Questions: The constant-growth dividend model will provide invalid solutions when: the growth rate of the stock exceeds the required rate of return for the stock. the growth rate of the stock is less than the required rate of return for the stock. the growth rate of the stock is equal to the risk-free rate. none of the above.

The answer is the first one: the growth rate of the stock exceeds the required rate of return for the stock.

Explanation for each option:

1. The growth rate of the stock exceeds the required rate of return for the stock.

   • This is correct. The constant-growth dividend model, also known as the Gordon Growth Model, assumes that the growth rate (g) is less than the required rate of return (r). If the growth rate exceeds the required rate of return, the model will produce invalid or nonsensical results because it implies that the stock's value would be infinite or negative, which is not realistic.

2. The growth rate of the stock is less than the required rate of return for the stock.

   • This is incorrect. The model is valid when the growth rate is less than the required rate of return. This is the fundamental assumption of the model, ensuring that the present value of future dividends converges to a finite number.

3. The growth rate of the stock is equal to the risk-free rate.

   • This is incorrect. While the growth rate being equal to the risk-free rate might have implications for the stock's valuation, it does not inherently invalidate the constant-growth dividend model. The key condition for the model's validity is that the growth rate must be less than the required rate of return, not specifically related to the risk-free rate.

4. None of the above.

   • This is incorrect because the first option is a valid condition under which the constant-growth dividend model would provide invalid solutions.

Summary: The constant-growth dividend model will provide invalid solutions when the growth rate of the stock exceeds the required rate of return for the stock.