### Chapter 8 Common Stock Valuation

```Chapter 8
Common Stock Valuation
•
What is the Intrinsic value and how it is
different from the market price
•
How to calculate the intrinsic value.
•
What are the fundamentals of security
evaluation.(RRR, time, and size of CFs)
•
The Discount Cash Flow models to evaluate
common stock
The Essence of Valuation
 One of the main objectives of valuation is to estimate
the intrinsic value.
 One of the main uses of the intrinsic value is to
determine if we are paying the fair value for the
security (Common stocks in this case) or its



Overvalued (intrinsic value<market price)
Undervalued (intrinsic value>market price)
Fairly valued (intrinsic value=market price)
What is the Intrinsic Value? And what is the
difference between it and the market price?
 Intrinsic value:
 An estimation of the stock “true” value




Not observable  hard to estimate  subjective.
The more info, the better the estimation of the stock true price
Its basically the PV of the future cash flows that the asset will
generate. These cash flows will be discounted at a required
rate of return (rrr) that reflect the riskiness of cash flows to
the investor.
 Market Price:
 Is the value of the stock determined by a competitive marketplace.


It is observable, especially for publicly traded firms.
but possible incorrect
 In equilibrium it is expected that intrinsic value is
equal to the market price.
Determining the Intrinsic value and its
determinants
Pˆ 0 
N


t 1
C f1
(1  rrr )
1

Cf2
(1  rrr )
2

Cf3
(1  rrr )
3
 ... 
Cf
(1  rrr )

Cf t
(1  rrr )
t
There are 3 determinants of the value of a security:
• The size of the furture CFs (+)
• The time of these CF (-)
• The discount rate: required rate of return (rrr) (-)
Overvalued (intrinsic value<market price)
Undervalued (intrinsic value>market price)
Fairly valued (intrinsic value=market price)
Determinants of the IV
 Expected Future CFs
 In Case of Stocks
 Future Dividends
 Expected Capital
gain/loss (when the stock
is sold at the end of the
holding period.
 In case of Bonds:
 Interest payment
 Loan Principal.
 Timing of the future CFs.
 The required rate of return (rrr)?
Determining the rrr
 rrr: is the minimum return you require to invest in that
stock.
 It can be determine using CAPM. (shows the relationship
between risk and expected retuns)
E(r) = rf + b(Rm-rf)
 Thus, rrr should at least compensate you for:


The risk-free rate of interest (return from investing in a zero-risk
asset) (delaying consumption)
b (systematic risk) the relevant risk. It shows the riskiness of the
stock relative to the market portfolio. The higher  more risky is the
stock. (b>1), (b<1), and (b=0)  stock is riskier, less risky, as risky as
market.
 Calculated by regressing the stock return on the market return
 (Rm-rf) Market risk premium (MRP). Shows how risk averse are
the market participants. The more risk averse, the higher the premium.
(see next slide)

Interpretation of Beta
 If beta = 1.0, the security is just as risky as the market (stock is as volatile as the
market)

This implies that the market portfolio has by definition beta of 1
 If beta > 1.0, the security is riskier than market (stock is more volatile than the
market)
 If beta < 1.0, the security is less risky than market (stock is less volatile than the
market.
 If beta is positive ( + )correlation between the stock and the market.
(regression line would slope upward) (most likely to observe that)
 If beta is negative ( - )correlation between stock and the market (regression
line would slope downward) (2there is a small chance to observe such situation)
• Beta of zero: means the stock have zero correlation with the market. The
movement of the stock is independent from the market movement market risk
is ZERO
The Concept of Risk-Aversion
ri (%)
SML3
B2
B1
A2
A1
SML2
SML1
SML4
SML5
Risk, bi
 (+) Slope indicate  risk averse investors
 Investor 2 is more risk averse than investor 1.
 However investor 3 is extremely risk averse.
 Investor 4 is risk neutral (his return will not change regardless of the
risk involved).
