PEG ratios

[banter]

PEG ratios
The PEG ratio can be used to try and find underpriced shares. It’s the PE ratio divided by the ‘growth rate’ – which is the investor’s estimate of likely annual percent growth in coming years.
Peter Lynch, wrote in his 1989 book One Up on Wall Street that "The P/E ratio of any company that's fairly priced will equal its growth rate", i.e., a fairly valued company will have a PEG of 1.
I got to wondering what was more important – growth or dividend yield? And by how much? What’s better – a company with a net yield of 13% and a growth rate of 4% - or a dividend yield of 4% and growth of 13%?
In the above example, Peter Lynch would say the 4% growth company should be on a PE of 4, and the 13% one on a PE of 13. I made a model to investigate this.
The model took some hypothetical companies with growth rates ranging from 4% to 14%. It assumed the companies pay out 70% of their earnings in dividends, all over a seven year period. It asked the question:
What should the PE be for each of these companies in order that an investor get the same compound annual growth rate (CAGR)?
The answers depend a bit on what CAGR is used, so the model looked at CAGRs of 14%, 15% and 16%.

	Equal-return PE values,
	for given CAGRs and %growth factors
	CAGR %
GF%	16%	15%	14%
5%	4.7	5.2	5.8
6%	5.3	5.95	6.8
7%	6.1	6.9	7.9
8%	7.05	8.1	9.5
9%	8.3	9.7	11.7
10%	10	12	15
11%	12.4	15.5	20
12%	16	21	30
13%	22	32	56
14%	34	62	300

The chart of this data (below) is asymptotic – almost linear for lower growth factor percentages, and then rising rapidly. Note the theoretical PE of 300 for 14% growth and 14% CAGR (omitted in the chart because it is literally off the chart)
peg.jpg
Note also that for lower CAGRs and higher GF% factors, the theoretical PE rapidly goes off the scale, to hundreds, thousands, or unattainable. For example, the theoretical PE for a CAGR of 10% and growth rate of 10% is 1,500.

So back to Lynch's statement that PEGs should be 1 - the table below shows theoretical PEG values, derived from the table above.
With CAGR% of 14-16%, and growth rates under 10%, Peter Lynch’s ‘PEG should be 1’ statement more-or-less holds. But for growth rates above 10%, the ‘equal return PE’ rapidly goes off the scale and generates very high (or infinite) PEs, and the theoretical PEG is much higher than 1.

	Equal-return PEG values,
	for given CAGRs and %growth factors
		CAGR
GF%	16%	15%	14%
5%	0.9	1.0	1.2
6%	0.9	1.0	1.1
7%	0.9	1.0	1.1
8%	0.9	1.0	1.2
9%	0.9	1.1	1.3
10%	1.0	1.2	1.5
11%	1.1	1.4	1.8
12%	1.3	1.8	2.5
13%	1.7	2.5	4.3
14%	2.4	4.4	21.4

Conclusions
1) This model suggests that the market might tend to undervalue high growth companies. And that’s its worth looking for companies that have high growth. I think this effect explains the very high PEs seen in, for example, the retirement sector.
2) It also suggests that the market tends to overvalue low growth companies.
3) It suggests that a higher PEG than 1 should apply for companies with growth factors above 10% - much higher above 13%.

By this model I think there are quite a few undervalued companies on the NZSE.

[Snow Leopard]

I have to say I believe that there is something very wrong with all of this - it does not stack up.

Best Wishes
Paper Tiger

[percy]

In NZ with very high dividends you may find using PEGD more practical.D=dividend.

[Snoopy]

Bunter, I am trying to understand your graph. You have graphed the PE 'required' to give a Compound Annual Growth rate of 14%, 15% and 16%. But PE is just a market valuation, entirely controlled by what investors are prepared to pay. OTOH compound anual growth rate generally refers to an internal company performance measure of sales or profits. There is no direct connection between these two measures, I would suggest.

SNOOPY

[banter]

You have graphed the PE 'required' to give a Compound Annual Growth rate of 14%, 15% and 16%... There is no direct connection between these two measures, I would suggest.

SNOOPY

Assume the market is perfect and all shares are fairly valued and it doesn't matter which one an investor picks - the return is the same.
Let's say the return, over 7 years, dividends reinvested, is 16% each year, for all stocks.

The investor's CAGR is then 16%.

Now consider 10 shares, with growth rates of 5%, 6% etc through to 14%.
Say each earns 10cps (growing at whatever % per annum)
Each pays 70% of earnings as a dividend, which the investor reinvests.

What price would each share need to start at, so that each share returned the investor 16% per annum at the end of seven years?

Put another way, *what PE is required* so that each share gives the investor a CAGR of 16% per annum?

That's the connection.

According to Lynch, the 4% share should be priced at a PE of 4 - or 40c, and the 14% one, at $1.40.
I got a different answer - PEs of 4.7 and 34 in that example.

[banter]

I have to say I believe that there is something very wrong with all of this - it does not stack up.

Best Wishes
Paper Tiger

I think the maths is OK, but happy to give the spreadsheet to anyone who wants to check it.

In my model, if a stock has a growth factor of, say, 20%, and you drop the start-of-modelling price, the CAGR will fall towards but never reach 20%. So it's impossible to get the CAGR below that - in my model.

The problem is probably that high rates of growth are not sustainable.

The market 'knows' this and at the end of seven years of, say, 20% annual growth in a stock, compounded, will begin begin to price the stock on lower growth percentages and lower PEs.

The model assumes the PE at the start is the same as the PE at the end. But it probably will be lower in practice, for a very high growth stock - because very high growth rates *must* fall.

That all said - I still think the market might not be giving enough weight to growth.

[Snow Leopard]

Given what you have said over the last couple of posts then the formula for the Price Earning Ratio R is:

R=0.7/(CAGR-GF)

giving these results:

Banter-Calc.PNG

Best Wishes
Paper Tiger

[banter]

Given what you have said over the last couple of posts then the formula for the Price Earning Ratio R is:

R=0.7/(CAGR-GF)

giving these results:

Banter-Calc.PNG

Best Wishes
Paper Tiger

Thanks for working that out PT! I decided it would take me a long time to work out so used than trial-and-error.

There is a small difference in the results, and I'm wondering if the formula takes account of dividend reinvestment. This is what put me off trying to get the formula.

Doesn't matter though - the formula gives about the same results, and gives the same shape curve: near-linear with typical GF and CAGR values, and then asymptotic growth with higher GF values.

Based on that I still wonder if high growth stocks should have a higher PEG (and higher PE) than the market gives.

Might post some real life NZ figures later.