Answer: 75%

## Explanation **Step 1: Understand the Gordon Growth Model** The Gordon Growth Model (also known as the Dividend Discount Model) formula is: \[ P_0 = \frac{D_1}{r - g} \] Where: - \( P_0 \) = Current stock price - \( D_1 \) = Expected dividend per share next year = $2 - \( r \) = Required rate of return - \( g \) = Constant dividend growth rate = 4% = 0.04 **Step 2: Calculate initial stock value (when r = 8%)** \[ P_{0\_initial} = \frac{2}{0.08 - 0.04} = \frac{2}{0.04} = 50 \] So the initial stock price is $50. **Step 3: Calculate new stock value (when r = 14%)** \[ P_{0\_new} = \frac{2}{0.14 - 0.04} = \frac{2}{0.10} = 20 \] So the new stock price is $20. **Step 4: Calculate percentage decrease** \[ \text{Decrease} = \frac{P_{0\_initial} - P_{0\_new}}{P_{0\_initial}} \times 100\% \] \[ \text{Decrease} = \frac{50 - 20}{50} \times 100\% = \frac{30}{50} \times 100\% = 0.6 \times 100\% = 60\% \] Wait, this gives 60%, but let me check the options... **Step 5: Verify calculation** Actually, let me recalculate more carefully: Initial price: \( \frac{2}{0.08 - 0.04} = \frac{2}{0.04} = 50 \) New price: \( \frac{2}{0.14 - 0.04} = \frac{2}{0.10} = 20 \) Percentage decrease: \( \frac{50 - 20}{50} = \frac{30}{50} = 0.6 = 60\% \) But the options are 50%, 60%, and 75%. The calculation shows 60%, which corresponds to option B. **Step 6: Check if there's a different interpretation** Looking at the problem again, the question asks "the value of the stock decreases by:" and the options are percentages. My calculation shows 60%, which is option B. However, let me double-check if I should use the formula differently: Percentage decrease = \( \frac{\text{Old Value} - \text{New Value}}{\text{Old Value}} \) = \( \frac{50 - 20}{50} = 0.6 = 60\% \) **Conclusion:** The correct answer is **60%**, which corresponds to **Option B**. **Key Insight:** The Gordon Growth Model is highly sensitive to changes in the required rate of return (r) because it appears in the denominator as (r - g). A 6% increase in r (from 8% to 14%) causes a 60% decrease in stock value because: 1. The denominator increases from 4% to 10% (a 150% increase) 2. This causes the stock price to decrease from $50 to $20 (a 60% decrease)

Author: LeetQuiz .