Digging Into Buffett's Numbers

Discounted Cash Flow (DCF)
The concept of Discounted Cash Flow model valuation is straightforward: We discount all future cash flows the company will produce to the present day, add them up, and voila, we have our company valuation. With that, I present The Discounted Cash Flow Equation!

DCF = CF₀ x SUM[(1 + g)/(1 + r)]ⁿ (for x = 0 to n)

OK, OK. That's not as pretty as my initial explanation. Here's the basic interpretation: DCF is Discounted Cash Flow, CF₀ is today's cash flow, g is expected growth, and r is the expected rate of return. For the many of you who wish that math had ended in third grade, let that suffice -- we will look at how you can easily translate all that gibberish into a spreadsheet in a minute. For those of you who have to know exactly where that equation came from, my previous article is for you.

Buffett's DCF valuations
As you read that section, I expect some of you were Foolishly thinking, "What kind of cash flows? What kind of growth? What is the expected rate of return? Did I remember to turn off the stove?"

Don't worry, you turned off the stove. For the answer to the rest of these questions, we look to Warren Buffett.

Cash Flows and Growth: Buffett uses "owner earnings," which he defines as:

Owner Earnings = Net Income + Depreciation - Capital Expenditures

Sound familiar? It should. This is essentially our beloved free cash flow (FCF)!

Obviously, then, it makes sense that the "growth" refers to FCF growth. We estimate future FCF growth from historical FCF growth -- averaging over five or more years to smooth out yearly variations.

Expected rate of return: The expected rate of return is the opportunity cost of investing your money -- that is, what you could reasonably expect your money could earn in a risk-free investment.

To find this number, Buffett uses the yield on the 30-year U.S. Treasury Bond -- currently around 5%. Historically, however, the 30-year T-bond rate has been much higher (the 25-year average is around 8%). Since the expected rate controls the influence of future values on our DCF calculation (the higher the expected return, the less the future influences our calculation), we will be conservative and use the higher value (as Buffett does).

The expected return (r) is used to calculate our discount factor (DF):

DF = 1 / (1 + r)⁽ⁿ⁾

The present value (PV) of any future value (FV) received n years from now is just:

PV = FV x DF

Margin of safety: The "Margin of Safety" is Buffett's signature investment principle, borrowed from Benjamin Graham. Buffett considers only companies that are trading at a significant discount (40% or more) to their DCF value. This margin of safety helps ensure reasonable return potential even if some of our assumptions are off.

Future growth assumptions
There are too many variables to accurately estimate what a company's growth is going to be down the road. To help minimize errors, we make two conservative assumptions:

1. Growth will be steady for the next five years.

2. By year nine, the growth rate will decline to 3% (the rate of inflation).

Example: The Washington Post Company
Buffett has owned shares in Washington Post (NYSE:WPO) since 1973. The chart below shows the company's free cash flow (and related values) over the past five years:

The variation in free cash flow growth is mostly due to fluctuations in capital expenditures -- net income and depreciation are relatively steady. Fluctuations in capital expenditures aren't unusual -- companies may acquire capital in one year that will provide benefits many years into the future (like a new factory). Still, this yearly fluctuation illustrates the need to use several years of historical data to calculate an average growth value.

For Washington Post, the average growth rate for the past five years is:

(-44 + 54 + 0 + 29 + 8) / 5 = 9.4 %

We now have all the information we need for our DCF calculation:

Estimated growth rate: 9.4%.

Expected return: 8%.

Assumption: During years six through eight, the growth rate will decline to 3% (the rate of inflation).

Creating our DCF calculation in a spreadsheet is simple.

1. Multiply the prior year's FCF by the appropriate growth factor to get the current year's FCF.

2. Multiply the current year's FCF by the discount factor (calculation shown above). This gives the discounted present value of free cash flow for the year (DPV of FCF).

Here's what the spreadsheet looks like (FCF values in $millions):

We're almost done (so hang in there).

What if the company is still around 50 years from now? Do we have to calculate the discounted present value of free cash flow from now until 2055? Fortunately, no. Once we reach steady FCF growth, as our model does in year nine, we can use the power of calculus to simplify our problem.

Black magic (aka calculus)
Here's our basic DCF equation (again):

DCF = CF₀ x ? [(1 + g)/(1 + r)]^x (for x = 0 to n)

Assuming our growth rate (g) is constant and less than our expected return (r), we can simplify this equation to express the terminal (total) DCF value at year n as:

DCF_n = CF_n / (r - g)

All we have to do then is discount our DCF value back to the present day. Let's plug our DCF_n value into the present value equation:

PV = DCF_n x DF

DF is simply our discount factor: 1 / (1 + r)^{(n - 1)}. (If you are wondering why this exponent is n - 1 rather than n, it's because DCF_n is the estimated value at the beginning of year n which is the same as the end of year n - 1).

So to calculate the present value of all cash flows from year nine and beyond, we have:

PV = [CF₉ / (r - g)] x [1 / (1 + r)⁸]
= [(587 x 1.03) / (0.08 - 0.03)] x [1 / (1 + 0.08)⁸]
= 12092 x 0.5402
= 6533

Add this calculation in your DCF spreadsheet, and you are ready to roll!

Finally, our DCF valuation for Washington Post
All that's left to do now is add up our discounted future FCF values:

DCF = 317 + 321 + 325 + 330 + 334 + 333 + 328 + 317 + 6533 = $9,138 (million)

As of market close May 10, Washington Post's market cap is $7.93 billion, a 13% discount to our DCF value ($9.1 billion). With such a limited margin of safety, Buffett would not consider this a new investment opportunity.

Major flaw: Sensitivity to variations
The DCF model is very sensitive to inputs -- that's why we treat assumptions so conservatively. The following table shows you how variations affect the DCF valuation for Washington Post.

More examples
The calculations below use the same expected return and future growth assumptions we used above (8% required return and growth declining to 3% by year nine). For simplicity, we use the analysts' five-year estimates for our expected growth value (from the Yahoo! Finance "Analyst Estimates" stock page):

(Note: The DCF performed on Washington Post and those that follow are calculated according to the most recent annual figures available.)

A few key conclusions:

1. Generally, popular companies (like Apple) are too heavily followed to present compelling values.

2. Companies with inconsistent or incomplete operating histories often have extreme valuations when subjected to the DCF model and are sometimes not well-suited for this sort of valuation.

3. The most attractive opportunities are often established businesses with straightforward business principles.

For more:

• Be Like Buffett
• Buffett by Numbers
• Using DCF Foolishly
• Present Value for Pretenders

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Fool contributor Jim Schoettler appreciates your feedback. Jim does not own any of the stocks discussed in this article.