
Answer-first summary for fast verification
Answer: payout ratio.
## Explanation In the Gordon growth model, the justified forward P/E ratio is given by: \[ \frac{P_0}{E_1} = \frac{D_1/E_1}{r - g} = \frac{b}{r - g} \] Where: - \(P_0\) = current price - \(E_1\) = expected earnings next period - \(D_1\) = expected dividend next period - \(b\) = payout ratio (\(D_1/E_1\)) - \(r\) = required rate of return - \(g\) = sustainable growth rate From this formula: 1. **Payout ratio (b)**: The justified P/E ratio is **positively related** to the payout ratio. As the payout ratio increases, the P/E ratio increases, all else equal. 2. **Dividend growth rate (g)**: The justified P/E ratio is **positively related** to the growth rate, but only when \(r > g\). However, the question asks for "always positively related," and this relationship holds only under the condition that \(r > g\). 3. **Required rate of return (r)**: The justified P/E ratio is **negatively related** to the required rate of return. As \(r\) increases, the denominator increases, reducing the P/E ratio. Therefore, among the three options, only the **payout ratio** has an **always positive** relationship with the justified forward P/E ratio in the Gordon growth model. **Correct Answer: A**
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