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September 9, 2022 17:50 Handbook of Investment Analysis, Portfolio Management. . . (in 4 Volumes) 9.61in x 6.69in EA1 b4699-v3-ch63 page 1
Chapter 63
Fundamental Analysis: A Practical
Approach
Andreas G. Koutoupis and Leonidas G. Davidopoulos
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Contents
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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Methods of Stock Valuation . . . . . . . . . . . . . . . . . . . .
Key Ratios According to Warren Buffet . . . . . . . . . . . . . .
Discounted Cash Flow Models: A Case Study of Apple . . . . .
63.4.1 Dividend discount model: A case study of Johnson and
Johnson . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63.4.2 H-model: A case study of Lowe . . . . . . . . . . . . . .
63.5 A Basic Framework . . . . . . . . . . . . . . . . . . . . . . . . .
63.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Abstract
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63.1
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Fundamental analysis is a simple concept which tries to isolate investing choices from
sentiment. Moreover, it is a mixture of science and art that breaks down to simple math.
Great value investors such as Warren Buffet, Benjamin Graham, and John C. Bogle very
vividly state that in order to successfully value a business, it does not take more than
Andreas G. Koutoupis
University of Thessaly, Thessaly, Larissa, Greece
andreas koutoupis@yahoo.gr
Leonidas G. Davidopoulos
Insurance and Financial Services “LazaridouDespoina”, Kozani, Greece
leonidas koz@hotmail.com
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common sense and simple math. In this chapter, we approach the very fundamentals in a
practical manner, showcasing a simple way to estimate the intrinsic value of a business.
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Keywords
Fundamental analysis • Value investing • Discounted cash flows • Intrinsic value.
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63.1 Introduction
Fundamental analysis refers to the business evaluation that is based on basic
accounting information and reasonable, conservative assumptions about the
future of the business. In this way, an investor relies only on the core, relative,
and reliable information, ignoring sentiment and therefore short-term market
price movements. At the end of this analysis, the investor ends with a number
which portrays the fair or intrinsic value of the stock and compares it with
the market price of the stock. The main difference between the two prices
is that the fair value reflects the real value of the business as derived from
its accounting and sound macroeconomic assumptions, while market price
is the outcome of the supply and demand of the stock. Consequently, the
market price of the business, which is represented by the stock price, contains
besides fundamental information the noise of traders who try to forecast
the price movements by employing historical data of the price. Moreover,
market price may contain the noise of irrelevant people who try to speculate
the market following some kind of a trend, for instance, Robinhood novice
investors who, during COVID-19, were sitting at home and feeding the bigtech bubble of 2020 by buying whatever stocks that went up like Apple and
Tesla (Tokic, 2020).
Value investors who employ fundamental analysis and plain logic are
sentiment-free individuals and view stock market as a pool of opportunities
and stock units as shares of ownership of the underlying business. Therefore, they ignore short-term price movements and value a business mostly
by discounting future, expected cash flows that that business can produce
reasonably. Warren Buffet is one of the greatest value investors who employs
simple math and logic in order to acquire business opportunities.
This chapter attempts to present key aspects of fundamental analysis
in a practical manner. Consequently, we briefly present the basic valuation
categories in order to provide the greater picture of fair value estimation
techniques. After that, we present key ratios that Warren Buffet employs
and supports his approach to business evaluation. Finally, through Apple’s,
Johnson and Johnson’s and Lowe’s case studies, we present in detail the
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Fundamental Analysis: A Practical Approach
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discounted cash flow models that is the cornerstone of the fundamental analysis and value investing.
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63.2 Methods of Stock Valuation
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Stock valuation has a fundamental purpose which is to estimate the intrinsic
value, the fair value of a stock. Generally, there are three main categories of
tools that allow us to estimate fair value, as follows:
• Present value models.
• Asset-based models.
• Multiples.
Many analysts use a combination of the above in order to double check their
research.
Present value models answer one main question that is “What are those
cash flows that we must use in order to come up with an intrinsic value?”
Two models answer this question, the discounted cash flow (DCF) model and
the dividend discount model (DDM). Particularly, the DCF model discounts
cash flows that are known as free cash flows (FCFs), which are calculated
from the net cash flows from operating activities minus capital expenditures.
Practically, it is the amount of money that is available to the company after
she covers all relative expenses and can be employed from the company in
order to pay its debt, to make dividend distributions, etc. Therefore, if we
want to approach a company as potential owners (like Warren Buffet), the
discount approach is one of the best methods.
