Stock Valuation.pdf

Page 1 of 18

Critical Thinking Questions

9.1 Why does the market price of a security vary from the true equilibrium price?

Let us start by first defining the market equilibrium price of a security as the price that

equates the demand for a security with the supply of the security. The role of the security

markets is to bring buyers and sellers together in the most efficient way such that

securities are bought and sold at the true equilibrium price. In reality, however, barriers

of various kinds including the geographic separation of the two parties make the market

price of a security slightly different than the true equilibrium price. The more efficient the

market place, the smaller the deviation between the two.

9.2 Why are investors and managers concerned about market efficiency?

The role of secondary markets is to bring buyers and sellers together. Ideally, we would

like security markets to be as efficient as possible. Markets are efficient when current

market prices of securities traded reflect all available information relevant to the security.

If this is the case, security prices will be near or at their equilibrium price. The more

efficient the market, the more likely this is to happen. This makes it easier for managers

to price the securities close to the equilibrium price.

What investors are most concerned about is having complete information

regarding a security’s current price and where that price information can be obtained.

Efficient markets allow them to trade at prices that are closer to the true equilibrium price

than otherwise possible.

Thus, both investors who provide funds and managers (firms) who raise money

are concerned when high transaction costs lead to inefficient markets.

9.3 Why are common stockholders considered to be more at risk than the holders of other

types of securities?

In the hierarchy of lenders of funds to a firm, common stockholders have the most to

lose. In the event of a firm becoming bankrupt, the law requires that creditors of different

types, including bondholders, be paid off first. Next, preferred stockholders are paid off.

Finally, common stockholders receive their investment if any funds are still available.

Thus, common stockholders receive their money back last and are placed at most risk.

This feature of common equity is referred to as residual claim.

9.4 How can individual stockholders avoid double taxation?

Stock Valuation

Page 2 of 18

Double taxation refers to the fact that in the United States a firm’s income is taxed first

and then any dividends paid to investors get taxed at the personal tax rate. Thus, investors

pay taxes twice. Some investors who desire to get around this problem try to invest in

growth firms that do not pay out dividends but instead reinvest in the firm. This allows

the firms to grow with internal capital and leads to the firm’s value growing faster.

Stockholders benefit from rising stock prices and can sell some or all of their holdings

and generate capital gains, which are taxed at a lower rate than income.

9.5 What does it mean when a company has a very high P/E ratio? Give examples of

industries in which you believe high P/E ratios are justified.

A high P/E ratio implies that investors believe that the firm has good prospects for

earnings growth in the future. In fact, they believe that the firm will have higher growth

potential than firms with lower P/E ratios. Companies in industries that are fast growing

like biotech or any hi-tech industry have high P/E ratios. In the past, firms like Cisco and

Intel had very high P/E ratios. As these firms matured and settled to annual growth rates

of 15 percent or less, their P/E ratios have declined.

9.6 Preferred stock is considered to be nonparticipating because

a. investors do not participate in the election of the firm’s directors.

b. investors do not participate in the determination of the dividend payout policy.

c. investors do not participate in the firm’s earnings growth.

d. none of the above.

c. Nonparticipating implies that the preferred dividend remains constant regardless

of any increase in the firm’s earnings. Thus, investors in a firm’s preferred stock will not

see higher dividends when the firm’s earnings increase. Nor will they see a decrease if

the firm’s earnings decrease.

9.7 Explain why preferred stock is considered to be a hybrid of equity and debt securities.

The law considers preferred stock as equity. Thus, holders are treated as the firm’s

owners. Also, like common stockholders, preferred stockholders have to pay taxes on

their dividend income. However, preferred stockholders do not have any voting rights. In

addition, they receive only a fixed dividend just like bondholders. If a firm is liquidated,

then they receive a stated value (par value) similar to bondholders. Preferred stock is

rated by credit rating agencies just like bonds. Some preferred issues are convertible to

the firm’s common stock just as convertible bonds. Some preferred issues are not

perpetual and have a fixed maturity just like bonds.

