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Discount Cash Flow Model Made Simple

September 10, 2005

Discount Cash Flow Model Made Simple

There is no perfect model in evaluating stocks. If there were, there wouldn't be market fluctuations and there wouldn't so many models competing for attentions.

Models exist to back up people's assertions. Good models can also provide order-of-magnitude estimates, and serve as sanity checks. Discount Cash Flow (DCF) is one such good model that has been widely used by people including gurus like Warren Buffett. But a cautionary note still: it only serves as one of the many reference points. If we rely solely on it, we are destined to make mistakes.

The central thesis of the DCF model is this: the price we pay for a company should be the present value of all its future cash flows. The idea makes a lot of sense except that the devil lies in the details. Can we predict a company's future cash flows? Do we know how they can be translated to the present values? Unless some assumptions are made about these two questions, we can't even take a first step following this sensible idea.

A typical assumption to the first question is based the company's historical cash flow growth. If it has grown 10% a year in the past, we assume it to grow 10% a year in the future. This is a pretty crude assumption. And of course, a company cannot grow forever. The growth will eventually taper down, at which point we may assume the cash flow grows with the inflation. But when will the growth taper down, and what will be the ensuing inflation rate? More assumptions, please!:-)

A common assumption to the second question is that future cash flows can be discounted back to present values using our expected rate of return. In other words, if we expect a 10% annual return, the $110 cash flow a year from now is only worth $100 to me now. The problem with this assumption is that the expected return should be based on the inflation rate. Investors naturally expect less when inflation is 2% than when inflation is 10%. This comes back again to the unknown of future inflation rates. Nobody, even Mr. Greenspan, has any idea how it will change in the future.

Despite all these unknowns, we can still attempt to get some concrete valuations by making whatever assumptions we have to. But as you can see, the exercise is getting increasingly more academic. We can never get it right. We can only hope we won't be grossly wrong. If we are lucky, the assumptions we make won't be too far off so that the numbers we get won't guide us to a completely wrong course.

We can only base our assumptions on historical numbers. As an exercise, we will assume that 1) a company will grow in the next X years at a constant rate; 2) After X years the company will forever grow at an inflation rate of 3%, which is close to the average in recent years but by no means for any period of time in history; 3) An constant expected rate of return, e.g., 12% annually, which is the historical average of S&P500. 4) The present cash flow is the owner's earning (Net Income + Depreciation & Amortization - Capex.), which according to Warren Buffett is a more realistic measure of what goes into the owners' pocket. Table 1 listed a tabulated form of valuations based on DCF with the above assumptions.
X=5
Growth Rate within X years 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32% 34% 36% 38% 40%
Fair Price/Owner's Earning 11.9 12.9 14.0 15.2 16.4 17.8 19.2 20.7 22.3 24.1 25.9 27.8 29.9 32.1 34.4 36.9 39.5 42.3 45.2
X=7
Growth Rate within X years 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 32% 34% 36% 38% 40%
Fair Price/Owner's Earning 12.1 13.4 14.9 16.6 18.4 20.5 22.7 25.2 27.9 30.8 34.1 37.6 41.5 45.8 50.4 55.4 60.9 66.9 73.4
It is common sense that the longer the growth lasts, the more valuable the company is (higher price to present owner's earning); the fast the growth is, the more valuable the company is. Table 1 gives us a quantitative representation of the common sense. For example, to justify the current S&P500's average PE ratio of 15 - assuming the net earning (E in PE) is roughly the same as the owner's earning, which is not a good assumption because growing companies typically have a lower owner's earning than net earning - the average S&P500 company has to grow its earnings about 9% a year for 5 to 7 years before slowing down. How likely this is in an investor's opinion directly affect his/her view of the market as a whole.

There is a oversimplified gauge of valuation of a growth company, the PEG ratio. PEG ratio is the PE ratio divided by the annual growth rate. A growth company is considered price right if PEG is 1, overpriced if PEG is larger than 1, and underpriced if PEG is less than 1. For example, a company that grows earnings 15% a year would deserve a PE of 15, according to the PEG measure.

PEG can be very misleading, because
  1. The reported net earning may not be a true indicator of a company's earning power; Owner's earning is usually a better measure.
  2. PEG does not factor in the investor's expected return; An investor's expectation fluctuates with the risk-free interest rate (and ultimately the inflation).
  3. Nor does PEG factor in the temporal nature of growth. A company cannot grow at the same rate forever.
Whenever I research a company, I always try to find out the owner's earning first, then look it up in the above table, assuming some reasonable growth rate and duration. The valuation I get serves as a ballpark number that I will weigh against other factors, such as the balance sheet, business risks, growth potential and predictability. Such an approach has so far served me well. I can't say I can pick a winner every time. I have missed a lot of good opportunities as well by being too conservative. But among the stocks I have selected, I am very confident of not having overpaid for them.

A full version of the table that contains more data points as an Excel spreadsheet is available to paid subscribers of Buffetteer.com.


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