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LG6 8-24 Dividend Initiation and Stock Value A firm does not pay a dividend. It is expected to pay
its first dividend of $0.25 per share in two years. This dividend will grow at 10 percent
indefinitely. Using an 11.5 percent discount rate, compute the value of this stock.
First compute the year 1 value of the stock using equation 8-6 and then discount this back one
year to get the present value of the stock price:
Constant growth model=P1=D2
i−g=$0 . 25/(0 . 115−0. 10 )=$16 .67
P0=( $16 .67 /1. 115 )=$14 . 95
LG7 8-25 P/E Ratio Model and Future Price Kellogg Co. (K) recently earned a profit of $2.52 per
share and has a P/E ratio of 13.5. The dividend has been growing at a 5 percent rate over the past
few years. If this growth rate continues, what would be the stock price in five years if the P/E
ratio remained unchanged? What would the price be if the P/E ratio declined to 12 in five years?
Under these two scenarios, the future price estimates using equation 8-10 are:
P5=
(
P
E
)
n
×E0×
(
1+g
)
n=13 . 5×$2 . 52 ×
(
1+0 .05
)
5=$43 . 42
P5=
(
P
E
)
n
×E0×
(
1+g
)
n=12×$2. 52×
(
1+0 . 05
)
5=$38. 59
LG7 8-26 P/E Ratio Model and Future Price New York Times Co. (NYT) recently earned a profit of
$1.21 per share and has a P/E ratio of 19.59. The dividend has been growing at a 7.25 percent
rate over the past six years. If this growth rate continues, what would be the stock price in five
years if the P/E ratio remained unchanged? What would the price be if the P/E ratio increased to
22 in five years?
Under these two scenarios, the future price estimates using equation 8-10 are:
P5=
(
P
E
)
n
×E0×
(
1+g
)
n=19 . 59×$1 .21×
(
1+0. 0725
)
5=$33 . 64
P5=
(
P
E
)
n
×E0×
(
1+g
)
n=22×$1. 21×
(
1+0 . 0725
)
5=$37 .77
advanced problems
LG5 8-27 Value of Future Cash Flows A firm recently paid a $0.45 annual dividend. The
dividend is expected to increase by 10 percent in each of the next four years. In the fourth year,
the stock price is expected to be $80. If the required return for this stock is 13.5 percent, what is
its current value?
Then use equation 8-3 as:
P0=D1
1+i+D2
(
1+i
)
2+D3
(
1+i
)
3+D4+P4
(
1+i
)
4
¿$0. 495/1. 135+$0 .5445/1 .1352+$0 .5990/1 .1353+( $0 . 6588+$80)/1 .1354=$49 . 87
LG5 8-28 Value of Future Cash Flows A firm recently paid a $0.60 annual dividend. The dividend
is expected to increase by 12 percent in each of the next four years. In the fourth year, the stock
price is expected to be $110. If the required return for this stock is 14.5 percent, what is its
current value?
Now use equation 8-3:
P0=D1
1+i+D2
(
1+i
)
2+D3
(
1+i
)
3+D4+P4
(
1+i
)
4
¿$0. 672/1 .145+$0 . 7526/1. 1452+$0 . 8430/1. 1453+( $0 . 9441+$110 )/1. 1454=$66. 27
LG5 8-29 Constant Growth Stock Valuation Waller Co. paid a $0.286 dividend per share in 2006,
which grew to $0.55 in 2012. This growth is expected to continue. What is the value of this stock
at the beginning of 2013 when the required return is 13.7 percent?
First calculate the growth rate from 2006 to 2012:
LG5 8-30 Constant Growth Stock Valuation Campbell Soup Co. (CPB) paid a $0.632 dividend per
share in 2003, which grew to $0.76 in 2006. This growth is expected to continue. What is the
value of this stock at the beginning of 2007 when the required return is 8.7 percent?
LG6 8-33 Variable Growth A fast growing firm recently paid a dividend of $0.35 per share. The
dividend is expected to increase at a 20 percent rate for the next three years. Afterwards, a more
stable 12 percent growth rate can be assumed. If a 13 percent discount rate is appropriate for this
stock, what is its value?
