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Stocks and their valuation
(chapter 9)
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Facts about common stock
Represents ownership
 Ownership implies control
 Stockholders elect directors
 Directors elect management
 Management’s goal: Maximize the stock
price

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Intrinsic Value and Stock Price


Outside investors, corporate insiders, and analysts use a variety
of approaches to estimate a stock’s intrinsic value (P0).
In equilibrium we assume that a stock’s price equals its
intrinsic value.
- Outsiders estimate intrinsic value to help determine which
stocks are attractive to buy and/or sell.
- Stocks with a price below its intrinsic value are undervalued
Buy or Sell?
- Stocks with a price above its intrinsic value are overvalued
Buy or Sell?
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Different Approaches for Estimating the
Intrinsic Value of a Common Stock
Discounted dividend model
 Corporate valuation model
 P/E multiple approach
 EVA approach (NOT for the exam)

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Dividend growth model


Value of a stock is the present value of the future dividends
expected to be generated by the stock.
r s is the required rate of return (think the one from CAPM)
D3
D1
D2
D
P0 


 ... 
1
2
3
(1  rs ) (1  rs ) (1  rs )
(1  rs ) 
^
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Constant growth stock

A stock whose dividends are expected to grow forever at a
constant rate, g.
D1 = D0 (1+g)1
D2 = D0 (1+g)2
Dt = D0 (1+g)t

If g is constant, the dividend growth formula converges to:
D 0 (1  g)
D1
P0 

rs - g
rs - g
^
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What happens if g > rs?
If g > rs, the constant growth formula leads
to a negative stock price, which does not
make sense.
 The constant growth model can only be
used if:
- rs > g
- g is expected to be constant forever

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If rRF = 7%, rM = 12%, and β = 1.2, what is
the required rate of return on the firm’s
stock?

Use the SML to calculate the required rate
of return (rs):
rs = rRF + (rM – rRF)β
= 7% + (12% - 7%)1.2
= 13%
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If D0 = $2 and g is a constant 6%, What
the stock’s market value?

Using the constant growth model:
D1
$2.12
P0 

rs - g 0.13 - 0.06
$2.12

0.07
 $30.29
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Find the Expected Dividend Stream for the Next
3 Years and Their PVs
D0 = $2 and g is a constant 6%.
0
g = 6%
D0 = 2.00
1
2
2.12
2.247
1.8761
1.7599
rs = 13%
1.6509
Total PV= 5.287
without D0
10
3
2.382
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What is the expected dividend yield, capital
gains yield, and total return during the first
year?

Dividend yield
= D1 / P0 = $2.12 / $30.29 = 7.0%

Capital gains yield
= (P1 – P0) / P0
= ($32.10 - $30.29) / $30.29 = 6.0%

Total return (rs)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%
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What would the expected price today
be, if g = 0?
The dividend stream would be a perpetuity.

PMT $2.00
P0 

 $15.38
r
0.13
^
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Supernormal growth:
What if g = 30% for 3 years before
achieving long-run growth of 6%?


Can no longer use just the constant growth
model to find stock value.
However, the growth does become constant
after 3 years.
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Valuing common stock with
nonconstant growth
0 r = 13% 1
s
g = 30%
D0 = 2.00
2
g = 30%
2.6
3
g = 30%
3.380
4
...
g = 6%
4.394
4.658
2.6/(1+0.13) = 2.301
2.647
3.045
66.54/(1+0.13)^3 = 46.114
54.107
P$ 3 
^
= P0
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4.658
0.13 - 0.06
 $66.54
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Calculations:
D1 = D0*(1+g1)= 2x(1+0.3)= 2.6
D2 = D1*(1+g1)= 2.6x(1+0.3)= 3.38
D3 = D2*(1+g1)= 3.38x(1+0.3)= 4.394
D4 = D3*(1+g2)= 4.394x(1+0.06) = 4.658
Present Value of D1= 2.6/(1+0.13) = 2.301
Present Value of D2= 3.38/(1+0.13)^2 = 2.647
Present Value of D3= 4.394/(1+0.13)^3 = 3.045
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Exam type question
The last dividend paid by Klein Company was $1.00. Klein’s growth rate is
expected to be a constant 5 percent for 2 years, after which dividends are expected
to grow at a rate of 10 percent forever. Klein’s required rate of return on equity (rs)
is 12 percent. What is the current price of Klein’s common stock?
a. $21.00
b. $33.33
c. $42.25
d. $50.16 *
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Corporate value model
Also called the free cash flow method. Suggests the value of the
entire firm equals the present value of the firm’s free cash flows.
Depr. and   Capital
FCF  EBIT(1 - T) 
  NOWC


