Chapter 9
Stock Valuation
Learning Objectives
1. List and describe the four types of secondary markets.
2. Explain why many financial analysts treat preferred stock as a special type of bond rather
than as a true equity security.
3. Describe how the general dividend-valuation model values a share of stock.
4. Discuss the assumptions that are necessary to make the general dividend-valuation model
easier to use, and be able to use the model to compute the value of a firm’s stock.
5. Explain why g must be less than R in the constant-growth dividend model.
6. Explain how valuing a preferred stock with a stated maturity differs from valuing a
preferred stock with no maturity date, and be able to calculate the price of a share of
preferred stock under both conditions.
I.
Chapter Outline
9.1
The Market for Stocks

Equity securities are certificates of ownership of a corporation.

Households dominate the holdings of equity securities, owning more than 36 percent of
outstanding corporate equities.
A.
Secondary Markets

In secondary markets, outstanding shares of stock are bought and sold among investors.

An active secondary market enables firms to sell their new debt or equity issues at a lower
funding cost than firms selling similar securities that have no secondary market.
B.
Secondary Markets and Their Efficiency

In the United States, most secondary market transactions are conducted on one of the
many stock exchanges.

In terms of total volume of activity and total capitalization of the firms listed, the
NYSE is the largest in the world and NASDAQ is the second largest.

In terms of the number of companies listed and shares traded on a daily basis,
NASDAQ is larger than the NYSE.

Firms listed on the NYSE tend to be, on average, larger in size and their shares
trade more frequently than firms whose securities trade on NASDAQ.

There are four types of secondary markets, and each type differs according to the amount
of price information available to investors, which in turn, affects the efficiency of the
market.
1. Direct Search

The secondary markets farthest from our ideal of complete price information are those
in which buyer and seller must seek each other out directly.

It is too costly to perform a thorough search among all possible partners done to locate
the best price.

Securities that sell in direct search markets are usually bought and sold so infrequently
that no third party, such as a broker or dealer, finds it profitable to serve the market.

The sales of common stock of small private companies and private placement
transactions are good examples of direct search markets.
2. Broker

Brokers bring buyers and sellers together to earn a fee, called a commission.

Brokers’ extensive contacts provide them with a pool of price information that
individual investors could not economically duplicate themselves.

By charging a commission fee less than the cost of direct search, brokers give
investors an incentive to make use of the information by hiring them as brokers.
3. Dealer

Market efficiency is improved if there is someone in the marketplace to provide
continuous bidding (selling or buying) for the security.

Dealers provide this service by holding inventories of securities, which they own, then
buying and selling from the inventory to earn a profit.

Dealers earn their profits from the spread on the securities they trade—the difference
between their bid price (the price at which they buy) and their offer price (the price at
which they sell).

The advantage of a dealer over a brokered market is that brokers cannot guarantee that
an order will be executed promptly, while dealers can because they have an inventory
of securities.

A dealer market eliminates the need for a time-consuming search for a fair deal by
buying and selling immediately from the dealers’ inventory of securities.

NASDAQ is the best-known example of a dealer market.

Electronic communications network (ECN) systems provide additional price
information to investors and increase marketability and competition, which should
improve NASDAQ efficiency.
4. Auction

In an auction market, buyers and sellers confront each other directly and bargain over
price.

The New York Stock Exchange is the best-known example of an auction market.

In the NYSE the auction for a security takes place at a specific location on the floor of
the exchange, called a post.

The auctioneer in this case is the specialist who is designated by the exchange to
represent orders placed by public customers.
C.
Reading the Stock Market Listings

The Wall Street Journal, the New York Times, and other newspapers in large
metropolitan areas provide stock listings for the major stock exchanges, such as the
NYSE and the relevant regional exchanges.

Exhibit 9.1 shows a section of the listing in the Wall Street Journal for the NYSE.
D.
Types of Equity Securities

The two types of equity securities are common stock and preferred stock.

