1. **State the problem:** We are given earnings per share (EPS) and dividends per share (DPS) for the past three years and need to find the expected dividend for the next year, given the firm maintains the same dividend policy. 2. **Given data:** - Earnings per share for past 3 years: $3.20$, $3.00$, $5.50$ - Dividends per share for past 3 years: $1.28$, $1.20$, $2.20$ - Expected earnings next year: $9.80$ 3. **Formula and approach:** The dividend policy can be interpreted as a constant payout ratio, which is the ratio of dividend to earnings: $$\text{Payout ratio} = \frac{\text{Dividend per share}}{\text{Earnings per share}}$$ We calculate the average payout ratio over the past three years and then apply it to the expected earnings next year to estimate the dividend. 4. **Calculate payout ratios for each year:** $$\frac{1.28}{3.20} = 0.4$$ $$\frac{1.20}{3.00} = 0.4$$ $$\frac{2.20}{5.50} = 0.4$$ 5. **Average payout ratio:** Since all three are $0.4$, the average payout ratio is: $$0.4$$ 6. **Calculate expected dividend next year:** $$\text{Expected dividend} = \text{Payout ratio} \times \text{Expected earnings} = 0.4 \times 9.80 = 3.92$$ 7. **Conclusion:** The firm is expected to pay a dividend of $3.92$ per share next year if it maintains the same dividend policy.