The P/E Ratio and the Gordon Growth Model

Antonio Fatas suggests that stocks may be undervalued:

The P/E ratio shows that the end of the 90s bubble was by far the period were stocks looked the most expensive relative to earnings. What do P/E ratios look like today? On the expensive side. With a ratio above 26 it stands right at the level before the 2008 crisis and a lot higher than previous similar historical episodes. Most tend to compare it to 16, as the average P/E ratio in recent decades, to signal that the stock market is very expensive. Without going back many decades, we could say that the stock market today looks as expensive as it has been since 1981 with the exception of the bubble of the late 90s. But that cannot be the end of the analysis as we know that the P/E ratio depends on several macroeconomic variables, in particular the level of real interest rates. And we know that real interest rates are at very low levels today and likely to say low for a long period of time.

While I agree with this, I must take exception to his use of the Gordon growth model:

Let's go back to the basic finance equation that links the P/E ratio to macroeconomic fundamentals. Start with a simple expression of the price of stocks as the net present (real) discounted value of earnings. Under the assumption that current earnings are expected to grow (in real terms) at a rate G and using R to denote the risk-adjusted discount rate we can write: P = E / (R-G). In other words the Price-to-Earnings ratio can be written as P/E = 1 / (R-G).

I have no problem using steady state models but earnings are not the same as cash flow. This was part of the problem with the DOW 36000 claim by James Glassman and Kevin Hassett as noted a long time ago by Paul Krugman. There are several ways of correcting for this slip up but my favorite way of doing so is to think about a steady state model of the value of the assets (V) of a company that sets cash flows equal to profits (P) net of the necessary increase in tangible assets (A) dictated by growth. For now just imagine a debt free firm. Let’s also assume G = 2% and consider Antonio’s sensible statement here:

And let's express the risk-adjusted discount rate as the sum of a risk-free rate (RF) and a risk premium (RP). E/P = RF + RP - G

Let’s consider a range for this risk-adjusted discount from 5% (says a 1% risk-free rate plus a 4% risk premium) to 8% (say a 3% risk-free rate plus a 5% risk premium). Let’s also consider two very different kinds of firms: a brick-and-mortar company that owns no valuable intangible assets versus a pure intangible firm. For the latter, V/P is given by the Gordon growth model as A = 0> For the former, however, V/P = 1/R. If the risk-adjusted discount rate were 8%, the V/P ratio for the brick and mortar company would be 12.5 while the value of the pure intangible company would be 16.67. Of course most companies own both tangible and intangible assets to their V/P ratio would be in between these two extremes. If the firm were levered in the sense of issuing debt, their P/E ratio would be less than their V/P ratio. Antonio closes with:

In summary, unlike the strong warning signals we get when looking at record-level nominal stock prices or even at the P/E ratio, a simple adjustment of P/E ratios by current levels of interest rates paints a very different picture of the stock market. Adjusted for current levels of real interest rates, P/E ratios tell us that the stock market today is on the cheap side relative to previous similar phases of the business cycle.

He is right that we should consider a lower risk-adjusted discount rate so let redo our discussion by assuming this discount rate is only 5%. In this case, the value of our brick and mortar company is 20 times profits while the value of the pure intangible company is 33.33 times earnings. If a company is purely equity financed with half of its value coming from intangible assets and half from tangible assets, we might be able to justify a P/E ratio near 26. But again the P/E ratio for a similar company with debt would be lower.