Common stock represents the basic ownership claim in a corporation.

One of the rights of the owners is to vote on all important matters that affect the
life of the company, such as electing the board of directors or voting on a proposed
merger or acquisition.

Owners of common stock are not guaranteed any dividend payments and have the
lowest-priority claim on the firm’s assets in the event of bankruptcy.


Legally, common stockholders enjoy limited liability.

Common stocks are perpetuities in the sense that they have no maturity.
Preferred stock also represents ownership interest in the corporation, but preferred stock
receives preferential treatment over common stock in certain matters.

If a preferred dividend payment is not paid due to the firm’s financial condition,
the firm is not in default technically. However, the market reacts as if the failure to
make the dividend payment is a default and punishes the stock accordingly.

Preferred stock owners are given priority treatment over common stock with
respect to dividends payments and the claims against the firm’s assets in the event
of bankruptcy or liquidation.

Dividends payments are paid with after-tax dollars subject to taxation.

Even though preferred stock is equity, the owners have no voting privileges.

Preferred stocks are legally classified as perpetuities because they have no
maturity. However, most preferred stocks are not true perpetuities because the
shares contain a call provision and the share contract often requires management
to retire a certain percent of the stock annually until the entire issue is retired.
E.
Preferred Stock: Debt or Equity?

Legally, preferred stock is equity.

Like the dividends on common stock, preferred stock dividends are taxable.

A strong case can be made that preferred stock is really a special type of bond.

First, regular preferred stock confers no voting powers.

Second, preferred stockholders receive a fixed dividend, regardless of the firm’s
earnings, and if the firm is liquidated, they receive a stated value (usually par) and
not the residual value.

Third, preferred stocks often have “credit” ratings that are similar to those issued
to bonds.

Fourth, preferred stock is sometimes convertible into common stock.

Finally, most preferred stock issues today are not true perpetuities. Increasingly,
preferred stock issues have the sinking fund feature, which require mandatory
annual retirement schedules.
9.2
Common Stock Valuation

Valuation of common and preferred stock is done by using the same basic methodology that
was discussed for bond valuations in Chapter 6.
1. Estimate the future cash flows.
2. Determine the required rate of return, or discount rate, which depends on the riskiness of
the future cash flows.
3. Compute the present value of the future cash flows to determine what the asset is
worth.

Applying the valuation procedure to common stocks is more difficult than applying it to
bonds for various reasons.

First, in contrast to coupon payments on bonds, the size and timing of the dividend
cash flows are less certain.

Second, common stocks are true perpetuities in that they have no final maturity date.

Finally, unlike the rate of return, or yield, on bonds, the rate of return on common
stock is not directly observable.
A.
A One-Period Model

A one-period model provides an estimate of the market price.

The value of an asset is the present value of its future cash flows—the future dividend
and the end-of-period stock price.
B.
A Two-Period Model

This model can be viewed as two one-period models strung together.
C.
A Perpetuity Model

A series of one-period stock pricing models is strung together to arrive at a stock
perpetuity model.

Though theoretically sound, this model is not practical to apply because the number of
dividends could be infinite.
D.
The General Dividend Valuation Model

Equation 9.1 is a general expression for the value of a share of stock. It says that the
price of a share of stock is the present value of all expected future dividends.
P0 

D1
D2
D3
D4
D5
Dinfinity




 ...
1
2
3
4
5
(1  R) (1  R)
(1  R) (1  R)
(1  R)
(1  R) infinity
The formula does not assume any specific pattern for future cash dividends, such
as a constant-growth rate.

It does not make any assumption about when the share of stock is going to be sold
in the future.

Finally, the model says that to compute a stock’s current value, we need to forecast
an infinite number of dividends.

Equation 9.1 implies that the underlying value of a share of stock is determined by the
market’s expectations of future cash flows that the firm can generate.

In efficient markets, stock prices change constantly as new information becomes
available and is discounted into the firm’s market price.