DCF and DDM can be used in order to evaluate blue chip companies,
such as Coca-Cola, Walmart, and McDonalds. Conversely, they do not seem
to be equally effective when applied to financial companies like banks and
insurance companies. Moreover, should a company pay dividends regularly
and they are in line with its profitability, then we employ DDM. Particularly, a firm must use dividends distributions as the main source of value
for shareholders in order for DDM to be properly used. The reason for this
is that DCF refers to cash flows that are available mainly to the company,
while DDM refers to cash flows that are directed toward investors.
The main advantage of these models is that both are based on fundamental analysis and they both are popular ways to estimate fair/intrinsic value.
On the other hand, their disadvantage is that we estimate future cash flows
(to the business or investors), thus intrinsic value is highly dependent on
our assumptions. However, they constitute the best method of fundamental
valuation.
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Another valuation method is the one that is based on the assets of a firm.
The theory behind this is that the fair value of every company is the value
of its assets minus the value of its liabilities. However, we do not refer to
the book value of the company. This method is ideal for companies that are
very close to liquidation. Moreover, asset valuation is suitable for companies
whose assets’ fair value is easily estimated. An example of such businesses
would be oil companies that estimate the amount of oil underground and are
able to report the exact quantity of them, thus enabling investors to value
future inventory. Nevertheless, asset valuation presents a major drawback,
that is the difficulty to estimate the fair value a company’s assets.
Finally, multiples valuation is among the most popular methods of stock
valuation. We can differentiate multiples valuation into two categories, enterprise value multiples and stock price multiples. Both of them share the common principle of the law of one price, which states that similar assets should
share the same price. Consequently, stocks of identical companies should
present similar multiples. When it comes to enterprise value multiples, they
are commonly used when firms present losses. On the other hand, price multiples, such as price per earnings, price per sales, price to book value and price
to FCF, are very popular. Usually, these multiples along with some other
ratios are used by analysts in order to get a rough estimate of the business
or the industry before they dig a little deeper into each firm’s financials.
Ultimately, due to difficulty in tracking the large number of ratios, analysts
employ only a few of them.
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63.3 Key Ratios According to Warren Buffet
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As we have already mentioned, there is a plethora of financial ratios that
investors can use in order to determine the intrinsic value of a stock. Nevertheless, Warren Buffet focuses on four principles in his investing strategy
(Brodersen, 2014), among which two of them can be expressed and verified
by key financial ratios. In this section, we analyze three of them that we
consider the most important and representative.
The first one refers to management and leadership and its ability to
serve shareholders’ interests at all times (Brodersen, 2014). This principal is fundamental, as in the real world, management focuses more on
its self-interest rather than returns’ optimization to the shareholders. For
this reason, Brodersen (2014) identifies some rules that reflect management
incentives and capabilities that refer to low debt, high current ratio, consistent return on equity, and quality corporate governance indicators.
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When analyzing corporate debt, an investor should not evaluate it differently from his personal debt. Ideally, companies should target and achieve
a zero debt strategy, although this is very rare. A quite common indicator
of leverage risk is the debt/equity ratio which needs to be kept as low as
possible, at least lower than 0.5. Moreover, moving on to the assets side, a
quite strict measure of a firm’s liquidity is the current ratio that portrays the
ability of the company to receive cash flows relative to its short-term payments. Particularly, when current ratio (current assets/current liabilities) is
equal to 2, this means that the company receives USD 2 every time a debt of
USD 1 must be paid within the next 12 months. A value lower than 1 means
that the company will need to raise new debt in order to pay off its short-term
debt obligations. Ideally, a current ratio between 1.5 and 2 is an indicator
of good health for most companies. Furthermore, net income/shareholders’
equity refers to the return that a firm gives back to the shareholders. Investing comes down to what someone gets back from an investment relative to
its acquiring cost. Return on equity (net income/total equity) is a measure
of management’s efficiency and a constant and upward trend, above 8% for
the past 10 years, is much desirable. Warren Buffet considers this ratio as
highly important right after debt-to-equity ratio (Brodersen, 2014). Finally,
management’s efficiency should be always rewarded based on performance;
therefore, corporate governance indicators should always be scrutinized by
investors. For instance, is executives’ compensation aligned with performance
excluding short-term stock price performance? Particularly, notes in the
annual report that do not describe in detail the compensation plan of the
management must be perceived as a red flag.
