Explanation

To calculate the justified forward P/E using the Gordon Growth Model, we use the formula:

Justified Forward P/E = Payout Ratio / (r - g)

Where:

• Payout Ratio = Average payout ratio over the period
• r = Required rate of return = 11.5%
• g = Sustainable growth rate

Step 1: Calculate the average payout ratio

Payout ratio = Dividends per Share / Earnings per Share

• Year 1: 1.60 / 2.50 = 0.64 or 64%
• Year 2: 1.71 / 2.44 = 0.7008 or 70.08%
• Year 3: 1.80 / 3.60 = 0.50 or 50%
• Year 4: 1.92 / 3.20 = 0.60 or 60%

Average Payout Ratio = (64% + 70.08% + 50% + 60%) / 4 = 61.02%

Step 2: Calculate the compounded annual earnings growth rate

We need to calculate the growth rate from Year 1 to Year 4:

Earnings per Share:

• Year 1: $2.50
• Year 4: $3.20
• Number of years: 3 (from Year 1 to Year 4)

Growth Rate (g) = (3.20 / 2.50)^(1/3) - 1 = (1.28)^(0.3333) - 1 = 1.0857 - 1 = 0.0857 or 8.57%

Step 3: Calculate justified forward P/E

Justified Forward P/E = Payout Ratio / (r - g) = 0.6102 / (0.115 - 0.0857) = 0.6102 / 0.0293 = 20.83

Step 4: Compare with options

The calculated justified forward P/E is approximately 20.83, which is closest to 21 (Option C).

However, let's double-check the calculation:

• r - g = 0.115 - 0.0857 = 0.0293
• 0.6102 / 0.0293 = 20.83

This suggests the correct answer should be C. 21.

Note: There might be slight rounding differences in the calculation, but 20.83 is clearly closest to 21 among the options (10, 12, 21).