For publicly traded companies, there is a constant stream of information about the firm
that reaches the market, with some having an impact on the stock price while other
information has no effect.
E.
The Growth Stock Pricing Paradox

Growth stocks are typically defined as the stocks of companies whose earnings are
growing at above-average rates and are expected to continue to do so for some time.

Fast growing companies typically pay no dividends on their stock during their growth
phase because management believes that the company has a number of high-return
investment opportunities and that both the company and its investors will be better off
if earnings are reinvested.

Equation 9.1 predicts and common sense says that if you own stock in a company that
will never pay you any cash, the market value of those shares of stock are worth
absolutely nothing.

In reality, these firms will eventually pay out dividends in the distant future.

If the internal investments succeed, the stock’s price should go up significantly, and
investors can sell their stock at a price much higher than what they paid.
9.3
Stock Valuation: Some Simplifying Assumptions

To make Equation 9.1 more applicable, some simplifying assumptions about the
pattern of dividends are necessary.

Three different assumptions can cover most growth patterns.

Dividend payments remain constant over time; that is, they have a growth rate of
zero.

Dividends have a constant-growth rate.

Dividends have a mixed growth rate pattern; that is, dividends have one payment
pattern then switch to another.
A.
Zero-Growth Dividend Model

The dividend payment pattern remains constant over time:
D1 = D2 = D3 = . . . = D∞

In this case the dividend-discount model (Equation 9.1) becomes:
P0 

D
D
D
D



 ...........
2
2
(1  R ) (1  R )
(1  R )
(1  R )3
This cash flow pattern essentially describes a perpetuity with a constant cash flow. In
Chapter 6 we developed the present value of a perpetuity with a constant cash flow as
CF/i, where CF is the constant cash flow and i is the interest rate. Similarly, Equation
9.2 gives the valuation model for a zero-growth stock.
P0 
D
R
Example: Suppose a stock is expected to pay a $2 dividend each period, forever, and the
required return is 10%. What is the stock worth?
P0 = 2 / .10 = $20
R = 12%
P0 = 2 / .12 = $16.67
Gesto, Inc., has an issue of preferred stock outstanding that pays a $5 dividend every year, in perpetuity.
If this issue currently sells for $84.12 per share, what is the required return?
R = D / P0
R = $5 / $84.12 = .0594 = 5.94%
B.
Constant-Growth Dividend Model

Cash dividends do not remain constant but instead grow at some average rate g from
one period to the next forever.

Constant dividend growth is an appropriate assumption for mature companies with a
history of stable growth.

While an infinite horizon is still hard to comprehend, far-distant dividends have a small
present value and contribute very little to the price of the stock.

Deriving the constant-growth dividend model is fairly straightforward. First, we need
to build a model to compute the value of dividend payments for any time period.

The constant-growth dividend model is easy to do because it is just an application of
Equation 6.6 from Chapter 6.
 Recall that the equation for a growing perpetuity in Chapter 6 is given by Equation 6.6:


PVA∞ = CF1/(i − g)
In other words, the constant-growth dividend model tells us that the current price of a
share of stock is the next period dividend divided by the difference between the
discount rate and the dividend growth rate.