Thus preferred stock is a hybrid security—like equity in some ways and like debt

security in others.

Page 3 of 18

9.8 Why is stock valuation more difficult than bond valuation?

Despite the availability of mathematical models to value stocks, it is more difficult to

apply valuation techniques to stocks than to bonds. First, unlike bonds, firms are not in

default if dividends are not declared. This makes it difficult to determine the size and

timing of the cash flows. Second, common stock, unlike bonds, does not have a fixed

maturity, and hence, it is difficult to determine a terminal value unlike bonds, which have

a maturity value. Next, it is easier to calculate the present value of a bond because the

required rate of return is observable. In the case of stocks, it is rather difficult to estimate

a required rate of return for many stocks and classify them into different risk groups.

9.9 You are currently thinking about investing in a stock valued at $25.00 per share. The

stock recently paid a dividend of $2.25 and is expected to grow at a rate of 5 percent for

the foreseeable future. You normally require a return of 14 percent on stocks of similar

risk. Is the stock overpriced, underpriced, or correctly priced?

This stock is underpriced at $25. Using the constant-growth model, we can arrive at a

price of $26.25 for this stock. This makes the stock underpriced, and it should be

considered a good buy.

9.10 Stock A and Stock B are both priced at $50 per share. Stock A has a P/E ratio of 17,

while Stock B has a P/E ratio of 24. Which is the more attractive investment, considering

everything else to be the same, and why?

Stock A is the more attractive investment because it has a lower P/E ratio. The lower the

P/E ratio, the larger the amount of earnings supporting the stock price. This makes Stock

A a more attractive investment than Stock B.

Page 4 of 18

Questions and Problems

BASIC

9.1 Present value of dividends: Fresno Corp is a fast growing company. The company

expects to grow at a rate of 30 percent over the next two years and then slow down to a

growth rate of 18 percent for the following three years. If the last dividend paid by the

company was $2.15, estimate the dividends for the next five years. Compute the present

value of these dividends if the required rate of return was 14 percent.

Solution:

0 1 2 3 4 5

├───────┼────────┼───────┼────────┼───────┤

D0 = $2.15 g1-2 = 30%; g3-5 = 18%; kCS = 14%

D1 = D0(1 + g1) = $2.15(1.30) = $2.795

D2 = D1(1 + g2) = $2.795(1.30) = $3.634

D3 = D2(1 + g3) = $3.634(1.18) = $4.288

D4 = D3(1 + g4) = $4.288(1.18) = $5.06

D5 = D4(1 + g4) = $5.06(1.18) = $5.97

$14.24=

++++=

+++

10.3$00

.3$89.2$80.2$45.2$

)14.1(

97.

)14.1(

06.5$

)14.

288.4$

)

14.1(

634.3$

)14.1(

795

.2$

)Dividends(PV

54321

9.2 Zero growth: Nynet, Inc., paid a dividend of $4.18 last year. The company does not

expect to increase its dividend for the next several years. If the required rate of return is

18.5 percent, what is the current price of the stock?

Solution:

D0 = $4.18; g = 0; R = 18.5%

$22.60=== 185.0

18.4$

9.3 Zero growth: Knight Supply Corp. has seen no growth for the last several years and

expects the trend to continue. The firm last paid a dividend of $3.56. If you require a rate

of return of 13 percent, what is the current stock price?

Solution:

D0 = $3.56; g = 0; R = 13%

$27.39=== 13.0

56.3$

9.4 Zero growth: Ron Santana is interested in buying the stock of First National Bank.

While the bank expects no growth in the near future, Ron is attracted by the dividend

Page 5 of 18

income. Last year, the bank paid a dividend of $5.65. If Ron Santana requires a return of

14 percent on such stocks, what is the maximum price he should be willing to pay?

Solution:

D0 = $5.65; g = 0; R = 14%

$40.36=== 14.0

65.5$

9.5 Zero growth: The current stock price of Largent, Inc., is $44.72. If the required rate of

return is 19 percent, what is the dividend paid by this firm, which is not expected to grow

in the near future?