Besides, quantitative indicators, when someone considers investing in a
company, should also be forward-looking regarding firm’s future perspectives. A crucial checkpoint regarding the sustainability of a business is its
products and particularly how plausible it is that the same products are
able to fulfill future demands. A great example is the lifelong Coke holdings of Warren Buffet — even though technology evolves, Coke satisfies the
particular need of people the same way (Brodersen, 2014).
Ultimately, every investment encloses a fair value that is reasonably paid
by the investor. Besides the DCF models, a quick way to estimate whether a
business is overpriced or not is by looking at price multiples such as price-toearnings ratio and price-to-book ratio. Price to earnings (market price per
share/earnings per share) is a popular and basic valuation metric. What it
simply does is to inform investors about the cost of one dollar of earnings. For
instance, a price-to-earnings ratio of 20 means that in order for an investor
to earn one dollar of earnings, he should pay USD20 in order to own one
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unit of stock. Consequently, it is reasonable to assume that the lower the
ratio the greater the opportunity. Warren Buffet, as a conservative investor,
suggests a price-to-earnings ratio below 15 (Brodersen, 2014). Similarly, the
price-to-book ratio (market price per share/book value or equity per share)
compares the market value of the firm with its book value. A firm with a
price to book value of 2 informs the investor that in order to acquire one
dollar of equity (total assets — total liabilities), he must pay two dollars.
Therefore, a low price to book ratio bellow 1.5 is much desirable and ensures
a part of the equity at a low price (Brodersen, 2014).
Finally, an investor must always keep in mind that ratios portray a relative value. This means that in order to come up with robust conclusions,
one needs to compare these ratios with competitors, the industry, and the
market in general.
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63.4 Discounted Cash Flow Models: A Case Study of Apple
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When we are referring to the intrinsic value of a stock, we essentially talk
about the present value of the expected, future FCFs.
Before we present a case study, in order for this model to provide robust
results we need to take the following assumptions for a company:
1. The company does not make dividend distributions.
2. The company needs to produce positive FCFs. Therefore, new companies
that may have future potentials are excluded since they do not present
adequate FCF for the time being. Conversely, well-established companies
are more suitable for this model.
3. FCFs should be in line with profitability.
In order to be able to employ the DCF model, the company needs to
meet one of the above criteria.
We employ accounting data from the financial statements available at
company’s website or US SEC website or Yahoo Finance, etc. The first
accounting number that we need is the FCF. However, there are two kinds
of cash flows, namely FCF to the firm and FCF to equity. FCF to the firm
refers to the cash that is available to the firm and bond investors (creditors),
while FCF to equity refers to the cash available to the common stockholders.
Consequently, the main difference between the two is the payment to interest
and taxes.
FCF to equity is used when the company’s leverage is stable, and here
is an example that demonstrates the difference. First of all, we assume that
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we analyze Apple company in 2019; therefore, our historical data are prior
to 2019 and we estimate for the years after 2019.
Net cash flows
from
operations
−CapEx
FCF to equity
(simple)
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2016
2017
2018
81,266,000
66,231,000
64,225,000
77,434,000
11,247,000
70,019,000
12,734,000
53,497,000
12,451,000
51,774,000
13,313,000
64,121,000
Source: Apple’s accounting data and authors’ calculations.
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Technically, the calculation above is false since we have to add net borrowings. Let’s see the difference.
Net cash flows
from
operations
−CapEx
+Net
borrowing
FCF to equity
(cleaner
formula)
2015
2016
2017
2018
81,266,000
66,231,000
64,225,000
77,434,000
11,247,000
29,305,000
12,734,000
22,057,000
12,451,000
29,014,000
13,313,000
432,000
99,324,000
75,554,000
80,788,000
64,553,000
Source: Apple’s accounting data and authors’ calculations.
We observe that after the adjustment of FCF to the net borrowing, the
2018 does not differ that much (64,553,000 instead of 64,121,000). However,
we observe that FCF to equity differs significantly between FCF to equity
(simple) and FCF to equity (cleaner formula) the years before 2018. This is
due to the great amount of leverage created each year which consequently
leads to high values of FCFs.
Most analysts employ the simple version of FCF because we simply cannot forecast net borrowings the way we forecast FCFs.
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The next step is to project FCFs for the years after 2019; however, in
order to do that, we have to come up with a projection rate.
We have already assumed that FCFs should always follow profitability,
hence we employ net income.
