# Valuing Stocks: Discounted Free Cash Flow

The single most important part of stock investing is not paying too much for the investment. To do this, one must gather the facts together, and make reasonable projections based on both future prospects and historical norms. Doing this, several techniques can be used to produce a "fair value" - a target price that the investor believes the company is worth. Then, the investor should wait until the market price is a sufficient percentage below this "fair value" (e.g. 30% or more). By doing this, the investor leaves him/herself a margin of safety, because it is almost guaranteed that his or her projections will not be correct. Once the stock price returns to a level near "fair value", the stock should be sold and the gain (or loss, if fair value has fallen), booked.

That is value stock investing in a nutshell, as described by the father of the discipline, Benjamin Graham.

One question begs to be asked from that description, however: What are the techniques to produce a "fair value"? In this series of articles, MagicDiligence will look at several methods that can be used to value stocks, provide some commentary on the practicality of each, offer suggestions as to possible alternatives, and go through some real-world examples using a current Magic Formula stock.

In this first article, we will take a look at one of the most common, and theoretically correct, ways to value a business - the discounted free cash flow calculation.

**Free Cash Flow**

The textbook value of a business is the present discounted value of all future cash flows. Producing cash for owners is the fundamental point of any company. The more cash the company produces, the more it is worth. Free cash flow is similar, but slightly different, than the net profits that are reported on the income statement (for more details, see this article).

Free cash flow can be easily calculated from the financial statements filed by public companies. The traditional equation for free cash flow is:

Free Cash Flow (FCF) = Cash from Operations - Capital Expenditures

**Discount Rate**

From there, we need to estimate the total of future free cash flows from the company is going to be, and then discount them to present value, as a dollar today is more valuable than a dollar a year from now. To do this, the first thing we need to do is to establish a discount rate. To keep it simple, think of this as a "required annual rate of return". MagicDiligence usually uses values between 9% (for extremely safe, stable firms) and 13% (for small firms with lots of risk). It is possible to go much more theoretical and get into a whole "weighted cost of capital" equation, but in my experience the effort does not often add much value.

**Growth Rates**

The next projection we need to make is the annual growth rate. This can be done on a year-by-year basis, but for a rough draft, I usually do a 5-year annual rate, followed by a 6-10 year rate, and then use 3% for a "perpetual" growth rate for years 11 and above (3% is roughly the long-term rate of inflation). This lets you express what you think the company's growth potential is over both the short and long term.

**The Equation**

Here is where things get ugly! The equation breaks down as the following, with the previous completed year's free cash flow listed as FCF, the discount rate as D (the percentage as a fraction), each year's expected growth rate as G#, and the discounted free cash flow for each year as DFCF#:

Year 1 DFCF1: (FCF * (1 + G1)) / (1 + D)

Year 2 DFCF2: (DFCF1 * (1 + G2)) / ((1 + D)^2)

Year 3 DFCF3: (DFCF2 * (1 + G3)) / ((1 + D)^3)

...

Year 10 DFCF10: (DFCF9 * (1 + G10)) / ((1 + D)^10)

Perpetuity DFCFP: ((DFCF10 * (1 + GP)) / (D - GP)) / ((1 + D)^10)

The DFCF values are then added all together, and then divided by the current number of outstanding shares to get the stock's fair value estimate.

I don't expect anyone to try to work that out, so here is a simple Excel spreadsheet that does the work for you. All you have to do is fill in the current free cash flow, discount rate, growth rates, and share count.

**Problems and Adjustments**

Obviously, the DFCF equation requires several assumptions, but this is true of any valuation method and cannot be considered a "problem".

However, in practical use, there are two problems I see consistently with using discounted free cash flow as described above - the capital expenditures ("cap-ex") penalty for growth firms, and the unpredictability of cash flows.

The first problem I've documented before. Cap-ex for the purposes of free cash flow should be limited to maintenance spending. However, in most financial statements it is not broken out. This unfairly penalizes firms that are aggressively investing in growth by opening new stores, offices, or whatever. The previously linked article demonstrates this fact using Home Depot (HD) in both its fast growth and slow growth stages.

To solve this issue, MagicDiligence looks at both the depreciation and the capital expenditures number, comparing the two and taking the number that represents less spending to subtract from "Cash from Operations". So, for example, a firm in slow-growth mode will use the Cap-Ex number, but a firm in fast-growth mode will use depreciation as a proxy for "maintenance cap-ex".

To solve the second problem (unpredictability), we need to try and "smooth out" cash flow. For companies that are not highly cyclical, operating earnings are usually a more stable number to measure to get an idea of growth. So, to get a starting free cash flow (FCF) number, I take the last 5 years of operating earnings, the corresponding free cash flows, and determine what the 5-year ratio of free cash to operating income is. This gives you a good normalized number for FCF that you can then apply analyst growth rates to, and it smooths out the often "jumpy" nature of free cash flows.