Equation 9.4 shows how to value a constant-growth stock:
P0 
D1
(R  g )
Since the dividend is expected to grow at a steady rate, then we have replaced the problem of
forecasting an infinite number of future dividends with the problem of coming up with a single
growth rate, a considerable simplification. In this case, if we take D0 to be the dividend just paid
and g to be the constant growth rate, the value of a share of stock can be written as:
As long as the growth rate, g, is less than the discount rate, R, the present value of this series of
cash flows can be written very simply as:
This dividend growth model, also referred to as the constant growth model, dividend discount
model, or the Gordon model, is used to find the value of a stock whose dividend is expected to
grow at a constant rate (g) forever. The other basic assumption for the model to hold requires R >
g. The value obtained, P0, is the “theoretical” or “intrinsic” value of the stock. We would then
compare this value to the actual price of the stock observed in the market.
We can actually use the dividend growth model to get the stock price at any point in time, not just
today. In general, the price of the stock as of time t is:
Banya, Inc., just paid a dividend of $2.20 per share on its stock. The dividends are
expected to grow at a constant rate of 4 percent per year, indefinitely. If investors
require an 11 percent return on Banya stock, what is the current price? What will the
price be in three years? In 15 years?
The constant dividend growth model is:
Pt = Dt × (1 + g) / (R – g)
So, the price of the stock today is:
P0 = D0 (1 + g) / (R – g)
P0 = $2.20 (1.04) / (.11 – .04)
P0 = $32.69
The dividend at year 4 is the dividend today times the FVIF for the growth rate
in dividends and four years, so:
P3 = D3 (1 + g) / (R – g)
P3 = D0 (1 + g)4 / (R – g)
P3 = $2.20 (1.04)4 / (.11 – .04)
P3 = $36.77
We can do the same thing to find the dividend in Year 16, which gives us the
price in Year 15, so:
P15 = D15 (1 + g) / (R – g)
P15 = D0 (1 + g)16 / (R – g)
P15 = $2.20 (1.04)16 / (.11 – .04)
P15 = $58.87
There is another feature of the constant dividend growth model: The stock price
grows at the dividend growth rate. So, if we know the stock price today, we can
find the future value for any time in the future we want to calculate the stock
price. In this problem, we want to know the stock price in three years, and we
have already calculated the stock price today. The stock price in three years will
be:
P3 = P0(1 + g)3
P3 = $32.69(1 + .04)3
P3 = $36.77
And the stock price in 15 years will be:
P15 = P0(1 + g)15
P15 = $32.69(1 + .04)15
P15 = $58.87
Antiques ‘R’ Us is a mature manufacturing firm. The company just paid a $7
dividend, but management expects to reduce the payout by 5 percent per year,
indefinitely. If you require a 10 percent return on this stock, what will you pay for a
share today?
The constant growth model can be applied even if the dividends are declining by a
constant percentage, just make sure to recognize the negative growth. So, the price
of the stock today will be:
P0 = D0 (1 + g) / (R – g)
P0 = $7.00(1 – .05) / [(.10 – (–.05)]
P0 = $6.65 / .15
P0 = $44.33
The next dividend payment by Carroll, Inc., will be $1.90 per share. The dividends
are anticipated to maintain a 5.5 percent growth rate, forever. If the stock currently
sells for $47.00 per share, what is the required return?
R = (D1 / P0) + g
R = ($1.90 / $47.00) + .055
R = .0954 or 9.54%
Barnard Corp. will pay a dividend of $3.05 next year. The company has stated that it
will maintain a constant growth rate of 5 percent a year forever. If you want a 15
percent rate of return, how much will you pay for the stock? What if you want a 10
percent rate of return? What does this tell you about the relationship between the
required return and the stock price?
Here, we need to value a stock with two different required returns. Using the
constant growth model and a required return of 15 percent, the stock price today is:
P0 = D1 / (R – g)
P0 = $3.05 / (.15 – .05)
P0 = $30.50
And the stock price today with a 10 percent return will be:
P0 = D1 / (R – g)
P0 = $3.05 / (.10 – .05)
P0 = $61.00
All else held constant, a higher required return means that the stock will sell for a
lower price. Also, notice that the stock price is very sensitive to the required return.
In this case, the required return fell by 1/3 but the stock price doubled.
“How can g ever be assumed to be constant?” The answer lies in the competitive equilibrium
model of classical macroeconomics. Since g represents not only the growth rate in dividends but
also in earnings and sales, assuming no change in the firm’s cost structure, we are simply
assuming that the product market the firm operates in “settles down” to a steady state in which
competing firms earn sufficient returns to remain in business, but not large enough to attract
outside capital. From a more practical standpoint, firms will often attempt to manage their
dividend policy so that there is a reasonably constant growth in dividends.
“Why do we assume that R > g?” At least two answers are possible. First, R may be less than g
in the short-run. The supernormal growth problem is an example of this situation. Second, in
equilibrium, high returns on investment will attract capital, which, in the absence of
technological change, will ensure that in succeeding periods, higher returns cannot be earned
without taking greater risk. But taking greater risk will increase R, so g cannot be increased
without raising R.
C.
Computing Future Stock Prices

