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Summary

  • Advance the Theory of Investment Value by John Burr Williams and his DCF method by incorporating equity-adjusted valuations.
  • Increase the profitability of your investments by performing more accurate equity valuations.
  • An increasing or decreasing equity base can significantly affect "per share" intrinsic value.

Equity-Adjusted Valuations

John Burr Williams was among the first to develop the Discounted Cash Flow (DCF) model in 1937 to estimate the intrinsic value of a common stock. After the overall intrinsic value of a business's common stock is estimated, the analyst must then divide the overall intrinsic value by the number of "total shares outstanding" to calculate the "per share" intrinsic value.

A key limitation of the DCF method is that cash flows are more easily predicted in the near future, and more difficult to predict farther out into the future. Another key limitation is that the changing underlying equity base is not being factored in, when calculating "per share" intrinsic value.

For instance, businesses like Coca-Cola (NYSE:KO) and Exxon Mobil (NYSE:XOM) possess a long-term consistent history of buying back shares of their common stock. Conversely, other businesses like Apple Inc (NASDAQ:AAPL) show a long-term consistent history of issuing additional shares of their common stock.

In other words, the total shares outstanding of Coca-Cola and Exxon Mobil are decreasing. Whereas, the total shares outstanding of Apple Inc and other business are increasing. (You can easily confirm this viewing the 10-year history of total shares outstanding of each business's income statement).

Therefore, when estimating the "per share" intrinsic value for each year in your DCF valuation analysis, it's important to account for the accretion or contraction of the number of shares outstanding for each year. Let's look at a 10-year history of some different businesses.

Let's look at Coca-Cola 's income statement. It confirms Coca-Cola has repurchased back shares every year for at least the past 10 years with consistency at an average rate of 0.72% per year.

More specifically, Coca-Cola 's income statement reveals 4,858 million shares outstanding at the end of 2004, and only 4,509 million shares outstanding at the end of 2013. This confirms our average rate of Coca-Cola repurchasing back about 0.72% of its shares outstanding year after year.

Now that we know this, do we possess a high degree of certainty that Coca-Cola will continue to repurchase its common stock shares at a rate close to its 10-yr average of 0.72% per year? Here's what an equity adjusted analysis looks like.

Total shares outstanding:

Starting amount: 4,509 million shares in 2013 (less 0.72% per year)

Year 1 (2014): 4,477 million

Year 2 (2015): 4,444 million

Year 3 (2016): 4,413 million

Year 4 (2017): 4,381 million

Year 5 (2018): 4,349 million

Year 6 (2019): 4,318 million Year 11 (2024): 4,165 million

Year 7 (2020): 4,287 million Year 12 (2025): 4,135 million

Year 8 (2021): 4,256 million Year 13 (2026): 4,106 million

Year 9 (2022): 4,226 million Year 14 (2027): 4,076 million

Year10 (2023): 4,195 million Year 15 (2028): 4,047 million shares

If we divide the estimated overall intrinsic value of Coca-Cola (numerator) by 4,509 million shares (denominator), we would estimate a very different valuation than if we were to divide the same overall intrinsic value (numerator) by only 4,047 million shares (denominator).

Remember, 4,047 million shares is the estimated number of total shares outstanding expected to exist in 2028 (15 years into the future).

Conversely, what if a business were issuing more common shares instead of reducing the number of shares outstanding with share buybacks? Are analysts accounting for the changing number of underlying shares outstanding into their "per share" intrinsic valuations?

Good question. I doubt they are. I hope this article will serve as a catalyst to change that.

If you think about it, ignoring the equity base will make valuations fluctuate farther away from the actual intrinsic value per share of the business. This may help explain how two analysts often arrive at very different "per share" intrinsic valuations when even looking at the same business.

I hope this will help bring about more common sense equity valuations to the financial industry. Therefore, be aware of the non-adjusted equity bias, and consider accounting for the accretion or contraction of the underlying equity base in your "per share" intrinsic valuations.

Now let's put it all together, using the following example. Let's call it "Business A."

EXAMPLE #1: If we were to perform a "vanilla" DCF analysis on "Business A" using a 2-stage valuation model, not adjusting for changes in the number of shares outstanding in the underlying equity base, the results would appear something like this:

