# Investment Math - ROIC

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Hi - was reading the piece "ROIC – The Underappreciated Variable in Valuation" from Kennedy Capital Management and am a little confused on the math behind deriving the chart I pasted below. Can someone show a simply DCF with the inputs listed and how that would convert into the investment multiples cited?

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If you have to rely on getting the growth rate correct within 5%, you're most likely in trouble.  It's more important for you to understand the hidden meaning behind those heuristics.  Enduring high ROIC/profit margin can imply wide moat.  Enduring growth on top of inflation normally imply the market is not fully tapped yet.  A company with both characteristics is generally considered a pretty good company.  You're better off learning from Li Liu here (https://roiss.substack.com/p/li-lus-investing-masterclass-at-columbia) than from KCM, IMHO.

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Posted (edited)
3 hours ago, tnathan said:

Hi - was reading the piece "ROIC – The Underappreciated Variable in Valuation" from Kennedy Capital Management and am a little confused on the math behind deriving the chart I pasted below. Can someone show a simply DCF with the inputs listed and how that would convert into the investment multiples cited?

I genuinely think the numbers in that might be made up and there probably wasn’t much thought behind the table.

Companies with a 10% ROIC wouldn’t have a consistent 10x multiple if one company had a 2% growth rate and the other 7%.  On what planet would they be a consistent 10x?

Edited by Sweet
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Posted (edited)
3 hours ago, Sweet said:

I genuinely think the numbers in that might be made up and there probably wasn’t much thought behind the table.

Companies with a 10% ROIC wouldn’t have a consistent 10x multiple if one company had a 2% growth rate and the other 7%.  On what planet would they be a consistent 10x?

The table isn't unique to KCM and the numbers aren't made up (though it may not be particularly useful!).  The numbers come right from a DCF.  The chart is using a 10% discount rate.  With that assumption, growth at 10% ROIC creates no present value.  Example, I earn \$1 today and invest all earnings incrementally at 10% ROIC.  Next year I have \$1.10 in earnings.  If I discount that back at a 10% discount rate, those future earnings are worth \$1 today:  1.1/(1+.1) = 1.  The next year will show the same thing -- I'd now have \$1.21 in earnings but the present value of those earnings remains \$1:  1.21/(1 + .1)^2 = 1.  [At a constant multiple, the stock would also be increasing at 10% per year.  That's consistent with no value creation IF you use a discount rate of 10%.]  That is why, at a 10% ROIC, the 2% and 7% grower have the same multiple.

If the chart used an 8% discount rate, then the 7% grower at 10% ROIC would have a higher multiple than the 2% grower, as they do in the chart for all ROICs greater than the assumed 10% discount rate.

Edited by KJP
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33 minutes ago, KJP said:

The table isn't unique to KCM and the numbers aren't made up (though it may not be particularly useful!).  The numbers come right from a DCF.  The chart is using a 10% discount rate.  With that assumption, growth at 10% ROIC creates no present value.  Example, I earn \$1 today and invest all earnings incrementally at 10% ROIC.  Next year I have \$1.10 in earnings.  If I discount that back at a 10% discount rate, those future earnings are worth \$1 today:  1.1/(1+.1) = 1.  The next year will show the same thing -- I'd now have \$1.21 in earnings but the present value of those earnings remains \$1:  1.21/(1 + .1)^2 = 1.  [At a constant multiple, the stock would also be increasing at 10% per year.  That's consistent with no value creation IF you use a discount rate of 10%.]  That is why, at a 10% ROIC, the 2% and 7% grower have the same multiple.

If the chart used an 8% discount rate, then the 7% grower at 10% ROIC would have a higher multiple than the 2% grower, as they do in the chart for all ROICs greater than the assumed 10% discount rate.

I understand your math, and agree, but I think you are reading the table incorrectly.

Growth is not 10%, ROIC is 10% (top axis).  Growth is on the left axis, and it ranges from 2-7%.

If ROIC is at 10%, and growth is at 2% it means the company is reinvesting 20% of earnings - not 100%.

If ROIC is at 10%, growth at 7%, the company is reinvesting 70% of earnings.

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Posted (edited)
7 minutes ago, Sweet said:

I understand your math, and agree, but I think you are reading the table incorrectly.

Growth is not 10%, ROIC is 10% (top axis).  Growth is on the left axis, and it ranges from 2-7%.

If ROIC is at 10%, and growth is at 2% it means the company is reinvesting 20% of earnings - not 100%.

If ROIC is at 10%, growth at 7%, the company is reinvesting 70% of earnings.