 Investor 5 is risk lover (he is willing to accept lower return for more
risk)
How to draw the SML in Excel and Make a
Decision regarding the stock fair value
The Security Market Line
9.00%
Expected REturn
8.00%
RRR= 8.00%
7.00%
6.00%
5.00%
4.00% Rf= 5.00%
3.00%
2.00%
1.00%
0.00%
0.00
Beta
0.10
0.20
0.30
0.40
0.50
0.60
Valuing Common Stock
 After we determine the fundamentals of security valuation
(future CF, timing of CFs, and RRR), we know go to how can
we use these fundamentals to evaluate common stock.
 There are several model we can use to estimate the current
value of a common stock:
First: Discount CFs Models (DCF)
A.
B.
C.
Dividend Discount Model (DDM)
Operating FCF Model (OFCF)
Free-cash-flow Model to Equity (FCFE)
Second: Relative Valuation Models:
Valuing stock relative to other, similar stocks or industry, using valuation
ratios such as:
A.
B.
C.
D.
P/E1 ratio.
P/CF1
P/BV1
P/Sales1
First: The Discount CF Models
A. Dividend Discount Model (DDM)
Why use Dividends to determine the stock intrinsic value?
 Because dividend is a proxy for the firm’s earnings (net
income).


Dividends are paid out of earnings.
If net income grows, then dividends grow if the firm maintain the
same payout ratio
 Expect that dividends to continue in the foreseeable
future:


Firms that initiate dividends reveal a good sign to investor, if they do
not have any growth opportunities.
So a firm that initiate dividend are going to be less likely to
discontinue these dividends because investors will view such action
negatively. (dividends are expected to continue in the foreseeable
future)
Dividend Discount Model (DDM)
 A stock that pays a dividends. If you are expecting to
sell that stock some time in the future (Ex. After 3
years), then the estimate current price should be:

=
+

+ +

+
+ +

 The expected price for a stock that pays dividends at end
of year 3 will also depend on future expected dividends.
Thus, a general form can be:
Pˆ 0 
D1
(1  rs )
1

D2
(1  rs )
2

D3
(1  rs )
3
 ... 
D
(1  rs )

The Constant-Growth DDM
 This model says that dividend will grow at a constant rate each year.
Thus, knowing the most recent dividend (Do) is equivalent to
knowing all future dividends.
 The reason for assuming such assumption is that
1.
Usually new firms will have low or negative earnings for several
years due to high investments in fixed and working capital.
2.
However, earnings after that will start to increase rapidly (growth
opportunities). Firm could earn return on investments higher
than their rrr by retaining more earning are reinvesting it in the
firm. Thus, have high growth periods.
3.
Then when the firms matures and its earnings stabilized its
earnings will grow at a constant rate. If the firm maintain a
constant payout ratio, then the constant growth in earning will
cause a constant growth in dividends.
The Constant-Growth DDM
ˆ 
P
0
D1
(1  rs )
1

D2
(1  rs )
2

D3
(1  rs )
ˆ  D 0 (1  g )  D 0 (1  g )
P
0
1
2
(1  rs )
(1  rs )
1
2

3
 ... 
D 0 (1  g )
(1  rs )
3
D
(1  rs )
3
 ... 

D 0 (1  g )
(1  rs )

ˆ  D 0 (1  g )  D 1
 P
0
rs  g
rs  g
 Note that for this model to work, it must be rs>g.
 Also, g must be constant.

The Constant-Growth DDM
D 0 (1  g )
D1
ˆ
P0 

rs  g
rs  g
 Rearranging the model we can obtain
rs
D1

 g
ˆ
P
0
 The required rate of return should be equal to the stock total
return (Dividend yield + capital gain/loss)
 This implies that, under the constant-growth DDM, the stock
price as well as the dividends will grow at the constant rate g.