2015
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Net income
53,394,000
FCF to equity
70,019,000
(simple)
FCF to
131%
equity(simple)/
Net income
2016
2017
2018
45,687,000
53,497,000
48,351,000
51,774,000
59,531,000
64,121,000
117%
107%
108%
We actually compare FCFs to the net income, and we conclude that FCFs
are generally in line with profitability.
Ideally, when we analyze a company, we develop an idea of where this
company is heading, her future, and her potentials in general. This notion
facilitates us when deciding whether FCFs will continue to present the same
course as profitability. For instance, in our case, after our research, we conclude that Apple’s FCF relationship with her profitability is not going to
differ dramatically in the future relative to the current state. Therefore, we
are going to employ 107% as the optimal relationship between FCF and net
income.
We now know what the relationship between net income and FCF will
probably look like in the future. However, how useful is this going to be if
we do not first estimate how Apple’s net income is going to evolve?
There are many ways to come up with net income projections, but we are
going to use revenue. Particularly, we can either use analysts’ revenue estimations or we can make our own estimations. Analysts’ estimations can be
found in Yahoo Finance (we select the ticker symbol, then from the analysis
section, we use the average estimate for the next couple of years).
If we choose to make our own estimates, we need to come up with a
suitable revenue growth rate for the next two years. In order to do that, we
first employ the historical revenue from the company’s annual reports and
calculate annual revenue growth:
2016 : (215.639.000 − 233.715.000)/233.715.000 = −0.77 or − 7, 7% ∼ −8%;
2017 : (229.234.000 − 215.639.000)/215.639.000 = 0.06 or 6%;
2018 : (265.595.000 − 229.234.000)/229.234.000 = 0.158 or 15.8% ∼ 16%.
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Revenue 233.715.000
Revenue
growth
rate
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2016
2017
2018
2019E
2020E
215.639.000
−8%
229.234.000
6%
265.595.000
16%
257.310.000
−3%
(analysts’
estimates)
269.680.000
5%
(analysts’
estimates)
Source: Apple’s accounting data and Yahoo Finance.
For the years 2019E and 2020E, we employ the average estimate of analysts, that is, 3% for 2019E and 5% for 2020E, in order to estimate Apple’s
revenue. Now, we calculate the average of the revenue growth rates, that is
(−8% + 6% + 16% − 3% + 5%)/5 = 3.2%.
A revenue growth rate of 3.2% for a company like Apple is quite logical
since her size could not allow a higher growth rate. We apply the growth
rate of 3% for years 2021E and 2022E:
2021 : 269.680.000 + 3%269.680.000 = 277.770.400;
2022 : 277.770.400 + 3%277.770.400 = 286.103.512.
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We have our revenue estimations and we want to convert them to net income
estimations. In order to do that, we calculate our net income margin (net
income/revenue):
Revenue
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Net income
Margin
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2015
2016
2017
2018
233,715,000
2019E
257,310,000
53,394,000
23%
215,639,000
2020E
269,680,000
45,687,000
21%
229,234,000
2021E
277,770,400
48,351,000
21%
265,595,000
2022E
286,103,512
59,531,000
22%
Source: Apple’s accounting data and authors’ calculations.
2015 : 53.394.000/233.715.000 = 0.228 or 22.8% ∼ 23%;
2016 : 45.687.000/215.639.000 = 0.211 or 21.1% ∼ 21%;
2017 48.351.000/229.234.000 = 0.21 ∼ 21%;
2018 : 59.531.000/265.595.000 = 22%.
We observe that Apple’s margins remain relatively constant. We now calculate margins’ average as
(23% + 21% + 21% + 22%)/4 = 21.75% ∼ 22%.
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However, due to the conservatism principle, we employ a net income growth
rate of 21% (net income margin = net income/revenue, net income = net
income margin × revenue) and then calculate our estimations for the years
2019–2022.
Re-venue
Net income
Margin
2015
2016
2017
2018
233,715,000
53,394,000
23%
215,639,000
45,687,000
21%
229,234,000
48,351,000
21%
265,595,000
59,531,000
22%
2019E
2020E
2021E
2022E
257,310,000
54,035,100
21%
269,680,000
56,632,800
21%
277,770,400
58,331,784
21%
286,103,512
60,081,738
21%
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Net income
Margin
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Source: Apple’s accounting data and authors’ calculations.
Finally, we employ the analogy FCF to equity/net income = 107%, as
previously calculated, in order to project our FCF:
2019E : 54.035.100 × 107% = 57.817.557;
2020E : 56.632.800 × 107% = 60.598.096;
2021E : 58.331.784 × 107% = 62.415.009;
2022E : 60.081.738 × 107% = 64.287.459.
