EquityAdjusted 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 CocaCola (NYSE:KO) and Exxon Mobil (NYSE:XOM) possess a longterm consistent history of buying back shares of their common stock. Conversely, other businesses like Apple Inc (NASDAQ:AAPL) show a longterm consistent history of issuing additional shares of their common stock.
In other words, the total shares outstanding of CocaCola 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 10year 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 10year history of some different businesses.
Let's look at CocaCola 's income statement. It confirms CocaCola 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, CocaCola '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 CocaCola 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 CocaCola will continue to repurchase its common stock shares at a rate close to its 10yr 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 CocaCola (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 nonadjusted 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 2stage 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 110 
1.00% 
Margin of Safety 
12.0% 

Growth Rate: Years 1115 
0.00% 
PricetoValue 
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" 10year 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 10year history is in the past. We make our money off what happens in the future, not what happened in the past. Therefore, while performing equityadjusted valuations, determine your level of certainty whether "Business A" will continue its 10year trajectory into the future, or not.
For the sake of this example, let's assume "Business A" will continue its consistent 10year history of share buybacks (close to its average rate of 3.95% per year) into the future. The equityadjusted 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 110 
1.00% 
Margin of Safety 
51.9% 

Growth Rate: Years 1115 
0.00% 
PricetoValue 
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 (NonEquity 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 "equityadjusted" 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."
Disclosure: I am long KO, XOM, BRK.B. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.