 If the stock offers a total return>rrr  stock is undervalued
 If the stock offers a total return<rrr  stock is overvalued
Example 1 (sheet 2)….What is the maximum price you should pay
for a stock that has currently paid \$2 dividends and such dividend is
expected to grow at a constant rate of 6% forever. The rf rate is 7% and
the expected market return is 12%, the stock’s beta is 1.2
 The required rate of return on the firm’s stock is
rs = rRF + (rM – rRF)b  7% + (12% – 7%)1.2 = 13%
Pˆ 0 
D1
rs  g

\$2.12
0.13  0.06

\$2.12
 \$30.29
0.07
 If the current market price of the stock is below (above) this value,
then the stock is undervalued (overvalued)
D1
\$2.12
E(r) 
g
 6%  13%
ˆP
\$30.29
0
 If stock offers us a return below (above) the rs, then the stock is
overvalued (undervalued)
 Also, this means that the stock price next year will growth by 6%. Thus,
30.29(1.06) = 32.11
Example 2 (Sheet 2)
 What is the expected price after 3 years for a stock that
has currently paid \$2 dividends and such dividend is
expected to grow at a constant rate of 6% forever. The
required rate of return is 13%

( + %) ( + %) .
=
=
=
=
= .
−
−
% − %
%
= . ( + %) = .
 Now, by knowing the estimated price after 3 year, we can do the
following:

=
+
=

+ +

.
+ %
+
+
+ +

.
+ %
+
.  + .
= .
+ %
Example 3 (g=0) (sheet 2)
 What is the maximum price you should pay for a stock that
has currently paid \$2 dividends and such dividend is expected
to continue forever. The rf rate is 7% and the expected market
return is 12%, the stock’s beta is 1.2
 The required rate of return on the firm’s stock is
rs = rRF + (rM – rRF)b
= 7% + (12% – 7%)1.2
= 13%
Pˆ 0 
D1
rs  g

\$2(1  0%)
 15 . 38
0.13
 This mean the stock price is not growing and the total return
from the stock is from the dividend yield. 2/15.38=13%
Example 4 (sheet 2)
 If the stock was expected to have negative growth
(g = -6%s forever), would anyone buy the stock,
and what is its value?
 Yes. Even though the dividends are declining, the
stock is still producing cash flows and therefore
has positive value.
ˆ 
P
0

D1
rs  g

D 0 (1  g)
rs  g
\$2.00 (0.94)
0.13  (-0.06)

\$1.88
0.19
 \$9.89
Cont’d Example 4
 Find Expected Annual Dividend and Capital Gains Yields?
 Capital gains yield
= g = -6.00%
 Dividend yield
= 13.00% – (-6.00%) = 19.00% = 1.88/9.89
 Since the stock is experiencing constant growth, dividend
yield and capital gains yield are constant.
 Dividend yield is sufficiently large (19%) to offset negative
capital gains.
Two-Stage Growth DDM
As mentioned before,
 Usually new firms will have low or negative earnings for
several years due to high investments in fixed and working
capital.
 After that the firm could experience high growth periods by
retaining more earnings if they can earn higher return on
investments than its rrr.
 Finally, that high growth rate cannot be sustained for ever
due to competition and other factors. Thus, earning growth
will decline and expect to growth at a lower long-run
constant rate.
Thus, the firm could initiate dividends, but that dividend may
grow at a fast rate. However, that growth rate is unlikely to
continue forever. Thus, the growth rate will start to decline
until dividend start to grow at a constant rate.
Examples 5/6 (sheet 3)
 Example 5:
What is the expected current price for a stock that has
currently paid \$2 dividends. Dividends will grow at a high
rate of 30% for 3 years before achieving the long-run
growth rate of 6%. The required rate of return is 13%
 Example 6:
What is the expected current price for a stock that has
currently paid \$2 dividends. Dividends will NOT grow
(g=0%) for 3 years before achieving the long-run growth
rate of 6%. The required rate of return is 13%
Example 5 (sheet 3)
0 rs = 13%
2
1
g = 30%
2
g = 30%
2.6
3
3.38
2.301
2.647
3.045
46.114
54.107 =Pˆ0
 HV refers to horizontal value
g = 30%
Pˆ 3 
4.39
4.658
0.13  0 . 06
4
g = 6%
4.658
 \$66.54(HV)
Example 6 (sheet 3)
0 r = 13%
s
g = 0%
D0 = 2.00
1.77
1
2
g = 0%
2.00
3
g = 0%
2.00
4
g = 6%
2.00
2.12
1.57
1.39
20.99
25.72 =Pˆ0
 HV is the horizontal value
Pˆ 3 
2.12
0.13  0 . 06
 \$30.29 (HV)
A note on the non-constant growth DDM

=
+

 If the growth rate of dividend is not constant, then
stock will grow at rate that is different from that of
dividends

Capital gain is NOT going to be equal to g
Example 7 (sheet 4)
 From Example 5, we were able to determine  =
54.11.