amortizati on expenditur es
1. Find the market value (MV) of the firm.
- Find PV of firm’s future FCFs
2. Subtract MV of firm’s debt and preferred stock to get MV of
common stock.
MV of
= MV of – MV of debt and
common stock
firm
preferred
3. Divide MV of common stock by the number of shares outstanding
to get intrinsic stock price (value).
- P0 = MV of common stock / # of shares

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Issues regarding the corporate
value model



Often preferred to the dividend growth model, especially when
considering number of firms that don’t pay dividends or when
dividends are hard to forecast.
Similar to dividend growth model, assumes at some point free
cash flow will grow at a constant rate.
Terminal value (TVn) represents value of firm at the point that
growth becomes constant.
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Given the long-run gFCF = 6%, and WACC
of 10%, use the corporate value model to
find the firm’s intrinsic value.
0 r = 10%
1
-5
2
3
10
-4.545
8.264
15.026
398.197
416.942
4
20
...
g = 6%
21.20
21.20
530 =
19
0.10 - 0.06
= TV3
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Calculations:
Present Value of CF1= -5/(1+0.1) = -4.545
Present Value of CF2= 10/(1+0.1)^2 = 8.264
Present Value of CF3= 20/(1+0.1)^3 = 15.026
CF 4= CF3*(1+g)=20*(1+0.06)= 21.2
Present Value of Terminal Value in 3 years (at time 3)=
= 530/(1+0.1)^3 = 388.197
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If the firm has $40 million in debt and has 10
million shares of stock, what is the firm’s
intrinsic value per share?


MV of equity = MV of firm – MV of debt
= $416.94m - $40m
= $376.94 million
Value per share = MV of equity / # of shares
= $376.94m / 10m
= $37.69
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Exam type question
An analyst is trying to estimate the intrinsic value of the stock of Harkleroad
Technologies. The analyst estimates that Harkleroad’s free cash flow during the
next year will be $25 million. The analyst also estimates that the company’s free
cash flow will increase at a constant rate of 7 percent a year and that the company’s
cost of capital is 10 percent. Harkleroad has $200 million of long-term debt, and
30 million outstanding shares of common stock.
What is the estimated per-share price of Harkleroad Technologies’ common stock?
a.
$ 1.67
b.
$ 5.24
c.
$18.37
d.
$21.11 *
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Exam type question
Which of the following statements is most correct?
a. If a company has two classes of common stock, Class A and
Class B, the stocks may pay different dividends, but the two classes must
have the same voting rights.
b. An IPO occurs whenever a company buys back its stock on the open market.
c. The preemptive right is a provision in the corporate charter that gives
common stockholders the right to purchase (on a pro rata basis) new issues of
common stock. *
d. Statements a and b are correct.
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Preferred Stock
Hybrid security.
 Like bonds, preferred stockholders receive
a fixed dividend that must be paid before
dividends are paid to common
stockholders.
 However, companies can omit preferred
dividend payments without fear of pushing
the firm into bankruptcy.

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If preferred stock with an annual dividend of $5
sells for $50, what is the preferred stock’s
expected return?
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D
Vp 
rp
$5
$50 
rp
$5
r̂p 
$50
 0.10  10%
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Learning objectives






Read from the text the following topics: control of the firm; types of common
stock; The market for common stock
Know how to apply the dividend growth model, constant and non-constant growth
Know how to calculate total return, dividend yield and capital gains
Know how to use corporate value model to value common stock
Preferred stock
Recommended end-of-chapter problems: ST-1, Questions 9-3, 9-4;
Problems 9-1 to 9-5, 9-11,9-1 to 9-17
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