Stock Valuation
For stock
valuation, analysts use the following five the most commonly used models containing the formula for stock valuation.
- Discounted Dividend Valuation
- Free Cash Flow Valuation
- Market-Based Valuation: Price and Enterprise Value Multiples
- Residual Income Valuation
- Private Company Valuation
Discounted
Dividend Valuation
Cash flows are
defined as dividends in the dividend discount model. The primary rationale for
utilizing this definition of cash flow is that an investor who buys and keeps a
share of stock typically receives only dividends in the form of cash returns.
In practice, analysts typically believe that earnings influence investment
value. Is it true that the concept of cash flow as dividends excludes earnings
that are not delivered to shareholders as dividends? Earnings reinvested should
create the foundation for future dividend increases. As a result, the DDM
accounts for reinvested earnings when calculating all future dividends.
Dividends are less volatile than earnings and other return ideas, hence DDM
values may be less vulnerable to short-run variations in underlying value than
alternative DCF models. Analysts frequently believe that DDM values indicate
long-run intrinsic value.
Dividends are
either paid or not paid by a stock. If a corporation is not profitable and has
no funds to distribute, it may not pay dividends on its stock. In addition, a
corporation may not pay dividends for the opposite reason: it is extremely
profitable. For example, a corporation may reinvest all earnings rather than
paying dividends in order to capitalize on profitable growth prospects.
Dividends may be initiated as the company matures and faces less appealing
investment prospects. In general, mature, profitable corporations tend to pay
dividends and are hesitant to lower payout levels.
When DDM should
be used
In general, the
DDM and the concept of returns as dividends are most appropriate when:
A. the corporation pays dividends (i.e., the analyst has a dividend
record to analyze).
B. the board of directors has set a dividend policy with a clear and
consistent relationship to the company’s profitability; and
C. the investor has a noncontrol perspective.
By answering
the questions, an analyst has final responsibility in the selection of
valuation models:
State whether a
dividend discount model is an appropriate choice for valuing Co, A. Also, state
whether a dividend discount model is a good fit for valuing Co, B.
The data in the
following display is from the last 15 years. (In the table, EPS stands for
earnings per share, DPS stands for dividends per share, and the payout ratio
equals DPS divided by EPS.)
Co, |
Co, |
|||||
Year |
EPS |
DPS |
PAR |
EPS |
DPS |
PAR |
2012 |
3.08 |
1.00 |
32.00 |
1.86 |
0.60 |
32.00 |
2011 |
3.08 |
1.00 |
32.00 |
1.74 |
0.51 |
29.00 |
2010 |
3.94 |
1.00 |
25.00 |
1.51 |
0.42 |
28.00 |
2009 |
3.56 |
1.00 |
28.00 |
1.27 |
0.38 |
30.00 |
2008 |
1.77 |
1.00 |
56.00 |
1.04 |
0.37 |
36.00 |
2007 |
2.17 |
1.00 |
46.00 |
1.07 |
0.30 |
28.00 |
2006 |
2.55 |
1.00 |
39.00 |
1.03 |
0.28 |
27.00 |
2005 |
2.53 |
1.00 |
40.00 |
0.91 |
0.26 |
29.00 |
2004 |
2.41 |
1.00 |
41.00 |
0.78 |
0.23 |
29.00 |
2003 |
3.40 |
1.00 |
29.00 |
0.67 |
0.21 |
31.00 |
2002 |
2.56 |
1.00 |
39.00 |
0.68 |
0.20 |
29.00 |
2001 |
1.07 |
1.00 |
93.00 |
0.65 |
0.19 |
29.00 |
2000 |
0.71 |
1.00 |
14.00 |
0.61 |
0.18 |
30.00 |
1999 |
0.37 |
1.00 |
27.00 |
0.54 |
0.17 |
31.00 |
1998 |
1.75 |
1.00 |
57.00 |
0.41 |
0.16 |
39.00 |
Interpretation
A DDM does not
appear to be a viable alternative for valuing CO, A based only on the data
shown in Exhibit. Since 1998, CO, A’s dividends have been $1.00 per share. CO,
A’s EPS was $1.75 in 1998 but dropped dramatically to $0.37 in 1999. EPS
recovered to $2.56 in 2002, but has since ranged from $1.77 to $3.94, with a
2012 value of $3.08. In short, from 2002 to 2012, CO, A grew at a compound
annual rate of 1.9 percent with significant variability, whereas DPS remained
unchanged. On the basis of the data supplied, it is difficult to detect an
understandable and consistent relationship between dividends and earnings.
Because dividends do not appear to alter to reflect changes in profitability,
applying a DDM to CO, A is most likely incorrect. It appears that valuing CO, A
on another basis, such as a company-level definition of cash flows, is more
acceptable.
With the
exception of 2003 and 2008, CO, B’s historical earnings indicate a long-term
rising trend. Although you should look at such differing payout percentages,
CO, B’s dividends have consistently tracked its profits growth. During the
entire time, earnings per share and dividends per share climbed at comparable
compound annual growth rates of 11.4 percent and 9.9 percent, respectively. EPS
and DPS grew at comparable rates over the last four years, indicating a
dividend payment ratio ranging from 28 percent to 32 percent. To summarize,
given CO, B pays dividends and dividends have a clear and consistent link with
profits, employing a DDM to evaluate CO, B is appropriate.