The constant-growth dividend model (Equation 9.4) can be modified to determine the
value, or price, of a share of stock at any point in time.

This results in Equation 9.5, which shows that the price of a share of stock at time t is
as follows:
Pt =
D.
Dt 1
(R-g )
The Relationship between R and g

The constant-growth dividend model yields solutions that are invalid anytime the
dividend growth rate equals or exceeds the discount rate (g ≥ R).

If g = R, the value of the denominator is zero and the value of the stock is infinite,
which makes no sense.

If g > R, the present value of the dividend gets bigger and bigger rather than smaller
and smaller, as it should. This implies that a firm that is growing at a very fast rate
does so forever.
E.
Supernormal Growth Dividend Model

During the early part of their lives, very successful firms experience a supernormal rate
of growth in earnings.

To value a share of stock for a firm with supernormal dividend growth patterns, we can
apply Equation 9.1, our general dividend model, and Equation 9.5, which gives us the
price of a share of stock with constant dividend growth at any point in time.

Thus, our valuation model is (Equation 9.6):
P0 = PV (Mixed dividend growth) + PV (Constant dividend growth)
P0 
Dt
Pt
D1
D2

  

2
t
(1  R ) (1  R )
(1  R ) (1  R ) t
The main reason to consider this case is to allow for “supernormal” growth rates over some finite
length of time. As we know, the growth rate cannot exceed the required return indefinitely, but it
certainly could do so for some number of years. To avoid the problem of having to forecast and
discount an infinite number of dividends, we will require that the dividends start growing at a
constant rate sometime in the future.
Common Stock Valuation under Supernormal Growth (two-stage growth)
P0 
N
D0 (1 g s )   1 g s  s  D 0 (1 g s ) Ns (1 g n )
1

(1  R)  Ns
 
 
(R g s )   1  R  
R g n


P0 = Intrinsic or theoretical value of the stock
D0 = The dollar amount of the last actual dividend on the stock
R = Required rate of return on the stock
gn = Expected constant growth rate of the dividends on the stock
gs = Expected supernormal growth rate of the dividends on the stock
Ns = Number of years of initial (supernormal) growth
The Glass Corp. is growing quickly. Dividends are expected to grow at a 20 percent rate for the
next three years, with the growth rate falling off to a constant 6 percent thereafter. If the required
return is 13 percent and the company just paid a $3.05 dividend, what is the current share price?
With supernormal dividends, we find the price of the stock when the dividends level off at a
constant growth rate, and then find the present value of the future stock price, plus the present
value of all dividends during the supernormal growth period. The stock begins constant growth
after the third dividend is paid, so we can find the price of the stock in Year 3, when the constant
dividend growth begins as:
P3 = D3 (1 + g) / (R – g)
P3 = D0 (1 + g1)3 (1 + g2) / (R – g)
P3 = $3.05(1.20)3(1.06) / (.13 – .06)
P3 = $79.81
The price of the stock today is the present value of the first three dividends, plus the present
value of the Year 3 stock price. The price of the stock today will be:
P0 = $3.05(1.20) / 1.13 + $3.05(1.20)2 / 1.132 + $3.05(1.20)3 / 1.133 + $79.81 / 1.133 = $65.64
Alternatively, using the equation above,
N
D0 (1 g s )   1 g s  s  D 0 (1 g s ) Ns (1 g n )
P0 
(1  R)  Ns
 
