# The Gordon Growth Model

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=D _{1}/(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. - ‘D
_{1}‘ 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 D_{1} of 191.81.

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

- P=D
_{1}/(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=D
_{1}/(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.

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