The Price to Earnings (P/e) ratio. This is one of the most popular investor ratios, and it’s calculated by simply taking the price of a stock *P* and dividing it by the Earnings Per Share (or *EPS*).

The P/e ratio shows you the price that you pay for a stock () *relative* to its Earnings Per Share ():

It’s showing you how much you’re paying, for every dollar of profit the firm earns.

Now if we think about the *EPS,* in its simplest form, it’s calculated by taking the Net Income of the firm and dividing it by the number of shares. That’s literally it.

Now of course, because accountants love jargon, there’s a good few terms for Net Income. And it’s important that you know that all of these mean exactly the same things.

So whether we call it “net profit” or “profit after tax” or “earnings” or “profit in general”, we’re referring to the net profit, or the net income of a firm.

## Expressions of the Price to Earnings Ratio

Given that the EPS is the Net Income divided by the Number of Shares, it actually allows us to express the P/e ratio in a slightly different way.

We could express the Price to Earnings ratio as the Market Capitalisation relative to the Net Income.

In other words, we could say that the Price to Earnings ratio (P/e) is equal to:

Why is that the case?

If you’ll recall, we said that the Price to Earnings ratio is equal to the Price divided by the EPS:

Given that the earnings per share (EPS) is equal to the Net Income divided by the Number of Shares, we can rewrite this equation like so:

And we can rewrite this equation like so:

This is then equivalent to writing:

And what is the Price multiplied by the Number of Shares? Well it’s nothing but the Market capitalisation! Thus…

## Interpreting the Price to Earnings Ratio

Perhaps more importantly though, the way we interpret the P/e is that it shows you how much you pay for every one dollar (or £) of profit the firm earns.

And this interpretation holds regardless of whether you take the Market Cap over the Net Income approach, or the Price divided by the EPS approach to measuring the P/e.

### The Payback Period View

Now, given that it shows you how much you pay for every one dollar of profit the firm ends, some people argue that the P/e is a measure of payback.

They argue it shows you how long it will take for you to make back your initial investment.

### The Growth vs. Risk View

But we’d argue that it’s actually more a proxy for a firm’s *growth prospects.* And we’re certainly not alone in this interpretation.

If you accept that it can be a proxy for a firm’s growth opportunities, then it can also be argued or seen as a proxy for *risk*.

### Exploring Both Views

And to see what we mean by this, let’s consider an example.

Consider a firm whose stock price is currently $100, and whose EPS is $5.

With this data, the firm’s Price to Earnings ratio would equate to 20. Because recall that the P/e is simply the Price divided by the EPS. Meaning:

Assuming the firm’s profits remain constant, and that it pays all of its profits as dividends every single year, it would take 20 years for you to make back your hundred dollar investment!

This is the payback period interpretation of the P/e ratio.

Of course, for this to be true, we would also need to assume that the stock price remains unchanged for 20 years (something which is practically impossible).

And this is why we don’t really see the Price to Earnings ratio as a measure for the payback period.

The fact that investors are willing to pay 20 times the current earnings must mean that they expect the firm’s value to grow or to increase by substantially more than what they’re paying today.

This means intuitively, investors are either:

- expecting the earnings of the firm to grow, or
- they’re expecting the value of the firm to increase

Or indeed both. Because an increase in the value and / or the earnings would allow investors to make back their money in less than 20 years.

That is the only way in which they would be able to make it back faster.

And this obviously means that investors are essentially betting on the firm’s future prospects, meaning while growth is possible, it certainly does involve some level of risk.

Because we’re dealing with the future, and the future is obviously not guaranteed / predictable with certainty.

Thus, if you were to see the Price to Earnings as a proxy for growth and risk, then we can say that firms that have high P/e ratios tend to have high growth prospects, and also carry a high level of risk. And on the other end of the spectrum, you have firms that have low P/e ratios, whose growth prospects are possibly low, and whose risk levels are relatively low.

## Universality and Contradictions

Now importantly by no means is this universally true.

Because of course you can have high growth firms that have low P/e ratios.

And you can have low growth firms that have high P/e ratios.

Having said that, you do need to know and bear in mind that there is an alternative *risk vs. growth interpretation.*

Which is that *growth firms* are less risky compared to *non growth firms*.

In other words, if we see the P/e as a proxy for growth and risk, we’re saying that firms that have high P/e ratios likely have high growth prospects, and also have a high level of risk.

Thus, essentially, we’re saying high growth firms (or firms with high growth prospects) are are highly risky.

But the alternative interpretation is that high growth firms are actually less risky compared to low growth or non growth firms.

And the intuition here is that firms that do not grow must ultimately go bust.

They must ultimately become insolvent or dissolve.

And this of course is relying on the notion that if you don’t grow, then your competition is going to come in and take your business away. and ultimately, the trickle down effect is that you end up becoming insolvent.

Ultimately though, while we might argue about which risk versus growth interpretation is more correct, I hope you’ll agree that the risk and growth interpretation of the P/e is a much better interpretation relative to the payback period interpretation.

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