Download Valuing Common Stock - Pearson Higher Education

Chapter 7
Introduction
 This chapter introduces common stocks
including unique features that differentiate
common stock from other securities and basic
common stock valuation models.
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©2005 Pearson Education, Inc.
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Organization of Chapter 7





Common stock as a residual ownership claim
on a corporation
The difficulty in estimating the value of
common stock relative to bonds and preferred
stock.
Common stock features
Basic common stock valuation
Relationship between investor required rate of
return, earnings and dividend growth, and
common stock value
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Common Stock as Residual Ownership

Common stock is quite different than bonds
and preferred stock:




Return is dependent upon success of firm
Provides a residual claim on firm’s assets
Ownership rights to cash flows remaining
after all other claims are paid
Not a contractual obligation and no stated
maturity
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Difficulty of Estimating
Common Stock Value

The value of a security is the sum of the present
values of its future expected cash flows.
Common stock is difficult to value because
future cash flows are uncertain.


Future common stock dividends are difficult to
forecast accurately.
The future common stock selling price is difficult
to forecast.
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Common Stock Features

The defining features of common stock include:

A residual claim on assets and cash flow

Variable return

Voting rights

No set maturity
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Common Stock Features

A corporation’s board of directors controls the
firm.

Members are elected by stockholders.

Has the power to hire, fire, and set
compensation for corporate executives

Determines corporate policy and strategy

Makes major corporate decisions
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Common Stock Financing—
Pros and Cons

Pros

It has lower risk than debt or preferred stock
financing due to the lack of a fixed dividend.

Fewer restrictions than debt financing; a debt
contract generally includes many restrictions on
future corporate actions.

Expansion of a firm’s equity generally increases
a firm’s debt capacity.
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Common Stock Financing—
Pros and Cons

Cons

The costs of issuing common stock are generally
much higher than the costs of issuing debt and
preferred stock.

Common stock is a riskier investment than
bonds or preferred stock. Investors require a
higher rate of return which translates into a
higher cost of raising funds with common stock.
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Valuing Common Stock

The value of common stock is the sum of the
present values of its future expected cash flows.
We will cover 4 basic models for valuing
common stock:




General valuation model
Zero-growth model
Constant-growth model
Multiple growth rates ending in constant growth
model
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Valuing Common Stock

First we will introduce the concept of growth of
a company’s earnings.

Earnings belong to the common stockholders:

They are paid back to the stockholders as
dividends or

Invested back into the company and called
additions to retained earnings.
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Valuing Common Stock

When earnings are retained and invested into
profitable projects, the company’s earnings
grow. The pace of growth depends upon:

The amount of earnings retained

The returns earned on the projects
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Valuing Common Stock

A firm’s earnings growth rate can be computed
as follows:

Growth = retention ratio x ROE

Growth = earnings growth rate

Retention ratio = 1 – dividend payout ratio

ROE = Return on Stockholders Equity
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Valuing Common Stock

For example, what is a firm’s earnings growth
rate if it pays 40% of earnings as dividends and
earns a 20% return on stockholders equity?

Growth = retention ratio x ROE

Growth = (1 – 40%) x 20% = 60% x 20% = 12%
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General Dividend Valuation Model

The value of common stock is the PV of the
expected dividends to be received plus the PV
of the expected price the stock is sold for in the
future:
d1
d2
dn
Pn
P0 

.....

2
n
n
1  k e  1  k e  1  k e  1  k e 

For simplicity we will assume a firm pays out
dividends just once a year.
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General Dividend Valuation Model

Suppose an investor expects a common stock’s
dividends to be $1.00, $1.05, and $1.10 at the
end of each of the next 3 years and expects to
sell the stock for $15 in 3 years. If the investor
requires a 15% rate of return, what is the
stock’s value today?
$1.00
$1.05
$1.10
$15.00
P0 



 $12.25
2
3
3
1  15% 1  15% 1  15% 1  15%
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Zero-Growth Dividend
Valuation Model

