Key Chapter 7 homework
5.
The Spinnaker Company has paid an annual dividend of $2 per share for some time.
Recently, however, the board of directors voted to grow the dividend by 6% from now on. What
is the most you would be willing to pay for a share of Spinnaker if you expect a 10% return on
your stock investments?
SOLUTION:
Apply the Gordon Model
P0 = D0(1 + g) / (k – g)
= $2(1.06) / (.10  .06)
= $2.12 / .04
= $53.00
6. The Pancake Corporation recently paid a $3 dividend, and is expected to grow at 5% forever.
Investors generally require an expected return of at least 9% before they'll buy stocks similar to
Pancake.
a. What is Pancake's intrinsic value?
b. Is it a bargain if it's selling at $76 a share?
SOLUTION:
a.
P0 
D 0 (1  g )
kg

$3.00 (1.05 )
.09  .05
 $78.75
b. That's not apparent. Although our calculated intrinsic price exceeds the market price, it
only does so by about 4%. The modeling technique isn't accurate enough to identify 4%
differences. Our result says that the stock has probably been priced about right by the market.
9.
Cavanaugh Construction specializes in designing and building custom homes. Business
has been excellent, and Cavanaugh projects a 10% growth rate for the foreseeable future. The
company just paid a $3.75 dividend to its stockholders. Comparable stocks are returning 11%.
a.
b.
c.
What is the intrinsic value of Cavanaugh stock based on this information?
Does this seem reasonable? Why or why not?
If Cavanaugh’s growth rate is only 8.5% and comparable stocks are really returning 12%,
what would the intrinsic value of Cavanaugh’s stock be?
d.
Do those relatively small changes in assumption justify the change in the intrinsic value
of the stock? Why or why not?
SOLUTION:
a.
The Gordon Model yields
[$3.75 (1.10)] / (.11 - .10) = $412.50
b.
No, it does not seem reasonable. The problem is that the growth rate of 10% and the
discount rate of 11% are too close together for the constant growth model to work
effectively.
c.
[$3.75 (1.085)] / (.12 - .085) = $116.25
d.
Probably not. The assumptions in part c. appear to be more reasonable than those in part
a., and they provide a sufficient spread in the growth and discount percentages for the
constant growth model to work more effectively.
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10.
The Miller Milk Company has just come up with a new lactose free dessert product for
people who can’t eat or drink ordinary dairy products. Management expects the new product to
fuel sales growth at 30% for about two years. After that competitors will copy the idea and
produce similar products, and growth will return to about 3% which is normal for the dairy
industry in the area. Miller recently paid an annual dividend of $2.60,which will grow with the
company. The return on stocks like the Miller Company is typically around 10%. What is the
most you would pay for a share of Miller?
SOLUTION:
First draw a time line for the problem and enter the following data.
g1 = 30%
0
1
D0=$2.60
D1=$3.38
g2 = 3%
2
3
D2=$4.39
𝑃2 =
D3=$4.52582
𝐷3
𝑘=𝑔
=
4.52582
.07
D1 = D0(1.30) = $2.60(1.30) = $3.38
D2 = D1(1.30) = $3.38(1.30) = $4.39
D3 = D2(1.03) = $4.39(1.03) = $4.52582
P2 = D3 / (k – g2) = $4.52 / (.10  .03) = $64.65
CF0 = 0
CF1 = $3.38
CF2 = $4.39 + $64.65 = 69.04
I = 10%
Computer NPV = 60.13
14.
Garrett Corp. has been going through a difficult financial period. Over the past three
years, its stock price has dropped from $50.00 to $18.00 per share. Throughout this downturn,
Garrett has managed to pay a $1.00 dividend each year. Management feels the worst is over, but
intends to maintain the $1.00 dividend for three more years, after which they plan to increase it
by 6% per year indefinitely. Comparable stocks are returning 11%. If these projections are
accurate, is Garrett stock a good buy at $18.00? How do you think the market feels about
Garrett’s management?
SOLUTION:
0
1
2
3
4
/-------------------/-------------------/-------------------/------------------/
$1.00
$1.00
$1.00
$1.06
Cash flows for the next three years will remain at $1.00 per year. Beginning in the fourth
year, the constant growth model can be used to determine the present value of the
remaining dividends:
$1.06/(.11 - .06) = $21.20
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The constant growth period begins at the end of the third period which means the
following cash flows should be used to compute the intrinsic value of the stock:
CF0 = 0
CF1 = $1.00
CF2 = $1.00
CF3 = $1.00 + $21.20
@ 11%, the PV of the cash flows is $17.94. This is very close to the current market price
of the stock, so apparently the market has some confidence that Garrett will be able to
deliver on its earnings and dividend projections. Garrett stock is not a bargain, but
appears to be priced just about right.
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