# Chapter 8- Common Stock Valuation

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```					Chapter 8: Common Stock Valuation

Placing a value on the equity of a company (Assets - Liabilities) is a "Holy Grail" of finance
Knowing what the true price of a share should, versus what it trades at, is the key to riches.
Why? You can test your wits against the market: if overvalued, sell; if undervalued, buy.
Valuation also lets you draw important conclusions from the observed price of assets.

Defining "Value"
"Price" and true "Value" are different
3 types of Value:
Book        Price of Asset minus Accumulated Depreciation
Does not necessarily represent market value.

Market        Price determined by competitive marketplace (i.e. "the Stock Market")
= Marginal PRICE an investor is willing to pay
Changes constantly; difficult to nail down

Intrinsic     The Fundamental, Unique Value to any one particular investor
Defined by DISCOUNTING FUTURE CASH FLOWS
The DISCOUNT is at an investor's individual REQUIRED RATE OF RETURN
Corporate finance deals with determining Intrinsic value

Fundamentals of Valuation
Important factors:
The Larger the cash flows, and the More Quickly they are received, the greater the value.
The investor's required return-- "Opportunity Cost" or "Hurdle Rate"
Stocks are riskier than bonds, so required return is higher for stocks.

N

Value of                                 Cash Flows in Period
Stock =
Ʃ               (1 + interest ) ^ Period
t=1

Hence need 3 things:
1. Expected Cash Flows
2. When Cash Flows Occur
3. Required Rate of Return for these Cash Flows

Required Rate of Return
The hardest part of valuation

Investors can be Risk Averse (prefers less risk), Risk Neutral (doesn't care about risk), or Risk Seeking (prefers r
We assume all investors are Risk Averse and hence require more return for more risk
Simple Risk Premium Model
Expected Return = Base Rate + Risk Premium
Base Rate = return of some benchmark security
Risk Premium is subjectively determined
This is too subjective

Capital Asset Pricing Model (CAPM)
Expected Return on a Particular Stock = Risk Free Rate + Beta * (Expected Market Return - Risk Free
E(Ri) = Rf + Bi * ( E(Rm) - Rf )
E(Ri) = expected return of Security i
Rf = risk-free rate (e.g. Treasury Bills)
Bi = measure of riskiness of Security i
E(Rm) = expected market return (e.g. S&P 500)
More objective-- commonly used in Finance.

The market return is a benchmark to which other portfolios are compared
Subtracting the Risk Free Rate from the market return gives the market premium for stock

Beta measures the risk of a particular security relative to the market return
Beta = 1 means a security is exactly as risky as the average stock (i.e. "the market")
Beta = 0 means a security has NO risk
Beta = 2 means a security has TWICE the riskiness of the average stock
Beta = (-1) means a security in INVERSELY proportional to the average stock (not comm
Research companies such as Value Line estimate betas based on a company's past performance

The Security Market Line shows visually and mathematically how different stocks can be valued
Gives Required Rate of Return for any stock given its Beta

Tangible Value Models (a.k.a. "The Income Approach")

First question: What is your strategy in buying a stock?
1. Dividend accumulation
2. Price appreciation as a result of earnings growth, with the intention of selling at a later period (i.e. "T

The Constant-Growth Dividend Discount Model
With Dividends, we estimate a stock's value based on dividends accruing as we hold the stock indefinit

Value of        Period 1 Dividend
Stock =       (1 + Req. Return ) ^ 1               +

Since the Dividends never change, this can be restated in closed form as:
Value of          Period 1 Dividend
Stock =                  r-g

Where   r   is the "Required Return", aka the expected return
And where g is the growth rate of the dividend stream

The Earnings Model
Whether they pay a dividend or not, most firms reinvest at least some of their earnings
Hence, a stock's value is equal to its current payout value plus its growth on reinvested earnings

Value of          Payout * Earnings
Stock =                 r-g
=

Where   r   is the "Required Return", aka the expected return
And where g is the growth rate of future earnings (only those earnings that are reinvested as opposed t
g   can be calculated as the % of reinvested earnings multiplied by the actual return (i.e. th
Hence, g = Return on Equity * Retention Ratio

Note 1: The Reinvestment % + Payout % = 100% of Earnings
Note 2: Return on Equity is expressed as a %, where Total Earnings in the numerator is expressed in do
Note 3: The larger g , the smaller the demonimator, and hence, the greater the value of future projects

Relative Value Models (a.k.a. "The Market Approach")

The above models depend on forecasting dividends and/or the future cash flows of tangible projects.
In reality:
Companies don't always pay dividends
Future cash flows are uncertain, often extremely so

As an alternative we can evaluate a stock by relating it to other, similar stocks using valuation ratios like the P/E (P
This takes the public markets' collective information into account, while applying it to a particular com
A company without positive Earnings can be valued using the P/S (Price-to-Sales) ratio, but this is VE

The P/E ratio is defined as:

Price per Share
P/E =           Earnings per Share

Similar companies in the same industry should have similar P/E ratios
Any differences in P/E ratios should be explained by differences in perceived risk or expected growth rates
Hence, you can solve the Price question of Company A by comparing its Earnings to Company B
y Grail" of finance
rades at, is the key to riches.
, sell; if undervalued, buy.

etplace (i.e. "the Stock Market")

y one particular investor
E CASH FLOWS
dividual REQUIRED RATE OF RETURN
h determining Intrinsic value

hey are received, the greater the value.
or "Hurdle Rate"
red return is higher for stocks.

