Explanation

Using the Gordon growth model formula for justified forward P/E:

Formula: $\frac{P_0}{E_1} = \frac{1 - b}{r - g}$

Where:

• $\frac{P_0}{E_1}$ = Justified forward P/E = 10
• $b$ = Retention rate = 40% = 0.40
• $1 - b$ = Payout ratio = 60% = 0.60
• $g$ = Growth rate = 3% = 0.03
• $r$ = Required rate of return (what we need to find)

Step-by-step calculation:

1. Plug in the known values: $10 = \frac{0.60}{r - 0.03}$

2. Rearrange the equation: $r - 0.03 = \frac{0.60}{10}$ $r - 0.03 = 0.06$

3. Solve for $r$: $r = 0.06 + 0.03 = 0.09$

Wait, this gives $r = 9$, which corresponds to option C. However, let me double-check the logic.

Actually, let me reconsider: The Gordon growth model formula for justified forward P/E is: $\frac{P_0}{E_1} = \frac{D_1/E_1}{r - g} = \frac{1 - b}{r - g}$

Given:

• P/E = 10
• Retention rate (b) = 40% = 0.40
• Payout ratio (1-b) = 60% = 0.60
• g = 3% = 0.03

So: $10 = \frac{0.60}{r - 0.03}$ $r - 0.03 = 0.06$ $r = 0.09 = 9$

This suggests the answer should be C. 9%.

Verification: If r = 9% and g = 3%, then r - g = 6%. With a payout ratio of 60%, the justified P/E = 0.60/0.06 = 10, which matches the given information.

Therefore, the correct answer is C. 9%.