# New Feature Announcement: Discounted Free Cash Flow Screener

kfh227
Jun 17, 2010
The Discounted Free Cash Flow Screener focuses on Free Cash Flow (FCF) and Total Equity. These measures can be used to determine an intrinsic value estimate for a company. This article discusses the importance of free cash flow and total equity and describes how GuruFocus arrives at an intrinsic value estimate.

Link: Discounted Free Cash Flow Screener

To understand the importance of free cash flow, please read the following from the 1992 Berkshire Hathaway Chairman's Letter in which Warren Buffett wrote the following:

"In The Theory of Investment Value, written over 50 years ago, John Burr Williams set forth the equation for value, which we condense here: The value of any stock, bond or business today is determined by the cash inflows and outflows - discounted at an appropriate interest rate - that can be expected to occur during the remaining life of the asset." -1992 letter(all letters)

Free Cash Flow is the money generated in a year which can be used to grow the business and pay dividends. Free cash flows can be thought of as being similar to the payout of a CD or bond. While CDs and Bonds reward the holder with cash, not all of the free cash flows are handed back to the investor as dividends. In some cases, no dividends are paid and all of the free cash flows are reinvested by the company on behalf of the owner.

With a company, the free cash flows are what is left for reinvestment. With CDs and bonds, the dividends can be used for reinvestment. In this manner, free cash flows can be thought of as being equivalent to the return of CDs and bonds. Free cash flow is what a business owner is interested in creating.

THE FORMULA

Based on the 6 year free cash flow average, total equity and free cash flow growth assumptions, the following formula is applied

Value = (Growth Multiple)*FCF(6 year avg) + 0.8*Total Equity(most recent)

The free cash flow growth assumptions translate into the Growth multiple in the above formula. In the case of negative total equity, the following formula is used (see the Total Equity section for the reason):

Value = (Growth Multiple)*FCF(6 year avg) + Total Equity(most recent)/0.8

The Growth Multiple, 6 year average of FCF and Total Equity are discussed in the sections that follow.

6 YEAR FCF AVERAGE

The screener uses a 6 year average of Free Cash Flow. The reason for this is to smooth the peaks and valleys that can occur in any single year of reported data. This average acts as a way to normalize the FCF data.

In addition to the past 6 years of annual FCF data, recent quarterly data is also included. So, this 6 year average is technically the average FCF over the past 6 to 6.75 years. The reason for the inclusion of quarterly data is simple. GuruFocus believes that the most recent data should be included in order to give the best results possible. For purposes of discussion, the term “6 year FCF average” is used, even though this is actually anywhere from 6 to 6.75 years.

There is still one small issue. The 6 year free cash flow average is currently treated as a trailing average. The 6 year free cash flow average is really an average centered around a date from 3 years prior. So, the 6 year FCF average needs to be adjusted forward by 3 years. For this purpose, we assume that inflation is 3.3% per annum This creates a multiple of 1.1023 (1.033) that is used to adjust the 6 year average slightly.

So, if free cash flow for ABC Corp were \$1, \$2, \$3, \$4, \$5 and \$6 million over the past 6 years the average would be \$3.5 million. However, this average is multiplied by 1.1023 to give an adjusted average of \$3.858 million. This \$3.858 million is the 6 year average that is used by the screener.

This 6 year FCF average is the basis for the “cash inflows and outflows” that Buffett refers to. By making assumptions about future free cash flows and discounting those free cash flows “at an appropriate discount rate”, the value of the future free cash flows in today's dollars can be determined.

The next section discusses the discounting of future free cash flows using the 6 year FCF average as a basis.

GROWTH MULTIPLE

The growth multiple is a multiple that is based on a growth assumption. GuruFocus uses various historical growth numbers (EBITDA growth, revenue growth, etc) to come up with an assumption of future growth. This growth assumption is determined and then restricted to a range of 4.5% to 11%. This growth assumption is then translated into a proper growth multiple which is in the range of 8.63 to 13.48. Multiplying the 6 year FCF average and the growth multiple together provides an approximation of the sum of all futures estimated free cash flows in today's dollars.

The following explains how the growth multiples were determined based on the various growth rates. To determine a formula, growth multiples for growth rates ranging from 4% to 15% were determined. Based on the samples, a best fit curve formula was created. The formula is as follows:

Growth Multiple = 8.3459 * 1.07(Growth Assumption-4)

To learn how this formula was created, read on. To gain a grasp of what discounting free cash flows really is, it is highly recommended that this section be read and understood. Otherwise, skip to the Total Equity section.