Net income
FCF to equity (simple)
FCF/N.I
2015
2016
2017
2018
53.394.000
70.019.000
107%
45.687.000
53.497.000
107%
48.351.000
51.774.000
107%
59.531.000
64.121.000
107%
2019E
2020E
2021E
2022E
54.035.100
57.817.557
107%
56.632.800
60.597.096
107%
58.331.784
62.415.009
107%
60.081.738
64.287.459
107%
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Net income
FCF to equity (simple)
FCF/N.I
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Source: Apple’s accounting data and authors’ calculations.
Now that we have our FCF to equity projections, we need to estimate our
required rate of return. This is quite interesting because, theoretically, this
rate is subject to our personal expectations, our risk tolerance, etc. However,
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if we want to determine this rate using a more sophisticated framework, we
can employ weighted average cost of capital (wacc).
Typically, a firm uses wacc, and in order to apply it, we need to calculate
FCF to the firm, but analysts in everyday practice use it in conjunction with
FCF to equity. Therefore,
R = wacc = wd rd (1 − t) + we re ,
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where:
w = weights,
wd = weight of debt, and
we = weight of equity.
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Interest expense (from the
income statement)
Short/Current debt
(borrowings maturing in the
current year)+Long term
debt = Total debt (from the
balance sheet)
3.240.000
8.784.000 + 93.735.000 = 102.519.000
Source: Apple’s accounting data and authors’ calculations.
We first calculate the cost of debt as follows:
rd = 3.240.000/102.519.000 = 3, 16%.
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Then, we calculate the tax rate, and for this, we use income before taxes
and income tax expense.
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Income before taxes (from the
income statement)
Income tax expense (from the
income statement)
72.903.000
13.372.000
t = 13.372.000/72.903.000 = 18, 34%.
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Consequently, Apple’s tax adjusted cost of debt = rd (1 − t) = 3.16%(1 −
18, 34%) = 2.58%.
Since we have calculated cost of debt, we now calculate cost of equity.
Capital asset pricing model (CAPM) is employed for that purpose:
CAPM = Rf + β(Rm − Rf ),
3
where:
Rf = risk-free rate,
Rm = expected market return, and
β = stock beta.
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8
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10
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12
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14
15
16
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20
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Risk-free rate can be found from Yahoo Finance in the markets section and
is depicted by the US Treasury bonds rates (10 years). The last price of the
10-year treasury bond is 2,32%. Stock beta can be found in Yahoo Finance
in the statistics section of the stock which at the time is 0,89. Finally,
the expected return of the market is calculated through the annual average returns of the S&P 500. Particularly, we can search the annual returns
of the S&P 500 on Google and then calculate averages. We assume that our
averages can be summarized as follows:
• 10-year average total return: 15%;
• 20-year average total return (since 1999): 6%;
• 30-year average total return (since 1989): 10%;
• 40-year average total return (since 1979): 12%;
• 50-year average total return (since 1969): 10%.
How do we pick the right expected market return?
We cannot use 15% since the last 10 years away from the Great Financial
Crisis theoretically have been relatively great and economy has been expanding. Moreover, using 6% means that we are 20 years away since 1999 when
economy was at its high before tech bubble burst. Consequently, we are going
to use the average of both average returns which is (15% + 6%)/2 = 10, 5%.
Therefore, CAPM = re = 2, 32% + 0, 89(10% − 2, 32%) = 9, 16%.
Finally, we have to calculate the weights which is relatively easy to do,
as we only need market capitalization and total debt. Market capitalization
can be found in Yahoo Finance and total debt has already been calculated
earlier. If Apple’s market capitalization is 826,629 and total debt is 112,63,
then the sum of these two is 826, 629 + 112, 63 = 939, 259. Now, we can
calculate the weight of debt which is 112, 63/939, 259 = 12% and the weight
of equity which is 826, 629/939, 259 = 88%.
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Finally, our required rate of return = wacc = 12% × 2, 58% + 88% ×
9, 16% = 8, 4%.
Now, we need to find the number of shares outstanding or the number of
common stocks. We can find this number from the annual report of Apple
or from Yahoo Finance. For instance, Apple’s number of common shares is
4.601.075.
One last number we employ is that of the expected growth of the developed countries like the US or Germany which is 2,5%. This perpetual growth
rate is how much we expect FCF of Apple to grow at forever.
