1. Stock valuation. Why does the value of a stock depend on dividends?

Because the dividend is the part of the profit of each share, that is, it is the utility value that
the share earns over time.

2. Stock valuation. A substantial percentage of companies listed on the New

York Stock Exchange and NASDAQ do not pay dividends but investors are
willing to buy their shares. How is this possible given your answer to the
previous question?

This action taken by companies could work thanks to the performance and growth analysis
of the long-term dividend discount model.

3. Dividend policy. In relation to the two previous questions. Under what

circumstances can a company decide not to pay dividends?

When your investment is long term

4. Dividend growth model. What are the two assumptions under which the
dividend growth model presented in the chapter can be used to determine
the value of a stock? Comment on the reasonableness of these assumptions.

Case 1. Zero growth: that is, the dividend remains perpetual over time, that is, it does not
have a growth rate or profit.

Case 2. Constant growth: this model includes dividends with a growth rate that varies over
time.

5. Common Stock vs. Preferred Stock. Suppose that a company carries out an
issue of preferred shares and another of common shares. Both just paid a $2
dividend. Which of them do you think will have a higher price: a preferred
stock or a common stock?

The common stock would have a higher price.

6. Dividend growth model. Based on the dividend growth model, what are the
two components of a stock's total return? Which do you think is typically
older?
1. Capital gains and losses.
 2. Dividends

Profits and losses are the result of movements in stock prices and are reflected in stock
market play sometimes excluding dividends.

7. Growth rate. In the context of the dividend growth model, is it true that the
dividend growth rate and the stock price growth rates are identical?

Yes, suppose a stock was purchased last year for $100, the current stock price is $120,
and the dividends paid at the end of the year are $5. The calculated yield returns are 0.25
i.e. 25%, if the stock price has reduced to $70, the yield returns will also be reduced by
25%

8. Price-earnings ratio. What are the three factors that determine a company's
price-earnings ratio?
1. Growth opportunities.
2. Risk
3. Accounting practices.

9. Corporate ethics. Is it unfair or unethical for corporations to create share

classes with unequal voting rights?

It is unethical, since they create classes of shares according to the quick-return benefit that
they have, that is, some partners only seek the short-term benefit of the shares, making
decisions that harm the rest.

10. Stock valuation. Evaluate the following statement: Managers should not
focus on the current value of the stock because doing so will place undue
importance on short-term profits at the expense of long-term profits.

It becomes unethical on the part of administrators, communicating to partners a short-term

benefit that may be less than expected in the long term.

1. Stock values. Starr Co. Just paid a dividend of $1.90 per share. Dividends are
expected to grow at a constant rate of 5% per year indefinitely. If investors
 require a 12% return on the stock, what is the current price? What will the
price be in 3 years? And in 15 years?

dividend 1,9
g rate 5%
performanc
e 12%
po= ?
po3= ?

(1+ g)
Po=¿
(R−g)

Po=28.50

(1+ g)3
P 3=¿
(R−g)

P 3=31.42

(1+ g)15
P 15=¿
(R−g)

P 15=56.43

2. Stock values. ECY, Inc.'s next dividend payment will be $2.85 per share.
Dividends are expected to maintain a 6% growth rate forever. If ECY shares
are currently selling for $58 each, what is the return required?

¿1
ℜ=
po

2.85
ℜ=
58

ℜ=0.04913793

¿1
ℜ= +g
po
 ℜ=0.04913793+0.06

ℜ=0.10913793

ℜ=10.91

3. Stock values. In the case of the company in the previous problem, what is the
dividend yield? What is the expected return on capital gains?

The dividend yield is the dividend next year, divided by the current price

2.85
ℜ=
58

ℜ=0.04913793

ℜ=4.91 %

4. Stock values. White Wedding Corporation will pay a dividend of $3.05 per
share next year. The company has committed to increasing its dividend
5.25% annually indefinitely. If you have a return of 11% on your investment.
How much will you pay for the company's shares today?

Po= ¿
(R−g)

3.05
Po=
(0.11−0.0525)

Po=53.0434

5. Stock valuation. Siblings, Inc. is expected to maintain a constant dividend

growth rate of 5.8% indefinitely. If the company has a dividend yield of 4.7%,
what is the required return on its shares?

