Adjusting P/E Ratios for Growth

Toward the end of my previous article on investing styles, I mentioned a simple way to adjust P/E ratios to incorporate some amount of future growth, which was just to subtract the excess growth from the P/E. Here, I’d like to give a quick explanation of why that works.

The Standard Model

Suppose that a stock has a current share price P and earnings of E. If two thirds of the earnings could be paid out as a dividend (a normal amount), then the Gordon growth equation says that the price of a share should be

where “Return” is the required rate of return and “Growth” is the future growth in earnings per share. If we divide both sides by “E”, then can write this equivalently as

which tells us the appropriate P/E ratio in terms of Return and Growth.

Let’s start with the normal case where we expect earnings to grow at the same rate as GDP and that this is also equal to the risk-free rate (bond yield), R. As is usual, we will require a rate of return equal to the risk free rate plus some extra amount, called the equity risk premium, ERP, which accounts for the fact that earnings are riskier than the payout of the government bonds paying the risk-free rate. The average value of ERP historically is around 4%.

With Growth = R and Return = R + ERP = R + 0.04, the formula says that

This gives us a P/E ratio of 16.67, which is a fairly normal historically.

Paying For Growth

Now, suppose that we expect the earnings to grow by some extra amount, G, faster than usual, for 5 years. That means that the earnings five years in the future would be larger than expected by a factor of (1 + G)⁵. For example, if G = 20% = 0.2, then earnings would be 1.2⁵ = 2.49 times larger than expected.

For the P/E ratio to still be 16.67 in five years, the price, P, has to also increase by this factor. If we are willing to pay this price today, then the P/E ratio would be larger by the same factor, i.e.,

We are paying a higher P/E today, but in 5 years, when E has grown by the expected factor of (1+G)⁵, the P/E ratio will be back to 16.67. So this is the price to pay today so that, in 5 years, when the stock is back to normal growth, the price we paid looks reasonable (for normal growth).

Note that we not assuming that earnings in 5 years will be exactly E(1+G)⁵. We are still discounting future earnings by the required rate of return, which includes an equity risk premium, to account for the uncertainty of future earnings (with that discount increasing exponentially the farther away those earnings are). In other words, we are still assuming that future earnings are unknown, that they will be drawn from some random distribution. The only change we made is to move the mean of that distribution to a higher value, as we believe that higher value is the most likely outcome.

Approximating 5 Years of Growth

To get the formula given in the prior article, let’s make this approximation:

This estimate is exact when G = 9%, and it is fairly good, in general, when G is less than 25% or so. (If the growth is larger than that, then the company should probably be valued differently anyway... It’s getting close to a “hyper growth” company, where we would use different stock selection criteria.)

As I suggested in the article, we can make this formula exact by changing the number of years. In other words, we write the equation as

and then solve for “Y” to find the number of years needed to make this exact. The following chart shows the correct value of Y for each value of G.

As you can see, the required years are between 4–6 when G is 1–24%.

In general, if we expect to see G% growth in earnings for 5 years, then it is safe to use this approximation. It always works for G > 9% since the required years (from the chart) are actually less than 5 in that case. And if G < 9%, then we might need up to one more year of growth at that rate, but since the growth is usually not going to suddenly drop back to GDP growth instantly — growth would normally decay from R + G down to R over time — we are likely to see earnings grow by a factor of 1+6G in that case as well.

P/E – Excess Growth

With that approximation in hand, we can go back to our formula of P/E = 16.67 (1 + G)⁵, and replace the factor of (1 + G)⁵ with 1 + 6G. That gives us the formula

Subtracting 100G from both sides gives us

The left hand side of this last equation is finally “P/E – Growth”. Note that if G = 9% = 0.09, then 100G = 9, and 9 is the number you want to subtract from the P/E, not 0.09. (Subtracting 0.09 would barely change the P/E.)

This final formula tells us that, if we subtract the expected 5-year growth rate from each stock — to account for our growth expectations over that time — then the stock should have a P/E around 17. If we find that the growth-adjusted P/E is lower then this, then we may have found a bargain.

An Example (— Not Financial Advice!)

Today (26 Feb 2021), Facebook has a P/E of 25.5. For the next five years, analysts expect annualized growth of 21.5% per year given the continuing growth of digital advertising and Facebook’s rising share of that market. If we believe that the average stock will grow earnings at 5% per year over that time, then Facebook has excess growth of 21.5 – 5 = 16.5. That gives Facebook a growth-adjusted P/E of 25.5 – 16.5 = 9, indicating a cheap stock.

If the price of Facebook does not rise considerably and it comes anywhere close to these growth rates, then its P/E ratio 5 years from now far too low for a reasonable person’s expectation. The only reasonable beliefs are that either (1) the analysts are way off in expectations of future growth or (2) the share price of Facebook will increase a substantial amount in the next 5 years. (Of course, it is anyone’s guess what the stock price will do near-term — its negative 6-month momentum suggests it could be headed lower, not higher!)

To me, Facebook has the sentiment of a value stock: it is surrounded by a cloud of pessimism — investors can only imagine its situation getting worse over time, not better. In my mind, then, a good valuation metric would mark Facebook as a value stock. The basic P/E ratio does not: it says the stock is actually expensive! The growth-adjusted P/E ratio properly indicates a value stock and is the better metric for Facebook in my opinion.

Afterward: the PEG Ratio

The work described above started a few years ago when I was trying to find a justification for the PEG ratio. If you are unfamiliar, this is the idea of sorting stocks by the ratio of their P/E to their (past) growth. It is an approach used by some GARP investors. (Tom Gardner has cited it at times, for example.)

The ratio is often associated with Peter Lynch. However, I have not been able to find a quote where he directly advocated for it. Instead, he advocated for buying stocks with P/E < Growth. That can be interpreted as saying you want PEG = (P/E)/Growth < 1. However, that is not the only way to interpret it, as we will see in a moment.

Despite working on this, off and on, for a few years, I have never been able to prove that, of two companies, the one with the lower PEG ratio is really cheaper. Nonetheless, I do believe that companies with P/E < Growth are usually undervalued (assuming past growth is a good indication of future growth), and I can argue this using growth-adjusted P/Es.

If the average stock is growing at 5%, then we calculate a growth-adjusted P/E as P/E – (Growth – 5) = P/E – Growth + 5. Thus, if P/E < Growth, then P/E – Growth < 0, so the growth-adjusted P/E is less than 5, indicating a very cheap stock. As in our prior example, either this growth estimate will be way off or the stock price will be much higher in 5 years.

Lynch said that the stock is even cheaper when P/E < (1/2) Growth. In that case, we would get a growth-adjusted P/E of 5 even if future growth is only half of past growth, and that is even more often the case.

In summary, you can view the“P/E – Excess Growth” formula as an alternative to the PEG ratio. Unlike the PEG ratio, this formula can be justified using standard valuation approaches, and it serves as an equally valid justification for Peter Lynch’s P/E < Growth and P/E < (1/2) Growth ideas.