From Dividends to EPS

PDF Version: P123 Strategy Design Topic 1B – From Dividends To EPS

In Topic 1A, we started, where else, at the beginning, the foundational idea that a stock should be valued based on the present value of expected future dividends. We also saw how day-to-day reality can make theory hard to literally apply. In this Topic, we’ll take the first step toward what we see every day in the real world.

We’re going to migrate from the ivory-tower world in which all we care about is the dividend, to the real world in which we care about EPS. And we’re going to wind up with another theoretical model; one that tells you what the correct PE is. By the time you get to it, you may consider it simplistic or obvious. In fact, however, it’s going to inform a lot about how to use PE factors in strategies. You’re also going to understand why GARP (growth-at-a-reasonable-price), is not “an” approach to value. It’s “the only” approach to value – even for asset plays. The only alternative to GARP is the value trap, the fancy name for a value strategy that fails.


Recapping the Core Theory

We concluded Topic 1A with the Gordon Dividend Growth Model, a simple equation that looks like this:

  • P = D/(k-g)
    • D is the Dividend
    • k is required rate of annual return which can be derived with reference to the factors introduced in the Capital Asset Pricing Model; returns available on risk-free treasury securities, a premium (a bonus) offered to incentivize investors to assume equity market risk, and the degree of risk inherent in an individual company
    • g is the expected dividend growth rate

For reasons mentioned in Topic 1A, you cannot simply plug in numbers and be good to go. A theory is not the same thing as an instruction manual. It’s value is in the way it sensitizes us to the important determinants of stock pricing; dividends, market rates of return, company-specific risk, and growth.

Let’s now stretch our consideration to the real world.

Reinvestment of profits

Perhaps the first frustration typically experienced with the Dividend Discount Model is that many companies do not pay dividends, and many more pay dividends that are so meager as to be almost equivalent to no dividends at all.

For better or worse, many companies today prefer to retain all or most of the profit they earn. In some instances, this can be motivated by a desire to preserve a cushion for a rainy day. That’s certainly commendable. But realistically, the amount retained is usually far in excess of what’s needed to enhance survival prospects. Typically, profits retained are reinvested for future growth. Either way, profits not given to shareholders as dividends are known as retained earnings.

Earnings retention and reinvestment are more desirable than dividend payments if the corporation can earn a higher return on the money than shareholders could get (by reinvesting dividends on their own). If all goes well, the reinvestment will enable the corporation to pay a higher dividend in the future than would otherwise have been the case.

Let’s consider an example. Suppose the long-term infinite dividend growth rate we assume for mature companies is five percent and that the market required rate of return is seven percent. If Company A’s initial dividend is $1.00, according the dividend discount model, the fair price for such a stock would be $50; based on $1.00 divided by .02, which is k (*.07) minus g (.05).

Suppose, instead, that Company A pays no dividends. But because it productively uses funds that it reinvests in the business, in year three it is able to introduce a dividend of $1.75, which will then grow five percent per year forever. Assuming k stays at seven percent, the Dividend Discount Model can be used to compute a three-years-from-now fair price of $87.50; based on $1.75 divided by .02, which is k (*.07) minus g (.05). But that’s three years into the future. What’s the fair price today? That’s easy (in theory). We compute the present value of $87.50 three years hence assuming a five percent discount rate. It works out to $75.59 ($87.50 divided by 1.05 to the third power).

Voila! There’s an example of how, using the framework of the Dividend Discount Model, we not only can value a stock that has a zero yield today but even come up with a higher valuation than we could get for shares that come with a healthy here-and-now dividend.

Expanding the Dividend Discount Approach

Essentially, you can find the above approach discussed in good valuation textbooks as “multi-stage” dividend-based models. Above, we assumed a company paying no dividends today would introduce one three years from now. We then applied a dividend based valuation post-dated three years out, and then translated it to a current stock price by applying the PV formula. Other variations might assume a dividend is introduced X number of years into the future, that dividend growth would be at a high rate in the initial stage, and that the rate of dividend growth would then settle into a presumed infinite growth rate. You might even have more than one stage for different levels of above-normal growth rates.