 Since dividend will not grow at a constant rate, then
CG ≠ g.
 Let us examine the stock price for the next 4 years
and examine its growth rate.
Cont’d Example 7 (sheet 4)
 For the first year ……. DY = D1/P0 = 2.60/54.11
rs
13%
-
DY
4.81%
= CG
= 8.19%
Thus, stock P end 1Y [E(P1)]
54.11 * (1+8.19%) = 58.54
 For the Second year……DY = D2/P1 = 3.38/58.54
rs
13%
-
DY
5.77%
= CG
= 7.23%
Thus, stock P end 2Y [E(P2)]
58.54 * (1+7.23%) = 62.77
 For the third year……. DY = D3/P2 = 4.39/62.77
rs
13%
-
DY
7.00%
= CG
= 6.00%
Thus, stock P end 3Y [E(P3)]
62.77 * (1+6.00%) = 66.54
 For the fourth year…….. DY = D4/P3 = 4.66/66.54
rs
13%
-
DY
7.00%
= CG
= 6.00%
Thus, stock P end 4Y [E(P4)]
66.54 * (1+6.00%) =
70.53
First: Discount CF (DCF) Models
B. Operating FCF Model
VF 
VF 
OFCF

1
(1  WACC )
1
OFCF 0 (1  g )
(1  WACC )
 VF 
OFCF
(1  WACC )
1
1

OFCF 0 (1  g )
WACC  g
2
2
 ... 
OFCF 0 (1  g )
(1  WACC )

OFCF
1
WACC  g
2
OFCF

(1  WACC )
2
 ... 

 Non _ Operating
OFCF 0 (1  g )
(1  WACC )
 Non _ Operating

_ Assets

 Non _ Operating
_ Assets
_ Assets ,
Then ,
V F  V D  V PS  V CS
P0 
V CS
SHO
 Non-operating assets such as marketable securities
Operating FCF Model
 OFCF: is the amount of cash available from operations for
distribution to all investors (including stockholders and
debtholders) after making the necessary investments to
support operations.
 It’s the operating cash flow after taxes less the reinvestments
in fixed assets (capital expenditure) and operating working
capital (which is essential to maintain ongoing operation and
positive growth)

Thus, OFCF shows the cash available to all investors (capital providers:
debt-holders, preferred stock holders, and common stock holders).
 Thus, the higher that FCF, the more valuable become the
firms (intrinsic stock value will increase).
Calculating Free Cash Flow in 5 Easy Steps
Step 1
Step 2
Earning before interest and taxes
Operating current assets
X (1 − Tax rate)
− Operating current liabilities
Net operating profit after taxes
Net operating working capital
Step 3
Net operating working capital
+
Net Operating long-term assets
Total net operating capital
Step 5
Step 4
Net operating profit after taxes
Total net operating capital this year
− Net investment in operating capital
− Total net operating capital last year
Free cash flow
Net investment in operating capital
30
Calculating OFCF (Gross of Dep.)

=
+ . & . − ∆
=  ( − )

=  +   _
=    −

=  +   +

=   +  +
Alternative Method (Net of depreciation)
=  − ∆
=  ( − )

=  +   _
=    −

=  +   +

=   +  +
Alternative Method to Calculating OFCF

=  + . & . − ∆  −   ()

=  − ∆  −    − . & .
= ∆    _
 CAPEX is the additional investment in long-term operating assets. These
investments are essential for growth and ongoing operations. These
investment goes from renovating a roof of a building all the way to buying
buildings, equipment, machinery
Interpretation of OFCF
 + FCF: shows that the firms generates more than enough
cash from its operations to finance its current
investments in fixed assets and working capital.
 - FCF: the firm have insufficient internal funds to finance
its investments in fixed assets ands working capital. Need
to raise additional funds to pay for these investments.
 Is negative free cash flow always a bad sign?

NO if the firm is growing.
