I consider myself a value investor. To me, all that means is that I am price and value conscious. The price on the ticker matters little to me as long as it is of good value. The bottom line is I refuse to pay more than an investment is worth.

If I am not going to pay too much, then I have to make an estimate of an investment’s value. There are different ways to calculate value – you have probably seen many of them. But today I want to focus on the discounted cash flow analysis.

Why the Cash Flow Statement the most important of the financial statements? The most important is its intent is very clear – either it generates cash or it doesn’t and it is not subject to many varying accounting interpretation. In other words, it is the least susceptible to fraudulent practice compared to the Income Statement or Balance Sheet. Since accounting is nothing but just an estimate, its outcome is as good as its input. And input in accounting relies a lot on assumption, for instance, the useful life of a company’s asset.

Compare to the Income Statement, its outcome is subject to many different interpretations. For instance, a business can use “mark-to-market” accounting to boost its earnings. A business which signed a 10-year contract worth $10 million can account all its earnings in one-single fiscal year while the business will only receive its earnings as the work is carried out through the ten years, intermittently.

John Burr Williams developed the idea in the 1950’s, and Warren Buffett has embraced and evangelized it in the years since. Despite its power and simplicity, there are areas we need to tread carefully. Used properly, DCF can be a great buddy; used foolishly, DCF can be our worst enemy. So let’s look at DCF carefully, because I don’t want you to pay too much for an investment.

First, we need the equation. Be prepared. You may already know it, but I'll present it here for reference:

Value = Sum[Cash Flow(t)/(1+k)^t] from t = 1 to infinity

We'll call this the long form. All you need to do is predict all of the future cash flows and discount them back to the present at the rate of k. K is the risk-free interest rate while t is the number of years which could be eternity. What could be easier? For simplicity, we'll define "cash flow" as cash flow from operations minus capital expenditures.

I know that sounds harsh, but it's the truth. We cannot consistently predict the cash flows and their growth rates with any accuracy; the business environment is far too dynamic – that’s why buying businesses you understand is of utmost importance. Of course, we should try to make the best estimates we can. And that means being careful about our assumptions and predictions because we don't want to have the pitfalls of the equation work against us.

Merck has been getting the attention of many value investors 2 years back. The Vioxx problems and the court ruling about early patent expirations have caused lots of uncertainty, knocking down the stock price. Using our definition, Merck earned $7 billion in cash flow in 2004. Should that be the starting point? No. Do we know the cash flow reduction from the two issues stated above? I read one report that said the Vioxx lawsuit could cost $4 billion to $30 billion. No precision there. Will two people using the same information predict the same value? Not likely.

The equation is not for calculating precise answers, like in physics and engineering. The better the judgment, the better the estimate.

There is a simplified form of this equation, assuming constant growth and a constant discount rate.

Value = Cash Flow(t = 0)*(1+g)/(k-g) where

g = growth

k = discount rate

t = 0 is the cash flow from the previous year

One reason we cannot rely on the equation for precise answers is that there is a point of critical mass. In 1946, scientist Louis Slotin died from radiation poisoning after he accidentally let two half-spheres of beryllium-coated plutonium touch during an experiment. When the two halves touched, they reached the critical mass required to sustain a nuclear reaction.

The equation above is valid only if the discount rate is greater than the growth rate (k > g). If k is less than or equal to g, the equation is undefined. Our critical mass pitfall comes when g starts to get close to k. As this happens, value starts to get really big, really fast.

For illustration, let's look at Google. My gut tells me that Google is overvalued. But my gut and a quarter won't get me a cup of Starbucks coffee. From 2004 financial statements, we know everything in the upper half of the table. We don't know the growth rate. So let's assume a discount rate and solve for growth.

Note: Dollar values in millions.If I am not going to pay too much, then I have to make an estimate of an investment’s value. There are different ways to calculate value – you have probably seen many of them. But today I want to focus on the discounted cash flow analysis.

Why the Cash Flow Statement the most important of the financial statements? The most important is its intent is very clear – either it generates cash or it doesn’t and it is not subject to many varying accounting interpretation. In other words, it is the least susceptible to fraudulent practice compared to the Income Statement or Balance Sheet. Since accounting is nothing but just an estimate, its outcome is as good as its input. And input in accounting relies a lot on assumption, for instance, the useful life of a company’s asset.

Compare to the Income Statement, its outcome is subject to many different interpretations. For instance, a business can use “mark-to-market” accounting to boost its earnings. A business which signed a 10-year contract worth $10 million can account all its earnings in one-single fiscal year while the business will only receive its earnings as the work is carried out through the ten years, intermittently.

