One of the trickiest elements of investing is finding out how much to pay for a stock.

To make things simple, investors often divide the current stock price of a company by its earnings-per-share to gauge how expensive or how cheap the company’s shares are. This is known as the price-to-earnings, or PE, ratio.

For instance, a company that is earning $1 a share and trades at $20 a share has a PE ratio of 20. Another company that is earning $1 a share and trades at $10 a share has a PE ratio of 10.

On the surface, the latter company seems cheaper. But that’s not always the case. Other factors such as growth rates, reliability of earnings, and durability of growth come into play.

With many variables influencing stock valuation, here’s a simple framework that helps me gauge what is the right PE ratio to pay for a stock.

## The DCF method

Before going further, we need to understand the discounted cash flow (DCF) valuation method. A DCF is the backbone behind valuing any stock.

The idea behind the DCF is that the value of a stock is the sum of all its future cash flows discounted back to today.

Let’s start with a simple example. Company A earns and pays out $1 a share in one year’s time before it closes down. If you are an investor, you will not want to pay $1 for a share of Company A today. You will want to pay less than $1 so that in one year’s time you will be able to reap a profit. Let’s say your required rate of return is 10% per year. In this case, you will only be willing to pay $0.909 ($1 discounted by 10%) a share. In a year’s time, you would be given back $1, which is 110% of your initial capital.

This is the thinking behind the DCF method of valuation. If a company will survive for more than a year, we can add more cash flows to the equation and solve for the net present value in order to ensure that we earn our required return.

## Setting the stage

The DCF is the core concept that drives stock valuation. The PE ratio that we discussed earlier is a shorthand that gives us a quick sense of how much we are paying for a company.

Using the DCF method, and making some assumptions, we can find out what is a fair PE ratio to pay. To make things simple, I will make a few assumptions and parameters for this exercise. They are:

- First, in the following examples, I use a 10% required rate of return.
- Second, I assume that the companies’ earnings are the same as free cash flow to the shareholder.
- Third, I assume that these earnings are distributed to shareholders who can invest the cash at a similar required rate of return (10% in this case).
- Fourth, the companies’ earnings grow or shrink at the stated CAGR (compounded annual growth rate) evely.
- Fifth, investors hold these stocks forever or until the business closes down.

## A no-growth company

Using the assumptions above, let’s start with how much we should pay for a no-growth company.

Let’s say Company B will earn $1 a share a year for eternity. As mentioned above, our required rate of return is 10%. The DCF formula to find the net present value of this company is:

*(E*(1+G))/(R-G), where E is next year’s earnings, G is growth and R is the required rate of return.*

Plug Company B’s numbers into the equation and you get a value of $10 a share.

In this case, an investor will need to pay $10 a share to earn 10% per year. This makes perfect sense as the earnings yield needs to meet our expected rate of return because the company is not growing. **In this scenario, the fair PE ratio is 10** (we need to pay $10 a share for Company B that is earning $1 per share).

## A growing company

Let’s take another example.

Company C will earn $1 a share next year but will grow its earnings at 2% a year for eternity. Using the same formula, we find that we can make a 10% return if we pay $12.75 for the company. This means we should be willing to pay a PE ratio of 12.75.

What happens if there’s a company that can grow even faster? Let’s say Company D, with $1 a share of earnings next year, can grow at 8% per year for eternity.

Plug those numbers into the formula and you will find that you can now pay $54 for the company. This translates to a PE ratio of 54.

As you can see, the higher the growth rates, the higher the multiple that you can pay.

## A shrinking company

The same formula works for a shrinking company too. For example, Company E will earn $1 a share next year, but from then on, its earnings will shrink by 5% a year.

Plug those numbers into the equation and you will find that in order to earn a 10% return on investment, you will have to pay $6.33 a share. That’s a PE ratio of 6.3. The table below is a compilation of the PE ratios that an investor should be willing to pay for companies with different growth profiles.

## Growth plateaus

In practice, however, companies don’t grow to perpetuity. They tend to grow fast during the early stages of their life cycle before growth plateaus or goes to zero.

For example, a company may grow 5% for ten years before its growth zeroes and its earnings will thus remain flat forever. In this scenario, a fair PE ratio would be around 14.8 to achieve a 10% rate of return. The table below shows the fair PE ratios to pay for companies growing for 10 years at different rates before growth reaches zero.

As you can see, even if a company’s growth goes to zero after 10 years, an investor would still be able to pay a PE ratio of 132 for a company that is going to grow its earnings per share by a compounded annual rate of 35% for the first 10 years.

## Limited life companies

In all of the above scenarios, I’ve assumed that the companies would last forever. However, in real-world scenarios, companies die out eventually.

As such, I have also modelled a scenario where a company grows for 10 years, before growth is zero for the next 30 years. From year 40 to 50, the company’s earnings then steadily falls to 0.

In this scenario, if the initial growth rate is 5%, a fair PE ratio to pay for the company is 14.8. The table below shows the fair PE ratios to pay for companies in the above scenario but with different initial growth rates.

But what if a company’s initial growth is more durable and lasts for 20 years instead of 10? Here are the reasonable PE ratios to pay for a company that will experience 20 years of growth before its growth is zero for 30 years and its earnings per share then slowly declines to zero from year 50 to year 60.

## Using this information…

A company’s CAGR and the duration of that growth rate can have a large impact on what is the right multiple to pay for a company.

Some investors may be more demanding and require a higher rate of return than 10%. Personally, I target a 12% rate of return on my investments which means I will be willing to pay a lower PE ratio than those who demand just a 10% rate of return.

While this exercise gives us a feel of what sort of PE ratios to pay for a stock, there are some limitations to this method. For instance, inaccurate projections and wide variations in outcome-probability can impact valuations. In addition, holding a company’s shares to perpetuity or till the company shutters may not be feasible for most investors.

In the former case, the exit multiple of the stock and the market’s required rate of return at the point of exit is an important consideration. This will be influenced by factors such as the prevailing interest rate environment at the time of exit.

So while this is not a foolproof method, this framework at least gives us a sense of whether a stock is cheap or expensive based on our own required rate of returns.

* Note: An earlier version of this article was published at *The Good Investors

*, a personal blog run by our friends.*

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*Disclosure: Jeremy Chia does not own shares in any of the companies mentioned.*