Monday, November 27, 2006

Stock Valuation

I have been trying to figure out a good method for stock valuation. There are of course many models for valuation mostly based on discounted cash flow models DCF. The idea is that a company is worth the sum of all future cash flows to the owners between now and infinity, discounted by some discount rate. This discounting is because money now is worth more than money in the future. If I had money now I could invest it and get about 10% per year so that in 7 years it will double. The discounting of future cash flows accounts for this simple fact.

Here is a good link to an overload of information on variations of DCF.

However for stock picking I think these complex models are not required. If you knew the inputs precisely (i.e. growth rates etc) then it might be good to include all of these details such as changes in working capital and changes in payout ratio. However you don't. I am looking for a good proxy to use for the whole class of stock that I like to invest in. I want a generally useful tool: a jacknife of sorts that I can quickly use to compare all stocks.

So a simple N-stage DCF model should suffice. I have written one in the IDL computer laguage. Of course, you need to pick a discount rate. This is always difficult. They way I figure it, you you simply fix the discount rate and keep it constant for all stocks. This is possible because I am only going to invest in one kind of company: companies with stable earnings and somewhat predictable growth rates. I don't need a variable risk premium, I don't need to work out the correct WACC etc.
I just use 10%. This of course specifies the relative weight I give to earnings now versus earnings in the future. However 10% seems reasonable because it is approximately the average stock return, is not far from the average bond rate (plus a constant risk premium). It is also the number of fingers that I have. This gives a fair value P/E of 10 for a perpetually zero growth company and a fair P/E of 20 for a perpetual growth rate of 4.8% which is about the long term bond rate. The way I figure one most needs a discount rate to decide whether to buy stock at all. Once you have chosen one, just use DCF to decide between stocks. Buy the cheapest relative to the DCF value with a few caveats.

Next choice: which earnings to use. Some just use accounting earnings. The Usual E. Others use DCF with the dividend D in which case P/E becomes P/D or inverse of dividend yield. There is the handy formula for the dividend discount model for constant growth.
Y= D/P = DR-G
where Y is dividend yield (D/P) and DR is the discount rate and G is the dividend growth. This is called the Gordon Growth Model and is easy to derive (it is just a geometric series). This only works for DR > G so that you don't get infinite value D/P = 0. I find this equation useful in that it tells you what the correct discount rate should be. DR= Y + G. If you buy the stock and sell in the future, after dividends and earnings have grown by G, and the valuation D/P stays the same then your anualized return will be R=Y+G which is the discount rate. In other words, the discount rate is your expected return. You want to buy things that give you a rate equal to or better than you expected return. This is somewhat circular but really gives you an idea of what the discount rate should be. 10% is not so bad of a return. Naturally I would like a higher return so if I use DR=10% in my N-stage DCF and find things that are selling for a significant discount to this rate, then I will buy them.

There are still other choices for earnings. I think using free cash flow (FCF) is probably the best. Buffett calls this Owner Earnings and in my code I use OE as FCF per share. This is cashflow-capital expenditure. The trick here is knowing whether the capital expenditure is really different from expenses and different from real investment. I don't have a good feel for this. Should I simply just trust the accounting line "Capital Expenditure" and subtract that off? If you do that you see that Home Depot has significant OE but Walmart does not. I doubt these two companies are that different so I am not sure if this is just differences in accounting.

So for a company reinvesting all of its money, use OE as earnings and look at growth in OE for the growth rates, G. For price I use enterprise value (EV). This is what you use if you were going to buy the whole company for market value and I think this is the right way to think about buying stocks. You get whatever cash and cash equivilents that the company owns and are stuck their debt as well. So EV = P - Debt + Cash. So now OE/EV is the measure of valuation that I estimate with DCF.

What about dividends? I still need to figure how to include these properly. I think you can simply augment the growth rate by
the dividend yield. This is because you can just buy more shares which is equivilent to having a faster growth rate. If a stock is growing OE at 12% with a dividend yield of 2% then use 14% for G. Not sure if this is entirely correct but will do for now.

