global delta-NP. Still, when you do consider delta-ROI what delta you are referring to? One interpretation is the difference between current total ROI and future ROI. The interpretation I’ve used is the net ROI of the move under consideration. Note, when the latter interpretation is positive then the former one is also positive, but they are not the same.

My concern with looking at the ROI before and after is that the delta itself could look very small, because the move we are considering is not big. Suppose the current ‘I’ is $50 Million and ROI of 8%, making NP of $4M. We are considering an investment of $50K, yielding 100% ROI by making additional NP (delta-T minus delta-OE) of $50K. The overall ROI will go up to 8.098% – not so impressive as generating 100% ROI of just the move. I like to encourage managers to come up with more and more ideas that return the specific investment in one year. The holistic picture is achieved by validating the total NP goes up by $50K per year.

Alejandro, it is great to increase the frequency of shipments to stores, but then what is your next move? Eventually you have to elevate your constraint, and in most cases, this involves an investment!

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