Solution:

P0 = $44.72; R = 19%; D = ?;

$8.50=×=

19.072.44$D 19.0

72.44$

9.6 Constant growth: Moriband Corp. just declared a dividend of $2.15 yesterday. The

company is expected to grow at a steady rate of 5 percent for the next several years. If

stocks such as these require a rate of return of 15 percent, what should be the market

value of this stock?

Solution:

D0 = $2.15; g = 5%; R = 15%

$22.58=

−

05.015.0

)05.1(15.2$

)1(

9.7 Constant growth: Nyeil, Inc., is a consumer products firm growing at a constant rate of

6.5 percent. The firm’s last dividend was $3.36. If the required rate of return was 18

percent, what is the market value of this stock?

Solution:

D0 = $3.36; g = 6.5%; R = 18%

$31.12=

−

=065.018.0

)065.1(36.3$

Page 6 of 18

9.8 Constant growth: Reco Corp. is expected to pay a dividend of $2.25 next year. The

forecast for the stock price a year from now is $37.50. If the required rate of return is 14

percent, what is the current stock price? Assume constant growth.

Solution:

D1 = $2.25; P1 = $37.50; R = 14%

$34.88=

−

+=−

−

0755.014.0

25.2$

%55.7

.39$

00.3$

g25.2g5.3725.2$25.

g25.225.2g5.3725.5$

g25.2

25.2$)g14.0(50.37$

g14.0

)g1

(25.2$

50.37$

)g1(D

9.9 Constant growth: Proxicam, Inc., is expected to grow at a constant rate of 7 percent. If

the company’s next dividend is $1.15 and its current price is $22.35, what is the required

rate of return on this stock?

Solution:

D1 = $1.15; P0 = $23.00; g = 7%

12.15%==

−=−−

=−

−

35.22

7145.2

R35.2215.1565.1

15.1$)07.0R(35.22$ 07.0R

15.1$

35.22$

9.10 Preferred stock valuation: X-Centric Energy Company has issued perpetual preferred

stock with a par of $100 and a dividend of 4.5 percent. If the required rate of return is

8.25 percent, what is the stock’s current market price?

Solution:

D = 4.5% ($100) = $4.50; R = 8.25%

Page 7 of 18

$54.55=== 0825.0

50.4$

9.11 Preferred stock valuation: The First Bank of Ellicott City has issued perpetual preferred

stock with a $100 par value. The bank pays a quarterly dividend of $1.65 on this stock.

What is the current price of this preferred stock given a required rate of return of 11.6

percent?

Solution:

Quarterly dividend = $1.65

Required rate of return = R = 11.6%

$56.90=

=116.0

)465.1(

9.12 Preferred stock: The preferred stock of Axim Corp. is selling currently at $47.13. If

your required rate of return is 12.2 percent, what is the dividend paid by this stock?

Solution:

P0 = $47.13; R = 12.2%

$5.75=

×=

122.013

.47$D 122.0

13.47$P0

9.13 Preferred stock: Each quarter, Sirkota, Inc., pays a dividend on its perpetual preferred

stock. Today, the stock is selling at $63.37. If the required rate of return for such stocks is

15.5 percent, what is the quarterly dividend paid by this firm?

Solution:

P0 = $63.37; R = 15.5%

82.9$

155.037.63

$D 155.0

37.63$P0

×=

Annual dividend = $9.82

Quarterly dividend = $9.82 /4 = $2.46

INTERMEDIATE

9.14 Constant growth: Kay Williams is interested in purchasing the common stock of

Reckers, Inc., which is currently priced at $37.45. The company expects to pay a

dividend of $2.58 next year and expects to grow at a constant rate of 7 percent.

a. What should the market value of the stock be if the required rate of return is 14

percent?

Page 8 of 18

b. Is this a good buy?

Solution:

$36.86=

−

=07.014.0

58.2$

b. The stock is overpriced and not a good buy.