Here’s are the parameters for an example of a four-stage model:

  • At all times, we assume k, the required rate of return, is 8% annually
  • First Stage:
    • No divided at all
  • Second Stage starting at the beginning of Year 5:
    • Introduce a $.25-a-share dividend that grows at an annual rate of 12%
  • Third Stage starting in Year 8:
    • Dividend growth rate slows to 8% per year
  • Fourth Stage starting in Year 12:
    • Dividend growth shifts down to a presumably infinite rate of 3%

To value the stock, let’s establish the dividend for each of the 12 years:

  • Start of Year 1: zero
  • Start of Year 2: zero
  • Start of Year 3: zero
  • Start of Year 4: zero
  • Start of Year 5: $0.25
  • Start of Year 6: $0.28
  • Start of Year 7: $0.31
  • Start of Year 8: $0.35
  • Start of Year 9: $0.38
  • Start of Year 10: $0.41
  • Start of Year 11: $0.44
  • Start of Year 12: $0.48 with an infinite period of 3% annual dividend growth thereafter

We’ll start with a Year 12 valuation. Applying the dividend discount model, 0.48/(.08-.03), we get $9.60. Use the basic present value formula to compute today’s equivalent.

  • PV = 9.60/(1.08^12) = 3.81
  • Compute the PV of each preceding dividend payment
    • 0.44/(1.08^11) = 0.189
    • 0.41/(1.08^10) = 0.190
    • 0.38/(1.08^9) = 0.190
    • 0.35/(1.08^8) = 0.189
    • 0.31/(1.08^7) = 0.180
    • 0.28/(1.08^6) = 0.176
    • 0.25/(1.08^5) = 0.170
  • Finish by adding up all of the PV components
    • 3.81+0.189+0.190+0.190+0.189+0.180+0.176+0.170 = 5.094 = $5.09

It’s important to reiterate that this is not an instruction manual. Do not try to plug numbers into an Excel spreadsheet built along these lines. Doing so would require far more precise forecasting than is feasible for ordinary humans. But the additional contribution it makes to our overall framework is invaluable.

As a result of the original dividend discount model and its multi-stage extension, we now understand that when evaluating stock prices, we need to consider (i) market rates of return, (ii) corporate risk, (iii) how much of a premium we expect to receive to compensate us for the risks we take, (iv) present dividends if any (v) future dividends, (vi) the amount of money retained by the company, and (vii) and how effectively the company is able to use the capital at its disposal.

Notice how we are now moving closer to the sort of fundamental analysis experienced investors recognize and apply. But we’re not all the way there yet. So let’s continue.

 The EPS fiction

The day-to-day reality you observe includes little discussion of dividends, present or future, except for those investors who specifically want to emphasize income stocks. In fact, we might even observe that investment analysis today seems to have become uncoupled from dividends. We understand the challenge of dividend-based investing; the multi-stage dividend model illustrated above would pretty much have to represent the template for most real-world situations, given our expectations relating to retained earnings and near-term, and even long-term, higher-than-infinite-rate growth expectations. Yet the model is too cumbersome for actual use.

The practical solution traces back to modern approaches to reinvestment of profits. For better or worse, the investment world has reached the point where shareholders are so supportive of management decisions to retain and reinvest profits in whole or in large part, that they behave as if all of the profits of the company were paid to them as dividends and as ifthey freely chose to reinvest the money back into the company. Obviously, this is fiction. But it’s a vital fiction. It’s what paves the way for valuing stocks on the basis of profit, or earnings per share (EPS), the source from which dividends come.

So now, instead of looking at dividend yields, we can substitute an earnings (E) yields, which are computed as follows:

Earnings Yield = E/P

Here comes another culture thing. Does E/P look familiar? It should. Turn it upside down and we get something you see all the time: P/E!

Now, here’s the fun part for those who love theory. We can substitute E into the dividend discount model and wind up with a formula that gives us an ideal P/E.