Use equation 8-8:
P0=D0
(
1+g1
)
1+i+D0
(
1+g1
)
2
(
1+i
)
2+
D0
(
1+g1
)
3+D0
(
1+g1
)
3
(
1+g2
)
i−g2
(
1+i
)
3
P0=$0 .35
(
1+0 .20
)
1+0 .13 +$0 .35
(
1+0 .20
)
2
(
1+0 .13
)
2+
$0 . 35
(
1+0 . 20
)
3+$0. 35
(
1+0 .20
)
3
(
1+0. 12
)
0 .13−0 .12
(
1+0 . 13
)
3
P0=$0 .372+$0 .395+$47 .36=$48 . 13
LG6 8-34 Variable Growth A fast-growing firm recently paid a dividend of $0.40 per share. The
dividend is expected to increase at a 25 percent rate for the next four years. Afterwards, a more
stable 11 percent growth rate can be assumed. If a 12.5 percent discount rate is appropriate for
this stock, what is its value?
Use equation 8-8:
P0=D0
(
1+g1
)
1+i+D0
(
1+g1
)
2
(
1+i
)
2+D0
(
1+g1
)
3
(
1+i
)
3+
D0
(
1+g1
)
4+D0
(
1+g1
)
4
(
1+g2
)
i−g2
(
1+i
)
4
P0=$0 . 40
(
1+0 . 25
)
1+0 .125 +$0 . 40
(
1. 25
)
2
(
1 .125
)
2+$0. 40
(
1 . 25
)
3
(
1. 125
)
3+
$0 . 40
(
1 .25
)
4+$0 . 40
(
1 .25
)
4
(
1+0 . 11
)
0. 125−0. 11
(
1 . 125
)
4
¿$0. 444+$0 . 494+$0 . 549+$45 .725=$47 . 21
LG5 8-35 P/E Model and Cash Flow Valuation Suppose that a firm’s recent earnings per
LG7 share and dividend per share are $2.50 and $1.30, respectively. Both are expected to grow at 8
percent. However, the firm’s current P/E ratio of 22 seems high for this growth rate. The P/E
ratio is expected to fall to 18 within five years. Compute a value for this stock by first estimating
the dividends over the next five years and the stock price in five years. Then discount these cash
flows using a 10 percent required rate.
C. What would the value be using a 6 percent growth rate after year 6 instead of the 5 percent
rate using each of these three discount rates?
D. What do you conclude about stock valuation and its assumptions?
SOLUTION:
At 5 percent growth:
Present
Value
11%
Discount
10%
Discount
12%
Discount
At 6 percent growth:
Present
Value
11%
Discount
10%
Discount
12%
Discount
a. From the table calculated in Excel, the value of the stock based on an 11 percent discount
rate would be $23.97.
b. From the table, the value of the stock based on a 10 percent discount rate would be
$28.92 and based on a 12 percent discount rate would be $20.44.
c. From the table, the value of the stock that grows at 6 percent (rather than 5 percent) in
year 7 and after causes a higher stock value than a future 5 percent growth.
d. Assumptions are crucially important in stock valuation. Minor changes in either the
discount rate or the growth assumption rate can have a big impact on stock valuation.
research it!
Stock Screener
Investors can choose from many thousands of stocks. The large number to choose from can be
quite daunting to new investors. Fortunately, some good stock screeners are available for free on
the Internet that will find only the kinds of companies the investor is looking for. Looking for
small value companies? A stock screen at Yahoo! Finance will show all the stocks that meet the
three criteria of (1) market capitalization between $250 million and $1 billion, (2) P/E ratio less
than or equal to 10, and (3) a quick ratio greater or equal to 1.0. In September of 2010, 127 firms
met all three of these criteria. Yahoo! Finance provides 18 screens like this one to choose from.
Pick one of these preset screens. Discuss the kinds of stocks the screen will find and report on
those companies.(http://screener.finance.yahoo.com/presetscreens.html)
SOLUTION: Consider the preset screen for Large Cap Value. The stock screener description is
integrated mini-case: Valuing Carnival Corporation
Carnival Corp. provides cruises to major vacation destinations. Carnival operates 100 cruise
ships with a total capacity of 180,746 passengers in North America, Europe, the United
Kingdom, Germany, Australia, and New Zealand. The company also operates hotels, sightseeing
motor coaches and rail cars, and luxury day boats. These activities generated earnings per share
of $1.67 for 2012. The stock price at the end of 2012 was $36.77. The previous stock prices and
dividends are shown in the following table.
Carnival is a firm in the General Entertainment industry, which is in the Services sector. The
following table shows some key statistics for Carnival, the industry, and the sector.
General
Use the various valuation models and relative value measures to assess whether Carnival stock is
(1) Determine the dividends to 2017, using the same growth rate at which the dividends had been
growing before the financial crisis and then use a terminal P/E ratio of 16 to compute the future
