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