Practice
Problems – Chapter 4
1.
The Trans-Pacific Utility Co.'s stock is expected to pay constant annual
dividends of $2.50 per share forever. If
the discount rate for the stock is 9% per year,
a)
what is the stock price today?
b)
what is the expected stock price at the end of one year?
2.
Sam’s Spades Co. had earnings per share last year of $3.50 and they
paid a dividend last year of $1.40. Assume
their payout ratio remains constant, and their ROE is also constant at 15%.
If their required return is 12% per year, what is the stock price today?
3.
Bootle Investments is expected to pay the following dividends for the
next three years:
Time
1 2
3
Dividend 0.90
1.05 1.16
After
time 3, dividends will grow at a constant rate of 8% per year.
If the required return on the stock is 16% per year, what should the
stock price be today?
4.
The Taj Mahal Corp.’s shares are selling for $65.
Their dividend last year was $3.28.
If their plowback ratio is 50% and ROE is 20%, what is the required
return for the stock?
5. Anabolic Steroid Inc., being a growth company, currently reinvests all
its earnings and does not pay any dividends.
It is expected to pay the following dividends over the next four years:
Time
1
2
3
4
Dividend 0
0
0.50
1.00
After
time 4, dividends will grow at a constant rate of 6% per year.
If the required return on the stock is 14% per year, what should be the
stock price today (time 0)?
6.
Peculiar Pumpkins Corporation is expected to pay a dividend of $2.50 next year. Its dividends are
expected to grow at 8% for the next three years, and at a constant rate of 4%
forever thereafter. What is the
price of its stock today, if the discount rate for the stock is 12%?
(15 points)
7.
Stop-n-Rob Convenience Stores Inc. has the following stream of expected
future dividends. Initially,
dividends will decline as the company reinvests most of its earnings in new
projects. From the fourth year
onwards, dividends will start to increase again, as the new projects start
contributing profits.
Time
1
2
3 4
5
6
Dividend
1.60 1.40
1.30 2.00
2.50
3.00
After
time 6, dividends will grow at a constant rate of 10% per year.
If the required return on the stock is 14% per year,
a)
what price should the stock sell for today?
b) what is your expected return if you
buy the stock today and hold it for four years?
8.
Ptolemy’s Ptennisnets Corp. generates a perpetuity of $8.50 per year
from its existing assets. Every
year they pay out 70% of these earnings, and reinvest the remaining 30% at a
return of 15%. If their required
return is 12%,
a)
What is their stock price?
b) How
much of this is PVGO?
c) If
they had no positive NPV investments, but they still maintained a payout ratio
of 70%, how much would they earn on their reinvestment?
What growth rate would they have?
9.
CSI has a 10% ROE and reinvests 40% of its earnings each year.
Their expected dividend next year is $4, and the stock is selling for
$100 today.
a)
What is the expected return on the stock?
b)
What is the expected EPS next year?
c)
What proportion of today’s stock price consists of PVGO?
d) Suppose CSI is able to scale up the size of their positive NPV investment opportunities. Instead of reinvesting 40% of their earnings each year they are able to reinvest 60% instead (still at a 10% ROE). How does this affect their stock price today? What is the percentage increase in PVGO?
10.
The Warshawski Paper Works is
expected to pay a dividend of $2.22 next year.
It has a dividend yield of 8%. Each
year it pays out 65% of its earnings; on the 35% that is reinvested, it earns a
return of 16%.
a) What is WPW’s growth rate?
b) What is their required
return?
c) What is the stock price
today?
d) How much of this is the PV of existing assets, and how much is PVGO?
(15 points)
11.
Newbie Inc. is a start-up firm with a required return of 15%.
They will invest $40 per share today, and earn 30% on this investment the
first year. For two years, they
will pay out 10% of their earnings and retain 90%. And they will continue to earn 30% on their assets.
However after two years, the payout ratio will increase to 60% and the
return on assets will drop to 20% (all assets, old and new).
These rates will stay constant forever.
a) Make a table showing the firm’s dividend per share for the first 5
years
b) Compute the value of Newbie’s shares today
c) What is Newbie’s PVGO?
(25
points)
(Clarifications and hints:
·
What is invested at time 0 earns 30%
for 2 years and then 20% thereafter. What
is invested at time 1 earns 30% for one year and then 20% thereafter. What is
invested at time 2 and later earns 20% forever.
·
Newbie’s existing assets today
consist of the initial investment of $40 per share.
In other words, “today” is time 0, after this investment has been
made.
·
PV of the existing assets is the PV of
the earnings expected to be generated by the existing assets. This has to be
computed given that the future earnings from the existing assets are not a
perpetuity.)