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Reading 46: Discounted Dividend Valuation - LOS q ~ Q11

11.An analyst has compiled the following financial data for ABC, Inc.

ABC, Inc. Valuation Scenarios

Item

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Year 0 Dividends per Share

$1.50

$1.50

$1.50

$1.50

Long-term Treasury Bond Rate

4.0%

4.0%

5.0%

5.0%

Expected Return on the S& 500

12.0%

12.0%

12.0%

12.0%

Beta

1.4

1.4

1.4

1.4

g (growth rate in dividends)

0.0%

3.0%

Years 1-3, g=12.0%

After Year 3, g=3.0%

Year 1, g=20%

Year 2, g=18%

Year 3, g=16%

Year 4, g=9%

Year 5, g=8%

Year 6, g=7%

After Year 6, g=4%

If year 0 dividend is $1.50 per share, the required rate of return of shareholders is 15.2 percent, what is the value of ABC, Inc.'s stock price using the H-Model? Assume that the growth in dividends has been 20 percent for the last 8 years, but is expected to decline 3 percent per year for the next 5 years to a stable growth rate of 5 percent.

A)   $19.85.

B)   $20.95.

C)   $24.26.

D)   $26.47.

12.An analyst has forecast that Apex Company, which currently pays a dividend of $6.00, will continue to grow at 8 percent for the next two years and then at a rate of 5 percent thereafter. If the required return is 10 percent, based on a two-stage model what is the current value of Apex shares?

A)   $133.13.

B)   $126.24.

C)   $127.78.

D)   $131.17.

13.A company’s stock beta is 0.76, the market return is 10 percent, and the risk-free rate is 4 percent.  The stock will pay no dividends for the first two years, followed by a $1 dividend and $2 dividend, respectively.  An investor expects to sell the stock for $10 at the end of four years.

What price is an investor willing to pay for this stock?

A)   $11.03.

B)   $13.00.

C)   $10.16.

D)   $9.42.

14.An analyst has forecast that Hapex Company, which currently pays a dividend of $6.00, will grow at a rate of 8 percent, declining to 5 percent over the next two years, and remain at that rate thereafter. If the required return is 10 percent, based on an H-model what is the current value of Hapex shares?

A)   $126.24.

B)   $129.60.

C)   $127.78.

D)   $131.17.

15An analyst has forecasted dividend growth for Triple Crown, Inc., to be 8 percent for the next two years, declining to 5 percent over the following three years, and then remaining at 5 percent thereafter. If the current dividend is $4.00, and the required return is 10 percent, what is the current value of Triple Crown shares based on a three-stage model?

A)   $91.11.

B)   $68.88.

C)   $92.23.

D)   $73.68.

答案和详解如下:

11.An analyst has compiled the following financial data for ABC, Inc.

ABC, Inc. Valuation Scenarios

Item

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Year 0 Dividends per Share

$1.50

$1.50

$1.50

$1.50

Long-term Treasury Bond Rate

4.0%

4.0%

5.0%

5.0%

Expected Return on the S& 500

12.0%

12.0%

12.0%

12.0%

Beta

1.4

1.4

1.4

1.4

g (growth rate in dividends)

0.0%

3.0%

Years 1-3, g=12.0%

After Year 3, g=3.0%

Year 1, g=20%

Year 2, g=18%

Year 3, g=16%

Year 4, g=9%

Year 5, g=8%

Year 6, g=7%

After Year 6, g=4%

If year 0 dividend is $1.50 per share, the required rate of return of shareholders is 15.2 percent, what is the value of ABC, Inc.'s stock price using the H-Model? Assume that the growth in dividends has been 20 percent for the last 8 years, but is expected to decline 3 percent per year for the next 5 years to a stable growth rate of 5 percent.

A)   $19.85.

B)   $20.95.

C)   $24.26.

D)   $26.47.

The correct answer was B)

Use the H Model to value the firm. The H Model assumes that the initial growth rate (ga) will decline linearly to the stable growth rate (gn). The high growth period is assumed to last 2H years. Hence, the value per share = DPSo(1+gn)/(r-gn) + DPSo*H*(ga-gn)/(r-gn) =

(1.5 * 1.05)/(0.152 - 0.05) + [1.5 * (5/2) * (0.2 - 0.05)]/(0.152 - 0.05) =

1.575/0.102 + 0.5625/0.102 =

15.44 + 5.51 = $20.95

12.An analyst has forecast that Apex Company, which currently pays a dividend of $6.00, will continue to grow at 8 percent for the next two years and then at a rate of 5 percent thereafter. If the required return is 10 percent, based on a two-stage model what is the current value of Apex shares?

A)   $133.13.

B)   $126.24.

C)   $127.78.

D)   $131.17.

The correct answer was A)

The current value of Apex shares is $133.13.

V0 = [($6 × 1.08) / 1.10] + [($6 × (1.08)2) / 1.102] + [ ($6 × (1.08)2 × 1.05) / (1.102 × (0.10 – 0.05))] = $133.13

13.A company’s stock beta is 0.76, the market return is 10 percent, and the risk-free rate is 4 percent.  The stock will pay no dividends for the first two years, followed by a $1 dividend and $2 dividend, respectively.  An investor expects to sell the stock for $10 at the end of four years.

What price is an investor willing to pay for this stock?

A)   $11.03.

B)   $13.00.

C)   $10.16.

D)   $9.42.

The correct answer was D)

The first step is to determine the required rate of return as 4% + [(10% – 4%) × 0.76] or 8.56 percent per year. The second step is to determine the present value of all future expected cash flows, including the terminal $10 stock price, discounted back four years to today. The solution is shown below.

Year

CF

1

0

2

0

3

1

4

2

4

10

0/1.0856 + 0/(1.0856)2 + 1/(1.0856)3 + (2 + 10)/(1.0856)4 = $9.42

14.An analyst has forecast that Hapex Company, which currently pays a dividend of $6.00, will grow at a rate of 8 percent, declining to 5 percent over the next two years, and remain at that rate thereafter. If the required return is 10 percent, based on an H-model what is the current value of Hapex shares?

A)   $126.24.

B)   $129.60.

C)   $127.78.

D)   $131.17.

The correct answer was B)

The current value of Hapex shares is $129.60.

V0 = [$6(1 + 0.05) + $6(2/2)(0.08 – 0.05)] / (0.10 – 0.05) = $129.60

15An analyst has forecasted dividend growth for Triple Crown, Inc., to be 8 percent for the next two years, declining to 5 percent over the following three years, and then remaining at 5 percent thereafter. If the current dividend is $4.00, and the required return is 10 percent, what is the current value of Triple Crown shares based on a three-stage model?

A)   $91.11.

B)   $68.88.

C)   $92.23.

D)   $73.68.

The correct answer was C)

V0 = $4(1.08) / 1.10 + $4(1.08)2 / (1.10)2 + [$4(1 + 0.08)2(3/2)(0.08 – 0.05) + $4(1.08)2(1.05)] / [(1.10)2(0.10 – 0.05)] = $92.23

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