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Simple Math in Investing - A Total Return Perspective
Posted by: Grahamites (IP Logged)
Date: June 12, 2014 01:39PM

I’ve been contemplating quite a bit recently with regards to the concept of total returns versus the usual intrinsic value calculation, which is the modern day norm. Too often we are inundated with all the data and noises that we forget that there is a simple logical formula for the total return of an investment in a stock.

If we think about it, the return from an investment in common stock of a company is made up of the following:

1. Dividend Yield

2. Earnings Growth/Contraction

3. Multiple Expansion/Contraction

4. The reinforcing or balancing interaction between earnings and multiples

Therefore, in simple terms, the mathematical total return can be expressed as the formula below:

Total Return = Dividend Yield + % Change in EPS + % Change in P/E + (% Change in P/E * % Change in EPS)

Let’s walk through a few scenarios.

Scenario 1:

 Present 1 Year Later % Change EPS 5 6 20% Dividend 1 1 0% P/E 20 25 25% Implied Stock Price 100 150 51% (50% price return + 1% dividend yield)

Plug in the numbers to the formula:

51% = 1% + 20% + 25% + (25%*20%)

Scenario 2:

 Present 1 Year Later % Change EPS 5 6 20% Dividend 1 1 0% P/E 40 30 -25% Implied Stock Price 200 180 -9.5% (-10% price return + 0.5 % dividend yield)

Plug in the numbers to the formula:

-9.5% = 0.5% + 20% - 25% + (20% x -25%)

Scenario 3:

 Present 1 Year Later % Change EPS 5 4 -20% Dividend 1 1 0% P/E 20 18 -10% Implied Stock Price 100 72 -27% (-28% price return + 1% dividend yield)

Plug in the numbers to the formula:

-27% = 1% - 20% - 10% + (-20%*-10%)

Scenario 4:

 Present 1 Year Later % Change EPS 5 4 -20% Dividend 1 1 0% P/E 4 6 50% Implied Stock Price 20 24 25 % (20% price return + 5% dividend yield)

Plug in the numbers to the formula:

25% = 5% - 20% + 50% + (-20%*50%)

All above four scenarios are in the most simplistic form for illustration purposes. Readers may have noticed that the first two scenarios resemble growth companies and while the latter two remind us of declining businesses. I purposely left out the scenarios where earnings are flat. I encourage the readers to try this exercise on their own.

What is clear from the above scenarios is that while the percentage changes are the same, the total return in our imaginary scenarios differ vastly. The question is why is that?

From my observation, most of the time, investors focus only on the first two parts of the equation. Namely, dividend yield and earnings growth. This is understandable because they are at the core of fundamental analysis. What is missing, obviously, is the anticipated change in multiple and the reinforcing or balancing interaction between earnings change and multiple changes. Said differently, the psychological part of investment analysis, or arguably what Howard Marks (Trades, Portfolio) calls the human side of investing.

In scenario 1 and scenario 2, the business grows its earnings by 20%. However, the expectations are so high in scenario 2 that an investor could actually lose almost 10% in a company growing earnings at a fabulous rate. If you think this is just all hypothetical, take a look at Wal-mart and Coca-Cola’s history; you will find repeated patterns of both scenario 1 and 2.

Similarly, in scenario 3 and scenario 4, the business shrinks its earnings by 20%. However, the expectations are so low in scenario 4 that an investor could actually make 25%. Recent examples include Dell (DELL) and Hewlett-Packard (HPQ). The expectations were so low and both businesses were still profitable. When a stock is selling at a P/E multiple of 8, a change from 8 to 9 is 12.5%, from 8 to 10 is 25% and from 8 to 12 is 50%. A 50% multiple expansion from low levels can perfectly offset the decline in earnings, as we can tell from the total return formula.

The lesson is clear: While earnings and dividends are enormously important, it would be foolish to ignore multiple expansion/contraction and the reinforcing or balancing interaction between earnings and multiples.

Before I end this article, let me point out that this total return formula is just a broad framework. It won’t apply to special situations and it won’t apply to cigar butts. When you apply it in reality, you won’t be able to figure out what will happen to either earnings or to the multiples. Faced with this dilemma, we have no choice but to resort to the core of value investing - margin of safety.

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Re Simple Math in Investing - A Total Return Perspective
Posted by: giovannivittorio (IP Logged)
Date: June 13, 2014 09:12AM

ok...ok...simpleeeeee....

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Re Simple Math in Investing - A Total Return Perspective
Posted by: Grahamites (IP Logged)
Date: June 13, 2014 11:01AM

Giovannivittorio - I'm not quite sure whether I get your point.

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Re Simple Math in Investing - A Total Return Perspective
Posted by: findrichard (IP Logged)
Date: June 13, 2014 01:07PM

I like it. Not sure how I can use it, but I like it. Guess I will just have to stick with the Graham Number caculations to help identify that margin of safety.

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Re Simple Math in Investing - A Total Return Perspective
Posted by: jtdaniel (IP Logged)
Date: June 15, 2014 07:08AM

Hi Findrichard,

I think Grahamites' suggestion is to project the rate of earnings growth + total dividends over a projected holding period, and then apply a reasonable multiple to the expected earnings at the end to estimate total return. Plugging in a low earnings multiple at the end of the holding period will provide a margin of safety. If I wanted to buy IBM shares today and hold them for five years, I could get a margin of safety by assuming a P/E of 10 or 12 on the projected 2019 earnings. My decision to buy or pass would then turn on whether the projected total return under that scenario is acceptable to me. If not, I would need to wait for a lower price before buying IBM.

Although return on equity (ROE) was beyond the scope of this article, it is an additional factor to consider in projecting total return. IBM's consistently high ROE provides a built in margin of safety, as long as its ROE remains high and a reasonable earnings multiple is assumed at the end of the projected holding period. Due to the rapidly increasing equity, the market has a tendency to place a fair if not premium multiple on companies that can produce a consistently high ROE.

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Re Simple Math in Investing - A Total Return Perspective
Posted by: Grahamites (IP Logged)
Date: June 15, 2014 10:38AM

Findrichard - Thanks for your comments. Jtdaniel did a fabulous job explaining my intended point. Graham's formula is a good starting point but it doesn't incorporate the current participant's expectation in my opinion. I would follow Jtdaniel's suggestion of plugging a conservative multiple to incorporate the margin of safety. If the resultant implied return is satisfacory, the investment may very well be worthy of considering.

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Re Simple Math in Investing - A Total Return Perspective
Posted by: Grahamites (IP Logged)
Date: June 15, 2014 10:39AM

Jtdaniel - Thanks for your comments. That's exactly what I would do:)

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Re Simple Math in Investing - A Total Return Perspective
Posted by: jtdaniel (IP Logged)
Date: June 15, 2014 02:34PM

Hi Grahamites,

Thank you for yet another insightful article. I find that this kind of analysis can be applied to numerous stocks found on the Buffett-Munger and Undervalued Predictable screens. Now is a great time to put together a shopping list and wait for Mr. Market's mood to grow darker.

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Re Simple Math in Investing - A Total Return Perspective
Posted by: Grahamites (IP Logged)
Date: June 15, 2014 09:04PM

Jtdaniel - You are absolutely right. It's more applicable to companies whose predictability are high. In fact, I would argue don't even think about applying it to stocks like Tesla. What I've found out about the Buffett-Munger list though, is that you have to be careful with regards to the moat trend of the companies as well as the actual predictability. I'd argue for quite a few of them, the moats are narrowing or the predictability is no longer that high. In both cases a much lower multiple is warranted. Examples are Bed Bath & Beyond and Panera Bread:)

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