The growth multiple is determined by projecting 20 years of free cash flows and discounting them to today's dollars. There are many discount rates that could be used. Historical average of inflation, historical average stock market returns, 75th percentile inflation. The list goes on and is open to personal preference and opinion. Choosing a discount rate is more art than science. Over the past 60 years, inflation was greater than 9% just 5 times (less than 10% of the time). Therefore, theDiscounted Free Cash Flow Screener uses a discount rate of 9%. That is, the projected future free cash flows are discounted by 9% per annum to arrive at the value of projected free cash flows in today's dollars.

To determine the projections for free cash flow over 20 years, the growth assumption is used to determine the first 10 years of free cash flows. For the purposes of the screener, this first 10 years of growth are limited to a range of 4.5% to 11%. The last 10 years are always assumed to grow at 4%. To understand what this all means, consider the following table which walks through a 10% growth assumption:

YearGrowthFCFdiscounted FCF (9% annually)
06 year average: \$100.00
110%\$110.00\$100.92
210%\$121.00\$101.84
310%\$133.10\$102.78
410%\$146.41\$103.72
510%\$161.05\$104.67
610%\$177.16\$105.63
710%\$194.87\$106.60
810%\$214.36\$107.58
910%\$235.79\$108.57
1010%\$259.37\$109.56
114%\$269.75\$104.54
124%\$280.54\$99.74
134%\$291.76\$95.17
144%\$303.43\$90.80
154%\$315.57\$86.64
164%\$328.19\$82.66
174%\$341.32\$78.87
184%\$354.97\$75.25
194%\$369.17\$71.80
204%\$383.94\$68.51
Discounted future free cash flows:\$1905.84
After 33% estimated taxes:\$1257.86

In the above table, 20 years of free cash flows are estimated using \$100 as the 6 year FCF average. This \$100 in annual free cash flow is assumed to grow at 10% annually for 10 years and then 4% for the next 10 years. These future free cash flow estimates are then discounted by 9% annually in the right most column. The right most column represents the future free cash flows discounted to today's dollars. In the bottom right, the discounted future free cash flows are totaled and reduced by 33% to account for taxes. In the above table, the initial \$100 of free cash flow is worth \$1257.86. This means that it is fair to pay \$1257.86 for this company since that is the value of the future free cash flows that are expected to be generated over 20 years. \$1257.86 represents a multiple of 12.57 on \$100. This multiple applies for any company that shares the assumption of 10% growth over the next 10 years. If the 6 year FCF average is \$200, all the numbers in the above table would simply double. So, \$1257.86 would double to \$2515.72. And 2515.72 divided by \$200 is still 12.57.

Using the above reasoning, growth multiples can be determined for various rates of free cash flow growth (for the first 10 years). The following table of growth assumptions to growth multiples was determined using the method described above:

Growth AssumptionGrowth Multiple
4%8.35
5%8.94
6%9.57
7%10.25
8%10.98
9%11.76
10%12.59
11%13.48
12%14.44
13%15.46
14%16.56
15%17.74

From these values, the following formula (best fit curve) was determined:

Growth Multiple = 8.3459 * 1.07 ((growth assumption)-4)

This formula correctly converts any growth assumption to the appropriate growth multiple.

TOTAL EQUITY

Total Equity is Total Assets less Total Liabilities. If all liabilities were to be paid off by assets, total equity is what would remain. In addition to the discounted future free cash flows (the 6 year FCF average multiplied by the growth multiple), the screener adds 80% of the most recently reported total equity to the intrinsic value calculation. The reasoning is that portions of companies are often bought and sold for various reasons. Because of this, it is fair to include a portion of total equity as part of the intrinsic value calculation.