If a company’s dividends are not growing, but
the company is paying out a constant dividend
every year, this is similar to investing in
preferred stock. The value of the common
stock would be the PV of a perpetuity.
d
P0 
ke
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Zero-Growth Dividend
Valuation Model

Suppose a company expects earnings of $5 per
share and because they do not expect to grow,
all earnings are paid out as dividends. Thus all
future dividends are expected to be $5.00 per
share. If investors require a 10% rate of return,
the stock’s value today is:
$5.00
P0 
 $50.00
10%
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Zero-Growth Dividend
Valuation Model


Treating zero-growth common stock as a
perpetuity seems to imply an investor will hold
the stock forever! What if the investor just plans
to hold the stock for 2 years and then sell it?
What would the stock’s selling price be in 2
years?
$5.00
P2 
 $50.00
10%
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Zero-Growth Dividend
Valuation Model

This investor expects to receive a $5 dividend
for each of 2 years and then sell the stock for
$50 in 2 years. The value of the stock today is:
$5.00
$5.00
$50.00
P0 


 $50.00
2
2
1  10%  1  10%  1  10% 

The investor’s holding period does not affect the
stock’s value!
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Constant-Growth Dividend
Valuation Model

A company with a constant dividend payout
ratio and constant return on equity will have a
constant growth rate.

For example, what is the growth rate for a
company earning 12% on equity and a 40%
dividend payout ratio?

Growth = (1 – 40%) x 12% = 60% x 12% = 7.2%
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Constant-Growth Dividend
Valuation Model

If we expect this company to have earnings of
$5 per share in the coming year and the 7.2%
growth rate is constant, we can compute the
common stock value to an investor requiring a
10% return with the following constant growth
model:
d1
P0 
k e  g 
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Constant-Growth Dividend
Valuation Model

The company’s dividend in the coming year
must be $2.00 per share:


d1 = $5.00 x 40% = $2.00
And thus the value of the stock is:
$2.00
$2.00
P0 

 $71.43
10.0% - 7.2% 2.8%
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Constant-Growth Dividend
Valuation Model

Why is the value in this example higher than for
the zero-growth example? Both examples
assume earnings of $5 per share and a 10%
rate of return.

The 7.2% growth rate makes the stock in the
constant-growth example worth more!
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Constant-Growth Dividend
Valuation Model

Notice in the constant-growth example we
made no assumptions about the investor’s
holding period.

As we illustrated in the zero-growth valuation
model, how long the investor plans to hold the
stock should not affect the stock’s value today!
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Constant-Growth Dividend
Valuation Model

The constant-growth model provides good
estimates of common stock value when a
company’s future growth is expected to be
stable.

The constant-growth model provides less
accurate estimates when growth is difficult to
estimate or large systematic differences year to
year are expected in growth.
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Valuing Stock with Multiple
Growth Rates

Now we will consider how to estimate the value
of common stock when several different growth
rates are expected and the growth rates can be
forecast with some degree of accuracy.

What if a company expects to pay a $2.15
dividend in a year and expects growth of 15%
through the end of year 2? After year 2 growth
is expected to decrease to 7.2% and stabilize at
7.2%.
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Valuing Stock with Multiple
Growth Rates

We can picture the growth rates and cash flows
as follows:

0 g = 15% 1 g = 15% 2
g = 7.2%
|________|________|________________________
–
$2.15
$2.47

What is the value of this stock to an investor
requiring a 10% rate of return?
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Valuing Stock with Multiple
Growth Rates

Remember, an investor’s holding period does
not affect the value of common stock value.

Thus, in our example, we can use any holding
period and it should not change the value of the
stock!

To make the computation as easy as possible
we will assume a 2-year holding period. The
investor expects to receive 2 dividends (d1 and
d2) and the selling price of the common stock in
2 years (P2).
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Valuing Stock with Multiple
Growth Rates

If we can estimate the common stock selling
price in 2 years, then we can use the general
dividend valuation model to compute the stock
value as follows:
d1
d2
Pn
P0 


2
3
1  10%  1  10%  1  10% 
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Valuing Stock with Multiple
Growth Rates

Notice the growth rate in this example is
constant at 7.2% annually after 2 years. This
allows us to adapt the constant-growth model to
estimate the price in 2 years.