1  
(R g s )   1  R  
R g n

3
$3.05(1.20)   1.20   $3.05(1.20)3 (1.06)
P0 
(1.13) 3
 
1  
(.13  .20)   1.13  
.13 - .06

P0 = -52.2857(-.19759068) + $79.8089(.69305)
P0 = $10.33117 + $55.31158 = $65.64

Components of the Required Return
Rearrange P0 = D1 / (R – g) to find R:
R = (D1 / P0 ) + g
D1 / P0 = Dividend yield
g = Capital gains yield
R = dividend yield + capital gains yield


The next dividend payment by Carroll, Inc., will be $1.90 per share. The dividends are
anticipated to maintain a 5.5 percent growth rate, forever. If the stock currently sells for $47.00
per share, what is the dividend yield? What is the expected capital gains yield?
The dividend yield is the dividend next year divided by the current price, so the dividend yield is:
Dividend yield = D1 / P0
Dividend yield = $1.90 / $47.00
Dividend yield = .0404 or 4.04%
The capital gains yield, or percentage increase in the stock price, is the same as the dividend
growth rate, so:
Capital gains yield = 5.5%
The total (expected) return on the stock:
R = D1 / P0 + g = 4.04% + 5.50% = 9.54%
Diamond Corporation will pay a $3.75 per share dividend next year. The company pledges to
increase its dividend by 5.5 percent per year, indefinitely. If you require a 12 percent return on
your investment, how much will you pay for the company's stock today?
D1 = 3.75, g = 5.50%, R = 12%
P0 = $3.75 / (.12 - .055) = $3.75 / .065 = $57.69
Merger?
You assume that if you merge, g will equal 8% and that R will equal 15%.
P0 = $3.75 / (.15 - .08) = $53.57
Don’t merge, since price of stock goes down.
$57.69 = $3.75 / (.15 – g)
8.6535 – 57.69g = 3.75
4.9035 = 57.69g
g = 4.9035 / 57.69 = .0850 = 8.50% (Merge if you expect a growth rate > 8.50%)
9.4
Valuing Preferred Stock

In computing the value of preferred stock, one needs to know whether the preferred stock has
an effective “maturity” because of a sinking fund option or call option.

The most significant difference between preferred stock with a fixed maturity and a bond is
the risk of default.

Since preferred stock dividends are declared by the board of directors, failure to pay dividends
does not result in default.

The failure to pay a preferred stock dividend as promised is a serious financial breach and
signals to the market that the firm is in serious financial difficulty.
A.
Preferred Stock with a Fixed Maturity

We can use the bond valuation model developed in Chapter 8 to determine its price, or
value.

Equation 8.2 can be restated as the price of a share of preferred stock (PS0):
Preferred stock price = PV (Dividend payments) + PV (Par value)
PS0 
D m   Pmn
D3 m
$D1 m
D2 m


   mn
1
2
3
(1  i m) (1  i m)
(1  i m)
(1  i m)mn
 Since most preferred stock make quarterly dividend payments, m equals 4.
B.
Perpetual Preferred Stock
 Some preferred stock issues have no maturity.


Dividends are constant over time (g = 0).