 For such firms, the needed investments in fixed assets
and working capital always exceed the cash flows from
existing operation. This is not bad as long as these
investments are profitable in the future and generate
future CFs.
OFCF
Usually there are 3 ways firms are financed:




Common stock (rs)
Debt (rd)
Preferred stock (rsp) : hybrid between common stock and equity,
where it guarantees the amount of dividends, but the firm can omit
such dividends without exposing the firm to bankruptcy.

Thus, when discounting OFCF to obtain the value of the
firm, we must used the weighted average of the minimum
acceptable return each investor requires. It is called the
weighted average cost of capital (WACC).
To the firm, WACC is the cost of obtained capital

We do not use required rate of return rs

Example 8 (sheet 5)
 If WACC = 10%, calculate the firm’s intrinsic value (expected
value of the stock) if OFCFs for Y1= -5, Y2=10, Y3=20 then
OFCFs will keep on growing a the long-run rate of 6%. Also,
the firm has 40 million in total debt and preferred stock and
has 10 million shares common stock outstanding.
 Note, that for the first 3 years OFCF grows at a non-constant
rate  Thus, cannot use the constant growth model.
 After the 3Y, OFCF will grow at the long-run growth rate of
6%  can use the constant growth model.
 Thus, we must use a 2 stage method.
Cont’d Example 8 (sheet 5)
0
WACC
= 10%
1
-5
-4.545
8.264
15.026
398.197
416.942
2
3
10
20
530 
4
g = 6%
21.20
0.10  0 . 06
=  +  +  = 40M +  = 416.942

376.94
0 =
=
= \$37.69

10
21.20
 HV 3
= 376.94
Preferred Stock Evaluation
 Hybrid security.
 Like bonds, preferred stockholders receive a fixed
dividend that must be paid before dividends are paid
to common stockholders.

Thus, g=0
 However, companies can omit preferred dividend
payments without fear of pushing the firm into
bankruptcy.
If preferred stock with an annual dividend of \$5 sells for
\$50, what is the preferred stock’s expected return?
Vp 
\$50 
ˆp 
r
D
rp
\$5
rp
\$5
\$50
 0.10  10%
Debt, Preferred stock, and Common Stock.
 From an investor's perspective, a firm's preferred stock is
generally considered to be less risky than its common
stock but more risky than its bonds.
 However, from a corporate issuer's standpoint, these risk
relationships are reversed: bonds are the most risky for
the firm, preferred is next, and common is least risky.

The cheapest form of capital is RE.
Important Note on the DCF models
(whether using the Dividend or OFCF)
 An important factor in the evaluation process is determining the level of
growth (g)-how fast the firm should grow.

The value of the firm depends on future growth in earnings, cash flows, and dividends.
 Growth depends on two main issues:
 The amount that the firm retains and reinvests in the firm. This is measured by the
retention ratio (RR)


RR= (1-payout ratio) = Net income –(Dividends/Net income)
 Payout ratio = Dividend/ Net income
The rate of return earned on the reinvested funds.

Can be measured by ROE and ROIC.


=
=

(1−)
=

=

+  _
Growth Analysis
  =    =
=

 g here is called the sustainable growth because it
represent the maximum level of growth in sales that can
be achieved without any external financing (raising debt
or equity).
 Note the firm cannot achieve the sustainable growth rate
unless there are growth opportunities. Thus, it not
uncommon to see firms growth at a rate lower than g.
Second: Relative Valuation Models:
Second: Relative Valuation Models:
Valuing stock relative to other, similar stocks or industry, using
valuation ratios such as:
P/E1 ratio.
A.
A.
B.
C.
D.
=
1
( −)
1
,
Higher PE ratio should be justified by lower risk (decrease in
rs, increase in growth (increase in g), or both.
P/CF1
P/BV1
P/Sales1
Practical Examples
 How to Calculate OFCF and sustainable growth
 Look Sheet 6 (Example 9)
 The full evaluation process:
 See the Walgreen Evaluation Excel file
 Calculating stock and market return.
 Estimating the required rate of return of common stocks
 Estimating the sustainable growth
 Performing the Dividend discount model (DDM)
 Performing the OFCF Model

This is part of what is expected from your term projects
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