Stock Valuation, Chapter 8
BA 180-1
Introduction to Stock Valuation
By now you have seen that the value of an
asset depends on the magnitude, timing, and
risk of the cash flows.
 Equity securities have the feature that the
cash flows are uncertain.
 We will also need to account for risk more
carefully.
 Remember that we are interested in cash
flows, not accounting earnings.

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Stock Valuation, Chapter 8
BA 180-1
Features of Common Stock
Residual claimants
 Limited Liability
 Voting Rights
 Eligible for dividends, but no guarantee

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Stock Valuation, Chapter 8
BA 180-1
Valuation Approach
To determine the value of a stock we need to
know something about the cash flows.
 Let’s start by assuming we will hold the stock
for one year.
 If we pay P0 today and get a dividend D1
when we sell for P1 we have:

D1  P1
P0 
1 r

It seems that both the future stock price and
the dividend matter.
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Stock Valuation, Chapter 8
BA 180-1
Valuation Approach

Now step forward to time 1 P1  D2  P2

Substitute into the Time 0 price
1 r
 D2  P2 
D1  
D1 D2  P2
1  r 

P0 


1 r
1  r (1  r ) 2

Repeating this substitution,

D3
Dt
D1
D2
D4
P0 



  
2
3
4
t
1  r (1  r )
(1  r ) (1  r )
(
1

r
)
t 1
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Stock Valuation, Chapter 8
BA 180-1
Zero Dividend Firms

If a firm is not currently paying dividends,
does this mean the stock is valueless?
NO: Just because a firm is not paying dividends now does
not mean it will never pay dividends in the future.
 If you knew a stock would never pay dividends (or some
other form of distribution) it would be worthless.


Why would a firm not pay dividends?
Investing the cash in profitable opportunities.
 This will make future dividends even larger.

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Stock Valuation, Chapter 8
BA 180-1
Special Cases in Stock Valuation

There are certain dividend patterns that make the
application of our valuation formula easier
Constant Dividends
 Constant Growth in Dividends
 Supernormal Dividend Growth


For the third case we split the problem into pieces
and use the tools we have already learned.
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Stock Valuation, Chapter 8
BA 180-1
Constant Dividends

Constant Dividend is simply a perpetuity:
P0 

D1
r
This is based on getting the first dividend
payment at the end of period. r is effective
rate of return per period. Again, we should
use rate ‘matching’ frequency of dividend
payment.
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Stock Valuation, Chapter 8
BA 180-1
Constant Dividends Example
Coca Cola pays and will pay dividends of
$0.56 per share end of each year. Using a
15% yearly rate of return, what is the value of
a share?
 P0 = D/r = 0.56/15% =$3.73

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Stock Valuation, Chapter 8
BA 180-1
Constant Dividend Growth
Now suppose that the Dividends grow at a
constant rate g per period.
 Here we have a perpetuity with a constant
growth rate:

P0 

D1
rg
Remember this only works if r > g.
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Stock Valuation, Chapter 8
BA 180-1
Constant Dividend Growth Example
Historically, Coca Cola has annual dividend
growth of 13%. What is the value of a share
with last dividend $0.56 and constant future
growth equal to the historic average?
(assume the required rate of return 15% per
year)
 G = 13% D0=0.56
 D1= (1+g) D0=(1+13%) 0.56 = 0.633
 P 0= D1/(r-g) = $31.64

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Stock Valuation, Chapter 8
BA 180-1
Supernormal Dividend Growth



If the expected dividend growth rate is higher than
the discount rate (g > r), our perpetuity formula does
not work.
This kind of growth is not sustainable but may occur
for some period of time.
We break the problem into pieces, value them
separately, then add them together.
Value the “normal” growth period (g < r) with existing
formulas.
 Value the supernormal period (g > r) by simply calculating
the present value of each cash flow and adding them up.

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Stock Valuation, Chapter 8
BA 180-1
Supernormal Growth Example

Coca Cola had 18% dividend growth over the
last 5 years. Assume this growth continues
for the next 5 years, then reverts to 13%
growth. D =0.633. How much is the stock
worth (what is P )? (assume the rate of return
15% per year)
1
0
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Stock Valuation, Chapter 8
BA 180-1
The Rate of Return
We have recognized that the riskiness of the
cash flows affects the value of an asset.
 The rate of return is what makes this
adjustment.

Riskier cash flows require a higher return.
 Risky cash flows are worth less than safe ones.


Where do we get the Rate of Return?
Capital Asset Pricing Model (CAPM) or other
model
 Historical or Peer Group

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Stock Valuation, Chapter 8
BA 180-1
A Warning




Determination of the rate of return is far from perfect.
Be aware that the answer to any present value
analysis is highly sensitive to the rate of return.
In the case of stocks, the cash flows themselves are
also very difficult to forecast accurately.
DO NOT OVER-EMPHASIZE THE ANSWER
YOU GET FROM A STOCK VALUATION
MODEL. IF IT IS DIFFERENT FROM THE
MARKET PRICE, YOUR ASSUMPTIONS
ARE PROBABLY NOT GOOD.
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Stock Valuation, Chapter 8
BA 180-1
Example 1: Stable Growth

A mature company paid a $2.10 dividend this
year (=D ) and you expect the future
dividends to grow 4% annually. What is the
value of the stock if the market demand a
10% rate of return?
0
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Stock Valuation, Chapter 8
BA 180-1
Example 2: Technology Company

Suppose a tech company will pay no
dividends for the next five years. It will then
(t=6) start paying a $1 dividend which will
increase 15% annually for the next five years
before it reaches its perpetual growth rate of
10%. How much is a share worth if the
market demand a 15% rate of return?
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Stock Valuation, Chapter 8
BA 180-1
Example 3: Finding the Dividend

A stock is trading for $75 per share on the
basis of 6% dividend growth and a 15% rate
of return. What must the current (time zero)
dividend be on the stock?
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Stock Valuation, Chapter 8
BA 180-1
Example 4: Negative Growth

A company in a declining industry currently
pays a $5 dividend. Because the industry
prospects are poor, you expect a negative
growth of 10% annually. With a 10% rate of
return, what is the value of a share?
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