R=rentabilidad del dividendo+rendimiento de la gananciadel capitañ

R=0.047+0.058

R=0.105

R=10.5 %
 6. Stock valuation. Suppose you know that a company's shares now sell for $64
each and that the required return on the shares is 13%. You also know that
the total return on stocks is divided evenly between the capital gains yield
and the dividend yield. If the company's policy is to always maintain a
constant rate of dividend growth, what is the current dividend per share?

We know that the stock has a 13% yield and the dividend and capital gains yield are the
same so

1
R= (0.13)
2

R=0.065

R=0.065+0.065

R=0.13

R=13 %

¿ 1=0.065(64)

¿ 1=4.16

¿ 1=¿ 0 ( 1+ g )

¿1
Divo=
(1+ g)

4.16
Divo=
(1+0.065)

Divo=3.9061

7. Stock valuation. Gruber Corp. Pays a constant dividend of $11 on its shares.
The company will maintain this dividend for the next nine years and then
stop paying them forever. If the required return on this stock is 10%, what is
the current price of the stock?
The price of any financial instrument is the present value of future cash flows. The future
dividends on these securities are annuities for 9 years, so the share price is the EPS,
which will be

R= ¿
Po

11
Po=
0.10

11
Po=
0.10

Po=110

8. Valuation of preferred shares. Ayden Inc., has an issue of preferred stock

outstanding that pays a dividend of 6.40 every year in perpetuity. If this issue
is currently selling for $103 per share, what is the required return?

R= ¿
Po

6.40
R=
103

R=0.0621

R=6.21 %

9. Growth rate. Newspapers reported last week that Bennington Enterprise

earned $28 million this year. The article also reported that the company's
return on equity was 15%. Bennington retains 70% of its profits. What is the
company's profit growth rate? How much will profits be next year?

Inversion Nueva=28000000 x 0.70

Inversion Nueva=19600000

28000000−19600000
Tasa de crecimiento=
28000000
 Tasa de crecimiento=0.30

Tasa de crecimiento prox año=28000000 x 0.30

Tasa de crecimiento prox año=28000000 x 0.30

Utilidad proximo año=8400000

10. Stock valuation. Universal Laser Inc. just paid a dividend of $2.75 on its
shares. The dividend growth rate is expected to remain constant at 6% per
year, indefinitely. Investors require a 16% return on the stock in the first three
years, a 14% return in the next three years, and finally an 11% return
thereafter. What is the current stock price?

Number of years 7

( 1+ g )7
P 6=¿ 0
(R−g)

7
(1+ 0.06)
P 6=2.75
(0.16−0.06)

P 6=82.70

First 3 years

(1+ g )4 ( 1+ g )5
P 3=¿ 0 +¿ 0
(R−g) (R−g)

4 5 6 7
(1+0.06) (1+0.06) (1+ 0.06) (1+0.06)
P 3=2.75 +2.75 +2.75 + 2.75
(1.14−0.06) (1.14−0.06)2
(1.14−0.06) 3
( 0.16−0.06 )4

P 3=64.33

11. Non-constant growth. Metallica Bearings Inc. is a young and entrepreneurial

company. It will not pay any dividends on its shares for the next nine years
because the company needs to reinvest its profits to drive growth. The
 company will pay a dividend of $9 per share in 10 years and will increase the
dividend 5.5% annually after that date. If the required return on this stock is
13%, what is the current price of the stock?

(1+ g)
Po=¿
(R−g)

1+0.055
Po=9
(0.13−0.055)

Po=126.60

12. Non-constant dividends. Bucksnort, Inc., has a strange dividend policy. It

just paid a dividend of $10 per share and has announced that it will increase
the dividend by $3 per share in each of the next five years and that thereafter
it will never pay as a dividend. If you require a return of 11% on the
company's shares. How much will you pay for the shares today?

