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]单项选择题
A
a. $60
B
b. $18
C
c. $50
D
d. $30

Question

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]

BlackTom AI · Accepted Answer

For a constant annual dividend with no growth the stock is valued as a perpetuity. Using the perpetuity form of the Gordon Growth Model with growth g = 0: P0 = D / (r − g) = D / r.

Relevant knowledge points:
- A perpetuity pays the same cash flow forever; its present value equals payment divided by the discount rate.
- The Gordon Growth Model reduces to the perpetuity formula when g = 0.
- Dividend yield = D / P0, and must equal the required return when price is set correctly for a no-growth dividend.

Step-by-step reasoning and calculations:
1. Identify the dividend D = $3 and the required return r = 6% = 0.06 (in decimal form).
2. Apply the formula P0 = D / r.
3. Compute P0 = 3 / 0.06.
4. Perform the division: 0.06 = 6/100, so 3 ÷ 0.06 = 3 × (1 / 0.06) = 3 × 16.6666667 = 50.

All intermediate arithmetic: 3 / 0.06 = 3 × (100/6) = 300/6 = 50.

Why this is correct:
- With P0 = $50, the dividend yield is 3 / 50 = 0.06 or 6%, which exactly matches the investors’ required return. That equality is the defining condition for fair price when dividends are constant forever.

Why the other options are incorrect:
- $60 would imply a yield of 3 / 60 = 5%, which is below the required 6%, so investors would pay less.
- $18 implies 3 / 18 ≈ 16.67% yield, far above the required return (price would be too low relative to required return).
- $30 implies 3 / 30 = 10% yield, again above the required 6% so the price is too low.

Conclusion: The correct price is $50, which matches option c.

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]单项选择题

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