9.15 Constant growth: Your required rate of return is 23 percent. Ninex Corp. has just paid a

dividend of $3.12 and expects to grow at a constant rate of 5 percent. What is the

expected price of the stock three years from now?

Solution:

R = 23%; D0 = $3.12; g = 5%

$21.07=

−

05.023.0

)05.1(12.3

)g1(D

9.16 Constant growth: Jenny Banks is interested in buying the stock of Fervan, Inc., which is

growing at a constant rate of 6 percent. Last year, the firm paid a dividend of $2.65. Her

required rate of return is 16 percent. What is the current price for this stock? What would

be the price of the stock in year 5?

Solution:

g = 6%, D0 = $2.65, R = 16%

$37.59

$28.09

−

06.016.0

)06.1(65.2$

06.0

16.0

)06.1(65.2$

9.17 Nonconstant growth: Tre-Bien, Inc., is a fast growing technology company. The firm

projects a rapid growth of 30 percent for the next two years, then a growth rate of 17

percent for the following two years. After that, the firm expects a constant growth rate of

8 percent. The firm expects to pay its first dividend of $2.45 a year from now. If your

required rate of return on such stocks is 22 percent, what is the current price of the stock?

Solution:

g1 = g2 = 30%, g3 = g4 = 17%, g = 8%, D1 = $2.45, R = 22%

D1 = $2.45, D2 = $2.45(1.30) = $3.19, D3 = $3.19(1.17) = $3.73

D4 = $3.73(1.17) = $4.36, D5 = 4.36(1.08) = $4.71

64.33$

08.022.0

71.4$

−

Page 9 of 18

$23.35=

+++=

432

15.1705.2$14.2$01.2$P

)22.1(

)64.3336.4($

)22.1(

73.3$

)22.1(

19.3$

22.1

45.2$

)R1(

9.18 Nonconstant growth: ProCor, a biotech firm, forecasted the following growth rates for

the next three years: 35 percent, 28 percent, and 22 percent. The company then expects to

grow at a constant rate of 9 percent for the next several years. The company paid a

dividend of $1.75 last week. If the required rate of return is 20 percent, what is the market

value of this stock?

Solution:

g1 = 35%; g2 = 28%; g3 = 22%; g4 = 9%; D0 = $1.75; R = 20%

$27.37=

+++=

−

==+=

332

323

212

101

16.21$14.2$10.2$97.1$P

)20.1(

57.36

)20.1(

69.3$

)20.1(

02.3$

20.1

36.2$

)R1(

57.36$

09.020.0

02.4$

02.4$)09.1(69.3$)g1(DD

69.3$)22.1(02.3$)g1(DD

02.3$)28.1(36.2$)g1(DD

36.2$)35.1(75.1$)g1(DD

9.19 Nonconstant growth: Revarop, Inc., is on a fast growth stock and expects to grow at a

rate of 23 percent for the next four years. It then will settle to a constant-growth rate of 6

percent. The first dividend will be paid in year 3 and be equal to $4.25. If the required

rate of return is 17 percent, what is the current price of the stock?

Solution:

g1-4 = 23%; g = 6%; D3 = $4.25; R = 17%

D4 = D3 (1.23) = $4.25(1.23) = $5.23

Page 10 of 18

$32.34=+=

+++=

−

69.29$65.2$P

)17.1(

)48.5023.5(

)17.1(

25.4

00P

)R1(

40.50$

06.017.0

)06.1(23.5$

9.20 Nonconstant growth: Quansi, Inc., expects to pay no dividends for the next six years. It

has projected a growth rate of 25 percent for the next seven years. After seven years, the

firm will grow at a constant rate of 5 percent. Its first dividend to be paid in year 7 will be

worth $3.25. If your required rate of return is 24 percent, what is the stock worth today?

