Transcript PowerPoint - cchristopherlee

Additional Problems with Answers
Problem 1
Pricing constant growth stock, with finite
horizon: The Crescent Corporation just paid a
dividend of $2.00 per share and is expected to
continue paying the same amount each year for the
next 4 years.
If you have a required rate of return of 13%, plan
to hold the stock for 4 years, and are confident that
it will sell for $30 at the end of 4 years,
How much should you offer to buy it at today?
7-1
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Additional Problems with Answers
Problem 1 (Answer)
In this case, we have an annuity of $2 for 4
periods, followed by a lump sum of $30, to be
discounted at 13% for the respective number
of years.
Using a financial calculator
Mode: P/Y=1; C/Y = 1
Input: N
Key:
4
Output
7-2
I/Y
13
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PV
PMT FV
?
2
30
-24.35
Additional Problems with Answers
Problem 2
Constant growth rate, infinite horizon
(with growth rate estimated from past
history: Using the historical dividend
information provided below to calculate the
constant growth rate, and a required rate of
return of 18%, estimate the price of Nigel
Enterprises’ common stock.
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
$0.35 $0.45 $0.51 $0.65 $0.75 $0.88 $0.99 $1.10 $1.13 $1.30
7-3
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Additional Problems with Answers
Problem 2 (Answer)
First, estimate the historical average growth
rate of dividends by using the following
equation:
g = [(FV/PV)1/n – 1]
Where FV = Div2008 = $1.30
PV = Div1999 = $0.35
n = number of years in between =9
g = [(1.30/0.35)1/9 – 1]
 15.7%
7-4
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Additional Problems with Answers
Problem 2 (Answer) (continued)
Next, use the constant growth, infinite horizon
model to calculate price:
i.e. Price0 = Div1/(r-g) = Div0(1+g)/(r-g)
Div0 = Div2008= $1.30;
Div1= Div0*(1+g) =$1.30*(1.157)$1.504;
r = 18%; g = 15.7% (as calculated above)
Price0 = $1.504/(.18-.157)
Price0 = $65.40
7-5
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Additional Problems with Answers
Problem 3
Pricing common stock with multiple dividend
patterns: The Wonder Products Company is
expanding fast and therefore will not pay any
dividends for the next 3 years.
After that, starting at the end of year 4, it will pay a
dividend of $0.75 per share to its common
shareholders and increase it by 12% each year until
it pays $1.50 at the end of year 10.
After that it will pay $1.50 per year forever. If an
investor wants to earn 15% per year on this
investment, how much should he pay for the stock?
7-6
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Additional Problems with Answers
Problem 3 (Answer)
First lay out the dividends on a time line.
Expected Dividend Stream of The Wonder Products Co.
…
T0
T∞
T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
--- $0.00 $0.00 $0.00 $0.75 $0.84 $0.94 $1.05 $1.18 $1.32
$1.50 …$1.50
Note: There are 3 distinct dividend payment
patterns Years 1-3, no dividends; Years 410, dividends grow at 12%; Years 11
onwards, zero-growth in dividends.
7-7
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Additional Problems with Answers
Problem 3 (Answer) (continued)
Next, Calculate the price at the end of Year
10, i.e. when the dividend growth rate is
zero.
Price10 = Div11/r = 1.50/.15 = $10;
Using the NPV function and the annual
cash flows calculate the price;
NPV(15,0,{0.00,0.00,0.00,0.75,0.84,0.94,1.0
5,1.18,1.32,1.50+10.00} $5.25
Price = $5.25
7-8
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Additional Problems with Answers
Problem 4
Pricing non-constant growth common stock: The
WedLink Corporation just paid a dividend of $1.25 to
its common shareholders.
It announced that it expects the dividends to grow by
25% per year for the next 3 years.
Then drop to a growth rate of 16% for an additional 2
years.
Finally the dividends will converge to the industry
median growth rate of 8% per year.
If investors are expecting 12% per year on WedLink’s
stock, calculate the current stock price.
7-9
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Additional Problems with Answers
Problem 4 (Answer)
Determine the dividend per share in Years 1-5
using the stated annual growth rates:
D1=$1.25*(1.25)=$1.56;
D2=$1.56*(1.25)=$1.95;
D3=1.95*(1.25)=$2.44;
D4=$2.44*(1.16)=$2.83;
D5=$2.83*(1.16)=3.28
Next, Calculate the price at the end of Year 5;
using the Gordon Model.
7-10
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Additional Problems with Answers
Problem 4 (Answer) (continued)
Using r = 12% and g = 8% (constant
growth phase)
i.e. P5 = D5(1+g)/(r – g)
P5 = $3.28*(1.08)/(.12-.08)
3.54/.04=$88.56
Finally calculate the present value of all
the dividends in Years 1-5 and the price in
Year 5, by using the NPV function….(TI-83
keystrokes shown here)
NPV(12,0,{1.56, 1.95, 2.44, 2.83,
3.28+88.56} = $58.60
7-11
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Additional Problems with Answers
Problem 5 (A)
Pricing common stock with constant
growth and finite life versus infinite life.
The ANZAC Corporation plans to be in business
for 30 years.
They announce that they will pay a dividend of
$3.00 per share at the end of one year, and
continue increasing the annual dividend by 4%
per year until they liquidate the company at the
end of 30 years.
If you want to earn a rate of return of 12% by
investing in their stock, how much should you
pay for the stock?
7-12
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Additional Problems with Answers
Problem 5 (A) (Answer)
Div1 = $3.00; r = 12%; g = 4%; n = 30
Using the formula for a growing annuity we
can solve for the current price.
Div   1 g 30 
1  1 


Price 

0 r  g   1 r  


  1.04 30 
$3.00

Price 0 
 1 

.12  .04   1.12  
Price0 = $37.5*0.89174 = $33.44
7-13
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Additional Problems with Answers
Problem 5 (B)
If the company was to announce that it
would continue increasing the dividend at
4% per year forever, how much more would
you be willing to pay for its stock, assuming
your required rate of return is still 12%?
7-14
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Additional Problems with Answers
Problem 5 (B) (Answer)
If the growth rate is 4% forever, the price of
the stock can be figured out by using the
Gordon Model;
D1=$3.00; r=12%
Div
1
Price 
0 r  g
 $3.00/(.12 - .04) $37.50
7-15
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