(doesn't care about risk), or Risk Seeking (prefers risk)
e require more return for more risk
Rate + Beta * (Expected Market Return - Risk Free Rate)

portfolios are compared
he market return gives the market premium for stocks

ive to the market return
s risky as the average stock (i.e. "the market")

the riskiness of the average stock
RSELY proportional to the average stock (not commonly used)
etas based on a company's past performance

how different stocks can be valued

with the intention of selling at a later period (i.e. "Terminal Value")

on dividends accruing as we hold the stock indefinitely

Period 2 Dividend                                     Period infinity Dividend
(1 + Req. Return ) ^ 2             +          …   +   (1 + Req. Return ) ^ infinity

ted in closed form as:
nvest at least some of their earnings
value plus its growth on reinvested earnings

Payout % * Total Earnings in dollars
Required Return - (ROE * Reinvestment %)

(only those earnings that are reinvested as opposed to paid out in a dividend)
ested earnings multiplied by the actual return (i.e. the Return on Equity) as opposed to the required return r

e Total Earnings in the numerator is expressed in dollars. They are referencing the same Earnings number
, and hence, the greater the value of future projects

future cash flows of tangible projects.

, similar stocks using valuation ratios like the P/E (Price-to-Earnings) ratio
n into account, while applying it to a particular company's fundamentals
d using the P/S (Price-to-Sales) ratio, but this is VERY risky and not recommended (see: dotcom crash)

es in perceived risk or expected growth rates
mparing its Earnings to Company B
Capital Asset Pricing Model

E(Ri) = Rf + Bi * ( E(Rm) - Rf )
Expected Return                       =      Risk-free         +            Stock    *
on a Stock                                   Rate                         Beta

Objective: Determine the Security Market Line so any stock can be valued according to our Required Rate o

The Security Market Line
Risk-free   Market      Stock X     Stock Y
Beta                                  0.0        1.0         0.5          1.5
Expected Return                     5.00%     11.00%         ???         ???
Use CAPM to calculate

The Security Market Line
Risk-free   Market         X               Y
Beta                                  0.0        1.0         0.5             1.5
Expected Return                      5.0%      11.0%        8.0%            14.0%

The Security Market Line
16.0%

14.0%                                     Stock X
12.0%
Risk
Expected Return

10.0%

8.0%                                                             Stock Y

6.0%
Market
4.0%

2.0%

0.0%
0.0      0.2       0.4      0.6         0.8       1.0   1.2
Beta
( Expected Market     -     Risk-free
Return                  Rate)

be valued according to our Required Rate of Return

Stock Y

1.4    1.6
Period
Cash Received                0                       1                    2
Dividends                   \$0                     \$2.40                \$2.40
Sale of Stock               \$0                      \$0                   \$0
Total                      \$0.00                   \$2.40                \$2.40

Recall that…

N
Cash Flows in Period
Value of Stock =
Ʃ             (1 + interest ) ^ Period
t=1

Suppose Required Rate of Return = 12% from CAPM
Period
Value                        0                       1                    2
Numerator:                 0.00                    2.40                 2.40
Denominator:               1.00                    1.12               (1.12) 2
Value:                     0.00                    2.14                1.91

If the current share price is \$25, you would Sell the stock if you had any
If the current share price is \$18, you would Buy more shares and wait for the true value to equalize.
3
\$2.40
\$20.00
\$22.40

3
22.40
(1.12) 3
15.94

or the true value to equalize.   = \$20.00
Period Dividend
Value of Stock =
Req. Return - Dividend Growth Rate

From Previous Example, dividends do not grow, so…

Value
Numerator:                        2.40
Denominator:                     0.12 - 0
Value:                           20.00

Period                                                    1      2      3      4      5
FCF                                                     2.4    2.4    2.4    2.4    2.4
Rate                                                  0.12   0.12   0.12   0.12   0.12
PVCF                                                \$2.143 \$1.913 \$1.708 \$1.525 \$1.362
NPV                               20.00
6      7      8      9     10     11     12     13     14     15     16     17     18
2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
\$1.216 \$1.086 \$0.969 \$0.865 \$0.773 \$0.690 \$0.616 \$0.550 \$0.491 \$0.438 \$0.391 \$0.350 \$0.312
19     20     21     22     23     24     25     26     27     28     29     30     31
2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
\$0.279 \$0.249 \$0.222 \$0.198 \$0.177 \$0.158 \$0.141 \$0.126 \$0.113 \$0.100 \$0.090 \$0.080 \$0.072
32     33     34     35     36     37     38     39     40     41     42     43     44
2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
\$0.064 \$0.057 \$0.051 \$0.045 \$0.041 \$0.036 \$0.032 \$0.029 \$0.026 \$0.023 \$0.021 \$0.018 \$0.016
45     46     47     48     49     50     51     52     53     54     55     56     57
2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
\$0.015 \$0.013 \$0.012 \$0.010 \$0.009 \$0.008 \$0.007 \$0.007 \$0.006 \$0.005 \$0.005 \$0.004 \$0.004
58     59     60     61     62     63     64     65     66     67     68     69     70
2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
\$0.003 \$0.003 \$0.003 \$0.002 \$0.002 \$0.002 \$0.002 \$0.002 \$0.001 \$0.001 \$0.001 \$0.001 \$0.001
71     72     73     74     75     76     77     78     79     80
2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
\$0.001 \$0.001 \$0.001 \$0.001 \$0.000 \$0.000 \$0.000 \$0.000 \$0.000 \$0.000

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