John Burr Williams developed the idea in the 1950’s, and Warren Buffett has embraced and evangelized it in the years since. Despite its power and simplicity, there are areas we need to tread carefully. Used properly, DCF can be a great buddy; used foolishly, DCF can be our worst enemy. So let’s look at DCF carefully, because I don’t want you to pay too much for an investment.

**Here's what we're up against**First, we need the equation. Be prepared. You may already know it, but I'll present it here for reference:

Value = Sum[Cash Flow(t)/(1+k)^t] from t = 1 to infinity

We'll call this the long form. All you need to do is predict all of the future cash flows and discount them back to the present at the rate of k. K is the risk-free interest rate while t is the number of years which could be eternity. What could be easier? For simplicity, we'll define "cash flow" as cash flow from operations minus capital expenditures.

**Pitfall No. 1: We don't know jack**I know that sounds harsh, but it's the truth. We cannot consistently predict the cash flows and their growth rates with any accuracy; the business environment is far too dynamic – that’s why buying businesses you understand is of utmost importance. Of course, we should try to make the best estimates we can. And that means being careful about our assumptions and predictions because we don't want to have the pitfalls of the equation work against us.

Merck has been getting the attention of many value investors 2 years back. The Vioxx problems and the court ruling about early patent expirations have caused lots of uncertainty, knocking down the stock price. Using our definition, Merck earned $7 billion in cash flow in 2004. Should that be the starting point? No. Do we know the cash flow reduction from the two issues stated above? I read one report that said the Vioxx lawsuit could cost $4 billion to $30 billion. No precision there. Will two people using the same information predict the same value? Not likely.

The equation is not for calculating precise answers, like in physics and engineering. The better the judgment, the better the estimate.

**Pitfall No. 2: Stay away from critical mass situations**There is a simplified form of this equation, assuming constant growth and a constant discount rate.

Value = Cash Flow(t = 0)*(1+g)/(k-g) where

g = growth

k = discount rate

t = 0 is the cash flow from the previous year

One reason we cannot rely on the equation for precise answers is that there is a point of critical mass. In 1946, scientist Louis Slotin died from radiation poisoning after he accidentally let two half-spheres of beryllium-coated plutonium touch during an experiment. When the two halves touched, they reached the critical mass required to sustain a nuclear reaction.

The equation above is valid only if the discount rate is greater than the growth rate (k > g). If k is less than or equal to g, the equation is undefined. Our critical mass pitfall comes when g starts to get close to k. As this happens, value starts to get really big, really fast.

For illustration, let's look at Google. My gut tells me that Google is overvalued. But my gut and a quarter won't get me a cup of Starbucks coffee. From 2004 financial statements, we know everything in the upper half of the table. We don't know the growth rate. So let's assume a discount rate and solve for growth.

The results tell us that cash flow needs to grow at 23.4% per year from now until infinity to achieve a 25% annual return. So in year 19, Google will have to generate $35.7 billion in cash. For comparison, Microsoft generated $13.5 billion of cash in its 19th year as a publicly traded company. That's a lofty goal. Does it mean that Google is overvalued? I don't think we can say from this equation. The validity of the answer breaks down because we are too close to the critical mass point, where k equals g.

**Pitfall No. 3: Money for nothing.**

So if the simplified form of the equation is breaking down, what about using the long form? We can break the equation into parts: a fast-growth part and a slower-growth part. Let's assume that Google can grow cash flow at 100% per year for the next five years and at a slower rate after that. Again, let's use a discount rate of 25%. I know you are wondering how I can have a growth rate higher than the discount rate. In the long form of the equation, there's nothing that says we can't. But let's think carefully about what that means.

Essentially, it means that we are getting money for nothing. It implies that the cash flows are more valuable simply because they are growing. It also implies that our investment has infinite value and that we are guaranteed a return no matter what price we pay. We both know those are foolish notions.

At the Berkshire Hathaway annual meeting, Warren Buffett referred to this as the St. Petersburg Paradox, based on a paper by David Durand. No investment has infinite value. So we have to be very careful using g > k for extended periods of time.

Should we throw DCF out the window?

An emphatic no! We just need to use it smartly. Here's what I recommend:

1. Be conservative.Aggressive analyses can lead to inflated values and cause you to pay too much. Pay too much, just like incurring high transaction costs, and you get lower returns. It is similar to how management adopting an aggressive accounting method.

2. Think about your assumptions and gather contrasting viewpoints.Poor assumptions based on viewpoints that are the same as yours can lead to aggressive analysis. And we know where that can lead.

3. Use a margin of safety.Sorry. Despite the fact that you are conservative doesn't mean your answers are more accurate. Have the courage to pay significantly less than your estimate of value. Your family will thank you down the road.

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