  • P = D / (k-g)
  • D = E * dp where dp is the Payout Ratio, the percent of profits that are paid out as dividends
    • Therefore . . .
  • P = (E * dp) / (k-g)
    • Now applying some basic algebra, we can divide each side of the equation by E and get . . .
  • P /E = dp / (k-g)

Again, the realities of the need for an infinite growth assumption and the prospect that a payout ratio might be zero make this difficult to use day to day in the real world (I think I’m safe in assuming nobody wants to take the trouble to use a multi-stage approach every time they look at a stock). But it nails down some very important things about P/E ratios:

  • Faster growing companies really do deserve higher P/Es (it’s not just something somebody on TV makes up to help him or her push stocks.)
    • We know this because as g rises, the denominator of the dp/(k-g) fraction shrinks, and as the denominator shrinks, the result, P/E, rises.
  • Shares of riskier companies should fetch higher P/Es (this, too, is real; it’s not something made up by TV cynics who want to argue against the other talking head who is advocating higher P/Es for growth stocks).
    • We know this because riskier companies have higher Betas and higher Betas make for higher k values, as we saw in the first installment of this series. And as k rises, the denominator of the (k-g) fraction rises and that translates to smaller numbers for the final result, P/E.

So now we understand that there are absolute and ironclad bases for asserting that P/E matters, that P/E should be higher for shares of companies that can grow more quickly, and that P/E should shrink as risk rises. This isn’t folklore. It isn’t just somebody’s opinion. It is part of the core of how we looking at stocks. We now understand that we can never simply look at a P/E and automatically say it’s too high, too low, or just right. We must always consider PE in light of risk and expectations of future growth.

And, by the way, we also understand now why interest rates are so important. Again, this is not something people on TV say just so they can get airtime. If the Fed tightens, that reduces the supply of money. If the supply of anything is reduced, all else being equal, the price goes up. The price of money is the interest rate. As interest rates rise, we have to plug in higher numbers for risk-free rate assumptions and that means k rises. As k rises, P/E comes down. So once again, this is not folklore or opinion. It’s for real.

Now, here’s what makes all this so hard. If interest rates rise, P/E drops. But what about P? Can P rise in the face of rising interest rates? Let’s go back to our earlier, longer, form of the EPS-based valuation model:

  • P = (E * dp) / (k-g)

Suppose the Fed tightens and ultimately drives k higher because it sees that the economy is strengthening, which, logically, is what could or would lead the Fed to do that. A stronger economy makes it likely corporate profits, E in the equation, will rise. If E rises, that means we have a higher numerator in the (E * dp) fraction. A higher numerator translates to a higher result; i.e., a higher P.

What this means is that we cannot automatically assume rising rates will hurt the market. It may or may not depending on whether the investment community believes the stronger economy will allow the company to drive E high enough to offset the impact of falling P/E ratios. Once again, this is not folklore or opinion. It’s real. (By the way, speaking of what’s for real, it’s my bona fide opinion that if/when rates rise, the market will get hammered, but I’ll have to postpone discussion of that until we get to a later, “behavioral,” addition to all this.)

Must it be All EPS All the Time?

Perhaps by now you are wondering about all the other fundamental notions you’ve seen and/or read about. What about Price/Sales? How about Cash Flows? (Isn’t Cash supposed to be King?) Where do asset plays fit in? Warren Buffett likes Return on Equity, what’s up with that? Does Current Ratio matter? And what about technical analysis? Is that all a bunch of voodoo?

So are a lot of people are committed to doing some really dumb things, or is Gerstein incredibly narrow-minded. I hope the latter isn’t true, but for purposes of this topic, the answer is: None of the above. We’ll see how and why in the next part of this series.

Post Script on Asset Plays

On reflection and after a self-edit, I just realized I can easily polish off the asset-play topic right now. Here goes:

If I’m contemplating sale of one or more corporate assets to a private buyer, I’d pretty much have to consider everything we talked about in this installment and in Part 1. What is the present value of the dividends/profits the buyer is likely to receive as a result of owning the assets.

The only significant difference in approach is what is referred to as a “control premium,” the expectation that a private buyer would pay more for a particular level of earnings than a buyer I the public equity markets. That sounds coolly quantitative. Actually, though, it’s ego. The private buyer is in effect saying to himself or herself “If I owned this asset instead of those Bozos and were the one making all the important decisions, the results would be much better, so I can afford to kick the growth assumption way up and pay the saps, oops, the public shareholders, a premium above the current market price and still make out like a bandit when all is said and done. And, of course, my compliance costs would be lower since I don’t have to deal with 10-Qs, guidance, and conference calls with the dumb . . . oops again, analysts.”




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