Using the Gordon growth model, a stock's price will increase if

Question

BlackTom AI · Accepted Answer

In the Gordon growth model P0 = D1 / (r − g), so an increase in the dividend growth rate g (with r > g) raises the numerator/denominator relationship and increases P0.

1. Relevant knowledge points and concepts
- Gordon (constant-growth) model: P0 = D1 / (r − g), where P0 is current price, D1 is next-period dividend, r is required rate of return, and g is perpetual dividend growth rate.
- The model requires r > g for the price to be finite.
- Price sensitivity: P0 moves inversely with (r − g); lowering the denominator increases price.

2. Step-by-step reasoning
- Holding D1 and r constant, raising g reduces (r − g).
- A smaller positive denominator yields a larger quotient, so P0 increases.
- Conversely, increasing r or decreasing g increases the denominator and reduces P0.

3. Calculations with intermediate steps (numerical example)
- Let D1 = $2.00, r = 10% = 0.10, initial g = 3% = 0.03:
  P0 = 2.00 / (0.10 − 0.03) = 2.00 / 0.07 = $28.571.
- Increase g to 5% = 0.05 (same D1 and r):
  P0 = 2.00 / (0.10 − 0.05) = 2.00 / 0.05 = $40.00.
- Price rises from $28.57 to $40.00, confirming that a higher g raises P0.

4. Why the correct answer is correct
- The algebraic structure shows P0 increases when g increases (r fixed), because the denominator (r − g) becomes smaller. The numerical example illustrates this clearly.

5. Why the other options are incorrect
- "The required rate of return on equity rises": If r rises (with g fixed), (r − g) increases, so P0 falls, not rises.
- "The expected sales price rises.": The Gordon model gives current value from dividends and r/g; an “expected sales price” is not a direct input to P0 in this model and does not imply a higher P0 unless it implies higher dividends or lower r − g.
- "The growth rate of dividends falls.": A lower g increases (r − g), reducing P0; thus price would decrease.

6. Conclusion
- Therefore, under the Gordon growth model (with r > g), the stock’s price will increase if the dividend growth rate increases. This matches the provided answer: "the dividend growth rate increases."

Using the Gordon growth model, a stock's price will increase if单项选择题

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