You are considering purchasing stock in Canyon Echo. You feel the company will increase its dividend at 3.2 percent indefinitely. The company just paid a dividend of $3.83 and you feel that the required return on the stock is 12.4 percent. What is the price per share of the company's stock?单项选择题
A
$41.63
B
$38.67
C
$42.96
D
$40.81
E
$30.89

Question

You are considering purchasing stock in Canyon Echo. You feel the company will increase its dividend at 3.2 percent indefinitely. The company just paid a dividend of $3.83 and you feel that the required return on the stock is 12.4 percent. What is the price per share of the company's stock?单项选择题

A

$41.63

B

$38.67

C

$42.96

D

$40.81

E

$30.89

BlackTom AI · Accepted Answer

Use the Gordon (constant-growth) dividend discount model: P0 = D1 / (r − g).

1) Relevant concepts
- Dividend discount model (Gordon Growth): values a stock as the present value of perpetually growing dividends, valid only when growth rate g < required return r.
- D0 = most recent dividend; D1 = dividend in one year = D0 × (1 + g).

2) Step-by-step reasoning and calculations
- Given: D0 = $3.83, g = 3.2% = 0.032, r = 12.4% = 0.124.
- Compute next year’s dividend: D1 = D0 × (1 + g) = 3.83 × 1.032.
  - Intermediate: 3.83 × 0.032 = 0.12256
  - So D1 = 3.83 + 0.12256 = 3.95256
- Compute denominator: r − g = 0.124 − 0.032 = 0.092
- Compute price: P0 = D1 / (r − g) = 3.95256 / 0.092
  - Division: 3.95256 ÷ 0.092 = 42.9613043478...
  - Round to two decimals: $42.96

3) Intermediate steps shown
- D1 = 3.95256
- r − g = 0.092
- P0 = 3.95256 / 0.092 ≈ 42.9613 ⇒ $42.96

4) Why this answer is correct
- The Gordon model requires next period’s dividend in the numerator; using D1 yields $42.96. Growth is less than required return (0.032 < 0.124), so the model is valid and produces the computed intrinsic price.

5) Why other options are incorrect
- $41.63 corresponds to mistakenly using D0 instead of D1: 3.83 / 0.092 = 41.6304.
- $38.67, $40.81, and $30.89 do not match the correct arithmetic with the given D0, g, and r—these reflect either incorrect dividend timing, incorrect growth/return inputs, or calculation errors.

6) Conclusion
The correct calculated price per share is $42.96, which matches the provided answer.

类似问题

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?

You are calculating the intrinsic value of a company that paid a dividend of $2.17 last year. Analysts believe that dividends will grow 14.6% this year, 4.6% next year, and 0.9% thereafter and the cost of equity is 8.7%. What is the current price of the stock? (Answer in $, so $16.21 is 16.21).

Using a dividend discount model, find the intrinsic value (price at time zero) for a firm whose expected dividend is $1.88 and growth in dividends for year 2, 3, and 4 is 23.8% and constant growth afterwards is 0.58%. The cost of equity is 6.91%. (Answer in 2 decimal places, 6.21 for $6.21).

A stock pays a constant annual dividend of $3. If investors require a 6% return, what price would an investor be expected to pay per share?[Fill in the blank]

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