Gordon's Tonic

Published in Investing on 1 March 2010

Put some fizz into your investing with a classic little formula.

The 'Gordon Growth Model' is the best known, and the simplest, of the valuation models. The point of a model is to offer investment analysts (and private investors) a structured way to make like-for-like comparisons. They're a set of rules and assumptions that help us to see which opportunities look most attractive.

Meet Mr Gordon

'Gordon' was in invented in 1959 by Myron J. Gordon. He's an American academic who, at 89, is still going strong at Toronto University. His model has been the bedrock of finance courses for decades. In its original form the model is rarely used today by professional analysts: big investment houses often use very complex 'proprietary models' that are guarded as trade secrets. But, at heart, they are often just expanded versions of Gordon's original.

Let's have a look at the model:

P=D1/(r-g)

It doesn't look much, does it? Four components are arranged in a simple ratio:

  • 'P' is what you're trying to calculate: the 'correct' price of a share, or a share index.

  • 'D1' is next year's dividend. It's important to use the expected (or 'forward') dividend for the year to come, and not the dividend just paid (the 'historic' or 'trailing' dividend).

  • 'r' is the return that you as an investor require from the share. This can be confusing. You are free to insert any number you like into 'r'. The higher the return that you personally require, the lower the price at which you should be prepared to buy a particular investment. When valuing an index using Gordon Growth it's normal to plug a long-term estimate of the Equity Risk Premium into 'r', plus the risk free rate.

  • 'g' is the growth. It's an estimate of the rate at which a company's earnings (or the aggregate earnings on an index) will grow in perpetuity. The 'in perpetuity' bit is worth mentioning, because this assumption is easy to challenge. Can any firm, or any economy, grow forever? More advanced versions of the model have two or more phases: a high growth phase, usually followed by a stability phase. But the original Gordon assumes constant growth until the end of the universe.

So we can now use the Gordon Growth Model to answer a question: do we think the FTSE 100 is overvalued?

Assumptions

Assumptions are needed: for the sake of argument (and what a colossal scrap we could have over this!) we will assume that the world economy will grow at 3% a year, on average, from now on. Don't all laugh at once; it's just an assumption. We will further assume a risk free rate of 3% and an Equity Risk Premium of 5%. Long-term estimates of the Equity Risk Premium tend to fall in the range 4-7%; leave the academics to fight over the 'correct' figure for now.

The FTSE 100 closed on Friday 19 February 2010 at 5,358, with a historic dividend yield of 3.46%. This means that the value of its dividend in numerical terms is 3.46% of 5,382, or 186.22. Apply the growth estimate of 3% to this number and we arrive at a D1 of 191.81.

The Gordon Growth Model can now tell me what the FTSE 100 should be worth:

  • P=D1/(r-g)

  • P=191.81/(0.08-0.03) (8% and 3% are expressed as decimals in the model)

  • P=191.81/0.05

  • P=3,836

Our conclusion, then, is that the FTSE 100, based on our estimates of equity returns and world economic growth, should be priced at 3,836. Knowing that the closing price on Friday was 5,358, we could further conclude that the index is overvalued by 1,522 points, or nearly 40%.

If an investor had total confidence in this conclusion he would charge off and short the FTSE 100 with all his might. But don't all rush at once: Gordon Growth is extremely sensitive to the assumptions you feed to it.

Sensitivity

Look what happens, for example, if we plug a smaller number than 8% into 'r': we might decide that 4% is a better long-term estimate of the Equity Risk Premium than 5%, and that we want to use a risk free rate, based on current Bank of England base rates, of 0.5%. 'r' is now 4.5%.

Running the formula a second time to reflect this change, we get:

  • P=D1/(r-g)

  • P=191.81/(0.045-0.03)

  • P=191.81/0.015

  • P=12,787

Quite a difference, isn't it? Just by tweaking our number for 'r' we have moved from an index overvalued by 40%, to one undervalued by 138.6%!

And here's the point: Gordon Growth is a tool, not an oracle. Simplicity is its strength as well as its weakness. At best, it can help an analyst to categorise a series of investment opportunities as 'Buy' or 'Sell' relatively quickly. At its worst, it can be like a detective who says "the chief suspect is a man, or woman, aged 18-80, between four feet six and six feet two; go get 'em!"

In that sense, Gordon Growth has much in common with Gordon's and Tonic: lots of fun, easy to make, but leads to tears in the morning if you hit it too hard.

More from R.J. Johnson:

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Comments

The opinions expressed here are those of the individual writers and are not representative of The Motley Fool. If you spot any comments that are unsuitable hit the flag to alert our moderators.

CGDaveS 01 Mar 2010 , 8:58am

Bit philosophical for a Monday morning but the article got me thinking. Intended to be just a bit of fun as Peter Snow used to say when he had control of the swingometer,

My gut feeling is that the stock market´s moves are somewhat akin to changes in scientific orthodoxy (Kuhn´s paradigm´s shifts).

http://www.imrecon.co.uk/comment/paradigms

Most analysts will have broadly similar numbers in their models and come up with similar answers. Some external change will lead them mass adjustment of the assumptions - to come up with new similar answers - the new paradigm - which may (or may not be) a better representation of reality.

There will always be outliers - but there´s less money in being Copernicus or Galileo if every one else is working on the basis of an earth-centred universe - even if you´re proved right in the long run.

Is this simply a long winded way of saying the trend is your friend... until the bend at the end?

But how long before the bend?
It took four hundred years for the Vatican is to complete its rehabilitation of the great scientist by erecting a statue of him inside the Vatican walls.
http://www.timesonline.co.uk/tol/comment/faith/article3478943.ece

But by that time most of the world outside the Curia had long moved on. Are stock market participants in danger of clinging onto similarly outdated assumptions?

SmudgeButt 01 Mar 2010 , 9:30am

I always say to people at work a small error can through a whole piece of work into question.

There is no such place as Toronto University. It's the University of Toronto. Even Wikipedia (which is otherwise riddled with errors)gets that right.

Ok I'll go back to pedant's corner now.

BarrenFluffit 01 Mar 2010 , 9:45am

Nice piece. Also illustrates the problem of multiplying uncertain numbers together.

Fingered 02 Mar 2010 , 10:39pm

Unless you have malaria risks, try instead Gordons and orange, you will get much less of a hangover without all that quinine. :-)

namron101 04 Mar 2010 , 9:14am

@SmudgeButt

Did you mean that "a small error can THROW a whole piece of work into question"?...

I will join you in pedants' corner.

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