The original constant-growth model is:
d1
P0 
k e  g 
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Valuing Stock with Multiple
Growth Rates

The constant-growth model can be viewed
more generally as:
d n 1
Pn 
k e  g 

Adapting this to our example, we can estimate
the stock’s price at the end of 2 years:
d3
P2 
k e  g 
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Valuing Stock with Multiple
Growth Rates

Estimate d3 by growing d2 at the 7.2% growth
rate.


d3 = $2.47 x (1 + 7.2%) = $2.65
Use this along with the 7.2% growth rate after
year 2 to estimate the price in 2 years:
$2.65
$2.65
P2 

 $94.64
10%  7.2% 2.8%
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Valuing Stock with Multiple
Growth Rates

Now use the selling price in year 2 ($94.64)
along with the expected dividends in the first 2
years ($2.15 and $2.47) to estimate the value of
the stock today:
$2.15
$2.47
$94.64
P0 


 $82.21
2
3
1  10% 1  10% 1  10%
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Valuing Stock with Multiple
Growth Rates

Holding Period Assumption

We assumed a 2-year holding period in our
computations. Assuming any other holding
period would not have changed the answer. It
would just change the computations and made
the estimation of the stock’s value an even more
difficult process!
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Valuing Stock with Multiple
Growth Rates

Simplest Computation and Holding Period

When a stock is expected to have multiple
growth rates, the easiest computation of the
stock’s value is obtained by assuming a holding
period exactly long enough to reach the point at
which the growth rate becomes constant.
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Value, Rate of Return, and Growth

What happens to a common stock’s value if the
investor’s required rate of return increases but
the future expected cash flows remain
constant?

With the same expected future cash flows, the
only way an investor can receive a higher rate of
return is to pay less for the stock! Thus, higher
rates of return cause stock values to decline!
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Value, Rate of Return, and Growth

Let’s use the constant-growth example to
illustrate this inverse relation between rates of
return and common stock value. Previously we
assumed a $2 dividend in 1 year, a 7.2% growth
rate, and a 10% rate of return, and obtained a
value of $71.43 as follows:
$2.00
$2.00
P0 

 $71.43
10.0% - 7.2% 2.8%
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Value, Rate of Return, and Growth

What if the general level of interest rates rises
and as a result investors now require a 12%
return on this common stock?
$2.00
$2.00
P0 

 $41.67
12.0% - 7.2% 4.8%

The stock value declines to $41.67. This same
relationship would hold for any of the common
stock valuation models we have presented in
this chapter.
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Value, Rate of Return, and Growth

What happens to a common stock’s value if the
earnings and dividends growth rate increases
but the rate of return remains the same?

With a higher growth rate dividends are now
expected to be greater. Of course with the same
rate of return, the value of the common stock will
increase to investors!
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Value, Rate of Return, and Growth

Let’s use the constant-growth example to
illustrate this direct relation between dividends
and earnings growth and common stock value.
Using the same beginning assumptions as
before:
$2.00
$2.00
P0 

 $71.43
10.0% - 7.2% 2.8%
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Value, Rate of Return, and Growth

What if the earnings and dividends growth rate
rises from 7.2% to 8.0% and, as a result, future
dividends are expected to be higher than
before?
$2.00
$2.00
P0 

 $100.00
10.0% - 8.0% 2.0%

The stock value increases to $100.00. This
same relationship would hold for any of the
common stock valuation models we have
presented in this chapter.
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Summary of Chapter 7 Topics

Common stock as a residual ownership claim

Features of common stock

Pros and cons of common stock financing
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Summary of Chapter 7 Topics

Valuing common stock — 4 models introduced:
General valuation model
 Zero-growth model
 Constant-growth model
 Multiple growth rates ending in constant growth
model


Relationship between common stock value, rates
of return, and earnings and dividend growth rates
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