Introductory Topics

Before you estimate a company's growth future growth rate, you must first determine that the company's business won't decline. To do this, you need to determine that:

1) The market that the company sells to isn't declining. For instance, suppose your friend Alice owns an auto insurance company, named the Alice Company. Since the law requires drivers to purchase auto insurance, people probably won't stop using it.

2) The company has a sustainable competitive advantage, or operates in an industry that is not particularly competitive. This will prevent it the company from losing marketshare (which would decrease the company's sales) and it will protect against pricing pressure (which would hurt its profit margins). For instance, suppose the Alice Company is the largest direct auto insurer in California. Since the company sells insurance directly to consumers, rather than through agents, its costs are lower than the industry average. And because of its large size, economies of scale will further reduce costs. This low cost structure will enable the company to offer good prices to consumers, giving the company a competitive edge. And this, in turn, is likely to keep Alice's business stable. Now that we have determined that a business is solid and sustainable, we can estimate its growth rate. It would be reasonable to expect auto insurance sales to grow with inflation, and with population growth. This would add up to 3% per year (Note: if the Alice Company's low cost structure allows it to gain marketshare, its growth rate will be higher than this). Now, assume the company earns a return on equity of 15%. If you set your discount rate to 10% (which is a reasonable return to expect for a stock in a low-interest-rate environment) then the company will need an earnings yield of 7% (a 7% dividend yield plus a 3% growth in the share price equals a 10% annual return). Since the company's return on equity is 15%, its free cash flow as a percentage of its net income (or, free cash flow/net income) should be around (15%-3%)/15%, or (0.8). So the Alice Company's earnings per share(EPS) multiplied by its (free cash flow/net income) should be 7% of the share price.

Putting this into an equation, we get:

EPS * (15-3)/15 = 7/100 * share price, or

EPS * 0.8 = 7/100 * share price

In order to determine a fair price/earnings ratio, we must rearrange this equation so that we have share price as a function of earnings per share. We get:

EPS=7/80 * share price

Share price=EPS * 80/7 = EPS * 11.4.

So the stock is worth buying at a price to earnings ratio in the 11-12 range.

Now, assume you are analyzing a retailer. You might expect it to grow at the same rate as the economy (which has averaged around 5% over the long term). So you anticipate that the company's revenue growth will be around 5%. In order to earn a 10% return, they comapny's earnings yield will need to be 5% (a 5% earnings yield + a 5% dividend yield will give a 10% return). Suppose its return on equity is 20%. Then, you can estimate that its (free cash flow/net income) will be (20-5)/20, or 0.75. So our new formula for EPS, as a function of the share price, is:

EPS * 0.75 = 5/100 * share price

Solving for share price, we get:

EPS = 5/75 * share price

Share price = 75/5 * EPS

Share price = 15 * EPS

So this company is worth buying if its P/E is 15.

What if you think the company will grow? Take Wal-Mart, for instance. This retailer has, and can maintain, lower costs than its competitors, so you expect it to gain market share. What will its growth rate be?

First, you'll want to look at the rate the company has grown over the past several years. You can set this as an upper bound for your future growth expectations. As for Wal-Mart, the company has been growing revenues at around 12-13% per year, and increasing its store count by about 8-10% per year.

You need to ask yourself, how long can this continue? For now, let's just look at the United States. As we can see, Walmart has been blanketing the country, so we can conclude that most parts of the country like Wal-Mart's low prices and would be willing to shop there. There are still plenty areas with no Wal-Mart, so there is room for growth. Eventually, however, Wal-Mart will start to run out of good locations and growth will slow. So we can predict that Wal-Mart will experience strong growth for a period of time, after which growth will slow to the rate of economic growth (or perhaps a little bit less).

If you look at Wal-Mart's Annual Report, you'll see that they have about 3000 stores in the United States, which corresponds to a bit over 1 store per 100,000 people (of course, it should be noted that some of these stores are larger than others).

Assume you believe Wal-Mart can increase this by 50%. Using historical growth as an upper bound, we might predict that they will increase their store count by 8% per year. So our question is: how long can they grow at 8% until total growth is 50%? Putting this into an equation, we get:

1.08^x=1.5, and we want to solve for x.

The solution to this equation is: log(1.5)/log(1.08), which equals 5.27.
(Note: if you don't know what logarithms are, see the Logarithims link.)

So we predict that Wal-Mart will be able to grow at 8% per year for approximately 5 years. But suppose you believe growth in their store count will grow by only 5% per year. If you divide log(1.5) by log (1.05), you'll find that Wal-Mart will grow at that rate for about 8 years.

Now let's assume that the 5% growth in store count corresponds to a 10% growth in sales, which you expect to continue for about 8 years. In the DCF calculator, put 10% in years 1-5 for growth, and 8% in years 6-10 (10% growth in years 6-8 and 5% growth in years 9-10, averages to around 8%. you don't need to be exact, since the value you are calculating is only a rough approximation of the company's true value). After that, predict 5% growth.

Looking at Yahoo! Finance's data on Wal-Mart (at http://finance.yahoo.com/q/ks?s=WMT) we see that they are earning a return on equity of 22%. So we predict that their free cash flow/net income will be (22-10)/22, or 0.55, in the first period, (22-8)/22 in the second, and (22-5)/22 in all other periods.

Plugging in 2.22 for the company's earnings per share and using a 10% discount rate, we get a buy price of $44.81.

Now, suppose we believe that, once Wal-Mart runs out of new places to put stores, their growth rate will be lower than 5%. Suppose you were to predict 3% growth (inflation plus population growth). Then our new buy price is $38.28.