Market Price

$5.11

Intrinsic Value

$453,099,571

Shares Outstanding

78,000,000

Intrinsic Value /share

$5.81

Growth Rate: Years 1-10

1.00%

Margin of Safety

12.0%

Growth Rate: Years 11-15

0.00%

Price-to-Value

0.880

Discount Rate

9.00%

Bargain

$0.70

Starting FCF Amount

$53,000,000

Year 1

$53,530,000

end of year

1.0%

growth

Year 2

$54,065,300

end of year

1.0%

growth

Year 3

$54,605,953

end of year

1.0%

growth

Year 4

$55,152,013

end of year

1.0%

growth

Year 5

$55,703,533

end of year

1.0%

growth

Year 6

$56,260,568

end of year

1.0%

growth

Year 7

$56,823,174

end of year

1.0%

growth

Year 8

$57,391,405

end of year

1.0%

growth

Year 9

$57,965,319

end of year

1.0%

growth

Year 10

$58,544,973

end of year

1.0%

growth

Year 11

$58,544,973

end of year

0.0%

growth

Year 12

$58,544,973

end of year

0.0%

growth

Year 13

$58,544,973

end of year

0.0%

growth

Year 14

$58,544,973

end of year

0.0%

growth

Year 15

$58,544,973

end of year

0.0%

growth

This example shows a 12.0% margin of safety between price and value.

EXAMPLE #2: Now let's look at "Business A's" 10-year history of total shares outstanding, and factor this into our "per share" intrinsic valuation. (Hint: We arrive at a very different valuation).

We notice that "Business A" has consistently repurchased back an average of 3.95% of its total shares outstanding year after year. At the end of 2004, "Business A" showed 129 million shares outstanding. Ten years later, at the end of 2013 "Business A" showed only 78 million shares outstanding. (This confirms our average annual decrease of shares outstanding of 3.95%). Now let's extrapolate this into the future:

Total shares outstanding:

Starting amount: 78,000,000 (less 3.95% per year)

Year 1: 74,919,000

Year 2: 71,959,699

Year 3: 69,117,291

Year 4: 66,387,158

Year 5: 63,764,865

Year 6: 61,246,153 Year 11: 50,068,624

Year 7: 58,826,930 Year 12: 48,090,914

Year 8: 56,503,266 Year 13: 46,191,323

Year 9: 54,271,387 Year 14: 44,366,765

Year 10: 51,127,667 Year 15: 42,614,278 shares

Remember, the 10-year history is in the past. We make our money off what happens in the future, not what happened in the past. Therefore, while performing equity-adjusted valuations, determine your level of certainty whether "Business A" will continue its 10-year trajectory into the future, or not.

For the sake of this example, let's assume "Business A" will continue its consistent 10-year history of share buybacks (close to its average rate of 3.95% per year) into the future. The equity-adjusted valuation would appear something like this:

Market Price

$5.11

Intrinsic Value

$453,099,571

Shares Outstanding

42,614,278

Intrinsic Value /share

$10.63

Growth Rate: Years 1-10

1.00%

Margin of Safety

51.9%

Growth Rate: Years 11-15

0.00%

Price-to-Value

0.481

Discount Rate

9.00%

Bargain

$5.52

Starting FCF Amount

$53,000,000

Year 1

$53,530,000

end of year

1.0%

growth

Year 2

$54,065,300

end of year

1.0%

growth

Year 3

$54,605,953

end of year

1.0%

growth

Year 4

$55,152,013

end of year

1.0%

growth

Year 5

$55,703,533

end of year

1.0%

growth

Year 6

$56,260,568

end of year

1.0%

growth

Year 7

$56,823,174

end of year

1.0%

growth

Year 8

$57,391,405

end of year

1.0%

growth

Year 9

$57,965,319

end of year

1.0%

growth

Year 10

$58,544,973

end of year

1.0%

growth

Year 11

$58,544,973

end of year

0.0%

growth

Year 12

$58,544,973

end of year

0.0%

growth

Year 13

$58,544,973

end of year

0.0%

growth

Year 14

$58,544,973

end of year

0.0%

growth

Year 15

$58,544,973

end of year

0.0%

growth

This example shows a 51.9% margin of safety between price and value.

Summary:

Example 1 was not adjusted for the change in shares outstanding. Whereas, Example 2 was "equity adjusted" for the change in shares outstanding. Notice the number of "Shares Outstanding" and "Intrinsic Value/share" within each valuation, show very different amounts.

In Example #1: DCF (Non-Equity Adjusted) valuation:

$5.81/share @ 12% margin of safety.

78,000,000 shares outstanding.

In Example #2: DCF (Equity Adjusted) valuation:

$10.63/share @ 51.9% margin of safety.

42,614,278 shares outstanding.

I've just demonstrated how two analysts may arrive at very different estimates of "per share" intrinsic value, even when looking at the same business. Valuation models will vary from firm to firm, and from analyst to analyst.

It's my goal this concept of "equity-adjusted" valuations will advance field of value investing, expand the capabilities of Discounted Cash Flow (DCF) analysis, and improve the accuracy of per share intrinsic valuations, for generations to come.

In the words of Berkshire Hathaway (NYSE:BRK.A), (NYSE:BRK.B) Chairman Warren Buffett, "You are neither right nor wrong because the crowd agrees or disagrees with you. You are right because your data and reasoning are right."

Source: Advanced Value Investing With Equity-Adjusted Valuations