I consider myself a value investor. To me, all that means is that I am price-conscious. It doesn't matter what type of company I look at or what its situation is. The bottom line is that 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 in the Fool's School. But today I want to focus on the discounted cash flow analysis.

John Burr Williams developed the idea in the '50s, and Warren Buffett has evangelized it in the years since. Despite its power and simplicity, there are areas where we need to tread carefully. Used Foolishly, DCF can be a great friend; 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. 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*. 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. 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** (NYSE: MRK ) has been getting the attention of many value investors lately. 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. I think it is Foolish for making estimates based on personal judgments. 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** (Nasdaq: GOOG ) . 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.

(on 12/31/2004) | |||||
---|---|---|---|---|---|

Diluted Shares |
272.8 | Market Cap |
$52,590 | CFFO |
$977 |

Price |
$192.78 | Debt |
$0 | CAPEX |
$319 |

Cash |
$2,100 | FCF |
$658 | ||

Enterprise Value |
$50,490 | ||||

Assume k |
10% | 25% | 50% | ||

Solve for g |
8.60% | 23.40% | 48.10% | ||

k - g |
1.40% | 1.60% | 1.90% |

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** (Nasdaq: MSFT ) 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 Fools 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 Foolishly. 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.

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.

At the *Inside Value* website, Philip Durell has a wonderful DCF calculator to help you with your analyses. Take a free trial of the newsletter for 30 days to access the tool and see how Philip is using it to value his recommendations. Not coincidentally, he is outperforming the market.

*Fool contributor David Meier learned to be price-conscious from his wife. He does not own shares in any of the companies mentioned in this article. The Motley Fool has a disclosure policy.*

## Comments from our Foolish Readers

Help us keep this a respectfully Foolish area!This is a place for our readers to discuss, debate, and learn more about the Foolish investing topic you read about above. Help us keep it clean and safe. If you believe a comment is abusive or otherwise violates our Fool's Rules, please report it via theReport this Commenticon found on every comment.## Report this Comment On June 11, 2008, at 12:02 AM,

prginwwwrote:There seems to be a typo one of the formulas. Instead of

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

the correct formula is

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

## Report this Comment On October 22, 2008, at 9:08 AM,

prginwwwrote:Actually, the formula in the article is correct. Here's the formula from another source, using dividends instead of FCF: http://www.globusz.com/ebooks/Valuation/00000020.htm

## Report this Comment On March 02, 2009, at 6:04 PM,

prginwwwrote:Good article. As the author correctly states: "Pitfall No. 1: We don't know jack

I know that sounds harsh, but it's the truth" .......

then why add a growth rate at all?

Is one to assume that a company's free cash flow (cash from operations less cap ex) will grow in line with a growth in revenue or EBITs etc. I certainly don't. My point is that the equation above would theoretically not work if the growth rate exceeds the discount rate.

Rather stay conservative by using a company's AVERAGE growth rate in perpetuity.

example above: (Google (on 12/31/2008, sorry don't have the 2004 numbers)

Diluted Shares 315,290,000.00 FCF $7,852,000,000

FCF per share: 7.852 M/ 315.2M = 24.90 per share

FCF/discount rate (WACC) 24.90/10% = 249.00 Add cash on hand per share and deduct debt per share ($31.74 cash minus $0 debt)

$ 249 +31.74= 280.74 intrinsic value

So at today's trade value at $327 GOOG is still overvalued.

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