**An Example**

There is a lot to digest here, so hopefully an example will help illustrate the process. For this, we will use current MFI stock Lockheed Martin (LMT), a relatively stable and predictable firm.

First, let's calculate free cash flow for the last reported year (all values in millions):

Cash from Operations - MIN(CapEx, Depreciation) = FCF

3,173 - MIN(852, 750) = 2,423

Compare this against LMT's operating profit of 4,466 and we get a free cash to operating income ratio of 54.3%. Repeating this process for the past 5 years gives us a total ratio of about 73%. I would also have noted that Lockheed's ratio has been declining for each of the past 5 years, a red flag to investigate. Considering the decline and the long-term rate, I've decided to use a multiplier of 70% to start my DFCF:

Operating Earnings * Multipler = Normalized FCF Approximation

4,466 * 0.70 = 3,126

For the discount rate I used 10.5%, which is rather low, but still accounts for risks related to the F-22 and F-35 programs. For growth, I assume 0% for 2010 (based on estimates), and 3% a year thereafter (based on historical growth and outlook).

Completing the DFCF calculations using these figures, I come out with a fair value of about $109, well above Lockheed's current $80 price tag.

It would seem to be a bargain, but there are other factors to keep in mind. For one, defense contractors are historically low multiple stocks, so the market is not that willing to pay full price. Also, the past 5 years represent a boom period for defense contractors. Our growth estimates could be too optimistic.

**Wrapping It Up (Finally!)**

Discounted free cash flow is the "by-the-book" way to value a stock. Adding some adjustments makes it easier to account for the inherent jumpiness of free cash flow and the growth stock cap-ex penalty. The result gives you a reasonable, ballpark fair value estimate to ensure you do not drastically over pay for a stock.

Joel Greenblatt and MagicFormulaInvesting.com are not associated in any way with this website. Neither Mr. Greenblatt or MagicFormulaInvesting.com endorse this website's investment opinions, strategy, or products. Investment recommendations on this website are not chosen by Mr. Greenblatt, nor are they based on Mr. Greenblatt's proprietary investment model, and are not chosen by MagicFormulaInvesting.com. Magic Formula® is a registered trademark of MagicFormulaInvesting.com, which has no connection to this website. The information on this website is for informational purposes only and solely represents the views and opinions of the author. No warranty is provided or implied as to the accuracy, completeness, or timeliness of this information. This information may not be construed as investment advice of any kind, nor can it be relied upon as the basis for stock trades. Alexander Online Properties LLC, the proprietor of this website, is not responsible in any way for losses or damages resulting from the use of this information. Alexander Online Properties LLC is not a registered investment advisor. All logos are trademarked properties of their respective companies.

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## Comments

Posted by buttj11 on 2010-05-25 14:37:41

This seems like a nice and easy way to run a DCF valuation.

Don't forget to subtract the company's current debt and add back cash when you sum up all the DFCF values. This will give you the value of the equity instead of the enterprise value of the company...

Posted by partlowjeff on 2010-05-27 04:35:31

Thanks for the great article.

I'm trying to understand what depreciation-related number to use from the financial statements in the calculation of FCF?

In the LMT example, $750M is used for depreciation. I noticed in LMT's 2009 Cash Flow Statement that the $750M is for Depreciation/Depletion and there is another $104M for Amortization.

In your prior article in March 2009, regarding the Home Depot example, you specified to use "Depreciation/Amortization" in your "Sensible Free Cash Flow" calculation.

I'm not an accountant, but would like to gain a better understanding of which number(s) for depreciation/amortization should be used in calculating FCF? And could you also please provide a brief explanation why?

Thanks for your consideration of this request.

Regards,

Jeff

Posted by Steve on 2010-05-27 06:29:09

Hi Jeff - Usually companies do not separate Depreciation and Amortization, so you are forced to use both. If they do separate them, use just Depreciation, as this is the amount that corresponds to Capital Expenditures (sometimes labeled "Additions to Property, Plant, and Equipment"). Amortization is generally the scheduled write-down of intangible assets, which does not correlate to CapEx.

Hope this helps!

Posted by zoabrain on 2011-12-31 11:12:22

Hi Steve,

I wanted to point you to a DCF calculator tool that I built at

http://stockzoa.com/dcf . It automatically pulls free cash flow data from Yahoo! Finance to make quick DCF valuations a piece of cake.

I'd love your thoughts on how to improve it and make it more useful for you.

Thanks,

Brian

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