Period (N )
10
11
12
13
14
15
16
17
13
FCF to
equity
(simple)
Discount
factor
Present
1.009.341.139
value
Required
8,4%
rate of
return
(r)
Perpetual
2,5%
groth (g)
Apple’s
1.009.341.139
today
value
No. of
4.601.075
shares
outstanding
Fair value
219
of equity
1
2
3
4
4
2019E
57.817.557
2020E
60.597.096
2021E
62.415.009
2022E
64.287.459
TV =end of 2022
1.116.858.400
1,084
1,175
1,274
1,381
1,381
53.337.230
51.569.539
49.000.577
46.559.5
808.874.206
We now need to calculate terminal value, that is, the value of Apple at
the end of 2022:
Terminal value = (FCF to equity at the beginning of 2022 × (1 +
g))/(r − g) = 64.287.459 × (1 + 2, 5%)/(8, 4% − 2, 5%) = 1.116.858.400.
Moreover, we need to calculate discount factor which will be equal to
(1 + r)N = (1 + 0, 084)N . Finally, we discount FCF using the discount factor
for each period N , present value of FCF = FCF/discount factor.
18
N
Discount factor
19
FCF to equity
(simple)
PV
1
2
3
4
4
2019E
(1,084)1
1,084
57.817.557
2020E
(1,084)2
1,175
60.597.096
2021E
(1,084)3
1,274
62.415.009
2022E
(1,084)4
1,381
64.287.459
TV = end of 2022
(1,084)4
1,381
1.116.858.400
53.337.230
(57.817.557/)
1,087)
51.569.539
(60.597.096/)
1,175)
49.000.577
(62.415.009/)
1,274)
46.559.588
(64.287.459/
1,381)
808.874.206
(1.116.858.400/
1,381)
September 9, 2022 17:50 Handbook of Investment Analysis, Portfolio Management. . . (in 4 Volumes) 9.61in x 6.69in EA1 b4699-v3-ch63 page 14
14 Handbook of Investment Analysis, Portfolio Management, and Financial Derivatives
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9
We add PV in each period in order to come up with Apple’s value
today. Particularly, 53.337.230 + 51.569.539 + 49.000.577 + 46.559.588 +
808.874.206 = 1.009.341.139. Now, in order to make this number useful and
comparable with the Apple’s market price, we divide it with the number of
shares. Consequently, 1.009.341.139/4.601.075 = USD 219/share.
Now that we have our fair value per share, we can compare it with the
Apple’s stock price in order to decide if there is an opportunity.
63.4.1 Dividend discount model: A case study of Johnson
and Johnson
Dividend discount model (DDM) is similar to DCF but simpler since we do
not make so many assumptions. Generally, the mathematical expression of
fair value given the dividend distribution is
Fair value = (Dividend1 + Price1 )/1 + r,
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11
12
13
14
15
16
17
18
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23
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25
26
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28
where Dividend1 is the cash dividend of the following year and Price1 is the
expected price of the stock the following year (the year that we plan to sell
the stock).
For instance, let us assume that we hold a stock which it is in our plans to
sell it in a year, in a price that we think that will be around USE100/share.
Furthermore, we expect this stock to make dividend distributions of USD5
in total. Therefore, we expect cash flows from the stock sale and from the
dividends paid to us in the holding period. That would make a total of
USD105. Now, if we could come up with a required rate of return of 10%,
we could discount those future cash flows to the present and calculate their
fair value which would be USD95,45 (105/1,1).
However, how could we possibly know the price of the stock in a year
from now?
The idea behind this calculation is to estimate the present value of future
dividends. However, we can see that the above formula refers to only one
period, assuming that we hold the stock in our portfolio for one year and
then we sell the stock. What happens if we do not want to sell the stock and
hold it for over a year? What happens if we want to keep the stock forever
and collect the cash dividends?
In order to be able to make use of the above formula, we make some
transformations that lead us to the following formula:
Fair value = D0 (1 + g)/(r − g),
29
30
31
where D0 is the cash dividends that the stock pays today. Practically, we
employ the dividends paid the previous year. r is the required rate of return
and g is the dividends’ expected growth.
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The idea behind this formula remains the same, but it is more appropriate
for stocks and dividend ETFs, while the previous formula is more useful
for bond valuations. This formula is widely known as the Gordon growth
model.
In order to provide a practical presentation, we use Johnson and Johnson
(JJ), which is a well-established dividend payer. We need its dividend distributions’ historical data, something that is easily retrievable from its 10K
or Yahoo Finance. If we want to use Yahoo Finance, from JJ stock page, we
select “historical data,” then “dividends only” option. We see the dividend
payments as follows.