Po= ¿
(1+ R)

Po= ¿ + ¿ + ¿ + ¿ + ¿
(1+ R) (1+ R)2 ( 1+ R )3 (1+ R)4 (1+ R)5

13 16 19 22 25
Po= + + + +
(1+ 0.11) (1+0.11)2 (1+ 0.11 )3 (1+ 0.11)4 (1+0.11)5

Po=67.92

Solving with the VPN or VNA function

Dividend year 13

Dividend year 16

Dividend year 19

Dividend year 22

Dividend year 25
 VPN =13+16+ 19+22+25

VPN =67.92

13. Non-constant dividends. North Side Corporation is expected to pay the

following dividends over the next four years: 9, 7, 5, and 2.50. The company
then commits to maintaining a constant 5% dividend growth rate forever. If
the required return on the stock is 13%, what will be the current price of the
stock?
14. Differential growth Hughes Co. is growing rapidly. Dividends are expected to
grow at a rate of 25% over the next three years, and the growth rate is
expected to decline to a constant 7% thereafter. If the required return is 12%
and the company just paid a dividend of $2.40, what is the current stock
price?
15. Non-constant growth. Janicek Corp. is experiencing rapid growth. Dividends
are expected to grow 30% annually for the next three years, 18% in the
following year, and 8% annually indefinitely. The required return on these
shares is 13% and the shares are currently selling for $65 each. What is the
projected dividend for the following year?
16. Negative growth. Antiques R Us is a mature manufacturing company. The
company just paid a $12 dividend, but management expects to reduce the
dividend payment 6% annually, indefinitely. If you require a return of 11 on
this stock, how much will you pay for a stock today?

(1+ g)
Po=¿
(R−g)

(1−0.06)
Po=12
(0.11+ 0.06)

Po=66.35

17. Dividend calculation. Today, Mau Corporation shares are selling for $49.80
each. The market requires a return of 11% on the company's shares. If it
 maintains a constant dividend growth rate of 5%, what was the most recent
dividend paid per share?
18. Valuation of preferred shares. Fifth National Bank just issued some new
preferred shares. The issue will pay an annual dividend of $7 in perpetuity,
starting in five years. If the market requires a 6% return on this investment,
how much will a preferred stock cost today?
19. Using stock quotes. You found the following stock quote for RJW Enterprise
Inc., in the financial section of today's newspaper. What was the closing
price of this stock that appeared in yesterday's period? If today the company
has 25 million shares outstanding, what was the net income in the last four
quarters?