The most recently reported value of Total Equity is used. The formula again is:

Value = (Growth Multiple)*FCF(6 year avg) + 0.8*Total Equity(most recent)

There is one issue that arises on occasion. Total Equity can be negative. Using the above formula, would actually provide undesirable results. For example, consider XYZ corp, having a growth multiple of 10, a 6 year FCF average of \$100 and total equity of -\$100. The following would occur:

Value = (10)*\$100 + 0.8*(-\$100) = \$1000 - \$80 = \$920

Because Total Equity is negative, it is not fully accounted for. The full value of the negative total equity should be used:

Value = (10)*\$100 + (-\$100) = \$1000 - \$100 = \$900

That is better, as the negative total equity is fully accounted for, Better yet, negative total equity should be more heavily weighted in order to represent a more pessimistic view. More than \$100 should be subtracted due to the negative equity. So, when a company has negative total equity, the following formula is instead applied:

Value = (Growth Multiple)*FCF(6 year avg) + (Total Equity(most recent))/0.8

So, in the case of XYZ corp, the following math occurs:

Value = (10)*\$100 + (-\$100)/0.8 = \$1000 - \$125 = \$875

EXAMPLE

Assume the following. FOO corp has a Growth Assumption of 8%. The 6 year average FCF of \$100 million and Total Equity is \$500 million, Value is determined by first determining the appropriate growth multiple. Applying the conversion formula:

Growth Multiple = 8.3459 * 1.07(growth assumption-4)

Growth Multiple = 8.3459 * 1.07(8-4)

Growth Multiple = 8.3459 * 1.07(4)

Growth Multiple = 8.3459 * 1.31 = 10.94

Now, applying the value formula:

Value = (Growth Multiple)*FCF(6 year avg) + 0.8*Total Equity(most recent)

Value = (10.94) * \$100 + 0.8*\$500

Value = \$1094+400 = \$1494

If there are 100 million shares of FOO corp, it's value is \$14.94/share (\$1494 million divided by 100 million shares).

ASSUMPTIONS

In creating this screener, several assumptions were made. They are discussed in the following paragraphs.

It was decided to use a 6 year FCF average. For explanatory purposes, consider 3, 6 and 9 year time frames. Supposing a 9 year average were used, companies with less than 9 years of data would be omitted. Also, the impact of more recent events would be minimized since each year has an in impact of about 11%. If 3 years of data were used, any single year which is “out of whack” could greatly impact the result since each year would have a 33% weighting. Because of these very simple reasons, a 6 year FCF average was chosen as a happy medium. With a 6 year FCF average, a valuation may be off due to one odd year of data, but it's effect would be to a much lesser degree since each year accounts for about 17% of the average. It is also thought that the 6 years of data is sufficient when normalizing most company data.

It was decided to weight total equity by 80% (multiple of 0.8). To better understand why, consider extreme cases of 0%, 100% and even 100%+ discussed in the following paragraphs.

A total equity weighting of 0% would mean that total equity has no impact. This is clearly not reasonable. As a simple example, most companies have cash and cash equivalents on the books. These items clearly hold some value. Therefore more than 0% needs to be accounted for.

A total equity weighting of 100% would have a possibly irrational impact. For example, 100% would assume that 100% of the assets are valid. For example, accounts receivable may not be collected in its entirety. The reason is simple. If a company owing money goes bankrupt, they will not necessarily repay their debts. And not paying their debts to the company being considered for investment is a possibility. 100% is the ideal case, but it is not always reasonable to account for all of the 100% since some of the assets might not turn out to be real assets.

As an odd case, a total equity weighting of more than 100% (100%+) is theoretically possible, but that would assume that a companies liabilities would not be resolved. It should always be assumed that a companies liabilities be resolved. If liabilities were not to be resolved, that would be akin to thinking the company being researched will not be able to pay it's debt and if that is the case, it is probably not worthy of investment due to more deeply rooted financial issues. Regardless, imagine total assets of \$100 million and total liabilities of \$50 million. This would result in a total equity of \$50 million (\$100m - \$50m). So, if only \$40 million in liabilities were to be accounted for, total equity would actually by \$60 million (\$100m - \$40m). A weighting greater than 100% should not normally be considered.

For the reasons in the above paragraphs, total equity weighting is more art than science and it should always be revisited in more detail when researching a company. Weightings from 0% to 100% to more than 100% are possible. 80% was chosen as a happy medium after taking the above ideas into consideration. Additionally, during the creation of the screener results were being reviewed. After reviewing the results that the screener was providing for larger well, known entities it was decided to use the 0.8 multiple (80%). As a side note, 70% was originally going to be used but it was later decided to increase that weighting slightly.

CONCLUSION

In using this screener, please remember that this is an idea generator and that further research and a more detailed valuation should be performed. The future free cash flow growth estimates and total equity weighting are not equal for all stocks. Each stock is an individual case which warrants deeper study.

NOTE: Companies that are more than 4 months delinquent with their annual reporting are not included in the results. Also, financial companies are excluded.

Link: Discounted Free Cash Flow Screener