Valuation III. Slow Growth

A few weeks ago I wrote two posts on valuation that covered (1) the baseline zero growth case [3/26/2007] and (2) low PE stocks implying declining earnings [see 3/27/2007].

The most important valuation work involves stocks with growing earnings. A simple starting model assumes a constant growth rate & that the Price P as a function of initial earnings E is given by P = E/(1+r) + E(1+g)/[(1+r)^2] + ... + E[(1+g)^(i-1) /(1+r)^i ] ... for all i. One can sum the infinite series and arrive at P = E/(r-g), so a "fair" PE is 1/(r-g). Unfortunately, unless the growth rate is well less than r, you find a divergence or a nonsensically high PE. Remember that a baseline discount rate is about the corporate bond rate plus a few percent for extra risk for weaker credits. So what to do?

First, suppose g "IS" well less than r -> such as a slow/moderate growth scenario. Suppose g is the long term real GDP growth rate of about 2.5 or 3%. What discount rate should you use? A medium quality bond yields about 6.6% nowadays and earnings are subordinate to bond payments, so at least 8% would be necessary for a stable, slow grower. You quickly find the PE = 1/(8%-3%) = 1/5% = 20x. I wanted to find an example, but from my Green Book of 35 year charts, I couldn't find any steady growers with 3% growth. Stable companies mostly had growth rates in the 8 to 12% range [Clorox, Proctor & Gamble, Sysco, most banks, etc.]. Plug those growth rates into the formula & you get a divergence.

You could argue that interest rates are unusually low, but history would contradict you. For very long periods before 1970, interest rates were as low or lower. An equity discount rate of 8% means a no growth PE of 12.5x. Since there do seem to be plenty of LBO and other private equity acquirers willing to buy companies with PEs even higher, I think an argument that the market return on equity of anything over 10% for stable growth is a stretch.

And remember that GDP growth rate was a REAL GROWTH RATE. Nominal GDP growth is about 2% more using the core inflation rate of about 2%. So nominal g is 5% or more. More divergences. Or you bump r to 10% and get a PE of 20x again.

What does this mean? Either the market is ridiculously CHEAP or the series is not infinite and "The End is Near" ;-)

The 35 year Green Book of charts casts doubt on the latter. So you can see another reason I think we are in for a great bull market.

I'll write about a simple composite model tomorrow morning that I use to guide my thinking about specific stocks.

PS: The reason I'm first writing about these analytic valuation solutions is that one needs to understand the mathematics of valuation and why PEs can have such a wide range of values. Real difference in the prospects for growth cause that wide range {& beefer mo-mo & anti mo-mo, too ;-) ].