You are correct.  My math would be for a 10% ROIC, 10% growth box, which is not shown on the chart.  The math for that box is easier to show and illustrates the point that higher growth under the assumptions doesn't warrant an increased multiple.  If you did the same DCF at any growth rate, it would produce the same thing under the assumption that non-reinvested cash flow is dividended out.

Do you agree with that or do you think that under a 10% discount rate assumption, growth at 10% ROIC creates value and thus 7% growth would should be valued higher than 2% growth?  [If you think that, why is the 10% growth box still at a 10 multiple?]

To be clear, I don't think 10% is actually the discount rate that has generally prevailed in equity markets given the interest rates we've had recently.

Edited by KJP
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The math is in the file. Multiple = (NOPAT*(1-(G/ROIC)))/(W-G). Plug in 1 for NOPAT and you'll get the multiples in the table.

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1 hour ago, KJP said:

You are correct.  My math would be for a 10% ROIC, 10% growth box, which is not shown on the chart.  The math for that box is easier to show and illustrates the point that higher growth under the assumptions doesn't warrant an increased multiple.  If you did the same DCF at any growth rate, it would produce the same thing under the assumption that non-reinvested cash flow is dividended out.

Do you agree with that or do you think that under a 10% discount rate assumption, growth at 10% ROIC creates value and thus 7% growth would should be valued higher than 2% growth?  [If you think that, why is the 10% growth box still at a 10 multiple?]

To be clear, I don't think 10% is actually the discount rate that has generally prevailed in equity markets given the interest rates we've had recently.

KJP, you have made assumptions that I haven't and which aren't explicit from the table.  I think I follow what you are saying, if the ROIC is 10% then reinvestment at any amount only produces 10% growth on the invested amount - get it.

This is where theory breaks down though, tax impacts dividends, so I expect there would be an actual multiple difference for those reasons alone.

To make this less theoretical, if I can get a 10% on a Gov bond and can reinvest at the same rate, and a company trading at a PE or 10 which only has 10% ROIC investment and the rest is paid out as a dividend or buybacks... I'm taking the bond every day because there is no added value from the company.

I don't like the table, I think it is not intuitive or clear... I hope you didn't write the report.

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Posted (edited)
19 minutes ago, Sweet said:

KJP, you have made assumptions that I haven't and which aren't explicit from the table.  I think I follow what you are saying, if the ROIC is 10% then reinvestment at any amount only produces 10% growth on the invested amount - get it.

This is where theory breaks down though, tax impacts dividends, so I expect there would be an actual multiple difference for those reasons alone.

To make this less theoretical, if I can get a 10% on a Gov bond and can reinvest at the same rate, and a company trading at a PE or 10 which only has 10% ROIC investment and the rest is paid out as a dividend or buybacks... I'm taking the bond every day because there is no added value from the company.

I don't like the table, I think it is not intuitive or clear... I hope you didn't write the report.

Ha! No, it’s not my chart, but it’s one I’ve seen many times.  And I agree with you that the chart (or any similar chart) has to make a number of simplifying assumptions, such as ignoring taxes, that matter in the real world.  And to really understand the chart you need to understand those assumptions.

But I don’t think you disagree with the gist of the chart, which is that, in general, multiples are related to expected growth rates and expected returns on invested capital.  That clicks for some people by reading Buffett describe See’s.  That clicks for others via charts like that and the underlying formulas and mathematics, and it is the mathematics that the original poster asked about.

Edited by KJP
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9 minutes ago, KJP said:

But I don’t think you disagree with the gist of the chart, which is that, in general, multiples are related to expected growth rates and expected returns on invested capital.

I def agree with that.  I think the best post of this I’ve ever read was by John Huber many years ago.  He’s an underrated communicator IMO.  Runs Saber Capital.

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2 hours ago, EBITDAg said:

The math is in the file. Multiple = (NOPAT*(1-(G/ROIC)))/(W-G). Plug in 1 for NOPAT and you'll get the multiples in the table.

It's definitely my ignorance, but I'm still having trouble translating this into the matrix. Essentially I understand the concept of ROIC and ROIIC and how it interplays with growth, but my trouble is converting that qualitative understanding into an actual solid understanding of what a fair price to pay is. I've seen multiple of these matrices, even ones that Mauboussin has but they never spell out the math behind the concept. Below is an additional Mauboussin excerpt. Can someone dumb the math down and show me simply???