Solution:

gconstant = 5%; R = 24%; D7 = $3.25; D1 – D6 = 0

$4.71=

−

)24.1(

96.1725.3

)R1(

96.17$

05.024.0

)05.1(25.3

9.21 Nonconstant growth: Staggert Corp. will pay dividends of $5.00, $6.25, $4.75, and

$3.00 for the next four years. Thereafter, the company expects its growth rate to be at a

constant rate of 6 percent. If the required rate of return is 18.5 percent, what is the current

market price of the stock?

Solution:

D1 = $5; D2 = $6.25; D3 = 4.75; D4 = $3; g = 6%; R = 18.5%;

$25.95=+++=

+++

−

42.14$86.

2$45.4$22.4$P

)185.1(

)44.25$

3($

)185.1(

75.4$

)185.1(

25.6$

185

44.25$

06.0185.0

)06.1(3

)R1(

)R1

(

)R1(

9.22 Nonconstant growth: Diaz Corp. is growing rapidly at a rate of 35 percent for the next

seven years. The first dividend to be paid three years from now will be worth $5. After

Page 11 of 18

seven years the company will settle to a constant growth rate of 8.5 percent. What is the

market value for this stock given a required rate of return of 14 percent?

Solution:

g1-7 = 35%; D3 = $5.00; g = 8.5%; R = 14%

D1 = D2 = 0 ; D3 = $5

D4 = 5(1.35) = $6.75

D5 = $6.75(1.35) = $9.11

D6 = 9.11 (1.35) = $12.30

D7 = $12.30(1.35) = $16.61

D8 = 16.61(1.085) = $18.02

$155.29=

++++=

++++++=

−

58.137$60.5$73.4$00.4$38.3$

)14.1(

)64.32761.16(

)14.1(

30.12$

)14.1(

11.9$

)14.1(

75.6$

)14.1(

)R1(

64.327$

085.014.0

02.18$

76543

9.23 Nonconstant growth: Tin-Tin Waste Management, Inc., is growing rapidly. Dividends

are expected to grow at rates of 30 percent, 35 percent, 25 percent, and 18 percent over

the next four years. Thereafter the company expects to grow at a constant rate of 7

percent. The stock is currently selling at $47.85 and the required rate of return is 16

percent. Compute the dividend for the current year (D0).

Solution:

g1 = 30%; g2 = 35%; g3 = 25%; g4 = 18%; g = 7%; R = 16%; P0 = $47.85

$2.15==

++++=

−

+++=

26.22$

85.47$

]00.1743.141.130.112.1[D

)16.1( 07.016.0

)07.1)(5886.2(D

)16.1(

)18.1)(25.1)(35.1)(30.1(D

)16.1(

)25.1)(35.1)(30.1(D

)16.1(

)35.1)(30.1(D

16.1

)30.1(D

85.47$

)g1(

ADVANCED

Page 12 of 18

9.24 Riker Departmental Stores has forecasted a high growth rate of 40 percent for the next

two years, followed by growth rates of 25 percent and 20 percent for the following two

years. It then expects to stabilize its growth to a constant rate of 7.5 percent for the next

several years. The firm paid a dividend of $3.50 recently. If the required rate of return is

18 percent, what is the current market price of the stock?

Solution:

g1-2 = 40%; g3 = 25%; g4 = 20%; g = 7.5%; D0 = $3.50; R = 18%

$73.94=

++++=

−

==+=

4432

434

323

212

101

34.54$31.5$22.5$93.4$

15.4$P

)18.1(

35.105

)18.1(

29.10$

)18.1(

575.8$

)18.1(

86.6$

18.1

90.4$

)R1(

)

R1(

)R1(

35.105$

075.018.0

06.

11$

06.11$)075.1(29.10$)g

1(DD

29.10$)20.1(575.8$)g1(

575.8$)25.1(86.6$)g1(DD

.6$)40.1(90.4$)g1(DD

90.4

$)40.1(50.3$)g1(DD

9.25 Courtesy Bancorp issued perpetual preferred stock a few years ago. The bank pays an

annual dividend of $4.27, and your required rate of return is 12.2 percent.

a. What is the value of the stock given your required rate of return?

b. Should you buy this stock if its current market price is $34.41? Explain.