Combining the
general DCF model with Gordon growth model
The first
two-stage DDM provides for a high initial growth rate, followed by a
sustainable and typically reduced growth rate thereafter. The multiple-period
model underpins the two-stage DDM.
The is a PV of the high growth period (1)
The is a PV of the constant growth period (2)
Where Vn is the
Gordon growth model to find Vn, such as
by evaluating
Vn, we combine it, general growth model, to obtain a two-stage DDM (3)
Two-Stage Dividend Discount Model (4)
Practical application of the formula for stock
valuation is discussed in the following video.
Multistage
Dividend Discount Models
The DDM’s fundamental phrase is too broad for investment analysts to utilize in practice
since they can only anticipate a limited number of payouts individually. The
most powerful simplifying assumption—a constant dividend growth rate
indefinitely, resulting in the Gordon growth model—is unrealistic for many, if
not most, businesses. Many public businesses’ growth is divided into three
stages, according to experts.
1) The initial stage of development. A firm in its growth stage usually has quickly growing markets,
strong profit margins, and an exceptionally high earnings per share growth rate
(supernormal growth). Because the firm invests substantially in growing
activities, companies in this phase frequently have the negative free cash flow to
equity. Because of the large potential returns on stock, growth-phase firms’
dividend payout ratios are frequently low, if not non-existent. Earnings growth
rates inevitably fall as the company’s markets mature or as unexpected growth
prospects attract competition.
2) Transition phase. Earnings growth slows during this phase, which is a transition to
maturity, as competition puts pressure on pricing and profit margins, or as
sales growth slows due to market saturation. Earnings growth rates may be above
average during this period, but they will eventually fall in line with the
general economy’s growth rate. In this period, capital requirements usually
decrease, leading to positive free cash flow and higher dividend payment ratios
(or the initiation of dividends).
3) Mature phase. When a firm approaches maturity, it reaches a point
when investment possibilities yield its opportunity cost of capital on average.
Earnings growth, the dividend payout ratio, and return on equity all approach
the necessary return on equity, and earnings growth, dividend payout ratio, and
return on equity all stabilize at levels that can be sustained over time. This
phase’s dividend and profits growth rate is referred to as the mature growth
rate. This period, in reality, corresponds to the point at which a firm may be
correctly evaluated using the Gordon growth model, which is one method for
evaluating a present high-growth company’s future.
Two-Stage
Dividend Discount Model
There are two
popular variants of the two-stage DDM. In Stage 2, both models assume continual
growth at a mature growth rate (for example, 7%). Stage 1 reflects a time of
extraordinary growth in the first version (“the basic two-stage model”), for
example, growth of 15%. In most cases, the shift to mature growth in Stage 2 is
sudden.
The H-Mode
During Stage 1,
the dividend growth rate is anticipated to fall from an abnormal rate to the
mature growth rate in the second version, known as the H-model. For example,
the growth rate may start at 15% and gradually decrease in Stage 1 until it
reaches 7%. After the overall two-stage model, the second model will be given.
A smoother
transition to the mature phase growth rate might be more realistic in some
situations. Fuller and Hsia (1984) created a two-stage model in which growth
starts off fast and then slows down linearly over the supernormal growth period
until it achieves a normal rate at the conclusion. In the H-model, the dividend
stream has a value of (5)
OR (6)
All else being
equal, the greater the share value, the longer the supernormal growth period
(i.e., the larger the value of H, which is one-half the duration of the
supernormal growth period) and the larger the additional growth rate in the
supernormal growth period (measured by g_{S} minus g_{L}).
Summary
Dividends, free
cash flow, and residual income are some of the various streams of projected
cash flows that may be utilized to assess shares. A discounted dividend method
is best suited for dividend-paying companies where the firm has a clear payout
policy with a clear link to profitability and the investor has a noncontrol
(minority ownership) perspective. A minority interest, also known as a
non-controlling interest, is an ownership position in which a shareholder holds
less than 50% of the outstanding shares of a company. As a result, minority
interest shareholders have no direct influence over company decisions or votes.
The value of
any asset in a DCF model is the present value of its (anticipated) future cash
flows. (8)
where V0
represents the asset’s value at time t = 0 (today), CFt represents the
(anticipated) cash flow at time t, and r represents the discount rate or
necessary rate of return. For assets with an unlimited lifespan, such as common
stocks, n is limitless.
With a single
holding term, the DDM calculates stock value as follows: (9)
D_{t} =
D_{t}–1(1 + g) in the Gordon growth model posits that dividends rise at
a constant rate g indefinitely. In the Gordon growth model, the dividend stream
has a value of (10)
Different
growth rates are used in Stage 1 and Stage 2 of the two-stage dividend discount
model. (11)
The H-model
posits that during Stage 1, the dividend growth rate falls linearly from a high
supernormal rate to a normal rate, and then rises at a steady normal rate
thereafter: (12)
Two basic
three-stage models exist. The growth rate in the middle stage is constant in
one variation. The growth rate in the second variant decreases linearly in
Stage 2 before becoming steady and normal in Stage 3.
