Global corporation projects to pay $1 quarterly dividends, has the current stock price at $60 and its cost of Equity is estimated to be 10%. What is the expected Dividend Growth rate?

Question

BlackTom AI · Accepted Answer

Gordon growth model (constant-growth dividend discount model) applies: P0 = D1 / (r - g), where P0 is current price, D1 is next-year total dividend, r is cost of equity, and g is dividend growth.

1) Relevant concepts:
- Convert quarterly dividends to an annual dividend: four quarters per year.
- Use the Gordon Growth Model because dividends are assumed to grow at a constant rate.
- Rearranging the model yields g = r - (D1 / P0).

2) Step-by-step reasoning and calculations:
- Quarterly dividend = $1, so annual dividend D1 = 4 × $1 = $4.
- Given: P0 = $60, r = 10% = 0.10.
- Plug into formula: P0 = D1 / (r - g) → r - g = D1 / P0.
- Compute D1 / P0 = 4 / 60 = 0.0666667 (6.66667%).
- Therefore g = r - (D1 / P0) = 0.10 - 0.0666667 = 0.0333333.

3) Intermediate steps shown:
- D1 = 4
- D1 / P0 = 4 / 60 = 0.0666667
- g = 0.10 - 0.0666667 = 0.0333333 → 3.33333%

4) Why the correct answer is correct:
- The model directly links price, expected dividend, required return, and growth. Using the annual dividend and the given required return, solving the formula yields a growth rate of 3.33%, which exactly satisfies P0 = 4 / (0.10 - 0.0333333) = 4 / 0.0666667 = $60.

5) Why the other choices are incorrect:
- 8.83%: would imply r = D/P + g = 6.667% + 8.83% ≈ 15.5%, not the given 10%.
- 1.17%: too low; 0.0117 + 0.066667 = 0.078367 ≠ 0.10, so it doesn't satisfy the model.
- 6.67%: equals the dividend yield (D1/P0), not the growth rate; plugging it in would make r - g = 0.10 - 0.06667 = 0.03333, inconsistent.

Conclusion: The calculated dividend growth rate is 3.33%, matching the provided correct answer.

Global corporation projects to pay $1 quarterly dividends, has the current stock price at $60 and its cost of Equity is estimated to be 10%. What is the expected Dividend Growth rate?单项选择题

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