Solution:

a. D = $4.27; R = 12.2%

$35.00=== 122.0

27.4$

b. Since the stock is worth $35.00 but can be bought for $34.41, you should buy this

stock.

9.26 Rhea Kirby owns shares in Ryoko Corp. Currently, the market price of the stock is

$36.34. The company expects to grow at a constant rate of 6 percent for the foreseeable

future. Its last dividend was worth $3.25. Roger Kirby’s required rate of return for such

stocks is 16 percent. She wants to find out whether she should sell his shares or add to her

holdings.

Page 13 of 18

a. What is the value of this stock?

b. Based on your answer above, should she buy additional shares in Ryoko Corp?

Why or why not?

Solution:

a. $34.45=

−

=06.016

)06.1(25.3$

b. No, she should not buy more shares. This stock is overpriced with the stock

selling at a higher price than what it is worth. She should sell her shares.

9.27 Perry, Inc., declared a dividend of $2.50 yesterday. You are interested in investing in this

company, which has forecasted a constant-growth rate of 7 percent for the next several

years. Your required rate of return is 18 percent.

a. Compute the expected dividends D1, D2, D3, and D4.

b. Find the present value of these four dividends.

c. What is the price of the stock four years from now (i.e., P4)?

d. Calculate the present value of P4. Add the answer you got in part (b). What is the

price of the stock today?

e. Use the equation for constant growth (Equation 9.4) and compute the price of the

stock today.

Solution:

a. D0 = $2.50 g = 7% R = 18%

277.3$)07.1(50.2$D

063.3$)07.1(50.2$D

86.2$)07.1(50.2$D

675.2$)07.1(50.2$D

$7.87=

+++=

69.1

$86.1$05.227.2$

)18.1(

277.3$

)18.1(

063.3$

)18.1(

86.2$

)18.

675.2$

)Dividends(PV

4321

$31.88=

−

==+=

07.018.0

506.3$

506.3$)07.1(277.3$)g1(DD

$24.31=

44.16$87.7$

)P(PV)Dividends(PVP

44.16$

)18.1(

88.31$

)P(PV

Page 14 of 18

e. For a constant-growth stock:

$24.32=

−

=07.018.0

675.2$

9.28 Zweite Pharma is a fast growing drug company. The company forecasts that in the next

three years, its growth rates will be 30 percent, 28 percent, and 24 percent, respectively.

Last week it declared a dividend of $1.67. After three years the company expects a more

stable growth rate of 8 percent for the next several years. Your required rate of return is

14 percent.

a. Compute the dividends for the next three years and find their present value.

b. Calculate the price of the stock at the end of year 3 when the firm settles to a

constant-growth rate.

c. What is the current price of the stock?

Solution:

g1 = 30%; g2 = 28%; g3 = 24%; g = 8%; D0 = $1.67; R = 14%

$6.37

=++=

++=

==+=

33.2$14.2$90.1$

)14.1(

446.3$

)14.1(

779.2$

14.1

171.2$

)R1(

)Dividends(PV

446.3$)24.1(779.2$)g1(DD

779.2$)28.1(171.2$)g1(DD

171.2$)30.1(67.1$)g1(DD

323

212

101

$62.03=

−

==+=

08.014.0

722.3$

722.3$)08.1(446.3$)g1(DD

$48.24=

87.41$37.6$

)P(PV)Dividends(PVP

87.41$

)14.1(

03.62$

)P(PV

9.29 Triton, Inc., expects to grow at a rate of 22 percent for the next five years and then settle

to a constant-growth rate of 6 percent. The company’s most recent dividend was $2.35.

The required rate of return is 15 percent.

Page 15 of 18

a. Find the present value of the dividends during the rapid growth period.

b. What is the price of the stock at the end of year 5?

c. What is the price of the stock today?

