# The P/E Ratio Part 3

Continuing from The P/E Ratio Part 1 and The P/E Ratio Part 2

So far we been using some unlikely assumptions, namely that this fictitious company we are going to buy has a constant earnings stream and that there is no risk involved in that earnings stream. Of course the real world is quite different! Let’s next decide on how a changing earnings stream can affect the present value of all those future annual earnings.

### The Math is Not Much Different

The math is not really different, we just have to take an extra step. Before, we were just assuming that a company would produce \$1 in annual earnings forever. But let’s now pretend that our company is expected to grow it’s earnings by 10% per year. Therefore, instead of an earnings stream that looks like this:

Year 1: \$1.00, Year 2: \$1.00, Year 3: \$1.00… etc.

It will instead look like this:

Year 1: \$1.00, Year 2: \$1.10, Year 3: \$1.21… etc.

If we just do the math for the first 3 years, you will get the picture of how a changing earnings stream can affect a price someone is willing to pay for a company. If you recall from Part 2 of this series on the P/E Ratio, we need to figure out what we need to invest TODAY at 3% (or whatever the “risk-free” rate of return is) to replicate the earnings that will be earned at some point in the future. In our new company here that grows it’s earnings at 10% per year we find that we might pay \$1.00 for this years \$1.00. But it is going to earn \$1.10 in the second year – so what amount of money invested today at 3% will give us \$1.10 in one year? The answer is \$1.07. Likewise for the \$1.21 it is expected to earn in Year 3 – what amount do we need to invest today at 3% in order to replicate that \$1.21 in two years from now? The answer is \$1.14.

At this point, I could show a revised graph which shows the present value of the income stream for a company that can grow it’s earnings at 10% forever, but not many companies can do that. What is more realistic is to look at the following situation:

### A Hypothetical Company’s Life Cycle

Suppose we have a relatively new company that is turning a profit and is still in it’s growth phase. During this growth phase it is expected to grow it’s earnings at 20% per year for 5 years as it gains market share and more customers. After the first 5 years, earnings growth slows down to about +10% per year for the next 5 years, and then slows down to +5% for the next 5 years. At this point, it has reached it’s market saturation point and perhaps earnings hold steady for the next 10 years. During that time, some competitor companies figure they can take a slice of their market and start up operations, and over time start to move some customers over away from “our” company. Our company therefore experiences an earnings decline of -5% per year for the next 10 years. At this time, our company and the competitors have found an equilibrium point and our company’s earning are now not declining further, nor are they increasing from this point on until the end of the 80 years.

The above Life Cycle might represent a more realistic earnings stream for a real-life company. Now that we have a projection of what the future income stream might look like, we can again add up all the present values of those annual earnings to figure out a fair price for those earnings. I have charted both the annual earnings (in red) and the present value of those future earnings (in green).

If we add up all the present values this time we get a sum of \$71.81. This is quite a bit higher than the \$30.20 we came up with in part 2, but remember part 2 assumed \$1/year for 80 years. Whereas in this case, the earnings grew from a start of \$1/year to as high as \$3.55/year, and then declined to about \$1.56 per year. So you can see how earnings predictions are so important and why the market seems to be so sensitive to them.

Ah, yes. Again we have yet to factor in that if we were to offer \$71.81 for this future earnings stream, we are assuming there is no risk involved – and of course, this couldn’t be further from the truth. There is the risk that this company goes out of business due to competitors, their product could be rendered obsolete by new technology, a poor economy in general, you name it. Any of those things could affect future earnings and there is a risk that our predictions for the income stream may not be fulfilled. We could put our \$71.81 in a high interest savings account at 3% and basically replicate this earnings stream with no risk, therefore we would be crazy to offer \$71.81 for this company – we would have to offer LESS money for this expected income stream to compensate us for this extra risk.

If you offered \$40/share for something you have calculated to be worth \$71.81 today, this discount represents the compensation for the risk you are taking. The constant bids/asks on the stock market for shares of companies are basically people weighing in on what their perception of a good discount is for that future earnings stream for those particular companies.

I’ll end Part 3 there, and Part 4 will conclude by tying it all together and giving a more realistic sense of how P/E ratios are used in the real world.

Preet Banerjee
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• Po

You have made this so clear with the way you write about intimidating topics (for a beginner like me) – you are really, really making me interested in learning more for myself – because I know there is so much – I am going to read every article on your blog.

• Deb

Hi Preet. I have a hard time wrapping my head around DCF and this was the clearest explanation I’ve read on the subject. Could you expand on the last paragraph…”If you offered \$40/share for something worth \$71.81, this discount represents the risk…”? How does one quantify this discount? I’m finding there’s a gap in my understanding from this last point to your follow-up in Part 4. Thanks!……Debra

• Preet

Hi Deb – no problem: If you are looking for an exact formula for calculating the discount you should offer, there really isn’t one (or one generally accepted model). Rather, the current stock trading price reflects what the market as a whole is valuing that discount as. They may not be right – and this is probably where your hang up is occuring. You might be looking for a method to exactly determine what discount you should offer for the stock, but no one can really do that. For example, one person may say in their mind that they believe company X will probably not go out of business in the next 10 years and they would be prepared to offer a price that has a smaller discount for risk. But they might see company Y (which is a competitor that might take big risks in company strategy) as having a small to good chance of going out of business, or having crippled future revenues if their riskier company business strategies don’t pan out. They might expect a bigger discount to account for the higher perceived risk.

So really, the discount quantification is more subjective. Investors who feel confident about making accurate risk assessments of a business might have a number in their head that they are willing to pay for a company and they will hold off on purchasing the stock until the market trades that stock’s price down to that value.

Let me know if that makes sense, or if you have any further questions. Have a great weekend!