A common stock pays an annual dividend per share of $1.80. The risk-free rate is 5%, and the risk premium for this stock is 4%. If the annual dividend is expected to remain at $1.80 per share, what is the value of the stock?Single choice
A
$17.78
B
$20.00
C
$40.00
D
None of these options are correct.

Question

A common stock pays an annual dividend per share of $1.80. The risk-free rate is 5%, and the risk premium for this stock is 4%. If the annual dividend is expected to remain at $1.80 per share, what is the value of the stock?Single choice

A

$17.78

B

$20.00

C

$40.00

D

None of these options are correct.

BlackTom AI · Accepted Answer

For a constant annual dividend, the Gordon growth model with zero growth (g = 0) applies: the stock is valued as a perpetuity, so P0 = D / r.

1) Relevant knowledge points and concepts
- Dividend discount model (Gordon growth model) reduces to a perpetuity when dividends are constant: P0 = D / (r - g) with g = 0 → P0 = D / r.
- Required rate of return r is the sum of the risk-free rate and the stock’s risk premium (r = rf + risk premium).
- Assumes dividends are paid annually and will remain constant forever.

2) Step-by-step reasoning
- Compute the required return: r = risk-free rate + risk premium.
- Substitute the constant dividend D and r into the perpetuity formula P0 = D / r.
- Solve for P0.

3) Calculations (all intermediate steps)
- rf = 5% = 0.05
- Risk premium = 4% = 0.04
- r = 0.05 + 0.04 = 0.09 (9%)
- D = $1.80
- P0 = D / r = 1.80 / 0.09
- 1.80 / 0.09 = 20.00

4) Why the correct answer is correct
Because the dividend is constant, the stock’s present value equals the perpetual dividend divided by the required return. Using the required return 9% gives P0 = $20.00, which correctly prices the perpetual $1.80 dividend stream.

5) Why the other options are incorrect
- $17.78 would imply a higher required return (~10.12%), not supported by rf + risk premium given.
- $40.00 would imply a required return of 4.5% (1.80/40), inconsistent with rf + risk premium = 9%.
- "None of these" is incorrect because one of the listed options ($20.00) matches the correct calculation.

6) Conclusion
The stock value is $20.00, which matches the provided correct answer.

A common stock pays an annual dividend per share of $1.80. The risk-free rate is 5%, and the risk premium for this stock is 4%. If the annual dividend is expected to remain at $1.80 per share, what is the value of the stock?Single choice

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