The final question is how many stages. You clearly need at least two since most companies that I look at grow at something close to or greater than DR=10%. There is no point in getting carried away and having more than four. For a stable company like JNJ I use 2 or 3. Sometimes I get creative with stocks like homebuilders which should see a decline in earnings and then a turn around. You can still use DCF for this.

The hard part of DCF of course are the growth rates. Garbage In = garbage out as they say. Here, you don't want to over estimate growth or you could end up paying way too much. I think the best way to do this is to use the historic growth rates over 10 years. I get these from S&P though my scottrade account. I think a good thing to do is to take the ten year pattern and divide into 2 five-year segments and get the growth rate for each. Use the lower of thr two and take off 2 percent to be conservative. By doing this you aren't assuming it can grow any faster than it already has. Avoid new companies that have grown quickly because they had no earnings to begin with. Avoid cyclicals that have just come off a huge bull market. Don't ever input very high growth rates like G=40% since they are not sustainable. In fact I want to find companies with high ROE since this tells you the sustainable growth rate. G = ROE (1-p) where p is the payout ratio. That is I will avoid the Googles and the unproven internet stocks etc with huge growth rates and low ROE. I would rather buy a company with G=10% and low valuations since these kind of growth rates are likely to persist and getting the growth rate correct as well as the period of growth is less important.

Finally an example. Johnson & Johnson (JNJ). A perfect company for me (see "My rules for investing" post).

Annual growth in OE over the past 10 years is 13.4% (by exponential fitting) and 14.8% (point to point). The two five year periods are
G=13.5% (first) and G= 17.6% (most recent) as determined by exponential fitting. The lesser is 13.5%. The dividend yield is
Y=2.3%. So I will use G=13.5+2.3-2=13.8%. I will use a 3-stage model with
N Years | Growth
10 13.8%
10 8.0%
20 4.0%

In IDL I simply type:
IDL> dcf,[10,13.8,10,8.0,20,4]
Using default DR 10.0000
12.1112 12.7136 13.6629
total V/E = 38.4878

This reports that the Value to Earnings of 38.5. That pretty high but I think reasonable for a great company like JNJ. Over the next 40 years that predicts a growth in earnings (dividend adjusted) of 17 or 7.7 adjusted for 2% inflation. Taking out the dividends it says that the company must grow by a factor of 6 or so in 40 years which I think is very reasonable considering that the developing world is getting richer and will desire the same level of health care as the developed world and also the developed world is ageing rapidly. The key to trusting high valuations that come out of DCF is to ask whether the company is truely great and is likely to remain a strong company in the extreme distant future. I am fairly certain Coke, JNJ and Budweiser will be around in 100 years unless they are bought by another company. I have no idea what will happen to Google or Yahoo.

So how much does JNJ cost? Since we are working with owner earnings, it is EV/OE that we look at for valuation. The inverse of this I call free yield FY=OE/EV. JNJ has FY = 5.43% or OE/EV=18.41. This is not too different from the usual P/E which for JNJ is 17.29.

So according to DCF it is underpriced by 50%. Quite a steal!

What will my return be? Over the next 20 years this is a rise of about 7.75 in earnings. If valuation stays the same that is an 11% annulaized return. Not bad. However as I mentioned, I think the right valuation is twice as high. So if it takes 10 years to obtain the right valuation this will be a 13% return. If it takes 10 years it is 19%. If it only takes 3 years, it is a 37% annualized return although over a shorter period. I figure this is a sure thing to obtain a 10% annulized return over some future interval and possibly as high as 30% as long as I hold on through any ups and downs. I will buy now and sell whenever it becomes overpriced. I would probably sell if P/E > 35 but may sell after a year if there are even better opportunities.

Of course the growth rates could be wrong. Lets try a simple 2-stage with 10% initial growth.
IDL> dcf,[10,7,20,5],val,e,de
Using default DR 10.0000
8.61628 9.64537
total V/E = 18.2617

That comes closer to the price but requires 10 years of only 7% growth followed by 20 years of 5%. I don't see anyone could think that JNJ would see such terrible growth rates especially with the demographics that we have. JNJ is definitely underpriced. A definite BUY. The only question is whether there are better buys out there which is always the source of all my stress.