Date
14
16
17
18
19
0.95
0.9
0.9
0.9
Source: Yahoo Finance.
12
15
Dividends
May 24, 2019
February 25, 2019
November 26, 2018
August 27, 2018
11
13
15
The sum of the above is 0.95 + 0.9 + 0.9 + 0.9 = 3.65 which is our D0 .
Now, we need to estimate the dividends’ expected growth (g), and in order
to do that, we need historical data for over a year. An easy and practical way
to come up with a fair estimation is to go back five years and get the annual
dividends. Then, we calculate the annual change, the five-year change, and
the three-year change and finally calculate the average of these changes.
Practically, we could create a table like the following one.
Year
2015
20
2016
Total dividends
per year
d1 + d2 + · · · +
dn = total
dividends
paid for 2015
d1 + d2 + · · · +
dn = total
dividends
paid for 2016
Annual changes
(annual growth)
Three-year
change
(three-year
growth)
Five-year
change
(five-year
growth)
(Total dividends
paid for
2016-total
dividends paid
for 2015)/total
dividends paid
for 2015
(Continued)
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16 Handbook of Investment Analysis, Portfolio Management, and Financial Derivatives
Year
d1 + d2 + · · · +
dn = total
dividends
paid for 2017
(Total dividends
paid for
2017-total
dividends paid
for 2016)/total
dividends paid
for 2016
2018
d1 + d2 + · · · +
dn = total
dividends
paid for 2018
(Total dividends
paid for
2018-total
dividends paid
for 2017)/total
dividends paid
for 2017
2019
d1 + d2 + · · · +
dn = total
dividends
paid for 2019
(Total dividends
paid for
2019-total
dividends paid
for 2018)/total
dividends paid
for 2018
Average
3
4
5
6
7
Annual changes
(annual growth)
2017
1
2
Total dividends
per year
(g2016 + g2017 +
g2018 + g2019 )/4
Three-year
change
(three-year
growth)
(Total
dividends
paid for 2017
− total
dividends
paid for
2015)/total
dividends
paid for 2015
(Total
dividends
paid for 2018
− total
dividends
paid for
2016)/total
dividends
paid for 2016
(Total
dividends
paid for 2019
− total
dividends
paid for
2017)/total
dividends
paid for 2017
(g2015−2017 +
g2016−2018 +
g2017−2019 )/3
Five-year
change
(five-year
growth)
(Total
dividends
paid for 2019
− total
dividends
paid for
2015)/total
dividends
paid for 2015
g2015−2019
The above table provides us with a clear picture of the dividend growth
scenarios of JJ. However, our perpetual growth will be the average of the
annual changes. Therefore, as presented in the following, our g = 5% which is
a very conservative number, and given the fact that JJ has a dividend payout
ratio (annual dividends paid/net income) of 60%, we can safely assume that
a constant 6% annual dividend growth is plausible.
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Fundamental Analysis: A Practical Approach
Year
Total dividends per year
Annual changes
(annual growth)
Three-year
change
(three-year
growth)
(3.15 −
2.95)/2.95 =
0.07 or 7%
(3.32 −
3.15)/3.15 =
0.05 or 5%
(3.54 −
3.32)/3.32 =
0.06 or 6%
(3.75 −
3.54)/3.54 =
0.06 or 6%
(0.07 + 0.05 +
0.06 + 0.06)/4 =
0.048 or 5%
(3.32 −
2.95)/2.95 =
0.12 or 12%
(3.54 −
3.15)3.15 =
0.12 or 12%
(3.75 −
3.32)/3.32 =
0.13 or 13%
(0.12 + 0.12 +
0.13)/3 =
0.12
17
Five-year
change
(five-year
growth)
2015 0.75 + 0.75 + 0.75 + 0.7 = 2.95
2016 0.8 + 0.8 + 0.8 + 0.75 = 3.15
2017 0.84 + 0.84 +0.84 + 0.8 = 3.32
1
2018 0.9 + 0.9 + 0.9 + 0.84 = 3.54
2019 0.95 + 0.95 + 0.95 + 0.9 = 3.75
Average
2
3
4
5
6
7
8
9
10
11
12
13
14
15
(3.75 −
2.95)/2.95 =
0.27 or 27%
0.27 or 27%
Now that we have our current dividend (D0 ) which is USD 3.65/share and
the expected perpetual growth (g) which is 5%, we can estimate the dividend
that we are going to collect the next year (D1 ). Therefore, 3.65(1 + 0.05) =
USD 3.83/share.
