Mathilda's Vineyard recently paid a $3.60 annual dividend on its common stock. This dividend increases at an average rate of 3.5% per year. The stock is currently selling for $62.10 a share. What is the market rate of return?

Question

BlackTom AI · Accepted Answer

Using the Gordon growth model (constant-growth dividend discount model) the required return r equals the next expected dividend divided by the current price plus the dividend growth rate: r = D1/P0 + g.

Knowledge points:
- D0 is the most recently paid dividend; D1 = D0(1 + g) is the dividend expected next period.
- For a stock with constant growth g, the market price P0 = D1 / (r − g). Rearranged, r = D1/P0 + g.
- The market rate of return equals the dividend yield (D1/P0) plus the growth rate.

Step-by-step calculation with all intermediate steps:
1. Identify given values: D0 = $3.60, g = 3.5% = 0.035, P0 = $62.10.
2. Compute next period’s dividend D1:
   D1 = D0 × (1 + g) = 3.60 × 1.035 = 3.60 + 0.126 = $3.726.
3. Compute dividend yield D1/P0:
   D1/P0 = 3.726 ÷ 62.10 = 0.0600 = 6.00%.
   (Note: 62.10 × 0.06 = 3.726 confirms the exact division.)
4. Add the growth rate to get r:
   r = 0.0600 + 0.035 = 0.0950 = 9.50%.

Why the correct answer is correct:
The Gordon model shows the required return equals the immediate yield from next dividend plus expected growth. Using D1 rather than D0 is essential; using D0 would understate the yield. The computed yield (6.00%) plus growth (3.50%) gives 9.50%.

Why the other options are incorrect:
- 6.0% equals the dividend yield D1/P0 only, omitting growth, so it understates the total required return.
- 5.5%, 3.5%, and 2.5% do not match the model’s result; 3.5% is just the growth rate, and 2.5% or 5.5% have no basis from the given dividend and price.

Conclusion: The market rate of return is 9.5%, which matches the provided correct answer.

Mathilda's Vineyard recently paid a $3.60 annual dividend on its common stock. This dividend increases at an average rate of 3.5% per year. The stock is currently selling for $62.10 a share. What is the market rate of return?单项选择题

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