Solution:

g1-5 = 22%; g = 6%; D0 = $2.35; R = 15%

$14.09=

++++=

+++

==+=

16.3$98.2$81.2

65.2$49.2$

)15.1(

351.6

)15.1

(

206.5$

)15.1(

267.4$

)15.1(

498.3

15.1

867.2$

)R1(

)R1

(

)R1(

)Dividends(PV

351.6$)

22.1(206.5$)g1(DD

206.5$)22.1

(267.4$)g1(DD

267.4$)22.1(498

.3$)g1(DD

498.3$)22.1(867.2

)g1(DD

867.2$)22.1(35.2$)g

1(DD

5432

434

212

101

$74.80=

−

==+=

06.015.0

732.6$

732.6$)06.1(351.6$)g1(DD

$51.28=

19.37$09.14$

)P(PV)Dividends(PVP

19.37$

)15.1(

80.74$

)P(PV

9.30 Ceebros Builders are expanding very fast and expect to grow at a rate of 25 percent for

the next four years. They recently declared a dividend of $3.60 but do not expect to pay

any dividends for the next three years. In year 4, they intend to pay a $5 dividend and

thereafter grow it at a constant-growth rate of 6 percent. The required rate of return on

such stocks is 20 percent.

a. Calculate the present value of the dividends during the fast growth period.

b. What is the price of the stock at the end of the fast growth period (P4)?

c. What is the stock price today?

d. Would today’s stock price be driven by the length of time you intend to hold the

stock?

Page 16 of 18

Solution:

a. g1-4 = 25% g5 = 6% D0 = $3.60 D4 = $5.00 kcs = 20%

$2.41=+++=

)20.1(

000)Dividends(PV

$37.86=

−

=06.020.0

)06.1(00.5$

$20.67=+=

)20.1(

86.37$

41.2$P

d. No, the length of the holding period has no bearing on today’s stock price.

Page 17 of 18

Sample Test Problems

9.1 Mason Corp. is a manufacturer of consumer staples and has experienced no growth for

the last five years while paying out a dividend of $3.50 every year. The CFO of the firm

expects the firm to have no growth for the foreseeable future. If your required rate of

return is 10 percent, what is the price of this stock today?

Solution:

D0 = $3.50; g = 0; R = 10%

$35.00=== 10.0

50.3$

9.2 Bucknell, Inc., recently paid a dividend of $2.10. The firm forecasts a growth of 6 percent

for the next several years. What is the price of the stock today given your discount rate of

13 percent?

Solution:

D0 = $2.10; g = 6%; R = 13%

$31.80=

−

06.013.0

)06.1(10.2$

)g1(D

P01

9.3 Bradley Corp. is growing at a constant rate of 7.2 percent every year. Last week the

company paid a dividend of $1.85. If your required rate of return is 15 percent, what will

be the stock’s price four years from now?

Solution:

D0 = $1.85; g = 7.2%; R = 15%

$33.58=

−

==+=

072.015.0

619.2$

619.2$)072.1(85.1$)g1(DD

9.4 Wichita Technologies is expected to grow at a rate of 35 percent for the next three years

and then settle to a constant-growth rate of 7 percent. The company will pay no dividend

for the first two years and then pay a dividend of $1.25 in year three. What is the

company’s price when the company’s supernormal growth ends? What is the price of the

stock today? The firm’s required rate of return is 12 percent.

Solution:

g1-3 = 35%; g = 7%; D1 = D2 = $0; D3 = $1.25; R = 12%

Page 18 of 18

$19.94=

+++=

−

==+=

05.19$89.0$P

)12.1(

76.26$

)12.1(

25.1$

0$0$P

)R1(

76.26$

07.012.0

338.1$

338.1$)07.1(25.1$)g1(DD

9.5 UNC Bancorp has issued preferred stock with no maturity date. It has a par value of $100

and pays a quarterly dividend of $2.25. If your required rate of return is 8 percent, what is

the price of the stock today?

Solution:

Quarterly dividend = $2.25

Required rate of return = R = 8%

$112.50=

=08.0

)425.2(

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