The next step is to calculate our required rate of return which is equal
to the weighted average cost of capital. We assume that it is equal to 8%,
and finally, we can calculate the fair value which is 3.83/(0.08 − 0.05) =
USD 127.66/share.
63.4.2 H-model: A case study of Lowe
Thus far, we have seen how we can discount FCFs under the condition that
are constant and sustainable in the future. JJ is the example of a dividend
payer that can actually sustain its dividend growth perpetually because a 6%
annual dividend growth is easy to maintain. What happens when a company
records a 16% annual dividend growth or 20% annual dividend growth?
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We notice from the table above that the average three-year dividend
growth of JJ is about 12%; therefore, it is not very reasonable to expect that
a company can actually increase its dividend 17% every year for an infinite
period. How do we adjust our valuations when we meet a company like this?
Our initial formula was
fair value = D0 (1 + g)/(r − g).
5
6
7
Now, it is logical to assume that since 18% is not sustainable growth, there
will be a transitional period when Lowe will commence to decrease its dividend growth until it reaches a 5% or 6% annual growth.
The mathematical expression and transformation of the above formula
which is known as the H-model is
fair value = D0 (1 + gl )/(r − gl ) + D0 H(gs − gl )/(r − gl ),
18
where gl is our long-term growth that can be sustained, gs is our short-term
growth that cannot be sustained, and H is the half-life of the total period
that the company will decrease its growth rate to a more sustainable level.
Consequently, we understand that in our case gl = 6% and gs = 18%, and
if we assume that in order for 18% to reach 6% it will take approximately
14 years, H will be 7 years (14/2).
We calculate the required rate of return the way we did with Apple, that
is 9%.
Finally, we calculate the fair value of Lowe that is USD 122/share. Particularly, 1.92(1 + 0.06)/(0.09 + 0.06) + 1.92 × 7(0.18 − 0.06)/(0.09 − 0.06) =
68 + 54 = USD 122/share.
19
63.5 A Basic Framework
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31
How can we combine the price multiples and ratios that Warren Buffet
employs with DCF models which are also his favorite method of valuation?
Well, as we have already demonstrated, the DCF approach is a much more
time-consuming and sophisticated method that takes a lot of time and familiarity with the accounting numbers and the sustainability of the business.
We definitely cannot use the DCF models for each and every firm in the
stock universe. That would be great for educational purposes, but to use
it in real life, one needs to have already established a quick and relatively
robust picture of the firm under valuation before making use of the DCF
models.
A very sound and quick approach would be to use a stock screener like
Yahoo Finance or Macrotrends in order to filter the basic ratios and price
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Fundamental Analysis: A Practical Approach
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multiples that will provide a sample of companies. Those companies would be
better to refer to an industry, as we have already said that homogeneity is of
the essence in order to make robust conclusions. Then, we could choose firms
that we understand and assume that they are sustainable for the next 10–20
years and probably their products will continue to satisfy consumers the same
way, no matter the technological changes. By this time, we will probably have
to choose around two to three competitive firms. We then could employ
the corporate governance section of the annual report in order to evaluate
qualitative indicators, such as risk reporting, management’s compensation,
and discussion for the present and the future. Finally, we research more
complex issues and use the DCF models in order to come up with the fair
value of the business.
13
63.6 Conclusion
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23
This chapter attempts to present in a simple and practical way the key
aspects of fundamental analysis. Particularly, we combine the key ratios and
multiples with DCF models that Warren Buffet employs in his analysis. We
arrived at a basic framework that investors can apply for everyday practice. Furthermore, we believe and aim to provide a stepping stone to novice
investors who, most of the time, are confused and do not really know what to
do and what is the big picture. Consequently, we provide a simple roadmap
to retail investors who, in time, can build up new knowledge and motivates
them to actually get familiar with basic concepts of accounting, finance, and
corporate governance.
AQ02
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References
Brodersen, S. (2014). Warren Buffett Accounting Book: Reading Financial Statements for Value.
Tokic, D. (2020). Robinhoods and the Nasdaq whale: The makings of the 2020
big-tech bubble. Journal of Corporate Accounting & Finance, 31(4), 9–14.
September 9, 2022 17:50 Handbook of Investment Analysis, Portfolio Management. . . (in 4 Volumes) 9.61in x 6.69in EA1 b4699-v3-ch63 page 20
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