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Posted (edited)

There is a qualitative element here which is very important: it isn't automatic that anyone can figure out if the reinvestment return can continue upward at those rates without end. It is important to figure out how long that can last as well. A business is a real thing. A good business is nice to know or have but the mechanics of reinvestment should be studied to see how stable those numbers can be and the term and why. These are real human beings producing these results in the real world. There are all kinds of obstacles from regulations to competitors as well as opportunities that go into that final number.

Edited by scorpioncapital
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2 hours ago, tnathan said:

It's definitely my ignorance, but I'm still having trouble translating this into the matrix. Essentially I understand the concept of ROIC and ROIIC and how it interplays with growth, but my trouble is converting that qualitative understanding into an actual solid understanding of what a fair price to pay is. I've seen multiple of these matrices, even ones that Mauboussin has but they never spell out the math behind the concept. Below is an additional Mauboussin excerpt. Can someone dumb the math down and show me simply???

I love Mauboussin but his can be hard to follow (and at least one of his tables I've never been able to reproduce and wondered if it was slightly off).

But this table is simpler. For the 9.4x in the top left - ( 1 * (1 - (2%/8%))) / (10% - 2%). The first one being a placeholder for NOPAT. The cost of capital of 10% is implied because that's the rate where ROIC is equal at every growth rate.

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1 hour ago, EBITDAg said:

I love Mauboussin but his can be hard to follow (and at least one of his tables I've never been able to reproduce and wondered if it was slightly off).

But this table is simpler. For the 9.4x in the top left - ( 1 * (1 - (2%/8%))) / (10% - 2%). The first one being a placeholder for NOPAT. The cost of capital of 10% is implied because that's the rate where ROIC is equal at every growth rate.

3 hours ago, tnathan said:

It's definitely my ignorance, but I'm still having trouble translating this into the matrix. Essentially I understand the concept of ROIC and ROIIC and how it interplays with growth, but my trouble is converting that qualitative understanding into an actual solid understanding of what a fair price to pay is. I've seen multiple of these matrices, even ones that Mauboussin has but they never spell out the math behind the concept. Below is an additional Mauboussin excerpt. Can someone dumb the math down and show me simply???

@tnathan It's not clear where you're getting tripped up.  I believe these are the steps:

1.  The ROIC and growth rates in the chart allow you to create a simple DCF model of cash flow to equity over time.

2. That DCF is assumed to go on in perpetuity.  @EBITDAg gave you the formula for calculating the PV of a perpetuity with constant return on reinvestment and constant growth rate.

3.  One input into the perpetuity calculation is usually referred to as the "discount rate".  It is the "r" in the traditional denominator notation "r - g".  This is normally thought of as accounting for the time value of money, risk, etc.  But another way to think about the discount rate in this model is the IRR you will receive on the assumed stream of payments if you pay the price calculated by the PV formula once you put in the return.  That is why footnote 1 in the paper you linked says "w = required return".  In other words, if you assume initial earnings are \$1, and given the stream of cash flow produced by the DCF, what price do you need to pay today to earn a 10% return?  For the upper left box, that's \$9.40, which is equal to 9.4x our assumed \$1 in earnings.

So, long story short, that chart is telling you the price you need to pay today to earn a 10% IRR on the perpetual stream of payments that would occur given the ROIC and growth assumptions.  Which step above is throwing you off?

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Thanks for the input everyone! I think I understand. Completely get that it is just a useful high level exercise to show how ROIC and growth interplay with each other but obviously these growth rates in perpetuity don't reflect the real world

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Additional question on ROIC, I read Mauboussin's paper on intangibles recently. What's everyone's thoughts on capitalizing intangibles like R&D, etc. to adjust NOPAT and Invested Capital for ROIC?

I like the idea of it, but I think it's extremely hard breaking those numbers out. Mauboussin provided a general adjustment:

- Capitalizing all of the R&D expense: 6 year amortization

- Capitalizing 30% of Non-R&D SG&A Expense: 2 year amortization

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2 hours ago, chenisheng said:

Additional question on ROIC, I read Mauboussin's paper on intangibles recently. What's everyone's thoughts on capitalizing intangibles like R&D, etc. to adjust NOPAT and Invested Capital for ROIC?

I like the idea of it, but I think it's extremely hard breaking those numbers out. Mauboussin provided a general adjustment:

- Capitalizing all of the R&D expense: 6 year amortization

- Capitalizing 30% of Non-R&D SG&A Expense: 2 year amortization

Seems like the right approach generally. 6 years feels a little long on R&D though.

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@EBITDAg thank you

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