Fixed dividend payments go on forever.
We can use Equation 9.2 to value such preferred stock issues.
P0 
D
R
(9.7)
Chapter 9 Sample Questions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. PV of dividends: Cortez, Inc., is expecting to pay out a dividend of $2.50 next year. After that it expects
its dividend to grow at 7 percent for the next four years. What is the present value of dividends over the
next five-year period if the required rate of return is 10 percent?
a. $10.75
b. $9.80
c. $11.88
d. $11.50
2. Zero growth: Xinhua Manufacturing Company has been generating stable revenues but sees no growth
in it for the foreseeable future. The company's last dividend was $3.25, and it is unlikely to change the
amount paid out. If the required rate of return is 12 percent, what is the stock worth today?
a. $39.00
b. $3.69
c. $27.08
d. $21.23
3. Constant growth: You are interested in investing in a company that expects to grow steadily at an
annual rate of 6 percent for the foreseeable future. The firm paid a dividend of $2.30 last year. If your
required rate of return is 10 percent, what is the most you would be willing to pay for this stock? (Round
to the nearest dollar.)
a. $58
b. $61
c. $23
d. $24
4. Constant growth: Ryder Supplies has its stock currently selling at $63.25. The company is expected to
grow at a constant rate of 7 percent. If the appropriate discount rate is 17 percent, what is the expected
dividend, a year from now?
a. $4.43
b. $3.25
c. $10.75
d. $6.33
5. Constant growth: Prior, Inc., is expected to grow at a constant rate of 9 percent. If the company's next
dividend is $2.75 and its current price is $37.35, what is the required rate of return on this stock? (Round
to the nearest percent.)
a. 16%
b. 17%
c. 20%
d. 21%
6. Preferred stock valuation: Ajax Company has issued perpetual preferred stock with a par of $100 and a
dividend of 5.5 percent. If the required rate of return is 7.75 percent, what is the stock's current market
price?
a. $12.90
b. $70.97
c. $53.27
d. $62.14
7. Preferred stock valuation: The Columbia Consumer Products Co. has issued perpetual preferred stock
with a $100 par value. The firm pays a quarterly dividend of $2.60 on this stock. What is the current price
of this preferred stock given a required rate of return of 12.5 percent?
a. $47.25
b. $80.00
c. $20.80
d. $83.20
8. Nonconstant growth: Grant, Inc. is a fast growth stock and expects to grow at a rate of 25 percent for
the next four years. It then will settle to a constant-growth rate of 10 percent. The first dividend will be
paid out in year 3 and will be equal to $5.00. If the required rate of return is 18 percent, what is the
current price of the stock?
a. $85.94
b. $97.19
c. $50.59
d. $65.68
Chapter 9 Sample Questions
Answer Section
MULTIPLE CHOICE
1. ANS: A
Learning Objective: LO 4
Level of Difficulty: Medium
Feedback: Expected dividends for Cortez, Inc., and their present value:
D2 = D1(1 + g) = $2.50(1 + 0.07) = $2.675
D3 = D2(1 + g) = $2.675(1.07) = $2.862
D4 = D3(1 + g) = $2.862(1.07) = $3.063
D5 = D4(1 + g) = $3.063(1.07) = $3.277
Present value of the dividends
= PV(D1) + PV(D2) + PV(D3) + PV(D4) + PV(D5)
PTS: 1
2. ANS: C
Learning Objective: LO 4
Level of Difficulty: Medium
Feedback: D0 = $3.25; g = 0;
R = 12%
PTS: 1
3. ANS: B
Learning Objective: LO 4
Level of Difficulty: Medium
Feedback:
D0 = $2.30;
g = 6%;
PTS: 1
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4. ANS: D
Learning Objective: LO 4
Level of Difficulty: Hard
Feedback:
P0 = $63.25;
g = 7%;
PTS: 1
5. ANS: B
Learning Objective: LO 4
Level of Difficulty: Medium
Feedback: D1 = $2.75; P0 = $37.35;
g = 9%
PTS: 1
6. ANS: B
Learning Objective: LO 6
Level of Difficulty: Medium
Feedback: D = 5.5% ($100) = $5.50;
R = 7.75%
PTS: 1
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7. ANS: D
Learning Objective: LO 6
Level of Difficulty: Hard
Feedback: Quarterly dividend = $2.60
Required rate of return = R = 12.5%
PTS: 1
8. ANS: C
Learning Objective: LO 4
Level of Difficulty: Hard
Feedback: g1-4 = 25%; g = 10%; D3 = $5.00; R = 18%
D4 = D3 (1.25) = $5.00(1.25) = $6.25; D5 = $6.25(1.10) =$6.875
PTS: 1
Prepared by Jim Keys
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