20. Taxes and stock prices. You have $100,000 invested in Smart Money shares.
Within a year you will receive a dividend of $1.50 per share. You will receive a
dividend of $2.25 in two years. He will sell the shares for $60 in three years.
Dividends are taxed at the rate of 28%. Assume there is no capital gains tax.
The required rate of return is 15%. How many shares do you have?
21. Non-constant growth and quarterly dividends. Pasqually Mineral Water, Inc.
will pay a quarterly dividend per share of $75 at the end of each of the next 12
quarters. From then on, the dividend will grow at a quarterly rate of 1%
forever. The appropriate rate of return on the stock is 10% and is
compounded quarterly. What is the current price of the stock?
22. Dividend calculation. Briley Inc. is expected to pay equal dividends at the end
of each of the next two years. From then on, the dividend will grow at a
constant annual rate of 5% forever. The current share price is $38. How much
will next year's dividend payment be if the required rate of return is 11%?
23. Calculation of required performance. Juggernaut Satelite Corporation earned
$10 million in the fiscal year that ended yesterday. Also yesterday the
company paid 20% of its profits as dividends. The company will continue to
 pay 20% of its profits as annual dividends at the end of the year. The
company retains the remaining 80% of the profits to use in its projects. The
company has 2 million common shares outstanding. The current share price
is $85 each. The historical return on equity (ROE) of 16% is expected to
continue into the future. What will be the required rate of return on the stock?
24. Dividend growth. Four years ago, Bling Diamond, Inc., paid a dividend of
$1.20 per share. In addition, yesterday it paid a dividend of $1.93 per share.
Dividends will grow over the next five years at the same rate they grew over
the past four years. After that, dividends will grow 7% annually. What will
Bling's cash dividend be in seven years?
25. Price-earnings ratio. Consider the case of Pacific Energy Company and US
Bluechips Inc., which reported profits of $750,000. Without new projects,
both companies will continue to generate profits of $750,000 in perpetuity.
Assume that all profits were paid as dividends and that both companies
require a 14% rate of return.
a) What is the current P/E ratio for each company?
b) Pacific Energy Company has a new project that will generate additional
profits of $100,000 each year in perpetuity. Calculate the company's new P/E
ratio.
c) US Bluechips has a new project that will increase profits by $200,000 in
perpetuity. Calculate your new P/E ratio
26. Growth opportunities. The Stambaugh Corporation has earnings per share of
$8.25. The company shows no growth and pays out all of its profits as
dividends. You have a new project that will require an investment of $1.60 per
share within a year. The project will last only two years and will increase
profits in the 2 years following the investment by 2.10 and 2.45 dollars,
respectively. Investors demand a 12% return on Stambaugh shares
a) What is the company's value per share assuming the company does not
undertake the investment opportunity?
b) If the company carries out the investment. What will the value per share be
now?
c) If the firm makes the investment. What will the price per share be after four
years?
27. Growth opportunities. Rite Bite Enterprises sells toothpicks. Last year gross
revenue was $6 million, and total costs were $3.1 million. Rite Bite has 1
million common shares outstanding. Revenue and costs are expected to
grow 5% annually. RIte Bite does not pay income tax. All profits are paid as
dividends.
a) If the appropriate discount rate is 15% and all cash flows are received at the
end of the year, what is the price per share of Rite Bite?
b) Rite Bite has decided to produce toothbrushes. The project requires an
immediate disbursement of 22 million dollars. Within a year another
disbursement of 8 million will be needed. A year later, profits will increase by
$7 million. That level of profits will be maintained in perpetuity. What effect
will undertaking this project have on the share price?
28. Growth opportunities. California Real Estate, Inc., expects to earn $85 million
per year in perpetuity if it does not pursue any new projects. The company
has the opportunity to invest $18 million now and $7 million within a year in
real estate. The new investment will generate profits of $11 million in
perpetuity, starting two years from today. The company has 20 million shares
of common stock outstanding and the required rate of return on equity is
12%. Investments in land are not susceptible to depreciation. Ignore taxes.
a) What will the price of a share be if the company does not undertake the new
investment?
b) What is the value of the investment?
c) What is the price per share if the company undertakes the investment?
29. Growth opportunities. Avalanche Skis, Inc.'s annual earnings will be $7 per
share in perpetuity if the company makes no new investments. In that
situation the company would pay out all of its profits as dividends. Assume
that the first dividend will be received exactly one year from now. On the
other hand, suppose that after three years, and in each following year in
perpetuity, the company can invest 30% of its profits in new projects. Each
project will earn 20% at the end of each year in perpetuity. The company's
discount rate is 11%.
a) What is today's price per share of Avalanche Skis, Inc., if the company does
not make the new investment?
b) If Avalanche Skis announces that it will make the new investment, what will
be today's price per share?
30. Capital gains vs. income. Consider four different stocks that have a required
return of 20% and a most recent dividend of $4.50 per share. Stocks W, X, Y
are expected to maintain constant dividend rates for the foreseeable future of
10%, 0% and -5% per annum, respectively. Stock Z is a growth stock that will
increase its dividends by 30% over the next two years and then maintain a
constant growth rate of 8%. What is the dividend yield for each of these four
stocks? What is the expected return on capital gains? Explain the
relationship between the various returns you calculate for each of these
stocks.
31. Stock valuation. Most corporations pay quarterly rather than annual
dividends on their common stock. If no extraordinary circumstances arise
during the year, the board of directors increases, decreases or maintains its
current dividend once a year and subsequently pays this dividend in equal
quarterly installments to its shareholders.
a) Suppose that a company currently pays a dividend of $3.60 on its common
stock in a single annual payment, and that management plans to increase
this dividend 5% annually indefinitely. If the required return on this stock is
14%, what is the current price of the stock?
b) Now suppose that the company cited in a) actually pays its annual dividend
in equal quarterly payments; So, this company just paid a dividend per share
of $.90 the same way it has done in the previous three quarters. What will be
the value of the current stock price? (Hint: Calculate the year-end equivalent
annual dividend each year.) Do you think this stock valuation model is
appropriate? Comment your answer.