Illustration
Finding the
Stock Price for a Five-Year Forecast Horizon
The yearly
dividends of a stock are anticipated to be Rs3.00, Rs3.10, Rs3.20, Rs4.25, and
Rs4.75 for the following five years. After addition, in five years, the stock
price is anticipated to be Rs100.00. What is the value of this stock if the
necessary return on equity is 10%? The projected future cash flows’ current
values can be spelled down as
Valuing a Stock
Using the Two-Stage Dividend Discount Model
The Zakir Group
owns 65 percent of Zakir Corp, which produces screening, diagnostic, and
therapeutic solutions for ophthalmologic disorders. Hasan, a buy-side analyst
covering Zakir Corp, examines the issue as of mid-August 2013, when it is
selling for Rs23.37, and projects that the present dividend of Rs0.40 would
rise by 9% per year over the following ten years. Following that, Hasan
predicts that the growth rate would fall to 5% and stay there permanently.
Based on a beta of 0.90 against the KSE-100, a 2.4 percent risk-free rate, and
a 5.2 percent equity risk premium estimate, Hasan calculates his needed return
on equity to be 7.1 percent (2.4 + 0.9(5.2)).
First,
calculate stock’s value at year 10 by using formula (3),
Vo = 47.3473 / (1.071)^{10}
= Rs23.8452
PV D_{1-10} =
0.40(1.09)^{1} / (1.071)^{1}+ 0.40(1.09)^{2} / (1.071)^{2}+0.40(1.09)^{3}
/ (1.071)^{3}+ 0.40(1.09)^{4} / (1.071)^{4} + 0.40(1.09)^{5}
/ (1.071)^{5}+ 0.40 (1.09)^{6} /(1.071)^{6} + 0.40(1.09)^{7}
/(1.071)^{7} + 0.40(1.09)^{8} /(1.071)^{8} +0.40(1.09)^{9}
/(1.071)^{9} + 0.40(1.09)^{10} /(1.071)^{10} = Rs4.4118
Total Present
Value = Rs23.8452 + Rs4.4118 = Rs28.2570
The Three-Stage
DDM with Three Distinct Stages
ABC Co pays a
dividend of Rs5.30 per year. A current price is Rs200.00. An analyst makes the
following estimates:
the current
required return on equity for ABC is 9 percent, and
dividends will
grow at 14 percent for the next two years, 12 percent for the following five
years, and 6.75 percent thereafter. Based only on the information given,
estimate the value of ABC using a three-stage DDM approach.
V0 = 575.92 / (1.09)7 = Rs315.05
PV D_{1-2} = 5.30(1.14)1 / (1.09)1 + = 5.30(1.14)2
/ (1.09)2 = Rs11.34
PV D _{3-7} = 3.30(1.14)2 (1.12)1 /
(1.09)3 + 3.30(1.14)2 (1.12)2 / (1.09)4 +3.30(1.14)2 (1.12)3 / (1.09)5 +3.30(1.14)2
(1.12)4 / (1.09)6 +3.30(1.14)2 (1.12)5 / (1.09)7 = Rs31.47
Total PV = RS315.05 + Rs11.34 + 31.47= Rs357.86
With Declining
Growth Rates in Stage 2, the Three-Stage DDM (H-Model)
For the XYZ
corporation, the following information is available:
$56.18 is the
current market price.
The current
dividend rate is $0.56 per share.
The analyst
predicts an initial 5-year profits and dividend growth rate of 11% per year.
The analyst
estimates that as a mature firm, XYZ can expand at a rate of 6.5 percent per
year, with a 10-year transition time.
The analyst utilizes
an adjusted beta of 1.2 based on two years of weekly observations, an estimated
equity risk premium of 4.2 percent, and a risk-free rate of 3 percent to
calculate the necessary return on equity using the CAPM.
The analyst
considers any security trading within a band of ± 20 percent of her estimate of
intrinsic value to be within a “fair value range.
The necessary
return on equity is r = 3% + 1.2 (4.2%), which is 8%.
The first stage
is to determine the current values of the five dividends from Stage 1 at an
interest rate of 8%. The H-model may be used to value the dividends in Stages 2
and 3, which estimates their value at the start of Stage 2. The dividends’
present value at t = 0 is calculated using this value. Exhibit 8 shows how to
calculate the five payouts in Stage 1 and their current values. The H-model (as
shown in 12) would be used to calculate the value of the Stage 2 and Stage 3
dividends at the start of Stage 2 (t = 5).
PV
D1-5 = 0.564(1.1)1 / (1.08)1 + 0.564(1.1)2 / (1.08)2 +0.564(1.1)3 / (1.08)3 +0.564(1.1)4
/ (1.08)4 +0.564(1.1)5 / (1.08)5