Reading 46: Discounted Dividend Valuation - LOS i ～ Q1-5 discount, require, percent, expected, forever

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1.A firm's dividend per share in the most recent year is $4 and is expected to grow at 6 percent per year forever. If its shareholders require a return of 14 percent, the value of the firm's stock (per share) using the single-stage dividend discount model is:

A)   $28.57.

B)   $53.00.

C)   $50.00.

D)   $71.33.

2.Jand, Inc., currently pays a dividend of $1.22, which is expected to grow at 5 percent. If the current value of Jand’s shares based on the Gordon model is $32.03, what is the required rate of return?

A)   9%.

B)   7%.

C)   8%.

D)   10%.

3.A firm currently pays a dividend of $1.77, which is expected to grow at a rate of 4 percent. If the required return is 10 percent, what is the current value of the shares using the Gordon growth model?

A)   $30.68.

B)   $29.50.

C)   $29.76.

D)   $31.75.

4.Jax, Inc., pays a current dividend of $0.52 and is projected to grow at 12 percent. If the required rate of return is 11 percent, what is the current value based on the Gordon growth model?

A)   $39.47.

B)   unable to determine value using Gordon model.

C)   $53.32.

D)   $58.24.

5.A company reports January 1, 2002, retained earnings of $8,000,000, December 31, 2002, retained earnings of $10,000,000, and 2002 net income of $5,000,000.  The company has 1,000,000 shares outstanding and dividends are expected to grow at a rate of 5 percent per year.

What is the expected dividend at the end of 2003?

A)   $3.00.

B)   $3.15.

C)   $13.00.

D)   $13.65.

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答案和详解如下：

1.A firm's dividend per share in the most recent year is $4 and is expected to grow at 6 percent per year forever. If its shareholders require a return of 14 percent, the value of the firm's stock (per share) using the single-stage dividend discount model is:

A)   $28.57.

B)   $53.00.

C)   $50.00.

D)   $71.33.

The correct answer was B)

The value of the firm's stock is: $4 x 1.06/(0.14 - 0.06) = $53.00

2.Jand, Inc., currently pays a dividend of $1.22, which is expected to grow at 5 percent. If the current value of Jand’s shares based on the Gordon model is $32.03, what is the required rate of return?

A)   9%.

B)   7%.

C)   8%.

D)   10%.

The correct answer was A)

The required return is 9%:

r = ( [$1.22(1 + 0.05)] / $32.03 ) + 0.05 = 0.09 or 9%

3.A firm currently pays a dividend of $1.77, which is expected to grow at a rate of 4 percent. If the required return is 10 percent, what is the current value of the shares using the Gordon growth model?

A)   $30.68.

B)   $29.50.

C)   $29.76.

D)   $31.75.

The correct answer was A)

The current value of the shares is $30.68:

V₀ = [$1.77(1 + 0.04)] / (0.10 – 0.04)] = $30.68

4.Jax, Inc., pays a current dividend of $0.52 and is projected to grow at 12 percent. If the required rate of return is 11 percent, what is the current value based on the Gordon growth model?

A)   $39.47.

B)   unable to determine value using Gordon model.

C)   $53.32.

D)   $58.24.

The correct answer was B)

The Gordon growth model cannot be used if the growth rate exceeds the required rate of return.

5.A company reports January 1, 2002, retained earnings of $8,000,000, December 31, 2002, retained earnings of $10,000,000, and 2002 net income of $5,000,000.  The company has 1,000,000 shares outstanding and dividends are expected to grow at a rate of 5 percent per year.

What is the expected dividend at the end of 2003?

A)   $3.00.

B)   $3.15.

C)   $13.00.

D)   $13.65.

The correct answer was B)

The first step is to determine 2002 dividends paid as $8,000,000 + $5,000,000 – 10,000,000 or $3,000,000. The next step is to find the dividend per share (i.e. $3,000,000 divided by 1,000,000 shares or $3.00 per share). Applying the 5 percent growth rate, next year’s expected dividend is $3.15 or $3.00 times 1.05.